Re: The Difference between a Set and an Element

On 17 Jan 2007 16:15:40 -0800, "Paul Holbach"
<paulholbachDELETETHENAME@xxxxxxxxxx> wrote:


Imho your are mixing up things here.

x = 1 v x = 12 v x = 345 v x = 9536 v x = 27364 v x = 876453

Is an _expression_ (i.e. a formula), but _not_ a concept.

But I'm afraid I cannot mention concepts without using [such]
expressions [i.e. formulas], can I?

Sure you can. For that purpose (in 2OL) we use concept symbols.


[...] when I speak of the concept <horse>, I use the word
"horse" in order mention something non-linguistic. [...]
What is a concept?

Good question! :-)


And open formulas qua functional expressions represent concepts [...]

Sure.


So the open formula "x = 1 v x = 12 v x = 345 v x = 9536 v x = 27364 v
x = 876453" represents either the concept <identity with 1, 12, 345,
9536, 27364, or 876453> or the property of being identical with 1, 12,
345, 9536, 27364, or 876453.

Right.

Still the expression / the formula

x = 1 v x = 12 v x = 345 v x = 9536 v x = 27364 v x = 876453

is not identical with the concept it represents. (Assuming there _are_
such entities like concepts.)


Likewise,

123

is an expression, but not a number.

123 is a number, and "123" is a numerical expression.

Right.


A formula does have a _length_ (the formula above consists of 38
symbols), but I would deny that a _concept_ has a length (or
consists of symbols).

Concepts [...] are indeed not likely to have a (syntactic) length.

See?


It's important (of course) not to mix up expressions with concepts.

Yes.

Fine.


F.

--

E-mail: info<at>simple-line<dot>de
.

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