Subject: Re: [HM] Kant and Manifolds
From: Gordon Fisher (gfisher@shentel.net)
Date: Mon Mar 13 2000 - 18:33:15 EST
[deletion]
Emili Bifet wrote: PS Norman Kemp Smith translates the quotation above as
follows:
>
> "By synthesis, in the most general sense, I understand the act of
> putting different representations together, and of grasping what is
> manifold in them in one [act of] knowledge. Such a synthesis is pure,
> if the manifold is not empirical but is given a priori, as is the
> manifold in space and time. Before we can analyse our representations,
> the representations must themselves be given, and therefore as regards
> content no concepts can first arise by way of analysis. Synthesis of a
> manifold (be it given empirically or a priori) is what first gives
> rise to knowledge. This knowledge may, indeed, at first, be crude and
> confused, and therefore in need of analysis. Still the synthesis is
> that which gathers the elements for knowledge, and unites them to
> [form] a certain content. It is to synthesis, therefore, that we must
> first direct our attention, if we would determine the first origin of
> our knowledge."
>
> Emili Bifet
Yes. I interpret Kant's "synthesis" to be analogous to what is more
commonly called nowadays "perception". There is of course a kind of
synthesising that goes on in perception, much studied by psychologists
and others. Humans have the ability to transform these perceptions
in various ways, one of which I take to correspond to Kant's "analysis".
Presumably Kant somewhere wrote or indicated that in the a priori
synthesising of what we might call our perceptual manifolds (the "spaces"
that we see with our eyes and brains), our perceptions necessarily
obey euclidean geometry.. But I expect he would have known about
attempts to prove the parallel postulate from the other axioms, which
of course began in antiquity? Quite aside from whether or not he knew
anything about what we today call non-euclidean geometries, it seems
probable that he knew about struggles with the parallel postulate.
However, maybe he thought this wasn't very significant for what he
wanted to say about the way we interact with our environments. If so,
I would agree with him on this point.
There is an old slogan which I think is a direct translation of
something Kant wrote, which bears on this: concepts without percepts
are empty, percepts without concepts are blind.
Gordon Fisher gfisher@shentel.net
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