Re: PC(1): An introductory formal logic

Frederick Williams wrote:
George Dance wrote:

An axiom is a formula that is true in every interpretation.

Your muddling the syntactic ("An axiom is a formula") with the semantic
("true in every interpretation").

There is absolutely no distinction, in this system, between the
semantic and the syntactic. Why do you think that there has to be?

.

Relevant Pages

  • Re: PC(1): An introductory formal logic
    ... Your muddling the syntactic ("An axiom is a formula") with the semantic ... There is absolutely no distinction, in this system, between the ... course other schools, where the idea of leaving 2 + 2 undefined ...
    (sci.logic)
  • Re: set theories
    ... Aatu Koskensilta wrote: ... Frederick Williams wrote: ... Sorry, I think this is wrong, the Axiom of Infinity must be replaced ...
    (sci.logic)
  • Re: "Theorem" in Mendelson ?
    ... On Fri, 16 Jun 2006 02:06:36 GMT, Frederick Williams ... What you have written is not a proof-in-L. ... That's not what Mendelson says, at least in the 4th edition where he ... it, it needs to be an axiom, and it isn't. ...
    (sci.logic)
  • Re: PC(1): An introductory formal logic
    ... Frederick Williams wrote: ... It is a reflection of the choice of the ... level of abstraction that is being formalized. ... distinction and so that distinction is not made. ...
    (sci.logic)
  • Re: Cantors "diagonal argument". My Objection.
    ... AS AN AXIOM! ... I'm not quite clear on the distinction myself. ... in some axioms system for the real numbers ... Hence we can derive theorems relying on this axiom, ...
    (sci.logic)