[FOM] Intensional identicity and identicity of proofs
Aatu Koskensilta
aatu.koskensilta at xortec.fi
Tue Jul 8 01:28:40 EDT 2003
In a post here some time ago I asked for a precise definition for
intensional identicity of concepts that does not make necessarily
co-extenensive concepts intensionally identical.
The reason I asked this is that the Carnapian account, which is used in
most intensional logic, makes the concepts "a non-identical object" and
"a bijection from the set of well-orderings of omega onto the reals"
intensionally identical if the continuum hypothesis is false. Now surely
these two are *not* intensinally identical under any condidition, and
thus the Carnapian definition for intensional identicity is flawed.
Receiving no response here, I later stubmled upon Y. N. Moschovaki's two
papers "Sense and denotation as algorithm and value" and "A logical
calculus of meaning and synonymity". (These can be found at
http://www.math.ucla.edu/~ynm/papers.htm). I haven't yet studied them in
detail, but it's obvious that they provide at least one possible real
answer to my question.
As far as I gathered from a quick browsing trough of these articles,
Moschovaki's begins noting the flaws of the Carnapian account, and then
proposes to replace Carnapian account of intensional identicity with one
that states that two concepts are intensionally identical if they, in an
abstract sense, define the same algorithm (in a general, idealised
sense, not in the sense of being a "recipe" for a recursive function)
for determining whether the concept applies to a particular object or
not. The rest of the paper is devoted to a development of a calculus
formalising this intuition.
I wonder whether these formulations could be used also in proof theory
to provide an adequate criterion for identicity of proofs, as the
problem there seems quite related.
--
Aatu Koskensilta (aatu.koskensilta at xortec.fi)
"Wovon man nicht sprechen kann, daruber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
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