17 Nov 2014

Frege (§4) Begriffsschrift, Chapter 1 (Geach transl.), summary

by Corry Shores
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[The following is summary. All boldface, underlying and bracketed commentary are my own.]

Gottlob Frege

Begriffsschrift, Chapter 1
(Geach transl.)


Brief Summary:

Frege examines different modifications to judgments, such as negation and necessary/possible modalities, and emphasizes his point that there is a conceptual content in judgments which is not affected by such logical variations.


[Frege is providing a notation system for describing conceptual relations. He previously distinguished the conceptual content, which is the basic meaning of a proposition (regardless of its subject-verb arrangement, and it is determined by its inferential behavior) from the judgment, which is this conceptual content plus ‘… is a fact’.] Since ‘… is a fact’ is not what would be universal or particular, these terms refer to contents and not to judgments.

The same holds for negation. [It seems that for Frege negation is not taking the proposition in quotes and speaking of it in a metalanguage and denying its truth in that metalanguage. Rather it seems that negation will have to at least on the level of the judgment itself involve a negation of the contents.] In fact, whether or not a content can be negated tells us if it can be a possible content of a judgment. (4)

The same thing holds good for negation. Thus, in an indirect proof one says ‘suppose the segments AB and CD were not equal.’ There is a negation involved here in the content: the segments AB and CD not being equal; but this content, though suitable matter for judgment, is not presented in the shape of a judgment. Negation thus attaches to the content, no matter whether this occurs in the shape of a judgment or not. I therefore hold it more suitable to regard negation as a mark of a possible content of judgment.

Later in this work Frege will support this claim he now gives: “The distinction of judgments into categorical, hypothetical, and disjunctive seems to me to have a merely grammatical significance.” (4)

Apodeictic judgments “indicate the existence of general judgments from which the proposition may be inferred,” while assertoric judgments do not (4). But if we say that a judgment is necessarily so [meaning that it is apodeictic] that will not change its content, and thus it will have no bearing on our current task of providing a conceptual notation.

When someone makes a possible [assertoric] judgment, they are refraining from judgment [judging the truth of the claim] and they are indicating that they are “not acquainted with any laws from which the negation of the proposition would follow”; otherwise they are “saying that the negation of the proposition is in general false.”(5a) This second case is called ‘a particular affirmative judgment’, and an example is ‘a chill may result in death’ [because the claim, ‘a chill may not result in death’ is generally (but not necessarily) false]. An example of the first case where the speaker is unacquainted with “any laws from which the negation of the proposition would follow” could be: ‘It is possible that the Earth will one day collide with another celestial body’ [because the speaker cannot think of a reason why this might be false] (5).



Frege, Gottlob. “Begriffsschrift (Chapter 1)”. Transl. P.T. Geach. In Translations from the Philosophical Writings of Gottlob Frege. Eds. P.T. Geach and Max Black. Oxford: Basil Blackwell, 1960, second edition (1952 first edition).



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