[FOM] Tolerance Principle

[Harvey Friedman]

On Sat, Feb 04, 2006 at 10:30:45AM +0100, Joseph Vidal-Rosset
wrote:

>My question is both to  Arnon Avron and Harvey Friedman: is
>Carnap's Tolerance Principle wrong (and then intolerable) ?

On 2/7/06 3:40 AM, "Roger Bishop Jones" <rbj01 at rbjones.com> wrote:

> Carnap's "principle of tolerance" is simply the recognition that
> there are many different languages in which one can reasonably
> talk about the world.  Its prime consequence in Carnap's
> philosophy is that he worked on phenomenalistic and
> physicalistic accounts of physics rather than (as a positivist
> might) taking a dogmatically phenomenalist position.
> His tolerance position, and all his work on languages, is
> pluralistic, and in the context of mathematics recognises that
> there are many different languages in which one can do
> mathematics.  This principle, it seems to me, cannot fail to
> apply anywhere. Languages inevitably involve many arbitrary
> choices, some of them trifling (e.g. which symbols to use)
> others not so trifling (and perhaps less "arbitrary").
> In the end, for Carnap, it comes down to pragmatics.
> 

I have only a comment about "Carnap's Tolerance Principle" as formulated
above. 

As I have mentioned many times before on the FOM, it appears from experience
that any for any two natural formal systems, each of which interprets a
small amount of arithmetic (or set theory), one of them is interpretable in
the other. The two systems are based on first order predicate calculus, but
may have entirely different languages.

Harvey Friedman