On 5/9/2013 2:47 PM, Zuhair wrote: > This is a philosophical line of thought that I'm suggesting to > characterize the subject matter of mathematics. > > For details see: http://zaljohar.tripod.com/notes.txt > > Zuhair >
If it sparks any interest for you, I would recommend that you look at Kant's "Critique of Pure Reason" in relation to the remarks of the paper above.
One inaccuracy, however, is that MacFarlane classifies the transcendental logic as a special logic. This is not consistent with Kant's statements.
In any case, what MacFarlane recommends is that questions about the nature of mathematics become more informed by the historical development than is typical. Among things that I discovered for example is that Leibniz' and Lesniewski's logic is intensional. Relative to the predicativist influence of Russell and the classifications given by Frege, this is "second-order" logic.
Ultimately, I had to go back to Aristotle to sort out the questions in which I had been interested, and, I find the predicativist bias in foundations inappropriate (for example, your mereological ideas all invoke first-order logic when, in fact, Lesniewskian ontology is definitely based on second-order logic). Of course, these are things that you must consider for yourself.
Your questions are different from mine, although I had been surprised to see your posts. But, since you are seeking a sense of these matters, MacFarlane's paper may give you some directions of which you may have been unaware.