Re: Turing machines and tape length

[Howard Pattee <***>]

Tim,

Yes, I agree we apparently do not have the same concept for what is
required for "commuting"  although I am at a loss to
express our difference clearly.  I will think about it for
awhile.

TG: It seems to come down to a difference in what we each consider "commute" to mean, or the requirements for a modelling relation to "commute". For me, I take Rosen's stance that it involves bringing the entailment structures into congruence via the encoding/decoding. Indeed, I agree that the encoding/decoding are creative acts. However, in Rosen's view, in order for a modelling relation to commute, there is the following requirement placed on those creative acts:

"The only condition on them is that they bring the two entailment structures into congruence -- that is, they satisfy the commutativity condition, which I have written as [1 = 2 + 3 + 4]". [EL p. 159]

HP: One likely difference, I think, is that Rosen's and your concepts of
commutation are indeed more precise than Hertz's and my own. My thought
is that one might be too precise about creative acts of interpretation
(i.e., "bringing the two entailments into congruence"). The
issue is whether this precision is necessary for a good model or is it
actually an unnecessary restriction on possible models.

As I said, I need to think more about it.

Howard