[hist-analytic] Methods of Proof: Re: Clarity Is Not Enough

Roger Bishop Jones rbj at rbjones.com
Mon Feb 23 10:56:40 EST 2009

On Monday 23 February 2009 15:27:26 steve bayne wrote:
> I'm pretty sure I get what you are talking about w.r.t
> the metalanguage stuff. But take this fragment:
> "represent the syntax of A in the ontology of B."
> Could you give an example of syntax being represented
> "in the ontology"?

Take arithmetisation.

The arithmetisation of syntax consists in assigning to
each syntactic entity a natural number so that talk
about syntax can be translated into talk about numbers
(and partially vice-versa).

The ontology of arithmetic is the natural numbers.
Arithmetisation provides numerical representatives
for syntactic entities, and hence represents syntax
in the ontology of arithmetic.

It would perhaps have been clearer to talk of
"the domain of discourse of B", but that is of
course just the set of things which exist so far
as B is concerned, i.e. "the ontology of B".
(is this an odd usage of "ontology"?
I have thought about foundations "ontologically"
for so long that I may have become accustomed to
a way of thinking and hence writing which is not common)


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