Suggested Answers to Philosophical Puzzles 1527589404, 9781527589407

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Suggested Answers to Philosophical Puzzles

Suggested Answers to Philosophical Puzzles By

Anguel S. Stefanov

Suggested Answers to Philosophical Puzzles By Anguel S. Stefanov This book first published 2022 Cambridge Scholars Publishing Lady Stephenson Library, Newcastle upon Tyne, NE6 2PA, UK British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Copyright © 2022 by Anguel S. Stefanov All rights for this book reserved. No part of this book may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the copyright owner. ISBN (10): 1-5275-8940-4 ISBN (13): 978-1-5275-8940-7

A FEW WORDS ABOUT THIS BOOK In this book I undertake an attempt at suggesting answers to some philosophical puzzles. These are problems, which have still not ceased to be a bone of contention, bearing different reasons for the controversial theoretical assessments they have initiated. Embarking on such an enterprise is a specific task and not an easy one for sure. It requires an attempt at adjusting and strengthening arguments for one of the already existing horns of a dilemma (for instance in chapter 5), finding a novel exit from a prolonged discussion (as is the case in chapter 1), defending unexpected answers (in chapters 3 and 4), and the like. Some of the subjects of the chapters included in this book are thematically correlated, and others are not. To be “naturally” expected then, the suggested answers to the title questions of the thematically correlated chapters ought to stay in a conceptual harmony. Otherwise, discrepancies among them would certainly lower the plausibility of each of the suggested answers. This is a necessary requirement for the answers to the title questions of chapters 4-6. The reached conclusions of chapters 1, 2, 3, 7 and 8, are not thematically correlated.

CONTENTS

A Few Words About this Book ................................................................. vi Chapter 1 .................................................................................................... 1 Is the Gettier Problem a Stumbling Block for Epistemologists? Chapter 2 .................................................................................................. 13 Do Self-Referential Incoherent Theories Refute Themselves? Chapter 3 .................................................................................................. 24 What is Non-Classical Theory? Chapter 4 .................................................................................................. 31 What is Time Travel? Chapter 5 .................................................................................................. 46 Spacetime: Substantive or Relational? Chapter 6 .................................................................................................. 62 Is Spacetime an Emergent Entity? Chapter 7 .................................................................................................. 73 Does Big Bang Cosmology Resolve the First of Kant’s Antinomies? Chapter 8 .................................................................................................. 95 Does the Anthropic Principle Explain the Appearance of Man in the Universe? Bibliography ........................................................................................... 108

CHAPTER 1 IS THE GETTIER PROBLEM A STUMBLING BLOCK FOR EPISTEMOLOGISTS? The Gettier Problem It is widely conceded that the Gettier problem is a real epistemological problem. It appears to be a stumbling block for the epistemologists (or, to be more correct, mainly for the epistemologists within the analytic tradition) for one, but for a good reason. This reason is that the so-called Gettier cases demonstrate the incompleteness of the common presentation of knowledge to be standardly defined as justified true belief. A necessary amendment of this standard definition – the JTB definition for short – is thus required, so that it could deal with the exceptional Gettier cases, which are said to undermine the JTB definition. However, a good deal of attempts at suggested solutions for changes in the JTB definition of knowledge has been shown to be unsatisfactory in some aspect or another, and to this effect, to provoke continuous debates. This is the Gettier problem in a nutshell. I shall try to defend a negative answer to the title question of this chapter, or to defend the claim that the Gettier problem ought not to be treated as a stumbling block for epistemologists, since Gettier cases do not undermine the JTB definition of knowledge at a conceptual level. What Gettier (1963: 121-123) tried to demonstrate was the thesis that the definition of propositional knowledge as justified true belief is not an adequate definition, since it is incomplete. This means directly that there might be cases of justified true beliefs that do not present knowledge. Gettier himself adduced two examples of this sort, which are intuitively taken to be cases of lack of knowledge for an agent who is supposed to have a justified true belief.

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The JTB definition of knowledge states that a subject S has knowledge of the proposition P, only if the following requirements are fulfilled: (a) P is true, (b) S believes that P, and (c) S is justified in believing that P. According to the Gettier thesis this JTB definition of knowledge is incomplete, because it is not immune to exceptions, now bearing the name “Gettier cases”. They are of different types, but each of them is a case, in which all of the upper three requirements (a) to (c) are met, while it is still agreed that S does not know that P. Let me refer to the first of the two original Gettier cases, which I’ll go back to later. The case is quite popular, so a brief retelling of it will suffice. Smith and Jones have applied for a job, and Smith has heard the president of the company say that Jones will get the job. Meanwhile, Smith has managed to count the number of coins in Jones’ pocket and found that there are ten. So, having reliable evidence that Jones will get the job, and that Jones has ten coins in his pocket, Smith easily reaches the conclusion (marked by (e) in Gettier’s original paper): (e) The man who will get the job has ten coins in his pocket. However, unbeknownst to Smith, he also has ten coins in his pocket, and he is the man who will get the job. On these factual grounds, Gettier insists that Smith does not know that (e), although the proposition (e) is true, Smith believes that (e), and he is justified in so doing. According to the JTB definition, Smith ought to know that (e), but nevertheless (our intuition shows that) he does not know that (e). The JTB definition fails to work in this case. Even if so, this fact does not yet set out a problem. If it is simply argued that some concrete definition of knowledge – the JTB definition – is incomplete, this may be avowed as

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an epistemological result (no matter how significant), and not as an epistemological problem. A problem arises, however, if the criticized JTB definition of knowledge has been officially and commonly accepted to be the definition of knowledge by the analytic philosophers before the publication of Gettier’s paper in 1963. Even if this might not be the case,1 a problem arises indeed, only if it has been accepted that the JTB definition of knowledge (even if not officially proclaimed) was the one, which was tacitly embraced by the epistemological community till the publication of Gettier’s paper. Namely, this presupposition is widely shared and it is exactly this presupposition, which makes the Gettier thesis emerge as a problem.

Attempts at a Solution The persisting difficulty with the Gettier problem is that there has been no arguable solution for it to be commonly accepted by the epistemological community for sixty years since the publication of Gettier’s challenging paper. This being the case, how then can the Gettier problem be solved, or conceptually circumvented? On the one hand, the JTB definition seemingly fails to be a general one. But on the other hand, its three requirements have never been evaluated to be epistemologically inadequate. This is why the first possibility directing the attempts at solving the Gettier problem, which occurred to philosophers, was the invention of some fourth condition for knowledge acquisition to be added to the requirements (a), (b), and (c), so that the new amended definition is not only a necessary, but also a sufficient condition for S to know that P.

1

See in this connection the well-defended claim of Julien Dutant (2015) that the JTB definition was not the traditional analysis of knowledge till the publication of Gettier’s paper in 1963.

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Chapter 1 After 1963 the justified true belief account of knowledge was seen to be defective and lost its exalted status; but even those convinced by Gettier that justification (along with truth) isn’t sufficient for knowledge still mostly think it necessary and nearly sufficient for knowledge: the basic shape or contours of the concept of knowledge is given by justified true belief, even if a quasi-technical fillip or addendum (‘the fourth condition’) is needed to appease Gettier. (Plantinga 1990: 45, his italics)

Unfortunately, nobody has managed to provide such a universal “fourth condition” and to thus convert the JTB definition into one that is capable of resisting all types of Gettier cases. This way out of the problem has now been almost relinquished, since it has turned out that a “quasi-technical fillip” can hardly supply a plausible result. Requirement (a) in the JTB definition cannot be altered, so the attempts at solving the Gettier problem were focused mainly on the elaboration of (c), and even of (b).2 In the first original Gettier case, for instance, Smith believes that (e), due to the false presupposition that Jones will get the job. To this effect, the so-called “no false lemma” rule to the JTB analysis of knowledge was offered, expressing the principal claim that knowledge cannot arise from false premises. Plausible as it may seem, this stipulation proved to secure no general solution, because in some types of Gettier cases the knowing agent does not make conclusions from false premises, but she still fails to know. Much hope was cherished for another solution, offered by the so-called “anti-luck epistemologists”. In many Gettier cases the knowing agent S fails to know that P, in spite of the fact that S is justified in believing that P, and P is true, simply because epistemic luck has helped S to think that she knows that P. As a convincing example, I’ll retell a short Gettier case, known as “the sheep-in-the-meadow case”:3

2

As B. Meyers-Schulz and E. Schwitzgebel (2013: 371) have argued for example, “we think there are cases in which it is intuitively plausible that a subject knows some proposition P without – or at least without determinately – believing that P”. 3 It is originally suggested by R. Chisholm, and I’m referring here to J. F. Rosenberg (2000: 30).

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It’s a bright sunny day and Smith is driving a car along a road, closely passing a meadow. He clearly sees a sheep in the meadow, so he has a justified true belief that there’s a sheep in the meadow. What Smith really saw was a white rock that looked like a sheep. However, there was an actual sheep at that time hidden behind the rock. Does Smith know that there’s a sheep in the meadow? As it seems, the answer is negative, in spite of Smith’s justified true belief. This is so, because what makes his belief to be true is the actual presence of a sheep in the meadow, but his belief is accidentally true, or true as a matter of epistemic luck. To avoid the factor of epistemic luck the anti-luck epistemologists have tried to solve the Gettier problem by the stipulation that in the terms of the JTB definition the cognitive success of S to believe that P is true is not a matter of luck. This is undoubtedly a plausible stipulation, yet it is not a sound solution to the Gettier problem. As Rodrigo Borges showed for instance (2016: 463), “[the] analysis of luck is of no help to the anti-luck epistemologists for it uses knowledge to explain luck, making this account of knowledge circular.” As Daniel Whiting puts it, and as it sounds non-optimistically: We used to think that knowledge is justified true belief. Then Edmund Gettier presented counterexamples to this view which appeared to refute it. Then philosophers spent years, decades even, trying to modify or supplement the view only to see their revised versions face further counterexamples. Then we gave up trying to say what knowledge is. (Whiting 2015: 237, my italics)

For now, we see that the notorious Gettier problem – being central for epistemology, because it concerns the definition of knowledge – has no commonly accepted solution. Suggested candidates for a solution fail to overcome all the various Gettier cases as counter-examples to the JTB definition. Thus, this naturally transforms the problem into a stumbling block for the epistemologists.

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If all that demonstrated so far holds true, it seems that the way to surmount the Gettier problem by a corrective widening of the standard definition of knowledge may not offer a plausible perspective.

My Claim This is why I will explore another possibility. It is the attempt at demonstrating that Gettier cases are not decisive counter-examples for the JTB definition to be declared as an inadequate one. I’ll try to show, in what follows, that there is a problem in accepting the Gettier problem as a genuine epistemological problem. This is so, because even if the Gettier cases intuitively appear to be counter-examples to the JTB definition of knowledge, these intuitive appearances are misleading. Thus, as a nontrivial and unexpected “solution” to the Gettier problem, the statement can be raised that there is no need for it to be formally solved. As far as I am aware, William Lycan was the first author to introduce the unexpected (and astonishing) expression, “the Gettier Problem problem”, into the heading of a paper, for the purpose of “explaining what is distinctively wrong with the Gettier project” (Lycan 2006: 150). I’ll not follow here, his argumentative reasoning, all the more that he has succeeded in analyzing the peculiarities of different unsuccessful attempts at solving the Gettier problem. I’ll try to provide instead an answer to the question (Q) “Why do Gettier cases not undermine the JTB definition of knowledge?” A similar question – “Why are Gettier cases misleading?” – was used as the title of a paper by Moti Mizrahi (2016). The thesis which Mizrahi (2016: 31) defends in his provocative paper is that [A]s far as Gettier cases are concerned, appearances are deceiving. That is, Gettier cases merely appear to be cases of epistemic failure (i.e., failing to

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know that p) but are in fact cases of semantic failure (i.e., failing to refer to x).4

I shall try to suggest an answer to (Q) that is different from that of Mizrahi. The gist of it is that the Gettier cases “are misleading”, because they are based on an implicit self-application of the JTB analysis of knowledge, in order for the conclusion to be always reached that the Gettier-hero (the knowing agent in the Gettier cases) does not know the proposition he believes in, although it proves to be true, and he is justified in believing its truth. Even authors who do not hesitate in their support of “the orthodox view in contemporary epistemology” that Gettier cases refute the JTB analysis of knowledge, contend that we have a strong intuition to say that the respective Gettier-hero (S) does not know that P.5 As it seems, this pretension for refutation, based on intuition (though a “strong” one), disguises a bit of skepticism. It percolates through the rational doubt that one can hardly reject a definition of knowledge by some kind of intuition about its alleged insufficiency. Let me direct my attention at the crucial claim that each Gettier case is aiming at: “S does not know that P”. My epistemological strategy is finding an answer to the question: (Q’) How does one know that S does not know that P? It may seem that (Q’) is a strange question. The inventor of a Gettier case contrives the plot of a short story in such a way for the reader to come to the conclusion that S does not know that P. And this looks to be quite convincing at first glance. At a second glance, however, (Q’) must not be grasped and answered in this trivial way. For the intended conclusion in a Gettier case (that S does not know that P) is a “truth” in a fiction tale, or a truth-in-fiction. If (Q’) is an epistemological question, it has to be supplied with a genuine epistemological answer. And there is only one way such an 4

See also (Mizrahi 2017). As Philip Atkins puts it for instance, “I cannot speak for everyone, but I have the strong intuition that Smith fails to know” (Atkins 2016: 381).

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answer is to be found: this is the explication of the manner in which the teller of a Gettier case can know that S does not know. If the teller does not know this intended conclusion and relies on contrived stories alone, the most she could pretend to tell us is some fabricated scenario. Furthermore, if the pretention of every Gettier case is that it is an instrument for criticizing a definition of knowledge (being a counterexample to it), then this critical argument must stay on an epistemological level. Otherwise, it gets outside of the sphere of knowledge acquisition, and comes to be a mere fabricated story that stays outside of a real cognitive context. Intuitions that somebody does not know something are just of this kind. So, it comes out that an instrument having an indirect cognitive nature is used to demonstrate the inadequacy not even of some statement bearing knowledge, but of a definition of knowledge. “The arguments made on the basis of Gettier cases are appeals to intuition, which are themselves a rather controversial sort of argument in philosophy” (Mizrahi 2017: 131). All this means that the contriver of a Gettier case must be at the same time involved in a real cognitive situation. She must be a meta-knowing agent in order to know that S does not know that P. Through this reasoning the key epistemological significance of question (Q’) is vindicated. As we have seen from the first Gettier case, its author insists that Smith does not know that (e). I have met the curious objection that Gettier’s knowledge that this is so is a second order knowledge, and to this effect Gettier is free to adopt JTB conditions about this second order knowledge, although intending to refute the JTB definition. I agree that Gettier’s knowledge is a second order knowledge, since (as I have just pointed out) he is a meta-knowing agent. But second order knowledge is also knowledge, as is the first order one; and if we stick to a definition of knowledge, then it must conceptually cover every case of knowledge, be it first order, or second order. Otherwise, the opponents of this claim must clearly show that for having knowledge at an object level, and for having knowledge at a meta-level, one can stick to different definitions of knowledge per se. Insofar as such a demonstration is hardly realizable (and not realized for now), one should not use the JTB conditions about

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possessing knowledge at a meta-level, in order to refute the JTB definition at an object level. What remains then is the explication of the way in which a meta-knowing agent does really know that a Gettier hero does not know something, although the hero believes he knows it. Going back for this purpose to the sheep-in-the-meadow case, let us assume that a friend of Smith who is traveling with him in the same car is playing the role of a meta-knowing agent who knows that (i) Smith does not know that (e’), where (e’) is the proposition “There is a sheep in the meadow”. Smith’s friend went along the same road a day ago, and found that there is a rock in the meadow that looks like a sheep. Now traveling together with Smith (and not being the driver), he also managed to see that there is an actual sheep behind the rock several seconds before hearing Smith say that there is a sheep in the meadow. He is thus not astonished to hear Smith’s statement that there is a sheep in the meadow, because of the rock’s resemblance to a sheep, while knowing at the same time that the statement is factually true. How then does Smith’s friend – in his quality of a meta-knowing agent – know the proposition (i)? His knowledge of (i) is guaranteed by the following three conditions: (a1) (i) is true (since Smith saw a rock, not a real sheep), (b1) He believes that (i) is true, and (c1) He is justified in believing that (i) is true (since he was a direct witness of Smith’s misrepresentation of the rock as a sheep). What comes out is that the way Smith’s friend acquires knowledge that (i) is true, is an application of the same JTB procedure that the Gettier case is intending to refute.

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By this conclusion, an answer to the question (Q’) was provided. One can find a similar answer when analyzing the first original case proposed by Gettier. I have demonstrated that this is so in another paper of mine (Stefanov 2016: 109-110), but there is a need for an additional comment here. Let me recall that the proposition which Smith does not know in this short story was (e), stating that “the man who will get the job has ten coins in his pocket”. The specification of (Q’) now is how Gettier, the inventor of this case, can know that (ii) Smith does not know that (e), in his quality of a meta-knowing agent, i.e., when involved in a real cognitive situation. For this purpose, Gettier has to know that Jones has ten coins in his pocket. Suppose that he was a secret eye-witness when Smith was counting them “ten minutes ago”.6 He is then certain that Smith knows that Jones has ten coins in his pocket. Let us further suppose that he managed to count the coins in Smith’s pocket as well (when Smith was buying a cup of coffee at the nearby counter, for instance) and found that Smith also had ten coins in his pocket, and that he had also heard the words of the president of the company, when he was assuring Smith that Jones would in the end be selected for the job for which both men had applied. And when Smith is getting the job, Gettier is correctly coming to know that (ii). But what does it mean that Gettier has knowledge that (ii) in his situation of a meta-knowing agent? His knowledge of (ii) is grounded on the following three conditions: (a2) (ii) is true, (b2) Gettier believes that (ii) is true, and (c2) Gettier is justified in believing that (ii) is true. 6

“Smith’s evidence… might be that the president of the company assured him that Jones would in the end be selected, and that he, Smith, had counted the coins in Jones’s pocket ten minutes ago” (Gettier 1963: 122).

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Thus, as a meta-knowing agent, Gettier comes to know that (ii) in the way paved by the JTB analysis of knowledge. However, a successful application of a cognitive procedure in order for its own inadequacy to be demonstrated cannot be used as an argument for reaching this intended aim. This, in its turn, is the answer to (Q), i.e., the answer to the question “Why do Gettier cases not undermine the JTB definition of knowledge?” This is so, because in spite of the demonstration that the main hero in the Gettier cases does not know something, which he is certain to know, the knowledge of his not knowing is controlled by the same JTB analysis of knowledge, the status of which Gettier wishes to undermine. One could still raise the claim that Gettier cases do formally refute the JTB definition of knowledge. Putting meta-knowledge aside, it suffices to adduce contrived examples of justifications that are misleading. Let me call them “wrong justifications”, although this phrase is somehow awkward. The possibility for wrong justifications is put forth as an argument against the adequacy of the JTB definition. Well, the whole history of human knowledge, and of what we call rational knowledge too, is full of wrong justifications. These contingent cases, however, in no way cancel the very need for justification. Justification remains as a necessary conceptual requirement for having knowledge. Accidental cases of wrong justifications cannot delete the conceptual requirement for knowledge to be defined as justified true belief. Wrongly justified true belief may simply not be accepted as genuine knowledge. Accidental cognitive traps are merely influences of misguiding situational factors that could be principally avoided. They do not entail a conceptual failure of the JTB definition of knowledge per se. Their emergence is contingent and has nothing to do with the conceptual setting of the JTB definition of knowledge. This definition – as bearing an understanding of what is it for S to know that P – must not be blamed for putative knowledge failures. There certainly are different kinds of justifications, which are valid for different types of cognitive situations. And the more strictly the pertinent

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requirements for a justification are followed, the less is the room left for accidental cognitive traps leading to wrong justifications. What follows in the end is that the JTB analysis of knowledge is not refuted at a conceptual level by the fabrication of Gettier cases. The presentation of the latter as counter-examples to the JTB definition of knowledge is backed up by this same definition. Hence the Gettier problem ought not to be looked upon as a stumbling block for epistemologists.

CHAPTER 2 DO SELF-REFERENTIAL INCOHERENT THEORIES REFUTE THEMSELVES? The Traditional Positive Answer A theory (or a statement) is said to be self-referential if theories (statements) and their basic features are included in its subject matter, or to put it in other words, if it is about theories (statements) and is included in its own domain. Thus, for example, the statement that “Every statement is false” is self-referential, because it refers to all statements and it is itself a statement. A self-referential theory may, or may not conform to its own criteria of validity or acceptability. The statement that “Every statement is false” certainly does not. Insofar as it refers to all statements, it also refers to itself. Let us assume that this statement is true. Then it follows, because of what it says, that it is not true. It thus runs counter to the assumption of its own truthfulness. A self-referential theory which does not satisfy its own criteria of validity, or breaks up in some way its own requirements, is said to be self-referentially incoherent (inconsistent). Self-referential incoherence is traditionally considered in its role of a powerful method of refutation. Sometimes, on learning that I am a philosopher, a non-philosopher who has gained the impression that it is difficult to get agreement in philosophy will tease me with the idea that philosophy can never definitely establish anything. I then like to point out to my would-be tormentor that he has just unwittingly provided me with all the material I need to refute that very thesis. For the idea that it is impossible definitely to establish any philosophical thesis is itself a substantive philosophical thesis. Therefore we can definitely establish that if my interlocutor ever definitely established his thesis that it is impossible definitely to establish any philosophical

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Chapter 2 thesis, then in establishing his thesis, he would have refuted it. Thus we can definitely establish that one can never definitely establish that one can never definitely establish anything in philosophy. So we can definitely establish something philosophical. (Zuboff 2015).

