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A303 7-8

THE OPEN UNIVERSITY Arts : A Third Level Course Problems of Philosophy Units 7-8

"Prooj and the Existence of God

s SY OC 3822!: 9

1 till Ill 111 III

ST. MARY’S COLLEGE LIBRARY BT12 6FE SHELVED AT

f/sut_ ope:

ST. JOSEPH'S COLLEGE OF EDUCATION LIBRARY This book is issued in accordance with current College Library Regulations. DATE DUE AT LIBRARY LAST STAMPED BELOW

-8. MOV. 1984

Arts: A Third Level Course Problems of Philosophy

Units y-8

PROOF AND THE EXISTENCE OF GOD Prepared by Stuart Brown for the Course Team

The Open University Press

The illustration on the front cover is based on P. P. Rubens ‘Incredulity of St. Thomas' 1613-15, Musk Roy ale de Beaux Art, Antwerp (Mansell Collection)

The Open University Press, Walton Hall, Milton Keynes. First published 1973. Reprinted 1973. Copyright © 1 973 The Open University.

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•All rights reserved. No part of this work may be reproduced in any form, by mimeograph or any ■other means, without permission in writing from the publishers. Designed by the Media Development Group of the Open University. Printed in Great Britain by The Open University. SBN 0 335 00893 3. This text forms part of the correspondence element of an Open University Third Level Course. The complete list of units in the course is given at the end of this text. For general availability of supporting material referred to in this text, please write to the Director of Marketing, The Open University, P.O. Box 81, Milton Keynes MK7 6AT. further information on Open University courses may be obtained from the Admissions Office, The Open University, P.O. Box 48, Milton Keynes MK7 6AB.

1.2

PROOF AND THE EXISTENCE OF GOD

.

1

1.1

INTRODUCTION

How to use this material Our question is: whether or not it is possible to prove that there is a god. As is characteristic of central philosophical problems it is a complex question to which there exists no definitive answer. There is not much one can say in philosophy to which no other philosopher will object. That is not to suggest, of course, that you can think what you like, that one opinion in philosophy is as good as another. Someone with a firm enough grasp of all the issues which relate to a particular philosophical problem might be able to forestall all the difficulties which arise in connection with his treatment of it. But a teacher of philosophy should not invite his students to assume that he is in such a position. Much of my advice as to how to get the best use out of this material follows from this point. In this correspondence text I am trying to help you learn how to do philosophy in three ways. Firstly, I offer you examples of philosophical reasoning which bear upon our theme. Secondly, I direct your attention to certain questions and ask you to consider how you would answer them before looking further at my text. Thirdly, I try to provide you with some way of assessing the answers you give. There are some words of advice I would like to give under each of these heads. (a) I have made no attempt to avoid saying what I think about various issues. Objections may occur to you to what I say. Do not assume that, since I have given no space to attempting to cater for a particular objection, it is not a pertinent one. Only accept my conclusions if you are satisfied with my argument. (b) Frequently, in the text, you will find points at which I expect you to take time out from reading the text to study some argument or think about some question. It requires some self-discipline not to allow your eye to glance further down the page to see what I have to say before thinking out things for yourself. But remember, the point of the exercise is to learn how to do these things for yourself. On the whole, then, it is best if you write down as clearly as you can what your answer to the question suggested is before you look at what I have to say. Some¬ times you may have a special difficulty with the question. You may not understand it or not know for the life of you how to set about answering it. That will probably be my fault. If you find yourself unable to use your time out from reading the text with advantage, go back to the text. You must be your own judge ofthis. But, as a rule, you should be spending no less time on these mini-assignments than in reading the text and, ideally, a good deal more. (c) Finally, some remarks are due about the self-assessment component of this material. There are a few exercises which are placed at points where it is rather important that you should have assimilated the main points of what has gone before. With tests of assimilation you should be able to find out from the text about the rightness or wrongness of your answer. But you are learning to do philosophy and not simply to assimilate the thoughts of philosophers. And in recognition of this you will often be invited to think about questions you cannot answer by a diligent reading of the text up to that point. To some of these ques¬ tions there are, I am sure, more reasonable answers than I have been able to

Introduction

8

imagine. You may well find, therefore, that I simply do not discuss the answer that you have given to the question. I am sorry if that turns out to be so, as it will be a source of frustration to you. I hope it does not happen too often. If it does happen, do not assume there is no merit in your answer.

1.2

Prescribed reading To use this material it is essential that you have to hand the following text: The Existence of God, edited by John Hick, Collier-Macmillan, 1964. No other reading is prescribed for these units. You will find, at various points in this text, that I have recommended some other publications for further reading in case you wish to pursue certain topics further.

1.3

Acknowledgements V arious members of the Problems of Philosophy course team have suggested improvements to earlier drafts of this material. I have been particularly helped by comments from Oswald Hanfling and Godfrey Vesey as well as by those from Professor Roy Holland of Leeds University.

CONTENTS

1

Introduction

1.1

How to use this material

1.2

Prescribed reading

1.3

Acknowledgements

2

What is it to prove something?

2.1

The idea of conceptual analysis

2.2

Towards an analysis of‘proof’

2.3

Two kinds of proof

3

Is an empirical proof of the existence of a god possible ?

4

How can an argument prove something?

4.1

5

Two kinds of argument for the existence of a god

Ontological arguments

5.1

The Cartesian version

5.2 5.3

Is existence an attribute ? Anselm’s ‘Second’ Ontological Argument

5.4

Is an ontological proof of God’s existence possible ?

6

Cosmological arguments

6.1 6.2

Aquinas’ Third Way Taylor’s cosmological argument

6.3 6.4

The Principle of Sufficient Reason Is a cosmological proof of God’s existence possible ?

7

Conclusion

Appendix on validity and proof

'

2

2.1

WHAT IS IT TO PROVE SOMETHING?

The idea of conceptual analysis Philosophers love nothing more than to begin at the beginning. Asked whether the existence of a god can be proved, a philosopher will likely inquire what the questioner intends by the word ‘proved’. He will attempt to persuade him that, until we are clear as to what a proof is, there is not much point in attempting to answer his question. A non-philosopher, though he may be over-confident about his understanding of the question ‘Can the existence of a god be proved ?’ may be puzzled at the question ‘What is a proof?’ For, on the one hand, he will be inclined to say that he must already know the answer. He is, after all, fluent in his use of the verb ‘to prove’ and its derivatives. He has, since he was a child, been talking from time to time about proving one thing and another and not found any difficulty in making himself understood. Surely, he may be inclined to think, it is a waste of time to ask what a proof is. On the other hand, he is aware to some extent that he couldn’t say right off what a proofis. And that is a rather curious fact if he already knows what a proofis. Philosophers, at least since Socrates, have asked such questions as: ‘What is knowledge ?’, ‘What is duty ?’, ‘What is truth ?’ and ‘What is beauty ?’ And I think that the question ‘What is proof?’ is like these. What is striking about them is that they are asked by people already skilled in the use of the concepts involved (who know how to use the verb ‘to know’, etc.) of others who are neither more nor less skilled in using these concepts. A man who asks, ‘What is antidisestablishmentarianism ?’ either wants to know what that word means or to check that someone else does. He assumes that the person to whom his question is addressed is either more skilled in his use of words or less so. And there is here a rather important difference. There are certain words which we learn to use without learning to define. And these include not only simple terms such as ‘red’, ‘rough’ and so on but also certain complex terms. Complex terms can, however, com¬ monly be taught by stating their meaning in simple terms. I doubt if there has ever been anyone who knew an antidisestablishmentarian when he met one who could not give a perfectly correct answer to the question ‘What is antidisestablishmentarianism ?’ But I have never heard of anyone being taught how to use words like ‘know’, ‘true’, ‘beautiful’ and so on by means of a definition. It is one thing to be able to use these words. It is quite another to be able to reply adequately to such questions as ‘What is knowledge ?’ I am suggesting that what is puzzling about such questions as ‘What is know¬ ledge ?’ is that, when asked by fluent speakers of the English language, they do not seem to be requests for information. For the man who asks them needs no further knowledge than what he already has to tell a right answer from a wrong one. Suppose, for instance, it is suggested to you that knowledge is nothing but true belief, would you think it an adequate answer to the question ‘What is know¬ ledge ?’ I expect you would not. I expect you will say that there are many cases where a man’s belief is a true one but where he was very lucky to be right. And we would not want to say that someone knew, if it was a matter of luck that he was right. Y ou may not have said this, of course, but now that / have said it I think

What is it to Prove Something?

10

you will feel I have only reminded you of something you knew already. To satisfy ourselves that it is false that knowledge is nothing but true belief we need make no observations, carry out no research. By what operation, then, do we satisfy ourselves in such a matter ? The answer is, I believe, that we satisfy ourselves by analysing our concept of knowing. We ask ourselves what must be involved in a given case if it is to be a case of knowledge. In asking ourselves such a question we are attempting to make explicit what must be true of a given case if, consistently with the conventions established for using the verb ‘to know’, it is held to be one of knowledge. In so far as we already know how to use the verb ‘to know’ we already know how to talk within those conventions. Analysis seems, then, only to make explicit what we already know implicitly. At any rate, it results in statements of what must be so given certain conventions. We do not ascertain the truth of those statements by any kind of empirical investigation or research. They are, that is to say, not a posteriori. Their truth is, rather, known independently of experience. It is, in the traditional philosophicaljargon, a priori. An example of an ‘analytic’ statement is the following: ‘Whatever is known is true’. Given the conventions which govern our use of the verb ‘to know’ one cannot consistently say both that it is not raining (for example) and that someone knows that it is raining. We do not discover from experience that whatever is known is true. That is why it is a priori. It is indeed a necessary truth about our concept of knowledge. Thus it is a logically necessary condition of the truth of‘John knows that it is raining’ that the statement ‘It is raining’ be true. If, that is to say, it were not true that it is raining neither John nor, for that matter anyone else, could know that it is raining. Mow this suggests a programme of analysis (I do not wish to imply it is the only one) of concepts such as knowledge along the following lines. The inquiry takes the form of asking what are the logically necessary conditions of statements, for instance, of the form ‘Someone X knows that something/? is true’. We can express one analytic truth by saying that X knows thatp only if p is true. But to say this is so far to offer but a very partial analysis of the concept. A complete analysis will list a set of logically necessary conditions which, taken together, are sufficient con¬ ditions of knowledge. A complete analysis will state under what conditions a statement of the form ‘X knows that />’ must be true, not merely what must be true if‘X knows that />’ is true. In the case of knowledge it has proved extremely difficult to provide such an analysis. But as this is a matter which is raised in the units on Knowledge and Belief, I shall not enlarge on it further here. I shall instead illustrate a complete analysis (or something like one) in terms of a philosophically uninteresting example. Suppose an analysis is sought of the concept ‘bachelor’. There are analytic truths about bachelors which will readily occur to you. ‘Bachelors are male’, ‘Bachelors are unmarried’ are the obvious ones. Something like the following seems satisfactory as an analysis: ‘X is a bachelor’ is true if, and only if, the following statements are true: 1 X is male; 2 X is eligible for marriage; 3 X is unmarried. The second condition is slightly vague. A boy of twelve is not a bachelor because his age renders him ineligible. Priests and monks who have taken vows of celibacy would not ordinarily be thought of as bachelors because, in taking those vows, they have removed themselves from the category of persons eligible for marriage. But here legal usage and common usage part. For vows of celibacy are not a legal

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bar to being married in the way that age or being already married are. There can be conflicting criteria of eligibility. That does not show there is anything wrong with the second condition. All it shows is that, without knowing what those criteria are, one would not be able to judge in a given case whether someone was a bachelor. This is the sort of analysis of what it is to prove something which we shall attempt in the next section. But, before turning to it, I suggest you check on how much you have picked up of what I have been saying by attempting an exercise.

Exercise i

All statements are either analytic or they are not. Which of the following state¬ ments are analytically true, which are analytically false and which not analytic at all? (i) ‘Bachelors are bold.’ (ii) ‘Murder is not wrong.’ (iii) ‘All ravens are black.’ (iv) ‘Unmarried males are bachelors.’ (v) ‘God exists.’ (vi) ‘Nothing can be red and green all over at once.’ (vii) ‘Grass is green.’ (viii) ‘Ifsomeone knows something he truly believes it.’

Comments (i) is not analytic. Some bachelors doubtless are bold, some perhaps are not, whether any or all are is clearly a matter for empirical investigation and not to be decided by reference to what is involved in the concept ‘bachelor’. (ii) is, I should say, analytically false. The use of the term ‘murder’ is restricted to wrongful killing (as opposed to, say, killing in self-defence) hence, speaking within the convention, it is self-contradictory to say that murder is not wrong. Someone who says ‘Murder is not always wrong’ may, of course, mean that it is not always wrong to commit what the law classifies as murder. That is a way of saying that murder is not always murder, which need not be self-contradictory. So-called ‘murder’ need not be murder. Understood in this second way (ii) is not analytic at all. (iii) is, I should say, not analytic at all. It could, however, be understood as analytic and would be understood in that way by someone who would not count any white, grey or otherwise coloured bird as a raven. But it is, I think, rightly understood as a generalization about a matter of fact, as subject to confirmation or disconfirmation in experience. (iv) looks like an attempt to state an analytic truth. It is not, however, analytically true. Minors may be unmarried males but not bachelors. There is not any contradiction, however, in (iv). So we cannot say that it is analytically false. Rather it is not analytic at all. For we could imagine circumstances in which all unmarried males were bachelors. If the crew of a ship wrecked off a desert island came to constitute its population then it would, as a matter of empirical fact, be true of that island that all its unmarried males were bachelors.

What is it to Prove Something ?

