In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 30 Jan., 12:53, fom <fomJ...@nyms.net> wrote: > > On 1/30/2013 5:29 AM, WM wrote: > > > > > On 30 Jan., 12:02, fom <fomJ...@nyms.net> wrote: > > > > >> As for those "logical considerations," I mean that > > >> one can develop a hierarchy of definitions that > > >> depend on actual infinity. To say that mathematics > > >> is "logical" is to concede to such a framework. I > > >> do not believe that mathematics is logical at all. > > > > > That is a very surprising statement. Why do you think so? > > > > In his papers on algebraic logic, Paul Halmos made > > the observation that logicians are concerned with > > provability while mathematicians are concerned more > > with falsifiability. > > Same is true for physicists. But I had the impression that > mathematicians are more concerned with proving. I, as a physicist, am > more concerned with showing counter examples. > > > > > It is also the exact question discussed by Aristotle > > when speaking of the relation between definitions and > > identity in Topics. > > > > Logical identity, in the modern parlance, is ontological > > "self-identity" arising from a combination of Russell's > > description theory and Wittgenstein's rejection of > > Leibniz' principle of identity of indiscernibles. > > Well in mathematics we can ask whether in a = a the right a can be the > same as the left a, because both can be distinguished by their > position.
That is due to WM's perpetually confusing the name of or pointer to an object with the object being named or pointed to. --