On 3/22/2013 1:53 AM, WM wrote: > On 21 Mrz., 20:14, fom <fomJ...@nyms.net> wrote: >> On 3/21/2013 8:11 AM, WM wrote: >> >> >> >>> But I am not interested in the set itself. Not at all! My claim is >>> that every member of the set of lines can be removed such that no >>> member remains, but every natural number is contained in the list. >> >> It would be difficult to find WM making >> a better statement of his presumption of >> completed infinities. >> >> One has the empty list. >> >> One has every natural number. >> >> WM confuses "natural number" with "representation >> of natural number" and his intentions to make >> such representations. >> > > That is nonsense. If the natural number is different from the set of > its representations, then one can never have, know, or use it.
In this case, the statement is referring to your methodology of interpreting crayon marks as standing in representation of natural numbers. The point is that talk of "aims" and "goals" in making your crayon marks means that your representations are, in fact, your intention to make crayon marks.
And, as pointed out to you in other posts, authorial intentions are problematic, and, therefore, rejected in semantic theories that apply to mathematics.