12

(v) is included to prepare you for what is to come. Nothing seems plainer to some philosophers than that any statement which asserts the existence of something cannot be analytic. But, if you think some ontological proof of the existence of a god succeeds, you will think ‘God exists’ is analytically true. This matter we shall consider in section 5. (vi) is also a teaser. This is one of a class of statements which seems to be true a priori all right but which is not so obviously analytic. There are philosophers who have maintained it is analytic and those who have denied this. Our account of analyticity has been too blunt for us to determine which view would be right. As a sharper account I recommend Anthony Quinton’s ‘The A Priori and the Analytic’, Proceedings of the Aristotelian Society, 1963-64, reprinted in Philosophical Logic, ed. P. F. Strawson, Oxford University Press, 1967. (vii) is, fairly obviously, not analytic. This is rather the same sort of case as (iii). Green is the characteristic colour of grass as black is the characteristic colour of ravens. Grass will, however, turn brown in a drought. But no one says it then ceases to be grass. (viii) is, according to some, analytic. But philosophers have taken all three of the possible views about the connection between knowledge and belief. Some have held that knowledge precludes belief, that you can’t both know and believe the same proposition at the same time. Others have held that whenever someone knows he must also believe what he knows to be true. Others again have held that knowledge neither precludes nor necessarily involves belief. So while there would be unanimous agreement that (viii) was analytically true in respect of that part which asserts that if someone knows something it is true, controversy remains about that part which asserts that if someone asserts something he also believes it. There are those who hold it to be analytically false (because knowledge precludes belief), those who hold it to be analytically true (because knowledge necessarily involves belief) and those who do not think it analytic at all. I will not here attempt to choose between these views. What matters here is that you should be clear as to what difference it makes to hold one view rather than the others.

2.2

Towards an analysis of‘proof’ There are all sorts of contexts, in ordinary life, in which we find ourselves called upon to prove something. We may be called upon to prove our identity, to prove where we were last Saturday afternoon between 4 and 4.30 p.m., to prove that we can do something, to prove we’ve paid our fares, and so on. And we may want to prove something for our own benefit even if no one else calls upon us to do so, to prove we are not scared of heights, that all equilateral triangles are equiangular, or whatever. But when is it true to say that a person has proved something to another ? Characteristically, when a person A proves something to a person B, A proves to B that some claim p is true. What we want to understand is just what exactly A would have succeeded in doing if he has proved to B that p. What conditions do you think would have to be met ? What conditions would you say are necessary conditions of the truth of a statement like ‘A has proved to B that p' ? You may find it easier to think in terms of examples. But remember, we don’t want to come to conclusions about what a proof is which are only true about particular examples.

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I think you will have quickly thought of, or will quickly agree to at least two conditions as ones which must be met if A is to have proved to B that p. One is that B must now be convinced ofp. Proof is very commonly offered where someone needs to be convinced. And the result, if it is successful, is that he is convinced. If you are doubtful about this condition or if it did not occur to you, it may be that you were thinking of other cases of proof, perhaps the sort of proof that is offered in geometry or logic. There are proofs, indeed, which can be given of such truths as that 7 +5 = 12, truths of which none of us needs to be convinced. And there are proofs about much more complicated propositions of logic or mathematics which are not deemed unsuccessful because some weak students of these subjects are not convinced by them. So you may be inclined to say that it is not a necessary condition of a proof being successful that the person to whom it is offered should be convinced of whatever is proved. You would, I think, be quite right to say this. But this does not mean those of us were wrong who would say that it is a necessary condition of A having proved to B thatp that B should now be convinced ofp. For there is a distinction which we mark in the way we speak about ‘proof’ between proving something to someone and proving something/or him. You can prove somethingfor someone even though he does not need to be convinced. It might, for example, add to someone’s M^er^aWm^ofarithmeticifit were provedybr him that 7 +5 = 12. Butit would make no difference to what he believed. And, indeed, it would not detract from its being true that ‘7+5 = 12’ had been provedfor someone if that individual did not understand the proof. You can imagine an exasperated if ineffective teacher saying to a pupil, ‘But I’ve proved itfor you twice already. Haven’t you got it yet?’ There is a problem which has baffled some writers on the arguments for the existence of God to which this distinction is relevant. Anselm, as you will see in the prescribed reading (Hick, p. 27), concludes his argument for the existence of God with the words:

Thanks be to thee, good Lord... because I now understand by thy light what I formerly believed by thy gift....

Some writers have inferred from these and other remarks that it was not Anselm’s concern to prove the existence of God. And, clearly, he cannot be construed as having tried to prove to himself that God existed. Of that he was already con¬ vinced. But the fact that his motive was to understand why the man who says in his heart ‘There is no God’ is a fool, as the Bible teaches (Psalms 14:1 and 53:1), does not show that he was not trying to prove the existence of God. On the contrary, I think it is quite proper to say that, in proving/or himself that God existed, he hoped for understanding. More importantly, however, the very same argument might be used to prove to the fool who says in his heart ‘There is no God’ that he is a fool. The same argument, that is to say, can be used both to prove something/or someone and to prove something to someone. And that suggests that, although it is essential to A’s having proved to B thatp that B becomes convinced thatp, it is not essential to proof as such that it results in conviction. In other words, if our question had been ‘What conditions must be met if A is to have proved that/) ?’ we should not have had to say that there is some individual person who has, as a result of A’s efforts, become convinced that/).

What is it to Prove Something ?

14

Still, as I hope will become apparent to you if it is not so already, the connection and difference between proving something to someone and convincing them is of particular importance for our inquiry. And this mention of a difference between proving and convincing brings us to the second condition of A’s having proved to B that/). It is that p be true. You can convince someone of the truth of a claim which is in fact false. But you can’t prove to someone that a claim which is in fact false is true. When you convince someone that something is true you establish (show, prove) to his satisfaction that it is true. Some people are more easily satisfied than others and so it is easier to convince some people than it is to convince others. It is not surprising, therefore, if people can sometimes be convinced of the truth of claims which are in fact false. Now I want to ask you whether you think these two conditions will suffice to distinguish a case where someone has proved something to someone from every other case which is similar to but falls short of it. In other words, if A has convinced B of the truth of a claim which is in fact true, does it follow that A has proved to B that the claim in question is true ?

I think you would have been wrong to have given ‘Yes’ in answer to the question. For there are a number of ways in which people can convince others of the truth of claims which are indeed true without proving the truth of those claims to them. There are, that is to say, exceptions or counter-examples to the thesis that if anyone convinces someone of the truth of some proposition which is indeed true then he proves it to him. That thesis is not, in that event, analytically true. What sort of exceptions or counter-examples are there ? Let me mention a few that occur to me. Perhaps similar cases will have occurred to you. (a) A man believes that the rest of humanity is in conspiracy against him. He is confronted with the evidence of people others would say were his well-wishers. Their friendly tone, their smiles, and so on conceal, he claims, their true attitude towards him. A doctor is consulted who gives him some drug. As a result of taking this drug he is now convinced by the friendly tone and smiles of those others would say were his well-wishers. He is now convinced that it is not true that the rest of humanity is in conspiracy against him. (b) Jones is a shop assistant. One day a customer complains to the manager of the shop that Jones has deliberately short-changed him, giving him, it is alleged, a 10-pence piece instead of a 50-pence piece in change. The till is found to be correct. Jones readily admits to having in his possession both 10-pence pieces and 50-pence pieces. But he stoutly denies the charge of having short-changed this customer. He reminds the manager that in his eight years of employment in the shop no similar complaint has been made against him. It is, moreover, he points out, only a few weeks since he won a substantial sum on the football pools. The manager is convinced that Jones is telling the truth (as indeed he is) and assures the customer that he must have been mistaken. (c) Sailors witness sea lions preying upon penguins and return with the story. Some scientists are sceptical, remembering the tales about mermaids and so forth. Others are convinced, holding that the sailors could not easily have been mistaken about such a matter.

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These three cases are all cases where, as I hope you will agree, people are able to convince others of the truth of some claim which is in fact true. But none of them is a case where, in doing this, they prove to those persons that those claims are true. It looks, then, as if we need some further condition which must be met in any case where someone proves something to someone but which does not have to be met in a case where one person convinces another of the truth of a claim which is in fact true. We ought indeed to be able to detect some clues as to what further conditions we need if we ask ourselves the question, ‘ Why are those three cases not ones where someone proves something to someone ?’ What do you think ?

Discussion (a) There are two peculiar features of this example which you may have noticed. The first is that the doctor produces no further evidence to convince his patient that he has well-wishers. All he does is to affect the way in which his patient is inclined to regard the evidence. The second (and related) feature is that it is not in virtue of anything the doctor does that we assume that his patient does have well-wishers. We could imagine a story in which the patient is elderly and rich but leads a life in which he only has to do with persons who might stand to benefit from his will. They might actually be conspiring against him and have brought him to the doctor because, suspecting this, he is planning to leave all his money to charity. The doctor in the example does nothing which rules out that possibility. To prove that someone is a well-wisher one would need to be in a position to discredit any suggestion to the contrary. He would need to be shown to have satisfied some test no one would satisfy who was not a well-wisher. But the doctor shows nothing like this. Nor indeed was he trying to prove anything. (b) This is the sort of case which is a matter of probability rather than proof. The manager is satisfied that it is not likely that Jones short-changed this customer, that it is much more likely that the customer made a mistake. His conviction stops short of knowledge. In this sort of circumstance it may be impossible for a man to prove his innocence. It need not be, of course. We can imagine what would prove Jones’s innocence. Suppose he can remember some unusual characteristic of the 50-pence piece he gave the customer—say, that two of its sides had fret marks on them. The customer might be asked to search his pockets again. If he then found just such a coin that would be taken as proving that Jones was telling the truth. For that is a test which would not have been satisfied if Jones’s story had not been a true one. We would, for practical purposes, discount the possibility that the customer had entered the shop with just such a curious 50-pence piece in his pocket. But, since he cannot show that his story passes such a test, Jones cannot prove that he is telling the truth. (c) The position of the sailors is not unlike that of Jones. They know their story is true but they cannot prove it. If they had filmed the scene they would have been in a different position. For then the truth of their story could be established beyond doubt. I think these examples will show that there is really quite a large difference between convincing someone of a claim which is in fact true and proving it to him. But the difference seems even greater than these examples show. For in

What is it to Prove Something ?

16

these cases we have been considering proof is lacking only in practice. It is not that that there are no procedures for establishing that someone is a well-wisher, or that someone did not give short change, or that sea lions take penguins. Only, in these particular cases, such procedures could not in practice be applied. But there seem to be cases where people are convinced of things where it is not clear what those procedures could be. A man may become convinced, for instance, that it is his mission in life to become a jungle doctor. But what would it be like to prove that he had such a mission ? He would not require to be convinced himself, of course. But others might need to be. Suppose he asks a missionary society to support him through his medical training. They will want to be convinced that he does have a mission. But will they want proof? There might be proof that he never had a mission to be a jungle doctor. If he turns his back on the idea as soon as he has qualified, that might be such proof. And the missionary society will need to be convinced that he is sincere and determined. Yet his being sincere and determined is not proof that he has a mission. It may indeed be that there are many statements which cannot be proved true because there is no recognized procedure for testing their truth. Of these, most are the kind of utterance for which proof would never be demanded. For instance, ‘All men are brothers’ is a statement of whose truth men may become convinced. But there are no recognized procedures for testing it. More commonly still, perhaps, a statement may be tested by means of one sort of procedure but not susceptible to proof by means of other procedures. Thus a statement which is held to be true a posteriori will be tested by procedures in which an appeal is made to experience. It will not be proveable by procedures appro¬ priate to a priori statements. And the same holds the other way around. It is an a priori truth that all equiangular triangles are equilateral. So one would not adopt empirical procedures, such as measurement, in order to prove it. To prove something one needs to adopt one of the recognized procedures for testing statements of that sort. What are we to infer from these considerations ? What further condition or con¬ ditions do we need to add for our analysis of what it is to prove something to someone ? What further conditions would you add ?

I should now be inclined to say that someone A has proved to another B thatp if, and only if, the following conditions hold: (i) B is now convinced of/>; (ii) p is true; (hi) there are recognized procedures for testing the truth of statements such as p; (iv) A convinces B of the truth ofp by adopting one such procedure and thereby showing that some test is satisfied which would not have been satisfied ifp had been false. For some purposes it would be necessary to say a good deal more than this. Indeed, we have here been considering one aspect of proof to the exclusion of another. We have been considering what it is to prove something to someone rather than what it is to prove something/or him. The same proof might, I

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suggested earlier, serve both purposes. But the account we now have relates only to the first purpose. The excuse for this is that, in asking whether the existence of a god can be proved, we are primarily interested in the possibility of convincing the sceptic.

2.3

Two kinds of proof There are two quite different kinds of proof. One may try to demonstrate that something is so by devising an empirical test. For instance, if someone wants to prove that he can do something he would, in most cases, do this by publicly doing it. On the other hand, one may try to demonstrate that something is so by means of an argument. Here certain statements are taken as not being open to question and it is shown that anyone who accepts them must, also accept the truth of the statement which required to be proved. There are specific requirements on proofs of this sort. These we shall consider in section 4. I distinguish these kinds of proofin terms of the different sorts of procedure involved. A similar distinction is sometimes intended by speaking of the first kind as ‘direct’ proof and the second as ‘indirect’. The implication is that the second, though not the first, kind of proof involves inference. I think empirical proof may well involve inference. There is, for instance, an inference from ‘John is riding a bicycle’ to ‘John can ride a bicycle’. So I do not think that the distinction between ‘direct’ and ‘indirect ’proof is very helpful here. In this case, however, it is the evidence of experience which is decisive, not any process of reasoning. There are also arguments which seek to demonstrate some conclusion from premisses which are empirical. And in these cases it is the argument which is decisive, not the fact that the truth of the premisses is established through experience. We shall consider these two possible ways of proving the existence of a god separately, beginning with the question whether the existence of a god admits of empirical proof.

3

IS AN EMPIRICAL PROOF OF THE EXISTENCE OF A GOD POSSIBLE?

Empirical proofs of the existence of things are often very straightforward. If I want to prove to someone that there is a cat in the living-room my procedure will normally be to take him there and ask him to look for himself. He is then likely to have visual experiences of a kind he would not have if it had not been true that there was a cat in the living-room. And that would clinch the matter. Gods, however, are commonly not thought of as spatial beings. Even though they may be associated with certain places rather than others, particular mountains for instance, deities cannot themselves be observed in those places. They manifest themselves is less direct ways. Pallas Athene, for example, assumed disguises; Jehovah sent messengers. Empirical proof in matters of religion is, therefore, of a rather indirect sort. For example, Gideon demanded ofjehovah proof that Israel would be delivered by his hand. The test is that, ifjehovah will deliver Israel by Gideon’s hand, then a fleece left outdoors overnight will be dry in the morning when the ground is covered in dew. In The Book ofjudges it is related that Jehovah provided this proof and later gave Midian and all the host into the hand of Gideon. Notice that, in this case, it is Jehovah and not Gideon who proves that Israel will be delivered. It is by the grace of God that Gideon has proof of this. And clearly an omnipotent god would be capable of establishing his existence no less than his his intentions. And there are all sorts of (to us) spectacular devices by which he might convince the sceptical. If the blasphemer were felled with the regularity of a law of nature, for instance, many would think the existence of a god established. And, if this were not enough for the sceptic, the evidence could be increased. That question, whether a god could establish his existence by affording evidence to human experience, was not the question I wished to raise. I think we may reasonably assume that there are no gods both eager and able to prove their existence in this way. My question was whether it is humanly possible to establish that there is a god by means of an empirical proof. What would you say to this question ?

