Proof

Recreating (and advancing) pk’s censored domains: Macroinformation.org &
Knatz.com / Teaching / Thinking Tools / Reason
@ K. 1997 10 13

Mission: to stimulate a critical attitude toward ‘proof’

Reason, supported by experience, differs from traditional authority in its open admission that the evidence must be wholly visible to all. The results of an experiment in science are validated only after other experiments in other laboratories by other scientists come up with the same result. All their results will still be invalidated if some future experiment or inquiry challenges those results. Anyone may make the challenge.

Science can disprove theories …
science can improve theories …
science can never prove theories.

Gregory Bateson

Alternate phrasing:

It is not possible to prove that something is true;
It is possible to prove that something is not true.

Authority, in contrast, plays a concealed hand. Its reasons are kept in a “black box.” Too arcane for mere mortals. (A great deal has been posted at my home page since the original note was processed. (See pk on Shakespeare’s Sonnets in particular.)

(Governments play it both ways. Our congress is open. The records are public. But then they go into committees. They meet in chambers. The Pentagon, the FBI, the CIA … work in black boxes.)
(And we know they’re dishonest: we want them to be dishonest. No kleptocracy will tolerate honesty for long.)


The word proof is ambiguous in a way not commonly understood. Science can prove a theory in the 1) progressive-proof sense of “Well, here are some reasons to believe it,” and in the 2) experiential sense of “test it further.” But science (a mere branch of reason) can not prove it in the tautological sense of quod erat demonstrandum. There can be no experiential tautologies.

All reason can do is to argue what seems reasonable.
(echoing Feynman)

Furthermore, with respect to sense 1), showing examples and reasons in support of a theory is simply the first step in rational theorizing. In order to be in accord with up to date reason, all reasonable effort must be taken to disprove the theory before it should be taken seriously. (See the Wason Test, just coming up.)

Proof is an idol before which the mathematician tortures himself.
Sir Arthur Eddington

Human Hubris: Mathematical, Political, Theological

Once upon a time man believed that he could make the rain rain, the sun rise (both ideas based on naive models of the universe). Primitive man, further along in time (like now), believes he can prove things: in a court, by law, on a blackboard, at an altar. Is a mathematician’s faith in the logic of his brotherhood charming? or embarrassing?

Disproof trumps proof.

Once upon a time we came to no longer trust our own individual, amateur magic. We transferred our trust to the shaman. Then we trusted that we could divine the nature of the god, control him; then we trusted the sorcerer in black robes, the chief sorcerer in gold silk. Now we can’t trust ourselves to know our own enemies: the shaman in the White House has to tell us who our enemies are: and he too trusts the magician at the blackboard.

A primate has to trust her perceptions or she’ll fall from the tree, fall on the ground, starve. I trust my own perceptions well enough not to fall out of bed more often that not. But to extrapolate that trust to a belief that mortal predators can know God, can know Truth, can Prove things … That’s a bit much.


Proof Scrapbook

Do you really believe that proof makes any difference?
Brecht, Galileo

2000 07 20 The magician saws the lady in half, the audience sees two halves, that proves that the magician has magic.
Then somebody says maybe it’s dummy legs in the other box, find dummy legs, that debunks it.

Now the magician saws the lady in half, the audience sees the sawed legs move, that proves that the magician has magic.
Then somebody says maybe it’s marionette legs in the other box, find marionette legs, that debunks it.

Now the magician saws the lady in half, the audience sees the sawed toes wiggle, that proves that the magician has magic.
Then somebody says maybe it’s a different assistant’s legs in the other box, find different assistant’s legs, that debunks it.

The magician starts using the assistant’s twin sister for the legs: a debunker in the audience getting DNA samples from the legs by laser is temporarily fooled.

Point: only fools and magicians talk about proof outside the strict limits of a tautology. See Gregory Bateson: “Science never proves anything.”

