Re: Galileo's Paradox and the Project of the Reals

Tony Orlow wrote:
David Marcus wrote:
Tony Orlow wrote:
MoeBlee wrote:
No, there are DIFFERENT uses of the word 'successor', as I took
ELABORATE pains to explain to you, and you now are just ignoring.
There is one general definition of successor(x): the element after x.

What does "general definition" mean?

One that is correct regardless of context.

So much nonsense in such few posts. But, this one stands out. So, you
are asserting that "the element after x" is the universal definition of
"successor(x)", despite the fact that a different definition is used in
set theory? Perhaps you don't believe us. Do you think we are lying? It
would be easy enough for you to check by looking in a math book.

Okay, by a "2-place predicate symbol" we mean a statement representing a
relation that yields a logical value, given two objects as input. I
think one can consider that a function, or a relation between elements.
NO!!! For about the FIFTH time now: NO.

A predicate symbol is a SYMBOL. It is not a statement. (Actually a
0-place predicate symbol is a sentence, but I'm talking about a 2-place
predicate symbol.)
Give me a break. A symbol alone has no meaning, Unless you apply meaning
to it, it';s just a graphic, a picture. What do you think 'e'
represents, most of a circle with a horizontal line through it?

So, in addition to having no knowledge of the existence of the subject
of measure theory, you have no knowledge of the existence of the subject
of mathematical logic. Have you taken any math courses past high school?

You're being an ass. I understand symbolic logic, but there is much more
to math than that. Symbols without meaning are checkers.

Considering your posts, I fear we can't take your word that you
understand any mathematical logic or symbolic logic. However, I am
willing to let you demonstrate that you do: Please define what a first
order system is.

Without ANYTHING except the logical symbols and the non-logical 2-place
predicate symbol 'e'.

HOW MANY TIMES do we have to say it for you?

ONE MORE TIME in an effort to get through your CAST IRON skull: EVERY
formula of set theory is equivalent in set theory to a formula in which
the ONLY non-logical symbol is 'e'.

Demonstrate it. Interpret y' in the axiom of infinity as something other
than successor. Boil it down to 'e'. Can't be done.

Why should axioms be "interpreted"? Such a strange idea.

So strange, to think that anything we think should actually lead us to
any kind of conclusion about reality. Weird...

Dyslexia again: What we use math for doesn't determine what it is.

--
David Marcus
.

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