[OT] Useless Discussion about Impossibility (and math)
levi at cold.org
Wed Sep 26 22:56:03 MDT 2007
Steve <smorrey at gmail.com> writes:
> All numbers are arbitrary symbols we apply to represent quantity.
> Therefore if we discard convention and say instead that 2 is really a
> symbol meaning two and one half units of a given quantity then 2 + 2
> does in fact equal 5.
> I mean if we can say that A = 10, B = 11 and etc, one should certainly
> be able to say that 2 = two and one half units.
The language of mathematics maps strings of symbols (the syntax) to
their meanings (the semantics). When I say '2 + 2 = 4' I'm not
talking about the syntax of the statement, I'm talking about the
When you say that with your new language, '2 + 2 = 5' is a true
statement, you've given a statement that is equivalent semantically to
'2.5 + 2.5 = 5' in real math. Since we're talking about meaning and
not form, you haven't shown that 2 + 2 = 5 at all, even in your new
Your new math would have to have an equivalent way to say that the
quantity two plus the quantity two equals the quantity four as well,
or it would not be consistent.
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