Written 11 July 2011.
Some time before 1884, Gottlob Frege had a discussion about existence with the Protestant theologian Bernard Pünjer (1850-1885). A record of the dialogue was found in Frege's Nachlass, and an English translation is available in Gottlob Frege: Posthumous Writings, eds. Hans Hermes et al., University of Chicago Press, 1979. Herewith, some critical commentary on part of the dialogue.
1. We have often discussed 'thin' or deflationary approaches to Being or existence. On a thin approach, existence is not a metaphysical or ontological topic, but a merely logical one. Consider the general existential, 'Cats exist.' For Frege, the content of such a general existential does not lie in 'exist' but "in the form of the particular judgment." (63) Frege uses the good old 19th century term 'judgment' (Urteil) but the point could also be put, with minor adjustments, in terms of indicative sentences, statements, and propositions. Particular judgments are the I- and O-judgments of the Square of Opposition: those of the form Some S is P and Some S is not P.
Frege's contention, then, is that the content of affirmative general existentials lies in the logical form: Some S is P. But how do we put 'Cats exist' into this form? We need a concept superordinate to the concept cat, say, the concept mammal. We can then write, 'Some mammals are cats.' If we acquiesce in the natural anti-Meinongian presupposition that there are no nonexistent items, then 'Cats exist' is true if and only if 'Some mammals are cats' is true.
This translation illustrates what Frege means when he says that the content of affirmative general existentials does not lie in 'exist' but in the [logical] form of the particular judgment. The logical form is Some S is P, which is just a bit of syntax, whence we are to conclude that 'exists' is bare of semantic content, whether sense or reference, and merely functions as a stylistic variant of 'Some ___ is ---.'
Those who take a deflationary tack, therefore, are the thin theorists. We who resist deflation can then be called thick theorists.
By showing that 'exist(s)' and cognates are eliminable, Frege thinks he has eliminated those hoary metaphysical subjects Being or existence which fascinate Thomists, Heideggerians, and such other 'thicks' as your humble correspondent.
2. But does Frege's schedule of elimination really work? We saw how 'Cats exist' can be rendered as 'Some mammals are cats.' But what about 'Mammals exist'? This in turn needs elimination. Assuming that the domain of quantification is a domain of existents, this can be translated salva veritate as 'Some animals are mammals.' And so on up the tree of Porphyry, or, if you deem that to be barking up the wrong tree, then supply some other scheme of classification. 'Animals exist' becomes 'Some living things are animals.' 'Living things exist' becomes 'Some bodies are living things.' 'Bodies exist' gets translated as 'Some substances are bodies.'
Clearly, we either now or very soon must call a halt to the ascent by resting in "a concept superordinate to all concepts." (p. 63) Superordinate to all concepts except itself, of course. And what concept might that be? Such a concept must have maximal extension and so will have minimal intension. It will be devoid of all content, abstracting as it does from all differences. Frege suggests 'something identical with itself' as the maximally superordinate concept. 'There are men' and 'Men exist' thus get rendered as 'Something identical with itself is a man.' (63)
3. In ordinary language, the role of maximally superordinate concept, a "concept without content," (63) is played by an hypostatization of the copula. In 'The sea is blue' the content of the predicate lies in 'blue': 'is' is contentless. But from the copulative 'is' we form a quasi-concept -- 'being' -- without content since its extension is unlimited. This makes it possible to say: men = men that have being; 'There are men' is the same as 'Some men are' or 'Something that has being is a man.' Thus here the real content of what is predicated does not lie in 'has being' but in the form of the particular judgment. Faced with an impasse, language has simply created the word 'being' in order to enable the form of the particular judgment to be employed. When philosophers speak of 'absolute being,' that is really an apotheosis of the copula. (64)
This is an excellent statement of the thin or deflationary or eliminativist line: there is in reality no such 'thing' or 'property' as Being or existence. Being (as a metaphysical topic) is a result of an illicit reification or hypostatization of the copula, an apotheosis (deification) of the copula.
4. Now why can't I accept this? We saw that to eliminate existence in all cases and make it disappear into the logical form Some S is P we must ascend a classificatory tree at the apex of which is a concept or "quasi-concept" unlimited in extension and empty in intension. This is the concept a being, an existent, something self-identical. Using this concept we can translate salva veritate every sentence of the form Fs exist into a sentence of the form Some being is an F. The availability of such translations seems to strip 'exist(s)' and cognates of all semantic content.
The problem with this was appreciated by Aristotle long ago when he argued that Being is not a summum genus, a highest genus, or a genus generallisimum, a most general genus. (See Metaphysics 998b22 and Posterior Analytics 92b14). Being, as that which makes beings be, does not abstract from the differences among beings. But a concept superordinate to every quidditative concept, which is what the concept a being and the concept something self-identical are, does abstract from the differences among beings. To put it another way, Being, as that which constitutes beings as beings, is not superordinate to every quidditative concept since it belongs to a different order entirely, the non-quidditative order of existence. The Being of a being is its thatness, not its whatness.
The mistake that Frege makes is to think that Being is a highest quidditative determination, a highest what-determination. The concept a being, ens, is such a concept, but this concept is not Being, esse.
In sum: Frege's elimination of existential judgments by translation into copulative judgments works only if Being (esse, das Sein) is a maximally abstract quidditative concept, the concept a being (ens, das Seiende). But this is precisely what Being is not. Ergo, etc.