On Feb 20, 10:26 am, J. Horikx <jVERWIJDERDIThor...@[EMAIL PROTECTED]
> wrote:
> 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.
Synthetic just means that mathematics is bound to the laws of
intuition.
Numbers have real meaning outside themselves. They have meaning for
real fingers, real toes, and real sticks. When adding two numbers
there
is contained the possibility of adding real things, the quantities
refer to
some real in intuition, and this is only made possible by synthesis,
that
is, by going outside the numbers and appealing to something real in
intuition. 1 + 1 = 2 because 1 finger + 1 toe = 2 digits in intuition.
The
fingers and toes don't add up because of the math, the math adds up
because of the fingers and toes.
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