On May 10, 3:33 am, fom <fomJ...@nyms.net> wrote: > 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 > > Zuhair, > > I think you might find this interesting, > > http://johnmacfarlane.net/dissertation.pdf > > 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.