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Notes on Logic: Difference between revisions
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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. | ||
A proposition is a standard with reference to which facts behave, but with names it is otherwise. Just as one arrow behaves to another arrow by being in the same sense or the opposite, so a fact behaves to a proposition; it is thus bi-polarity and sense come in. In this theory p has the same meaning as not-p but opposite sense. The meaning is the fact. A proper theory of judgment must make it impossible to judge nonsense. [''Cf.'' 5.5422.] The "sense of" an | A proposition is a standard with reference to which facts behave, but with names it is otherwise. Just as one arrow behaves to another arrow by being in the same sense or the opposite, so a fact behaves to a proposition; it is thus bi-polarity and sense come in. In this theory p has the same meaning as not-p but opposite sense. The meaning is the fact. A proper theory of judgment must make it impossible to judge nonsense. [''Cf.'' 5.5422.] The "sense of" an ab function of a proposition is a function of its sense. [''Cf.'' 5.2341.] In not-p, p is exactly the same as if it stands alone (this point is absolutely fundamental). Among the facts which make "p or q" true there are also facts which make "p and q" true; hence, if propositions have only meaning, we ought, in such a case, to say that these two propositions are identical. But in fact their sense is different, and we have introduced sense by talking of all p's and all q's. Consequently the molecular propositions will only be used in cases where their ab-function stands under a generality sign or enters into another function such as "I believe that", etc., because then the sense enters. | ||