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Topic: [HM] uninterrupted connectedness
Replies: 12   Last Post: Jul 23, 2004 9:43 PM

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 Siegmund.Probst Posts: 16 Registered: 12/3/04
Re: [HM] uninterrupted connectedness
Posted: Jul 21, 2004 4:26 AM

Dear all,

it seems to me that Dedekind's statement

> Mit vagen Reden ÃÂ¼ber den ununterbrochenen Zusammenhang in den kleinsten
> Teilen ist natÃÂ¼rlich nichts erreicht (Naturally nothing is attained with
> vague talk about the uninterrupted connectedness of the smallest parts)
>

alludes to the traditional Aristotelian definition of continuity:

"A thing that is in succession and touches is 'contiguous'. The 'continuous'
is a subdivision of the contiguous: things are called continuous when the
touching limits of each become one and the same and are, as the word
implies, contained in each other: continuity is impossible if these
extremities are two. This definition makes it plain that continuity belongs
to things that naturally in virtue of their mutual contact form a unity. And
in whatever way that which holds them together is one, so too will the whole
be one, e.g. by a rivet or glue or contact or organic union." (from Physics,
Book V, Part 3, Translated by R. P. Hardie and R. K. Gaye; at
http://classics.mit.edu/Aristotle/physics.5.v.html )

Best regards

Siegmund Probst