Tom Caylor wrote: > Brent Meeker wrote: > > Tom Caylor wrote: > > > 1Z wrote: > > >> Bruno Marchal wrote: > > >>> Le 09-nov.-06, à 14:07, 1Z a écrit : > > >>> > > >>>> Bruno Marchal wrote: > > >>>>> Le 31-oct.-06, à 19:37, 1Z a écrit : > > >>>>> > > >>>>>> Well, I think numbers don't exist AT ALL.... > > >>>>> I have not the slightest idea what you mean by that. > > >>>> If you don't understand anti-Platonism, that would certainly explain > > >>>> why you don't argue against it. > > >>> > > >>> I still don't understand what you mean by numbers does not exist at > > >>> all. > > >>> If that is "antiplatonism", it would help me if you could explain > > >>> what is "antiplatonism", or better what could it mean that the numbers > > >>> don't exist. We already agree they don't exist physically, but saying > > >>> they does not exist at all ??? > > >> It means they don't non-physically exist either. > > >> > > >> Mathematical claims about existence can be true > > >> of false, but so can fictional claims like "Harry Potter exists > > >> in Middle Earth" > > >> > > >>> Even Licorne exists in some sense, > > >>> without referent in "the physical world", but with referent (meaning) > > >>> in some fantasy worlds? > > >> Fantasy worlds don't exist -- that's why they are called fantasy > > >> worlds, -- > > >> Licornes don't exist, and Licornes' don't exist in fantasy worlds. > > >> > > >> Meaning is *not* the same thing as reference (Bedeutung). That is the > > >> box the anti-Platonist has climbed out of. Some terms have > > >> referents (non-linguistic items they denote), others have only > > >> "sense" (Sinn). Sense and reference are two dimensions > > >> aspects of meaning, but not every term has both. > > >> Sense is internal to langauge, it a relationship between a > > >> word/concept > > >> and others. It is like a dictionary definition, whereas reference is > > >> like > > >> defining a word by pointing and saying "it is one of those". > > >> But no-one has ever defined a Licorne that way, since > > >> there is no Licorne to be pointed to. Mathematical concepts > > >> are defined in terms of other mathematical concepts. > > >> Mathematical reference is impossible and unnecessary. > > >> > > >>> Why could numbers not exist in some similar > > >>> sense, except that the number fantasy kiks back (as Tom has recalled > > >>> recently). > > >> Saying that Licornes exist in a fantasy world > > >> is a cumbersome way of saying they don't > > >> literally exist. Well, numbers don't literally > > >> kick back. They don't interact causally > > >> with my reality. > > > > > > What about: > > > If (2^32582657)-1 is a prime number, I will not eat my hat. > > > In all possible worlds where I always keep my promises, I will not eat > > > my hat. > > > This is causally a result of the fact that (2^32582657)-1 is a prime > > > number. > > > > > > Tom > > > > I think a clue is in the fact that you picked (2^32582657 -1) instead of 7. > > > > Brent Meeker > > OK. I'll go with 7. Compare > > If 7 is a prime number, I will not eat my hat.

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