Two things strike me particularly in connection with this question. Firstly, not only are there not established procedures for putting such a statement as ‘There is a god’ to the test, but it is not clear what those procedures would be. Secondly, even if there might be, it would be impossible to engage in such a test without the tacit consent of the god concerned. For he would hardly be a god whose existence could be proved contrary to his will. Such a god whose existence can be empiri¬ cally proved must either wish to have his existence proved or be indifferent as to whether humans can establish his existence or not. But then he would hardly be a god who wished to have his existence proved but could not do it himself. So a god who does not do it himself must either set a particular premium on humans

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proving it for themselves or be quite indifferent as to whether humans can prove his existence. I know of no theologies in which a god is characterized in either of these ways. If there are none then we should be entitled to conclude that it is not humanly possible to establish by an empirical proof that there is a god of the sort humans are actually inclined to worship. When, then, we consider proofs of the existence of a god we would seem to be justified in concentrating upon the proofs offered in the form of arguments. These do not purport to establish the existence of any particular deity but only the existence of a certain sort of deity or a deity of a certain sort. The obj ections I have mentioned to empirical proofs of the existence of a deity do not apply to these. Part of the reason for this is that if such an argument did prove the existence of a god that in no way contravenes the wishes of a particular deity that his existence should not be an established fact among humans.

4

HOW CAN AN ARGUMENT PROVE SOMETHING?

Let us turn now to consider briefly a special kind of proof in which the means of establishing the truth of the claim in question is an argument. Speaking very broadly, someone can be said to be ‘arguing’ for a claim when he gives reasons for accepting it. He will commonly advertize his belief that these reasons entitle one to accept the claim in question by linking his statement of those reasons to the claim he infers from them by such words as ‘... so ..‘If.. .then . . ‘.... therefore ... hence..and so on. An argument thus consists basically of two parts: (a) what are called ‘the premisses’, which are cited as a basis on which one would be entitled to believe that something is so: and (b) the ‘conclusion’, which is what one is said to be entitled to believe on that basis. By no means every argument constitutes a proof of its conclusion in that sense of ‘proof’in which we are interested. Some of the conditions which must be met if someone is to have proved something to another by means of an argument are given by John Hick in his Introduction to The Existence of God. I suggest that you now read the first five paragraphs of Part II of that Introduction, together with the first two sentences of paragraph six, down to the words *... prove the conclusion’ on page 5. Try to state what conditions Professor Hick suggests must be met by any case in which someone has proved something to another in his third sense of‘proof’.

We might say that, according to Professor Hick, one person (let us call him ‘A’) has in this sense ‘proved’ something to another (let us call this other person ‘B’) only if the following conditions hold: (1) A has offered B a valid argument; (2) the premisses of this argument are true; (3) B acknowledges the truth of these premisses. As you will see from Hick’s explanation, a valid argument is one whose conclusion cannot be consistently denied by anyone who accepts its premisses. For, if the premisses of a valid argument are true, its conclusion must also be true. Thus, if these conditions are met, at least one of the conditions we noted in section 1.3 above will have been met, namely, that what has been proved be true. Now you may not have agreed with the account I have given of what it is to prove something to someone. But, as a test of your assimilation and of my clarity, suppose now that the account I gave is right. What I would like you to do is to ask yourselfwhat further conditions, if any, would need to be added to the three conditions required by Hick ifwe are to have a set of conditions which are met only by cases where someone has proved the truth of some claim to someone by means of an argument.

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Discussion I suggested in section 2.2 that, if A is to have proved to B that/>, B must be convinced of the truth ofp. The conditions given by Hick, however, might be met in a case where B acknowledges (and therefore by implication is convinced) that the premisses are true but, owing to stupidity, ignorance, lack of concentra¬ tion or whatever, does not follow the argument. The result in that case is likely to be that B is not convinced by the proof that p is true. Hick does not, in fact, claim that the conditions he gives are sufficient. He only maintains that they are ‘required’, i.e. necessary. It would indeed not matter much if his analysis were incomplete in only this respect. For our condition (i) (seep. 16 above) bears not on the success of the proof in itself but only on the success of its rehearsal for B’s benefit. If B was not listening and later complained that he had been given no proof oip, A might quite properly retort that he had proved itfor him and might have been able to prove it to him if only he had been able to prove it to him if only he had been paying attention. It is in respect of this other dimension of success rather than non-success than the person-relative one that I think Hick’s account is inadequate. The question is whether it is a sufficient test of the truth ofp that it can validly be derived from premisses which are acknowledged as true by B. It is enough to convince B, enough even to secure that B knows thatp. But it does not follow from the fact that something is so that he or anyone else can prove it. If, then, the premisses of a valid argument cannot themselves be shown to satisfy a test which would not be satisfied if they were false, can the argument be called a proof? I would be inclined to say that the argument would then fall short of being a proof. Suppose I am asked where I was last Saturday evening and I say ‘I don’t know where exactly but I saw the film £azi dans le Metro.' Someone establishes that the only place in the country where that film was being shown last Saturday evening was in the Cameo, Bethnal Green. So now I know that I was in the Cameo, Bethnal Green. But has it been proved to me that I was in the Cameo, Bethnal Green last Saturday night ? I am assuming that it has been proved to me that the Cameo was the only place where the film was being shown at that time. What do you think ?

There is a temptation to think that it could in this way be proved to me that I was in the Cameo last Saturday night. For if it is proved that nowhere else was the film showing then there could be no doubt in my mind that I was in the Cameo that evening. But if we call this proving it to me, there seem to be odd consequences. For, in the first place the man who proved that the Cameo was the only place where the film was showing last Saturday evening did not prove to himself that I was there. For he has no proof that I saw £azi dans le Metro at that time. In the second place, I may be unable myself to prove that I saw that film at that time. I could perhaps prove that I had seen Zazi at some time by showing the kind of knowledge (about how certain scenes were photographed, for instance) that could not be squared with my not having seen it. But that would not be enough. The odd consequence is something has been proved to me which I can’t prove to anyone else and which the person who proved it to me cannot prove to himself.

How can an Argument Prove Something ?

This consequence jars with my understanding of the public character of proof. I am inclined to say that it was not proved to me that I was at the Cameo, though indeed I became convinced to the point of certainty that I must have been at the time. What, I would say, is proved is that if l saw Zazi dansle Metro last Saturday night, I must have been at the Cameo, Bethnal Green. But more than that, I am inclined to say, cannot be proved. My criticism of Hick is that he over-emphasizes the person-relative side of proof. Ifit were sufficient that B acknowledges the truth of the premisses (they being therefore true and known by B to be true) and that A convinces B of the truth ofp by deriving it validly from those premisses—if that were sufficient for proof, we should have a Pandora’s Boxful of arguments to consider as putative proofs of God s existence. For we often do not know whether or not someone knows something. If not, and if he claims to have proved something to himself by means of an argument using it as a premiss, we cannot discount the possibility that he has in fact done this on the ground that the truth of this premiss has not been established. He could then prove the claim in question to anyone who acknow¬ ledged the truth of the premiss. For instance there might in this way be a proof of God’s existence from religious experience. If, for instance, the following argument is produced, someone might concede it was valid but say he cannot allow that the second premiss is true: If there are genuine experiences of divine forgiveness then there is a god. There are genuine experiences of divine forgiveness. Hence, there is a god. He might then come to know, as a result of experiencing divine forgiveness, that some such experiences are genuine. But if we were right in concluding that God’s existence does not admit of proof from experience we could not allow this as a case of proof. If he cannot establish that there are genuine experiences of divine forgiveness this ofitselfis no bar to his knowing that there are. But if he has something inferior to proof for his premisses he has something inferior to proof for his conclusion. What conditions need to be met, then, in any case where someone A has proved to another B that something p is true by means of an argument ? What, in the light of my remarks, would you now be inclined to say ?

Comment I think the following conditions should be met: (i) Bis convinced of/); (ii) pis true; (in) A convinces B of/) by offering him a valid argument of which p is the conclusion; (iv) the truth of the premisses of this argument has been established beyond doubt.

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Two kinds of argument for the existence of a god An argument for the existence of God will only serve as a proof if it is deductive in character, if, that is to say, its conclusion is put forward as following strictly from certain premisses. If one can consistently affirm the premisses of such an argument and deny its conclusion, that will show that it does not strictly follow from those premisses and hence that the argument is not valid. There are, of course, many different patterns of valid deductive reasoning. But, as one may adopt different patterns of such argument to derive the same conclusion from the same premisses, these differences will not concern us here. If, then, there are differences of consequence between various arguments that may be used to prove the existence of a god, we may look for those differences in the character of the premisses. There are, indeed, only two sorts of argument which begin from premisses firm enough to merit consideration as possible proofs of the existence of a god. In the one kind of case, all the premisses are allegedly established a priori whereas in the other at least one premiss is based upon experience, is, that is to say, a posteriori. Arguments of the first kind, where all the premisses are a priori will be versions of what is called ‘the Ontological Argument’. Arguments of the second kind will be versions of what is known as ‘the Cosmological Argument’. In the next two sections we shall be looking at arguments of these two kinds in turn.

5

ONTOLOGICAL ARGUMENTS

W e philosophers of religion often speak of ‘ The Ontological Argument’ .But there are in fact a number of ontological arguments for the existence of a god. We shall here be looking at two of them, the Cartesian argument and the Anselmian argument as reformulated by Professor Norman Malcolm. They have in common the feature that they attempt to show that the essence of God (which they take to be known a priori) is such that there must exist such a being. In more modern terminology, we might say they share the feature of purporting to derive God’s existence from som z a priori statement about the concept ‘God’. If you understand the concept ‘God’ adequately, so they seek to show, you cannot fail to see that God necessarily exists.

5.1

The Cartesian version You will find Descartes’ version of the Ontological Argument as formulated in his Meditations included in the Hick volume, pp. 34-7. Read through Descartes’ argu ment carefully and try to state it in your own words, bringing out the premisses which strike you as crucial.

The simplest formulation of Descartes’ argument that I can think of is something like this: The idea of God is of a being possessing every perfection; existence is a perfection; hence, the idea of God is of a being possessing existence, i.e. God cannot be thought of as not existing, i.e. God necessarily exists. I hope your formulation differed from this, ifat all, in being more complicated. Taking this formulation I have given of Descartes’ argument, we now want to ask whether it constitutes a proof ofGod’s existence. I hope by now that it will be clear that we need to be satisfied on two points if we are to be satisfied that an argument constitutes a proof. We need, firstly, to be satisfied that the argument is valid. We need also, however, to be satisfied that the truth of the premisses is an established fact. It does not really matter in which order we consider these points. But I suggest you ask yourself whether the two premisses I have attributed to Descartes in my formulation of his argument are true as a matter of established fact.

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The first premiss is relatively unproblematic. The statement ‘God has all the perfections’ is analytically and therefore a priori true. Some there may be who will countenance imperfection in their deities. But that does not detract from this premiss. For the premiss is true in virtue of that convention whereby ‘imperfect deity’ is a contradiction in terms. The second premiss is much more troublesome. It does, indeed, raise very fundamental philosophical issues into which we cannot go here to the extent their interest merits. For Descartes’ thesis is that existence is as much a perfection in God as is omnipotence, being wholly good or being all-knowing. The implication is that existence is an attribute of God just as omnipotence, etc., are, that in saying ‘God exists’ we are as much ascribing a property or quality to God as we are if we say ‘God is omnipotent’. This tacit premiss of Descartes’ reasoning has provoked considerable controversy. In the Hick volume you will find that both Kant (especially pp. 44 ff.) and Malcolm (pp. 50 ff.) object to the predicate ^ ‘exists’ being treated like such ordinary predicates as ‘is green’, ‘knows about many things’, ‘is 10 feet tali’, ‘is in pain’, and so on. I suggest you now read these passages of Kant and Malcolm and see whether you can formulate for yourself what the difference is between ‘exists’ and other predicates such as ‘is green’. If you cannot formulate it in your own words try simply to summarize the views of Kant and Malcolm.

5.2

Is existence an attribute? Kant, in the passage to which I have referred, is struggling to justify the view that existence could not be contained in the concept of a thing and hence that an ontological proof of God’s existence is impossible. Many of his points are confused and confusing. And he shows a certain awareness of this by the way he tries again and again to make the same point in a different way. To Kant’s way of thinking what Descartes sought to show is that the claim ‘God exists’ is analytic, that is to say, that the predicate ‘exists’ is contained in the concept of the subject, viz. ‘God’. And indeed those who have defended the Ontological Argument would agree that what they are attempting to do is precisely to show that, upon a careful analysis of the concept ‘God’, it will be apparent that ‘God exists’ must be true. Kant distinguishes between judgements which are ‘analytic’ in the sense I have explained and those which are ‘synthetic’. For him a synthetic judgement is, quite simply, any judgement which is not analytic. And he opposes the suggestion that ‘God exists’ is analytic with the assertion that ‘all existential propositions are synthetic’ (p. 44, line 2). So whereas Descartes would, in Kant’s terminology, have said that all existential propositions, with the sole exception of‘God exists’, are ‘synthetic’, Kant will not grant even one exception. Descartes allows that he ‘cannot conceive anything but God himself to whose essence existence (necessarily) pertains’ {Hick, p. 37, line 2 ff.). He thus maintains that there is one and only one existential proposition, namely ‘God exists’, which is analytic. Kant’s thesis is that no existential propositions are analytic. Well now, if it could be established that no existential proposition could be analytic, we should have a proof that there could be no ontological proof of the existence of anything. But can it be established ? Look now at Malcolm’s objec-

Ontological Arguments

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tions to this part of Kant’s case for rejecting Descartes’ argument. Do you think it is true that no existential propositions are analytic ?

