Random thoughts on random topics


Logic and why it works

Proposition logic done in the usual manner with truth tables and Wittgenstein’s account in the Tractatus result in the same logic. So, why appeal to more than just truth tables? One answer is provided by Wittgenstein’s insistence (in 4.441) that T(rue) and F(alse) are not objects. That makes the usual way of stating the semantics or propositional logic an abstraction, i.e., something that itself requires philosophical explanation (foundation). Wittgenstein’s ‘situation semantics’ (association intended) in the Tractatus is exactly such an explanation (foundation), though not the only one possible. And therein resides its added value: it is not the logic per se, but the attempt to explain how it is possible, what it means, to do logic in this way, i.e., with T‘s and F‘s and truth tables. So, the Tractatus is best viewed as an answer (one answer, not the only one) to the question that is not asked often enough: ‘What is it that we are doing here? What makes it possible to define this logic in this particular way?’ And that means that the so-called ‘superfluousness’ of the Tractarian situation-ontology, and of the picture theory that is connected with it, is a formal superfluousness, one that goes only for the logic as a formal, abstract system, and which can be acknowledged only because we do not ask the pertinent philosophical question.  

Martin Stokhof
from: Aantekeningen/Notes
date: 12/10/1990