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Oct 16, 2002, 10:00:42 PM10/16/02

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sci.logic, this bud's for you

On Thu, 17 Oct 2002 00:48:25 +0000 (UTC), Kleuskes & Moos

<some...@over.the.rainbow> wrote:

> 1) Proof by referral to non-existent authorities

> 2) Reduction ad nauseam

> 3) Proof by assignment

> 4) Method of least astonishment

> 5) Proof by handwaving

> 6) Proof by intimidation

> 7) Method of deferral until later in the course

> 8) Proof by reduction to a sequence of unrelated lemmas

> 9) Method of convergent irrelevancies

>--

>As 'n tied komt, komt 'n ploag.

>

Oct 17, 2002, 1:05:22 AM10/17/02

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Let's not forget:

Proof by diversionary obfuscation

Oct 17, 2002, 12:10:40 PM10/17/02

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"Thad Coons" <toc...@citlink.net> wrote in message news:<uqsg8dg...@corp.supernews.com>...

And the ultimate: Proof by Gregory Chaitin: ""

Did anybody see his latest article with the mistakes in his "proof" of

the unsolvability of the Halting Problem? It's funny. He's been

writing about Godel and Turing for 20 years (he says he 1st learned

Godel's Proof(s) when he was 12, he "out-Godeled Godel", his Omega is

more efficient than Turing's number, etc.), however ...

1. He only talks about the water downed version (based on soundness)

given by Godel in the introduction ("This is unprovable."), never

mentioning the more powerful version based on w-consistency given in

the body of Godel's 1931 paper. [Did he actually "under-Godel

Godel"?]

2. He never mentions Rosser's extension to that in 1936.

3. He can't even prove Turing's result at all.

4. His Omega "probability of a program halting" was greater than one

for years until he tried to fix it. (I understand he now has a 3rd

version that is the probability of one particular program halting.)

Speaking of which, here's a simple puzzle: Show a program that has no

"probability of halting" (Hint: it doesn't converge), thus showing

that the whole concept of Omega is not well-defined.

Have any of his definitions (much less subsequent conclusions) not

been shown to be ill-defined?

Charlie Volkstorf

Cambridge, MA

www.mathpreprints.com/math/Preprint/CharlieVolkstorf/20021008.1/1

www.arxiv.org/html/cs.lo/0003071

Oct 17, 2002, 1:11:06 PM10/17/02

to

>> 1) Proof by referral to non-existent authorities

>> 2) Reduction ad nauseam

>> 3) Proof by assignment

>> 4) Method of least astonishment

>> 5) Proof by handwaving

>> 6) Proof by intimidation

>> 7) Method of deferral until later in the course

>> 8) Proof by reduction to a sequence of unrelated lemmas

>> 9) Method of convergent irrelevancies

>> 2) Reduction ad nauseam

>> 3) Proof by assignment

>> 4) Method of least astonishment

>> 5) Proof by handwaving

>> 6) Proof by intimidation

>> 7) Method of deferral until later in the course

>> 8) Proof by reduction to a sequence of unrelated lemmas

>> 9) Method of convergent irrelevancies

The following is taken from an article entitled "How To Prove It",

by Dana Angluin of the Yale Computer Science Dept., which appeared in

Vol. 15, Number 1 (1983) of the Association for Computing Machinery's

journal SIGACT News.

HOW TO PROVE IT

1. Proof by example:

The author gives only the case n = 2 and suggests that it contains most of

the ideas of the general proof.

2. Proof by intimidation:

"Trivial."

3. Proof by vigorous handwaving:

Works well in a classroom or seminar setting.

4. Proof by cumbersome notation:

Best done with access to at least four alphabets and special symbols.

5. Proof by exhaustion:

An issue or two of a journal devoted to your proof is useful.

6. Proof by omission:

"The reader may easily supply the details."

"The other 253 cases are similar."

"..."

7. Proof by obfuscation:

A long plotless sequence of true and/or meaningless syntactically related

statements.

8. Proof by wishful citation:

The author cites the negation, converse, or generalization of a theorem from

the literature to support his claims.

9. Proof by funding:

How could three different government agencies be wrong?

10. Proof by eminent authority:

"I saw Karp in the elevator and he said it was probably NP-complete."

11. Proof by personal communication:

"Eight-dimensional colored cycle stripping is NP-complete [Karp, personal

communication]."

12. Proof by reduction to the wrong problem:

"To see that infinite-dimensional colored cycle stripping is decidable, we

reduce it to the halting problem."

13. Proof by reference to inaccessible literature:

The author cites a simple corollary of a theorem to be found in a privately

circulated memoir of the Slovenian Philological Society, 1883.

14. Proof by importance:

A large body of useful consequences all follow from the proposition in

question.

15. Proof by accumulated evidence:

Long and diligent search has not revealed a counterexample.

16. Proof by cosmology:

The negation of the proposition is unimaginable or meaningless. Popular for

the proofs of the existence of God.

17. Proof by mutual reference:

In reference A, Theorem 5 is said to follow from Theorem 3 in reference B,

which is shown to follow from Corollary 6.2 in reference C, which is an easy

consequence of Theorem 5 in reference A.

18. Proof by metaproof:

One proves that a proof must exist, using any of the techniques described

herein.

19. Proof by picture:

A more convincing form of proof by example. Combines well with proof by

omission.

20. Proof by vehement assertion:

It is useful to have some kind of authority relation to the audience.

21. Proof by ghost reference:

Nothing even remotely resembling the cited theorem appears in the reference

given.

22. Proof by forward reference:

Reference is usually to a forthcoming paper of the author, which is often

not as forthcoming as at first.

23. Proof by semantic shift:

Some standard but inconvenient definitions are changed for the statement of

the result.

24. Proof by appeal to intuition:

Cloud-shaped drawings frequently help here.

Oct 18, 2002, 3:59:33 AM10/18/02

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Hello,

> >> 1) Proof by referral to non-existent authorities

> >> 2) Reduction ad nauseam

> >> 3) Proof by assignment

> >> 4) Method of least astonishment

> >> 5) Proof by handwaving

> >> 6) Proof by intimidation

For what it's worth, i really think this should be

"Proof by complete intimidation"

as that reminds one more of "complete induction".

Cheers,

Herman Jurjus

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