The just quoted excerpt is a nice consolation for the philosophers. And I surely would not make up my mind to oppose its clever setting. But what can further attract philosophical interest is the analysis of the pretention of a thesis that gives a clear positive answer to the title’s question: (R) Do self-referential incoherent theories refute themselves? It is an established, though non-obtrusive, tradition (R) to be accepted as a valid thesis without any relevant critical comments. This means further that as a normative claim, and if ascertained for some self-referentially incoherent theories, (R) could be used as a trustworthy method for the refutation of all such theories. Thus, for instance, the famous Carl R. Kordig (1983) has avowed the universality of this method and declares, by applying it, some well-known epistemological views (theories about theories) to be false. According to him, Toulmin’s evolutionary epistemology must be rejected, because it appears to be a false theory about theories just on the grounds of (R).7 A. Zuboff (2015) goes along with the same line of reasoning, and declares the refutability of Wittgenstein’s description of language as a game, as well as of the position of deconstructors of texts with respect to their own texts.

7

Other epistemological views that Kordig (1983: 208) finds to be self-referentially inconsistent, and thus self-refuting, are the Quine-Duhem thesis, Salmon’s account of factual content, Quine’s ontological relativity, the claims that not everything has an explanation and cause, and some others. In fact, Kordig puts forward a bilateral claim which runs to the following: If a self-referential theory is incoherent, then it is necessarily false; its denial, however, is self-validating and hence necessarily true. I have hopefully shown that this claim may face some specific difficulties (Stefanov 1998: 135-136).

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The aim of this chapter is to defend the claim that the method of refutation, based on (R), is not always reliable, and that at least some seemingly self-referential incoherent theories ought not to be looked upon as self-refuting. I don’t maintain any doubts that from a formal logical point of view, and when all theories are taken to be expressed within a common language, (R) is undoubtedly a valid thesis. Let us consider for example the statement: (S) Every statement expressed in English is false. (S) refers to all statements expressed in English, and it is itself a statement formulated in the same language. If all such statements are false, then as one of them, (S) must also be necessarily false. But if so, its negation comes to be true, which means that at least one sentence in English is true. The latter conclusion shows that (S) is incoherent, what it states is not true, and thus, according to (R), it is self-refuting. Let us now have a look at another example of a statement that allegedly refutes itself: The renowned pragmatist W. V. Quine famously claimed that in our proper theories of the world (…) no statement is unrevisable. But isn't this statement, Quine's statement that no statement is unrevisable, meant by Quine to be unrevisable, that is, to represent always what is true about revisability whether or not there were pragmatic grounds for maintaining that supposed truth? … Quine's statement refutes itself… [I]f next we try to think of his statement as unrevisable, we find that it would of course at the same time be false since it says there are no unrevisable statements. (Zuboff 2015).

But does Quine's statement really refute itself? I am inclined to say “Yes, it refutes itself”, if this statement is construed as one formulated within a definite language, all of the sentences of which, expressing different statements, refer to one common domain. Thesis (R) is a good method for refutation in this case, and can be safely applied in a formal logical reasoning. Indeed, if no statement formulated within a

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language is unrevisable, then the very statement bearing this message, as being self-referential, falls under this factual situation. This leads to the acceptance of its revisability, and hence to its falsity, since the statement must be either true, or false. However, I can also say “No, Quine's statement does not refute itself”, because it appears to be not properly self-referential. By saying that “it is not properly self-referential”, I mean that this statement is formulated in an epistemological context, which differs from the one encompassing the set of all statements to which it refers. Thus, its prescription directed to the latter statements may not (directly) refer to itself. Indeed, in the case being considered, all of the referent statements belong to “theories of the world”, that is to say, to factual scientific theories. However, Quine’s statement is a theory about scientific theories, and not a statement belonging to their sphere of validity; it is not a statement describing any fragment of, or state of affairs in the natural world. If so, Quine’s statement does not belong to the set of statements about which it prescribes something. It is not properly self-referential. Its prescription might prove to be valid for the statements it refers to, being at the same time invalid for Quine’s statement itself. Hence, (R) cannot be used as a method for the refutation of Quine’s statement. The conclusion just reached is a counter-example to thesis (R) taken in its formal logical pretention. It is enough for the defense of my suggested claim that the method for refutation, based on (R), is not always reliable.8

8 Looking back at Quine’s statement, this same conclusion does not, however, mean that the statement is necessarily true, and on these grounds, it is unrevisable. But even if this statement is really revisable, its putative revisability is not due to the application of (R) to its semantical content. Its revisability may be contended on epistemological grounds, exploiting arguments eventually provided by some kind of strong metaphysical realism.

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Mavrodes’ Broad Answer George Mavrodes does not examine why a given self-referential theory is incoherent, but the problem what if it is such a theory. We shall want to ask whether various theories which do not satisfy themselves are vulnerable in different degrees to the force of this kind of refutation. (Mavrodes 1985: 66)

Beyond any doubt, posing this question implies some kind of amended version of the thesis (R), or some other solution to the title question of this chapter.9 In fact, Mavrodes does not supply such a worked-out solution. Nevertheless, he shows that the problem itself (about the refutability of self-referentially incoherent theories) is not a pseudo-problem, and that its solution depends on some special presuppositions which he calls “principles of evaluation”. I shall make use of his two straightforward examples here (Mavrodes 1985: 66). Let us examine the proposal: (T) Truth is beauty. Mavrodes supposes that in criticizing (T) we have managed in some way to show that (T) does not satisfy itself. This would mean that (T) is not beautiful. From here we can infer that if (T) is true, then (T) is not true. But the last conclusion could present enough grounds for the refutation of (T) only in combination with the following principle of evaluation: (P1) For the analysis of truth, it is a desideratum that the analysis be true. And insofar as (P1) seems to be quite arguably a principle, (T) must be rejected as an unsatisfactory analysis of truth. If we apply the same argumentation, however, in order to ascertain the refutability of another, though similar claim, the result will be different. The claim is; (F) Falsehood is ugliness. 9

Kordig’s paper (1983) is not among the references of Mavrodes’ paper (1985).

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Let us assume that we can show the self-referential incoherence of (F) as well. By using exactly the same way of reasoning as in the preceding example we can reach the conclusion that (F) is not false. To refute (F) will suffice to introduce the evaluation principle (P2) For the analysis of falsehood, it is a desideratum that the analysis be false. But insofar as (P2) is not at all an acceptable principle, the self-referential incoherence of (F) itself cannot present sufficient grounds for the refutation of (F). By the way, this second example suffices to show that we cannot rely on a general principle of evaluation of the form: (P3) For any property ݊, it is a desideratum that the analysis of ݊ should itself have the property ݊. That is why we must look for a convenient and acceptable principle of evaluation, each time deciding whether a self-referentially incoherent theory should be rejected as unsatisfactory. This requirement bars Mavrodes from getting at a more detailed solution to the problem “What if a theory is self-referential and incoherent?”, and makes him content with the following general conclusion: In some cases, most notably those of truth and falsehood, the subsequent argument is straightforward and powerful. But in other cases the argument soon leads us into complexities which leave the force of the intended refutation much more in doubt. (Mavrodes 1985: 72)

For the sake of precision, someone could raise the objection that claims (T) and (F) are not convenient examples for the analysis of self-referential incoherence. And she will certainly be right, insofar as both of these claims are semantically incorrect. Truth and falsehood are not the qualities which are supposed to fall into the range of applicability of the corresponding predicates “beautiful” and “ugly”. But even if this is so, this circumstance does not run counter to Mavrodes’ warning that the thesis (R) alone is not a sufficient condition for the refutation of every selfreferential incoherent theory. A sufficient condition for this is the

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combination of (R) with a relevant principle of evaluation. Mavrodes’ kind of solution to the title question of this chapter thus stays in harmony with my claim that “the method of refutation, based on (R), is not always reliable, and that at least some seemingly self-referential incoherent theories ought not to be looked upon as self-refuting”. Mavrodes’ kind of solution, however, is not an explicit one, since it relies on the fabrication of principles of evaluation, having different degrees of relevance for each separate case of a self-referential incoherent theory.

My suggested solution I suggest another kind of solution, which is based on an attempt at providing an explicit typology of self-referential incoherent theories, which are susceptible to refutation on the basis of (R). I shall denote by (A) the class of self-referential, incoherent, singular, and semantically correct statements. An (A)-type statement is represented for instance by the sentence: (1) This very sentence is in Spanish. All three requirements are satisfied by (1). It presents a singular statement, and the demonstrative reference of its subject is (1) itself. Furthermore, (1) is semantically correct, because the reference of its subject is included in the range of applicability of its predicate. Indeed, the predicate “Spanish” can well be referred to sentences, and (1) is surely a sentence. But the obvious inconsistency demonstrated by the presented statement makes it false and thus it is self-refuting. (B)-type incoherent theses are singular statements resembling those from class (A), but semantically incorrect. It is namely this semantical incorrectness that is responsible for their incoherence. A (B)-type sentence is: (2) This very sentence is green. Linguistical structures – and (2), as a sentence, is one of them – do not naturally fall into the range of applicability of the predicate “green”. That

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is why (2) is semantically incorrect. And since it is incoherent and selfreferential, it is self-refuting. Unlike (A) and (B), class (C) covers all general statements and theories which are properly included in their own domains, and fail to satisfy themselves. (C)-type theories are clear instances of self-referential incoherence, and are refuted merely because of this. Such is e.g., the general statement: (3) Every statement is false. Such is also the Quine-Duhem epistemic thesis taken in the form: (4) No hypothesis whatsoever can be conclusively falsified. The negation of (4) is itself a hypothesis. That is why it too cannot be conclusively falsified. The negation states that some hypotheses can be conclusively falsified. Thus, for all we know, some hypotheses can be conclusively falsified… It is therefore not true that we know that no hypothesis whatsoever can be conclusively falsified. Thus, if we know that no hypothesis whatsoever can be conclusively falsified, it follows that we do not know that no hypothesis whatsoever can be conclusively falsified… Quine-Duhem epistemic thesis is self-referentially inconsistent and hence ought to be rejected. (Kordig 1983: 209)

There is a very special class of statements, which I shall denote by (C’). All statements within (C’) are of the type of the Liar Paradox: (5) This very sentence is false. (6) Everything said by me is false. These are examples of self-referential incoherent claims. Nevertheless, I do not unite (C) and (C’) because of the presence of singular statements like (5) in (C’) and their absence in (C). And I do not unite (C’) and the class (B) for another reason, in spite of the fact that (5) and (6) cannot pass the standard procedure for semantical correctness (Martin 1976: 298-

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303).10 This is because the (C’)-statements refer to another convention for semantical incorrectness: namely that each sentence which explicitly mentions itself (appearing at the object- and meta-language level simultaneously) must be looked upon as semantically incorrect. However, the problem is not in accepting the convention, but in the fact that it is too discriminative. Together with all incoherent sentences that explicitly mention themselves, it rules out all self-referential coherent sentences as well. Such is for example the declaration that “This sentence is in English”. That is why the convention ought to be specified for the purpose being here pursued. I do not see any other possibility for an appropriate specification of the set of semantically incorrect statements of the type considered, except the following proposal: we must have in mind all sentences which explicitly mention themselves, and contain as a predicate the self-qualification “false”. Thus, the separation of the class (C’) obtains its justification. Now I come to the last class of allegedly self-referential incoherent theories which, in contrast to (A), (B), (C), and (C’), are not susceptible to the refutational strength of (R). The biggest problem lies namely within this class of theories which I shall denote as (D)-type theories for short. There are theories about the nature and functions of scientific theories which exhibit incoherence, as in the already mentioned case (at the beginning of this chapter) with Toulmin’s evolutionary theory. Their contingent refutations are of great interest to philosophers, insofar as their metatheoretic character has an epistemological lineament. The alleged incoherence within Toulmin’s theory, according to Kordig, is the discrepancy between its evolutionary normativeness, and the necessity for it, if it should itself conform to the latter, to evolve into a nonevolutionary theory. Let me recall the examples used by Toulmin in his Human Understanding, to illustrate his idea about the change in the general intellectual goals and explanatory ideals in the course of scientific growth. 10

Instead of (6) Martin considers the statement “Everything said by a Cretan is false (said by a Cretan)”. There is no need, indeed, to show the inconsistency equivalence of Martin’s example and (6).

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The first one concerns Max Planck’s analysis of the altering explanatory demands which have historically guided the development of physics, presented in the exchange of papers between him and Ernst Mach, printed in the Physikalische Zeitschrift for 1910-11 (Toulmin 1977: 232). Toulmin points out, as another example, the debate among representatives of classical genetics (Avery and his colleagues) and physicists/biologists (Delbrück and others) in the years between 1944 and 1953. The third example is taken from quantum physics, and concerns J. Schwinger’s and G. Chew’s approaches to the explanation of the nature and character of the elementary particles. Here again, the subject faces theoretical difficulties that call, not for more elegant mathematics or more ingenious experiments alone, but rather for a strategic reappraisal of basic aims and explanatory ideals. (Toulmin 1977: 234-235)

These examples from the history of science clearly outline the pretension of Toulmin’s epistemological view. This refers to scientific theories and how new theories supersede old ones because of changing intellectual goals and ideals. The intellectual goals in science and the general ideals of scientific understanding are the factors that historically evolve, but not the epistemological goals that guide Toulmin’s own evolutionary theory. In this sense, I would say, Toulmin’s evolutionary theory is not properly included in its own domain. It is about scientific theories, and not about epistemological views. Hence, in contrast to (C)-type self-referential incoherent theories, which are properly included in their own domains, Toulmin’s evolutionary epistemology cannot be refuted on these same grounds. Of course, an immediate objection may be raised that even if Toulmin’s pretensions do not spread over epistemological metatheories, this is, and could be no argument to change the situation. Because theories are human cognitive constructions, and being such, they must exhibit a common nature and common basic features independently of whether they are theories about regions of the outer world, or theories about theories. To this effect, Toulmin’s metatheory must be necessarily considered as

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properly included in its own domain, and hence, should be rejected as selfreferentially incoherent. Is this objection correct? It is, except with respect to one crucial assumption; the general assumption that a metatheory about theories, because it is a theory itself, must necessarily possess the conceptual features of the theories it describes. A special instance of this general assumption (reporting on a single property) is the evaluation principle (P3) pointed to by Mavrodes. But if even (P3) is not an acceptable principle, what about the general assumption which functions rather as a prejudice, than as an established normative rule? Let us examine another, far simpler, but no less paradigmatic example of a (D)-type theory: (7) All theories have a restricted sphere of validity. And let us assume that (7) tells us the truth. Then, insofar as it is itself a theory about theories, it follows that its own sphere of validity is restricted. But since it is about theories, this implies that some theories are not characterized by a restricted sphere of validity. So, (7) runs counter to its own assumption. It is self-referentially incoherent. Can (7) be refuted because of this? Yes, if we involve an additional premise in the form of (P3) which states that for an adequate analysis of the sphere of validity of theories the analysis itself should possess the same type of validity. But the cognitive necessity of such a premise has never been proved. Thus, it comes out that the alleged self-referentially incoherent theory about theories (7) is not refutable on the grounds of the thesis (R). It becomes clear in the end that (R) has a real refutational strength for selfreferential incoherent theories covered by the classes (A), (B), (C), and (C’), but cannot be directly applied to (D)-type theories. This in no way means that the theories of this type are not liable to criticism. However, the criticism is based on various arguments, and stays out of the grip of the thesis (R).

CHAPTER 3 WHAT IS NON-CLASSICAL THEORY? The aim of this chapter is for an arguable answer to the title question to be reached. If I succeed in so doing, it might be expected that the answer ought to provide a necessary and sufficient condition according to which a given scientific theory could be accepted as a non-classical one. I concede at the outset that I cannot suggest such a complete answer, since I cannot provide its first “necessary” component. I shall try, however, to suggest a sufficient condition for a scientific theory to be looked upon as a non-classical one. But why does the title question deserve philosophical attention? The answer (at least) to this second question is not difficult. It is a fact that the quality of “non-classicalness”, attributed to scientific theories, has a historical usage. R. Descartes laid the beginnings of a new philosophy which buttressed the new science of his time. It could be qualified as non-classical, regarding the previous system of thought. This notwithstanding, Descartes is wellknown nowadays as a prominent representative of classical rationalism. Non-Cartesian epistemology was taken by some thinkers to be a nonclassical trend in philosophy.11 Quantum mechanics was proclaimed to be a genuine non-classical theory about the nature of the micro-world, but since the 1990s it has often been referred to as “classical quantum theory”, in order to be differentiated from quantum field theory, superstring theory, or later quantum achievements 11

About non-Cartesian epistemology see, for example, Bachelard (1934: ch. 6). Till 1984 the book underwent 16 editions in France.

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like quantum gravity models. Almost the same, is the case of the theory of general relativity being declared as a non-classical one within the range of more than five decades since its birth in 1916. Mathematical physics has today incorporated general relativity into larger non-classical models of spacetime geometry and material dynamics, so that Einstein’s theory is also often dubbed as “classical relativity theory”. The usage of expressions like “(non-)classical theory” and “(non-)classical approach” has recently become so usual that it seems nobody cares for their proper meaning, while philosophers rely only on the context in which they are mentioned. Both this fact, and mainly the historical ladenness of the notion “non-classical scientific theory”, make the attainment of some definite answer to the title question an enterprise, which is worth undertaking, but not an easy one, as well. No doubt, some theories may be qualified as non-classical only against the background of a knowledge that has already been construed as classical. So, the notion of “non-classicalness” is a relative one. It is, but in the same sense in which the ordinary concept of novelty is also relative. It seems the difference must be sought not in the fact of some extant novelty, but in the specific scope and depth of the alleged theoretic novelty. Each non-classical theory is certainly new with respect to its classical predecessor, while the reverse statement (that each new theory is also a non-classical one) does not hold water. There are lots of new conceptions which are not qualified as non-classical. To this effect, one may stick to the contention that a new theory is at the same time a non-classical one, if its basic principles and/or its theoretical structure display essential differences when compared with the cognitive system of the existing classical knowledge. But what do “essential” differences really mean? The answer that might occur to philosophers of science could lead to the notion of a “scientific revolution”. Such a step can elucidate the answer to this question only if the usage of the term “scientific revolution” is

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methodologically clear and non-controversial. But I can hardly say that this is exactly the case. Thomas Kuhn has really developed a clear concept of a scientific revolution, but it is intrinsically connected with his conception of paradigm change, and the latter with the notorious thesis of incommensurability. Insofar as both this conception and this thesis are not unanimously accepted by philosophers (and the doctrine of incommensurability among theories is often criticized), Kuhn’s concept of a scientific revolution shares their own dissimilar assessments, as well. It seems that the term “scientific revolution” is practically used in concrete historical contexts as is the above-mentioned usage of the term “non-classical theory”. One may seek the criterion of non-classicalness in the result of a more or less successful transfer of concepts from one scientific discipline being incorporated into the ontological dictionary of another. For instance, let me have a look at Ilya Prigogine’s pretension for a new scientific approach whose building blocks are his theory about the constructive role of irreversible processes and the non-equilibrium states in physics and chemistry, as well as his new idea of time (Prigogine 1996). A “nonlinear” (and allegedly non-classical) attempt at grasping complex social phenomena has been adumbrated by enthusiastic philosophers, based on a conceptual analogy with Prigogine’s view. The “non-classical” character of this approach, as far as I am aware, still seems to stay rather at a verbal than at a genuine ontological level; and it is related more to the problem of ascertaining the adequacy of similar conceptual transfers from the ontological vocabulary of a scientific discipline directed to the vocabulary of another one, pretending to deal with a visibly remote subject of research. What then can further be done in the search for an answer to the title question? I suggest that getting an answer may envisage two relevant steps. The first one is such an example of a theory to be chosen, which conforms best among other examples, to the qualification of “non-classical theory”. And

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then the second step could be based on the presupposition that this case may prompt a sufficient criterion for non-classicalness. So, what can be the result from the first step? One can scarcely doubt that from the standpoint of a radical (and surprising) theoretical novelty quantum mechanics has no rival. To this effect, it was unanimously declared to be a non-classical theory in comparison to classical physical knowledge accommodating the “Newtonian” world of human experience. The experimental behavior of quantum objects is very different from that of classical physical objects. Specific theoretical concepts and principles have been invented for modeling the properties of micro-systems, like quantum leaps, discreteness of energy, superposition of states and the like, which are quite unfamiliar in the description of our ordinary world, already dubbed the “macro-world”. Not to mention the “paradoxes” confronting our usual experience, like the outcome from the double slit experiment, or the one from the experiments confirming “the spooky actions at a distance” predicted by the Einstein-Podolsky-Rosen paradox (which were quite surprising for Einstein). All of these strange peculiarities of the first quantum theory – quantum mechanics – which certainly also stay within the conceptual base of all its further theoretical extensions stimulated the Nobel laureate Richard Feynman to make his famous confession: “I think I can safely say that nobody really understands quantum mechanics.” And commenting on the peculiarities of the double slit experiment with electrons he said: “But the deep mystery is what I have described, and no one can go any deeper today” (Feynman 1985: 145). Here I find the direction for making my second step. It is marked by the endeavor for an understanding. And it is namely this endeavor, which provoked the strong need for an additional interpretation. Thus, it is not strange that it was established together with the birth of quantum mechanics as a theory, and not surprisingly by the chief authors of the theory itself (Niels Bohr and Werner Heisenberg). The interpretation is well-known as the Copenhagen interpretation, which also later obtained the name “orthodox interpretation” of quantum mechanics.

