On 07 Jan 2015, at 19:23, John Clark wrote:
On Wed, Jan 7, 2015 Bruno Marchal <[email protected]> wrote:
> all logicians have agreed that "existence" is a logical symbol.
And what does that symbol symbolize? The above tells me nothing, a
symbol can symbolize anything and a symbol can symbolize nothing
too. Logical sybols don't necessarily sybolize anything, they can
just be a typographic set built from a set of axioms, but meanings
can often be assigned to them; otherwise physicists would have no
use for mathematics, or even words for that matter.
OK, I understand now why you don't read the second part of sane04. You
don't understand what is logic. You have clearly never studied even
just an introduction. You are not alone.
But this means you are not aware at all of my contribution. You
criticize me since years, but you don't know what I have done at all.
The logical symbol are entirely defined by the operative meaning. In
the case of the symbol "E" (read "it exists) the only rule rule is
P(n) / ExP(x), and that's all.
This is basically why first-order logic makes it possible to make
theory without any metaphysical baggages. It makes also mathematical
logic (and some philosophical logics) into a branch of math. Church's
thesis extends this to a large part of computationalist "philosophy".
>>> Nothing exist = not one thing exists
>> Then nothing doesn't exist,
> Why?
Because otherwise something does exist.
> if nothing exist, not one thing exist.
Then nothing doesn't exist so....
We were going from the base level to the meta-level. As I said, this
can be formalized with the reflexion theorem (or axiom) in set theory.
>> so something must exist, but it says nothing exists. And welcome
to the self contradiction Merry-Go-Round.
> It looks like the contradiction is brought by you, here. Or you
are perhaps just playing with the words.
And to me a statement like that sounds like the last refuge of
someone losing an argument. Words are symbols too, and there is
another word for playing with words, thinking.
If playing with words is thinking, you are a great thinker ...
> In our finitist context ExP(x) can be seen as an abbreviation of
P(0) v P(1) v P(2) v P(3), v ... That is existence is an infinite
disjunction (like AxP(x) is equivalent with an infinite
conjunction). Of course existence and non existence have still
consequences. Ex (prime-number(x)), for example, and ~Ex(prime(x) &
even(x) and x > 2), ...
You are perhaps just playing with symbols.
No, I explain basic undergraduate logic.
> Philosophers knows that to make existence into a property re-
introduce essentialism and category confusion.
Essentialism is the idea that things have a set of properties that
they need to function. Well duh. Your pal Plato came up with the
idea and it's true but it seems pretty bland dull and
uncontroversial to me.
It is Aristotle, and logicians avoid it by the notion of axiomatic,
essentialism is either a regression toward the use of intuitive
meaning instead of axiomatic. It can be formalized through the use of
modal logic, or second order logic, where we loose all the important
theorems of first order logic (compactness, completeness). In fact,
with essentialism, we do just intuitive math again, not formal logic.
Bruno
John K Clark
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