2001 08 31 It took the inventor of what has been called the greatest mathematical discovery ever — the Mandelbrot Set — to get people to see something that should have been obvious once the telescope and microscope were invented: one’s measurement of the length of a coastline will be determined by the length of one’s ruler. A roadrunner, a snail, and a nematode would each get radically different readings for say the perimeter of a rock: or the coast of Maine. OK, you can’t get a nematode to cover the coast any more than you can get a boy to make one turn of the Rubik cube each second for two hundred and fifty million years — without sleeping, without eating, without a Christmas vacation — but get the point anyway. I intrude those examples onto Mandelbrot simply in order also to warn us of the practical absurdity of much of the mathematical imagination. Mandelbrot merely talked about men using different length rulers. If your ruler is three Angstrom units you’ll get a very different reading for the coast of the main British island than if you’re walking, wading, climbing, swimming, sailing, flying … around the coast with a yard stick. The truth seems to be fractal and the fractal seems to be infinite.

Any coastline is infinite in “length.”

2003 04 04 One possible translation: Tautologies (such as two-dimensional geometry) don’t map well onto actual experience.

I now wish to generalize Mandelbrot’s principle to the concept of proof. The possibility of “proof” of an issue will depend on the sophistication of your epistemology. The Egyptian priests proved whatever they wanted to prove about the god Ra by turning staffs into snakes. Or was that Moses proving something about Yahweh? The shaman can prove to his people that the missionary is a devil. Had the missionary time to convert the people, the missionary could have proved to them that their shaman had only superstition and no magic. Had the pk of 1960 been in England in the 1860s, Thomas Huxley could have proved Darwin to him while he was failing to prove it to Bishop Wilberforce. Had the pk of 2001 been in England in the 1860s, he might have been able to prove to Huxley that Huxley didn’t have Darwin quite right. Of course it’s even more unlikely that Huxley in 1860 would have listened to a pk from 2001 than that pk from 2001 would have been in England in 1860.

Of course once you’ve read Gregory Bateson’s Mind and Nature, you won’t pay any mind to anyone talking about proof unless they’re quite specific about the tautology being referred to. The Euclidean proof is no good with a different set of axioms. The jury’s proof is no good with a different set of “facts.”

I still say that short of that sophistication, where the proof has no meaning apart from a specific tautology, the tautology never being demonstrably the same as the universe, there is an infinity of possibilities of proofs for lesser tautologies.

What about still more sophisticated epistemologies? Time will tell. Or not.

2003 03 13 bkMarcus just sent an email with a wealth of links taking a variety of positions with regard to the old saw that “the exception proves the rule.”

In the phrase, “the exception proves the rule” does “proves” mean “tests“?

(Yes & No):
“Vin’s hypothesis that the relevant sense of ’prove’ is closer to ’proof’ (v): ; ”
[But then the page also cites the legal etymology that the OED does.] [pk adds: I link the following URLs when I can, meantime you can copy and paste.]
http://www.icsi.berkeley.edu/~nchang/personal/exception.html

(Yes):
“This phrase now obtains a diametrically opposed meaning to its original intent,
where proves meant breaks.”
http://livingcode.manilasites.com/discuss/msgReader$332

(No):
“The common misconception is that ’proves’ in this phrase means ’tests’.
That is *not* the case…”
http://alt-usage-english.org/intro_c.shtml#exceptionprovestherule

(No):http://www.greenapple.com/~words1/070599.html#exception

(Yes):http://www.bartleby.com/68/30/2330.html

(Yes):http://www.m-w.com/cgi-bin/dictionary?book=Dictionary&va=prove

— -cut here — –

The YES position is that to prove meant to proof or to test and that therefore the common usage is not just wrong but backwards!

The NO position is that the origin of the phrase is in old English law, in which case the exceptions and rules being referred to are legal and artifactual, not natural.

So either way, the common usage is wrong.

2003 04 23 Brian also recently teased an important concept upward in my vocabulary toward regular usage: model theism. I was making some generalization about “religious” people, specifying that I meant the congregation of a secular faith like democracy (or Communism) as well as any particular superstition (that is, any untested or ill-tested body of beliefs), and Brian paused me to make sure I wasn’t going to add anything about my recent Illichian / Durkheimian jag about people believing that they can distinguish reliably between sacred and profane. He then said, “Oh, you mean model-theism.” Ah. Now had I been familiar with that term a few years ago, I might not have had to invent my own term Cartamania! Yes, exactly, I answered: belief that your thought-model is Real.

