Maverick Philosopher: Strictly Philosophical

Being as the Apotheosis of the Copula: Frege's Dialogue with Pünjer on Existence

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.

Kenny, Geach, and the Perils of Reading Frege into Aquinas

(Written 23 December 2013)

I have been studying Anthony Kenny, Aquinas on Being (Oxford 2002).  I cannot report that I find it particularly illuminating.  I am troubled by the reading back of Fregean doctrines into Aquinas, in particular in the appendix, "Frege and Aquinas on Existence and Number." (pp. 195-204)  Since Kenny borrows heavily from Peter Geach, I will explain one of my misgivings in connection with a passage from Geach's important article, "Form and Existence" in God and the Soul.  Geach writes,

Frege, like Aquinas, held that there was a fundamental distinction in rebus answering to the logical distinction between subject and predicate -- the distinction between Gegenstand (object) and Begriff (concept). [. . .] And for Frege the Begriff, and it alone, admits of repetition and manyness; an object cannot be repeated -- kommt nie wiederholt vor. (45-46)

So far, so good.  Geach continues:

Understood in this way, the distinction between individual and form is absolutely sharp and rigid; what can be sensibly said of one becomes nonsense if we try to say it of the other. [. . .] Just because of this sharp distinction, we must reject the Platonic doctrine that what a predicate stands for is is some single entity over against its many instances, hen epi pollon. On the contrary:  the common nature that the predicate 'man' (say) stands for can be indifferently one or many, and neither oneness nor manyness is a mark or note of human nature itself.  This point is made very clearly by Aquinas in De Ente et Essentia.  Again we find Frege echoing Aquinas; Frege counts oneness or manyness (as the case may be) among the properties (Eigenschaften) of a concept, which means that it cannot at the same time be one of the marks or notes (Merkmalen) of that concept. (46)

I smell deep confusion here.  But precisely because the confusion runs deep I will have a hard time explaining clearly wherein the confusion consists.  I will begin by making a list of what Geach gets right.

1. Objects and individuals are unrepeatable. 
2. Concepts and forms are repeatable.
3. Setting aside the special question of subsistent forms, no individual is a form, and no object is a concept.
4. Frege distinguishes between the marks of a concept and the properties of a concept. The concept man, for example, has the concept animal as one of its marks.  But animal is not a property of man, and this for the simple reason that no concept is an animal.  Man has the property of being instantiated.  This property, however, is not a mark of man since it is not included within the latter's conceptual content:  one cannot by sheer analysis of the concept man determine whether or not there are any men.  So there is a sense in which "neither oneness nor manyness is a mark or note of human nature itself."  This is true if taken in the following sense: neither being instantiated singly nor being instantiated multiply is a mark of the concept man.

But how do these points, taken singly or together, support Geach's rejection of "the Platonic doctrine that what the predicate stands for is some single entity over against its many instances"?  They don't!

It seems obvious to me that Geach is confusing oneness/manyness as the relational property of single/multiple instantiation with oneness/manyness as the monadic property of being one or many.  It is one thing to ask whether a concept is singly or multiply instantiated.  It is quite another to ask whether the concept itself  is one or many.  It is also important to realize that a Fregean first-level concept, when instantiated, does not enter into the structure of the individuals that instantiate it. 

Aquinas is a constituent ontologist, but Frege is not.  This difference is deep and causes a world of trouble for those who attempt to understand Aquinas in Fregean terms.  For Frege, concepts are functions, and no function enters into the structure of its argument.  The propositional function x is a man is not a constituent of Socrates.  What's more, the value of the function for Socrates as argument is not a state of affairs with Socrates and the function as constituents. The value of the function for Socrates as argument is True; for Stromboli as argument, False.  And now you know why philosophers speak of truth-values.  It's mathematical jargon via Frege the mathematician.

The Fregean concept man is one, not many.  It is one concept, not many concepts.  Nor is it neither one nor many.  It can have one instance, or many instances, or no instance.   The Thomistic form man, however, is, considered in itself, neither one nor many.  It is one in the intellect but (possibly) many in things.  In itself, however, it is neither.  And so it is true to say that the form is not "some single entity over against its many instances."  It is not a single entity because, considered in itself, it is neither single nor multiple.

But this doesn't follow from point (3) above.  And therein lies Geach's mistake.  One cannot validly move from the "sharp distinction" between individuals/objects and forms/concepts  to the conclusion that what a predicate stands for is not a single entity.  Geach makes this mistake because of the confusion  exposed two paragraphs supra.  The mutual exclusion of objects and concepts does not entail that concepts cannot be single entities.

There is another huge problem with reading Frege back into Aquinas, and that concerns modes of existence (esse).  A form in the intellect exists in a different way than it does in things.  But if Frege is right about existence, there cannot be modes of existence.  For if existence is instantiation, then there cannot be modes of existence for the simple reason that there cannot be any modes of instantiation.

I'll say more about this blunder in another post.  It rests in turn on a failure to appreciate  the radically different styles of ontology practiced by Aquinas and Frege.  In my jargon, Aquinas is a constituent ontologist while Frege is a nonconstituent ontologist.  In the jargon of Gustav Bergmann, Aquinas is a compex ontologist while Frege is a function ontologist.