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Notes on Logic: Difference between revisions
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Neither the sense nor the meaning of a proposition is a thing. These words are incomplete symbols. It is clear that we understand propositions without knowing whether they are true or false. But we can only know the meaning of a proposition when we know if it is true or false. What we understand is the sense of the proposition. To under stand a proposition p it is not enough to know that p implies "p is true", but we must also know that ~p implies "p is false". This shows the bi-polarity of the proposition. We understand a proposition when we understand its constituents and forms. [''Cf.'' 4.024.] If we know the meaning of "a" and "b" and if we know what "xRy" means for all x's and y's, then we also understand "aRb". I understand the proposition "aRb" when I know that either the fact that aRb or the fact that not aRb corresponds to it; but this is not to be confused with the false opinion that I understand "aRb" when I know that "aRb or not aRb" is the case. | Neither the sense nor the meaning of a proposition is a thing. These words are incomplete symbols. It is clear that we understand propositions without knowing whether they are true or false. But we can only know the meaning of a proposition when we know if it is true or false. What we understand is the sense of the proposition. To under stand a proposition p it is not enough to know that p implies "p is true", but we must also know that ~p implies "p is false". This shows the bi-polarity of the proposition. We understand a proposition when we understand its constituents and forms. [''Cf.'' 4.024.] If we know the meaning of "a" and "b" and if we know what "xRy" means for all x's and y's, then we also understand "aRb". I understand the proposition "aRb" when I know that either the fact that aRb or the fact that not aRb corresponds to it; but this is not to be confused with the false opinion that I understand "aRb" when I know that "aRb or not aRb" is the case. | ||
Strictly speaking, it is incorrect to say we understand the proposition p when we know that "p is true" | Strictly speaking, it is incorrect to say we understand the proposition p when we know that "p is true" ≡ p; for this would naturally always be the case if accidentally the propositions to right and left of the symbol ≡ were either both true or both false. We require not only an equivalence but a formal equivalence, which is bound up with the introduction of the form of p. What is wanted is the formal equivalence with respect to the forms of the proposition, i.e. all the general indefinables involved. | ||
There are ''positive and negative facts:'' if the proposition "This rose is not red" is true, then what it signifies is negative. But the occurrence of the word "not" does not indicate this unless we know that the signification of the proposition "This rose is red" (when it is true) is positive. It is only from both, the negation and the negated proposition, that we can conclude about a characteristic of the signification of the whole proposition. (We are not here speaking of the negations of ''general'' propositions, i.e. of such as contain apparent variables. Negative facts only justify the negations of atomic propositions.) Positive and negative facts there are, but not true and false facts. | There are ''positive and negative facts:'' if the proposition "This rose is not red" is true, then what it signifies is negative. But the occurrence of the word "not" does not indicate this unless we know that the signification of the proposition "This rose is red" (when it is true) is positive. It is only from both, the negation and the negated proposition, that we can conclude about a characteristic of the signification of the whole proposition. (We are not here speaking of the negations of ''general'' propositions, i.e. of such as contain apparent variables. Negative facts only justify the negations of atomic propositions.) Positive and negative facts there are, but not true and false facts. | ||