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The Copenhagen interpretation of quantum mechanics is not going to be a subject matter for comment. What is of philosophical interest here is not its content organized around Bohr’s idea of complementarity, but what I have just brought out; it is the very need of an additional interpretation, to go together with the structure of quantum mechanics as a scientific theory. I use the term “additional interpretation” to stress the fact that it is something different from the two standard interpretations of any fullyfledged scientific theory, to be named empirical and semantic interpretation. The first one exhibits the links of the abstract theoretical structure with the observed phenomena when testing the empirical consequences of the theory, while the other interpretation draws the meaningful picture of the theory’s domain of application. What I call the additional interpretation has a different cognitive role. And it is to make the ontology of the theory comprehensible. It supplies an understanding as to why the main structural elements of the theoretical ontology display a paradoxical behavior verbally covered by the expression “non-classical objects”. For example, one easily prescribes this expression to all of the elementary particles. The additional interpretation gives an arguable understanding of verbal labels like this one, by presenting explanations for the strange properties inherent to quantum objects, which are rooted in broader conceptual outlooks, like that of the principle of complementarity, on some broader ontology of the sort of the many-words interpretation of quantum mechanics, etc. Thus, the additional interpretation that I outline here has the cognitive task to provide a noncontradictory understanding about the nature of the subject of research – the nature of the micro-world and its formative contribution to the macroworld. In a few words, the additional interpretation provides an understanding of the nature of physical reality. To this effect, a conclusion could be drawn that a scientific theory may be qualified as a non-classical one, only if it is in need of an additional interpretation, which contributes to the constitution of a complete ontological picture of the research field of the theory. The need for an additional interpretation can play the role of a sufficient condition for a theory to be accepted as a non-classical one.

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Yet there is one further specification to be made, in order for this criterion to overcome a legal methodological objection. It is raised by the question “Why is the additional interpretation taken to be concomitant to the alleged non-classical theory, e.g., quantum mechanics, and not to be incorporated within the theory itself?” I call this a “legal methodological objection”, insofar as there are no conspicuous obstacles against the possibility for such a conceptual incorporation. The answer to this objection is the following. The non-classical cognitive status of a theory is not exhausted by the mere presence of an additional interpretation. The theory will cease to be non-classical, if the proposed additional interpretation is transformed into a part (though an essential part) of its proper ontology. Its “non-classicalness” is also nourished by the specific condition about the presence of competing additional interpretations. In the case of quantum mechanics, this means that the behavior of quantum systems is surprising for scientists to such an extent, that attainment of its understanding is not anchored to only one additional interpretation shared by all of them. Quantum mechanics goes hand in hand with several rival interpretations. This reasoning prompts a relevant change in the formulation of the sufficient condition reached so far. Its amended version now states that: The need of an additional interpretation and the presence of extant rival interpretations play the role of a sufficient condition for a theory to be accepted as a non-classical one. I can put here an end to this chapter, since I have just provided an answer to its title question. Yet, a necessary clarification ought to be made, concerning a specification that was made at the beginning. And it is the attitude of contemporary physicists for the original quantum mechanics to be dubbed “classical quantum theory”. Does this qualification mean that quantum mechanics has already ceased to be accepted as a non-classical theory? My answer is negative. The term “classical quantum theory” is sometimes used by contemporary scientists only as an indication that new quantum theories have appeared since the birth of quantum mechanics, which have widened and deepened

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its theoretical apparatus. These are, for instance, the quantum field theory, string theory, loop quantum gravity, and others. One can admit to this effect that these successors of quantum mechanics have succeeded in deepening our understanding of the nature of the micro-world, so that the additional interpretations of quantum mechanics could be left aside. This contention is not true for two different reasons. The first one is that quantum gravity models, as well as string theory, are not yet commonly accepted theoretical systems. Their chief aim is a theoretical unification of gravity with the other three physical interactions that are well described by quantum field theory (strong, weak, and electromagnetic interactions). Even more, there are assessments made by quantum physicists that string theory leads us in a wrong direction, the strongest of which is presented by the title of Woit’s book about string theory Not Even Wrong (Woit 2006). This first reason is theoretically feeble, since a future theory may principally be suggested, which could pretend to unite the four physical interactions into a wider quantum theoretical system, sometimes referred to as a theory of everything. The second reason why quantum field theory, which is quite successful in its predictions, or even an eventual theory of everything, could not cancel the need for an additional interpretation, really does hold water. This is due to the fact that all strange features of the quantum objects go on to be present in the extended quantum theory as well: the uncertainty principle, wave-particle dualism, quantum superpositions, “spooky actions at a distance”, etc. That is to say, all of the “paradoxical” features of the microworld that are crying out for an additional interpretation will be incorporated in the final quantum theory as well, through one theoretical model or another. Unless specialists come to decide that the eventual discovery of “the God equation” in terms of Michio Kaku (2021: ch. 7), standing at the base of a theory of everything, will not remove (or at least suppress) the need for any additional interpretation.

CHAPTER 4 WHAT IS TIME TRAVEL? Let me begin this chapter with Paul Davies’ revelation: “there has probably been more nonsense written by philosophers on the subject of time, from Plato onwards, than on any other topic” (1995: 252). No doubt, this declaration by a well-known physicist and writer, on the background of continuing philosophical discussions about the nature of time, and specifically about the possibility of traveling in time, is a sufficient reason for suggesting an answer to the title question of this chapter. I shall not try to invent any objection to Davies’ declaration, as the deeper the problem, the bigger is the probability for nonsensical solutions. Yet it depends on the conceptual viewpoint according to which an answer about the nature of time is declared to be nonsensical. (Ancient and/or phenomenological approaches for instance are very remote from contemporary physical theories of time, and this might be a motive for P. Davies’ evaluation.) But I have no doubt that the problem of understanding time may be avowed as a fundamental philosophical and scientific problem. And this encourages me to make an attempt at reaching an answer to the title question, not fearing a possibility for it to be assessed as nonsensical. There are skeptics of stories about time travelers, which put forward the following counter-argument: Let us suppose that we meet somebody who is insisting that she is visiting us from some future moment of time in comparison to our present. Then we may expect that she would be willing to inform her relatives about the final results of “today’s” horseracing, and thus to make them rich people – something that will benefit her subsequently, as well. But either putative

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travelers in time are too moral to undertake such frauds, or all intendedly informed winners in horseracing games all over the world are suspiciously silent about the cause of their success. This counter-argument, although bearing some kind of validity, is not a scientific one. It could also be added that even if the counter-argument were taken quite seriously, we can say that there are no travelers in time coming from the future, but traveling in time into the future may still be possible. Yet I have never met legal breaking news about a one-way-ticket visitor from the past. Besides, there are peculiar counter-arguments against journeys through time. What kinds of constraints and problems are they related to? I can divide them into two types: paradoxical and nonparadoxical.

1. Paradoxes of time travel 1.1. “Loop” paradoxes The paradox of the grandmother (of the grandfather, and the like) is a paradigmatic one of this sort. Let us assume that, provided I can travel in time, I go back into the past in the years when my grandmother was a young lady. Imagine further, that I have some “good reason” to kill this woman, or I have done this quite unwillingly, for example in a road accident. But if my grandmother was killed when she had not yet met and married my grandfather, then how could I have possibly been born, and then grown up until the moment of my backward travel in time? This is surely not only a logical, but also an ontological paradox, laying specific limitations to possible strolls through time.

1.2. Changing the past If time travel were possible, then it would also be possible for me, by traveling into the past, to change some situation that has already occurred, but that has brought about some bad effect in my life. I didn’t pay attention to the instructions of my guide high in the mountain, for instance. I didn’t take my new alpine shoes with me when climbing a steep peak, I slipped and fell, and broke my leg. And “now” I want to go back into my

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past, in order to correct my mistake. Although such an action seems to convey no logical contradiction, it is ontologically impossible; because everything that has already happened, and is thus a constituent of the frozen past, cannot be changed. And not because the past is said to be “frozen” by itself, but because nothing could be changed as an isolated event out of a chain of other events that are certainly following it. My friends for instance must suddenly stop knowing of my trouble, everything connected with it must disappear as well, so the world must become different, but it is only one, having no “copies”. The paradox of this thought experiment seems to reject the possibility for changing past events, that have already happened. It does not ban time travels into the past in principle, when somebody could even be a participant in a historical situation, but does not change its course.12 I’ll go back to this option, no matter how curious it might seem, at the end of the last section of the chapter. A way out of this paradox is suggested within the Many Worlds interpretation of quantum theory. The gist of it is that it successfully resolves the puzzle with the instantaneous reduction of the state function. It interprets all possible states that a quantum system could have, as potential realities with different probabilities for realization. When observed, the system immediately “chooses” to be found in only one of its possible innumerous states. Instead, the Many Worlds conception postulates the real existence of parallel universes, each of which contains a possible outcome from the observation of a property of the system. Thus, each universe is characterized by its unique state of affairs, comprised of a physical world together with the human beings whose conscious behavior (free will) has engendered the concrete universe. The existence of parallel universes could then enable, at least in principle, such traveling back in time that is aimed at changing the past. I’ll make use of Brian Greene’s story to this effect, telling of a man who, led by hatred, makes up his mind to kill his father several minutes before he has

12 A nice presentation of this curious possibility is provided by Barry Dainton (2001: 112-113).

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become acquainted with his mother at a New Year party on December 31, 1965: When you travel to 11:50 p.m. on December 31, 1965, pull out your weapon, aim at your father, and pull the trigger, the gun works and you hit the intended target. But since this is not what happened in the universe from which you embarked on your time travel odyssey, your journey must not only have been through time, it must have been also from one parallel universe to another. The parallel universe in which you now find yourself is one in which your parents never did meet — a universe which the Many Worlds interpretation assures us is out there (since every possible universe consistent with the laws of quantum physics is out there). And so, in this approach, we face no logical paradox, because there are various versions of a given moment, each situated in a different parallel universe… In the universe of origination, your parents met on December 31, 1965, you were born, you grew up, you held a grudge against your father, you became fascinated with time travel, and you embarked on a journey to December 31, 1965. In the universe in which you arrive, your father is killed on December 31, 1965, before meeting your mother, by a gunman claiming to be his son from the future. A version of you is never born in this universe, but that’s okay, since the you who pulled the trigger does have parents. It’s just that they happen to live in a different parallel universe. Whether anyone in this universe believes your story or, instead, views you as delusional, I can’t say. But what’s clear is that in each universe — the one you left and the one you entered — we avoid self-contradictory circumstances. (Greene 2004: 457)

I agree with B. Greene that the Many Worlds interpretation affords changing the past, and can even resolve the above-mentioned “loop” paradoxes. But it displays embarrassments of its own. One of them is of a purely existential character. If the son should go to prison after the murder of his father, against whom he has nursed a grudge, this is meaningful in the “original” universe, since only this act possesses a historical context. Killing innocent people in another universe is a sheer crime without any motivation. The second embarrassment concerns the high ontological price one pays when embracing the super realism of the Many Worlds interpretation. And the third concerns our original notion of freedom. At first glance, the conception of the many universes seems to be a theoretical remedy against the difficulties of the unique block universe of the theory

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of relativity. But suppose you are sitting at a table, and you are asked which of two refreshing drinks to order – tea or coffee? According to Paul Davies (1990: 141): [The Many Worlds] interpretation says that the universe immediately divides into two branches. In one of the branches you have tea, in the other coffee. This way you have everything!… Yet the victory seems a pyrrhic one. If you can’t avoid making all possible choices, are you really free? The freedom seems overdone, destroyed by its own success. You want to choose tea or coffee, not tea and coffee.

1.3. Impacts from the future The paradoxes of this type do not resemble the (1.1)- and (1.2)-type paradoxes, but allow for definite activities, inspired by information, coming from the future. A time traveler might become aware of circumstances not known within her proper present that she has abandoned for a while, but which affect her life on her arrival back into her present. I shall adduce here the curt example, suggested by B. Dainton (2001: 125). It considers the decision of a hesitating girl to settle her marriage (and thus her future life): Mary is torn between two suitors. She can’t decide whether to marry Tom or Jack. So she travels to the future and finds out that she is happily married to Tom. She then travels back, and marries Tom for this reason.

The paradoxical situation is based on the possible gain of information from the future, together with the causal effect this information can produce. The key words here are: “for this reason”. Mary determines her own future as a married woman only by virtue of shedding a beam of light on moments of her future, without thinking over rational causes and without listening to heart whisperings for her decision. What if her decision was due to a passing whim for instance? Anyhow, other options are possible: Mary might take either another decision (if only we believe in an open future), or the same decision, but not “for this reason”.

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1.4. The “discrepancy” paradox This appears whenever we assume that someone embarks on a journey through time which takes far less time for its accomplishment than the span of time being traveled along. In Theodore Sider’s words: Before entering my time machine, I may say: ‘in two minutes I will gaze upon a dinosaur’. This utterance appears paradoxical: how can the event of my gazing at the dinosaur be two minutes after my utterance (since, as I say, I ‘will’ gaze at a dinosaur), and also two hundred million years before my utterance, back at the time of the dinosaurs? (Sider 2005: 329-330)

David Lewis (1986: 67) paid special attention to this “discrepancy between time and time”. He suggested a way out of the paradox by discerning between “personal time” and “external time”. The first is the time registered by the traveler in her time machine, while the second is grasped as time itself, as the amount of time that has been passed along, or covered, by the traveler into the past. D. Lewis’ suggestion seems quite plausible, unless a person gives herself an account that the suggestion is not quite clear, having in mind the space-time ontology of the theory of relativity. Within this ontology there is no “external time”, analogous to the absolute time of Newton’s theory, to be compared to “personal times”. Each registered time is but a personal one. One may contend, of course, that Lewis’ “external time” is but the “personal time” for the Earth inhabitants from the time of the dinosaurs till now. If so, the paradox ceases to be a logical one, though still concealing an ontological conundrum (see 2.2).

2. Non-paradoxical constraints 2.1. Does the arrow of time affect traveling in time? As far as I am aware, due attention has not been paid to this question. Maybe there are two reasons for this. The first one is the implicit belief in the symmetry of time, insofar as the fundamental physical laws are invariant in relation to the change of the time variable t with –t. The idea of the homogeneity of time stays in

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support of this belief. In addition to this, if the flow of time is minddependent, while the universe – in accordance with the theory of relativity – is a four-dimensional static universe, then whatever “direction” of time is hardly imaginable. The second reason is the yet unelucidated answer to the question “What is the arrow of time?” There are different pretenders to be the arrow of time, and they are not all even directed equally – e.g., the thermodynamical arrow of time, based on the increase of entropy (and unidirectional with the cosmological one), and the historical one, pointing to the permanent emergence of highly organized systems, thus requiring a decrease of entropy. It is often declared that the arrow of time is marked by the course of change of the so-called irreversible processes. But the fundamental problem arises as to whether these processes determine the arrow of time, or they are possible, because there is an arrow of time. It seems that the second option relies on deeper arguments than the first, among which are the simple, but convincing thought experiments suggested by D. H. Mellor (1998: 120-121).13 The subject about the arrow of time supposes a serious investigation and subtle argumentation that can’t be provided here. My aim was only to explain why the initial question “Does the arrow of time affect traveling in time?” has not been tackled with enthusiasm. What I can say as an answer right now is the following. If there is an arrow of time itself – and there are some interesting arguments that the universe is “lopsided”14 – then it may certainly affect time travel. Although common sense has not proved to be a good advisor in theoretical research, I find the contention that traveling against the arrow of time is, if not entirely forbidden, at least connected with limitations making it not trustworthy. It might be the case that it is namely due to the arrow of time that (1.1)-type loop paradoxes, as well as actions changing settled events from the past, are impossible in our world. And about traveling into the future, I can only recall my joke from the beginning of the chapter that 13

More arguments for this second option can be found in Anguel Stefanov (2020: 133-138). 14 Such arguments are examined by Paul Davies (1995: 208-218).

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“yet I have never met legal breaking news about a one-way-ticket visitor from the past” even if this may turn out to be possible.

2.2. Where to go? Their paradoxical nature notwithstanding, (1.1) and (1.2) cases of contrived time travel stories presuppose the traveler reaching not only a definite moment in the past, but also a definite place in space in order for the accident with the potential grandmother to actually happen, or the potential father to be killed. But how could these special locations really be reached only by traveling back in time? According to our contemporary established knowledge, traveling in time is “at the same time” traveling in space. This follows from the spacetime ontology of general relativity, in which space and time are indivisibly intertwined in a four-dimensional spacetime. This implies that a “movement” from one four-dimensional event within spacetime to another one, would certainly be a transfer through time, as well. So, if somebody wants to visit her future or her past at an exactly chosen moment, she also has to take into account her space position at the final point of the travel, for it would be a disappointment, if she wanted to travel back in time to say, 80 years ago, in order to become a witness of her grandfather’s success in the elections of the President of the United States, to find herself in the same remote year in London, instead of Washington. A suspicion may arise, however, that every event in space-time is equally well accessible from a previously chosen one. At least, we have no reliable proof in favor of this claim. The clocks (known also as the twin) paradox, that I shall comment on below, assures us that some types of cosmic travels are possible, when an astronaut can meet his twin brother and see that he is older than him. But the claim that it probably would not be possible for me to travel from my spacetime position to another spacetime destination that I have arbitrarily chosen to visit, presents a specific ontological constraint for time travelers. This was exactly my point when, at the end of my comment on the (1.4)paradox, concerning the possibility of gazing at living ancient dinosaurs, I said that even if we remove the paradoxical element from it, there still

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remains an ontological conundrum. The conundrum is whether such positions from the remote past are ever accessible to us – either principally, or technologically.

3. My suggestion for an answer to the title question There are three possibilities for us to be time travelers. Two of them are possibilities only in principle, while the third is a possibility that has been realized as the natural way of being in the world for humans – the conscious grasping of the surrounding world as a world evolving through time. I call this a genuine-and-natural travel in time. 3.1. The first possibility is making use of the already mentioned twin paradox. It is worth noticing right now that naming this well-known relativistic effect as a “paradox” is obsolete, since the effect is not paradoxical in itself, as some people once accepted. But this name has strengthened its use to such an extent, that any change of it may lead to misunderstandings. A consistent presentation and relevant explanation of the twin paradox can be found in V. Petkov’s intriguing book (2013: ch. 8). Yet I’ll make a short presentation of the twin paradox for two reasons. First, to show why it offers time travel, and second, to use it as an argument in favor of the static conception of time (represented by B-theories of time) instead of the dynamic one (represented by A-theories of time). Let us suppose that one of two identical twins, symbolized by A, remains on Earth, while the other – symbolized by B – undertakes a space voyage in a rocket ship flying very fast. He reaches a goal point (e.g., some planet around a distant star), and returns to Earth to see his twin brother again. Denoting the spacetime point of departure with D, and the spacetime point of the meeting of the twins with M, let us further suppose that the elapsed time for twin A, who remained on Earth, is ǻtA = 10 years. It is well known then, that the respective time interval (between the same events D and M) for twin B will be ǻtB < ǻtA. If the speed of B’s space ship is great

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enough,15 it could be the case, that when B returns to Earth, the time that has passed for him is twice as short as that of his brother, i.e., ǻtB = 5 years (see Fig. 1).

Thus, when the twins meet in M, the one who remained on Earth, A, will be 5 years older than his twin brother B. But this means that B meets his brother in a future moment of his life. While on Earth, 10 years pass, twin B experiences only 5 years. He arrives back to see his planet being 5 years ahead from the 5 years, which he and his space ship have really gone through. His adventure is a travel in time. The faster his space ship could fly, the further into the future he could visit the world he once left for his cosmic trip. One may say that such an experiment has not yet been carried out. This is true of course, and the reason is trivial: the lack of appropriate technical possibilities for the realization of the experiment. The twin paradox, however, as a direct consequence of the special theory of relativity, has been observed many times as the effect of prolongation of the life time of fast-moving elementary particles. Now let us see whether the dynamic view of time can explain the twin paradox. According to this view, the flow of time is real, and the world 15 It could be easily calculated (by using the Lorentz transformations) that the speed of the ship in this case must be about 261 thousand km/s.

