Refutation vs. Disconfirmation

We continue our observations about Verification (essay here) and Modus Tollens (essay here).

It has been maintained that there is an important asymmetry between the verification and the refutation of a theory in empirical science.   Refutation has been said to be conclusive or decisive, while verification was claimed to be irremediably inconclusive. … The falsity of [the theory] is indeed deductively inferable by modus tollens.

-- “The Falsifiability of Theories”, in: Adolf Grünbaum, Collected Works, vol. I (2013), p. 62

That is basically because an empirical law is, in general, a universal: ∀x P(x).   Given any  ¬P(a), that is falsified.    Whereas successive confirming instances, while perhaps increasing one’s confidence in the hypothesized law, do not deductively entail it.   Nor need that fact be, in practical terms, a mere quibble, in cases of an infinite domain:  thus, a conjecture in number theory might be verified for all values of n up to a billion -- a trillion -- a googolplex -- yet still turn out to be false.  (Indeed, toy conjectures of this sort  are trivially easy to dream up.  E.g. “No integer is evenly divisible by a googolplex.”)   Taking confirming instances ‘too seriously’, is the Fallacy of Affirming the Consequent.

Grünbaum then, however, in a Duhemian vein, weighs in against such modus-tollentic tyranny, with the observation that, in empirical science, you are really assuming (ex hypothesi) not merely a theory, but (in unspoken conjunction therewith) various Auxiliary Assumptions:  and one or more of these, rather than your pet theory, might be the ones to suffer the fury of the tollendum.  Thus,  “Isolated component hypotheses of far-flung theoretical systems are not separately refutable but only contextually disconfirmable” (id., p. 63).

The same idea, more sociologically stated:

Typically  a theory is abandoned, not because of recalcitrant observations on their own, but because of these together with some, perhaps quite complex, reasoning from them:  in the extreme case, the observations may all be quite well known already, and all that is new  is the reasoning.

-- Michael Dummett, Truth and other enigmas (1978), p. 409

Compare:

… that falsity, not truth, is the primary notion.

-- Michael Dummett, Truth and other enigmas (1978), p. xl

~

It is seldom that a theory is decisively k.o.’d by a Popperian uppercut to its predictive jaw.   Often the process happens slowly, like a river silting up;  there is no single Aha! moment (or rather, Oy veh! moment).   In science, as in life,  sometimes love grows old and love grows cold.  As, assessing a certain philosophical program:

The further one goes down the reformist path, the more implausible the consequences of one’s theory are likely to become, until  at some point  the implausibility of the consequences  comes to outweigh the initial attractiveness of the theory.

-- Scott Soames, Philosophical Analysis in the Twentieth Century (2003), vol. I, p. 299

That gradual, einsickernd, process of disenchantment, lacks the drama of Popperian refutation, or of Kuhnian paradigm-shift;  it is more reminiscent of the dissatisfying phenomenon (if it even is one) of truth decay.

~

The history of science -- though not the historiography of science -- is littered with once-flourishing theories that somehow just … faded, without necessarily ever having been decisively confronted or refuted.  It is no fun to research and write about these, since
(a) they are losers in the lottery (rightly or not), and scarcely known today (so that one’s potential readership is infinitessimal -- and indistinguishable from zero among working scientists); and
(b) there is seldom a clear-cut moral in the tale.

The occasions on which one does get an insight into some defunct theory  tend to be biographies of otherwise-great scientists -- e.g.  Theodore Porter’s fine account of the (as we now reckon him) statistician Karl Pearson, which must needs notice that hero’s period of infatuation with, mm, ahh, … ether squirts (pas devant les enfants!);  or Thomas Hankins‘s  of William Rowan Hamilton.  Or, sometimes, a historian of science rolls up his sleeve and deconstructs/resurrects  some particular thread of experiment.  As, Gerald Holton’s commendable study of “Subelectrons and Presuppositions”, involving the “classic” Millikan experiment, of which we all get a telescoped and sanitized version in high school physics.  The actual saga is more anfractuous, and less rich with easily digestible lessons.

[Millikan] found himself working with the wrong presupposition, but he knew how to rid himself of it eventually.  Millikan launched into that work with the same energy and obstinacy  as into his earlier work on the quantization of the charge of the electron, yet with the opposite assumption.

