Paulo Garrido wrote:
> Marshall Clemens wrote:
>
> > As pointed out by Marvin Minsky amoung others, this is the
> > glaring flaw
> > with 'absolute' holism: once you say something is a whole and
> > cannot be
> > broken down (reduced) into the interaction of simpler
> > components, that
> > is the end of the discussion. To deal with something as a
> > irreducible
> > whole means that you do not understand it at all, except
> > possibly
> > describing its input-output behavior.
>
> Just a comment:
>
> Implicit in the above sentences is a direction of flow of
> understanding from the whole to the parts. From a formal axiomatic
> point of view, one may ask why the direction of understanding
> could (or should) not be reversed. Ie, if to understand an entity
> doesnt mean exactly to be able to put the entity inside the frame
> or context of a larger entity. Being by this that the entity may
> be understood.
>
> In set terms: the first direction of flow means that to understand
> an entity X1, one should take it as a set, one should be able to
> discriminate the elements x1, x2 ...xn of X and to establish the
> relations Ri holding among them, as elements of X.
> The second direction of flow means that to understand an entity
> X1, one should be able to take it as an element of a set XX,
> discriminate the other elements X2,...Xn of XX and to establish
> the relations Ri holding among them, as elements of XX.
>
> I dont see any reason apriori to exclude any of the directions of
> understanding flow. (In particular both give rise to infinite
> regresses, which can only be stopped by some postulated
> nominalistic stops like "the fundamental particles" or "all that
> is"). Its seems to me that one may gain from putting the two
> directions of understanding flow to work together.
This issue is dealt with by Rosen in tems of analytic vs synthetic
models. He shows how sets can be assempled using either direct sums or
direct products into reducable and irreducible models.
>
>
> Paulo Garrido
Don