Frege (§2) Begriffsschrift, Chapter 1 (Geach transl.), “Judgment”, 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.)

§2
Judgment

Brief Summary:

In Frege’s conceptual notation system, ⊢ is the sign used for a judgment such that

could for example mean “unlike magnetic poles attract one another.”

Summary

[Frege is providing a notation system for describing conceptual relations.] The sign used for judgment is ⊢

“This stands to the left of the sign or complex of signs in which the content of the judgment is given” (1d)

[The whole sign itself seems to represent a whole judgment or proposition. The horizontal line seems to just be for the ideas in the judgment, and by adding the vertical line we seem to be indicating that certain ideas are predicated to certain subjects. For,] by omitting the vertical line, we are left with a ‘mere complex of ideas’. So if we take

to mean, “unlike magnetic poles attract one another,” then

will only “produce in the reader the idea of the mutual attraction of unlike magnetic poles.”

[Frege seems to be saying that this mere complex of ideas can then be developed into a fuller judgment perhaps by adding to it (qualifying it) with expressions such as ‘the circumstance that’ or ‘the proposition that’. I suppose this would mean it would produce something like in this example ‘the circumstance that unlike magnetic poles mutually attract…’ and then something would be inferred by this by implication, but I am not sure. Please interpret the following sentences for yourself:]

it will be intended just to produce in the reader the idea of the mutual attraction of unlike magnetic poles-so that, e. g., he may make inferences from this thought and test its correctness on the basis of these. In this case we qualify the expression with the words 'the circumstance that' or 'the proposition that.'
(2)

Some contents cannot be made into judgments merely by adding the ⊢ in front of them. One example is the idea of ‘house’.

 

[Frege then goes on to further distinguish the horizontal from the vertical line. You will have to interpret the following for yourself, but the main idea seems to be that the horizontal line is for the contents whose logical relations are not inherently specified and the vertical is for the judgment that predicates or otherwise relates those contents.]

As a constituent of the sign ⊢ the horizontal stroke combines the symbols following it into a whole; assertion, which is expressed by the vertical stroke at the left end of the horizontal one, relates to the whole thus formed. The horizontal stroke I wish to call the content-stroke, and the vertical the judgment-stroke. The content-stroke is also to serve the purpose of relating any sign whatsoever to the whole formed by the symbols following the stroke. The content of what follows the content-stroke must always be a possible content of judgment.
(2)

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).