From: simon@dcs.warwick.ac.uk (Simon Clippingdale)
Subject: Re: A little food for thought (pizza?)
Organization: Department of Computer Science, Warwick University, England
Date: Tue, 5 Jan 1993 18:30:31 GMT

In article <3PXqwB10w165w@anarky.tch.org> nightsng@anarky.tch.org (Nightsong) writes:
>
> I have myself defined pretty clearly; it is just who to believe (or  if 
> to believe anyone) that I wonder about.  Such as --
> 
> 1. Is there a way to prove the people who believe in a God right or 
>     wrong?
> 2. Is there a way to prove the people who believe in many gods right or 
>     wrong?
> 3. Is there a way to prove the people who believe in no gods right or 
>     wrong?
> 4. Is there a way to prove the people who believe in reality right or 
>     wrong?
> 5. Is there a way to prove the people who do NOT believe in reality 
>     right or wrong?
> 6. Is there a way to prove ANYTHING is right or wrong?
> 
> All these questions assuming that you do not know for sure that this is 
> reality.  Although some of them are about this.
>
> The answer to all of them is no and I cannot believe all of them at once 
> to be yes without doublethink (triplethink? quadruplethink?) so I am 
> *EXTREMELY*  confused.  


If it's any consolation, and without wishing to sound patronising, IMHO the
confusion you feel may be both temporary and worthwhile. You seem to be in
the process of realising how problematic, and compounded by subjectivity, is
the notion of `proof'. If you don't mind, I'll rant on and on and on about how
crap I reckon such concepts as `proof', `truth' and even good old `evidence'
are, and propose tossing the lot firmly into the garbage other than for the
purposes of idle chat where, for example, "There is no evidence for the
Biblical Flood" is sufficiently precise to convey the intent (but misleading
if taken much further since `evidence' is a lousy referent).

The pivotal word in all your questions above is `prove', and there's an
implied `prove to the satisfaction of <somebody>' which one can never factor
out. One can't assume that others will, or should, be convinced by what one
personally finds to be a satisfactory `proof', nor can one assert that if
they disagree they are big-W Wrong. Only in one's own view can they be wrong.

The same problems, by extension, beset notions like `evidence' and `truth'.
Many theists, for example, consider the universe to be `evidence' that their
God created it. I am a (strong-sense) atheist because, among other reasons,
I do not agree that the universe *is* such `evidence'. And so it goes on.

All this forces one to consider what it is that these words are such glib,
easier-said-than-defined labels for, and if you reach the same conclusion
as me (your mileage may vary), it's that these are profoundly unhelpful
abstractions describing various aspects of a problem of inference. That
problem can be rephrased in engineering terms as the estimation of random
signals in random noise, which is of course a statistical matter ("random"
here means `described statistically'). Luckily it's also something I know
a bit about, which is no doubt why I see it in those terms, but the point
is that any inference made in the presence of noise and uncertainty (as
inevitably are *all* human inferences about the nature of things external)
requires a move away from determinism and into statistics.

So is the move into statistics an advance or a retreat? I reckon it's an
advance because it acknowledges the uncertainty inevitably associated with
such problems and allows it to be handled in a consistent and meaningful way,
and even to be quantified to some extent. If we desire to have `truth' or
`proof' in black'n'white, we are simply more likely (almost certain, actually,
given the presence of uncertainty :-) to be wrong. Less confused, perhaps,
but wrong.

What statistics does is to replace the simplistic and emotively loaded
language of `evidence', `proof', `truth' and so on by a system of conditional
probabilities or probability densities, the stuff of Bayesian analysis. We
need not nail colours to masts, although we still may draw brazen conclusions
*after* the stats are done (just covering my ass, bearing in mind my recent
rants about how I can feel so damn certain that you-know-who doesn't exist).

We don't need to haggle over what is and what is not `evidence' (and `for'
or `against' this or that); *every* observation is evidence (poof! `evidence'
is seen to be redundant and loaded terminology, and in the bin it goes). In
principle, every observation should cause us to adjust upward or downward some
notional and -- importantly in the context of your questions -- *personal*
running estimates of [the posterior conditional probabilities of] various
hypotheses being correct given the totality of observation thus far.

`Truth' and `proof' are replaced by such a nominal and subjective estimate
of probability of correctness for any conceivable hypothesis(*). Standing
convicted of being dangerous oversimplifications, and of neglecting the
fundamental problems of noise and uncertainty in inference, in the trash
they both go, and not a moment too soon.

  (*) One word about science here; I guess that this approach which
  I seem to find myself evangelising (eeek!) is a superset of science,
  since science specifically requires that propositions be empirically
  falsifiable. While this is appropriate if the conclusions reached are
  to be held as empirical `truth' (aargh), one can envisage situations
  in which empirical falsifiability is not required for an *individual*
  to come to a rational but *personal* conclusion about `reality' (aargh
  again) on statistical grounds.

  Example: I hear a voice in my dreams telling me "Hi, this is God. Yeah,
  *that* God. As a demonstration of my existence for you, I will cause
  <highly improbable event> to occur at noon tomorrow. Be there or be square.
  Over and out." Said event happens. Maybe I even have the presence of mind
  to tell a load of friends up front, who also witness the event. While this
  is not scientific, I think I could rationally, and on solid foundations,
  conclude that this should indeed bump up my estimate of the correctness of
  various related hypotheses (e.g. existence of God/s, existence of unknown
  technologically-advanced wiseguys trying to mess with my brain, or the
  slightly solipsistic but entirely reasonable I'm-dreaming-all-this).

Enough burbling.

Uncertainty is not the same as confusion unless it's handled wrongly,
and statistics is the right way to handle it IMHO.

Uncertainty is your Friend, and loves you. Just open your heart and embrace
It, and you will experience True .... oops.

>-Nightsong

Cheers

Simon
-- 
Simon Clippingdale                simon@dcs.warwick.ac.uk
Department of Computer Science    Tel (+44) 203 523296
University of Warwick             FAX (+44) 203 525714
Coventry CV4 7AL, U.K.
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