On Mon, 18 Feb 2008 04:19:48 -0500, "Phil Roberts, Jr." wrote:
>It has been many years since I've read the Critique of Pure
>Reason, and perhaps I am misrembering, but I was always
>perplexed by Kant's insistence that 1 + 1 = 2 is a
>synthetic proposition. If an analytic proposition is
>simply one that is true by denfintion, e.g.,
>all unmarried men are bachelors, wouldn't 1 plus 1
>equals 2 be in this category as well?
I think it has to do with the so called "Copernican turn"* as well,
meaning that we do no apprehend the "things outside", but rather that
those things outside can only be understood forsofar it fits in our
mode(s) of knowledge. Since mathematics is a pre-condition of all
physical knowledge and all physical things are interlacing, at least
in our minds, in mathematical terms (and because interlacing is the
same as synthesis), all mathematics is seen as synthetic. I think Kant
followed this line of thinking or something akin to it.
With mathematics it is possible to "construct" all kinds of (correct)
predictions (e.g. the amount of energy in a gallon of petrol and/or in
other sources of energy, due to the way atoms with their specific
properties organize themselves to molecules) that could not be made
without it. Without these mathematics we could not make (physical)
structures like these. Construction, synthesis, stucturing and (theo-
retical) interlacing are all the same.
The fact that it is possible to rewrite math and/or to study it on an
analytical basis does, in my opinion, not contradict what is said
above because logic and nature do not contradict each other: they work
together in the human mind.
JH
--
* Copernican turn: "...Similarly, the fundamental laws of the motions
of the heavenly bodies gave established certainty to what Copernicus
had at first assumed only as an hypothesis, and at the same time
yielded proof of the invisible force (the Newtonian attraction) which
holds the universe together. The latter would have remained for ever
undiscovered if Copernicus had not dared, in a manner contradictory
of the senses, but yet true, to seek the observed movements, not in
the heavenly bodies, but in the spectator." Source: Kant, Preface of
the second edition of his first critique (Pure Reason), Bxxiii.
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