[lit-ideas] Re: numbers
- From: Donal McEvoy <donalmcevoyuk@xxxxxxxxxxx>
- To: lit-ideas@xxxxxxxxxxxxx
- Date: Wed, 27 Oct 2010 10:05:11 +0100 (BST)
--- On Wed, 27/10/10, Robert Paul <rpaul@xxxxxxxx> wrote:
>As there’s usually an embarrassing surfeit of numbers on hand when it comes to
>counting things (for the number of countable things is not infinite), these
>poor, surplus-to-need entities play no role in counting or enumerating.>
"for the number of countable things is not infinite"
This surely depends on the unspoken assumption that the number of "things" is
finite/"not infinite". But even if we assume this is true, the number of
_countable things_ would only then be finite if we further assume that we
cannot count any thing more than once; for if having counted everything once we
can simply go back to first thing counted and continue counting "n + 1" from
the last counted thing, this counting process could go on indefinitely - to
infinity.
It is also unclear to me why, even if "the number of countable things is not
infinite", this would necessarily mean "these poor, surplus-to-need entities
play no role in counting or enumerating". They may not be needed to put a
number on a thing, but this would not mean they do not have any "role" given
their necessary relationships with the numbers we need to put on things.
Donal
Not sure where he's going with any of this
London
They seem to be no more than the playthings of mathematicians (most of whom are
seriously challenged when it comes to actually counting things); they serve no
practical need. If I were pedantic enough, I’d suggest that numbers are not
themselves ‘ways,’ even though they seem to make certain things possible.
I’m not sure what an abstract tally is; certainly keeping track of ‘how many’
(tallying) isn’t the only function numbers have. Numerals, as you say, are
different. On certain views, they represent numbers, just as ‘nine’ represents
a number in ordinary English. On my view—surely long outdated—numbers are
objects: not every object need be the kind of thing one can touch and fondle.
‘Frege Against the Formalists,’ was the name Peter Geach and Max Black gave to
a section of their Frege translations. One would hate to be a Formalist, coming
across it in a math journal in the Mutton College library. Spoil one’s
digestion, it would.
Robert Paul,
somewhere south of Reed College
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