Re: Infinite sets.

"Andrew Usher" <k_over_hbarc@xxxxxxxxx> writes:

It does not make writing "There exists 2" any less wrong.

2 isn't an arbitary symbol.

Quite right!

When we write 2, we mean the number after
1. More generally, whenever we use a 'constant' symbol, we mean the
thing with such-and-such properties.
Saying 'there exists a 2 such that 1 + 1 = 2' is just a definition of
2, and saying 'for all 2 such that 1 + 1 = 2' is no different than 'for
2'.

No, you're simply wrong. In every presentation of first order logic
that I have seen, one cannot quantify constants. And it is utterly
standard (as you say) to interpret the symbol 2 as a constant symbol.
It would be intentionally confusing to use it as anything other than a
constant, an act of stubborn defiance for no real purpose.

--
Jesse F. Hughes
"Certainly he who can digest a second or third fluxion need
not, methinks, be squeamish about any point in divinity."
George Berkeley, 1734
.

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