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

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Posts: 1,968
Registered: 12/4/12
Re: Ideal Constructivism
Posted: May 9, 2013 8:33 PM
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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:
> Zuhair


I think you might find this interesting,

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.

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