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Tractatus Logico-Philosophicus (English): Difference between revisions
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(Therefore instead of Russell's "(∃ ''x'', ''y'') . ''f'' (''x'', ''y'')": "(∃ ''x'', ''y'') . ''f'' (''x'', ''y'') . ∨ . (∃''x'') . ''f'' (''x'', ''x'')".) | (Therefore instead of Russell's "(∃ ''x'', ''y'') . ''f'' (''x'', ''y'')": "(∃ ''x'', ''y'') . ''f'' (''x'', ''y'') . ∨ . (∃''x'') . ''f'' (''x'', ''x'')".) | ||
5.5321 Instead of "" we therefore write ''e.g.'' "" | 5.5321 Instead of "(''x'') : ''f'' ''x'' ⊃ ''x'' = ''a''" we therefore write ''e.g.'' "(∃''x'') . ''f'' ''x'' . ⊃ . ''f'' ''a'' : ~(∃ ''x'', ''y'') . ''f'' ''x'' . ''f'' ''y''". | ||
And the proposition "''only'' one satisfies " reads : "". | And the proposition "''only'' one ''x'' satisfies ''f''()" reads : "(∃''x'') . ''f'' ''x'' : ~(∃ ''x'', ''y'') . ''f'' ''x'' . ''f'' ''y''". | ||
5.533 The identity sign is therefore not an essential constituent of logical notation. | 5.533 The identity sign is therefore not an essential constituent of logical notation. | ||
5.534 And we see that apparent propositions like : "", "", "", "", etc. cannot be written in a correct logical notation at all. | 5.534 And we see that apparent propositions like : "''a'' = ''a''", "''a'' = ''b'' . ''b'' = ''c'' . ⊃ ''a'' = ''c''", "(''x'') . ''x'' = ''x''", "(∃''x'') . ''x'' = ''a''", etc. cannot be written in a correct logical notation at all. | ||
5.535 So all problems disappear which are connected with such pseudo-propositions. | 5.535 So all problems disappear which are connected with such pseudo-propositions. | ||
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What the axiom of infinity is meant to say would be expressed in language by the fact that there is an infinite number of names with different meanings. | What the axiom of infinity is meant to say would be expressed in language by the fact that there is an infinite number of names with different meanings. | ||
5.5351 There are certain cases in which one is tempted to use expressions of the form | 5.5351 There are certain cases in which one is tempted to use expressions of the form "''a'' = ''a''" or "''p'' ⊃ ''p''". As, for instance, when one would speak of the archetype Proposition, Thing, etc. So Russell in the ''Principles of Mathematics'' has rendered the nonsense "''p'' is a proposition" in symbols by "''p'' ⊃ ''p''" and has put it as hypothesis before certain propositions to show that their places for arguments could only be occupied by propositions. | ||
(It is nonsense to place the hypothesis before a proposition in order to ensure that its arguments have the right form, because the hypothesis for a non-proposition as argument becomes not false but meaningless, and because the proposition itself becomes senseless for arguments of the wrong kind, and therefore it survives the wrong arguments no better and no worse than the senseless hypothesis attached for this purpose.) | (It is nonsense to place the hypothesis ''p'' ⊃ ''p'' before a proposition in order to ensure that its arguments have the right form, because the hypothesis for a non-proposition as argument becomes not false but meaningless, and because the proposition itself becomes senseless for arguments of the wrong kind, and therefore it survives the wrong arguments no better and no worse than the senseless hypothesis attached for this purpose.) | ||
5.5352 Similarly it was proposed to express "There are no things" by "" But even if this were a proposition — would it not be true if indeed "There were things", but these were not identical with themselves? | 5.5352 Similarly it was proposed to express "There are no things" by "(∃''x'') . ''x'' = ''x''" But even if this were a proposition — would it not be true if indeed "There were things", but these were not identical with themselves? | ||
5.54 In the general propositional form, propositions occur in a proposition only as bases of the truth-operations. | 5.54 In the general propositional form, propositions occur in a proposition only as bases of the truth-operations. | ||
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5.541 At first sight it appears as if there were also a different way in which one proposition could occur in another. | 5.541 At first sight it appears as if there were also a different way in which one proposition could occur in another. | ||
Especially in certain propositional forms of psychology, like "A thinks, that is the case", or "A thinks ", etc. | Especially in certain propositional forms of psychology, like "A thinks, that ''p'' is the case", or "A thinks ''p''", etc. | ||
Here it appears superficially as if the proposition stood to the object A in a kind of relation. | Here it appears superficially as if the proposition ''p'' stood to the object A in a kind of relation. | ||
(And in modern epistemology (Russell, Moore, etc.) those propositions have been conceived in this way.) | (And in modern epistemology (Russell, Moore, etc.) those propositions have been conceived in this way.) | ||
5.542 But it is clear that "A believes that ", "A thinks ", "A says ", are of the form " | 5.542 But it is clear that "A believes that ''p''", "A thinks ''p''", "A says ''p''", are of the form "'''p''<nowiki/>' says ''p''": and here we have no co-ordination of a fact and an object, but a co-ordination of facts by means of a co-ordination of their objects. | ||
5.5421 This shows that there is no such thing as the soul — the subject, etc. — as it is conceived in contemporary superficial psychology. | 5.5421 This shows that there is no such thing as the soul — the subject, etc. — as it is conceived in contemporary superficial psychology. | ||
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A composite soul would not be a soul any longer. | A composite soul would not be a soul any longer. | ||
5.5422 The correct explanation of the form of the proposition "A judges " must show that it is impossible to judge a nonsense. (Russell's theory does not satisfy this condition.) | 5.5422 The correct explanation of the form of the proposition "A judges ''p''" must show that it is impossible to judge a nonsense. (Russell's theory does not satisfy this condition.) | ||