[FOM] nieve continuum metaphysics

Stephen Lavelle icecube at maths.tcd.ie
Fri Feb 27 18:35:15 EST 2004

I abhor metaphysical questions, but I just can't help myself:

A set is traditionally defined as something {a,b,c, etc.} whatever.
People think of sets in this way, however you look at it.  If one accepts
infinity to be the infinity of the natural numbers, then one has via the
usual embedding infinity of the reals.  However, that the reals (i.e. the
continuum) cannot be put into 1-1 correspondence with the integers could
perhaps in itself be used as evidence that the continuum is not a set, in
that it cannot be represented as a set of things, so that it is
fundamentally different....,

i know it's mathematically a rather pointless arguement (pun
unintended), becuase mathematically what i have called sets above are
called countable sets and what i have called a continuum is viewed as
being an uncountable set, but in terms of understanding the intuitive
"nature" of such objects i think the traditional definitions are very

Stephen Lavelle

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