Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.


Math Forum
»
Discussions
»
sci.math.*
»
sci.math
Notice: We are no longer accepting new posts, but the forums will continue to be readable.
Topic:
Cantor's absurdity, once again, why not?
Replies:
77
Last Post:
Mar 19, 2013 11:02 PM



fom
Posts:
1,968
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/identityrelative/#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 >



