# Re: FOL and Infinity

*From*: sudhir <sudhir_sh@xxxxxxxxxxx>*Date*: Tue, 12 Apr 2011 12:27:14 -0700 (PDT)

On Apr 12, 11:24 pm, MoeBlee <jazzm...@xxxxxxxxxxx> wrote:

On Apr 12, 1:10 pm, sudhir <sudhir...@xxxxxxxxxxx> wrote:I know you do not have a definition for AxPhi(x). All you have is a

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.

intuition

captured in your rule UI-'For all constants c, AxPhi(x) implies

Phi(c).'

..

Phi(i) is not even a formula of sentential logic.I thought the meaning was clear -if Phi(1), Phi(2) and so on are

sentence symbols, then no

wff of sentential logic could imply each of them.

..Of course you are not formally introducing the notion of a limit.YouPrecisely 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.

are informally

looking for a sentence from which you can infer each of the sentences

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

In sentential logic, you do not find such a sentence. So you introduce

the sentence AxPhi(x)

(you could use any other symbol ) and claim that from it you can infer

each of Phi(1) ,Phi(2) and so on.

It is nothing but a finite shorthand for an infinite amount of

information.

.

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

**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

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

- Prev by Date:
**Re: The Impossibility of Proving the Truth Set Productive** - Next by Date:
**Re: FOL and Infinity** - Previous by thread:
**Re: FOL and Infinity** - Next by thread:
**Re: FOL and Infinity** - Index(es):