Showing posts with label proof. Show all posts
Showing posts with label proof. Show all posts

Wednesday, April 15, 2020

“Refutation” inflation (re-updated)


[The present note is an exercise in logic and linguistic hygiene.  It is not political per se, and in particular is agnostic as to the facts and merits of the tangled case under discussion.]

[Original post-date 16 May 2017]
One of the top stories in today’s crowded news:

The family of slain Democratic National Committee staffer Seth Rich rejected Fox News reports that he had leaked work e-mails to WikiLeaks before he was fatally shot last year in the District.
The reports, which gained traction on social media, said an FBI forensics examination showed Rich transferred 44,053 DNC e-mails and 17,761 attachments to a now-deceased WikiLeaks director.
Rich’s parents, Joel and Mary Ann, said Tuesday through a spokesman that they do not believe their son gave any information to WikiLeaks.
https://www.washingtonpost.com/local/public-safety/family-of-slain-seth-rich-says-reports-he-fed-wikileaks-dnc-info-are-untrue/2017/05/16/9b32ef9c-3a46-11e7-8854-21f359183e8c_story.html?utm_term=.f0f43ca07a0f

That is admirably and neutrally stated.  However, some news sources are reporting the same facts with headlines like “Seth Rich Parents Refute New Claims On Wikileaks Contact”.   Therein lies a confusion.

To refute is (in its original, non-catachrestic sense) to disprove.  The allegations in question are perfectly precise and emprical, subject to either (partial) refutation or (partial) confirmation.
But the only party in a position to refute the allegations is someone who professionally and forensically examined the laptop in question.    Does it contain such material, or does it not?  The family is in no position to “refute” the allegation, however false it may be.  Indeed, on the Post account, they cannot really be said even to have denied the allegations;  they simply said they don’t believe them.  A perfectly rational stance; but not exactly a denial (for after all, how would they know -- if their son had been secretly betraying his employer, why would he inform his family?), and certainly not a refutation.

Increasingly, the less careful media uses refute where deny would be appropriate.  Part of this may be simple semantic weakness on the journalists’ part (to which many other technical terms, like impeach, are subject), but partly also to the fact that deny has accumulated invidious connotations, as though anyone who “denies” X  is himself shady in some way.   That is a legitimate worry;  other synonyms are available (the family discounted/pooh-poohed/scoffed at/… the allegations) which lack such connotations.  Better to use these than to induce a crucial ambiguity in the verb refute, in a way that renders it inapt for precise usage.


Part of the problem in the fluidity of use of refute  might be  not political, but cognitive and linguistic:  confusion with the paronym rebut.  A rebuttal is not quite as decisive as a refutation, but supposed to be more evidential and structured than a mere denial.  Mere denial is a weak defense indeed, available even to the ghosts of five-year-olds, as in the comic strip "The Family Circus".


A further semantic distinction:  re discussions within the first Nixon administration, of Kevin Phillips’ The Emerging Republican Majority:

Phillips had not been refuted by the West Wing,  but his thesis had been rejected.
--  Patrick Buchanan,  Nixon’s White House Wars (2017), p. 146


Note:  There are other ways of disposing of an allegation, other than outright refutation:  you may undermine, or infirm, or discredit it, in various ways.   Thus, if a witness presenting himself as Dr. Smith (M.D. Harvard) testifies that the deceased died of psoriasis, another doctor (or team thereof) might refute that testimony (on its own ground) by presenting evidence that the deceased had a huge malignant brain tumor but had never had a skin condition.  But anyone -- say, a lowly clerk at Harvard Medical School -- could discredit the testimony on entirely other grounds, by showing that Smith never attended Harvard Medical School, nor (with a bit of extra digging) ever so much as finished high school.  That would be devastating counter-evidence, but not a “refutation” in the technical sense.  (Logically, Smith might nonetheless have blundered upon the correct explanation of the demise.)


One can’t help suspecting that the media’s terminological laxity might be connected to an epistemological weakness:  presenting counter-allegations as evidentially telling (whether or not they are actually awarded the accolade “refutation”) although (consider the source) they are suspect or undermined at the outset, as coming from the accused's family, or attorney, or partner in crime.  Some of these are treated with great journalistic reverence, and actually pass into folklore  --  "he didn't do nuttin' " (spoken while the perp is actually in flagrante), or, post-hoc, “he didn’t have a gun” (though one was found in his possession, surrounded by spent cartridges), and where all else fails and guilt is  ... irrefutable, “he was hoping to go to college”, “he was starting to turn his life around”.