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events possess reality only when they are elements of the present. Past events do not already exist, and future events do not exist yet. Thus, the physical presence of the twins is realized by their three-dimensional bodies changing in time. But if this is so, 5 years after his departure twin B will exist in the event M, and will not be able to meet his brother, since for the same period of time twin A will be in the middle of his history between the event of the departure D and the event of the meeting M. (Let me recall that 10 years are needed for twin A to meet his brother.) The dynamic view fails to explain the twin paradox. On the contrary, the static conception of time provides a sound explanation. According to this, past, present, and future events possess one and the same ontological status, they are equally real. Twins A and B are existing in the world with the whole of their history, and particularly by their worldlines between the events M and D. But if their four-dimensional bodies are actually present between these two events, they will surely meet at the event of B’s arrival on Earth. The result of the twin paradox – B seeing the future of the world he once left – is easily explained by the fact that the (four-dimensional) worldline of B is twice as short as the worldline of twin A. Since the personal time of the twins is measured along their respective worldlines (personal histories), A’s time is twice as long as B’s time between the events D and M. Thus, according to the static conception of time, being in harmony with the theory of relativity, the flow of time is “personal”, and there are as many personal times, as the number of observers to be found in relative motion among each other. 3.2. The second possibility for time travels could depend on the features of the physical spacetime, according to the general theory of relativity. It is mathematically modeled by a four-dimensional Riemannian geometrical space (comprised of three space and one time dimension). Traveling in spacetime means then accomplishing a movement from one spacetime event (one point of the Riemannian space) to another spacetime event (to another point). But such movements can hardly be arbitrarily accomplished, because they ought to satisfy the already considered constraints. At that, they cannot be represented as usual movements in spacetime, since the temporal dimension is in itself, and it is not taken to be a subspace of a more dimensional spacetime, including at least one additional temporal

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dimension. Such travel would require additional dimensions to enable the intended journey to be “sliding” over the four-dimensional manifold. For all we know, such dimensions, even if we may hypothetically think that they are “out there”, are not at our disposal. Thus, it seems that time travels of this kind are reduced to “movements” within spacetime, represented by strange “translations” from one spatiotemporal event to another one, and so I can say that they seem to be impossible (for macro objects). But there is another possibility of traveling in time. It is based on the wellknown idea of using hypothetical worm-holes in the texture of spacetime. Time-travel would thus be possible not over spacetime, but through holes within it. For now, candidates for gates of spacetime worm-holes are the black holes. According to Carl Sagan’s optimistic opinion (1975, 264): An object that plunges down a rotating black hole may re-emerge elsewhere and elsewhen – in another place and another time. Black holes may be apertures to distant galaxies and to remote epochs. They may be shortcuts through space and time.

If this is true, namely that we can rely on black holes to transfer us to remote epochs, we have to concede that gazing at dinosaurs two hundred million years from “now” is not an impossible adventure, and thus the “discrepancy” paradox (1.4) may be evaded. Unfortunately, this possibility remains only as a speculative project. As it has already been explained, this idea is committed to serious obstacles.16 “Plunging down” a black hole for instance is not safe, since the huge gravitational gradient would tear apart the cosmic traveler together with her flying machine. The conclusion reached so far allows for a specific class of time travels, representing positional shifts in spacetime that satisfy the already discussed ontological constraints. Evidence for this hypothesis comprises the rarely published stories of people pretending to have experienced time travels, if we take them seriously, of course. If not, we may accept that 16

See for example Hawking and Mlodinov (2005: ch. 10).

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such time travels are possible only in principle. Nobody has proved, indeed, that she has constructed a working time-machine. A comment is needed, however, concerning the hypothetical time travels. Let us suppose for example, that we have read a newspaper story about a curious discovery of a paleontological expedition: human shoe-prints around the big petrified foot-prints of an ancient dinosaur, dating from one and the same epoch. Let us further suppose that, believing the story, we do not believe that humans resided on the Earth together with dinosaurs. As it seems, the only conclusion left then is to concede that a clever man from the future has managed to construct a time-machine, and has successfully achieved a long-distance time trip into the past. But this may not be the only explanation. Besides, as we already know, backward time travels meet the constraint of not changing the past. This constraint is a very delicate one, because even slight changes of details that constitute the past, can eventually lead to sizable changes in the future. Then, what other explanation may we rely on? This is an explanation which attracts no actual time travel. If the static conception of time is to be preferred instead of the dynamic one (since it better complies with the spacetime ontology of the theory of relativity, and explains the twin paradox as we have seen above in 3.1), then a possibility, somehow strange, but devoid of paradoxes, may be envisaged. The possibility that for some, yet unknown reason, or simply occasionally, the otherwise integral history of an object can be separated into temporal parts, situated within different places of spacetime. Thus, a temporal part of the four-dimensional body channel of an individual may be laid in another region of spacetime. Since the individual is conscious of herself all the time of her existence, she would have the impression of a queer time travel into the past. In this way the individual could take part in forming the past, without changing it. In this sense, Barry Dainton admits the activity of a man from our present who takes part in the building activities of the Egyptian pyramids. You may have been born in 1975, but unbeknownst to you and your parents this was not your first appearance in the world’s affairs: you first entered history as a thirty year old, assisting with the building of the

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My only remark is that Dainton would not speak of a “departure” to ancient Egypt, since an actual travel in time does not take place, but of an inception of a conscious presence in a reality, to be found in the remote past of the hypothetical hero. Yet I would like to draw the readers’ attention to the fact that even if such time displacements of separate individual histories (of temporal parts from their four-dimensional life lines) were possible in principle, such rarely reported events are not authentic travels in the proper sense of the word “time-travel”; because first, they are not realized as trips in time per se, and second, they are in no means intended attempts at traveling in time. 3.3. In the end I come to the third possibility of traveling in time which I find to be the natural human presence in the world. This is the real humanlike way of life, based on the perception of the surrounding world as a reality, given to human consciousness, and in turn to be temporalized by it. No matter how “Kantian” this may seem, it is a well-known corollary of the static conception of time that the flux of time is minddependent. Human beings are travelers in time. They experience time through perceiving changes in events and among events, as well as through the sense of duration. Time travel is thus expressed in the human awareness of change and duration, despite the four-dimensional world neither changing, nor having any duration along an additional time dimension.

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I call this “a genuine-and-natural travel in time”. Positively interpreted, time travel is but the conscious grasp of the world, when human consciousness “sheds light” upon the consecutive present events along the unique world-tube, encompassed by a man’s living body, i.e., along the whole of man’s history. Time travel may thus be interpreted as a conscious positioning within one’s history, experienced as a flow of time. Metaphysically interpreted, the genuine-and-natural travel in time is the permanent revealing of Being by the unique human mode of being. It is the temporal stretch of human existence. And it has its human limits: we can remember the past, not the future. “It is not for you to know times or seasons which Father has put in His own authority.”17 In other words, the genuine-and-natural time travel is the unique, purely human way of giving meaning to the world – being unveiled to human consciousness as a non-ceasing sequence of life events. Man has no God power to represent for himself the entire world at once, not even his entire life-span. Otherwise, man would lose his essence – the sense of freedom.

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The Acts 1:7.

CHAPTER 5 SPACETIME: SUBSTANTIVE OR RELATIONAL? Introductory Words Since the Newton-Leibniz debate about the substantive or the relational nature of space and time the problem continues to be a bone of contention among philosophers, because of the necessity for grasping the nature of space and time; and because “science is still struggling to understand what space and time actually are” (Greene 2004: IX). My aim in this chapter is to present and to analyze relevant arguments in support of the substantive view of spacetime. In so doing I shall not consider historical facts concerning the relationalistsubstantivalist debate. Yet, although the title question concerns the nature of spacetime, and not of space and time as separate entities in the ontological picture of classical science, I shall begin with three arguments in favor of the relational character of space and their respective criticisms, bearing a conceptual impact on contemporary spacetime physics as well. These are sections 1.1-1.3 in this chapter. According to the substantive view, absolute Newtonian space and time, as well as spacetime within the ontology of general relativity, are autonomous entities having an existence of their own, and thus being independent of the way of existence of material objects and fields. On the contrary, according to the relational view, only material objects and fields really exist, while space and time are nothing other than the entire set of spatial and temporal relations among them. My considerations in favor of substantivalism will not involve mathematical language, e.g., formal transformations of spacetime metrical structures, with the exception of the analysis of the well-known basic equation in the theory of general

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relativity within the last section of this chapter (2.3). All of the adduced arguments are of a conceptual nature.

1. Classical relationalist arguments and their critical comments 1.1. Leibniz’s Shift Argument Revisited Leibniz’s famous objection against the substantive conception of Newton’s absolute physical space is his so-called “shift argument”. I shall analyze its initial premise, but instead of re-telling the argument myself, I will set out here its clear presentation made by Frank Arntzenius (2012: 126): Leibniz, the continental rival of Newton, gave a famous argument against the existence of space. His argument was as follows. Suppose that space did in fact exist. Now (…) imagine a universe that is exactly the same as ours, except that every material object, throughout the history of that universe, is shifted to a different location in space. Say, every material object is shifted 5 feet in the direction that the Eiffel tower now points. Such a universe would not differ in any discernible way from the actual universe. Therefore, God could have had no reason to create our universe rather than such a shifted universe. But God has a reason for everything he does. So it cannot be that there is such a choice to be made. Now, if there is no space, if all that exists is material objects, which stand in certain distance relations, then there is no such choice to be made. For, all the distance relations between material objects are the same in the actual universe and in the shifted universe. Thus, if all that exists is material objects, which stand in distant relations to one another, then there are no such two distinct possibilities, and thus there is no choice for God to make…

Shorn of religious zeal, the argument boils down to this. If space exists, there is a difference between a universe and a shifted universe. But that is a difference without a difference. And why introduce such an elusive difference if you do not need it? Leibniz concluded that space does not exist – that there are only bits of matter which stand in spatial (distance) relations.

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Leibniz’s shift argument seems to be convincing. It is easily seen that it relies on the well-known principle of the identity of indiscernibles, and I am not going to contest the applicability of this principle. Nevertheless, I’ll try to develop a counter-argument. As a counter-argument to the shift argument, it is at the same time an implicit argument in support of the substantive view of space. It aims at elucidating the dubious role of the initial premise of Leibniz’s argument, that is to say, the presupposition for a spatial shift. This presupposition can be interpreted in two different ways, depending on the understanding of how the assumed shift is possible. The first possible way is to admit the existence of a Newtonian absolute space, as well as the principal possibility of shifting material objects through space. Thus, the entire system of worldwide objects together with their interactions could hypothetically be shifted by a finite distance away from their actual place in space, so that during the translation process until its end all material objects and their interactions remain identical to themselves. The problem that I see here is that this initial presupposition already conceals the very conclusion of the shift argument. Just admit the existence of absolute space, which “invites” any shifts of material objects within it, and you’ll reach the intended conclusion that no absolute space exists. However, the only conclusion that could really be made within this interpretation of the shift argument (with the help of the principle of the identity of indiscernibles) is the conclusion about the one-ness, or in other words, about the uniqueness of the universe, and not directly about the non-existence of space. Let me turn now to the second possible construal of the initial premise of the shift argument, i.e., of the very presupposition for a spatial shift. Here again the talk of two allegedly different universes comes to the fore: the actual one, and another one, which is the result of the shift of the former carried out at a finite distance. The difference now is that each universe is initially taken to be situated within its own space. But if so, then a superspace is needed, in order for a universe to be shifted to another region of it. Though being identical to the actual universe, the other one occupies another region of super-space, which encompasses the two spatial universes. In this case, the shift argument can be used to reject the

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existence of super-space, but not for reaching the sought conclusion about the non-existence of space at all – the space of the actual (and unique) universe. So, by exploring the two possibilities as to how the spatial shift of the whole universe could be construed, it comes out that the shift argument is not a cogent argument against the substantive nature of space. Leibniz’s shift argument was “transformed”, using the mathematical language of general relativity, with the aim of demonstrating the relational character of spacetime as well, and received a new name – the “hole argument”. It presupposes formal considerations concerning diffeomorphic transformations of the metric tensor field18 of Riemannian spacetime. For this reason, and insofar as I admit the critical strength of two detailed theoretical analyses that the hole argument fails against substantivalism, I shall not touch upon it. I shall only point to the sources of these detailed analyses. The first one is the extended consideration offered by Arntzenius (2012: 139-145), which shows in a cogent way that the hole argument does not fulfill its aim to vindicate the relational nature of spacetime. The second detailed analysis convincingly defends the claim “that Einstein and the generations of physicists and mathematicians after him were right to reject the hole argument. It is based on a misleading use of the mathematical formalism of general relativity” (Weatherall 2018: 329).

1.2. The Void Argument Yet a follower of Leibniz may relinquish the shift argument and replace it with another one, which can be called the “void argument”. What is its pretention? Void Argument: Let us assume that besides all material objects and fields in the world there is space in which all of them are situated, and that space is something that has a reality of its own. Now let us imagine that all material objects and fields are taken away. What would remain then is the presupposed universal space. But this empty space would then be only a 18 It is usually called a “tensor field" in this argument to the extent to which it steps in a kind of equality with the tensor of matter – see the last section 2.3.

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void deprived of material objects and interactions among them, and to this effect it would turn into an imaginary thing, which displays no property of its own. But a thing without properties whatsoever is nothing rather than something. However, God created the world as something, not as nothingness. This is why space does not exist as an entity of its own. It is an idea that emerges through the reification of the entire set of relations among material objects. A strong objection to the void argument would be a claim that an empty space is not deprived of intrinsic qualities. Let us turn to this effect in the concept of a triangle. The sum of the inner angles of every triangle drawn on a plane equals 180 degrees. However, if the triangle is to be found on the surface of a sphere, the sum of its inner angles is more than 180 degrees. Thus, the basic properties of triangles may differ, when they reside within different spaces. And this difference is not due to the triangles proper, but due to a difference of the spaces themselves. A geometrical space can be flat, or otherwise can have a positive or negative curvature, a space can possess a homogeneous or non-homogeneous metric, and spaces can exhibit different topologies, for instance they can be orientable, or non-orientable. All of these are properties of a geometrical space per se, so every space is characterized by a list of the aforementioned qualities. On these grounds, the claim that an empty space has qualities of its own must be avowed to be true, and hence it follows that space may be viewed as an entity of its own. Of course, an objection may be raised that the qualities of a geometrical space just pointed out, do support a view about some ideal autonomy of geometrical spaces, but not the stronger thesis about the substantive character of an empty physical space (spacetime). I agree with this objection; but I also have a straightforward answer to it. And it is the following: if an entity different from the material objects can affect their behavior, then it could be taken as certain that such an entity is substantial. And as it is well known, it is the curvature of the fourdimensional spacetime that is said to affect the motion of material bodies, as well as the direction of light beams passing near massive cosmic objects.

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A counter-objection may be raised that my criticism of the void argument, even if taken to be sound in some sense, still does not hold water. And this is so, because from a historical point of view non-Euclidean geometries were (probably) unknown to Leibniz. I do step here into a delicate argumentative field. I must confess that if one presumes that what is taken to be the physical space is correctly represented geometrically by the flat three-dimensional Euclidean space, then the void argument might go well. And this was the undoubted presumption at the time of the Newton–Leibniz debate. However, this same argument does not work nowadays. As already mentioned, light beams are not straight lines when spreading through the cosmic space. And this is so, because of the Riemannian character of spacetime. The geometrical feature of a space to be either flat, or to possess a kind of curvature, can affect the motion of material objects. Thus, the void argument may well be rejected.

1.3. Argument based on chirality Incongruent counterparts are mirror objects which, though being quite similar like the left and right human hands still cannot be superimposed on each other with the help of translations and rotations within a fixed orientable space. A left glove cannot fit a right hand, and vice versa. For the first time, the possibility of the existence of such objects was taken as an argument for the existence of the absolute Newtonian space in the last pre-critical work of Immanuel Kant (1991).19 In a nutshell, Kant’s claim in this essay is that if incongruent counterparts (as for instance left and right human hands) do really exist, then absolute space must also exist. This is usually known as Kant’s argument of 1768. But if this argument is correct, and the absolute Newtonian space exists, then the physical space is substantive, not relational. If only one human hand existed in the world, Kant contends, it would be either a left, or a right hand. 19

This work was published in 1768 under the original title: “Von dem ersten Grunde des Unterschiedes der Gegenden im Raume”. Academic edition of Kant’s works: Kant AA II: Vorkritische Schriften II, 1757-1777, S. 373-384.

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Relationists disagree, insisting that a single hand could neither be qualified as a left, nor as a right one, since there is no other object to be involved in relation to the solitary hand, for its handedness to be ascertained. Let us imagine to this effect the existence of a suitable “referent object” alongside the lonely hand, and let the referent object be a handless human body. Then we can see which of the two wrists of the body the hand will match. Suppose it matches the right wrist. Thus, the right-handedness of the hand would be ascertained. But without the referent body no righthandedness of the solitary hand exists. Its right-handedness comes as a result of a relation to the handless body and is not a property of the hand itself, if it were the only existing thing in the universe. There is a clear objection to this view. Let us revisit Kant’s story with the solitary hand. It was accepted that it was the only existing thing in the universe, till the handless human body came into being. The objection states that the hand was a right one even before the appearance of the referent object. Indeed, the appearance of the handless body does not affect the nature of the hand that was created before the body. Nor does the appearance of the latter affect the spatial characteristics of the region where the hand was situated. But if so, then it certainly follows that the solitary hand was right for all the time of its existence, and the referent body serves only for its right-handedness to be observed, and in no way to be created. This objection supports the substantive nature of space, since it is an argument that space has something to do with the concrete handedness (chirality) of the hand. But what answer could be suggested to the question of why a lone hand is either right or left per se. A general idea for such an answer was proposed for the first time in the same work of Kant (1991: 28, original italics): [M]y aim in this treatise is to investigate whether there is not to be found in the intuitive judgments of extension, such as are contained in geometry, an evident proof that absolute space has a reality of its own, independent of the existence of matter, and indeed as the first ground of the possibility of the compositness of matter.

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That absolute space, as a reality of its own, can be looked upon “as the first ground of the possibility of the compositness of matter” is an original idea that has an explanatory potential. It implies the assumption that some inherent features of space – for instance the specific metric and topology of a space – could affect not only the (in)congruency of geometrical objects, but also the “compositness” of material bodies. Thus, incongruent geometrical figures drawn on a plane, to continue the story with the images of left and right human hands, can become congruent counterparts, if placed on a Möbius strip, representing a non-orientable two-dimensional space. Kant was not in a position to further develop his original idea on the background of the classical physical and mathematical knowledge of his time. Nevertheless, he was not surprised that incongruent counterparts might display a functional asymmetry concerning some of their exhibited properties, like those of left and right human hands, eyes, and ears: But if some investigators, e.g. Borelli and Bonnet, are to be believed, while the right hand seems to have the advantage over the left in mobility, the left has the advantage over the right in sensibility. Borelli likewise assigns to the left eye, and Bonnet to the left ear, the possession of a greater sensibility than the corresponding organ on the right side (Kant 1991: 30).

Having in mind the parity violation in the micro-world, Kant’s argument of 1768 could be extrapolated to the effect that if there were only one weak interaction breaking the mirror symmetry, and more precisely the CP-symmetry (the charge conjugation and parity symmetry) in the universe, it would do so. The difference now is that such a quantum process takes place in spacetime. But what is the role of time here? Its role is to restore the symmetry at a deeper level. A quantum physical system is invariant only with respect to the triple CPT transformation, including the operation of time reversal. A breaking of the CP-symmetry is equivalent to time asymmetry. If spacetime had a relational nature, the last two statements could hardly be taken to be meaningful, because in a purely relational context they would have no reasonable explanation. Moreover, if spacetime had a relational nature, it would hardly have an impact on the symmetry of physical interactions, because spacetime is accepted as emerging out of the relations among material objects and force fields. But if it is true that

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symmetries are sometimes broken in isolation, or in couples, it comes out that spacetime affects the compositeness of matter (to use Kant’s own expression), and thus has a substantive nature. Of course, relationists may still insist that spacetime has a relational nature and refer the breaking of symmetries to some definite peculiarities of the physical interactions themselves, but this explanatory transfer would require additional theoretical assumptions that are still not clearly set out. The conclusion reached here stays in harmony with a reasonable understanding of the so-called Einstein-Podolsky-Rosen paradox exhibiting what Einstein once called “spooky action at a distance”. It seems that spacetime is really contributing to “the compositeness of matter” of quantum particles in an entangled state, since a measurement carried out on one of such particles affects the other one as well, no matter the distance that separates them. This holistic quality of spacetime is hardly explainable if its nature were relational. As it is seen, the end of this section throws a bridge towards the next ones, the aim of which is to provide relevant arguments for the substantive nature of spacetime.

