On 7/16/2013 12:55 AM, Albrecht wrote: > > And you are a second time wrong: Parts of math are proveable by physical evidence.
And what would that be when one is rejecting logical bases for the subject?
The entire argument of "finitists" and "predicativists" seems to rely upon the fact that they can "count" material objects of a *compact* nature.
But, none of these promoters produce a natural number in material form.
So they next begin speaking of "objects" in the abstract or as ideas.
But they reject the philosophical views that are directed at delineating such views with precision.
When WM lists monotone inclusive chicken scratch, he follows the Russian discussion of constructive objects that interpret Brouwer or Hilbert's "intuitive" construction when he turns to proof theory.
But, these are little more than Kant's motivating example of the schema of number (it is not the "intuition" associated with Kantian temporality).
Just as WM uses words like 'name' and 'definition', you are using 'proof' and 'evidence' while denying the considerations of those who have asked how statements such as your own are to be believed by others.
And, please accept my apology for a recent reply I made to one of your posts. In reading the other thread I went from a sincere question to ridicule between two replies. I should not have done that. I believe that one should understand the differences in these views before deciding between them. But, I cannot see how saying some bounded natural number is "more real" than some transfinite number makes it so. Neither has a material existence (to my knowledge), and, the positions rejecting completed infinities that appeal to the "definiteness" of bounded natural numbers are not based on logic and reason. Nor, in my opinion, are arguments of the predicativists who think "a little infinity" that accommodates most usage is acceptable whereas a theory of transfinite arithmetic is not.
My simplifications are unfair. But they reflect that these positions want me to accept "abstract objects" or "ideas" as if they were "given" with the same force as are material objects. My criticisms are based upon the very first assumption I am asked to accept in order to give them credence.
This assumption is simply not an acceptable starting point.