So, what I’d been building toward saying to Brian had to do with what I’ve already said in this file, recapitulating Bateson’s iteration in Mind and Nature: science never proves anything: and tagging on the pk whipping-horse, it’s only the religious, the faithful — lawyers, priests … and their Blackshirts, who knee-jerk demand proof at the drop of a hat.

Can you prove that? Of course not. No rational man can prove anything. One can merely argue its reasonableness.

I repeat Richard Feynman’s point: all we have is belief. The question is: have our beliefs been groomed for their reasonableness?

2004 12 14 I’m just beginning Simon Singh’s Fermat’s Enigma [NY, 1998]. Singh distinguishes scientific proof from mathematical proof: experiential proof from logical proof. Mathematics has always struck me as hubris-filled. Sure I marvel at Pythagoras’s Theorem. Sure I can’t refute any of the famous theorems (neither have I spent thirty seconds trying). But what do I know? I remain reluctant to trust the reasoning of any mortal creatures (and any supposed immortal entities) too far.

I trust logic about two whits more than I trust theology.
I trust experience three or four whits more. I don’t trust anything completely:
not evolution, not the universe, and not any deity: certainly none man-made.

The teacher makes a generalization: No two snowflakes are alike. Has she really examined every single snowflake? in the whole universe? Haven’t most of them melted before she could see them? Aren’t most of the remainder locked in ice where she can’t see them? Did she have a proof? Was it logical or experiential?

I’m with the scientific proof: the fallible kind.

Proof requires agreement on a set of axioms.
Anti-state.com

2005 05 21 from a different blog piece on Originality

Science can prove error, not truth.
Plagiarism can be proved, originality cannot.
Theft can be proved; not ownership.
One could prove that the devil isn’t God,
God himself could not prove that God is God.

2008 06 22 We can never prove that a theory is true: all we can do is declare that we have as yet noticed no evidence to contradict it. What new evidence may get noticed tomorrow can never be known: except by Authority which can proscribe anyone mentioning new evidence.


The concept of proof is dealt with throughout my writing. A couple of specific comments were posted at my IonaArc blog in 2005: in February and in December. When all my domains were censored, once back out of jail, I resurrected some of my Thinking Tools at pkTools blog. Now all moves to pKnatz, where menus and categories are once again possible.

2012 04 28 The Exception Proves the Rule

I saw a good explanation of the confusions commonly following the phrase “the exception proves the rule”: I now see that the points are covered by some of the comments above quoted by bk, but it clarifies the issue with a new force to me:
Here’s a rule: “What goes up must come down”: Hss sends a rocket out of the solar system. Therefore, the “rule” is proved: to be false!
But consider this: “No Parking: except for the Brinks truck, Wednesdays at 1 PM”
The Brinks truck may park there, Wed, at 1, you may not park there anytime. The exception proves the rule to be true: unless you’re the Brinks truck, unless it’s Wed at 1, you may not park there!

So: you may not kill: unless you’re a Roman, or a priest, and it’s Jesus you’re killing.
Natural law, gravity, has no exceptions, human order is all exceptions.

2012 98 13

Everyone assuming the same thing is not proof.

2016 09 04 Now that the internet is 90% written and edited by illiterates I spend less and less time browsing yahoo. This morning a doosy caught the corner of my eye: Vox Sets Out To Prove All … Watch out for anything that wants to prove “all” of anything. Doyle’s Sherlock accomplished untold damage to the already weak human capacity for reason. Sherlock trots around pretending to have deduced the facts by deduction: he waits till all the facts are known, then he concludes … When I was twelve years old twelve year olds were famus for their genius. There was always a twelve year old who understood things the school board did not: me for instance. Sherlock presented such as “proofs”. No, no, no. Unless you could prove that all facts had now been gathered, no facts were false, no fallacy had been committed …
http://thefederalist.com/2015/02/02/vox-sets-out-to-prove-all-religions-are-equally-violent-and-fails/

Talk about illiterates, about morons in charge, how’s this?
Geese serve no purpose …
http://thefederalist.com/2016/09/03/geese-worst-animals-planet-end/

Gee, just like Jews! just like Nazis! just like humans!
Just like religions, just like gods.

K. Teaching Thinking Tools Reason
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About pk

Seems to me that some modicum of honesty is requisite to intelligence. If we look in the mirror and see not kleptocrats but Christians, we’re still in the same old trouble.
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