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Frege's Ontology: Being, Existence, and Truth

BEING

"One of Frege's main semantic principles, is however, missing in Dummett's book, [Frege: philosophy of language] and it is has been ignored by most Frege scholars. That principle is the thesis concerning the ambiguity of the word 'is'. Angelelli come close to attending to it when he makes some remarks on identity and predication, and Matthias Schirn puts special emphasis on the role of the thesis in Frege's work. However, the great majority of Frege scholars have neglected the ambiguity doctrine, even when they have commented on each of the allegedly different meanings of 'is' separately. This is strange in view of the fact that it was Frege and Russell who proposed the thesis and established it as one of the basic ingredients of modern logic. They have in fact been followed by most philosophers. For instance, in the Tractatus Ludwig Wittgenstein emphasizes the ambiguity of the verb 'to be' and stresses the importance of constructing a language which prevents confusions between the different meanings of 'is'. Wittgenstein also remarks that Frege's and Russell's conceptual notation: is such a language although it does not succeed in excluding all mistakes (Tractatus, 3.323 - 3.325). This work sets out to show that a large part of Frege's philosophy is an attempt to make us realize the importance of keeping the different meanings of 'is' apart and to catch the philosophical mistakes brought about our failure to see the ambiguity.

But how is the verb 'is' ambiguous in Fregean logic? 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) ⊃ 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.

TRUTH

"When entering upon the study of a science, we need to have some idea, if only a provisional one, of its nature. We want to have in sight a goal to strive towards; we want some point to aim at that will guide our steps in the right direction. The word 'true' can be used to indicate such a goal for logic, just as can 'good' for ethics and 'beautiful' for aesthetics. Of course all the sciences have truth as their goal, but logic is concerned with the predicate 'true' in a quite special way, namely in a way analogous to that in which physics has to do with the predicates 'heavy' and 'warm' or chemistry with the predicates 'acid' and 'alkaline'. There is, however, the difference that these sciences have to take into account other properties besides these we have mentioned, and that there is no one property by which their nature is so completely characterized as logic is by the word 'true'. (...) Now it would be futile to employ a definition in order to make it clearer what is to be understood by 'true'. If, for example, we wished to say 'an idea is true if it agrees with reality' nothing would have been achieved, since in order to apply this definition we should have to decide whether some idea or other did agree with reality. Thus we should have to presuppose the very thing that is being defined. The same would hold of any definition of the form 'A is true if and only if it has such-and-such properties or stands in such-and-such a relation to such-and-such a thing'. In each case in hand it would always come back to the question whether it is true that A has such-and-such properties, or stands in such-and-such a relation to such-and-such a thing. Truth is obviously something so primitive and simple that it is not possible to reduce it to anything still simpler. Consequently we have no alternative but to bring out the peculiarity of our predicate by comparing it with others. What, in the first place, distinguishes it from all other predicates is that predicating it is always included in predicating anything whatever."

From: Gottlob Frege - Logic (1897) - in: Posthumous Writings - Edited by Hans Hermes, Friedrich Kambartel, Friedrich Kaulbach - Chicago, The University of Chicago Press 1979 pp. 128-129.

"7. What true is, I hold to be indefinable.

8. The expression in language for a thought is a sentence. We also speak in an extended sense of the truth of a sentence. 12. Logic only becomes possible with the conviction that there is a difference between truth and untruth.

13. We justify a judgement either by going back to truths that have been recognized already or without having recourse to other judgements. Only the first case, inference, is the concern of Logic.

14. The theory of concepts and of judgement is only preparatory to the theory of inference.

15. The task of logic is to set up laws according to which a judgement is justified by others, irrespective of whether these are themselves true.

16. Following the laws of logic can guarantee the truth of a judgement only insofar as our original grounds for making it, reside in judgements that are true.

17. No psychological investigation can justify the laws of logic."

From: Gottlob Frege - [17 Key Sentences on Logic] (1906 or earlier) - in: Posthumous Writings - Edited by Hans Hermes, Friedrich Kambartel, Friedrich Kaulbach - Chicago, The University of Chicago Press 1979 pp. 174-175.

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