Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
Drexel University or The Math Forum.
|
|
fom
Posts:
1,038
Registered:
12/4/12
|
|
Re: Cantor's absurdity, once again, why not?
Posted:
Mar 19, 2013 9:09 PM
|
|
On 3/19/2013 3:50 PM, WM wrote:
> On 19 Mrz., 15:48, fom <fomJ...@nyms.net> wrote:
>>
>> What, then, did you come here to teach?
>>
>> I demand to know the meaning of your terms from
>> first principles.
>
> Try to forget what you have learned about mathematics and philosophy.
> Start with the four species +,-,*,: and the tables. That is the
> foundation from which all sensical mathematics follows. And that is
> given. There is no need to try to find principles.
ALERT!
Please compare with the previously posted
criticism of Weyl's trick, reproduced
for WM's readers below:
> But, a few pages earlier, Weyl makes an
> interesting statement concerning the nature
> of "objective" fact.
>
> Note the explicit rejection of logic
> and definition in his statement,
>
> "Therefore, how two sets (in contrast to
> properties) are defined (on the basis of
> the primitive properties and relations
> and individual objects exhibited by means
> of the principles of section 2) does not
> determine their identity. Rather, an
> objective fact which is not decipherable
> from the definition in a purely logical
> way is decisive; namely, whether each
> element of the one set is an element
> of the other, and conversely. [...]"
>
>
> So, as a reader of this statement, I
> am first expected to reject prior
> definitions and to reject logical
> relations. Then, I am expected to
> understand the discursive assertion
> explaining what it is that cannot
> be explained.
>
> However, I am to understand that this
> is sensible with respect to some
> other prior principles explained
> elsewhere. And, I am to understand
> that what cannot be explained to
> me can sensibly be expressed as
> a rule.
>
> The statement goes on to say,
>
> "Moreover, we see that the description
> of a finite set in individual terms
> is, considered formally, just a special
> case of that based on a rule. For
> example, if a,b,c are three objects
> of our category, then
>
> P(x)=J(xa)+J(xb)+J(xc)
>
> is the judgement scheme of the derived
> property 'being a or b or c'; and the
> set having just those three objects
> as its elements correspond to this
> property."
>
>
> What is relevant from section 2 that
> I am expected to not ignore while
> being told to ignore is the following:
>
> "By simple or primitive judgment scheme
> we mean those which correspond to the
> individual immediately given properties
> and relations. To these we add the
> identity scheme J(xy) (meaning 'x is
> identical to y' i.e., 'x=y')"
>
>
> So, once again, the situation resolves
> to the concept of "immediately given
> individual properties" or the objective
> fact that the purport of singular
> reference suffices as an establishment
> of singular reference.
>
> And, once again, searching through these
> philosophies and the definitions leads
> to the fact that presentations of
> Leibniz law such as
>
> http://plato.stanford.edu/entries/identity-relative/#1
>
> misrepresents what, in fact, Leibniz
> actually wrote:
>
> "What St. Thomas affirms on this point
> about angels or intelligences ('that
> here every individual is a lowest
> species') is true of all substances,
> provided one takes the specific
> difference in the way that geometers
> take it with regard to their figures."
>
> Leibniz
>
|
|
|
|
