Das Kalenderblatt 091231

30/12/2009 - 13:32 von WM | Report spam
(a) Labels are used merely as labels: if the world is finite, so is
the set of labels, and it is
impossible the label all “objects” in the world.
(b) Labels form a structured set. In this case the labelling process
can become more economical
and more efficient, but it remains the case that the set of labels
stays finite.
(c) Labels form a structured set inserted in a theoretical framework.
Here two subcases can be distinguished:
(c1) There are interpretations of the theoretical framework that refer
to “objects” in the world.
Obviously in this case everything remains finite again on the
assumption that the world is finite.
(c2) There are no specific interpretations that refer to “objects” in
the world. It is then always
possible to find finite quasi-models that are derived from the
classical infinite models of the
theoretical framework. In some cases (as shown in the example above)
these quasi-models can
be seen as extensions of the classical model since it is possible to
keep all classically true
statements true in the quasi-model. Thus in those cases no truths are
lost.
The last case also applies to all labels that can be imagined by a
labelling machine, if the
requirement is that the labels should be communicable. Hence, if it is
representable, it is obvious
that we can imagine something larger, as we usually represent
something in an environment,
hence additional space is available. What we have to imagine, is a
label such that if we try to
represent it, we should fail to do so. Hence the agreement with
Priest’s description quoted at the
beginning of this paper: “so large that it has no physical or
psychological significance …”. It is
paradoxical to be sure. If formulated in terms of questions, the
problem becomes immediately
obvious. The question “What is the largest label or numeral that is
not imaginable?”, should not
be answered by “The label so-and-so with properties such-and-such”,
because then it has been
imagined, thereby not answering the question. The answer must be:
“Whatever it is, that label”.
An alternative reply would be: “The largest label is that label about
which questions such as the
question posed cannot be asked”. It is that label that ceases to be
that label as soon as something is said about it. {{Eine Eigenschaft,
die sich àndern kann - potentielle Unendlichkeit.}} A conclusion that
fits in nicely with the argued for vagueness of the largest label.

[Jean Paul Van Bendegem: "Why the largest number imaginable is still a
finite number"; p. 16]
http://www.vub.ac.be/CLWF/members/j...inable.pdf

Gruß, WM
 

Lesen sie die antworten

#1 Vogel
01/01/2010 - 10:14 | Warnen spam
WM wrote in
news::

(a) Labels are used merely as labels:



Ises nicht wahr!

.. if the world is finite, so is the set of labels, and it is
impossible the label all “objects” in the world.



Was soll der Blödsinn?



"if the world is finite", kann man selbstverstàndlich "all “objects” in
the world", labeln.



Irgendwie scheinst du in das ansehnliche Alter gelangt zu sein, in
welchem du meinst deine Klugheiten der Nachwelt überlassen zu müssen.



Es könnte sein, dass die Nachwelt dich überholt hat. Vor allem machen
deine aus dem Kontext gerissenen Zitate keinen Sinn.

(b) Labels form a structured set. In this case the labelling process
can become more economical and more efficient, but it remains the case
that the set of labels stays finite.



Undefinierter Blödsinn.

(c) Labels form a structured set inserted in a theoretical framework.
Here two subcases can be distinguished:

(c1) There are interpretations of the theoretical framework that refer
to “objects” in the world. Obviously in this case everything remains
finite again on the assumption that the world is finite.



Wirklich hinreissend klug.
"everything remains finite", "on the assumption that the world is
finite"
So ein banaler Blödsinn hat in der Mathematik nichts zu suchen.
Der gehört dahin wo du ihn her hast, in die Freizeitliteratur.


[Jean Paul Van Bendegem: "Why the largest number imaginable is still a
finite number"; p. 16]



oder:
"how you can do money with bullshit"


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