We have seen that one way to test general claims made by philosophers is to try to think of counter-examples to them. And what Malcolm suggests is that there are such counter-examples to the claim that no existential proposition is analytic. I think he is right on this point. The assertion ‘There is a prime number between 30 and 33’ is one whose truth, if it could be proved, would be proved from a priori premisses. It would be natural to expect that such a proof would be ontological and that the conclusion drawn from it would be analytic. The same would seem to hold for Malcolm’s example, ‘There exists an infinity of prime numbers’. Kant himself, however, would not have conceded that these examples disproved his contention that there were no judgements which were both analytic and existential. For he maintained that such arithmetical judgements were ‘synthetic’, i.e. not analytic. We cannot here enter into Kant’s reasons for maintaining that there were synthetic a priori truths. He was, I believe, wrongly impressed by the thought that analytic truths must be trivial. Mathematical judgements are often very far from trivial, in the way in which ‘Bachelors are male’ is trivial. And this seems to have been one factor which led him to hold that they were ‘synthetic’. It was by no means the only consideration, however. Kant thought that experience played a role in our recognition of, for instance, the truths of arithmetic and geometry. Still, Kant would never have supposed the truths of logic to be other than analytic. And the history of logic since the time of Kant has shown both that its truths are not confined to trivialities and that logic and mathematics, if distinguishable subjects at all, are at any rate closely allied. I think, then, that Kant was at least over-confident in his assertion that ‘every reasonable person’ would concede that no existential proposition is analytic. And, to the extent that his case against the Ontological Argument depends upon it, we may at least conclude that he did not establish that a proof of the existence ofagod by means ofsuch an argument is impossible. Nor can we appeal to this thesis to make the difference between ‘exists’ and other predicates. Malcolm’s view is that, although it is not true that all existential propositions are synthetic, there is none the less something right about Kant’s insistence that ‘being’ is not a ‘real predicate’. Malcolm agrees that it is at least intuitively absurd to regard existence as an attribute. He tries to bring out the absurdity by showing what one would be reduced to saying if one supposed it was. (See especially the bottom two paragraphs o{Hick, p. 50.) He gives as an example a king who invites two of his councillors, A and B, to draw up lists of the sorts of quality they think a perfect chancellor has. Their lists turn out to be identical, except that A included in his list the word ‘existence’ which does not appear in B’s list. Malcolm invites us to recognize that no description is given in A’s list which is not also given in B’s. W e can imagine the kind of argument that might occur between A and B, if A were to maintain that his list was more complete than B’s:

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‘Your list,’ A may complain, ‘leaves out a quite vital quality—that of existence.’ ‘That’s not a quality,’ B may retort. ‘We’re not interested in appointing non-existent candidates!’ A: ‘But that’s my point. That’s just why existence is such a vital quality. No candidate who didn’t exist would be worth considering.’ B: ‘Now you’re just playing with words. Someone who didn’t exist wouldn’t be a candidate for chancellor. But he wouldn’t be a candidate for being a candidate, nor a candidate for being a candidate for being a candidate ... My point is, he wouldn’t even be a someone... there wouldn’t even be a “he” to be or fail to be a someone. There would be nothing of which we could say either that it has or that it lacks any quality. To say of something that it has or lacks some quality you have to be able to refer to it and say “This has quality-” or “This lacks quality—But if you refer to something and say “This exists’ ’ what you say is quite empty. Whereas if you say of it “This does not exist” you contradict yourself. What B’s reasoning points to is that existence is not a property of individuals. For, if it were, one could point out or otherwise refer to an individual and go on to say of it whether or not it had that property. But, of course, one can only point out or otherwise refer to existing individuals. So existence cannot be a property an individual may or may not have. It can only be a property of existing individuals, of which indeed it would be an essential property. But nothing except confusion is likely to be accomplished by saying this. It would be better to say existence was a property of classes (having at least one member) or of concepts or general terms (having something to which they can truly be applied), or something of that sort. And it does seem right to yield to the temptation to say that, when you say, e.g. ‘God exists’, you are saying something about something. But, if you are, it has to be about the very thing you would be saying something about if you said ‘God does not exist’. That cannot be an individual. But it could be a class, concept, general term, or something of that sort. Not only, then, does Descartes not establish his premiss that existence is a perfection but it seems that premiss is actually false. For it would only be true if existence were a property, attribute or whatever. And I have given reasons for saying that it is not a property of the sort it would have to be to be a perfection. We have not discussed whether or not the argument is valid. In one way, however, this turns out not to be a separate question. Some have claimed the argument to be invalid because there is no logically proper way of formulating the claim that existence is a perfection. Contemporary logicians largely agree that, in stating the logical form of arguments whose validity or invalidity depends upon the relations of predicates to one another, ‘exists’ should not be treated as a predicate. In Russell’s predicate logic, for instance, ‘Some tame tigers growl’ would be taken as meaning ‘There is at least one individual which is a tiger, tame and growls’. Whereas ‘Tigers exist’ would be taken to mean ‘There is at least one individual which is a tiger’. There is no coherent formulation of the Cartesian version of the Ontological Argument in the terms of Russellian predicate logic. But, as the case for saying the argument is therefore invalid

Ontological Arguments

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is the same as the case for rejecting the premiss that existence is a perfection, we need not consider it further here. Not all versions of the Ontological Argument assume that existence is an attribute. Professor Norman Malcolm has suggested that there is in Anselm’s writings a version of the argument which makes no such assumption. We shall now turn to Malcolm’s defence of this argument. Further reading In this section we have been touching upon some fundamental problems of philosophical logic. And there are at least apparent difficulties with my state¬ ment of why existence is not a property of individuals. But rather than attempt to add the necessary qualifications and clarifications here I shall mention some other treatments of this problem to which you may turn if you are not satisfied with mine. G. E. Moore: ‘Is Existence a Predicate ?’ Proceedings of the Aristotelian Society, Supplementary Volume, 1936. This paper is reprinted in a useful collection, The Ontological Argument, ed. Alvin Plantinga, Macmillan Papermac, 1968. J. Schaffer: ‘Existence, Predication and the Ontological Argument’, Mind, 1962. D. F. Pears:‘Is Existence a Predicate ?’ in Philosophical Logic, ed. P. F. Strawson, Oxford University Press, 1967. Jonathan Barnes: The Ontological Argument, Macmillan, 1972, Ch. 3.

5.3

Anselm’s ‘Second’ Ontological Argument In his paper ‘Anselm’s Ontological Arguments’, Professor Norman Malcolm suggests that we may detect two versions of the Ontological Argument in Anselm’s writings. As the first version is open to objections similar to those raised against that of Descartes, we need not examine it in detail. You will find Malcolm’s account of the second version in Section II of his paper {Hick, pp. 51-7). When you have read it through I suggest you look carefully at the summary of the proof given on p. 56. Having done this I’d like you to state the premisses of the argument summarized in that middle paragraph ofp. 56.

What we are trying to do at this stage is to note the assumptions of the argument. These are: 1 God is a being a greater than which cannot be conceived; 2 whatever comes into existence is either caused to come into existence or happens to have come into existence; 3 whatever ceases to exist is either caused to go out of existence or happens to have gone out of existence; 4 anything dependent on chance or other factors is limited; 5 the concept ‘God’ is not self-contradictory. To show that these are the assumptions of the argument would be to show how the rest of the reasoning offered by Malcolm is inferred from them. Try now to construct Malcolm’s argument, taking these five assumptions as your startingpoint.

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Here is how I think the argument is derived from these assumptions. Firstly, from (1), (3) and (4) we derive, on Malcolm’s reasoning, (i) ‘IfGod exists, His existence is necessary’. For, were God to cease to exist He would either have been caused to go out of existence or happen to have gone out of existence, in either case He would be then a limited being. But by definition God is not a limited being, since such a being would not be one a greater than which cannot be thought. Hence, Malcolm infers, (i) ‘IfGod exists, His existence is necessary’. By similar reasoning from (1), (2) and (4) he arrives at the conclusion (ii): ‘IfGod does not exist, His existence is impossible.’ Now we can construct a formal argument: (i) If God exists, His existence is necessary (from 1,3 and 4) (ii) if God does not exist, His existence is impossible (from 1,2 and 4); (iii) either God exists or He does not exist; (iv) either God’s existence is necessary or it is impossible (from i, ii and iii) (v) God’s existence is not impossible (from 5); (vi) God’s existence is necessary (from iv and v); (vii) it is necessarily true that God exists (from vi). This is the argument which we are invited to consider as a proof of God s existence. We may consider it in three stages:

A Are the assumptions 1—5 of the argument true as a matter of established fact ? B Do premisses (i), (ii) and (v) follow from these assumptions ? C Is the formal argument (i)-(vii) valid ? I’d like you first to consider, then, whether the truth of any of the premisses 1-5 is in doubt.

A

Assumptions (1) and (4) are put forward as analytically true, as explanations of the meaning of the words ‘God’ and ‘limited’ respectively. Assumption (5) is discussed by Professor Malcolm later on in his paper. (See Hick, pp. 64-6.) I think he is right to say that there is no onus on him to establish the non-contra¬ dictoriness of a concept which has a place in the thinking and in the lives of human beings. Matters might be different where divine omnipotence is spelt out in a certain way or where a theologian is trying to articulate a detailed conception of the deity. But even here it will be in virtue of apparent inconsis¬ tencies that some argument will be called for. Where there are not even apparent inconsistencies in the offing there is no case to answer. I think, then, that there is no reason to doubt assumption (5). Malcolm treats (2) and (3) as symmetrical. But there is an important a-symmetry between coming into existence and going out of existence. There is something self-contradictory about the idea of a being bringing itself into existence. For it would have to have existed prior to its existing, which is logically impossible. But there is nothing self-contradictory about the idea of a being putting itself out of existence. That is what many people think suicide is. And there is nothing

self-contradictory about that idea. Assumption (3), is, it seems, at least ambiguous. It may mean ‘caused to go out of existence by something else'. Or it may mean ‘caused to go out of existence in any way'. On the first reading it is not true, since there are at least possible cases

where something goes out of existence but where it is neither true that something

Ontological Arguments

else caused it to go out of existence nor true that itjust happened to go out of existence. It is not an established fact that nothing can destroy itself. But the second reading is the more natural one and, since that covers the possibility of self-destruction as well, assumption (3) is, so understood, true.

B

Let us not drop the point, however, but press it to this next stage of our inquiry. Do you think that premisses (i), (ii) and (v) follow from these assumptions 1-5 ? Particularly, do you think that, if assumption (3) is taken in the sense in which it is true, premiss (i) can be derived ?

I shall, for the sake of continuity, deal with the particular question first. Premiss (i) is arrived at by a subsidiary argument from assumptions 1,3 and 4. But it can only be derived from assumptions 1, 3 and 4 if (3) is taken in the sense in which it is false. For if (3) is taken in the sense in which it is true, the objection, that the terms on which God could cease to exist would require Him to be limited, does not apply. For were God to bring about His own non-existence that would not prove Him ‘limited’. On the contrary He would be limited if He could not do this. Ifone understands as ‘limited’ any being who cannot perform whatever he wishes to perform, and understands by the remark that God is ‘omnipotent’ that God is in precisely in this respect unlimited, one will be led to quite the opposite conclusion from that expressed by Malcolm’s premiss (i). For that premiss must be understood as meaning ‘If “God exists” is true, “God exists” is true as a matter of logical necessity’. It must mean this, or there would be equivocation at (v). For (v) means ‘It is logically possible, i.e. not logically impossible, that “God exists” is true’. And the inference from (vi) to (vii) depends on ‘It is necessarily true that God exists’ being just another way of saying ‘God’s existence is necessary’. So ,then, to avoid equivocation premiss (i) must be understood as meaning ‘If “God exists” is true, “God exists” is true as a matter oflogical necessity’. The opposite conclusion to which, ifone understands God’s unlimited nature in the way I have suggested, one will be led is that if ‘God exists’ is true it can be no more than a contingent fact that it is true. And if something is a ‘contingent’ truth it is precisely contrasted with those truths which are so as a matter oflogical necessity. My argument for this conclusion is quite simple. If God can do anything— except, let us suppose, what is self-contradictory—then He can bring about His own non-existence. His continued existence depends, if He exists, upon His not choosing to bring about His own non-existence. It seems then to be at best a contingent fact that God continues to exist. For if He is free to decide whether or not to continue to exist, it cannot be a logical truth that He continues to exist. Ifyou look, however, at Malcolm’s remarks at the top of page 55 in the Hick volume, you will find an objection to talking in the way I have done about God continuing or ceasing to exist. For God, so understood, is a being having endless duration rather than eternity. And Malcolm holds that if God is thought of as a

being than which a greater cannot be thought He must be thought of as having eternity rather than endless duration. What do you make of his argument for holding

this ?

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I must confess that I do not entirely grasp the reasoning offered by Malcolm at this point. He wants to say that ifa being has endless duration it would be to some extent limited. Ifa being has endless duration, he reasons, the following assertions about it—however manifest their falsity—will at least make sense: (a) ‘.. .it will cease to exist’. (b) ‘something will cause it to cease to exist’. I think Malcolm infers that (b) will make sense on any view on which (a) makes sense. I do not know whether Malcolm holds that self-contradictory assertions ‘make sense’ or not. If he supposes they do not, I would deny the inference. For (b) isself-contradictoryifitis being asserted of an unlimited being that something apart from itself will cause it to cease to exist. Let us suppose that self-contradictory assertions make sense but are manifestly false. In that sense of‘make sense’ I would allow that both (a) and (b) make sense as statements about an unlimited being. Here I am not confident how the argument goes. But Malcolm appears to take the view that, if (b) even makes sense when asserted of a being, then that being is more limited than one of whom it does not even make sense. The idea seems to be that something has a property to an absolute degree if it makes no sense to suppose it lacks it. But this way of thinking leads to absurdities. It makes no sense to say of a number that it is wanting in virtue. But no one in his right mind would infer from this that numbers are absolutely virtuous. I do not think that Malcolm succeeds in showing that a being, to be that than which a greater cannot be thought, must have eternity rather than endless duration. Still, the argument might be patched up by making ‘God is eternal’ an assumption having the same status as ‘God is that than which a greater cannot be thought’. If we call it assumption (6) we can then ask whether premiss (i) follows from it or from it together with some of the other assumptions 1-5. Do you think it does follow that ‘If “God exists” is true, “God exists” is necessarily true’, given this further assumption ?

