[lit-ideas] Re: "Synthetic A Priori" -- Revisited
- From: "Andreas Ramos" <andreas@xxxxxxxxxxx>
- To: <lit-ideas@xxxxxxxxxxxxx>
- Date: Tue, 21 Sep 2004 17:07:23 -0700
> But the meaning of 12 is indeed implied in the meaning of 5 and 7.
>
> It may be possible that someone _knows_ that the year has _twelve_ months,
> and yet be unaware that it has _five_ and _seven_ years. That is, someone may
> possess the concept "twelve" (or "five" and "seven") and not the concept of
> any other 'natural number'.
It's certainly possible that someone may think that, but it also means he
doesn't understand
numbers. He just hasn't thought about it.
> Consider:
>
> Henry VIII had six wives.
>
> Therefore
>
> Henry VIII had three wives.
>
> That is logic...
No, that's not necessarily an issue of logic. That could be understood in
various ways.
Mike has had seven wives and Mohammed also had seven wives, but each had their
wives in an
entirely different sense. Mike married them one after the other, but Mohammed
(may his tribe
increase!) had them all at once.
> It seems that each number represents a different "concept" --, and in the
> case of additions, and equations, we must also consider the very concept of
> "adding" and "equating" -- as Kant noted. All this is notably synthetic and
> mostly a posteriori.
See? You're mixing up the concept of the number with the various meanings of
the numbers.
For example, 2 boys plus 4 boys = trouble and every mother knows that.
A number is a quantity, for example: X. If you have 2 X (written out as XX),
then it's just
two of the X. The concept of XX includes the concept of one X and one X. The
concept of one
X includes the possiblity of multiple X. Five X (XXXXX) is just that: five X,
and each X is
equal. There are 1X+4X, 2X+3X, 3X+2X, 4X+1X, and 5X, all implied in the concept
of XXXXX.
This can go on forever, thus arithmetic is infinite and has no surprises: 6
bazillion + 3
bazillion = 9 bazillion, and we don't have to test this to find out, and we
don't need a
calculator with a bazillion place holders.
This is quite different from many other branches of mathematics, where you
don't know what
the results could possibly be and you have to carry out empirical tests to find
out.
yrs,
andreas
www.andreas.com
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