[lit-ideas] Re: numbers
- From: Robert Paul <rpaul@xxxxxxxx>
- To: lit-ideas@xxxxxxxxxxxxx
- Date: Tue, 26 Oct 2010 20:41:01 -0700
David Savory says
…numbers are a way to keep track of how many items we have. Originally
for counting it turned out they could also be used for measuring how
much we have and for dividing what we have into fractions. Later still,
numbers were used for sequencing and coding. Now they are used to
represent information. And I think I should be pedantic and say there is
a difference between a number which is an abstract tally and a numeral
which is the notational sign that represents it.
Possibly, here one has in mind the cardinal numbers (used for counting
and enumerating), and maybe too the ordinals, so precious to those who
still think that where one is in a ticket line matters, and not of
Cantor’s Paradise. 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. 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long outdated—numbers are objects: not every object need be the kind of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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