Tractatus Logico-Philosophicus (English): Difference between revisions

Tractatus Logico-Philosophicus (English) (view source)

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 .42 With regard to the agreement and disagreement of a proposition with the truth-possibilities of n elementary propositions there are <math>\sum_{k=0}^{K_n} \binom{K_n}{k} = L_n</math> possibilities.
+Agreement with the truth-possibilities can be expressed by co-ordinating with them in the schema the mark "T" (true).
+Absence of this mark means disagreement.
+.431 The expression of the agreement and disagreement with the truth-possibilities of the elementary-propositions expresses the truth-conditions of the proposition. The proposition is the expression of its truth- conditions.
+(Frege has therefore quite rightly put them at the beginning, as explaining the signs of his logical symbolism. Only Frege's explanation of the truth-concept is false: if "the true" and "the false" were real objects and the arguments in ~''p'' etc., then the sense of ~''p'' would by no means be determined by Frege's determination.)
+.44 The sign which arises from the co-ordination of that mark "T" with the truth-possibilities is a propositional sign.
+.441 It is clear that to the complex of the signs "F" and "T" no object (or complex of objects) corresponds; any more than to horizontal and vertical lines or to brackets. There are no "logical objects".
+Something analogous holds of course for all signs, which express the same as the schemata of "T"and "F".
+.442 Thus e.g.
+{| style="margin: 0 auto 0 auto;"
+|-
+| &quot;
+|
+{| class="wikitable" style="margin: 0 auto 0 auto;"
+|+
+!p
+!q
+!
+|-
+|T||T
+|T
+|-
+|F||T
+|T
+|-
+|T||F
+|
+|-
+|F||F
+|T
+|}
+| &quot;
+|}
+is a propositional sign.
+(Frege's assertion sign "<math>\vdash</math>" is logically altogether meaningless; in Frege (and Russell) it only shows that these authors hold as true the propositions marked in this way.
+"<math>\vdash</math>" belongs therefore to the propositions no more than does the number of the proposition. A proposition cannot possibly assert of itself that it is true.)