Notes on logic

I've spent the day at a workshop on Wittgenstein's Notes on Logic at the University of Stirling. The programme contained four talks, all centered around NoL, but in a indirect fashion, that is, through Michael Potter's (Cambridge) unpublished work The Notes on Logic. Among other things, Potter argues that NoL should be regarded as an important work in its own right, not only as pre-Tractarian notes where the ideas of the early Wittgenstein have yet to be fully developed. Nevertheless, Potter seeks with this work to give a detailed story of how Wittgenstein's Tractarian thoughts developed in the early years of the NoL. (I am tempted to conjure up a compound name à la Kripkenstein, but I'll leave this for the imaginative reader.)Among the chief questions are the influences from Frege (after his visits in Jena 1912-13) and Russell, and how Wittgenstein arrived at his subsequent critique. In general, I have to admit that this smacks a bit too much of mere Wittgenstein-interpretation to interest me, but that being said, a lot of interesting points in philosophy of logic were discussed.

The debate which I found most intriguing was one on W's Tractarian claims that (1) there exists no logical objects\constants, and (2) that logic is "a subject without a subject matter", i.e., logic is contentless. The question of the interrelation between these two claims was raised early in the first talk (by Peter Milne and with comment by Michael Potter), and was later touched upon several times throughout the workshop. It seems clear that Frege, in comparison, held in regard to (1) that there are in fact logical constants\objects - namely the True and the False. However, the question of whether he also believed that logic had a subject matter requires some further investigation. Potter indicated that Frege would take truth to be the subject matter of logic, but assuming that Frege also held that truth was non-substantive, he could still maintain that logic was contentless. As Potter had already endorsed Milne's claim that Frege was an identity theorist for truth, he went on to argue that this still could be consistent with some kind of redundancy for truth.

A question that struck me later is how these above claims relate to logic's alleged topic neutrality. This is a description frequently applied in philosophy of logic, but in my view it may not amount to the same thing as contentlessness. It seems perfectly natural to say that if logic is contentless (without a subject matter), then it is topic neutral. But how about the other way around? Assume that logic is not contentless, that is, there is logical constant which is its subject matter, namely truth (in some robust, non-redundant sense). Would this compromize the topic neutrality of logic? I think not. To believe this would be to conflate two different aspects of logic. Topic neutrality is not really a claim about the content of logic, it is a claim about the inferences of logic. Topic neutrality says that these inferences are unbiased; they do not favour certain contents of the propositions involved in the inferences. The point here is the difference between content of logic per se and the content of the involved propositions.