2. Arguments for the substantive nature of spacetime 2.1. Argument concerning the cosmological constant When Einstein first wrote his equation of the general theory of relativity, he introduced an additional term, known as the cosmological constant, so that the equation could describe a static universe. When astronomic observations showed that this was not the case, he removed this term. However, in 1998 (43 years after Einstein was gone) observations showed not only that the universe is expanding, but that its expansion is accelerating. Contemporary cosmologists re-introduced Einstein’s cosmological constant. They have done this for the sake of a consistent explanation for the observed acceleration of the expansion of the universe. But even if this acceleration could not be confirmed by interpreting new astrophysical observational data, the universal expansion is an established fact, and it is certainly in need of an explanation.

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As well as matter, the universe may contain what is called ‘vacuum energy’, energy that is present even in apparently empty space… vacuum energy causes the expansion to accelerate, as in inflation. In fact, vacuum energy acts just like the cosmological constant… that Einstein added to his original equations in 1917, when he realized that they didn’t admit a solution representing a static universe. (Hawking 2001: 96-97)

The energy ruling the expansion of the universe, known by its popular name today as dark energy, is a fundamental quality that cosmologists refer to as the “empty” spacetime itself. Dark energy opposes the effect of the universal gravitation that is empirically expressed by the well-known force of attraction among material bodies. This force is inversely proportional to the square of the distances among material bodies, so that the gravitational interaction becomes weaker in an expanding space shifting material configurations aside from each other. However, if dark energy expressed by the cosmological constant is a quality of spacetime itself, its anti-gravitational effect ought to be one and the same independently of how much the universal space has been expanded. Thus, one may certainly expect that there must be a stage in the evolution of the universe, when the effect of the dark energy would become stronger than the gravitational attraction. From this stage on the universal expansion would exhibit acceleration. And this is exactly what astronomers found to be the case in 1998. But then, as ordinary matter spread out and its gravitational pull diminished, the repulsive push of the cosmological constant (whose strength does not change as matter spreads out) would have gradually gained the upper hand, and the era of decelerated spatial expansion would have given way to a new era of accelerated expansion. (Greene 2004: 300, his italics)

If the nature of spacetime were relational, then spacetime could hardly possess such an intrinsic dynamic quality as dark energy. Energy is a fundamental property of material systems, and they have an existence of their own. So, we must concede that spacetime, possessing energy of its own, also has an existence of its own; or in other words, it has a substantive nature.

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2.2. Argument Concerning Gravitational Waves Since the birth of Einstein’s general theory of relativity in 1916, it has been suggested that gravitational waves could exist. They are ripples in the fabric of spacetime that propagate as waves at the speed of light. One hundred years after Einstein hypothesized their existence, on February 11, 2016, the LIGO Scientific Collaboration and Virgo Collaboration teams (covering the international participation of scientists from several universities and research institutions) announced that they had made the first observation of gravitational waves. They originated from a pair of merging black holes at a distance of 1.3 billion light years from the Earth, somewhere beyond the Large Magellanic Cloud in the sky of the southern hemisphere. The discovery is a great triumph for three physicists – Kip Thorne of the California Institute of Technology, Rainer Weiss of the Massachusetts Institute of Technology and Ronald Drever, formerly of Caltech and now retired in Scotland – who bet their careers on the dream of measuring the most ineffable of Einstein’s notions. (Overbye 2016)

I will not comment here on how precisely the experiment was carried out, although the history of its planning and realization deserves special attention. As far as I am aware, its positive result has been accepted by the scientific community. Besides, the LIGO–Virgo Scientific Collaboration teams announced on June 15, 2016, that a second detection of gravitational waves from coalescing black holes was observed. What is important here for my purpose is the following. If the gravitational waves could not be detected for some principal reason, then this would be no good news for the proponents of the substantive view of spacetime. But what happened after their existence was confirmed? The observation of gravitational waves represents a clear argument in support of substantivalism. Relationism could hardly account for the existence of such waves. Indeed, from a relationist point of view, only material objects really exist, while space and time are specific relations among them. However, relations are relational properties of objects, and as such properties they have no existence of their own. But if so, relational

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properties cannot possess non-relational properties on their part, and in particular, spacetime cannot transmit gravitational waves, being a genuine disturbance of spacetime. On the contrary, only if spacetime exists as an entity of its own and exhibits local curvatures responsible for the gravitational interaction, then collisions of massive cosmic objects like galaxies and black holes can certainly account for the appearance of detectable gravitational waves. They are emitted by bodies that are under acceleration, i.e., by bodies whose worldlines are not geodesic, but deformed, so inertial forces can arise. And gravitational waves do carry energy with them – a non-relational property – although not exactly “gravitational”, but inertial energy.20 All these facts undoubtedly stay in support of the substantive nature of spacetime.

2.3. Argument from a Consistent Interpretation of the Basic Equation in General Relativity I have in mind the so-called Albert Einstein field equation, or his wellknown tensor equation of the general theory of relativity, the one hundredth anniversary of the publication of which was celebrated in 2016: RDE - 1/2gDER = NTDE As is well known, the left side of this equation is now usually called Einstein’s tensor, and it refers to the geometry of spacetime, but more ontologically speaking, to the entire set of spatiotemporal events. The tensor on the right side is the tensor of matter, also known by the name of energy-momentum tensor, which is taken to structurally represent the state and distribution of the different kinds of matter. However, Einstein himself had a problem concerning the construal of his field equation: But, it is similar to a building, one wing of which is made of fine marble (left part of the equation), but the other wing of which is built of low grade wood (right side of equation). The phenomenological representation of matter is, in fact, only a crude substitute for a representation which would correspond to all known properties of matter. (Einstein 1936: 311)

20

The origin and nature of gravitational waves are explained in detail by V. Petkov (2021: ch. 6).

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At that, there is another interpretative problem concerning the motion of material objects according to the general theory of relativity: The theory incorporates the effect of gravity by saying that the distribution of matter and energy in the universe warps and distorts spacetime, so that it is not flat. Objects in this spacetime try to move in straight lines, but because spacetime is curved, their paths appear bent. They move as if affected by a gravitational field. (Hawking 2001: 35)

So, we are faced with a curious situation: material bodies warp spacetime, while at the same time spacetime curvatures determine the way of motion of material bodies. The just outlined two problems point to the need for a consistent interpretation of Einstein’s basic equation of general relativity. As it seems, there are two interpretative possibilities. The first one is to construe the equation as a mere mathematical equality of two different kinds of tensors, representing independent kinds of entities: Einstein’s tensor and the matter tensor, which refer respectively to spacetime’s geometry, and to the distribution of matter and energy. Of these, the tensor of matter is of primary significance, since it is said that material bodies do cause the curvature of spacetime. In this case, however, the curious situation at hand could not be consistently elucidated. That is to say, this interpretation provides no arguable answer to the question “Why, and how do material objects warp space-time?” The remaining alternative is to construe the equation as expressing an identity, and not merely a correlation of equality between its left and right sides. Thus, both these sides ought to be taken as theoretical constructs that refer to one and the same entity. It is certainly represented by the “fine marble (left part of the equation)”, or in other words, this initial entity is spacetime.21

21

A tribute must be paid to Hermann Minkowski, who, it seems, was the first to realize that the four-dimensionality of spacetime should not be accepted as a convenient descriptive language, but that the real physical world is fourdimensional. See in this connection V. Petkov (2013: 65-75).

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There is still one more reason in favor of the identity interpretation, and this is of a logical character. As is well known, the covariant derivative of the tensor on the right side of the equation – the tensor of matter, or the energy-momentum tensor – must be zero. Applying a covariant derivation includes the Christoffel symbols of the second kind (which are the affine connections of the four-dimensional Riemannian spacetime). The Christoffel symbols, however, are functions of the metric tensor and its ordinary derivatives. Thus, it comes out that in order to see whether the tensor on the right side of the equation is really a matter tensor, one has to know beforehand the metric of the spacetime. This vicious circle could only be overcome by the identity interpretation, since within it spacetime and matter (or, it is better to say spacetime without and with material bodies) belong to one and the same initial, or fundamental essence.22 What is this fundamental essence? The identity interpretation takes the referents of the tensor structures on both sides of Einstein’s basic equation to be, or to fall into one and the same, ontological essence. The latter ought to be identified with spacetime, but not only with the geometry of spacetime. It would not be correct for the geometry of spacetime and matter to be separated as two independent entities. On the contrary, they must be construed as two cognitively separable parts of a unique ontological essence. This could certainly be neither “empty” spacetime, i.e., spacetime deprived of any material structures, nor “pure” matter without spacetime, which could hardly be conceived of. It could be provisionally named “prime matter”, or “primal matter”, in order to remind us of the ancient Greek idea of a primeval essence giving birth to the variety of all visible and tangible natural objects, or of something like Anaximander’s apeiron. When Einstein’s tensor equals zero, then prime matter is reduced to “empty” Riemannian spacetime; and when it is different from zero, then prime matter presents itself as spacetime filled with material structures. Prime matter is the fundamental essence that is looked for, since it unites

22 To my knowledge it was Anastassov (1973: 250) who raised for the first time the idea about such a fundamental essence.

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spacetime as an entity described by a geometrical language with the material structures emerging within it. The identity interpretation of Einstein’s basic equation provides an ontological framework for the meaningfulness of the two previous arguments for the substantive nature of spacetime, as well as for the validity of the argument based on the APR-paradox that was mentioned at the end of section 1.3. Spacetime, interpreted as prime matter, is the genetic background for the emergence and compositeness of matter. And it also possesses an immutable feature of matter – energy of its own. This is not strange at all, since according to the suggested interpretation, spacetime – accepted as prime matter – is the fundamental concept in the theory, while all material objects, taken with their properties and interactions, are specific energetic states of prime matter. Gravitational waves as ripples in the fabric of spacetime are features of this same prime matter. The final conclusion in the end is that the identity interpretation of Einstein’s equation of general relativity, being the only consistent one, certainly excludes the possibility of the relational nature of spacetime. The latter could in no way be thought of as a set of relations among any material objects whatsoever, because, on the contrary, it is spacetime in its quality of prime matter, which gives birth to material structures, and not vice versa. Spacetime has a substantive nature but not in the traditional sense of this qualification as it was stated at the beginning of the chapter; spacetime within the ontology of general relativity is an autonomous entity having an existence of its own, and is thus independent of the way of existence of material objects and fields.23 As we have already seen, however, it could 23

“There are two venerable traditions in the philosophy of space and time. One is ‘substantivalism’, which maintains that space and time (relativistically, spacetime) are objects that exist in addition to ordinary material objects such as tables and chairs. The opposing tradition, ‘relationism’, rejects the existence of space and time (spacetime) and maintains that all that exists is material objects. According to traditional relationism at each time there are spatial distances between material objects and there are temporal distances between events involving these material objects. But

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be said that spacetime does not merely exist in addition to material objects; it is the very basis for their existence. This last conclusion throws a bridge to the next chapter which maintains the contention that spacetime may not be considered as an emergent entity.

these are just relations that obtain between those objects and those events” (Arntzenius 2012: 125, my italics).

CHAPTER 6 IS SPACETIME AN EMERGENT ENTITY? 1. Short Introduction It seems that during the last two decades or so the claim about the emergent character of spacetime, not to speak of the three-dimensional space of our experience, has been getting support from the camp of physicists embarked on constructing models of quantum gravity. What is the reason for this claim, in spite of the fact that there is still no fullyfledged theory of quantum gravity to be accepted as such by the scientific community, and also having in mind that quantum field theory and the theory of general relativity (in the framework of which spacetime is a fundamental concept), are taken to be undoubtedly very well corroborated theories? The reason for this claim is the conviction that While spacetime is used in this theory [quantum field theory], it is not described by the theory. GR [general relativity], on the other hand, is a theory of spacetime. It describes spacetime itself as a dynamical field (that does not exist in some further ‘background’ spacetime, and so is background independent), and says that gravity is due to the curvature of spacetime. Both of these theories are incredibly successful, yet, neither theory is thought to be fundamental. (Crowther 2019) QG [quantum gravity] is supposed to be more fundamental than both these theories. (Crowther 2021)

As Crowther clearly states, the argument about spacetime emergence is that quantum gravity is supposed to be a more fundamental theory than general relativity and quantum field theory. Even if this is the case, however, this argument is epistemological, not ontological. I do have it in mind at the end of the chapter (see section 5), and this is the reason for my negative rather than positive answer to the title question. But if spacetime is taken to be an emergent entity, then from a philosophical point of view some conceptual approach must be contrived for the purpose of explaining

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what exactly is meant by the very notion of emergence in the case of spacetime, and not about any material system within spacetime. The aim of this chapter is to present an alternative view. It is a “dissident” philosophical position in comparison to the emergentist doctrine about the nature of spacetime that is gaining popularity nowadays. My argument will be ontological, and based on the idea that spacetime is a universal and fundamental entity by itself. A rather negative answer to the title question is thus reached at the end of the chapter. What is meant by a “rather negative answer” is also clarified there.

2. What Is It for Spacetime to Be Emergent, and not a Fundamental Entity? One clear answer is that spacetime does not merely exist by itself, because it is emergent from something else – from some deeper non-spatiotemporal reality. This conceptual position is an eliminativist view of spacetime, since it denies its existence on a quantum scale. It is, however, a rather radical ontological view. It could be supported by quantum gravity physicists, but is reluctantly accepted by a philosopher with an ontological outlook like mine. I say this not because I cherish some conservative sympathy for spacetime, but because when denying the standard ontological status of spacetime one meets two conceptual difficulties. The first one requires an explanation about our false experience not only about a flowing time (that has already been accepted by a lot of philosophers and scientists to be mind-dependent), but about our false experience of space, as well. As far as I am aware, an arguable explanation for the latter illusory misperception has not yet been suggested. The second difficulty refers to carrying out experimental tests and empirical predictions of physical theories which are always accomplished at definite places and intervals of time. But quantum gravity theoretical schemes could not be tested in this way, and this raises a problem about their empirical confirmation. There are rare voices against undertaking theoretical attempts at quantizing gravity. This is, for instance, the clearly exposed consideration

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made by Antoine Tilloy (2018) about the cogency of the alleged necessity for quantizing everything. I find his view to be convincing, but I shall not have it in mind here, since I’ll stick to my own philosophical predilections. Alongside the strong eliminativist doctrine there is a milder emergentist view that is usually known under the name of “derivative spacetime view”. Since I find it to be the topical emergentist view nowadays, I dedicate my further analyses to this view. It states that although spacetime exists, it does not exist fundamentally. Thus, two modes of existence are presupposed: one derivatively fundamental – that of spacetime, and another, “genuinely” fundamental – that of a nonspatiotemporal quantum basis. The derivative spacetime view pretends to show how a spacetime structure is related to the more fundamental quantum structure, or how spacetime qualities emerge from other kinds of entities. A paradigmatic construal in this respect is the functionalist one.

3. Functionalism Functionalism is a legal step for saving a realist standpoint about the existence of spacetime. Many philosophers find a refuge in what space functionalism can provide. It is connected by default to a meaningful recovering of spatial features as we perceive them in human experience. The conceptual backbone of functionalism is the claim that spacetime is exactly what plays the role of spacetime in the framework of a quantum gravitational model. David Chalmers (2020) and Sam Baron (2019) are proponents of functionalism. As in the case of color, I think we’ve moved from primitivism to functionalism. We started with a kind of intuitive spatial primitivism where space involves these primitive qualities that we’re acquainted with, and everything is spread out in that primitive space. We’ve ended with a spatial functionalism. To use a familiar functionalist slogan: space is as space does. Or better: space is whatever plays the space role. As with color, spatial properties need not themselves be functional properties (…), but they are picked out as what plays the functional role. This is analogous

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to various other familiar sorts of functionalism where we pick out Xs as whatever play the X role. Colors are whatever plays the color role. (Chalmers 2020: 6)

All this means that there are some real entities and relations at a microlevel that engender something playing the role of space in human experience (Lam, Wüthrich 2018). And this is so, because spacetime itself is an emergent conceptual construct from the standpoint of theoretical approaches to quantum gravity. This is an easy claim to be stated, insofar as these theoretical approaches like loop quantum theory, causal set theory, configuration space realism (wave function realism), and others, describe quantized fields underlying the spatial characteristics of observable events. But how should the declared spacetime emergence per se be gathered? As Sam Baron has shown (2019) this kind of accepted emergence is not of a mereological type. To this effect functionalism is welcomed, all the more so since it is a good explanation about the appearance of mental states. However, as he has demonstrated, even this standard form of functionalism does not work, and what he calls “partial functionalism” has to be resorted to. To be clear, I am not positing an entity ‘approximate spacetime’ and saying that this new entity exists. The idea, rather, is that while spacetime as we normally conceive of it does not exist, the relevant functions of spacetime are performed by the ontology of a theory of quantum gravity, and they are performed in such a way that we can speak loosely of spacetime’s existence, even though such talk is strictly speaking false. (Baron 2019, my italics)

This way or not, by a standard or a weakened construal, functionalism tries to recover spacetime “as we normally conceive of it”, or space as it is experienced by us. There are even other sorts of functionalism, but as Le Bihan has pointed out, all of them are not in a position to resolve the explanatory gap of spacetime emergence. However, philosophers debating spacetime emergence through the lens of functionalism should adopt a clear view on the ontological picture they are relying on, if only for the sake of clarity and consistency of their proposal.

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My ontological position suggested in section 5 is an alternative to “analytic functionalism which remains completely silent about the ontological implications of spacetime emergence”. Chalmers is also not very content with his own analogy, otherwise widely extended in his work, between color perceptions and the experience of spatial characteristics (e.g., distances among objects). The reason is that the analogy is ostensibly backed by a phenomenal functional recovery of space. However, space and spacetime are elements of well corroborated classical and semi-classical theories; and although recently contended to be only derivatively fundamental, space hardly resembles the phenomenal nature of colors in an ontological perspective. Colors are not theoretical constructs of scientific theories, being accepted only as mental representations and not as really existing features of things in the world. While on the contrary, space is an absolute entity in the Newtonian picture of the natural world, and material objects are situated in the four-dimensional spacetime of Einstein’s general relativity, which has not ceased to receive observational confirmations. A space functionalist need not recover only phenomenal properties. She ought to explain how spatial qualities, for instance metrical properties, could emerge outside human experience. In other words, an ontologically minded emergence that was thrown away by the common functional methodology peeps behind it. Still more, as it was briefly mentioned, there are different theoretical models pretending to quantize gravity (or spacetime), and this fact represents an additional difficulty. And it is probably the need for attaining a lucid ontological emergence that prompts Chalmers to look along this direction: The hardest case is grounding a reduction of space with a nonphenomenal analysis of the pretheoretical concept. It may be that the roles in interaction and motion that I’ve been gesturing towards can be used to deliver something even closer to the manifest image of space, picking out

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underlying properties in a quantum-mechanical or string-theoretic world as the grounds of motion and interaction… I take that to be an open question which is going to involve a lot of detailed work in the philosophy of physics combined with philosophical and/or psychological analyses of our concepts. (Chalmers 2020: 17-18, my italics)

Loop quantum gravity seems to be quite popular among quantum gravity theories. This theory exploits as basic theoretical constructs granular quantum fields as elementary grains of matter, and the web of their interactions. The webs, in turn, transform into each other in discrete leaps, described in the theory as structures called ‘spinfoam’. The occurrence of these leaps draws the patterns that on a large scale appear to us like the smooth structure of spacetime. On a small scale, the theory describes a ‘quantum spacetime’ that is fluctuating, probabilistic and discrete. At this scale, there is only the frenzied swarming of quanta that appear and vanish. (Rovelli 2019: 110, my italics)

Although Rovelli does not use, in this case, a specific philosophical vocabulary and does not speak of spacetime functionalism, he quite lucidly points to the spinfoam leaps as drawing “the patterns that on a large scale appear to us like the smooth structure of spacetime”. In other words, he points to the very structure in loop theory that plays the role of spacetime on a large scale. Unfortunately, this presentation of the “derivative fundamentality” of spacetime is not yet the last word of contemporary physics. Rovelli’s intellectual honesty is expressed by the following words: Loop theory is not a ‘unified theory of everything’. It doesn’t even begin to claim that it’s the ultimate theory of science. It’s a theory made up of coherent but distinct parts. It seeks to be ‘only’ a coherent description of the world as we understand it so far. (Ibid: 108, his italics)

And also: Am I certain that this is the correct description of the world? I am not, but it is today the only coherent and complete way that I know of to think

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There is no need to say that these words can also be taken to refer to the other attempts at constructing a fully-fledged theory of quantum gravity.