It might be thought that if God is eternal, that means it would be nonsense to suppose He might ever cease to exist. Hence it might seem that if God exists His existence is necessary. For it would in that event make no sense to contemplate His going out of existence. It might seem therefore that premiss (i) can be inferred from this further assumption alone. Unfortunately, however, the supposition that God does exist or does not exist at this or any other time is exposed to precisely the same charge as the supposition

that He might cease to exist at some future time. If, that is to say, we do assume that by ‘God is eternal’ all talk of God which implies that He is a temporal being is ruled out as making no sense, this goes equally for present-tense talk about God as future-tense talk about God. But Malcolm himself, in deriving his premisses (i) and (ii) must be using the words ‘exist’ and ‘exists’ in a tensed way. For his argument was that if (at a given time—say the present) God does not exist, then neither at that nor any later time can He come into existence: hence if He does not exist, His existence is impossible. Again, if God does exist at any given time then neither then nor thereafter is it possible for Him to cease to

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exist. So it seems that this further assumption that God is eternal, so far from licensing these premisses, rules them out as nonsensical. I have brought out the temporal character of the assertions made about God in Malcolm’s defence of these premisses. But it might be said that what appears to be a present tense, for instance in ‘God exists’ or ‘God does not exist’ is in fact not such but the timeless so-called present tense. The ‘is’ in ‘3 is the successor of 2’ is such a timeless or tenseless use of that word. And in the same way the ‘exists’ in ‘God exists’ might be construed as a ‘timeless’ use of the word ‘exists’. But now we will have a short way with the idea that God could come into or go out of existence. This further assumption now displaces the first four of our previous assumptions. For it is now because it makes no sense to conceive of an eternal being as one which could come into existence or go out of existence that the argument can be restated as follows: (i) ‘God exists’ is either eternally true or eternally false; (from assumption 6) (ii) it is eternally false that God exists if the concept ‘God’ is self-contradictory; (iii) the concept‘God’is not self-contradictory; (from 5) Hence (iv) It is eternally true that God exists. With this argument we have come some way from Malcolm and lost touch with Anselm altogether. Still, what do you make ofit as a proof ofGod’s existence ?

We are taking premisses (i) and (iii) as established, (ii) seems solid as well, since analytic truths are eternal truths, being truths about concepts, and if the concept ‘God’ is self-contradictory it will be an analytic truth that God does not exist. Hence, ifthe concept ‘God’ were self-contradictory, it would be eternally false that God exists. The argument, however, is not valid. 11 contains a fallacy known by logicians as the ‘Fallacy of Denying the Antecedent’. One can consistently maintain both that the statement ‘God exists’ is eternally false arc*/that the concept ‘God’ is free of contradiction. Nor does premiss (ii) deny this. It would lose its solidity if it did. The fallacy is involved in inferring from (ii) and (iii) that it is not eternally false that God exists. The form of the argument is: p, ifq notq Hence notp If you have done some logic you will be familiar with this fallacy. If not, perhaps I can bring out the error by offering you an argument having the same form but where it is perhaps clearer that the conclusion does not follow from the premisses: Ifyou have stolen you have committed a crime; you have not stolen; hence, you have not committed a crime. Since there are many other crimes than stealing it is quite consistent with the premisses of this argument being true that its conclusion should be false. The argument is, in short, not valid. And neither is that from (ii) and (iii) to ‘It is not eternally false that God exists’.

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We have not yet considered whether the formal argument I stated on page 29 is valid. This has been disputed by some philosophers. They have charged that Malcolm equivocates between two senses of‘necessary’. My own view is that this is not strictly correct and that Malcolm, in that argument, is speaking of logical necessity throughout. But, if you remember, I found it desirable on page 30 to re-express the vague assertion ‘God’s existence is necessary as a clear statement of logical necessity: ‘ “God exists” is true as a matter of logical necessity.’ I think that better reflects Malcolm’s intention. But if my rephrasing did not express what Malcolm meant by ‘God’s existence is necessary’ then he would in that context have been using ‘necessary’ in a different sense from that in which statements are logically necessary. And if he was, he would be open to the charge of equivocation. And his argument would have been invalid for that reason. As it is, I think he is not liable to the charge of equivocation. My own view, therefore, is that the argument is valid. I must, however, leave you to satisfy yourself on this point. My objection to Malcolm has been that he does not establish the truth of the premiss that if God exists, His existence is necessary. I have tried to show that it follows neither from God being that than which a greater cannot be thought nor from God being eternal. On the contrary, I suggested, if God is unlimited in what he can do, it would be more reasonable to suppose that if‘God exists’ is true, it is at best a contingent truth. The argument is transformed once we introduce ‘God is eternal’ as a further premiss, though this might be the right way for Malcolm to rejoin to my suggestion that an unlimited being could bring about its own non-existence. But I was unable to find an alternative argument using the premiss ‘God is eternal’ by means of which it might be proved that God exists.

.4

Is an ontological proof of God’s existence possible? Serious consideration of ontological arguments demands of us a careful attention to detail. In the absence of such attention to particular arguments, we cannot consider the general question as to the possibility of an ontological proof without oversimplifying the issues. So ifyou have skipped over some of the discussion of particular attempts to provide an ontological proof of God s existence, you are likely to have considerable difficulty in following the discussion of this section. We have already considered, at least briefly, one attempt to show that it would be impossible to produce a proof of God’s existence by means of an ontological argument. Kant’s argument to this effect rests, I suggested (see section 5.2), on the assumption that all existential propositions are synthetic. A valid onto¬ logical argument would have for its conclusion an analytic existentialjudgement. Since there cannot be such analytic cxistentialjudgements, there can be, on this view, no ontological proofs. But since there is good reason to believe that there are statements about existence (to the effect either that something does or that it does not exist) which are analytic there is good reason to believe that there can be ontological proofs. Hence we should, I think, reject as failing to prove

that there can be no proof of God’s existence by means of an ontological argument any argument which assumes that ontological arguments in general must fail.

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We should reject, then, two sorts of argument: (a) Arguments which assume that all existential propositions are synthetic; and (b) arguments which have the consequence that there can be no ontological proof of the existence of any thing. In his editorial Introduction to The Existence of God, Hick offers the following argument for supposing that an ontological proof of God’s existence is impossible:

The basic philosophical objection to this reasoning is well-developed and widely agreed. The objection is that one is never entitled to deduce from a concept that anything exists which corresponds to that concept. The nature of thought on the one hand and of extra-mental reality on the other, and of the distinction between them, is such that there can be no valid inference from the thought of a given kind of being to the conclusion that there is in fact a being of this kind. The mind is free to form concepts of various species of beings which do not exist, and it is impossible to tell from inspection ofa concept alone whether or not there is an extra-mental entity answering to it. Only experience can determine this.* 1

Do you think this objection to the possibility of an ontological proof of God’s existence is a good one ?

You will, I hope, have noticed that the objection Hick states is not essentially different from that made by Kant. Indeed, the final sentence of the paragraph the rest of which I have just quoted, credits Kant with just this objection. Saying that only experience can determine whether or not there is an extra-mental entity answering to a concept is just another way of saying that statements to the effect that some extra-mental entity exists cannot be analytic. But it would not be quite true to say that the objection Hick states fails for just the reasons we have noted in connection with Kant. For Hick makes a distinction, in his statement of the objection, between what we might call ‘thought-entities’ and extra-mental’ entities. And it is not so clear that the reasons given on page 26 for rejecting Kant’s objection apply equally to the claims: (i) There can be no ontological proof of the existence o (extra-mental entities.’ (ii) ‘All statements asserting the existence ofextra-mental entities are synthetic.’ It is not so clear, since it could be argued that the kind of entities for which ontological proofs can be given are ‘thought-entities’. It could be argued, for instance, that although it can thus be proved that there exists a prime number between 30 and 33 and that the existential statement ‘There is a prime number between 30 and 33’ is analytic, numbers are not ‘extra-mental’ entities. It is significant, I think, that we had to resort to statements about mathematical entities in order to find counter-examples to the Kantian thesis. And we shall return to this point. But even if our counter-examples could thus be rendered harmless against the thesis (ii), that of itself would not establish the thesis. Why should not the statement ‘God exists’ be the only statement about an ‘extra-

1

J. Hick (ed.), The Existence of God, Collier-Macmillan, New York, 1964, p. 3.

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mental’ entity which is analytic ? If we want a proof that an ontological proof of divine existence is impossible we should not assume, as Kant and Hick seem to do, that the existence of‘extra-mental’ entities must be known through experience if it is to be known at all. However, there is another way of objecting to the possibility of an ontological proof. An ontological argument for the existence of a god needs to start with some statement about the concept ‘god’. Such a statement, being analytic, will be universal in character. Thus the statement ‘God is eternal’ must be under¬ stood in such a context, not as ascribing some property to an individual (for then the existence of that individual would already be presupposed and the question at stake begged), but as a statement like one of the following: ‘All gods are eternal.’ ‘Anything worthy of the name “God” is eternal.’ ‘Whatever is God is eternal.’ But, though the premiss about the concept ‘God’ is universal, the conclusion of an ontological argument is not. It is not, like the premiss, about all things of a certain kind. It asserts that there is at least one individual who is (worthy of the name of) God. Logicians agree that at least certain universal statements should be construed as hypothetical in form. Thus ‘All triffids are plants’ should be construed as ‘ F or any individual whatever, if it is a triffid, it is a plant’. Now such an hypo¬ thetical statement as this does not imply that there are members of the class mentioned in its antecedent. In the case of‘All triffids are plants’ it is not implied that there are any triffids. No more does such a statement as ‘God is eternal’ imply that there is a god. It is a universal hypothetical statement as is any analytic statement of the kind which will serve as the main premiss of an ontological argument. By contrast with such universal hypothetical statements, there are statements which are called particular. Such statements as ‘Some politicans are corrupt’ and ‘My dog is a spaniel’ are, by contrast, particular. Particular statements assert or imply the existence of something. The existential import—to use a favoured phrase—of‘Some politicians are corrupt’ is that there are politicians and that there are men that are corrupt. Universal hypothetical statements, by contrast, lack existential import. ‘All triffids are plants’ does not imply that there are plants any more than it implies that there are triffids. ‘God is eternal’ does not imply either than there is a god or that anything is eternal, only that if anything is a god, it is eternal. Given, then, that statements which are universal (hypothetical) do not have existential import and that those which are particular do, particular statements cannot be validly inferred from universal ones. Anyone who inferred a particular conclusion from premisses which were all universal (hypothetical) would be guilty of importing an implication into his conclusion which is nowhere to be found in the premisses, namely, that there is at least one particular of a kind mentioned in the premisses. This inference would be an invalid one. The fallacy involved is, appropriately enough, labelled by some logicians as ‘the Existential Fallacy’.

Ontological Arguments

This fallacy is involved, for example, in the following argument: All trespassers are prosecuted There are trespassers who are prosecuted. The premiss of this argument might be true and its conclusion false. It does not follow from the fact that any trespasser would be prosecuted that anyone does trespass. Now the ontological argument has premisses which are wholly a priori. But for it to be a valid argument having a particular conclusion it must have a particular premiss. But what particular premiss could it have which is also established a priori ? Only, it seems, a premiss which is itself the conclusion of another onto¬

logical proof. Yet just the same problem will arise with this other ontological proof, with the ontological proof that establishes its a priori particular premiss, and so on to infinity. The alternative is that the ontological argument must be invalid. Moreover, it seems, its invalidity must involve this particular fallacy, the Existential Fallacy. Do you see how this fallacy is involved in the following arguments ? A

God is a being having all the perfections. Necessary existence is a perfection. God necessarily exists.

B

God is eternal. Eternal beings are beings whose non-existence is inconceivable. God’ s non-existence is inconceivable. God exists.

C

God is that than which a greater cannot be thought. Whatever is that than which a greater cannot be thought exists in all possible worlds. Whatever exists in all possible worlds exists in this world God exists in this world.

None of these arguments would be invalid, of course, if the first premiss were not construed as a universal statement. But any particular statement about God already implies His existence. To construe these premisses as particular, however, would be question-begging. For the statement ‘God is eternal’, so construed, would be true only if God existed. So to prove that ‘God is eternal’ is true one would need already to have proved that God existed. And any argument whose premisses can only be established once the conclusion has been established cannot be used to demonstrate the truth of the conclusion. We need, then, first to make explicit that these first premisses are universal in character. Neither Descartes, nor I believe Malcolm, have realized that this is necessary. But once this is realized and made explicit, it is not difficult to state

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what may be validly inferred from these arguments. I suggest you now try to state what does follow from arguments (A), (B) and (C).

Here is what I think are valid versions of these arguments: A

Whatever is worthy of the name ‘God’ has all the perfections. Whatever has all the perfections has necessary existence. Whatever is worthy of the name ‘God’ has necessary existence.

Note: it is not implied by this conclusion that there is anything worthy of the

name ‘God’. B

Whatever is worthy of the name ‘God’ is eternal. Whatever is eternal is something whose non-existence is inconceivable. Whatever is worthy of the name ‘God’ is something whose non-existence is inconceivable.

C

Whatever is worthy of the name ‘God’ is something than which a greater cannot be thought. Whatever is that than which a greater cannot be thought exists in all possible worlds. Whatever exists in all possible worlds exists in this world. Whatever is worthy of the name ‘God’ exists in this world.

There are, as I have indicated, other ways of making the universality of the first premiss and therefore of the conclusion explicit. I have taken the premisses to be conceptual statements and therefore to be a priori, indeed analytically, true. If my reasoning has been sound, it gives some teeth to the claim that from statements about the concept ‘God’ it is not possible to prove the conclusion that God exists. There is one difficulty with the reasoning I have given which cannot, however, pass unmentioned. And that is that such reasoning appears to preclude any form of ontological argument, not simply ontological proofs of the existence of God. If then, as I earlier admitted, there are ontological proofs in mathematics, there must be something wrong with any line of reasoning which has the consequence that there cannot be. I think that this difficulty is lessened if we consider that, while it is natural enough to speak of the existence of numbers, arithmetic does not presuppose their existence. When we make such existential claims as ‘There exists an infinity of prime numbers’ or ‘There is a prime number between 30 and 33' we can re¬ express what we are saying in non-existential terms. We might say, for instance, that a complete list of the prime numbers cannot be drawn up or that anyone who counts properly from 30 to 33 will mention a prime number. And one could attempt to prove these propositions, for instance by showing the absurdity ofsupposing them to be false, as well as one could prove their existential equivalents. We can distinguish between what we may term ‘strong’ and ‘weak’ existential claims. A strong existential claim is one which cannot be re-expressed in terms

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which are not either covertly or explicitly existential. For example, terms such as ‘find’, ‘refer to’, ‘name’, and so on, are covertly existential. ‘The California Condor can still be found’ implies that species still exists. Certain uses of the verb ‘to be ’are explicitly existential, i.e. the verb ‘to exist’ may in those cases be substituted for the verb ‘to be’. A weak existential claim is one which can be re¬ expressed in non-existential terms. For example, the claim ‘There exists an infinity of prime numbers’ can be re-expressed by the claim ‘No one could compile a list of all the prime numbers’ or ‘The series of prime numbers admits of indefinite extension’. The difficulty I have mentioned about ontological proofs of divine existence is that they attempt to draw particular conclusions from premisses which, in the nature of the case, must be wholly universal. And the difficulty with the difficulty is that, if it really were one, it would preclude any kind of ontological proof. We might be able to off-set the difficulty with the difficulty by distinguishingweak and strong existential claims. For if the difficulty were only with ontological proofs of strong existential claims and existential claims which admit of onto¬ logical proof are invariably weak, we should be able to put aside the difficulty with our difficulty. It might be, that is to say, that weak existential claims may be inferred from universal premisses. Let us explore this way of defending the difficulty I mentioned for an ontological proof of God’s existence against this objection. First, we need to investigate the distinction I drew between strong and weak uses of existential terms. Then we shall consider whether it is reasonable to suppose that ontological proofs are possible only for weak existential claims. We may combine the first objective in a self-assessment exercise.

