Path: utzoo!utgpu!water!watmath!clyde!att!osu-cis!tut.cis.ohio-state.edu!mailrus!ames!zodiac!joyce!sri-unix!garth!smryan
From: smryan@garth.UUCP (Steven Ryan)
Newsgroups: comp.ai
Subject: Re: The Ignorant assumption
Message-ID: <1391@garth.UUCP>
Date: 11 Sep 88 00:26:44 GMT
References: <1383@garth.UUCP> <2362@uhccux.uhcc.hawaii.edu>
Reply-To: smryan@garth.UUCP (Steven Ryan)
Organization: INTERGRAPH (APD) -- Palo Alto, CA
Lines: 37

>" Isn't adopting provisional assumptions an act of faith?
>
>Not really.  Consider the provisional assumption of a reductio ad
>absurdum argument.
>
>" ... I define faith as adopting assumptions without proof.
>
>It's an odd definition -- if we adopt it, we are led to the conclusion
>that all of us have faith and are therefore religious.
>
>" That's it. Any formal system requires such assumptions.
>
>Well, I would say that some natural deduction systems of logic have
>no assumptions -- only rules of derivation.  But you can probably
>find a definition of 'assumption' that makes what you say true.

I really was hoping people would be content with an intentionally imprecise
and informal discussion. If we want to be rigourous, I think it is important
to define a process. I will propose:

A process P is an orderred triple (S,M,Q).
S is a undefined set (of states).
M is a set of pdfs m:S->[0,1].
Q is a relation on MxM called transistions, denoted m->n.

P is probablistic if for any m,s, 0<m(s)<1.
P is not probablistics if for all m,s, m(s)=0 or m(s)=1.

P is deterministic if Q is a function.
P is nondeterministic if Q is not a function.

P is a formal system if S is denumerable and Q is effectively computable.

I think science and religion and CT could be explained as different constraints
on S, M, and Q. If the consensus is to move the discussion into a cryptoformal
notations, that's fine by me, since my education was in math anyway rather than
philosophy.