4. A Remark about the Posited Existence of Non-Spatiotemporal Grains of Matter The same expression, “grains of matter” for naming non-spatiotemporal elements on a small scale is not a metaphor used only by Carlo Rovelli in the light of his already broadly admitted merit of being “the poet of physics”. George Musser for instance speaks about “primitive grains of matter”, depicted in the quantum gravity ideological canvas, “that do not exist within space, but simply exist – and stringing them together to form space” (Musser 2017: 218-219). My remark about the posited existence of the non-spatiotemporal grains of matter concerns the spatial brim over the boundary of which space ceases its “derivatively fundamental” existence. Or, in other words, what is the spatial limit of the spatiotemporal (mode of) existence of spacetime as such? It is conjectured to be about the Planck length of 10-33 cm (Rovelli 2019: 76) that equals 10-35 m. Let me now turn to the recent announcements by the LIGO and Virgo Scientific Collaboration team from 2016 onwards about the registration of gravitational waves. What kind of waves are they? The accepted answer is that they are ripples in the spacetime fabric of the universe. These registered ripples, or waves within spacetime, could hardly be conceived of, if at distances having the average scale of their lengths spacetime would cease to exist. Their measured amplitude with strain is about 10-21 m. But spacetime is there to carry their permanently diminishing amplitudes from their cosmic source. They are longer than the Planck length, but yet represent minute spatial distances. Scientific teams are preparing to register gravitational waves with amplitudes of about 10-30 m, or high frequency waves, which stay closer to the ultimate edge of spacetime non-existence, contended by proponents of quantum gravity

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models. (At that, we shall probably not have any experimental “confirmation” of spacetime non-existence around the Planck length.) Even a length of 10-18 m is 1000 times smaller than the diameter of a proton. This means that spacetime still really exists at extremely small distances before its physical reality to be hypothetically devoured by the grains of matter. This remark clearly shows that spacetime is avowed to have a real physical existence on a very small scale, so we need not resort to Baron’s rescue advice “that we can speak loosely of spacetime’s existence” at least within the boundaries of our present experience. Concerning functionalism, gravitational waves stay out of human perceptive abilities and their physical existence is accepted to be not controversial. So, there is still no need for “foam leaps”, or any other conjectured grains of matter to be taken to appear for us as space, if spatial distances are admitted to exist on such small scales. Thus, it seems that still there is no empirical urge for functional emergentism to recover spacetime out of a non-spatiotemporal reality. If this reasoning is not convincing for the upholders of the emergent nature of spacetime, let me recall the posited basic elements of string theory, which is an alternative theory to encompass quantum gravity. These basic elements, the strings, are so minute to be estimated at 10-35 m in size, i.e., to be no larger than the Planck length itself. And yet, ontologically speaking, they produce different vibrational patterns to give birth to the different elementary particles. But where do they vibrate? In a tendimensional space is the answer. And the latter is an ontological entity that is wider than four-dimensional spacetime, and if it were taken to exist, then spacetime also exists as a part of it, and thus it is not properly emergent. To the objection that the strings are looked upon as still hypothetical basic elements of micro-reality, my answer is that they are at least components of a fully-fledged mathematical theory (with wide explanatory power), while the metaphorically suggested grains of matter are still not. Besides, string theory is a quantum gravity theory that does not presuppose non-spatiotemporal elements at the start, but relies on the

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quantum field hypothesis of the graviton to be responsible for the gravitational interaction.

5. My Answer to the Title Question I said at the beginning of the chapter (section 1) that I shall give a rather negative answer to the title question. The answer is: “No, spacetime is rather not an emergent entity.” I’ll firstly give my ontological reason for the negative character of the answer, and secondly, I’ll explain why I also decided to insert the specifying word “rather”. Like the proponents of the emergentist view of spacetime I admit a fundamental existence of the so-called “grains of matter”, no matter what their accepted quantum qualities. Unlike them, however, I do not take their existence to be separated from the entity they underlie – the physical spacetime. By this claim I am not saying that the quantum grains of matter exist within spacetime. I merely say that they are the building bricks of spacetime. To this effect, they do not comprise a separate quantum base being an entity ontologically distinct from spacetime, while the latter appears only as an emergent side-product of them. On the contrary, the granular quantum base is a proper part of spacetime itself (or of a more dimensional space like that of the superstring theory). By this claim I defend a methodological standpoint providing an interpretation of spacetime as an ontologically larger entity than is merely given by its standard geometrical presentation. I have adduced a quite different argument for this in section 2.3 from the previous chapter. The following example is a pertinent one. Let us have in mind a definite volume of gas, e.g., ordinary air. Shall we say that the whole volume of air – as a thermodynamic entity – is not an entire entity, because it emerges out of its constituent molecules, and because its basic thermodynamic features like temperature and pressure are derivable from a theory referring to a lower level of structural description? No, we shall hardly say so. We shall certainly argue that the volume of air is one self-identical entity. And we shall do so notwithstanding that its constituents at a micro-

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level and its thermodynamic features at a macro-level are described by two different theories. Well, my ontological claim is that we confront a similar situation concerning spacetime. Its deep quantum structure together with its higherlevel metrical and topological qualities constitute one and the same entity – global spacetime. It is a fundamental entity by itself, notwithstanding the fact that different theories describe it on a large and on a small scale, as is the case with the corresponding theoretical presentations of the volume of air – a thermodynamical and a micro-structural one. The adduced analogy with the volume of gas is illustrative for my metaphysical claim about the fundamental character of spacetime; so, it does not bear “a burden of proof”, which is more desirable for the contenders of opposite emergentist views. Yet another similar argument can be adduced in favor of my ontological contention about the global (or universal) nature of spacetime, one that is suggested by Brian Greene (2004: 334-5): Take a glass of water. Describing the water as a smooth, uniform liquid is both useful and relevant on everyday scales, but it's an approximation that breaks down if we analyze the water with submicroscopic precision. On tiny scales, the smooth image gives way to a completely different framework of widely separated molecules and atoms. Similarly… Einstein's conception of a smooth, gently curving, geometrical space and time, although powerful and accurate for describing the universe on large scales, breaks down if we analyze the universe at extremely short distance and time scales. Physicists believe that, as with water, the smooth portrayal of space and time is an approximation that gives way to another, more fundamental framework when considered on ultramicroscopic scales. What that framework is – what constitutes the ‘molecules’ and ‘atoms’ of space and time – is a question currently being pursued with great vigor. It has yet to be resolved.

Even if the last question obtains its future resolution, as is the expectation of many physicists, this would not be an obstruction to my claim that there are two theoretical approaches – on a large and on a small scale – to one and the same entity, be it a glass of water, or universal spacetime. To this

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effect (though probably intuitively), B. Greene writes about “molecules” and “atoms” of space and time, and not of a non-spatiotemporal reality. A rather negative answer to the title question is a negative answer, of course, but with a specification. It does not change the logical status of the answer that concerns the ontological status of spacetime as a universal and fundamental entity. The specification indicates the epistemological need for using different kinds of theories for the description of spacetime, at least for now – general relativity and quantum gravity theories. The latter are constructed with the hope of supplying a derivative explanation of the inherent geometrical qualities of spacetime. (Also, not forgetting the hope for a general theory that could encompass without conceptual problems all four types of interactions.) This is an epistemological reason for the chosen form of the answer (see Crowther’s quotation at the beginning of the chapter, in section 1). At that, we must also have in mind that another way was adumbrated by the string theory for both quantizing gravity and preserving spacetime.

CHAPTER 7 DOES BIG BANG COSMOLOGY RESOLVE THE FIRST OF KANT’S ANTINOMIES? 7.1. Introductory Words The problem of whether the world has a beginning in time, or not, falls into the content of the first of Kant’s antinomies, presented in his renowned Critique of Pure Reason (Kant 1998). Prominent cosmologists and physicists like Stephen Hawking, Paul Davies, and Steven Weinberg share the firm opinion that big bang cosmology presents a clear solution to this antinomy by pointing to the validity of the statement that the universe has a beginning in time. The aim of this chapter is to show that the antinomies of pure reason, the first one included, and the assessment of contemporary cosmology about the birth of the universe some 13,8 billion years ago have different meanings and cognitive pretensions. Hence the answer to the title question runs to the negative. In section 7.2, I shall adduce the opinions of the prominent cosmologists and physicists mentioned at the outset regarding the first part of the first antinomy of pure reason, reducing my comments to a necessary minimum. In the next section 7.3, on the contrary, the analyses of these opinions will prevail, against the Kantian philosophical background concerning his first antinomy in particular, and the dialectical character of the antinomies in general.

7.2. Stephen Hawking and Others about the First of Kant’s Antinomies In his transcendental dialectic Kant considers four antinomies of pure reason, which represent the conflict of reason with itself, through the clash of transcendental ideas. The cosmological ideas comprising the first antinomy are stated as a thesis, and an antithesis.

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Thesis: “The world has a beginning in time, and in space it is also enclosed in boundaries” (Kant 1998: 470, CPR, A: 426, B: 454).24 Antithesis: “The world has no beginning and no bounds in space, but is infinite with regard to both time and space” (Ibid.: 471, CPR, A: 427, B: 455). Both the thesis and the antithesis are supplied with their own proofs, and so an antinomy comes to the fore. The antinomy might appear to be an obstacle in front of human rational knowledge of the boundaries and the history of the universe. Stephen Hawking focuses primarily on the first part of this first antinomy of Kant concerning a probable beginning of the universe in time, and contends that contemporary big bang cosmology, based on Albert Einstein’s general theory of relativity, provides a resolution to it. In his bestseller A Brief History of Time he indulges in the following reasoning: The questions of whether the universe had a beginning in time and whether it is limited in space were later extensively examined by the philosopher Immanuel Kant in his monumental (and very obscure) work, Critique of Pure Reason, published in 1781. He called these questions antinomies (that is, contradictions) of pure reason because he felt that there were equally compelling arguments for believing the thesis, that the universe had a beginning, and the antithesis, that it had existed forever. His argument for the thesis was that if the universe did not have a beginning, there would be an infinite period of time before any event, which he considered absurd. The argument for the antithesis was that if the universe had a beginning, there would be an infinite period of time before it, so why should the universe begin at any one particular time? In fact, his cases for both the thesis and the antithesis are really the same argument. They are both based on his unspoken assumption that time continues back forever, whether or not the universe had existed forever. As we shall see, the concept of time has no meaning before the beginning of the universe. (Hawking 1988: 8-9)25

24

CPR in the brackets indicates Kant’s first Critique – Critique of Pure Reason. The quotation goes on with the remark that time has no meaning before the universe was created from a theological point of view, as well: “This was first pointed out by St. Augustine. When asked: What did God do before he created the 25

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It is of course true, according to the contemporary (and most widespread) scientific picture of the birth and subsequent development of the universe, that “time has no meaning before the beginning of the universe”. Well, but as you see, Kant presupposes either an infinite time through which the universe might have had a real existence, or an infinite time before it got started at a definite moment of time. So, both the thesis and the antithesis, as Stephen Hawking insists, rest on one and the same argument about an unlimited time, existing independently of the universe. But this “unspoken assumption” of Kant is not correct, and thus his antinomy loses the conflict of the two cosmological claims. This tacit assumption of Kant is a relic of the strong influence exerted on him by the Newtonian conception of absolute time and space. This last assertion is not directly included in the adduced quotation above, but as we shall see, S. Hawking explicitly supports it elsewhere, and implicitly has it in mind here when saying that the concept of time (in the Einsteinian universe of course) “has no meaning before the beginning of the universe”. The Newtonian universe, on the contrary, inhabits an absolute space and exists in an absolute time that can afford itself to be an infinite entity, being independent of the universe. However, this has proved to be an obsolete and wrong cosmological picture, and thus, once again, Kant’s first antinomy may be looked upon as resolved by contemporary science. Stephen Hawking revisited Kant’s “monumental (and very obscure) work, Critique of Pure Reason” once again in his lovely illustrated book The Universe in a Nutshell. There he makes a reconstruction of Kant’s antinomy in the following way: Isaac Newton gave us the first mathematical model for time and space in 1687. . . Time itself was considered eternal, in the sense that it had existed, and would exist, forever. By contrast, most people thought the physical universe had been created more or less in its present state only a few thousand years ago. This worried philosophers such as the German thinker Immanuel Kant. If the universe had indeed been created, why had there universe? Augustine didn’t reply: He was preparing Hell for people who asked such questions. Instead, he said that time was a property of the universe that God created, and that time did not exist before the beginning of the universe” (Hawking 1988: 9, my italics).

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Chapter 7 been an infinite wait before the creation? On the other hand, if the universe had existed forever, why hadn’t everything that was going to happen already happened, meaning that history was over? In particular, why hadn’t the universe reached thermal equilibrium, with everything at the same temperature? Kant called this problem an ‘antinomy of pure reason,’ because it seemed to be a logical contradiction; it didn’t have a resolution. But it was a contradiction only within the context of the Newtonian mathematical model, in which time was an infinite line, independent of what was happening in the universe. However, as we saw... in 1915 a completely new mathematical model was put forward by Einstein: the general theory of relativity. In the years since Einstein’s paper, we have added a few ribbons and bows, but our model of time and space is still based on what Einstein proposed. (Hawking 2001: 32-34, my italics)

It now becomes clear, in accordance with my previous comment, that S. Hawking refers to the antinomical character of the considered cosmological ideas in “the context of the Newtonian mathematical model, in which time was an infinite line, independent of what was happening in the universe”. The big bang cosmological model, based on Einstein’s general theory of relativity, offers no room for the first part of the first antInomy of pure reason. The following clarification of S. Hawking is worth mentioning: The issue of the beginning of time is a bit like the issue of the edge of the world. When people thought the world was flat, one might have wondered whether the sea poured over its edge. . . In the early universe – when the universe was small enough to be governed by both general relativity and quantum theory – there were effectively four dimensions of space and none of time. That means that when we speak of the ‘beginning’ of the universe, we are skirting the subtle issue that as we look backward toward the very early universe, time as we know it does not exist! We must accept that our usual ideas of space and time do not apply to the very early universe. That is beyond our experience, but not beyond our imagination, or our mathematics. If in the early universe all four dimensions behave like space, what happens to the beginning of time? The realization that time can behave like another direction of space means one can get rid of the problem of time having a beginning, in a similar way

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in which we got rid of the edge of the world. (Hawking and Mlodinov 2010: 108-109, my italics)

I’ll go back to this clarification in the next section. For now, two statements suffice as an “explanation” as to why Kant’s first antinomy can be evaded in the context of the big bang cosmological model. The first one is that when we speak of the “beginning” of the universe, we must have in mind that “as we look backward toward the very early universe, time as we know it does not exist!” And the second statement is that if time behaves as another spatial dimension, then “one can get rid of the problem of time having a beginning, in a similar way in which we got rid of the edge of the world”. Paul Davies (1995: 186) suggests a reconstruction of the first of Kant’s antinomies, concerning an alleged beginning of the universe in time, in a manner quite similar to that launched by S. Hawking. For this reason, I’ll not present it here. And because of the coincidental way of reasoning, Paul Davies suggests a resolution to the antinomy by the same theoretical argument of change of cosmological paradigms: Many people have an image of the epoch before the universe as a dark, inert, empty space. But for the modern cosmologist, neither time nor space existed before the big bang. The origin of the universe means the origin of space and time as well as matter and energy. (Davies 1995: 186)

However, P. Davies realizes that this type of resolution of (the first part of) the first antinomy of Kant leads to another paradox. Let me call it “the paradox of the first event”. This paradox and P. Davies’ solution to it will be considered at the end of the next section 7.3. Steven Weinberg does not explicitly consider the first antinomy of Kant, but boldly criticizes his “intransigent metaphysics” that embarrasses the understanding that there are no moments of time before the big bang (Weinberg 1993: 137-138). To this effect, he also does not see any antinomy in the clash of the cosmological ideas about the beginning of the world or its eternal boundaries. But this could hardly be assessed as a

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surprise, taking into account S. Weinberg’s negative attitude towards philosophy in general.26

7.3. The First Antinomy of Pure Reason and Big Bang Cosmology Does big bang cosmology resolve the first of Kant’s antinomies? It seems that we can accept the positive answer. The contemporary big bang cosmology, based on the inflation model, successfully explains the birth and the successive evolution of the universe. And insofar as the age of the universe is estimated today to be about 13,8 billion years, notwithstanding the impossibility of this amazing period of time to be imagined by human consciousness, this period is a finite interval of time. Thus, the existence of the world has a beginning. But if so, we can say that the thesis in the first of Kant’s antinomies is true, and the antithesis ought to be rejected. Contemporary scientific knowledge overcomes an antinomy, which appeared as a conceptual child of the classical Newtonian epoch of the growth of science. Generally speaking, this is the conclusion that we can draw from the reconstruction of the antinomy suggested by Stephen Hawking, and also by Paul Davies, presented in the previous section. It is my task here to analyze how pertinent is their solution to the first part of the first of Kant’s antinomies. But let me firstly consider the adequacy of Steven Weinberg’s position on the matter, since it conceals a way of thinking, common to the three eminent physicists, and probably to a great number of contemporary scientists. According to S. Weinberg: Kant taught that space and time are not part of external reality but are rather preexisting structures in our minds that allow us to relate objects and events. To a Kantian the most shocking thing about Einstein’s theories is that they demote space and time to the status of ordinary aspects of the physical universe, aspects that could be affected by motion (in special relativity) or gravitation (in general relativity) . . .

26 See the seventh chapter of his book (Weinberg 1993) entitled “Against Philosophy”.

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This intransigent metaphysics comes to the surface especially in discussions of the origin of the universe. According to the standard bigbang theory the universe came into existence in a moment of infinite temperature and density some ten to fifteen billion years ago.27 Again and again when I have given a talk about the big-bang theory someone in the audience during the question period has argued that the idea of a beginning is absurd; whatever moment we say saw the beginning of the big bang, there must have been a moment before that one. I have tried to explain that this is not necessarily so. (Weinberg 1993: 137-138)

S. Weinberg’s way of thinking, which ensures an easy exit from the antinomy, conceals a mistake resembling that of the curious listener to his lectures, who objects that there always must be a moment of time that precedes the moment of the big bang at which the universe was born. This way of thinking urges S. Weinberg not to have a bit of suspicion that there are natural entities called space and time, and because of this we should have only one notion for each of them, which more or less correctly represents those entities. Kant’s notions are mistaken, while the corresponding notions of contemporary physics and cosmology are correct representations of spacetime. But as we know, and have to keep in mind, Kant’s terms “space” and “time”, and the corresponding terms in physical science, do not have one and the same referent. Space and time within Kant’s transcendental aesthetic are not concepts of physical science about whatever reality space and time might have as natural qualities or as constituents of the physical universe. As we know, they are pure forms of the human capacity for receptivity; they are purely sensuous intuitions, providing the possibility of any empirical intuition. To this effect, they are void of any ontological meaning that is inherent in the theoretical constructs within physical knowledge representing the structure of the universe. Kant’s transcendental “space” and “time” refer to the human faculty for direct knowledge of the phenomenal world, and thus they bear a gnoseological burden, while “space” and “time” within physical theories refer to either natural attributes of the material world or to autonomous entities through which it exists, and thus they bear an ontological burden.

