Re: Turing machines and tape length

[Tim Gwinn <***>]

-----Original Message-----
From: ROSEN Forum [mailto:***On Behalf Of Howard Pattee
Sent: Tuesday, December 28, 2004 10:59 AM
To: ***
Subject: Re: Turing machines and tape length

Tim,
I understand Rosen's overall argument. My problem is that I do not follow Rosen's "for the sake of argument" hypothesis about what would follow if the formal computable "mechanisms" corresponded to empirical causal models of Nature. As you state his hypothesis, a formal computable inferential entailment,  "must entail (e.g., reductionism, context-independence, etc.) and also what it must not allow (e.g., causal loops, context-dependence, etc.)."

What I do not follow is why the formal inferential entailments of computable functions (that exist only on the unencoded right side of the modeling diagram) must necessarily "entail" reductionism, no causal loops (and the rest) in the encoded empirical models of Nature. As Einstein and I see it, the formal inferential entailments say nothing certain about the causal entailments of Nature.  

 

 

TG: Yes, indeed:"...the formal inferential entailments say nothing certain about the causal entailments of Nature".  Neither Rosen nor I have argued that, regarding the class of computable models. Instead, we are talking about the limits of what kind of hypothetical world that such a class of models are adequate to describe. That world would be a world limited by Church's Thesis. Do you agree?

 

If what it means to be an "empirical model" is to be a formal model in a commuting modelling relation with some natural system, then if that formal model is a member of the class of computable models, then do you not also agree that that model is likewise limited to being capable of modelling only aspects of the natural world which meet the limits of Church's Thesis?

 

Regards,

Tim