Tractatus Logico-Philosophicus (English): Difference between revisions

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 A sphere in which the proposition, simplex sigillum veri, is valid.
+.46 When we have rightly introduced the logical signs, the sense of all their combinations has been already introduced with them: therefore not only "''p''∨''q''" but also "~(''p''∨~''q'')", etc. etc. We should then already have introduced the effect of all possible combinations of brackets; and it would then have become clear that the proper general primitive signs are not "''p''∨''q''", "(∃''x'') . ''fx''", etc., but the most general form of their combinations.
+.461 The apparently unimportant fact that the apparent relations like ∨ and ⊃ need brackets — unlike real relations — is of great importance.
+The use of brackets with these apparent primitive signs shows that these are not the real primitive signs; and nobody of course would believe that the brackets have meaning by themselves.
+.4611 Logical operation signs are punctuations.
+.47 It is clear that everything which can be said ''beforehand'' about the form of ''all'' propositions at all can be said ''on one occasion''.
+For all logical operations are already contained in the elementary proposition. For "''f a''" says the same as "(∃''x'') . ''fx'' . ''x'' = ''a''".
+Where there is composition, there is argument and function, and where these are, all logical constants already are.
+One could say : the one logical constant is that which ''all'' propositions, according to their nature, have in common with one another.
+That however is the general form of proposition.
+.471 The general form of proposition is the essence of proposition.
+.4711 To give the essence of proposition means to give the essence of all description, therefore the essence of the world.
+.472 The description of the most general propositional form is the description of the one and only general primitive sign in logic.
+.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.)
+In a certain sense we cannot make mistakes in logic.
+.4731 Self-evidence, of which Russell has said so much, can only be discarded in logic by language itself preventing every logical mistake. That logic is a priori consists in the fact that we ''cannot'' think illogically.
+.4732 We cannot give a sign the wrong sense.
+.47321 Occam's razor is, of course, not an arbitrary rule nor one justified by its practical success. It simply says that ''unnecessary'' elements in a symbolism mean nothing.
+Signs which serve ''one'' purpose are logically equivalent, signs which serve ''no'' purpose are logically meaningless.
+.4733 Frege says: Every legitimately constructed proposition must have a sense; and I say : Every possible proposition is legitimately constructed, and if it has no sense this can only be because we have given no ''meaning'' to some of its constituent parts.
+(Even if we believe that we have done so.)
+Thus "Socrates is identical" says nothing, because we have given ''no'' meaning to the word "identical" as ''adjective''. For when it occurs as the sign of equality it symbolizes in an entirely different way — the symbolizing relation is another — therefore the symbol is in the two cases entirely different; the two symbols have the sign in common with one another only by accident.
+.474 The number of necessary fundamental operations depends only on our notation.
+.475 It is only a question of constructing a system of signs of a definite number of dimensions — of a definite mathematical multiplicity.
+.476 It is clear that we are not concerned here with a ''number of primitive ideas'' which must be signified but with the expression of a rule.
+.5 Every truth-function is a result of the successive application of the operation (- - - - T)(''ξ'', . . . .) to elementary propositions.
+.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.
+(Thus if  has the 3 values P, Q, R, then = (P, Q, R).)
+The values of the variables must be determined.
+The determination is the description of the propositions which the variable stands for.
+How the description of the terms of the expression in brackets takes place is unessential.
+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 "" whose values for all values of "" are the propositions to be described.
+# Giving a formal law, according to which those propositions are constructed. In this case the <span data-page-index="137" data-page-name="Page:Wittengenstein - Tractatus Logico-Philosophicus, 1922.djvu/137" data-page-number="133" id="133" class="pagenum ws-pagenum ws-noexport"><span class="pagenum-inner" id="pageindex_137"></span></span>terms of the expression in brackets are all the
+terms of a formal series.
+.502 Therefore I write instead of "(- - - - T)(, . . . .)", "".
+is the negation of all the values of the propositional variable ξ.