[FOM] Re: On the Nature of Mathematical Objects
Timothy Y. Chow
tchow at alum.mit.edu
Mon Aug 9 13:02:14 EDT 2004
Dmytro Taranovsky <dmytro at mit.edu> wrote:
> One can try to define what a star is by noting some properties that all
> stars have (such as being heavy) and some properties that no star has,
> but the definition will be in some cases ambiguous (for example, are
> brown dwarfs stars? what about neutron stars?). By contrast, a
> mathematical definition, such as that of an even integer, has no
> ambiguity.
So for example, if
/ the empty set, if the continuum hypothesis holds, and
x = <
\ the class of all sets, otherwise,
then it is unambiguous whether x is a set?
> The reach of particular physical objects is ambiguous (for
> example, is solar corona a part of the sun?), but no such ambiguity
> exists, say, for the set of prime numbers: The set reaches those only
> those natural numbers that have exactly two different divisors.
And no ambiguity exists about whether x (as defined above) "reaches," say,
the set of all integers?
Whether you answer yes or no to these questions, it seems that the answer
is far from uncontroversial.
Tim
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