[Update 17 August 2017]  Bringing it back to Wikileaks:

Assange once told me that he did not “accept” the allegation that Russia had provided him e-mails through a third party,  which of course was different from saying that the allegation was untrue.
-- Raffi Khatchadourian, in 21 Aug 2017 The New Yorker]

But nor did he make any move to refute or cast doubt on the allegation:

I asked if he was even able to know the chain of custody of his election material before it came to him.  He declined to answer.

[Side-note:  for that phrase of forensic science chain of custody,  cf. the term of hadith stemmatology,  isnâd.]

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A particularly piquant use of the term “refutation” occurs in the mathematical polylogue by Imre Lakatos, Proofs and Refutations (1976).  The title impishly echoes that of Karl Popper’s better-known Conjectures and Refutations (1962).  But whereas that title reflected the expection rough-and-tumble of normal science, Lakotos’ phrase produces a double-take:  if a “proof” gets “refuted”, it wasn’t really a proof to begin with, but only a purported proof.  But Lakatos is not referring to those (relatively rare) instances of purported proofs that turned out to be fatally flawed, and left no progeny in mathematics.  Rather, he considers mathematical demonstrations that were all right so far as they went, but which contained hidden assumptions.  These being unearthed in a “refutation”, the original proof, or something much like it, gets deepened, until further unsuspected subtleties become revealed.    He offers a dialectic analysis of the process of mathematizing.   The result does not demote mathematical truth to a mere just-so story, as among nihilists and relativists.  It rather offers a more epistemologically modest picture of the mathematical enterprise (the fallible human excavation of a transcendental reality, a Platonist would say), in which the notions of “proof” and “refutation” both get toned down a bit, and the process becomes a bit more like developing a software package, finding and fixing bugs along the way.  The result is real progress.

For a more technical discussion of refutation and its semantic field, try


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The flip side of the coin, by which the media use artificially strengthened language when presenting the allegations of the victim class and their attorneys, is artificial down-grading when the allegations come from the authorities.   As, a headline from a moment ago:

South San Francisco police officers on Wednesday morning shot and killed a man who they say was allegedly armed with a shotgun.

Either “they say” or “allegedly” would be an adequate and appropriate editorial distancing from the official police statement.   Together, they are at best redundant, or, if taken literally, false:  the police did not state “He was allegedly armed with a shotgun”;  such a statement would be in place if, say, the police had not actually seen the shotgun, but a bystander reported -- alleged -- such possession of a shotgun (which had  been abstracted from the crime scene by the time the police arrived).  

~

[Addendum] Further vocabulary.

In the following sophisticated example, the verb nullify is used, not in the sense ‘refute’ exactly, but ‘to render null and void’
-- not to prove the falsity of a statement, but to disable its presuppositions:

I turn now to the objection that, even if probability-scepticism does not nullify the concept of truth, it does nullify the idea that science should aspire after truth.
-- John Watkins, Science and Scepticism (1984), p. 162


Indeed, Lakotos’ impish use of refute is roughly the same idea.


~

A bonus from Classical Antiquity:

Pericles, also, was a hearer of Zeno, the Eleatic, who treated of natural philosophy  in the same manner as Parmenides did, but had also perfected himself in an art of his own, for refuting and silencing  opponents in argument;  as Timon of Phlius describes it --

Also the two-edged tongue  of mighty Zeno, who,
say what one would, could argue it untrue.
-- Plutarch’s Lives (Dryden’s translation)

Saturday, December 12, 2015

Ernest Gellner on Truth


“Truth” is, on the one had, a bland and boring concept:  “Paris is the capital of France” is true, “Las Vegas is the capital of France” is false.
Yet in other venues, fraught:  as in, Pravda.  Shading into metaphysical mysticism (“The Search for Truth”).  If I am trying to find out, for which X the sentence “X is the capital of Albania” is true, then in a sense I am Searching for Truth; but really, only for a truth; and indeed, not really under that description:  I merely wish to know what Albania’s capital is called.

~
Ernest Gellner on Truth

Relevant quotes, bridging the gap, from works by Ernest Gellner.  (For our full essay on the subject of truth, click here.)

Re Orwell’s Nineteen Eighty-Four:

Freedom is the recognition that 2 plus 2 makes 4 :  not because there is no escaping such necessity, but because only such necessity is a refuge from arbitrary social power. [It is] an extra-social objective truth, which account for why such fuss should be made  of a morally and emotionally rather neutral piece of arithmetic.
-- Ernest Gellner, Contemporary Thought and Politics (1978),  p. 4



On a strategy of self-validating beliefs (which he dubs “auto-functionalism”, a term which seems not to have caught on):

It consists of establishing the soundness of one’s beliefs, not directly, in the ordinary and straightforward way, by showing them to be true, but, on the contrary, of deriving their soundness by showing them to play an essential role, to be ‘functional’, in the internal economy of one’s own personality or society … The first step is to put forward a theory of truth: truth ‘really is’ the fulfilment of a biological, or social, linguistic, etc., function.
-- Ernest Gellner, Contemporary Thought and Politics (1978), p. 14-15

(Truth, soundness, validity, provability -- actually an interesting Wortfeld;  a topic for another day.)