Exercise 2

From what you have gathered from my account of the distinction, which of the following should be regarded as strong existential claims and which weak ones ? In the case of the weak ones, what non-existential formulations would you think could be substituted ? (i) There is a distinction between universals and particulars: (ii) There is an idea ofgod as that than which a greater cannot be thought. (iii) There is no golden mountain. (iv) There is no proof of the existence of a devil. (v) There is no fifth movement to Beethoven’s Fifth Symphony. (vi) Dodos are now extinct. (vii) There is a difference between any two individuals each of which is identical with one of two different individuals. (viii) Pickwick exists.

Comments

(1) is a weak use of‘is’ in an existential sense, I would say. It might be re-expressed by saying ‘No universal is a particular’ or ‘One must distinguish between universals and particulars . If one took the ‘is’ to be a strong use, one would have the distinction existing over and above the things distinguished. One would be

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saying there was a distinction between the distinction and the things dis¬ tinguished. And that, of course, would be a further distinction. And so on, to infinity. To avoid such a regress to infinity one must, I think, construe any talk about the existence of distinctions in a weak sense. (ii) is also a weak existential ‘is’. We can rephrase it by saying ‘Some think of god as that than which a greater cannot be thought’. (iii) is a strong use of‘is’. Such a sentence as ‘No one has ever seen a golden mountain’ is by no means equivalent, neither is ‘No one ever will see a golden mountain’. The non-existence of a golden mountain does not follow from either of these. (iv) is a weak use of the existential ‘is’. Although we sometimes talk of discovering proofs, as though they were there all the time waiting for someone to notice them, I think we would accept as equivalent such a rephrasing as ‘No one has proved the existence of a devil’. (v) is again a weak use, I would say. If, and only if, Beethoven never wrote a fifth movement then there is no such movement. If he wrote one and it was subsequently lost we should not, I am assuming, say that it no longer exists. But perhaps we have no firm conventions here. Works of art such as paintings do exist in a strong sense. Poems, symphonies and so on, precisely because they are not identical with some spatio-temporal thing such as their manuscripts, are more elusive. That is why one is inclined to say that if the manuscript and all copies of a symphony are destroyed then the symphony has been irretrievably lost rather than that it from then on ceased to exist. (vi) is clearly a strong existential claim. To be extinct is not any longer to exist. (vii) is a weak use of the existential ‘is’. It might be re-expressed by saying that, if any two individuals w and x are such that w is identical withy and x is identical with z but wherejy is not identical with £ ,then those two individuals w and x are not identical. It is indeed a logical truth about the relation of identity. The existential claim (‘There is a difference ... ’) is proved true by a proof of the logical truth I have just mentioned. Such a proof would be an ontological one. But the existent thus established (the distinction) is only a courtesy existent. As we have seen (see my comment on (i) above), we face serious difficulties if we suggest that distinctions exist in just the sense that the things distinguished may do. (viii) is, again, a weak use of the word ‘exists’. ‘Pickwick exists in fiction’ means that there is an individual known as ‘Pickwick’ mentioned in a recognized work of fiction. Pickwick is represented as a nineteenth-century gentleman. We are encouraged to think of him imaginatively. And if we do so we will quite naturally be inclined to think of him as having a mother. But, so far as I know, Dickens never mentions her. So ‘Pickwick’s mother exists in fiction’ is false. Nothing exists in fiction except what is mentioned in a recognized work of fiction. I think it is quite clear that ‘God exists’ is a strong existential claim. In the case of at least some weak existential claims (see, for instance, my comment on (vii) above), an ontological proof seems possible. In the case ofsuch claims a particular conclusion can be drawn from wholly universal premisses because it is another way of expressing a universal statement which follows from those premisses. It is not, then, irreducibly particular. For that reason no fallacy need be

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involved in ontological reasoning where the conclusion is a weak existential claim. In other words the objection I mentioned to the possibility of an ontological proof of God’s existence applies only to ontological arguments whose conclusion is a strong existential statement. It is proofs of that sort which seem, for the reasons I gave earlier, to be impossible. Part of the difficulty with trying to produce such a proof is, I suggested, that such an ontological argument needs something it cannot have, namely a particular premiss whose truth can be established a priori. This difficulty could be avoided if we were able to establish the truth of the particular premiss a posteriori. But then we would be engaging in a diffei ent project, that of attempting a cosmological rather than an ontological proof of God’s existence. VVe must now consider the prospects for carrying out that project with success. Further reading

The Ontological Argument is one of the most discussed arguments in the history of philosophy. I will mention here only two books on the subject, both inexpensive and both valuable in different ways: Jonathan Barnes: The Ontological Argument, Macmillan, 1972. Alvin Plantinga (ed.): The Ontological Argument, Macmillan Papermac, 1968. The book by Barnes deals with a number of the issues we have touched on both in greater detail and with more rigour. The Plantinga volume is a collection of essays, including some discussions of Malcolm’s paper.

6

COSMOLOGICAL ARGUMENTS

A ‘cosmological’ argument, in contrast with an ‘ontological’ one, begins with a premiss whose truth is recognized a posteriori. It is a premiss about the universe. Hence the name of this kind of argument is ‘cosmological’, being derived from the Greek word ‘cosmos’ which means ‘universe’ or ‘world’. The most famous such arguments are the Five Ways ofThomas Aquinas. We shall be looking at the Third Way and also at a more recently produced cosmological argument, that of Professor Richard Taylor. There are similarities between them, so you could without much loss omit discussion ofone or other of them. I think Taylor’s argument is the more instructive of the two and have included the most favoured of Aquinas’ Ways at least partly for historical reasons.

6.1

Aquinas’ Third Way You will find Aquinas’ statement of this Third Way he offers of proving the existence of God on page 84 of the Hick volume. There is, as you will find on page 89, some helpful commentary on this argument by Father F. C. Copleston. I suggest you read these short passages now and make a list of those assumptions which you think are made by Aquinas.

These are the assumptions which, it seems to me, are made by the Third Way: (i) There are in nature things which are generated and corrupted; (ii) it is possible for anything which is generated and corrupted to exist and it is possible for it not to exist; (iii) anything for which non-existence is possible does at some time not exist; (iv) whatever does not exist comes into existence only through something already in existence; (v) a necessary being either contains its necessity within itself or derives it from another; (vi) it is impossible to go on to infinity in necessary things which have their necessity caused by another. Assumption (i) is the a posteriori premiss from which the argument begins and, since the argument purports to be demonstrative of God’s existence, marks the argument as a ‘cosmological’ one. If (i) is true, so the argument purports to show, there must be a being ‘having ofitselfits own necessity’, having, that is to say, underived necessity. Can you see how the conclusion is derived, using these assumptions ?

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We can state the argument of the Third Way as follows: 1 There are contingent things (things which are generated and corrupted); (from (i)) 2 contingent things may or may not exist; (from (ii)) 3 if anything may not exist, there is some time at which it does not exist; (from (iii)) 4 if anything is contingent there is some time at which it does not exist; (from 2 & 3) 5 at some time there were no contingent things; (from 4) 6 contingent things owe their existence to a necessary being; (from 5 and (iv)) 7 there is a necessary being whose necessity is underived, whom we calTGod’. (from 6,1, (v) & (vi)) Once again, let us consider this argument in two stages. Firstly, let us consider whether its assumptions are true as a matter of established fact. Are there any you think are questionable on this score ?

The first assumption is that there are ‘contingent’ things, things which are liable to corruption, i.e. to decay and destruction. Such things, as assumption (ii) makes explicit, may or may not exist. And (iii) asserts that, for every such contingent thing, there is some time at which it does not exist. The truth of these assumptions seems to be beyond dispute. Assumption (iv), however, is a statement of a principle whose truth seems not to be a matter of established fact. It is not clear why there must be, for everything that comes into existence, some cause of its existence. On the other hand a complaint against the argument simply on account of this assumption might lay one open to the charge of obscurantism. For if that assumption were supposed false one would seem committed only to the view that there are some things for whose existence there is no causal explanation, whose existence is therefore presumably mysterious. So let us simply note here that no proof of this assumption is given nor does it seem readily available. (v) and (vi) need more explanation. Aquinas evidently thought that it was in some sense impossible that human souls should cease to exist and that in a corresponding sense souls were necessary beings. But their necessity was, for him, of a derived sort. Many will find difficulties with the suggestion that there are beings having a derived necessity. For, to the extent that their necessity is derived they would seem to depend for their existence upon something independent of themselves and thus to be to that extent contingent beings. We may, however, simplify matters for ourselves by noting that Aquinas’ argument does not commit him to such derived necessary beings. If a necessary being had to contain its necessity within itself then his argument could be shortened. He could move directly from step 6 of his argument to his conclusion using only assumptions (i)-(iv). Assumptions (v) and (vi) guard against an objection he presumably thought might otherwise be levelled against him.

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With the reservation expressed about assumption (iv) we may take the assumptions of the argument as established and pass to the question whether it is valid. Is there any point in the argument where you think an invalid inference is drawn ?

Aquinas argues that there are contingent things, since generation and corruption take place, and that of any given contingent thing it is true that at some time it does not exist. He concludes from this as follows: ‘Therefore, if everything can not-be, then at one time there was nothing in existence.’ This is the step from 4 to 5 in the argument I have outlined. Does 5 follow from 4 ? Is it inconsistent to suppose that it is true that no given contingent thing exists at all times and false that there is a time at which no contingent things exist ? What do you think ?

I think there is no inconsistency here and that the argument is therefore invalid. The fallacy in Aquinas’ reasoning may be brought out by showing that there is a logically analogous argument which is also, but more obviously fallacious. He argues from the fact that, for every given contingent thing, there is some time at which it does not exist, to the conclusion that there is some time at which all contingent things do not exist. Substitute ‘boy’ for ‘contingent thing’, ‘girl’ for ‘time’ and ‘he loves’ for ‘it does not exist’, and we have the following argument: For every given boy, there is some girl he loves; there is some girl whom all boys love. If this last argument does not strike you as fallacious, note that in relation to the ‘some girl’ mentioned in the conclusion one can ask ‘Which girl ?’ and get an answer. But there is no particular girl whose name could be demanded of someone who asserts the premiss. The ‘some’ of the premiss means ‘some ... or other’ while ‘some’ in the conclusion means ‘a particular ...’ Similarly, one can ask of the ‘some time’ mentioned in the conclusion of Aquinas’ argument ‘What time ?’ and get some date for an answer. But there is no one date which could be men¬ tioned in connection with the ‘some time’ of the premiss. It is, moreover, not clear how this deficiency in the argument could be made good. Some other route to the conclusion that there was a time at which no contingent thing existed would need to be found. Ifit were possible to establish such a conclusion then the existence of contingent things might require an explanation which would be favourable to religious belief. Professor Taylor does not make this fallacious step of Aquinas. But, like Aquinas, he is concerned to argue that, unless we suppose a necessary being, no explanation can be given of the existence of the world.

Cosmological Arguments

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Taylor’s cosmological argument I will now quote at length from that part of Professor Taylor’s book Metaphysics where he offers a cosmological proof of God’s existence. It is quite a complex argument but, as Taylor writes so well, I will let him speak for himself rather than summarize any part of it for you. I have numbered the paragraphs so that when we discuss the argument we may refer back with ease. I suggest you now read the argument through carefully, several times if necessary, and then try to summarize it in such a way as to bring out its assumptions and the way in which the conclusion is presented as following from them.