-- Gerald Holton, The scientific imagination (1978), p. 72

And re the related experiments of Felix Ehrenhaft:

There was never a direct laboratory disproof of Ehrenhaft’s claims.  … Lorentz … remark[ed]:  “The question cannot be said to be wholly elucidated.” In his review of the case, R. Bär noted …: “the experiments left, at the very least, an uncomforable feeling.”  Like most such controversies, this one also faded into obscurity, without anything as dramatic as a specific, generally agreed-upon falsification taking place at all.  Indeed, Ehrenhaft continue to publish on subelectrons into the 1940s, long after everyone else had lost interest in the matter.

-- Gerald Holton, The scientific imagination (1978), p. 79

And that, within (central, classical) physics.  The less rigorous (natural and social) sciences  are much pocked with such as well.

~

Science, not as logically implying some new phenomenon (such as the gravitational bending of light), but as suggesting likely places to look.   Thus:

The search, which has proved so successful, for chemical atoms  having specific nuclear and electronic constitutions, and for chemical molecules having specific atomic constitutions, has been stimulated by the previous construction of theories to explain the consitution of atoms or of molecules already known, theories which had, as it were, ‘gaps’ in them.

-- Richard Braithwaite, Scientific Explanation (1953), p. 70

And indeed, not only the existence of, say, atoms or isotopes with a given atomic weight and atomic number  are thus -- not exactly ‘predicted’ in the deductivist sense, but pointed to -- but additionally, we shall expect certain behaviors, or ranges of behaviors, based upon the place in the periodic table of that species (should it exist).

Thus, when the eka-aluminum that Mendeleev hypothesized  was eventually identified (by a Frenchman, who thus had naming-rights and called it gallium) and turned out to have behavioral values very close to those predicted,  while not proving the theory of atomic chemistry as it then stood, was still much more than just one more danged black raven.

[A footnote on another such predicted discovery, that nicely illustrates consilience in the sciences, combining both forefront atomic physics  and practical geology:

At the time Bohr was developing his theory, the element following lutecium was undiscovered.  But Bohr … asserted that, in this unknown element, the added electron would have to be placed in the level n = 5. This would imply that the unknown element would have an electronic configuration analogous to that of zirconium.  Inasmuch as elements that are chemically analogous  are usually found in the same minerals, Bohr claimed that the missing element should be sought in minerals containing zirconium.  It was indeed in such ores that the missing element, called hafnium [after the Latin name of Bohr’s hometown] was detected.

-- A. D’Abro, The Rise of the New Physics (1939),  p. 549.  ]

This “guiding-light” role of a theory, not being a formal entailment, is likewise not subject to modus tollens (though of course it might be abandoned in the face of an accumulation of recalcitrant instances):

Whereas discovery of observable properties which fill such gaps in a theory  is rightly thought to provide a weighty confirmation of the theory …  failure to discover such properties would not be regarded as weighing against the theory, except perhaps in very special cases.

-- Richard Braithwaite, Scientific Explanation (1953), p. 70

Minimalism vs. Nihilism

I’m currently reading an intermittently entertaining book by Jim Holt, with the simultaneously catchy and off-putting title  Why Does the World Exist?   (2012).    I actually gave my mother a copy for Christmas when it came out:  not having yet read it myself, but counting on that ever-companionable writer to make big ideas plain to the public, the notion being that she would read it, and then we would discuss it in our weekly phone-calls (we live on opposite seaboards:  she in a nursing-home on the west coast,  I in a sheltered workshop on the east).   Unfortunately, Alzheimer’s intervened, and we can no longer discuss anything substantive;  her days of wine and metaphysics are behind her.  Though, now, as I finally get around to reading it myself, it would seem that, in this particular case, she hasn’t missed much.  The problem is, his clear-headed addressal of that perennial topic of sophomore seminars -- Why is there Something, rather than Nothing? --  would have made an excellent laconic magazine-article, but Holt somehow wound up with a book contract for this ultimately (indeed, quickly) sterile subject, and has to pad things out.  So he takes various nugatory arguments by e.g. “metaphysical nihilists” more seriously than they warrant, and duly deflates them, but takes several pages doing so.

(Mr. Holt’s genteel approach to such gentlemen  is to humor them -- though, to his credit, ultimately to refute them.  Ours is rather to rip their throats out;  cf.  our diatribe contra Eliminative Materialism.)

The exercise calls to mind James Surowiecki’s canny column in this week’s New Yorker, “Punditonomics”, where he notes the (obvious) economic incentive to spew out short-shelflife twaddle if all you want is eyeballs.   A lot of that has been evoked by the disappearance of Malaysia Air Flight 370 (I actually work a few feet away from some Bureau integrees who are involved with that case, and poll them every so often.  BLUF:  UFOs are not involved.)   As Surowiecki reports,

The peak (or nadir) of the speculative frenzy  came when CNN anchor Don Lemon wondered aloud whether the plane might have been swallowed up by a mini black hole.

