From: Steele, Kirk A (SteeleKA@nafm.misawa.af.mil)
Date: Mon Mar 04 2002 - 00:33:58 MST
would you believe the fascist bastards that run my firewall says that URL
you gave me below contains hate speech and won't let me at it!!! Bloody
Sod!!!
-----Original Message-----
From: L' Ermit [mailto:lhermit@hotmail.com]
Sent: Monday, March 04, 2002 2:08 PM
To: virus@lucifer.com
Subject: RE: virus: RFC - Definitions: Truth, Acceptance, Belief, Trust
and Faith
[Hermit 1]
[Kirk 1]
[Hermit 2]
[Hermit 1] [b]Discussion is requested. Does anyone have objections to or
suggestions or queries about the following proposed definitions?[/b]
[Hermit 1] [b][u]1 Truth[/b][/u][list]
[Hermit 1] Gödelian incompleteness and Popperian falsifiability together
necessitate that outside of a formal system of limited application, a
"truth", to have any measure of rational support, must by necessity, always
be provisional, incomplete and falsifiable, in other words, there must
always, at least hypothetically, exist some evidence which would permit that
supposed truth to be rejected.
[Hermit 1] This implies that outside of formal systems, the truth of a thing
is not an absolute, but encompasses a range of probabilities which will have
varying truth values (i.e. from "false" through "insufficient evidence to
adduce a truth value" to "true") depending on the evidence for or against
such a thing.[/list]
<snip>
[Kirk 1] hate to be a nit picker but could you pass me a proof of paragraph
1 please.
[hr]
[Hermit 2] 1 Enclosed Proof:[url=http://www.ddc.net/ygg/etext/godel/]Gödel's
Incompleteness Theorem On Formally Undecidable Propositions[/url] tells us
that in any system (other than a trivial definitionally complete system
(e.g. A=A)), there will always exist propositions that cannot be proven
either true or false using the rules and axioms of that system. You might be
able to prove every conceivable statement about something within a
particular system by going outside the system in order to come up with new
rules and axioms, but by doing so you'll only create a larger system with
its own unprovable statements. The implication is that all logical system of
any complexity are, by definition, incomplete; each of them contains, at any
given time, more true statements than it can possibly prove according to its
own defining set of rules. [Refer Note 1]
[Hermit 2] 2 Implication: The implication being that no matter how complex a
system is built, that a truth value cannot absolutely be asserted. The
Universe is a complex system. Thus there are truths which cannot be proven
to be true within the Universe. As Hoftadter put it,[quote]How can you
figure out if you are sane? ... Once you begin to question your own sanity,
you get trapped in an ever-tighter vortex of self-fulfilling prophecies,
though the process is by no means inevitable. Everyone knows that the insane
interpret the world via their own peculiarly consistent logic; how can you
tell if your own logic is "peculiar' or not, given that you have only your
own logic to judge itself? I don't see any answer. I am reminded of Gödel's
second theorem, which implies that the only versions of formal number theory
which assert their own consistency are
inconsistent.[/quote][url=http://www.amazon.com/exec/obidos/ASIN/0465026567/
thehermit0d]"Gödel,
Escher, Bach : An Eternal Golden Braid", Douglas R. Hofstadter, Basic Books,
1999[/url] A must read to be deemed literate.
[Hermit 2] 3 Definitional: It is rational not to assert things as absolutely
true which are not provably true.
[Hermit 2] 4 Definitional: An unprovable proposition cannot posses an
absolute truth value.
[Hermit 2] 5 Definitional: In the Universe, all things interact to a greater
or lesser degree depending only on space-time which is shared by everything
in the Universe.
[Hermit 2] 6 Enclosed Proof: Popperian falsification demonstrates that only
hypothesii capable of falsification (clashing with observation) are allowed
to count as scientific. [Refer Note 2 for justification]
[Hermit 2] 7 Definitional: A property of a hypothesis is contingent or
inherent according to whether or not possession of the property depends on
factors external to the hypothesis.
[Hermit 2] 8 Conclusion: All hypothesii are to a greater or lesser extent
contingent on unprovable propositions. [5 & 7 syl]
[Hermit 2] 9 Conclusion: All 'useful' truths (i.e. makes statements about
observations) are based upon contingent hypothesii. [6 & 8 syl]
[Hermit 2] 10 Conclusion: All 'useful' truths are contingent on unprovable
propositions.[6 & 9 syl]
[Hermit 2] 11 Conclusion: All 'useful' truths are contingent. [10 reduc]
[Hermit 2] 12 Conclusion: The consistency (truth) of a consistent or a
falsified 'useful' hypothesis is an inherent but unprovable property, while
its falsity is a contingent property. [7 & 10 syl]
[Hermit 2] 13 Conclusion: No 'useful' truth is absolute. [4 & 12 syl]
[Hermit 2] 14 Conclusion: It is irrational to assert things as absolutely
true. [3 & 13 syl]
[Hermit 2] 15 Restatement (with references to proofs): Gödelian
incompleteness [1 & 2] and Popperian falsifiability [6] together necessitate
that outside of a formal system of limited application [1], a "truth", to
have any measure of rational support, must by necessity, always be
provisional [6 & 14], incomplete [11] and falsifiable [6], in other words,
there must always, at least hypothetically, exist some evidence which would
permit that supposed truth to be rejected [10].
[Hermit 1] This implies that outside of formal systems [1], the truth of a
thing is not an absolute[13 & 14], but encompasses a range of probabilities
which will have varying truth values (i.e. from "false" through
"insufficient evidence to adduce a truth value" to "true") depending on the
evidence for or against such a thing [12].[/list]
[Hermit 2] Good enough?
