Gottlob Frege

Logician Germany

1848-1925

Frege was the father of modern mathematical logic. In 1879 he published Concept-notation, a work that included a formal language which was able to express generality through the quantifier-variable notation. This work also set forth a version of second order quantificational logic whcih he used to develop a logical definition for the ancestral of a relation. He was incredibly influential on the later works of Wittgenstein, Russell, George Boole, and Ernst Schroeder.
Frege distinguishes between the following meaning.; of 'is':

(1) the 'is' of identity (e. g., Phosphorus is Hesperus; a=b),

(2) the 'is' of predication, i. e., the copula (e. g., 'Plato is blond'; P(a)),

(3) the 'is' of existence,

(i) expressed by means of the existential quantifier and the symbol for identity (e. g., 'God is'; ($x) (g=x)), or

(ii) expressed by means of the existential quantifier and the symbol for predication (e. g., 'There are human beings'/'There is at least one human being'; ($x) H (x)),

and

(4) the 'is' of class-inclusion, i. e., generic implication (e. g., 'A horse is a four-legged animal''; (x) (P(x) É Q(x)))."

From: Leila Haaparanta - Frege's doctrine of Being - Helsinki, Acta Philosophica Fennica, vol. 39, 1985 pp. 13-14.

EXISTENCE

"If you want to assign a content to the verb `to be', so that the sentence `A is' is not pleonastic and self-evident, you will have to allow circumstances which the negation of `A is' is possible; that is to say, that there are subjects of which being must be denied. But in that case the concept `being' will no longer be suitable for providing a general explanation of `there are' under which `there are B's' means the same as `something that has being falls under the concept B'; for if we apply this explanation to `There are subjects of which being must be denied', then we get `Something that has being falls under the concept of not-being' or `Something that has being is not'. There is no way of getting over this once a content of some kind-it doesn't matter what it is-is agreed to the concept of being. If the explanation of `there are Bs' as meaning the same as `Something that has being is B' is to work, we just have to understand by being something that goes entirely without saying. For this reason the contradiction still remains if we say `A exists' means `The idea of the A has been caused by something affecting the ego'.

(...) We can say that the meanings of the word `exist' in the sentences `Leo Sachse exists' and `Some men exist' display no more difference than does the meanings of `is a German' in the sentences `Leo Sachse is a German' and `Some men are Germans'. But then the sentence `Some men exist' or `Something existing is a man' only means the same as `There are men' if the concept `existing thing' is superordinate to the concept man. So if such forms of expression are to have the same meaning in general, the concept `existing thing' must be superordinate to every concept. This is only possible if the word `exist' means something that goes entirely without saying, and if therefore nothing at all is predicated in the sentence `Leo Sachse exists', and if in the sentence `Some men exist' the content of what is predicated does not lie in the word `exist'. The existence expressed by `there is' is not contained in the word `exist' but in the form of the particular judgement. `Some men are Germans' is just as good an existential judgement as `Some men exist'. But once the word `exist' is given a content, which is predicated of an individual thing, this content can be made into the characteristic mark of a concept-a concept under which there falls the individual thing of which existence is being predicated. E. g. if one divides everything into two classes

1. What is in my mind, ideas, feelings etc.

and

2. What is outside myself, and says of the latter that it exists, then one can construe existence as a characteristic mark of the concept `centaur', although there are no centaurs. I would not acknowledge anything as a centaur that was not outside my mind; this means that I shall not call mere ideas or feelings centaurs. The existence expressed by `there is' cannot be a characteristic mark of a concept whose property it is, just because it is a property of it. In the sentence `There are men' we seem to be speaking of individuals that fall under the concept `man', whereas it is only the concept `man' we are talking about. The content of the word `exist' cannot well be taken as the characteristic mark of a concept, because `exists', as it is used in the sentence `Men exist', ,has no content. We can see from all this how easily we can be led by language to see 'things in the wrong perspective, and what value it must therefore have for philosophy to free ourselves from the dominion of language. If one makes the attempt to construct a system of signs on quite other foundations and `with quite other means, as I have tried to do in creating my concept-script, ,we shall have, so to speak, our very noses rubbed into the false analogies in language."

From: Gottlob Frege - Dialogue with Punjer on Existence (written before 1884) - in: Posthumous Writings - Edited by Hans Hermes, Friedrich Kambartel, Friedrich Kaulbach - Chicago, The University of Chicago Press 1979 pp. 65-67.