Re: Moore on Skolem's Paradox

Me:
> An interpretation (as
> >I understand) is the information which we must have about a sentence in
> >order to understand it.
>
> You really haven't been paying attention. I _know_ that that's
> what you understand an interpretation to be. That's one of
> the reasons I say you simply don't understand what you're talking
> about - when we say things like "an interpretation of set theory"
> that is simply _not_ what the word "interpretation" means.

On whether I have understood "interpretation" right (I said it was the
information that must be added to a string of symbols, specifying what
the symbols mean), I looked at three other, presumably authoritative
sources, including Quine and Hodges book on Logic.

1. My dictionary says an interpretation is "An allocation of
significance to the terms of a purely formal system, by specifying
ranges for the variables, denotations for the individual constants &c".

According to Hodges (p222), an interpretation is an abbreviation scheme
which assigns symbols to sentences or schemes in ordinary language.
Thus

J: Sauvignon is the juiciest of Bordeaux grapes
Gx: x is a species of grape
Mxy: x is made out of y
b: Blue Burgundy
c: Pinot Noir

Quine (Methods of Logic 2nd edition p22) says it is a "specification"
of things that must be "imagined" to take place of a letter.

Hodges was also the one (in an introduction model theory) who said an
interpretation is information that must be added to a string of
symbols, specifying what the symbols mean.

.

Relevant Pages

  • Re: Moore on Skolems Paradox
    ... >> David C. Ullrich ... >language" is assigning a reference to all of the terms that we learn. ... >language+ the interpretation given to it as a part of learning the ... >purely formal system, by specifying ranges for the variables, ...
    (sci.logic)
  • Re: Moore on Skolems Paradox
    ... >> what you understand an interpretation to be. ... >information that must be added to a string of symbols, specifying what ... including Quine and Hodges book on Logic. ... Sauvignon is the juiciest of Bordeaux grapes ...
    (sci.logic)