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Tractatus Logico-Philosophicus (English): Difference between revisions
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In order that propositions connected together in a definite way may give a tautology they must have definite properties of structure. That they give a tautology when ''so'' connected shows therefore that they possess these properties of structure. | In order that propositions connected together in a definite way may give a tautology they must have definite properties of structure. That they give a tautology when ''so'' connected shows therefore that they possess these properties of structure. | ||
6.1201 That ''e.g.'' the propositions "''p''" and "~''p''" in the connexion "~(''p'' . ''~p'')" give a tautology shows that they contradict one another. That the propositions "''p'' ⊃ ''q''", "''p''" and "''q''" connected together in the form "(''p'' ⊃ ''q'') . (''p'') : ⊃ : (''q'')" give a tautology shows that "''q''" follows from "''p''" and "''p'' ⊃ ''q''". That "(''x'') . ''f x'' : ⊃ : ''f a''" is a tautology shows that ''fa'' follows from (''x'') . ''f x'', etc. etc. | {{ParTLP|6.1201}} That ''e.g.'' the propositions "''p''" and "~''p''" in the connexion "~(''p'' . ''~p'')" give a tautology shows that they contradict one another. That the propositions "''p'' ⊃ ''q''", "''p''" and "''q''" connected together in the form "(''p'' ⊃ ''q'') . (''p'') : ⊃ : (''q'')" give a tautology shows that "''q''" follows from "''p''" and "''p'' ⊃ ''q''". That "(''x'') . ''f x'' : ⊃ : ''f a''" is a tautology shows that ''fa'' follows from (''x'') . ''f x'', etc. etc. | ||
{{ParTLP|6.1202}} It is clear that we could have used for this purpose contradictions instead of tautologies. | {{ParTLP|6.1202}} It is clear that we could have used for this purpose contradictions instead of tautologies. | ||