[hr]
[Hermit 2] Note 1: After
[url=http://www.amazon.com/exec/obidos/ASIN/0691001723/thehermit0d]"Infinity
and the Mind: The Science and Philosophy of the Infinite", Rudy Rucker,
Princeton UP, 1995[/url](An excellent book)[quote]
The proof of Gödel's Incompleteness Theorem is so simple, and so sneaky,
that it is almost embarassing to relate. His basic procedure is as follows:
Someone introduces Gödel to a UTM, a machine that is supposed to be a
Universal Truth Machine, capable of correctly answering any question at all.
Gödel asks for the program and the circuit design of the UTM. The program
may be complicated, but it can only be finitely long. Call the program
P(UTM) for Program of the Universal Truth Machine.
Smiling a little, Gödel writes out the following sentence: "The machine
constructed on the basis of the program P(UTM) will never say that this
sentence is true." Call this sentence G for Gödel. Note that G is equivalent
to: "UTM will never say G is true."
Now Gödel laughs his high laugh and asks UTM whether G is true or not.
If UTM says G is true, then "UTM will never say G is true" is false. If "UTM
will never say G is true" is false, then G is false (since G = "UTM will
never say G is true"). So if UTM says G is true, then G is in fact false,
and UTM has made a false statement. So UTM will never say that G is true,
since UTM makes only true statements.
We have established that UTM will never say G is true. So "UTM will never
say G is true" is in fact a true statement. So G is true (since G = "UTM
will never say G is true").
"I know a truth that UTM can never utter," Gödel says. "I know that G is
true. UTM is not truly universal."
Think about it - it grows on you ...
With his great mathematical and logical genius, Gödel was able to find a way
(for any given P(UTM)) actually to write down a complicated polynomial
equation that has a solution if and only if G is true. So G is not at all
some vague or non-mathematical sentence. G is a specific mathematical
problem that we know the answer to, even though UTM does not! So UTM does
not, and cannot, embody a best and final theory of mathematics ...
Although this theorem can be stated and proved in a rigorously mathematical
way, what it seems to say is that rational thought can never penetrate to
the final ultimate truth ... But, paradoxically, to understand Gödel's proof
is to find a sort of liberation. For many logic students, the final
breakthrough to full understanding of the Incompleteness Theorem is
practically a conversion experience. This is partly a by-product of the
potent mystique Gödel's name carries. But, more profoundly, to understand
the essentially labyrinthine nature of the castle is, somehow, to be free of
it.[/quote]
Note 2: [url=http://www.eeng.dcu.ie/~tkpw/]The Karl Popper Web[/url][quote]
In 1934 Popper published what many regard as his Magnum Opus The Logic of
Scientific Discovery. The famous chemist Wachtershauser said that this is a
"gem" and that it liberated him from a sterile accounting view of science.
Wachtershauser subsequently went on to develop one of the main theories of
the origin of life. Frank Tipler, the famous cosmologist, regards this as
the most important book this century. In one majestic and systematic attack,
psychologism, naturalism, inductionism, and logical positivism are swept
away and replaced by a set of methodological rules called Falsificationism.
Falsificationism is the idea that science advances by unjustified,
exaggerated guesses followed by unstinting criticism. Only hypotheses
capable of clashing with observation reports are allowed to count as
scientific. "Gold is soluble in hydrochloric acid" is scientific (though
false); "Some homeopathic medicine does work" is, taken on its own,
unscientific (though possibly true). The first is scientific because we can
eliminate it if it is false; the second is unscientific because even if it
were false we could not get rid of it by confronting it with an observation
report that contradicted it. Unfalsifiable theories are like the computer
programs with no uninstall option that just clog up the computer's precious
storage space. Falsifiable theories, on the other hand, enhance our control
over error while expanding the richness of what we can say about the world.
Any "positive support" for theories is both unobtainable and superfluous;
all we can and need do is create theories and eliminate error - and even
this is hypothetical, though often successful. Many superficial commentaries
are keen to point out that other people stressed the importance of seeking
refutations before Popper. They overlook the fact that Popper was the first
to argue that this is sufficient.
This idea of conjecture and refutation is elaborated with an orchestration
suggestive of someone who loves great music. (Popper loved Mozart and Bach,
and took great pleasure in composing his own music.) The common idea that
Popper neglected to consider whether Falsificationism itself is falsifiable
is already scotched here. You can falsify a description, but not a rule of
method as such (though obviously a rule can be criticized in other ways).
The notion that science offers proof is now only advanced by popular
treatments of science on TV and in (many) newspapers - most journalists
(with a few important exceptions) are sadly completely devoid of theoretical
knowledge: a side-effect of overspecializing on the immediate moment. But
then, anyone can improve!
Most people who think they have a ready rebuff to Popper's position have
never read his work. If they only read the original works, in most cases
they would see that their supposed "Point that Popper neglected" had already
been considered and exploded. A good example of this is Lewis Wolpert's
remarks on Popper's works in his otherwise excellent book The Unnatural
Nature of Science. He seems to think that Popper's falsifiability criterion
ignores hypotheses about probabilities - overlooking the blatant fact that
The Logic of Scientific Discovery devotes more than a third of its pages to
the two fundamental problems of probability in an effort to find a solution
that will also allow hypotheses about the probability of events to be
capable of clashing with the evidence! Popper was in fact fascinated by
probability and even produced his own axiomatisation of the probability
calculus.[/quote]
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