Last time you raised the question of numbers, and I responded, Chris Menzel
told me off for raising something NOT relevant. Note to ChrisM - PatH raised
> > 1. Are there certain things like e.g. numbers and possible worlds?
> > 2. Are they abstract or concrete?
> > Even the first may be controversial, but even if you agree that
> > these things
> > exist, whether they are considered abstract or not is a different
> > question
> > (and arguably more controversial).
> Whether they exist or not, I think you have to say that numbers are
> not concrete. You can't weigh seven.
As I think you must know there is a Fregean concept of number (where 2 is
the set of all sets with two members). This Fregean proposal has modern
supporters - e.g. Crispin Wright http://en.wikipedia.org/wiki/Crispin_Wright
There is debate about whether sets are abstract - David Lewis asks why we
cannot say the set of cars in the car park is located in the car park - and
if it is located, it cannot be abstract. Hence, there is an account of
numbers that says they are not abstract. (05)
There seems to me to be gap between the mathematician's notion of number and
the common sense (or engineer's) notion.
For historical reasons, mathematicians wanted mathematics to be devoid of
ontological commitment. So, if I say there are four books on the table - how
this four relates to the (set of?) books is unclear. (Ditto, the 4lb of
apples on the table.) Assume there is an abstract thing that is the number
four - how does it get related to the books/apples? Hope you see the
problem. Note: this is simple for the Fregean. It seems to me that engineers
would be happier with a Fregean approach for counting and weighing. (06)
Maybe one cannot practically weigh seven (or locate it - as it is far too
scattered). But similar problems occur for things like the mereological sum
of all milk (or gold, or water). These are also too scattered, but seem to
me irredeemably concrete. (07)
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