# Re: FOL and Infinity

*From*: MoeBlee <jazzmobe@xxxxxxxxxxx>*Date*: Tue, 12 Apr 2011 11:24:50 -0700 (PDT)

On Apr 12, 1:10 pm, sudhir <sudhir...@xxxxxxxxxxx> wrote:

On Apr 12, 12:39 am, MoeBlee <jazzm...@xxxxxxxxxxx> wrote:> On Apr 11, 1:27 pm, sudhir <sudhir...@xxxxxxxxxxx> wrote:

.

How does the sentence AxPhi(x) imply Phi(1) ,

unless some intuitive semantic content

is read into AxPhi(x)?

No matter what the interpretation of the language, AxPhi(x) implies

Phi(c) for any constant 'c' in the language. That is, for any constant

'c' in the language, there is no model in which AxPhi(x) is true but

Phi(c) is false.

This is precisely what I said.

No, it's not.

Your definition of AxPhi(x) is "For any

constant c

in the language, AxPhi(x) implies Phi(c)'.

No, I didn't give a "definition" of a formula AxPhi(x). Indeed, I said

that I don't know what you mean by a "definition" of such a formula.

You skipped what I wrote.

You cannot explain or define AxPhi(x) without using 'For any(all)'

That is where you are into

an interminable regress.

I already addressed this in a previous post. You skipped what I wrote.

there is no sentence of sentential

logic which will imply

Phi(i) for every i.

Phi(i) is not even a formula of sentential logic.

Precisely such a sentence is introduced in FOL , namely AxPhi(x) .In

a way, AxPhi(x) is

a limit to the sequence

Phi(1), Phi(1)&Phi(2), Phi(1)&Phi(2)&Phi(3), and so on.

You like to use words like "limit" in your own personal way, it seems.

The big assumption is that such a limit exists;

No, there's no notion of such a limit when we formulate a language so

that "AxPhi(x)" is a formula of the language.

You're just making stuff up.

that such a sentence

(comprising of a finite string of symbols)

can convey that each of the independent sentences Phi(1),Phi(2) and so

on is true.

Why don't you just read a book where you'll find the inductive

definition of "true in an interpretation"?

AxPhi(x) is a shorthand for

an infinite amount of information ; it is the first idol in the Temple

of Infinity.

Right, by saying "idol" and "Temple" you really convinced me that you

have a cogent argument even though you don't know Jacques about

anything here.

MoeBlee

.

**Follow-Ups**:**Re: FOL and Infinity***From:*sudhir

**References**:**FOL and Infinity***From:*sudhir

**Re: FOL and Infinity***From:*MoeBlee

**Re: FOL and Infinity***From:*sudhir

**Re: FOL and Infinity***From:*MoeBlee

**Re: FOL and Infinity***From:*sudhir

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