27 With greater precision the age of the universe is now estimated to be about 13,8 billion years.

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S. Weinberg seems to be aware of all this, having in mind the first sentence of his quotation. Yet he makes a methodological error to compare Kant’s and Einstein’s notions of space and time, as if they have one and the same referent, and to declare that “To a Kantian the most shocking thing about Einstein’s theories is that they demote space and time to the status of ordinary aspects of the physical universe, aspects that could be affected by motion (in special relativity) or gravitation (in general relativity).” Curious as it may seem, a very similar declaration was also made by Miliþ ýapek (1971: 43) who tries to convince us that Kant “would be equally shocked by the Riemannian geometry as by Lemaître’s and Gamow’s cosmogonies assuming the finiteness of the cosmic past bounded by the initial ‘zero-time’”. We meet here a common root of the criticism of Kant’s transcendental concepts of space and time and of the cognitive status of his cosmological ideas. This is the error undertaken by the eminent critics of Kant that he has allegedly ascribed an ontological status to his conceptions of space and time when imagining the temporal and spatial dimensions of the real universe. His critics shove their own realist scientific understanding of space and time into Kant’s transcendental conception, and then declare that Kant was wrong since a contradiction appears with the contemporary scientific picture of the universe. It is no surprise that S. Weinberg sticks to physical concepts of space and time, having in mind his conviction that Physicists do of course carry around with them a working philosophy. For most of us, it is a rough-and-ready realism, a belief in the objective reality of the ingredients of our scientific theories. But this has been learned through the experience of scientific research and rarely from the teachings of philosophers. (Weinberg 1993: 133)

S. Weinberg’s way of thinking that brings about the considered misunderstanding is shared by S. Hawking and P. Davies, as well. Even more, they look at Kant’s transcendental conception of space and time as taken from, or as akin to, Newton’s classical cosmological model; because, as it is known, Kant was strongly influenced by Newton’s mechanics. But classical mechanics rests on the theoretical picture of

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absolute space and time, which on its part, was to be blamed for the birth of the first of Kant’s antinomies. Let me recall, to this effect, S. Hawking’s statement from his The Universe in a Nutshell, that Kant’s antinomy “was a contradiction only within the context of the Newtonian mathematical model, in which time was an infinite line, independent of what was happening in the universe”.28 Further in this same book he declares: If the stars had just been sitting there forever, why did they suddenly light up a few billion years ago? What was the clock that told them it was time to shine? As we’ve seen, this puzzled those philosophers, much like Immanuel Kant, who believed that the universe had existed forever. (Hawking, 2001: 73, my italics)

P. Davies is certain that: “Kant accepted that to escape from his temporal dilemma would mean denying ‘the existence of an absolute time before the world,’ yet this he was not prepared to do” (Davies 1995: 186). Here, once again, the appearance of the first antinomy is explained by Kant’s alleged acceptance of the model of absolute time, taken from the theoretical basement of Newton’s classical mechanics. But how does the depicted misunderstanding, attributed to the “critical” Kant, to the author of Critique of Pure Reason who considers the dialectical confrontation of reason with itself, become possible? This becomes possible due to two reasons. The first of them is the specific way of thinking, placing the transcendental concepts of space and time on a par with the theoretical constructs of space and time, taken from scientific theories of the physical world. As we have already seen, Kant’s critics relate Kant’s conception of time and space with Newton’s absolute time and space from his classical mechanics.29 Hence Kant’s transcendental conception of space and time is precipitately, though incorrectly, dressed 28

See S. Hawking’s quotation in 7.2 (Hawking 2001: 32-34, my italics). Karl Popper for example contends that “Kant. . . was convinced that Newton’s theory was true” (Popper 1989, 190-191). This contention may truly speak of Kant’s theoretical predilection, but during his pre-critical creative period (see for instance ch. 5, 1.3), and not during his critical creative period. 29

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in the ontological garments, suited to the zeitgeist of the Newtonian intellectual epoch. And the second reason for the here analyzed misunderstanding of Kant’s philosophical position concerning his first antinomy, as we shall see further, is that his critics have not paid due attention to Kant’s warning about the regulative vs. the constitutive role of the cosmological ideas at hand. By imputing Kant’s transcendental philosophy to a classical cosmological basement, eminent contemporary scientists like S. Hawking and P. Davies suggest a simple solution to the first antinomy of pure reason. As was pointed out at the end of the previous section, it amounts to a change of cosmological paradigms: Many people have an image of the epoch before the universe as a dark, inert, empty space. But for the modern cosmologist, neither time nor space existed before the big bang. The origin of the universe means the origin of space and time as well as matter and energy. (Davies 1995: 186)

If “for the modern cosmologist, neither time nor space existed before the big bang”, then the world started its existence before some finite interval of time. So, the thesis that “The world has a beginning in time” within the first of Kant’s antinomies turns out to be true, and the antithesis ought to be rejected. This seeming conclusion, however, is based on the above considered methodological misunderstanding. The latter does not permit this conclusion to be accepted as a solution to the first antinomy of pure reason, despite the fact that the claim that the universe has a beginning in time, taken as a separate claim, independent from the first antinomy of pure reason, is taken to be true by “the modern cosmologists”. This claim has a different meaning in the context of big bang cosmology, while the first thesis of Kant’s antinomy has another meaning in the context of the dialectic of the two confronting theses of pure reason. Within the antinomy they have a speculative origin and pretention that are different from the scientific meaning and pretention of the claim that the universe, as we know it from astronomical observations, started its existence 13,8 billion years ago. S. Hawking “resolves” the antinomy, but under the false prerequisite that

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Kant embraces the ontological concept of time “within the context of the Newtonian mathematical model, in which time was an infinite line, independent of what was happening in the universe”.30 However, in Kant’s transcendental conception and in the scientific model of big bang cosmology, time and space have a different cognitive status. Now I may say that the answer to the title question of the present chapter tends to the negative. But for a cogent argumentation I must make an additional argumentative step. The first one, which I have just finished, clearly shows that the declaration of some eminent contemporary cosmologists like S. Hawking, that the first antinomy of pure reason appears only because Kant was allegedly committed to Newton’s theory of space and time, does not hold water. The second argumentative step that I have to make is to show why big bang cosmology, with its highly corroborated claim that the universe has a beginning in time, does not resolve the first of Kant’s antinomies, notwithstanding whether Kant accepted Newton’s cosmology, or not. I have already outlined the direction of this second argumentative step by the statement that within Kant’s antinomy the first of its thesis (that “The world has a beginning in time”) has another origin and meaning than the scientific claim about the beginning of the universe in the event of the big bang. I must explain further why this is so. Kant’s first antinomy must not be considered separately from the other three antinomies of pure reason. All of them are explications of the four cosmological ideas of pure reason, according to the four categories (of the understanding) whose absolute completeness is being sought: of the composition of the given whole of all phenomena,31 of the division of a given whole in phenomenal appearance, of the origination of a phenomenon in general, and of the dependence of the existence of the changeable in phenomenal appearance (Kant 1998: 464, CPR, A: 415, B: 443). As Kant first remarks, the idea of absolute completeness or totality refers to nothing else but the exhibition of phenomena, so that reason postulates the

30 31

See fn. 28. This idea underlies the first antinomy of pure reason.

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absolute completeness of the conditions of their possibility. Thus, reason indulges in an absolutely complete synthesis, whereby phenomena could be expounded according to the laws of the understanding. Second, it is properly only the unconditioned that reason seeks in this synthesis of conditions, which proceeds serially, and indeed regressively, hence as it were the completeness in the series of premises that together presuppose no further premise. Now this unconditioned is always contained in the absolute totality of the series if one represents it in imagination. Yet this absolutely complete synthesis is once again only an idea; for with appearances one cannot know, at least not beforehand, whether such a synthesis is even possible… Yet the idea of this completeness still lies in reason, irrespective of the possibility or impossibility of connecting empirical concepts to it adequately… Now one can think of this unconditioned either as subsisting merely in the whole series, in which thus every member without exception is conditioned, and only their whole is absolutely unconditioned, or else the absolutely unconditioned is only a part of the series, to which the remaining members of the series are subordinated but that itself stands under no other condition. * In the first case the series is given a parte priori without bounds (without a beginning), i.e., it is given as infinite and at the same time whole, but the regress in it is never complete and can be called only potentialiter infinite. In the second case there is a first [member] in the series, which in regard to past time is called the beginning of the world. (Kant 1998: 464-465, CPR, A: 416-418, B: 444-446)

The four cosmological ideas, and the first one in particular that gives birth to the first antinomy, have their origin in the fact that human reason aspires to thinking of the world not as mundus phaenomenon, where time is an a priori form of sensibility attributing temporal order and permanence of the objects of experience, but as mundus intelligibilis, which leads to a deceptive reification of time. Such an illusionary substitution by pure reason is inevitable, because of the necessity of widening the conceptual applicability of empirical judgments about temporal and spatial order among phenomena, above the span of the faculties for receptivity and understanding, for searching for a beginning and spatial limits of the world as a whole, taken as a complete totality of phenomena. Thus, the first cosmological idea gives birth to a thesis and an

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antithesis, as specifications of the two possible cases for construing the unconditioned, as pointed out by Kant in the adduced quotation above. The thesis is based on grasping the unconditioned as an unconditioned “first” member in a series of conditioned phenomena, and states in this sense that the world has a beginning in time. The antithesis, on the contrary, is based on grasping the unconditioned “as existing in the whole series only, in which all members without exception are conditioned and the whole of them only absolutely unconditioned”, and states that the world has no beginning in time. The antinomy is a result of the aspiration of reason to encompass the world as a whole, that is as a totality of phenomena. But this totality is not itself a phenomenon. It stays outside of the cognitive potential of the understanding, whose conceptual resource reason tries to make use of, out of the real or possible experience where this conceptual resource has only a proper usage. Because of this pure reason could support both the thesis and the antithesis of a cosmological idea, and so the first antinomy appears in particular, which is a matter of interest here. Its thesis emerges as we have already seen, as one of the two possible modes of interpreting the unconditioned in a series of consecutive phenomena. The thesis says of course that the world has a beginning in time. However, this statement is meaningful in the context of the antithetic of pure reason alone, and is conceptually different from the scientific claim in the context of big bang cosmology, although formulated in the same words. The latter here has the status of scientific concepts with precise theoretical definitions: the world as the physical universe encompassing all (directly and indirectly) observable material and field structures and interactions, and time as a constituent of the universe as a fourth dimension of spacetime. As Kant further specifies, “the cosmological idea would always be either too large or too small for any concept of the understanding”, independently of the way it realizes the unconditioned of the regressive synthesis of phenomena – whether in the manner of the thesis or in that of the antithesis.

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And this is actually the case with all the world-concepts, which is why reason, as long as it holds to them, is involved in an unavoidable antinomy. For assume: First, that the world has no beginning; then it is too big for your concept; for this concept, which consists in a successive regress, can never reach the whole eternity that has elapsed. Suppose it has a beginning, then once again it is too small for your concept of understanding in the necessary empirical regress. For since the beginning always presupposes a preceding time, it is still not unconditioned, and the law of the empirical use of the understanding obliges you to ask for a still higher temporal condition, and the world is obviously too small for this law. (Kant 1998: 508-509, CPR, A: 486-487, B: 514-515)

The first antinomy of pure reason as an explication of the first cosmological idea emerges, because no real object of experience corresponds to the cosmological idea.32 The thesis and the antithesis are by themselves sophistical (dialectical) propositions of pure reason, each one free from contradiction and thus giving rise to an antinomy. A dialectical theorem of pure reason must accordingly have the following feature, distinguishing it from all sophistical propositions: it does not concern an arbitrary question that one might raise only at on’'s option, but one that every human reason must necessarily come up against in the course of its progress; and second, this proposition and its opposite must carry with them not merely an artificial illusion that disappears as soon as someone has insight into it, but rather a natural and unavoidable illusion, which even if one is no longer fooled by it, still deceives though it does not defraud and which thus can be rendered harmless but never destroyed. (Ibid.: 304, CPR, A: 421-422, B: 449-450)

So, the thesis and the antithesis of the first antinomy of pure reason are dialectical propositions which speculative reason must necessarily encounter in its ambition for obtaining a complete knowledge about a range of phenomena. But a dialectical proposition is a “natural and unavoidable illusion, which even if one is no longer fooled by it, still 32

“ It is possible experience alone that can give our concepts reality; without it, every concept is only an idea, without truth and reference to an object” (Kant 1998: 510, CPR, A: 489, B: 517).

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deceives though it does not defraud and which thus can be rendered harmless but never destroyed”. Principles and laws, as well as consequences of scientific theories and theoretical models are not dialectical propositions. And such is the claim that the universe came into existence before a definite period of time, which follows from big bang cosmology. Some scientific claims might prove to be false and contradictions may occur among claims of competing theoretical models, but such claims do not persist as the equally provable thesis and antithesis of an antinomy, because of a “natural and unavoidable illusion” of speculative reason. Sooner or later the scientific community will decide which out of two confronting claims should be accepted as an adequate one, and which should be dispatched to the realm of the history of science.33 That the universe has no beginning in time is a long-believed classical scientific claim, which is revisable, and which was really revised. The statement that the universe has a beginning, in the context of big bang cosmology, is an opposing scientific statement that has now been taken to be true by modern cosmologists. On its part, the first thesis from the first of Kant’s antinomies is a dialectical proposition of pure reason in its search for perfection of knowledge; it is a persisting idea of reason that traces out some definite direction of human thought. This dialectical proposition is an “unavoidable illusion” that cannot be replaced by its antithesis (and vice versa) in the same way in which hypotheses are rejected on the basis of experiments and observations in the course of the growth of scientific knowledge. So, the conviction that big bang cosmology supplies an appropriate solution to the first of Kant’s antinomies does not hold water. 33

On this ground Vincenzo Fano and Giovanni Macchia (2010) contend that modern cosmology bypasses Kant’s first antinomy of pure reason to the extent to which the universe within contemporary scientific knowledge is not set out in a speculative dialectical context as a totality, but as a concept. “Cosmology does not produce a complete description of the Universe, with a capital “U”, but it formulates possible models of a few important physical features of the Universe” (Ibid.: 121).

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Anyhow, some additional comments are needed here. * One may be left with the impression that Kant’s transcendental philosophy does not pay due attention to the results of scientific knowledge, insofar as Kant’s attention was attracted mainly by the antithetic of pure reason, thus leaving the epistemological role of fundamental scientific theories on the backstage of human knowledge. I will show that such an impression is not correct. It is true of course that speculative reason has no direct connection with experience, which is attributed to the union of sensibility and understanding. Reason never relates directly to an object, but solely to the understanding and by means of it to reason's own empirical use, hence it does not create any concepts (of objects) but only orders them and gives them that unity which they can have in their greatest possible extension. (Kant 1998: 590591, CPR, A: 643, B: 671)

This function of arrangement of concepts and of leading them to “their greatest possible extension” is accomplished by the ideas of pure reason. What is “the mechanism” of reason in imparting perfection to knowledge through concepts, borrowed otherwise from the understanding, being really a faculty for concepts? We know that concepts can refer to their objects only through the schemata of sensibility. It is the schema that is both intelligible and sensuous, which allows the application of pure concepts of the understanding to the variety of phenomena. Well then, what can play the role of a schema, when concepts formed by the understanding have to produce some complete knowledge with the help of reason? Kant does not hesitate to say that an analogue to the schema in this case is the idea of pure reason. The understanding constitutes an object for reason, just as sensibility does for the understanding. To make systematic the unity of all possible empirical actions of the understanding is a business of reason, just as the understanding connects the manifold of appearances through concepts and

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brings it under empirical laws. The actions of the understanding, however, apart from the schemata of sensibility, are undetermined; likewise the unity of reason is also in itself undetermined in regard to the conditions under which, and the degree to which, the understanding should combine its concepts systematically. Yet although no schema can be found in intuition for the thoroughgoing systematic unity of all concepts of the understanding, an analogue of such a schema can and must be given, which is the idea of the maximum of division and unification of the understanding's cognition in one principle… Thus the idea of reason is an analogue of a schema of sensibility, but with this difference, that the application of concepts of the understanding to the schema of reason is not likewise a cognition of the object itself (as in the application of the categories to their sensible schemata), but only a rule or principle of the systematic unity of all use of the understanding. (Ibid.: 602-603, CPR, A: 664-665, B: 692-693)

In a few words, the “mechanism” of imparting perfection to knowledge through concepts, borrowed otherwise from the understanding (being really a faculty for concepts) is realized through what Kant has dubbed the “schema of reason”. This is the general idea “of the maximum”. I am not going to take up with terminological precisions here, but basic hypotheses, guiding the development of scientific knowledge, are just “rules or principles for the systematical unity of all use of the understanding”, prompted by the application of concepts of the understanding to the schema of reason. So, from one side, objects are produced for the human knowledge only through the application of concepts of the understanding to the schemata of sensibility, and this is enough for the birth of (what is usually accepted to be) everyday knowledge. On the other side, concepts of the understanding could also be applied to the idea of pure reason, as a general schema of reason. This application does not provide knowledge of the object itself, as in the case of the application of the categories to sensible schemata, but only a rule or principle for the systematical unity in the whole use of the understanding. Theoretical hypotheses are thus being formed. In this way Kant accounts for the origin of what is called today ontology of a scientific theory, insofar as such ontology is a systematical unity of hypothetical objects, governed by rules and principles, i.e., by laws

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determining their behavior. Hypothetical objects are represented by theoretical constructs. The latter are abstract concepts of directly unobservable objects, which are basic constituents of the ontology of contemporary scientific theories. Terms like “electron”, “quark”, “tendimensional string”, and the like, represent theoretical constructs in the field of quantum theories. Kant’s transcendental philosophy does not set up a conceptual barrier in front of the intellectual production of theoretical constructs through the faculty of imagination, provided they do conform to human experience. Accordingly, the objects of experience are never given in themselves, but only in experience, and they do not exist at all outside it. That there could be inhabitants of the moon, even though no human being has ever perceived them, must of course be admitted; but this means only that in the possible progress of experience we could encounter them; for everything is actual that stands in one context with a perception in accordance with the laws of the empirical progression. Thus they are real when they stand in an empirical connection with my real consciousness, although they are not therefore real in themselves, i.e., outside this progress of experience. (Ibid.: 512, CPR, A: 492-493, B: 521)

Kant thus accepts for example the reality of the magnetic field (called by him “magnetic matter”), notwithstanding the abstract character of its concept, since it hangs together with a perception, according to the laws of empirical progress.34 Moreover, Kant values highly the role of mathematics in the formation of theoretical knowledge, although he was not a witness of the accelerated development of theoretical knowledge in the natural sciences, being expressed by complex mathematical structures, from the end of the 19th century to the present day. Even the proper dignity of mathematics (that pride of human reason) rests on the fact that since in the great as well as the small, in its order and regularity, and in the admirable unity of the forces moving nature, mathematics guides reason’s insight into nature far beyond every

34 “Thus we cognize the existence of a magnetic matter penetrating all bodies from the perception of attracted iron filings, although an immediate perception of this matter is impossible for us given the constitution of our organs” (Kant 1998: 325326, CPR, A: 226, B: 273).

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expectation of any philosophy built on common experience, it gives occasion and encouragement even to the use of reason which extends beyond all experience, just as it provides to the philosophy concerned with nature the most excellent materials for supporting its inquiries, as far as their character allows, with appropriate intuitions. (Kant 1998: 496-497, CPR, A: 464, B: 492)

I hope that the analysis carried out so far, has managed to show that in his critical creative period Kant really pays due attention to the results of scientific knowledge of his day. * At the end of the previous section, I mentioned that Paul Davies, though not solving Kant’s first antinomy, still gains a paradox that I named “the paradox of the first event”. I shall try now to account for the nature of this paradox. It is based on the usage of the classical theoretical concept of time. Some theoretical concepts refer to hypothetical unobservable entities, and some such concepts turn out to be fruits of erroneous hypotheses. They are rejected together with the falsification of the theory of which they are a part. This is, for instance, the fate of the concept of phlogiston, taken from the chemistry of the 18th century. But it is not only theoretical constructs of hypothetical unobservable entities that may sometimes bring problems for scientific knowledge. Problems may also arise when common concepts of classical science are applied to a new field of research. Such is the case with the classical concept of time, taken as a theoretical concept from Newtonian mechanics. In the context of this theory, time, to use S. Hawking’s words, is “an infinite line, independent of what was happening in the universe”.35 This concept, however, ceases to be adequate in the context of the cosmology of the big bang. Within this theory time is neither “an infinite line”, nor “independent of what was happening in the universe”.

35

See the quotation of S. Hawking (2001: 32-34) adduced in 7.2.

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The inadequacy of the classical concept of time can be seen when one tries to answer a simple question, based both on the assumption that the universe (according to the big bang cosmology) has a beginning, and on the classical concept of time. The question is: “If the universe has a beginning in time, then which is the first event, connected with the first moment of its existence?” The answer to this question leads to the paradox of the first event. If time didn’t always exist, then surely there must have been a discontinuity at which time abruptly “switched on”? And this means there would have been a first event – or First Event. The First Event can’t be like other, ordinary events, because nothing came before it. It would be an event without a cause – a singular, supernatural event, surely? (Davies 1995: 186)

From the point of view of big bang cosmology, the universe started from the so-called singularity – a minute “egg”, containing the entire stuff of the universe. The idea of a singularity, from which the universe came into existence through a big bang, is easily formed when one tries to imagine what happens with the constantly expanding universe, when looking from the present into the past. An imaginative excursion into the past of the universe would show a process opposite to that of an expanding universe. We shall expect a universe constantly decreasing in size when time is followed in a backward direction. This opposite process, as it seems, will come to an end in a singularity, thought to be a boundary state of the universe. In this state, no space and time would exist anymore, because spacetime had been stuck into a point with infinite curvature. So, one can boldly say that the First Event we are looking for is just this singularity. But is this a plausible answer? Not exactly. There is a subtlety here. The singularity (which is in any case a mathematical artifact) is defined to be a boundary to time, not strictly part of time itself – not actually an event as such. The singularity bounds time in the past, implying that time has not endured forever. Nevertheless, there need not have been a first moment. (Ibid.: 187)

And here the paradox emerges. If time has not endured forever, there must have been a first moment. And even if the singularity itself is not the First

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Event that is looked for, yet there must have been such an event, corresponding to the first moment of the existence of the universe. P. Davies’ objection to this assumption is as follows: No. Is there a smallest number greater than zero? Clearly not. Try picking a number (one-billionth, one trillionth . . .). That number can always be halved, and halved again, to obtain ever-smaller numbers. If time is continuous, then at no moment (one-billionth of a second, one trillionth of a second . . .) would there have been no preceding moments. (Ibid.)