The principle of sufficient reason

1

2

3

4

Suppose you were strolling in the woods and, in addition to the sticks, stones, and other accustomed litter of the forest floor, you one day came upon some quite unaccustomed object, something not quite like what you had ever seen before and would never expect to find in such a place. Suppose, for example, that it is a large ball, about your own height, perfectly smooth and translucent. You would deem this puzzling and mysterious, certainly, but ifone considers the matter, it is no more inherently mysterious that such a thing should exist than that anything else should exist. Ifyou were quite accustomed to finding such objects of various sizes around you most of the time, but had never seen an ordinary rock, then upon finding a large rock in the woods one day you would be just as puzzled and mystified. This illustrates the fact that something that is mysterious ceases to seem so simply by its accustomed presence. It is strange indeed, for example, that a world such as ours should exist j yet few men are very often struck by this strangeness, but simply take it for granted. Suppose, then, that you have found this translucent ball and are mystified by it. Now whatever else you might wonder about it, there is one thing you would hardly question; namely, that it did not appear there all by itself, that it owes its existence to something. You might not have the remotest idea whence and how it came to be there, but you would hardly doubt that there was an explanation. The idea that it might have come from nothing at all, that it might exist without there being any explanation of its existence, is one that few people would consider worthy of entertaining. This illustrates a metaphysical belief that seems to be almost a part of reason itself, even though few men ever think upon it; the belief, namely, that there is some explana¬ tion for the existence ofanything whatever, some reason why it should exist rather than not. The sheer nonexistence ofanything, which is not to be confused with the passing out of existence ofsomething, never requires a reason; but existence does. That there should never have been any such ball in the forest does not require any explanation or reason, but that there should ever be such a ball does. If one were to look upon a barren plain and ask why there is not and never has been any large translucent ball there, the natural response would be to ask why there should be; but ifone finds such a ball, and wonders why it is there, it is not quite so natural to ask why it should not be, as though existence should simply be taken for granted. That anything should not exist, then, and that, for instance, no such ball should exist in the forest, or that there should be no forest for it to occupy, or no continent containing a forest, or no earth, nor any world at all, do not seem to be things for which there needs to be any explanation or reason; but that such things should be, does seem to require a reason. The principle involved here has been called the principle ofsufficient reason. Actually, it is a very general principle, and is best expressed by saying that, in the case of any positive truth, there is some sufficient reason for it, something which, in this sense, makes it true in short, that there is some sort of explanation, known or unknown, for everything. Now some truths depend on something else, and are accordingly called contingent, while others depend only upon themselves, that is, are true by their very natures and

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are accordingly called necessary. There is, for example, a reason why the stone on my window sill is warm; namely, that the sun is shining upon it. This happens to be true, but not by its very nature. Hence, it is contingent, and depends upon something other than itself. It is also true that all the points of a circle are equidistant from the center,

5

but this truth depends upon nothing but itself. No matter what happens, nothing can make it false. Similarly, it is a truth, and a necessary one, that if the stone on my window sill is a body, as it is, then it has a form, since this fact depends upon nothing but itself for its confirmation. Untruths are also, of course, either contingent or necessary, it being contingently false, for example, that the stone on my window sill is cold, and necessarily false that it is both a body and formless, since this is by its very nature impossible. The principle of sufficient reason can be illustrated in various ways, as we have done, and if one thinks about it, he is apt to find that he presupposes it in his thinking about reality, but it cannot be proved. It does not appear to be itself a necessary truth, and at the same time it would be most odd to say it is contingent. If one were to try proving it, he would sooner or later have to appeal to considerations that are less plausible

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than the principle itself. Indeed, it is hard to see how one could even make an argument for it, without already assuming it. For this reason it might properly be called a presupposition of reason itself. One can deny that it is true, without embarrassment or fear of refutation, but one is then apt to find that what he is denying is not really what the principle asserts. We shall, then, treat it here as a datum

not something

that is provably true, but as something which all men, whether they ever reflect upon it or not, seem more or less to presuppose. It happens to be true that something exists, that there is, for example, a world, and while no one ever seriously supposes that this might not be so, that there might exist

ie existence of a world

nothing at all, there still seems to be nothing the least necessary in this, considering it

7

just by itself. That no world should ever exist at all is perfectly comprehensible and seems to express not the slightest absurdity. Considering any particular item in the world it seems not at all necessary in itself that it should ever have existed, nor does it appear any more necessary that the totality of these things, or any totality of things, should ever exist. From the principle ofsufficient reason it follows, of course, that there must be a reason, not only for the existence of everything in the world but for the world itself, meaning by “the world” simply everything that ever does exist, except God, in case there is a god. This principle does not imply that there must be some purpose or goal for everything, or for the totality of all things; for explanations need not, and in fact seldom are, teleological or purposeful. All the principle requires is that there be some sort of reason for everything. And it would certainly be odd to maintain that everything

8

in the world owes its existence to something, that nothing in the world is either purely accidental, or such that itjust bestows its owr. being upon itself, and then to deny this of the world itself. One can indeed say that the world is in some sense a pure accident, that there simply is no reason at all why this or any world should exist, and one can equally say that the world exists by its very nature, or is an inherently necessary being. But it is at least very odd and arbitrary to deny of this existing world the need for any sufficient reason, whether independent of itself or not, while presupposing that there is a reason for every other thing that ever exists. Consider again the strange ball that we imagine has been found in the forest. Now we can hardly doubt that there must be an explanation for the existence ofsuch a thing, though we may have no notion what that explanation is. 11 is not, moreover, the fact of its having been found in the forest rather than elsewhere that renders an explanation necessary. It matters not in the least where it happens to be, for our question is not how it happens to be there but how it happens to exist at all. Ifwe in our imagination annihilate the forest, leaving only this ball in an open field, our conviction that it is a contingent thing and owes its existence to something other than

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itself is not reduced in the least. If we now imagine the field to be annihilated, and in fact everything else as well to vanish into nothingness, leaving only this ball to constitute the entire physical universe, then we cannot for a moment suppose that its existence has thereby been explained, or the need ofany explanation eliminated, or that its existence is suddenly rendered self-explanatory. Ifwe now carry this thought

9

one step further and suppose that no other reality ever has existed or ever will exist, that this ball forever constitutes the entire physical universe, then we must still insist on there being some reason independent of itself why it should exist rather than not. If there must be a reason for the existence ofany particular thing, then the necessity ofsuch a reason is not eliminated by the mere supposition that certain other things do not exist. And again, it matters not at all what the thing in question is, whether it be large and complex, such as the world we actually find ourselves in, or whether it be something small, simple and insignificant, such as a ball, a bacterium, or the merest grain ofsand. We do not avoid the necessity of a reason for the existence ofsomething merely by describing it in this way or that. And it would, in any event, seem quite plainly absurd to say that if the world were comprised entirely of a single ball about six feet in diameter, or of a single grain ofsand, then it would be contingent and there would have to be some explanation other than itself why such a thing exists, but that, since the actual world is vastly more complex than this, there is no need for an explanation of its existence, independent of itself. It should now be noted that it is no answer to the question, why a thing exists, to state

Beginningless existence

how long it has existed. A geologist does not suppose that he has explained why there should be rivers and mountains merely by pointing out that they are old. Similarly, if one were to ask, concerning the ball ofwhich we have spoken, for some sufficient reason for its being, he would not receive any answer upon being told that it had been there since yesterday. Nor would it be any better answer to say that it had existed since before anyone could remember, or even that it had always existed; for the question was not one concerning its age but its existence. If, to be sure, one were to ask where a given thing came from, or how it came into being, then upon learning that

10

it had always existed he would learn that it never really came into being at all; but he could still reasonably wonder why it should exist at all. If, accordingly, the world— that is, the totality of all things excepting God, in case there is a god—had really no beginning at all, but has always existed in some form or other, then there is clearly no answer to the question, where it came from and when; it did not, on this supposition, come from anything at all, at any time. But still, it can be asked why there is a world, why indeed there is a beginningless world, why there should have perhaps always been something rather than nothing. And, if the principle of sufficient reason is a good principle, there must be an answer to that question, an answer that is by no means supplied by giving the world an age, or even an infinite age.

Creation

This brings out an important point with respect to the concept of creation that is often misunderstood, particularly by those whose thinking has been influenced by Christian ideas. People tend to think that creation —for example, the creation of the world by God—means creation in time, from which it of course logically follows that if the world had no beginning in time, then it cannot be the creation of God. This, however, is erroneous, for creation means essentially dependence, even in Christian theology. Ifone thing is the creation ofanother, then it depends for its existence on that other, and this is perfectly consistent with saying that both are eternal, that 11

neither ever came into being, and hence, that neither was ever created at any point of time. Perhaps an analogy will help convey this point. Consider, then, aflame that is casting beams of light. Now there seems to be a clear sense in which the beams of light are dependent for their existence upon the flame, which is their source, while the flame, on the other hand, is not similarly dependent for its existence upon them. The beams of light arise from the flame, but the flame does notarise from them. In this sense, they are the creation of the flame; they derive their existence from it. And none of this has any reference to time; the relationship of dependence in such a case

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would not be altered in theslightest ifwcsupposcd that the flame, and with it the beams of light, had always existed, that neither had ever come into being. Now if the world is the creation of God, its relationship to God should be thought of in this fashion; namely, that the world depends for its existence upon God, and could not exist independently of God. If God is eternal, as those who believe in God generally assume, then the world may (though it need not) be eternal too, without that altering

12

in the least its dependence upon God for its existence, and hence without altering its being the creation of God. The supposition ofGod’s eternality, on the other hand, does not by itself imply that the world is eternal too; for there is not the least reason why something of finite duration might not depend for its existence upon something of infinite duration—though the reverse is, of course, impossible.

God

Ifwe think of God as ‘the creator of heaven and earth’, and if we consider heaven and earth to include everything that exists except God, then we appear to have, in the foregoing considerations, fairly strong reasons for asserting that God, as so conceived, exists. Now of course most people have much more in mind than this when they think of God, for religions have ascribed to God ever so many attributes that are not

13

at all implied by describing him merely as the creator ofthe world; but that is not relevant here. Most religious persons do, in any case, think of God, as being at least the creator, as that being upon which everything ultimately depends, no matter what else they may say about him in addition. It is, in fact, the first item in the creeds of Christianity that God is the ‘creator of heaven and earth’. And, it seems, there are good metaphysical reasons, as distinguished from the persuasions of faith, for thinking that such a creative being exists. If, as seems clearly implied by the principle of sufficient reason, there must be a reason for the existence of heaven and earth—i.e., for the world—then that reason must be found either in the world itself, or outside it, in something that is literally supranatural, or outside heaven and earth. Now ifwe suppose that the world—i.e., the totality of all things except God—contains within itself the reason for its existence, we are supposing that it exists by its very nature, that is, that it is a necessary being. In that case there would, of course, be no reason for saying that it must depend upon God or anything else for its existence; for if it exists by its very nature, then it depends upon nothing but itself, much as the sun depends upon nothing but itselffor its heat. This, however, is implausible, for we find nothing about the world or anything in it to suggest that it exists by its own nature, and we do find, on the contrary, ever so many things to suggest that it does not. For in the first place, anything which exists by its very nature must necessarily be eternal and indestructible. It would be a selfcontradiction to say of anything that it exists by its own nature, or is a necessarily existing thing, and at the same time to say that it comes into being or passes away,

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or that it ever could come into being or pass away. Nothing about the world seems at all like this, for concerning anything in the world, we can perfectly easily think of it as being annihilated, or as never having existed in the first place, without there being the slightest hint of any absurdity in such a supposition. Some of the things in the universe are, to be sure, very old; the moon, for example, or the stars and the planets. It is even possible to imagine that they have always existed. Yet it seems quite impossible to suppose that they owe their existence to nothing but themselves, that they bestow existence upon themselves by their very natures, or that they are in themselves things of such nature that it would be impossible for them not to exist. Even ifwe suppose that something, such as the sun, for instance, has existed forever, and will never cease, still we cannot conclude just from this that it exists by its own nature. If, as is of course very doubtful, the sun has existed forever and will never cease, then it is possible that its heat and light have also existed forever and will never cease; but that would not show that the heat and light of the sun exist by their own natures. They are obviously contingent and depend on the sun for their existence, whether they are beginningless and everlasting or not.

Cosmological Arguments

There seems to be nothing in the world, then, concerning which it is at all plausible to suppose that it exists by its own nature, or contains within itself the reason for i ts existence. In fact, everything in the world appears to be quite plainly the opposite, namely, something that not only need not exist, but at some time or other, past or future or both, does not in fact exist. Everything in the world seems to have a finite duration, whether long or short. Most things, such as ourselves, exist only for a short while, they come into being, then soon cease. Other things, like the heavenly bodies,

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last longer, but they are still corruptible, and from all that we can gather about them, they too seem destined eventually to perish. We arrive at the conclusion, then, that while the world may contain some things which have always existed and are destined never to perish, it is nevertheless doubtful that it contains any such thing and, in any case, everything in the world is capable of perishing, and nothing in it, however long it may already have existed and however long it may yet remain, exists by its own nature, but depends instead upon something else. While this might be true of everything in the world, is it necessarily true of the world itself? That is, ifwe grant, as we seem forced to, that nothing in the world exists by its own nature, that everything in the world is contingent and perishable, must we also say that the world itself, or the totality of all these perishable things, is also contingent and perishable ? Logically, we are not forced to, for it is logically possible that the totality of all perishable things might itself be imperishable, and hence, that the

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world might exist by its own nature, even though it is comprised exclusively of things which are contingent. It is not logically necessary that a totality should share the defects ofits members. For example, even though every man is mortal, it does not follow from this that the human race, or the totality of all men, is also mortal; for it is possible that there will always be human beings, even though there are no human beings which will always exist. Similarly, it is possible that the world is in itself a necessary thing, even though it is comprised entirely of things that are contingent. This is logically possible, but it is not plausible. For we find nothing whatever about the world, any more than in its parts, to suggest that it exists by its own nature. Concerning anything in the world, we have not the slightest difficulty in supposing that it should perish, or even, that it should never have existed in the first place. We have almost as little difficulty in supposing this of the world itself. It might be somewhat hard to think of everything as utterly perishing and leaving no trace whatever of its ever having been, but there seems to be not the slightest difficulty in imagining that

17

the world should never have existed in the first place. We can, for instance, perfectly easily suppose that nothing in the world had ever existed except, let us suppose, a single grain ofsand, and we can thus suppose that this grain ofsand has forever constituted the whole universe. Now ifwe consider just this grain ofsand, it is quite impossible for us to suppose that it exists by its very nature, and could never have failed to exist. It clearly depends for its existence upon something other than itself, ifit depends on anything at all. The same will be true ifwe consider the world to consist, not of one grain ofsand, but of two, or of a million, or, as we in fact find, of a vast number ofstars and planets and all their minuter parts. It would seem, then, that the w'orld, in case it happens to exist at all—and thisis quite beyond doubt—is contingent and thus dependent upon something other than itselffor its existence, ifit depends upon anything at all. And it must depend upon something, for otherwise there could be no reason why it exists in the first place. Now that upon which the world depends must be something that either exists by its own nature or does not. If it does not exist by its own nature, then it, in turn, depends for its existence upon something else, and so on. Now then, we can say either of two things; namely, (1) that the world depends for its existence upon something else, which in turn depends on still another thing, this depending upon still another, ad infinitum; or (2) that the world derives its existence from something that exists by its own

18

nature and which is accordingly eternal and imperishable, and is the creator of heaven and earth. The first of these alternatives, however, is impossible, for it does

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not render a sufficient reason why any thing should exist in the first place. Instead of supplying a reason why any world should exist, it repeatedly begs off giving a reason. It explains what is dependent and perishable in terms of what is itself dependent and perishable, leaving us still without a reason why perishable things should exist at all, which is what we areseeking. Ultimately, then, it would seem that the world, or the totality of contingent or perishable things, in case it exists at all, must depend upon something that is necessary and imperishable, and which accordingly exists, not in dependence upon something else, but by its own nature.* 1 2 3 4 5 6 7 8 9 10 11

The main line of Taylor’s argument may, I think, be summarized as follows: 1 In the case of any positive truth there is some sufficient reason why it is so. (Assumption) 2 Everything that exists either depends for its existence upon something else or ‘exists by its own nature’. (Assumption) 3 There is some sufficient reason why the world exists. (From 1) 4 The world either depends for its existence upon something else or ‘exists by its own nature’. (From 2) 5 It is not true that the world ‘exists by its own nature’. (Assumption) 6 The world depends on something else for its existence. (From 4 and 5) 7 If the world does not ultimately depend for its existence upon something which ‘exists by its own nature’ there is no sufficient reason why the world exists. (Assumption) 8 The world does ultimately depend upon something which exists by its own nature. (From 7 and 3) 9 Only God exists by His own nature. (Assumption) 10 There is a world. (Assumption) 11 There is a God. (From 8,9 and 10) I think you will readily be able to satisfy yourself that this argument is valid, that if we allow its assumptions we cannot consistently deny its conclusion. To be a proof of God’s existence, of course, it must be a matter of established fact that these assumptions are true. There are, as you will see, six of them and they are made at steps 1, 2, 5, 7, 9 and 10 of the argument I have given in summary. Assumption (10) is that kind of simple statement of established empirical fact from which cosmological reasoning begins. The assumption made at step (9) need not detain us either. For it can be proved from other assumptions. For Taylor the ‘world’ is everything which exists apart from God, in case there is a God. If then the world does not exist by its own nature the only thing that can exist by its own nature is outside the world. And God is all there is apart from the world. Assumption (9) may be more rigorously stated as ‘Only God, if there is a God, exists by His own nature’. If God does not exist by His own nature then there is nothing that exists by its own nature. It follows from other assumptions of the argument that this cannot be true. But I think that Taylor would want to 1

Richard Taylor, Metaphysics Foundation of Philosophy Series, Prentice-Hall, 1968.

