Re: syllogism
From: Paul Bramscher (brams006_nospam_at_tc.umn.edu)
Date: 09/30/04
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Date: Thu, 30 Sep 2004 17:54:03 -0500
Wolf Kirchmeir wrote:
> Paul Bramscher wrote:
>
>> Wolf Kirchmeir wrote:
>>
>>> Paul Bramscher wrote:
>>>
>>>> For a statement to be genuinely scientific, IMHO, it must stand on
>>>> its own, fully disrobed of provable (by definition) components.
>>>
>>>
>>> This reduces scientific statements to mere description.
>>
>>
>> I've given this more thought, and come to conclude that a better way
>> to phrase it is that "science must be *at least* empirically
>> verifiable description of phenomena." If it's not that, I'm not sure
>> what to call it. So my point is to strip out the stuff which is
>> non-empirical, so we can carefully look at what we consider to be the
>> non-trivial (logic, syllogistic, tautological) aspect to theory: bare
>> assumptions, categories, etc.
>
>
> I'm not sure what to call it either, but that's because it looks like
> "empirically verifiable description of phenomena" means "factually true
> statements." A factually true statement is - merely a factually true
> statement. So your claim that "science must be *at least* empirically
> verifiable description of phenomena" I would rephrase as "Science is
> about phenomena that can be described in factually true statements." But
> science goes a step or two beyond decription.
I agree, particularly when you lump science theory (leading toward
knowledge) and science methodology (procedure, rules, experiment, model,
etc.) together, under the same heading: science.
Now if you argue that science is all method -- even that theory is
method -- then I agree with you completely. I'm trying to tease out
scientific method from theory, wondering what happens when one creeps
into the other, perhaps dominating it.
> Science is one answer to the question " How come?" It differs from
> religion, for example, by insisting on three things, namely (in no
> partuicular order) hat the answer be logical, that it be verifiable, and
> that the observations entailed in verfying the answer can be made by
> anyone. Hence logic is of the essence of science - necessary, but not
> sufficient.
Necessary methodologically, certainly, but I believe it really forms no
part of end knowledge, since it can be cancelled out by its inverse
function, if you will, independently of the knowledge it grants. I
think we're not talking about the same thing here.
>
>> Whereas the art of engineering is to combine description with
>> algorithm (not tautology, not to balance a formula but to develop a
>> set of rules which produces some behavior which may or may not be
>> bounded in a tight/logical sense) and something physical.
>
>
> That set of rules is of necesity logical, else it cannot be a set of
> rules. Just how tightly bounded the rules are, or whether the bounds are
> knowable, etc, is also a matter of logic - rules imply their own bounds.
> The application to the physical is always a matter of experiment - of
> empirical observation.
>
>> The claim that science needs to predict is, arguably, a pre-scientific
>> desire (from religion, fortune telling, astrology, etc.)
>
>
> You're using the sense "predict = foretell the future". That's not what
> logical/scientific prediction means. A logical/scientific prediction has
> the form "If this theory is true, then the following statements are true
> also." That is not at all the same as foretelling the future, even
> though some of those statements may very well be statements about a
> future state of affairs, such as "This bridge will fall down if the load
> exceeds 75 tons."
This is one example of prediction, in a pop sense. The point is
cause-effect, whether this is temporal (present->future) or sideways (A
requires or necessitates B) is not so important for my point.
>
>> Certainly not an undesirable byproduct of science -- but it is the
>> stuff, also, of non-science. I'm just unsure that it's the primary
>> goal of science. Accurate predictions might be possible with
>> non-scientific methods, for example, in limited cases at least.
>
>
> What non-scientific methods????
Folk psychology, folk anything, for example. When science makes a
statement about X and we see Y, we don't necessarily dismiss statement
X. We just say it didn't apply. To the billions of humans who've lived
on this planet and enjoyed no modern Western formal logic, what "works
for them" works for them. Superstition has a way of working, even
predicting within that epistemology. Failures may be dismissed as
exceptions to the rule, successes as exemplary.
In any case, even without pointing at an example of a non-scientific
system which can predict well (no system is 100%), I'd like to pose the
question. If such a system did exist, what do you think of it? I can
flip a coin to any decision and predict (again -- future or sideways,
doesn't matter) with 50/50 accuracy off the bat.
So it's not merely prediction of a binary set of choices (karnaugh
again), but bringing the multitude of choices to the table in the first
place and narrowing the final contenders to the most useful ones. If
you believe this is, also, a karnaugh function, then I submit that a
coin toss gets me at least 50% accuracy. Some other non-scientific
method might bump it to 51%.
>
> I see in your ruminations several problematic conceptualisations.
>
> For one, you seem to think that logic is about what's neecssarily true.
> It isn't. It's about what combinations of statements may have what truth
> values. For several very practical reasons, mathematics (which, as a
> logician, I consider to be a part of mathematics; mathematicians tend to
> hold the complementary opinion), mathematics deals in necessary truths,
> and no engineer could get along without particular necessary truths -
> not because they necessary turths, but because they happen to be
> excellent models of how bridges and electronic circuits and chemical
> systems and so on work. Your disdain for "mere logic" is
> incomprehensible, considering that in your work you constantly use logic
> as a primary tool of analysis. Maybe you equate syllogism with logic.
> That's like equating arithmetic with mathematics.
I agree -- logic is not necessarily true. I'm asserting that a logic
statement can be formally proven to be true -- and when a logic
statmenent IS proven to be true, it is necessarily true/valid. In
science, on the other hand, there is no ability to prove positive, and
actually no desire to do so. So this component of knowledge, if still
present, should be removed as a distraction.
> For another, you havent sorted the difference between logical prediction
> and foretelling the future.
>
> For another, your focus on practical work seems to have misled you into
> thinking that you don't deal in theory, yet everything you do is theory.
> An algorithm is a theory, in the technical sense - it's a model of a
> computation. It had better be logically sound, or you can't rely on its
> results. NB that my contention that an algorithm is a model of a
> computation is supported by the fact that different algorithms can be
> used to produce identical computations, that is, transformations of
> input into output data. Your work appears to be the search for more
> efficient algorithms, that is, better mnodels.
Algorithms are quite different (though not entirely independent of)
mathematics and logic, in that state of the system (including inputs and
outputs) is unpredictable, and not necessarily repeatable due to nature
of varying inputs. Other exceptions include random functions and their
seeding, data collection and sampling from the "real world", some
one-way cryptographical techniques, and all functions which rely on a
date/time stamp or time counter function, etc. -- 'state' is an organic
entity.
Here's an interesting illustrative example:
Zeno's paradox is a mathematical ghost that's solvable with summation
and calculus shortcuts. We know that, through math, going half the
remaining distance will ultimately 'limit' toward or add up to the full
distance of the amphitheater.
But in algorithmic format, it utterly fails -- because algorithms have a
different nature about them:
Start out at x
repeat until x <= 0 {
go to x / 2
}
end
In algorithmic format, Zeno is unsolvable unless restated:
Start out at x
repeat until x <= 0 {
go to x - 1
}
end
(There are several other ways as well). That Zeno can be solved in
native format with math, but must be rephrased in algorithmic format to
be of any use whatsoever (other than as a continual loop with a
never-reached exit condition) is one example of how math and algorithm
differ. Not that algorithm doesn't rely on math (note the switch from
division to subtraction, though), but where fundamental differences show
themselves.
I can provide many other examples if time allowed -- believe me, I've
thought about this more carefully than your critical analysis of
weakness in my presentation warrants.
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