It follows from here that there is no first moment of time in the history of the universe. But such a moment ought to exist, since the universe is not eternal and, in this sense, it has a beginning in time. So, we meet a paradoxical situation. Its origin is due to the involvement of the classical concept of time. This concept is built on the intuitive concept of time, dressed in a mathematical garment, and thus rendered into a theoretical concept. This concept is the representation of time as a continuous line independent of the evolution of the universe. But in this case the beginning of time itself does not correspond to some first moment of it, which leads to the paradox of the first event. There are two ways out of this paradox. The first one is to attract nonclassical quantum effects that can provide a non-contradictory account for the beginning of the universe. This is P. Davies’ solution.36 The second way out of the paradox is an entire theoretical model of the history of the universe to be contrived, rejecting the classical concept of time as an inadequate one. This is S. Hawking’s solution. He has suggested such a cosmological model, introducing an “imaginary time” in it, which bears a resemblance to the three spatial dimensions. Also, suggesting his no boundary condition, S. Hawking succeeded in explaining the birth of the

36 “It all changed, however, when physicists started taking quantum effects into account. The crucial property of quantum physics is that cause and effect aren’t rigidly linked, as they are in classical, commonsense physics. There is indeterminism, which means some events ‘just occur’ – spontaneously, so to speak – without a prior cause in the normal meaning of the word. Suddenly physicists became aware of a way for time to ‘switch itself on’ – spontaneously – without being ‘made to do it’” (Davies 1995: 188).

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universe not out of a singularity, traditionally perceived as some mysterious initial edge of the universe.37 It is not my task here to consider the content of his solution. What was of interest to me was to show that although S. Hawking does not resolve the first antinomy of pure reason (resolved on the base of the critical analysis of Kant himself), he succeeded in resolving the paradox of the first event.

37 For this kind of solution see (Hawking 1988: 143-149) and (Hawking and Mlodinov 2010: 109-111).

CHAPTER 8 DOES THE ANTHROPIC PRINCIPLE EXPLAIN THE APPEARANCE OF MAN IN THE UNIVERSE? 8.1. Necessary Introduction Before laying out my answer to the title question of this chapter to be defended here, it is supposed that I ought to say what is the puzzle concerning the so-called, by Brandon Carter, “Anthropic Principle” (Barrow and Tipler 1986: 1). This is a well-known term coined by him in 1974, which is now indicating a view that embraces specific claims (separate formulations of the Anthropic Principle) about the appearance of man in the universe, and is still continuing to be a bone of contention among philosophers and scientists. To illustrate this fact, I am making use of Nick Bostrom’s observation: A total of over thirty anthropic principles have been formulated and many of them have been defined several times over – in nonequivalent ways – by different authors, and sometimes even by the same authors on different occasions. Not surprisingly, the result has been some pretty wild confusion concerning what the whole thing is about. Some reject anthropic reasoning out of hand as representing an obsolete and irrational form of anthropocentrism. Some hold that anthropic inferences rest on elementary mistakes in probability calculus. Some maintain that at least some of the anthropic principles are tautological and therefore indisputable. Tautological principles have been dismissed by some as empty and thus of no interest or ability to do explanatory work. Others have insisted that like some results in mathematics, though analytically true, anthropic principles can nonetheless be interesting and illuminating. (Bostrom 2002: 6, my italics)

In fact, there are two different general ideas standing behind the Anthropic Principle (AP), which make it of special interest for philosophers and scientists.

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The first idea is a typical one for AP which is expressed by the claim that (C1) Our universe has not an accidental material constitution, and also has no accidental historical dynamics, but is endowed with the unique conditions leading to the appearance of man – in the sense of Homo sapiens – at a definite state of its evolution. The other idea is even more intriguing, and I may also add, more intricate. It is characteristic for the strongest formulation of AP and is expressed by the contention that (C2) The universe itself is in need of man, in his quality of a sentient and conscious observer of it, for its own existence. Thus, the conclusion comes to the fore that both man and the universe demand each other, since they are in need of each other. The different attitudes that philosophers have to both of these claims, being expressed through the accents they put into the formulations of AP (according to Bostrom’s quotation), or merely rejecting them, form the specific puzzle around the cognitive status of AP concerning its explanatory power for the appearance of man in the universe. In spite of the fact that there are different formulations of AP, they are accepted as falling into three versions according to their explanatory pretention. The first is the so-called weak version of AP usually presented by the following formulation: The weak anthropic principle (…) is the truism that the universe must be found to possess those properties necessary for the existence of observers.38

The weak version of AP is practically of little interest among philosophers and scientists, namely because of its tautological content: the universe possesses such and such properties, since we, humans, are observing a universe that has given birth to us as observers. All this amounts to the

38

https://www.britannica.com/science/anthropic-principle/Forms-of-the-anthropicprinciple.

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“truism” that our universe allowed the birth of human beings, which is a sheer fact, and not an explanation of it. The so-called strong version of AP is its genuine and popular version, which is based on the claim (C1). From now on, using the abbreviation AP, I shall have in mind especially this version, the concise formulation of which is the following: “The basic structural and dynamical features possessed by the universe are of such a kind, in order to lead to the appearance of man at a definite stage of its evolution, in his quality of a conscious observer of the universe.”

In fact, a curt and non-anthropocentric formulation of AP runs to the declaration that the qualities of the universe are of such a kind, in order for intelligent life to appear at a definite stage of its evolution. But, insofar as we do not know with certainty about the existence of extraterrestrial intelligent inhabitants of the universe, the anthropocentric formulation of AP goes without saying. The strongest version of AP, which is also known as the Participatory Anthropic Principle (PAP), is based on the presupposition (C2), and it will be presented and analyzed in section 8.2. Notwithstanding our predilection for either AP or PAP, they both impart a teleological explanation about the appearance of man in the universe. However, the cogency of their teleological explanatory pretentions depends on the validity of the interpretation of the empirical evidence in favor of AP, and of PAP, respectively. Thus, my suggested answer to the title question of this chapter is positive, if the relevance of the teleological explanation of AP or PAP is readily admitted, and negative, if this is not so. Section 8.3 is dedicated to the assessment of an alternative interpretation of the empirical evidence for AP, which presupposes a negative answer to the title question.

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8.2. Taking AP or PAP Seriously As we already know from the end of the introductory section 8.1, my answer to the title question is positive, if the teleological explanation of AP is readily admitted. For its part this would mean that first, there is clear empirical evidence for AP, and second, that this evidence could be unproblematically interpreted to the effect that AP does really provide a relevant teleological explanation for the appearance of man in the universe. For this purpose, let me adduce an extended formulation of AP, based on the claim (C1) as an avowed prerequisite. Extended formulation of AP: The elementary particles building all physical atoms and the respective strength of the natural interactions underlying all material structures in the universe, the metrical and topological features of spacetime and the cosmological constant that rules the way of the expansion of the universe, the sum total of all cosmic characteristics near the orbit of the Earth, and the orbit’s own characteristics as well, possess values and properties, which are exactly of the kind they really have, in order for man to appear as an intelligent observer at a definite stage of the evolution of the universe. At that, the building elements of the universe and their properties, as well as the other conditions of an astronomical nature, are finely tuned, so that even minute mutual variations in their characteristics would prevent the appearance of man in the universe. This broad formulation of AP contains what may be called its clearly stated empirical evidence. Thus, for instance, if the masses and the charges of the elementary particles in the structure of the physical atoms – the proton, the neutron and the electron – were slightly different, and/or if the electromagnetic and gravitational interactions were slightly different in strength, then atomic and molecular structures, which are the building blocks of matter, could not be formed. If this is so, stars and planets could also not exist, so the appearance of man in the universe would be impossible.

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If space were not three-dimensional, but for example two- or fourdimensional, the appearance of man as an intelligent observer of the universe would meet similar inevitable hindrances: A two-dimensional animal would have a hard job digesting food. If it had a gut that went right through it, it would divide the animal in two, and the poor creature would fall apart. So two flat directions are not enough for anything as complicated as intelligent life. On the other hand, if there were four or more nearly flat directions, the gravitational force between two bodies would increase more rapidly as they approached each other. This would mean that planets would not have stable orbits about their suns. They would either fall into the sun (…) or escape to the outer darkness and cold. (Hawking 2001: 88)

If the real value of the cosmological constant related to the specific way in which our universe is expanding were different, then the universe would either expand more quickly or more slowly, but in both cases stars and galaxies could not be formed, and again no human being could appear throughout the history of the universe. These are only several though important prerequisites entering the empirical evidence of AP. For some thinkers this empirical evidence, which contains a list of many more necessary conditions for the emergence of life in the universe to later produce the appearance of man, is a sufficient reason for admitting the teleological explanation of AP. Yet, for a philosopher the empirical evidence is only of factual importance, and to this effect could not be a sufficient reason per se. It certainly secures a formal scheme for a teleological explanation, but based on no theoretical argument, the explanation is a trivial one. The empirical evidence as a mere factual happening is a realization of a lucky chance, i.e., a “happy” result with a probability near to zero. In myriads of other cases of the birth of a universe, other universes would not contain such a rarely met combination of prerequisites needed for the appearance of human beings. But the extremely small probability for such a chance trivializes the accidental presence of the empirical evidence and thus (not only diminishes but) removes the strength of the teleological explanation of AP.

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What is still needed for an arguable teleological answer is some adequate explanation for the very presence of the empirical evidence encompassing a lot of requirements of different kinds, which are finely tuned at that, for the appearance of man in the universe as a conscious observer of it. As it seems, the most unproblematic interpretation that can secure a relevant support to the teleological character of AP is the theological interpretation. This is because the creation of the precise combination of numerous prerequisites weaving the texture of the universe, which lead to the appearance of man, is an act so complex and intricate that only God can achieve it. The theological interpretation of the empirical evidence of AP has not only been readily accepted by the enlightened community of non-scientists devoted to the Christian religion, but is at heart of some scientists as well.39 The reason for this is that this interpretation, based on the miracle of God’s creation of the universe, is stronger in its explanatory power than any other alternative teleological interpretation based on naturalistic grounds. Traditionally, Christian theology has been well aware of its limits, and has sought to avoid excessively confident affirmations in the face of mystery. The leading schools of faith have insisted that faith is ultimately a longing, trust, and conviction directed away from ourselves towards its ultimate ground and goal – something that can never be totally or adequately grasped or represented, yet whose reliability is beyond question. (McGrath 2006: 51, my italics)

However, in spite of the strength of the undoubted explanatory contribution of the theological interpretation to the teleological pretention of AP, this interpretation is not embraced by most of the members of the scientific community. This fact can be easily understood having in mind what kinds of theoretical constructs are welcomed in the realm of scientific reasoning. Even if we presume that all contemporary cosmologists were religiously minded and could accept the theological interpretation as a kind of internal faith, they do not introduce super-natural agents as elements in the structure of their scientific theories. To this effect they would not admit the

39

See in this connection the book by Francis S. Collins (2006).

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intervention of God for the ingenious planning of the complex empirical evidence of AP as a proper scientific explanation. Hence the scientific answer to the title question of this chapter is negative, if AP were taken with its theological interpretation. But is there a putative outcome for AP that can preserve the strength of its teleological explanation, and at the same time evade the active intervention of super-natural agents? There is such an outcome, if AP is reformulated into its strongest version, which is based on the presupposition (C2). This version of AP is often dubbed the Participatory Anthropic Principle (PAP) – a name suggested by John Wheeler.40 It can be formulated in the following way: (PAP) The existence of the universe is a result of its observation. The appearance of man as a conscious observer is necessary in order for the universe to be set into existence. PAP, together with (C2), rests on arguments coming from the interpretation of quantum mechanics and being raised before PAP’s formulation. These arguments ascribe an active part of human consciousness in the creation of the quantum properties of micro-objects as a result of the realization of a concrete experiment. As it is known, what kinds of qualities of these objects would come into existence depends on the specific choice of the experimental setting constructed by physicists as observers. In other words, bringing a quantum system into real existence out of its virtual mode of existence (before an experiment to be carried out), is due to the conscious choice of the observers. The human consciousness has thus been ascribed a central part for the birth of the specific values of physical properties being actualized in a process of experimental observation. The proponents of PAP enhance the scope of this interpretation to involve the necessity of the universe to be observed, in order to gain an actual existence. But for this purpose, the universe must possess all the unique conditions, in order for the appearance of man to be inevitably achieved. 40

See Barrow and Tipler (1986: 22).

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To this effect PAP offers not only a teleological explanation for the appearance of man in the universe, but “a double one” as well, since the appearance of man is taken to be a necessary condition, in order for the universe to obtain its actual existence. The double teleological explanation that PAP offered for grasping both the existence of the universe and the appearance of man in it could be assessed as an extreme (and also a) subjectivist view about the important role of man to bring the whole huge universe into existence and to support it. Even not having in mind this double teleological pretention of PAP, but only the “single” one of the standard (strong) AP, Stephen Hawking declares: A second objection to the strong anthropic principle is that it runs against the tide of the whole history of science. We have developed from the geocentric cosmologies of Ptolemy and his forebears, through the heliocentric cosmology of Copernicus and Galileo, to the modern picture in which the earth is a medium-sized planet orbiting around an average star in the outer suburbs of an ordinary spiral galaxy, which is itself only one of about a million million galaxies in the observable universe. Yet the strong anthropic principle would claim that this whole vast construction exists simply for our sake. This is very hard to believe. Our Solar System is certainly a prerequisite for our existence, and one might extend this to the whole of our galaxy to allow for an earlier generation of stars that created the heavier elements. But there does not seem to be any need for all those other galaxies, nor for the universe to be so uniform and similar in every direction on the large scale. (Hawking 1988: 133, my italics)41

This objection, however, does not lie upon a clear theoretical argument, but only expresses a suspicion as to why AP may not be correct: because “This is very hard to believe”. The same may certainly be said about PAP with an even greater reason, insofar as it states that the appearance of man is necessary for the existence of the “whole vast construction” of the entire universe.

41

The first objection made by Hawking considers the hypothesis about the existence of other universes or of separate regions of our universe, which would lead to the reduction of AP to its weak version (Hawking 1988: 132).

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Suspicions, however, cannot replace conceptual objections. This is why I shall adduce below two such objections to PAP. But now I shall draw the reader’s attention to the following curious situation: notwithstanding his negative attitude towards the validity of AP, Hawking raises an original view, which stands in support of PAP. The usual assumption in cosmology is that the universe has a single definite history. One can use the laws of physics to calculate how this history develops with time. We call this the ‘bottom-up’ approach to cosmology. But since we must take into account the quantum nature of the universe as expressed by the Feynman sum over histories, the probability amplitude that the universe is now in a particular state is arrived at by adding up the contributions from all the histories that satisfy the noboundary condition and end in the state in question. In cosmology, in other words, one shouldn’t follow the history of the universe from the bottom up because that assumes there’s a single history, with a well-defined starting point and evolution. Instead, one should trace the histories from the top down, backward from the present time… This leads to a radically different view of cosmology, and the relation between cause and effect. The histories that contribute to the Feynman sum don’t have an independent existence, but depend on what is being measured. We create history by our observation, rather than history creating us. (Hawking 2010: 200-201, my italics)

According to this view the appearance of man is not a natural product of an evolving universe according to definite physical laws. Man is the active agent who establishes the real history of the universe “backward from the present time”. So, this view about the quantum nature of all of the virtual histories of the universe to be actualized by man in his quality of a conscious observing agent stays in apparent harmony with the teleological pretention of PAP for the appearance of man in the universe. Are there counter-arguments that could be raised against the explanatory pretention of PAP? I adduce two of them here. The first one is expressed by the lack of an arguable answer to the following question: How could man possibly appear as a living creature, which possesses a material body and is endowed with consciousness, out of a universe whose actual existence has not yet been available? One

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might admit of course that unknown acts of decoherence,42 which either do not require the engagement of any consciousness, or require some nonhuman one, had materialized a part of the universe that would further favor the appearance of man. But in this case the important role of the human consciousness for taking the universe out of its virtual mode of existence would be strongly diminished, if not obviated. The other counter-argument is hypothetical, but this does not make it negligible. It pays attention to the principal possibility for the universe to also be a home of non-human conscious observers, because of its practical infinity. But if this is the case, the different types of observers will actualize through their observations of only isolated regions of the universe, which are accessible for their own abilities and means for observation. Well, but these observed regions of the universe must combine in an appropriate way, i.e., they must match all the structural and dynamical features of their actual modes of existence; and this is of crucial importance for their overlapping parts that are actualized by different types of consciousness. All this demands the presence of “some Ultimate Observer who is in the end responsible for coordinating the separate observations of the lesser observers and is thus responsible for bringing the entire Universe into existence” (Barrow and Tipler 1986: 470). Otherwise, the universe would lose its actual integrity. But all this seems to be a super-Berkeleyan view: the whole universe exists solely because of the active observation of “some Ultimate Observer”, since the prerequisite for its real global existence is to be perceived. The doctrine “esse est percipi” refers to the existence of the entire universe. The conclusion is that the answer to the title question of this chapter is negative, if the last two objections to the double teleological pretention of PAP were taken as valid ones, and positive, if they were not (and there are no other objections, as well).

42 By “decoherence” physicists denote the act of bringing a quantum system into an actual existence out of its virtual mode of existence, when the system is found to be in a superposition of all its possible states related to measurable properties. Every measurement carried out for finding the value of a concrete property of the system reduces the quantum superposition into only one of its possible states.

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* For the sake of completeness, I can add a few words about one more objection concerning both versions of AP. It is of a principal character, because it questions the validity of their main prerequisite: the unique role of human consciousness for bringing a quantum system into existence through the act of its observation. This prerequisite is not at the heart of the proponents of realist interpretations of quantum mechanics, since acts of decoherence of quantum systems (see note 42) can also occur without any previously planned observation made by a conscious observer. However, I decided not to make this objection against the validity of the anthropic teleological reasoning, because the objection (although being of a principal character) is formally external to this reasoning. It is connected with the conceptual acceptability of various interpretations of quantum mechanics from the standpoint of different philosophical positions, which is not a subject matter of analysis in this chapter.

8.3. (P)AP Explained Away Let me state at the outset of this section that even if the already analyzed interpretations of (P)AP43 were rejected, or not taken seriously (because of some conceptual discrepancies for instance), the strong empirical evidence behind their formulations cries out for an explanation. The absence of an alternative explanation would maintain the interest in the explanatory potential of (P)AP to be kept intact, notwithstanding the pertinence of any objections whatsoever. So, are there alternative explanations of the empirical evidence for (P)AP, which are based on natural grounds? As we have already seen, there is at least one such interpretation. It is expressed by the curious contention that no matter how complex is the considered empirical evidence, it is sheer cosmic chance for it to compose the texture of the universe. But as commented in section 8.2, the realization of such a lucky chance is very near to zero. So near indeed that 43 By the abbreviation (P)AP I indicate both versions of the Anthropic Principle: AP and PAP.

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even scientists who point to this naturalistic interpretation as an alternative to (P)AP’s teleological explanation for the appearance of man, hardly believe in its manifested validity. However, there is another explanatory alternative and relatively topical one. The key word for it is multiverse. This word is the name of a cosmological view that besides our universe, many other universes are also avowed to exist. This view is not a new cosmological revelation, but has been recently resurrected on the base of the explanatory power of the string theory whose ontology propels the fundamental idea about the multiverse quite seriously. As Stephen Hawking has clearly explained, according to the string theory the ten-dimensional space of its inhabitants – that give birth to all of the intrinsic qualities of the quantum texture of a possible universe – possesses seven dimensions, which are “curled up” in different ways. The estimated number of possible internal spaces structuring a universe is an enormous one, which means that the number of different universes in the multiverse could amount to 10500! (Hawking and Mlodinov 2010: ch. 6). Leonard Susskind introduced to this effect a purely theoretical cosmological construct called the “cosmic landscape” to represent this huge possibility of different universes that could emerge out of the quantum vacuum (Susskind 2005: ch. 3). What is important for my analysis here about an alternative way of explaining the empirical evidence for (P)AP on natural grounds is the following: Although the probability for exactly this empirical evidence allowing the appearance of man in our universe is very low, the number of universes within the multiverse is so huge, that it is beyond any doubt that not only our special universe could have naturally emerged out of the cosmic landscape of the multiverse, but also many other universes resembling our universe have certainly also had the chance to exist. Thus, the cosmological theory of the multiverse evades the teleological pretention of (P)AP to explain the appearance of man in the universe.

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8.4. Conclusion I suggest three answers to the title question of this chapter, connected with the explanatory pretentions of AP and PAP to account for the appearance of man in the universe. These answers do not bear a resolute, but a conditional formulation. The reason for this is that the answers may be positive or negative, depending on the philosophical outlook, or on the weltanschauung of their upholders. About AP: a scientifically laden answer to the title question is negative, if AP goes together with its theological interpretation, but the answer may be positive from the standpoint of a devoted Christian believer. About PAP: the answer to the title question is negative, if the two objections presented in section 8.2 to the double teleological pretention of PAP were taken as valid ones, and positive, if they were not. If the contemporary cosmological view about the multiverse as a maternity home for universes is accepted as a valid one, then AP and PAP have no need to explain the appearance of man in our universe.

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