On 21 Dec 2013, at 17:09, John Mikes wrote:

'Implicit assumptions'? Jason seems to me as standing on the platform of physical sciences -

I let Jason answer, but this is not my feeling. It seems to me that Jason is quite cautious on this, and open to put physics on an arithmetical platform instead.

at least on a mthematical justification of theorems. Even Bruno's "we see" is suspect: we THINK we see, in adjusted ways as we can absorb phenomena, potentially including a lot more than we know about 'today'..

"seeing" is an 1-p experience. "seeing" is always "thinking seeing". Even provably so with the comp assumption.

About Bruno's remark on 'agnosticism' (also callable: ignorance) : I don't know (!) if a 'theory' (the partial one within our existent knowledge) is working indeed, or it just SEEMS working within the limited circumstances.

Here, even without comp, I would say that a theory can only seem to be working. WE never know if our theories are true or not. We might know that they are refuted, as just one element of reality can demolish a theory, locally.

Refuted? No one can include into a 'refutation' the totality, only the elements of a content of the present model.

At some level, you are right, we might have dreamed the refutation!.

But that level is impractical, and we will say that a theory is empirically refuted if it is contradicted by a sufficiently repeatable fact (a notion which ask in some faith in or waking state!). If comp predicts that the electron has a mass of one tun, then comp is refuted, (again, unless I wake up, and realize that electron does weight one tun), which needs we have to make small or big change in the assumption.

Finally: I don't consider agnosticism a philosophy (oxymoron). The 'practical' results we achieve in our limited science-technology are commendable and useful, subject to Bruno's "just be cautious to not draw conclusions".


(Scientific humility?)


I may include a whole wide world beyond the mathematical computations into the term of 'compute'. That is semantic and requires a wider vocabulary than just ONE language.

Comp offers an infinity of equivalent language. Your last remark would make sense if Church thesis is false, which I doubt, but is part of my assumption anyway. If you doubt Church thesis, it will be up to you to explain why. Church thesis is very solid for two main reason: 1) all attempts to define computable give rise to the same class of functions (be it by Babbage machine or quantum topological functors, etc.) 2) that class of computable functions is immune to the universality- destructive cantor diagonalization.



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