(Ceci renoue avec notre thème du néant.)  When a retired general who now shills as a CNN commentator, failed to cough out an equally (yet distinct!) OTT hypothesis, suggesting we wait and look at the facts,  the Host replied, revealingly,

“You know how cable news works, don’t you?  We got time to fill here!”

And thus, likewise, Mr Holt has some pages to fill, that were better left (in the spirit of Nothingness) elegantly blank.

On pp. 59-62, Holt gamely attempts a riff on nothingness as, “as Leibniz was the first to point out, the simplest of all possible realities,”  adding solicitiously, in case the reader has instinctually at this point  razzed in disgust, “Simplicity is greatly prized in science.”  (So, pipe down, you-all in the back row.)  In mathematics, by contrast, the technical term for this (the null group, or anything else) is:  trivial.

In the course of this, though, he does raise a somewhat interesting question:  “If our world turns out to have an infinite census of objects, why should it be, say, aleph-2 rather than aleph-29?  Only the Null World escapes this kind of arbitrariness.”  (The same observation applies to a finite ontology as well, of course.)  And the answer to that, we would suggest, as we have argued in a series of essays (Theologia Mathematica), is to take the invisible world seriously, quite on a par (as Gödel argued) with the visible (and  arguably  moreso).  Such infinities as exist, exist, and those that don’t, don’t, and there you have it.  (Of course, should there turn out to be some unexpected supremum like aleph-29, we will look for a principled understanding of that surprising fact.)   This line of thought has been applied more seriously to the problem of the cardinality of the continuum:  aleph-1 seems the only non-arbitrary value.

~

So what do you do when the puns on Nothingness run out?   If you’re a good author, like Jim Holt, you don’t simply repeat yourself, or inflate a chapter like a bicycle-tire:  You take the show on the road.   And so we are treated to a travelogue of several European and American capitals, meeting various Colorful Characters along the way.   It’s like a thematic tour, only instead of the theme being Chocolate or Wines,  it’s Big Ideas;  and instead of Mansions of the Rich and Famous,  it’s Cramped Apartments of the Brainy and Loquacious.

And thus we are whisked to Pittsburgh, where we make the acquaintance of the legendary Adolf Grünbaum, a Morris-Zapp-like personality, still robustly vigorous in advanced age.   And in addition to various choice philosophical obiter dicta, we are regaled with a memorable tale of the nighttime drive to the restaurant atop Mount Washington, the voluble crusty atheist at the wheel.  (B.L.U.F. : Never drive with the guy.)

[Afternote:   I have just begun reading the Collected Works of Adolf Grünbaum, the first volume of which  came out in 2013.  Evidently the wily old philosopher was delighted by the rather Zorba-the-Greek portrait he gets in Jim Holt’s book, for the dust jacket quotes Why Does the World Exist to the effect that “In the philosophical world, Grünbaum is a man of immense stature.  He is arguably the greatest living philosopher of science.”  On page one of the Introduction, the editor goes on to quote Holt at greater length along those lines.]

“…Mmmyess… Immmmense, that is quite the word ….”

Then before you know it -- like James Bond hopping from metropolis to metropolis -- we are in Paris, this time without the excuse of any actual philosopher to interview, the slender connective being the Café de Flore, where Sartre used to squat, and doodle about le néant (Why is there quelque-chose rather than rien du tout?, that is to say).   We never get any philosophy here, but the author does offer a vivid tableau of the nightlife of fashionable Eurotrash:

At a table in the back  I spotted Karl Lagerfeld, with his characteristic ponytail, dark glasses, and high white collar, in hushed conversation with one of his muses, who was wearing what looked like black lipstick.  Other than that, the place was pretty much empty: le Néant.

But then there was a noisy burst of activity.  A woman of a certain age … breezed through the front door, accompanied by a pair of what appeared to be Cuban gigolos  dressed in shell suits.  Giggling and grinding their teeth, this trio sat down with us  and began to jabber away.  The woman’s face was a sallow mask of leathery jollity, and she talked in a low croak  that put me in mind of Jeanne Moreau. … It seemed a good time to leave.

(Should you ask:  Why are there gigolos, rather than nothing -- the question is unanswerable.)

[Update 10 May 2014]  Jim Holt takes on Derek Parfit; wins by forfeit:
http://worldofdrjustice.blogspot.com/2014/05/have-theory-will-travel.html