Hi Neil:

I think we are in general agreement on those points. I could never get on board with arithmetic being synthetic. I mean, yeah, there are some additional properties of twelve that are not shared by 5 and 7. For example, there is a non-commutative group of order twelve, whereas there is no non-commutatitive group of order 5 or 7. But, that just a quirk of group theory, not a quirk of twelve.

I think that I was always under the influence of the algebraic nature of modern mathematics, that there was a definition of what constitutes a group, what comprises a Euclidean geometry, what comprises a definition of the complex numbers, what comprises a definition of an open set in topology, and then to think that given this conventional definition, that certain properties then logically follow. So that it all seemed to be conventional, constructed in the sense of Chihara, and so therefore analytic. Intuition is shoved aside, just like Bolzano and the intermediate value theorem proof might have done to Kant's intuition.

But, I can still sympathize with Kant and his line of thought, just given the mathematics and logic of his time.

It may seem that I have been arguing that Wittgenstein is some kind of Truth by Convention theorist, but I think that that is not really an apt characterization of his philosophy. It applies to the Vienna Circle of logical positivists, no doubt, but not to Wittgenstein exactly. Remember that in Urpflanze msg #305 LW sees that "The geometry of visual space is the syntax of sentences that deal with the objects in visual space.The axioms, for example, of Euclidean geometry are masked rules of syntax." [Phil. Bemerkungen, XVII.178].

It's not like these mathematical theories are contrived by mathematicians, but that they comprise a set way within which we articulate concepts according to the perceptions that inspire them. I'm not sure if I'm expressing LW's thought here aright or not. But it is like if someone said "We was at home until ten o'clock". It would not be right to say "That's not true", as if there were a conventional truth that had been broken. It would be right to say, correcting the grammar: "You mean to say 'We were at home until ten o'clock', right?" And in fact, the ungrammatically expressed propositon "We was at home..." could in fact be true, only not incorrectly expressed. The same goes for LW's conception of geometric propositions. These propositions are not made true by convention, but they capture in a schematic way the form in which we should be guided to enunciate propositions that concern the physical layout of spatial perception.

In the next few posts, I will attach some points that are made by Baker and Hacker in this regard.

Uh, I'm not sure whether this is an issue, but I will say that it's not pointless to ruminate over these things. I am (maybe we are) trying to achieve some standpoint reflecting a certain clarity about what some prior thinker actually thought (say, Wittgenstein) as well as what is actually correct (LW vs. the Vienna Circle of logical positivists). Comparative efforts may help (so I am inclined to believe) in this regard.
More a little bit later on Baker & Hacker's notes pertaining to this issue. Thanks! --Ron