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Topic: Ideal Constructivism
Replies: 2   Last Post: May 10, 2013 2:16 AM

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Zaljohar@gmail.com

Posts: 2,665
Registered: 6/29/07
Re: Ideal Constructivism
Posted: May 10, 2013 2:16 AM
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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.


Thanks alot.

Zuhair



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