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say—and this point is different from a point of Malcom’s only in expression— that God would not be God if He did not exist by His own nature. The assumption drawn at (2) is also unproblematic. For either everything depends for existence upon something else or ‘exists by its own nature’ is true in virtue of how Taylor defines the phrase ‘exists by its own nature’. One might say: either something’s existence is self-explanatory or it must be explained by reference to the existence of something else. (2) thus rests on the Principle of Sufficient Reason, rests then on assumption (1). Let us look then at the assumption made at step (5). Taylor argues (in paragraphs 16 and 17) that while ‘it is logically possible that the totality of all perishable things might itself be imperishable’ it is not plausible to believe this. Do you think he establishes that the world does not exist ‘by its own nature’ ?

Taylor identifies the ‘world’ with the ‘totality of existing things except, if there is one, God’. He seems to think it logically possible that every single perishable thing should be as it is and yet the totality of perishable things not be perishable. But, if that totality is of all perishable things, past, present and future, his point must be that there is no inconsistency in supposing that the ‘world’ has and will exist for ever. And this is a point we have already considered in connection with Aquinas. Taylor’s objection to supposing that the world depends on nothing else for its existence is, then, different from that of Aquinas, who wrongly supposed that what is true of each contingent thing must be true of contingent things considered as a whole. Taylor’s objection is not that we would be inconsistent in thinking that the totality of perishable things might itself be imperishable. It is that we should then have to say either that the existence of the world is inexplicable or that it is self-explanatory. There does, indeed, seem something strange about the idea that the existence of the world is self-explanatory. No contradiction is involved in the thought that there might have been no contingent things at all. That being so, either the existence of the world is inexplicable or its existence must be explained by reference to something else. But if the Principle of Sufficient Reason is assumed, we may discount the possibility that the existence of the world is inexplicable. We are left then with the assumption that the world’s existence must be dependent upon something other than itself, that its existence is not ‘by its own nature’. Turning to the assumption made at step (7), we will find that, given the definition of the word ‘world’, there could be no contingent thing on which the existence of the world depended. For any contingent thing we care to mention will qualify under Taylor’s definition as part of the world, as part of that totality of perishable things whose existence Taylor believes requires explanation. Once again, if we assume the Principle of Sufficient Reason, we can infer that the existence of the world must ultimately depend upon something which exists ‘by its own nature’. And that is just another way ofstating the assumption we have been considering. It seems then that, if only assumption 1 may be regarded as beyond contention, Taylor’s argument will constitute a proof ofGod’s existence. We should now consider, then, whether that assumption (that the Principle of Sufficient Reason is true) is beyond contention.

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The Principle of Sufficient Reason The Principle of Sufficient Reason seems almost to be what Taylor says it is: ‘a presupposition of reason itself’. And there would be no point in our asking for explanations of why things are as they are if such a principle did not normally hold. We confidently ask what the explanation is for things being as they are, not whether any, and if so what, explanation is available. But is the Principle applicable without exception ? Is it always reasonable to demand an explanation for the way things are ? What do you think ?

There seems to me to be at least one class of cases where it would be treasonable to invoke the Principle of Sufficient Reason. Suppose you are motoring in a remote part of the country and you find yourself behind another car whose registration number is that immediately prior in sequence to the vehicle you are in. You remark upon it. ‘Here we are’, you say to your passenger, ‘SOB 234 D behind SOB 233 D!’ Well, would you go on to ask how it could be that in this spot at this time SOB 234 D should be immediately behind SOB 233 D ? I think you would not. You would simply say ‘What a coincidence!’ and leave matters there. For while there is some explanation of your being there at that time and doubtless an explanation of why the driver of SOB 233 D is on that road then, neither of these explanations, separately or jointly taken, does anything whatever to make what seemed mysterious less so or the coincidence less of a coincidence. We would think someone who wanted an explanation of the coincidence silly. Here then is one kind of case where we would regard it as tantamount to super¬ stition to invoke the Principle of Sufficient Reason. We distinguish in practice between coincidences and concurrences of events which do require explanation. For instance, if what seems a coincidence is repeated often enough, we start to think some explanation is called for. Suppose you are travelling into work in one of those old-fashioned trains with separate compartments. There you are in the corner seat with three people to the left of you and four facing you. Suppose now one of your companions breaks the silence with the remark: ‘I wonder why the eight of us come to be together in this very compartment at this very time. Surely there must be some explanation, in addition to the explanations there are for each of us being here, for this totality of persons being now here!’ What would you think ? If I were you, I’d think he had taken leave of his senses. I’d say: ‘Why should there be a reason for this totality of persons being here over and above the reasons there are for each of us being here?’ On the other hand, if the very same people were in the very same compartment for several mornings running, we might begin to think there ought to be an explanation of this fact. Well now, you will remember that Taylor makes the following inference (in paragraph 8) from the Principle of Sufficient Reason:

From the principle of sufficient reason it follows, of course, that there must be a reason, not only for the existence of everything in the world but for the world itself, meaning by ‘the world’ simply everything that ever does exist, except God, in case there is a god.

Cosmological Arguments

52

The question I’d like you to think about is this: is Taylor like the man on the train who wanted to know why the totality of persons in the carriage was there at the time in question ? Is he like someone who asks: ‘I wonder whyjust this totality of perishable things exists. Surely there must be some explanation, in addition to the explanations there are of the existence of each perishable thing, for there being this totality of perishable things we call “the world”!’

The question I was asking, of course, is whether there is any difference between the totality of things which comprise what Taylor calls ‘the world’ and that totality of individuals who comprise the occupants of the compartment on that morning train. The obvious differences, for instance, that there are only eight individuals in the train and indefinitely many in the world, are not relevant to our purpose. I would not have thought the question asked by the passenger in the train any the less silly if there had been many more people in the compartment. The silliness of the question is not affected by whether there are two or indefinitely many individuals involved. Nor is there any difference of substance made by the fact that the individuals who ‘coincide’ on the train do so at a particular place at a particular time. All the perishable things there ever have been, are and ever will be—they do not coincide in place or time. But they do coincide in one spatio-temporal universe, i.e. the actual universe. Indeed, ifyou subtract one of them from the actual universe you are no longer thinking of the same totality but of another possible universe differing only in lacking that individual. So our question is, why did all these individuals coincide in this actual universe, why is there actually a universe containingjust these individuals ? So long as ‘the world’ is thought of as nothing but the totality of perishable things, I do not see why it is different in kind from the occupants of this railway compartment. I would be inclined to reject the invocation of the Principle of Sufficient Reason in either case. An explanation of the existence of‘the world’ as Taylor understands it would have to be an explanation of why any two indivi¬ duals were, are or will have been both in existence. It is by no means an established fact that there must be such an explanation. Does this mean that no explanation is called for of the existence of the world ? I do not think this follows. For Taylor does not speak of‘the world’ as it is usually spoken ofin this kind of connection. Usually the world is thought of as having some sort of unity and not as the mere aggregate of contingent things. And this does make a difference to the question whether one can ask for an explanation of its existence. What I am saying is that it is not true in every case that once you have explained the existence of the members of a group you have explained the existence of the group. The phrase ‘the army’ is commonly used, for instance, to refer to the totality of personnel who comprise a country’s land-moving defence force. But if someone asks, ‘How did the army come into existence ?’ one will expect a quite different explanation from those which may be given of the existence of those who make up the army. The reason for this is that there is a unity to the army, a unity offunction and a common chain of command. And an explanation of the

A303

Proof and the Existence of God

Units 7-8

53

existence of the army—which need not mention any actual members of it—is given once we have given an explanation of how it came about that a particular group began to exercise this function. What must be done, then, to make it reasonable to invoke the Principle of Sufficient Reason for the purposes of a cosmological proof? Notice first that it is Taylor’s empirically established premiss which has proved insufficient for his purposes. It is necessary to replace that premiss with another which is both (a) as firmly established and (b) attributes to the world a certain sort of unity. I say ‘a certain sort’ of unity. For not any kind of unity whatever will serve our purpose. Some unity may be ascribed to the universe if it were established that every individual in it is spatio-temporally related to every other individual. But that would not help. For a cosmological proof to be possible there must be some established fact which requires an explanation different in kind from that afforded by the natural sciences. Do you think there is such a fact ? In short, do you think a cosmological proof is possible ?

6.4

Is a cosmological proof of God’s existence possible? The characteristic form of a cosmological proof is, as Professor Hick observes, an elaboration of this idea: Either there is a god or the existence of the world (or some basic fact about it) is ultimately inexplicable; the world (or this basic fact about it) is ultimately explicable: hence, there is a god. Hick follows Copleston in thinking that it is a general weakness of this way of arguing that someone could retort that, since there is no god, the world is ultimately inexplicable. (See Hick, pp. 6 ff.) This reflects the fact that someone can, without contradiction, reject the Principle of Sufficient Reason. We might be content to say that a cosmological proof is impossible for just this reason, namely, that it is not a matter of established fact that the Principle of Sufficient Reason holds without exception. But the cosmological argument, unlike the ontological argument, could be directed to something less than proof. Provided, that is to say, it is at least reasonable to accept its assumptions and the argument is valid, it will be at least reasonable to accept the conclusion. My point has been that since it is in exactly similar kinds of case unreasonable to invoke the Principle, it cannot reasonably be invoked to prove the existence of God from a universe which lacks any unity. I think, then, that Taylor not only fails to prove God’s existence—which, in a strict sense, he would not perhaps claim to have done—he does not show that it would be reasonable to believe that God existed. Still, we have agreed that under certain conditions it would be reasonable to invoke the Principle of Sufficient Reason. And the question I mainly wanted you to ask yourself was whether those conditions could, in your opinion, be fulfilled. I do not see any ^compatibility of a logical sort between the requirement that our starting-point be a matter of established fact and the requirement that it be of a kind it Is reasonable to suppose needs explaining. But it is not easy to imagine the conditions being met. If it could be established that there is a unity of purpose to contingent things or that contingent things have a common origin, then it would be reasonable to suppose that the existence of contingent things is due to a necessary being. But that there is a unity of purpose in the universe is at best an

Cosmological Arguments

hypothesis and not a matter of established fact. Whether it is a reasonable hypo¬ thesis is a question which will be discussed in the units on Religious Belief . The other possibility I mentioned is that it might be established that contingent things have a common origin. But it is not clear how this could be empirically established. It might be established that the universe as we know z/has a common origin. But that would not be good enough. We should need to establish further that the universe as we know it comprises the totality of contingent things. It is not clear to me that this further thesis could be established by any empirical inquiry. I think we may conclude, then, that not only does it seem impossible for a cosmological argument to prove the existence of a god, it is doubtful whether the belief that there is a god can be made a reasonable one by such a means.

54

7

CONCLUSION

We have been concerned in these units with the question whether the existence of a god can be proved. W e have not been concerned with the question whether there is any reason at all to believe that there is a god. That question will come up for discussion in the units on Religious Belief. Also, we have not considered here whether the existence of a god can be disproved. Proving negative existential claims is in general rather difficult. That is why it is difficult to disprove the claim that there is a monster in Loch Ness. And one would not expect there to be an empirical disproof of the existence of a god. Ontological disproofs, on the other hand, are by no means difficult to produce. For if you can show that a contradiction is involved in the concept ‘X' you show thereby that there can be no X’s. For this reason there are no saintly devils. There have been attempts at producing ontological disproofs of God’s existence. One of the most interesting of these is Professor J. N. Findlay’s paper, ‘Can God’s Existence be Disproved ?’ This paper originally appeared in Mind in 1948 and is reprinted in an influential collection of papers edited by Antony Flew and Alasdair MacIntyre called New Essays in Philosophical Theology, S.C.M. Press, London, 1955. We cannot here enter into the merits of this or any other purported proof of the non-existence of a god. Suffice it to note that such ontological disproofs are clearly possible. One can easily, that is, think up an idea of a deity having contradictory features. Such disproofs could not establish that there was no god at all, only that there could be not be anything answering to a particular concep¬ tion of deity. They acquire interest only in so far as the conception of deity from which they begin approximates to one religious persons actually have. The arguments I have offered you would favour concluding that the existence of a god is not susceptible of proof. There is nothing remotely novel in that conclu¬ sion. You may, indeed, have been quite convinced of it before you began working on this material. It would not disappoint me if you were now less convinced than you were. For, in philosophy, it is better to have good reasons for holding a view even though it turns out not to be quite right than to have bad reasons for holding a view which is quite right.

APPENDIX ON VALIDITY AND PROOF

I have not assumed, in preparing this material, that those who will use it have studied any logic. I may have appeared, in doing so, to make formal logic look only of passing relevance to proving something by means of an argument. I add this appendix to correct that impression by indicating where our account of validity and proof would be improved by introducing some very elementary considerations from formal logic. The main account I offered of validity was that an argument is valid if, and only if, it would be inconsistent to assert its premisses and deny its conclusion. But there are difficulties with such an account. Suppose the premisses are q and r and the conclusionp. On the account I offered the argument: q and r, thereforep is valid if, and only if, it would be inconsistent to assert ‘