And, re the egregious Althusser:

He argues, in effect, not that Marxism is true, but that the Marxist epoch is still with us.  What is defended, in the end, is not the truth of a doctrine, but its alleged role.
-- Ernest Gellner, Contemporary Thought and Politics (1978), p. 17

Now,  that all sounds rather feckless and po-mo; but to add some perspective, it is reminiscent of the “regressive justification” in axiomatics, particularly for set theory.  (More here.)

A somewhat more degenerate version of this auto-functionalist approach, endemic to the America of “pot, pop, and protest” -- degenerate in that, unlike that of Althusser et alia, it makes little reference to the world outside the speaker’s individual ego-bubble (indeed, it works best for pure solipsists, for whom the external world need not exist):

In America, it possesses a theory of knowledge, and above all an associated style of expression, which goes back to populism and beyond it … Its basic idea is that sincerity is the key to truth.
-- Ernest Gellner, Contemporary Thought and Politics (1978), p. 82

(It’s amusing to hear such a stance referred to as a “theory of knowledge”, but social scientists really do talk that way, speaking  for instance  of a baby’s “theory of the world”.)


“The hysteria of complacency of the postwar period,
and the hysteria of protest of more recent times.” (1971)


And again, back to the math connection, reporting the fantasies of Michael Oakeshott:

What is proof? -- he asks.  There is no such thing as proof in general, he answers himself.  There is only proof  persuasive for this, that, or the other kind of man.   Cogency of proof  is relative to what you are.  he notices that this does not seem to apply to mathematics, and brazenly comments that just this has always made him suspicious of mathematics.
-- Ernest Gellner, Contemporary Thought and Politics (1978), p. 180

Actually Oakeshott  put his case too weakly:  varying standards of proof are relevant in mathematics -- indeed, it is only within mathematics  that such scruples have structure and are in point.   In pre-Cauchy/Weierstrass analysis, proof was a bit of a kludge.   Later on, Constructivist qualms  came into play.  And in our own day, we distinguish between theorems whose proof requires the (disputed) Axiom of Choice, from those that can dispense with it.

The ultimate selbst-aufhebung of all such alethic egalitarianism is plain:

If almost everything is true in its own fashion, truth cannot matter very much.
-- Ernest Gellner, Contemporary Thought and Politics (1978), p. 16

~


Bonus nuggets, from the bottom of Gellner’s crackerjacks-box:

It is a travesty to say that martyrs die for Truth.  Real truths seldom require such dramatic testimony.
-- Ernest Gellner, The Devil in Modern Philosophy (1974), p. 55

the feminine theory of cognition:  that truth is not a matter of exploring or penetrating an external reality, but of gestation and parturition.
-- Ernest Gellner, The Devil in Modern Philosophy (1974), p. 62

Only psychoanalytic interpretations that tally with what is real in the patient, can mediate veridical insight.
-- Adolf Grunbaum, quoted in Ernest Gellner, The Psychoanalytic Movement (1985; 2nd edn. 1993), p. 185

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Thursday, January 30, 2014

Arnoldian Epigram





            Proofs are to mathematics  what spelling is to poetry.
            -- V.I. Arnold





Thursday, October 25, 2012

Conclusive Proof, that All the World is but a Footnote to the Rootabaga Stories


Ladies, Penguins, and Gentlemen of the Jury:
If it please the Court –

In the Rootabaga Stories, we find foreshadowed, everything that has ever been thought or written  before or since.  Evidential examples:

=> Scrooge McDuck: a straightforward rewriting of Johnny the Wham, who slept in his money bin, covered with money.

=> The Catcher in the Rye: an obvious ripoff of the “ball towns hidden in the tall grass.”

=> Homer the Bard: a knockoff of the Potato Face Blind Man, minus the accordion.

=> The Riemann Hypothesis: just like the grasshoppers that learned to count, and kept on  counting and counting.   Same basic idea.


Go ahead – just try to stump me.

“OK try this one:  ‘Four score and seven years—‘ “
“—The Potato Face Blind Man said that.”

“ ‘To be or not to—‘ “
“—Dippy the Wisp said that.”

You see?

Does any man argue to the contrary?  No?  Good then.
I  rest  my  case.