BS Detector Annex

[Beady]

I was browsing some of my archived files and ran across the following. I have no idea where I got it or who wrote it, but it's amazing how many of these I've seen used here:

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How to Prove It


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Proof by example: The author gives only the case n = 2 and suggests that it contains most of the ideas of the general proof.​

Proof by intimidation - "Trivial."​

Proof by vigorous handwaving - Works well in a classroom or seminar setting.​

Proof by cumbersome notation - Best done with access to at least four alphabets and special symbols.​

Proof by exhaustion - An issue or two of a journal devoted to your proof is useful.​

Proof by omission - "The reader may easily supply the details" "The other 253 cases are analogous" "..."​

Proof by obfuscation - A long plotless sequence of true and/or meaningless syntactically related statements.​

Proof by wishful citation - The author cites the negation, converse, or generalisation of a theorem from the literature to support his claims.​

Proof by funding - How could three different government agencies be wrong?​

Proof by eminent authority - "I saw Karp in the elevator and he said it was probably NP-complete."​

Proof by personal communication - "Eight-dimensional coloured cycle stripping is NP-complete [Karp, personal communication]." (Beady adds: I guess this is another name for "The lurkers support me in email.")

Proof by reduction to the wrong problem - "To see that infinite-dimensional coloured cycle stripping is decidable, we reduce it to the halting problem."
​

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.​

Proof by importance - A large body of useful consequences all follow from the proposition in question.​

Proof by accumulated evidence - Long and diligent search has not revealed a counterexample.​

Proof by cosmology - The negation of the proposition is unimaginable or meaningless. Popular for proofs of the existence of God.​

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.​

Proof by metaproof - A method is given to construct the desired proof. The correctness of the method is proved by any of these techniques.​

Proof by picture - A more convincing form of proof by example. Combines well with proof by omission.​

Proof by vehement assertion - It is useful to have some kind of authority relation to the audience.​

Proof by ghost reference - Nothing even remotely resembling the cited theorem appears in the reference given.​

Proof by forward reference - Reference is usually to a forthcoming paper of the author, which is often not as forthcoming as at first.​

Proof by semantic shift - Some of the standard but inconvenient definitions are changed for the statement of the result.​

Proof by appeal to intuition - Cloud-shaped drawings frequently help here.​

 

[Cuddles]

Nice list. Not sure I agree with this one though :

Proof by accumulated evidence - Long and diligent search has not revealed a counterexample.

While not technically proof, this is all science actually has. We can never prove that Newton was right (in non-relativistic settings), but we sure have an awful lot of evidence that he was, and it would be fairly silly to assume otherwise. From an absolutely strict scientific point of view this is a fallacy, but from a realistic point of view, proof by accumulated evidence is a perfectly valid form of proof.

 

[JoeTheJuggler]

Many of these are legitimate.

The first one for example is fine if you're arguing a claim of the form "all x are p". You only need one case of an x that is not p to refute it.

I don't get what the problem is with with "cumbersome notation"--if the topic can be approached more readily with equations or symbols, it's appropriate. (Why not another one of these such as "proof that uses big words I don't understand"?)

I think most of the BS we see around here uses the plain old fallacies we already know about.

 

[Steven Howard]

Nice list. Not sure I agree with this one though :


While not technically proof, this is all science actually has. We can never prove that Newton was right (in non-relativistic settings), but we sure have an awful lot of evidence that he was, and it would be fairly silly to assume otherwise. From an absolutely strict scientific point of view this is a fallacy, but from a realistic point of view, proof by accumulated evidence is a perfectly valid form of proof.

From the rest of Beady's list, it's clear that we're in the realm of mathematics and computer science (references to things being NP-complete, the halting problem, etc.). So it's using "proof" in the mathematical, rather than colloquial, sense.

 

[elgarak]

It's a list of tricks primarily used by professors during the teaching of classes in math, theoretical physics or computer science.

A student of math or computer sciences encounters all of these during his attendance of classes of said professor.

Some are also found in textbooks (the reference ones, for instance).

The use of such teaching and writing tricks usually is the source of much of the frustration the student experiences.

 

[Cuddles]

From the rest of Beady's list, it's clear that we're in the realm of mathematics and computer science (references to things being NP-complete, the halting problem, etc.). So it's using "proof" in the mathematical, rather than colloquial, sense.

But even then it can be valid in the real world. For example, the Riemann hypothesis has not been proven mathematically, but has enough of a proof by example that it can be considered true for many practical purposes. In a maths class, sure the Riemann hypothesis is in no way proven. In a computing class you can assume it is proven. It all just depends on context.

 

[Michael Redman]

This one is popular here:

Proof by ghost reference - Nothing even remotely resembling the cited theorem appears in the reference given.

The list reminds me of an article on alternatives to evidence based medicine: www.bmj.com/cgi/content/full/319/7225/1618

My favorite:

Diffidence based medicine---Some doctors see a problem and look for an answer. Others merely see a problem. The diffident doctor may do nothing from a sense of despair. This, of course, may be better than doing something merely because it hurts the doctor's pride to do nothing.