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Notes on Logic: Difference between revisions
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We are very often inclined to explanations of logical functions of propositions which aim at introducing into the function either only the constituents of these propositions, or only their form, etc., and we overlook the fact that ordinary language would not contain the whole propositions if it did not need them. | We are very often inclined to explanations of logical functions of propositions which aim at introducing into the function either only the constituents of these propositions, or only their form, etc., and we overlook the fact that ordinary language would not contain the whole propositions if it did not need them. | ||
Names are points, propositions | Names are points, propositions arrows—they have ''sense''. [''Cf.'' 3.144.] The sense of a proposition is determined by the two poles ''true'' and ''false.'' The form of a proposition is like a straight line, which divides all points of a plane into right and left. The line does this automatically, the form of the proposition only by convention. It is wrong to conceive every proposition as expressing a relation. A natural attempt at such a solution consists in regarding "not-p" as the opposite of "p", where, then, "opposite" would be the indefinable relation. But it is easy to see that every such attempt to replace functions with sense (ab-functions) by descriptions, must fail. | ||
When we say "A believes p", this sounds, it is true, as if we could here substitute a proper name for "p". But we can see that here a ''sense,'' not a meaning, is concerned, if we say "A believes that p is true", and in order to make the direction of p even more explicit, we might say "A believes that 'p' is true and 'not-p' is false". Here the bi-polarity of p is expressed, and it seems that we shall only be able to express the proposition "A believes p" correctly by the ab-notation (later explained) by, say, making "A" have a relation to the poles "a" and "b" of a-p-b. The epistemological questions concerning the nature of judgment and belief cannot be solved without a correct apprehension of the form of the proposition. | When we say "A believes p", this sounds, it is true, as if we could here substitute a proper name for "p". But we can see that here a ''sense,'' not a meaning, is concerned, if we say "A believes that p is true", and in order to make the direction of p even more explicit, we might say "A believes that 'p' is true and 'not-p' is false". Here the bi-polarity of p is expressed, and it seems that we shall only be able to express the proposition "A believes p" correctly by the ab-notation (later explained) by, say, making "A" have a relation to the poles "a" and "b" of a-p-b. The epistemological questions concerning the nature of judgment and belief cannot be solved without a correct apprehension of the form of the proposition. | ||