The existential quantifier

Geach explains why in this second sense it cannot be existence which functions as predicate:3 if, in that sense of 'x exists' in which it figures as an answer to a question whether there are any such things as xs, you treat the grammatical predicate '... exists' as a logical predicate, as if ascribing some attribute of existence to what 'x' refers to, then you will find yourself in all sorts of muddles, familiar to readers of Plato, about how to handle negative statements of existence. To take, in the first instance, existential statements about individuals, we can see why, in 'N does not exist', you cannot treat'... exists' as a predicate denied of the person 'N stands for, since clearly in such expressions N cannot stand for anything at all. Supposing a child, having seen the play Hamlet, were to ask where Hamlet's grave is, you could in reply say, 'It's not like that - unlike Ian McKellen, Hamlet does not (really) exist.' Now, leaving aside complex further questions which arise concerning judgements of existence and non-existence in fictional contexts,4 it is quite clear that in 'Hamlet does not exist' we cannot treat 'Hamlet' as functioning logically as a proper name, and '... does not exist' as a predicate attributing non-existence to him. For if we do, then we are forced into the analysis that 'Hamlet' stands for a person, as names do, which person, on the other hand, lacks the attribute of existence; as if to say, absurdly, 'There is some person, Hamlet, who does not exist.' And that is clearly nonsense, as implying first that 'Hamlet' 'stood for something and then in effect denying that it does so'.5 But if the negative form cannot be analysed logically in subject - predicate terms, neither can the affirmative, since what holds for affirmations must hold also for their corresponding negations. Hence,

3 Peter T. Geach, 'Form and Existence', in God and the Soul, London: Routledge & Kegan Paul, 1969, pp. 42-64. Much of the argument of this chapter is indebted to Geach's seminal paper.

4 For example, we can quite legitimately say that, at the end of the play, Hamlet, who was once alive, no longer exists and is presumably buried somewhere in Elsinore.

it cannot be the case that in 'Ian McKellen exists','... exists' is a predicate either. As Geach says, the difference asserted between 'Hamlet' and 'Ian McKellen' in 'Hamlet does not exist and Ian McKellen does' is not that between two persons, Hamlet and Ian McKellen, but between two uses of the grammatically proper names 'Hamlet' and 'Ian McKellen'. To say that Ian McKellen does exist is to say that the proper name 'Ian McKellen' has reference, whereas 'Hamlet' in 'Hamlet does not exist' does not. It makes no sort of sense to treat both as having reference, the one possessing the attribute of existence, the other not possessing it.

But a second sort of case is more immediately relevant to Thomas's distinction. Where what are in question are propositions which answer to the query whether there are any, but whose grammatical subject is an unquan-tified general term, the same holds true - that existence is not a predicate -though in other respects their logic is different from those whose subject-terms are proper names. No more is some reference made to dragons in the case of'Dragons do not exist', of which the attribute of'existence' is then denied, than in 'Hamlet does not exist' is reference made to a person, Hamlet, who lacks 'existence'. In just the same way, in affirmative existential statements of this sort, such as 'cows exist', it is not the case that reference is made to cows as being in possession of the attribute of existence, though in this sort of case we do not say, as we do in the other, that 'cows' is in use as a proper name, whereas 'dragons' is not. In fact, in 'Dragons do not exist' we are not predicating anything at all of dragons, for 'dragons' is itself a predicative expression and 'Dragons do not exist' takes analysis in terms of, as the logicians say, the 'existential quantifier', so as to read, 'Nothing at all is a dragon'; just as in the case of the affirmative 'Cows exist', we do not predicate existence of cows, for it takes the analysis 'Some things or other are cows.' Now it is clear that when Thomas distinguishes between a statement of God's esse as a statement of God's actuality (actus essendi) and a statement of God's esse as a predicative statement, he is treating 'God exists' in this second sense (as when answering the question 'Is there a God?') as having the same logical form as 'Cows exist' (as when answering the question, 'Are there any cows?'). Hence, just as 'Cows exist' bears the analysis, 'Some things or other are cows', so 'God exists' bears the analysis, 'Something or other is God.' That is to say, in 'God exists' in this sense we are not predicating existence of God, but rather we are predicating 'God' of something or other.

Of course, this analysis of 'God exists' is defensible only if 'God' is treated as functioning in 'God exists' not as a proper name, such as 'Daisy', but as a descriptive, predicable expression, such as 'cow' - what Thomas calls a nomen naturae. For proper names cannot function as predicates, whereas 'cow' can, for it is used to predicate of some animal or other the sort of thing that it is, its 'nature'. But Thomas is emphatic that 'God' is not, logically, the proper name of God, which is why, he says, though undoubtedly mistaken, polytheism is not incoherent; you would be making a mistake of fact, not of logic, were you to think that there are many Gods, whereas to think that Peter can be many (as distinct from thinking that there can be many called 'Peter') is to fail to understand how to use the name 'Peter'.6 To say 'God exists', therefore, as answering to the question 'Is there a God?', is to say that something or other answers to the description 'God', in the same way as to say 'Cows exist' in answer to the question 'Are there any cows?' is to say that some things or other are cows. And, Thomas says, 'God exists' in that sense is what his proofs prove to be true: they prove that something or other answers to the descriptive term 'God'.

But it is just at this point that the objection first raised in the passage cited earlier raises its head again. It may be objected now, as then, that to maintain that 'God' is a descriptive predicable expression, a nomen naturae, and that 'God exists' is analysable as 'something or other is God', must be inconsistent with Thomas's also saying that we do not know what God is. For, the reformulated objection now goes, if 'God exists' is analysable into the existential quantifier as 'Something or other is God', where this means 'Something or other answers to the description "God"', then, to know that the proposition is true we must be in possession of a description of God, and so we must know what God is. But the objection contains a confusion. What we need to know is the logic of the word 'God' and to know how to use the word. And, as Thomas says, we do not need to know what God is in order to know how to use the word 'God' as having the logical character of a nomen naturae, any more than we do in many another parallel case. To adapt an example of McCabe's:7 I do not know, in any technical sense, what a computer is. But I know very well the effects computers have, for example, in editing a text for publication, and through my knowledge of the effects on my writing -for example, of my being able to cut and paste with ease - I know how to use the word 'computer'. Of course, just because I know how to use the word 'computer' from its effects on my writing it does not follow that 'computer' means 'machine for cutting and pasting text'.8 Nor ought I

6 ST 1aq11 a3 corp.

7 Herbert McCabe op, 'Aquinas on the Trinity', in God Still Matters, London and New York: Continuum, 2002, pp. 37-8.

8 For, in general, as Thomas says, that on account of which we use a word to describe something or other is not always the same as what the word means: 'aliud est quandoque id a quo imponitur nomen ad significandum, et id ad quod significandum nomen imponitur'. ST 1a q13 a2 ad2.

to suppose that I do know what computers are, or how they do what they do, just because I know how to use them to cut and paste text. In just the same way, Thomas says, though we do not know what 'God' means, we do know from God's effects how to use the word 'God', and by what logic the word is governed; nor, by virtue of that ought I to conclude that what God is, and what 'God' means, is confined to our knowledge of those effects.9 So there is no obstacle to the word's being understood as a nomen naturae, logically functioning in the same manner as 'cow', in the fact that we do not know the 'nature' which it denotes.

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