On 3/25/2013 9:01 PM, david petry wrote: > On Monday, March 25, 2013 1:42:27 PM UTC-7, fom wrote: > >> Frege once characterized the empty set as a "forest without trees". > >> Modern mereology follows Lesniewski in denying the existence of >> an empty set. > >> Shall these be accepted as arguments to ban speaking of zero? > > > Mathematics can be thought of as a conceptual framework for > reasoning about the real world. You would have trouble convincing > me that "zero" is not an essential concept within that conceptual framework > >
I have no difficulties with my own or anyone else's philosophy of mathematics. I have no intention of trying to change your beliefs.
I observe, however, that Western European culture had pursued science prior to the introduction of zero. I am fairly certain that the classic civilizations did not have zero.
So, you must have a different understanding of the term 'essential' than do I.
But, I am more interested in your statement that "mathematics can be thought of as a conceptual framework".
Is mathematics a conceptual framework?
If it may only be thought of as such then what alternative shall we propose concerning the nature of what it is?
> > >> Even if Cantor viewed his own conception in terms of >> realism, why do you presume that this is required of >> everyone else? > > Ockham's razor. Keep it simple. Yada, yada. >
That really does not seem to answer my question. You seem to presume for everyone else. In any case, at least one account of Ockham's razor seems to suggest that you use it a little differently from its namesake,