Das Kalenderblatt 090722

21/07/2009 - 23:36 von WM | Report spam
Belief in the existence of the infinite comes mainly from five
(1) From the nature of time-for it is infinite.
(2) From the division of magnitudes-for the mathematicians also use
the notion of the infinite.
Further, how can the infinite be itself any thing, unless both number
and magnitude, of which it is an essential attribute, exist in that
way? If they are not substances, a fortiori the infinite is not.
It is plain, too, that the infinite cannot be an actual thing and a
substance and principle.
This discussion, however, involves the more general question whether
the infinite can be present in mathematical objects and things which
are intelligible and do not have extension, as well as among sensible
objects. Our inquiry (as physicists) is limited to its special subject-
matter, the objects of sense, and we have to ask whether there is or
is not among them a body which is infinite in the direction of
We may begin with a dialectical argument and show as follows that
there is no such thing. If 'bounded by a surface' is the definition of
body there cannot be an infinite body either intelligible or sensible.
Nor can number taken in abstraction be infinite, for number or that
which has number is numerable. If then the numerable can be numbered,
it would also be possible to go through the infinite.
It is plain from these arguments that there is no body which is
actually infinite.
But on the other hand to suppose that the infinite does not exist in
any way leads obviously to many impossible consequences: there will be
a beginning and an end of time, a magnitude will not be divisible into
magnitudes, number will not be infinite. If, then, in view of the
above considerations, neither alternative seems possible, an arbiter
must be called in; and clearly there is a sense in which the infinite
exists and another in which it does not.
We must keep in mind that the word 'is' means either what potentially
is or what fully is. Further, a thing is infinite either by addition
or by division.
Now, as we have seen, magnitude is not actually infinite. But by
division it is infinite. (There is no difficulty in refuting the
theory of indivisible lines.) The alternative then remains that the
infinite has a potential existence.
The infinite exhibits itself in different ways-in time, in the
generations of man, and in the division of magnitudes. For generally
the infinite has this mode of existence: one thing is always being
taken after another, and each thing that is taken is always finite,
but always different.

[Aristoteles: Physik (350 v. Chr.)]


Gruß, WM

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#1 Herbert Newman
22/07/2009 - 01:10 | Warnen spam
Am Tue, 21 Jul 2009 14:36:14 -0700 (PDT) schrieb WM:

[Aristoteles: Physik (350 v. Chr.)]

Ja, bekanntlich hat Aristoteles ja auch auf dem Gebiet der Logik und der
Physik das letzte Wort gesprochen. :-)

Herr Mückenheim, jemand wie Sie hàtte besser ins Hochmittelalter gepasst:
dort hàtten sie mit Aristoteles-Zitaten sicher punkten können! :-)


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