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Tractatus Logico-Philosophicus (English): Difference between revisions
Tractatus Logico-Philosophicus (English) (view source)
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5.473 Logic must take care of itself. | 5.473 Logic must take care of itself. | ||
A ''possible'' sign must also be able to signify. Everything which is possible in logic is also permitted. ("Socrates is identical " means nothing because there is no property which is called "identical". The proposition is senseless because we have not made some arbitrary determination, not because the symbol is in itself unpermissible.) | A ''possible'' sign must also be able to signify. Everything which is possible in logic is also permitted. ("Socrates is identical" means nothing because there is no property which is called "identical". The proposition is senseless because we have not made some arbitrary determination, not because the symbol is in itself unpermissible.) | ||
In a certain sense we cannot make mistakes in logic. | In a certain sense we cannot make mistakes in logic. | ||
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5.5 Every truth-function is a result of the successive application of the operation (- - - - T)(''ξ'', . . . .) to elementary propositions. | 5.5 Every truth-function is a result of the successive application of the operation (- - - - T)(''ξ'', . . . .) to elementary propositions. | ||
5.501 An expression in brackets whose terms are propositions I indicate — if the order of the terms in the bracket is indifferent — by a sign of the form "". "" is a variable whose values are the terms of the expression in brackets, and the line over the variable indicates that it stands for all its values in the bracket. | 5.501 An expression in brackets whose terms are propositions I indicate — if the order of the terms in the bracket is indifferent — by a sign of the form "<math>( \bar{\xi} )</math>". "''ξ''" is a variable whose values are the terms of the expression in brackets, and the line over the variable indicates that it stands for all its values in the bracket. | ||
(Thus if has the 3 values P, Q, R, then = (P, Q, R).) | (Thus if ''ξ'' has the 3 values P, Q, R, then <math>( \bar{\xi} )</math> = (P, Q, R).) | ||
The values of the variables must be determined. | The values of the variables must be determined. | ||
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How the description of the terms of the expression in brackets takes place is unessential. | How the description of the terms of the expression in brackets takes place is unessential. | ||
We may distinguish 3 kinds of description: | We may distinguish 3 kinds of description: Direct enumeration. In this case we can place simply its constant values instead of the variable. Giving a function ''f x'' whose values for all values of ''x'' are the propositions to be described. Giving a formal law, according to which those propositions are constructed. In this case the terms of the expression in brackets are all the terms of a formal series. | ||
5.502 Therefore I write instead of "(- - - - T)(''ξ'', . . . .)", "<math>N ( \bar{\xi} )</math>". | |||
<math>N ( \bar{\xi} )</math> is the negation of all the values of the propositional variable ξ. | |||
is the negation of all the values of the propositional variable ξ. | |||