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From: pindor@gpu.utcc.utoronto.ca (Andrzej Pindor)
Subject: Re: rereRe: The end of god
Message-ID: <Cy6x49.3tJ@gpu.utcc.utoronto.ca>
Organization: UTCC Public Access
References: <36vt2m$g6m@scapa.cs.ualberta.ca> <383kau$5q2@scapa.cs.ualberta.ca> <Cxzo7E.91v@gpu.utcc.utoronto.ca> <388th4$foh@scapa.cs.ualberta.ca>
Date: Mon, 24 Oct 1994 18:38:32 GMT
Lines: 86

In article <388th4$foh@scapa.cs.ualberta.ca>,
Kevin Wiebe <kevin@tees.cs.ualberta.ca> wrote:
>Andrzej Pindor (pindor@gpu.utcc.utoronto.ca) wrote:
>: Your example just illustrates the Goedel theorem.  The point I was trying to 
>: make was that to know something 'for sure' we also use mathematics, even
>: if applied to a system external to the one in which this something is true.
>: Short of divine inspiration, what we hold to be true in science is arrived at
>: by logical reasoning at some level. We may propose various conjectures and
>: even have a deep, unfaltering belief that such a conjecture is true, it only
>: becomes a scientific truth if proven using logic. Penrose seems to suggest
>: that there are some scientific (mathematical) truths which logic cannot prove.
>: I have yet to hear an example. Yours does not cut it.
>: Andrzej
>
>I guess this is where I quietly duck out of the conversation.  It is too
>difficult for me to start getting down to the nitty gritty over
>the net, especially since I am not an expert in "teaching".  What I
>suggest, Andrzej, is that if you are serious about your "I have yet to 
>hear an example" attitude, that you look into some more "professional"
>explanations on Godel's proofs - ie. go to the library.  (I assume you are
>not merely trying to bug me with your question.)  I am not trying to
>be rude, but if you are not interested in this question enough to put
>some effort into reading a book, I don't feel our discussions here will
>be fruitful.  I find it very difficult to explain my thoughts, (but
>when I read someone else explain it, I go "yeah, that's what I meant!")
>Maybe I just don't have a "teacher" in me.  
>
As you realise, there has been enough written about Goedel theorem to 
occupy a mathematician full time to read all this. Consequently one has to be 
very selective. Are you saying that what I have said indicates an inadequate
knowledge of what Goedel's theorem is about? Hiding behind "I am not a good
teacher" is suspect - in my experience if someone can't explain him/herself
it usually indicates a lack of understanding on his/her part.

>...........................................I, too, would like to
>read a clear explanation on the philosophical implications of Godel's
>theorems on what we believe to be truth, logic, and what we seem to
>believe is "reasonable".

Then how do you know that I am wrong and need to read more about what Goedel's
theorem is about?

>Let me just end with this thought...  you said:
>: We may propose various conjectures and
>: even have a deep, unfaltering belief that such a conjecture is true, it only
>: becomes a scientific truth if proven using logic. 
>
>Well, I propose that logic is, at it's heart, nothing more than a formal
>appeal to our deep, unfaltering beliefs.  It is these beliefs that allow
>us to get at the "truth", and logic is merely a clean cut path to follow.

In a sense I agree with the above. I believe that logic is a formalization
of reasoning schemes which we have found are giving us "useful" results, i.e.
lead to actions which promote our survival. They are a set of tools which
evolution has provided us with and our survival proves their correctness.
Planing actions we run various scenarios in our minds and use logical 
reasoning to prune out "wrong" combinations of actions and outcomes. It
seems to work so we use these tools in other mental processes, even those
which do not immediately lead to practical actions (mathematics). Interestingly
enough, many even very abstract mathematical theories find "real world"
applications, perhaps precisely for the reason that they are developed using
tools (logical schemes) which are ultimately drawn from our interaction with
the "real world".
............
>once I realize WHY B should be true, given the rules of logic.  Most of us
>(except for maybe flatworlders) operate on reason and rationality, so we
>don't play the above game - but it just shows me that logic (or even
>"scientific truth") is fundamentally based on our feelings of what makes
>sense. 
>
Right, see above. Now the point is whether we can be somehow "be sure" of
some statements, without running them through the logical verification.
Penrose claims that we can and he is not alone, but I have not seen examples
of the above. Please not that Goedel talks abouth "truths" which cannot be
proven within a given system, but these are known to be "true" because they 
can be proven in a larger system.
>
>-Kevin-
>

Andrzej
-- 
Andrzej Pindor                        The foolish reject what they see and 
University of Toronto                 not what they think; the wise reject
Instructional and Research Computing  what they think and not what they see.
pindor@gpu.utcc.utoronto.ca                           Huang Po
