Ludwig Wittgenstein on the concept of logical consequence

The aim of this article is to analyze the early Wittgenstein's concept of logical consequence. Wittgenstein rejects Frege and Russell's views about some real laws of inference which can supposedly justify our moving from one proposition that is accepted as true to another. On the contrary - as postulates in 5.132 - if one proposition follows from another then only these two propositions themselves without any laws of inference can justify the inference. In order to show what does it means I consider the notion of truth-grounds. Truth-grounds of a proposition are by definition those truth-possibilities of its truth-arguments that make it true. And I argue that in cases of propositions from statement 5.101 which are truth-functions of two elementary propositions the best illustration of how does their truth-grounds can determine their structures is so-called Gergonne's relations. I argue that basing on exactly such structures Wittgenstein rejects «laws of inference». Valid inference from q to p, as Wittgenstein sees it, is a matter of p being contained in q - and also depends on truth-grounds and particular structures in logical space.

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