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

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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.

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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.

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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

On Tarski’s “Convention T” (expanded)

Accolades:

Convention T embodies our best intuition as to how the concept of truth is used.

-- Donald Davidson

My lone dissent:

More boredom thou shalt never see

than Tarski’s Truth Convention T.

“Snow’s white” is true -- let’s get this right --

if, but only if,  snow is white.

A.T.,  logician and skirt-chaser

[Footnote]

When Tarski’s logical machinery is used to provide languages with an interpretation, it should not be seen as giving us a definition of truth. [Emphasis in original.]  When used in this way, it gives us a theory that, for each of the infinitely many sentences of the language, assigns a condition that obtains if and only if that sentence is true -- where truth is something we takes ourselves to understand antecedently, without definition.

-- Scott Soames, Philosophical Analysis in the Twentieth Century (2003), vol. II, p. 293

For a major empirical research program, investigating the validity of Convention T, click here.
 

 ~

A fellow dissenter:

See for example the panegyrics in Wallace:  “It may strike the reader that Convention T is an astonishingly powerful intellectual device…” (etc.)  Wallace’s expressed admiration for the achievements of modern logic  is of course sincere, and I share it (not always for his reasons).  But these achievements should not be used to terrorize the reader …

-- Saul Kripke, “Substitutional Quantification”, in Evans & McDowell, eds., Truth and Meaning (1976), p. 340

The (In)scrutability of Reference

In our post below (Doctor Justice’s Petting Zoo), we offered an ontological fable, inspired by Quine’s celebrated demonstration, in Word and Object and later writings, that an investigator faced with the problem of “radical translation” cannot determine, by behavioristic methods alone, whether the expression in the exotic language refers to rabbits as unified individual enduring entities, or as (potentially contingent) conglomerates of undetached rabbit parts, or as ontological instantons (what you see before your eyes right now), or individual doses of the mass-term Rabbit Fusion (the way puddles instantiate water), or as incarnations of the Urkaninchen, or what have you:  the reference of the expression is insofar inscrutable.   From this potential modus tollens  he decides to hang on to the behaviorism  and to ditch various purported mental entities instead -- a process which, if carried to what some (Scott Soames, for one) deem its logical conclusion, then  “Quine’s position has several consequences that are so unpalatable as to make it …  self-undermining.”  (Philosophical Analysis in the Twentieth Century (2003), II 282).  But the spice of the tale is in the telling, and Quine tells it exceedingly well.

Likewise delightful is his fable of referential ontogenesis, a tale broached in Word and Object  and taken up again in Roots of Reference.  Here we are given poignant glimpses of Quine’s tortured infancy (“More mama!  More water!  More red!), and offered careful, psychologically plausible reconstructions of how we acquire mass terms, collectives, quantifiers, relative pronouns and so forth, along with their associated ontologies.

In “Reference and its Roots” (in: Hahn & Schilpp, eds., The Philosophy of W. V. Quine (1986), p. 523), Strawson has a bone to pick with Quine’s (psycho)logical account of the acquisition of singular versus general reference:

It must be part of [the learner’s] mastery of ‘Fido’, that Fido is unique.   A plurality of Fidos simutaneously soliciting his attention  must be ruled out by his understanding of the term -- semantically ruled out. … But if it is ruled out, then what becomes of the claim that ‘Fido’ is semantically simpler than ‘dog’? The answer  at least  is simple:  we just reverse the terms. … ‘Fido’ is a more, not a less, sophisticated acquisition than ‘dog’.  ‘Dog’ has individuation;  ‘Fido has individuation plus.

But here Quine is surely correct, as regards the sequential ontologenesis.  Initially, Mama (for let us revert to her, for dignity, leaving Fido in his kennel)  simply is what she is, as presented (well, and as supplemented by instinct, but in this connection  the point is a distraction, though we revert to it later):  Die Mutti ohne Eigenschaften, as it were (nurse, nurse, nurse).  There is initially no reason to posit that she, or Fido, are representatives of any  larger Natural Kind, any more than is Yuri the Unicorn (the family pet, and unique of his species, as it happens).  Later we learn and add layers to this initial baldly-presented UrMutti:  she turns out to be an example of the class of Women, and moreover a painter, and a Clinton Democrat, and foreign-born (which accounts, in retrospect, for certain oddities of her accent, though it sounded fine to us as an infant);  so eventually the term Mama does become enriched beyond that of woman;  it just happens that we met her prior to such enrichment, unlike the case of such other specializations as, say, topologist as against person, where we don’t meet the former term until our including ontologies are well in place.  -- The situation is quite general, not especially connected with singular terms.  As, there is a certain commonality in the notion ‘atom’ that has persisted since the days of Democritus, yet the concept has repeatedly deepened, from the periodic table and the notion of valence, to the Rutherford model, then the Bohr model, and eventually SU(3).

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Let us now take leave of Quine’s idealized account of the logic of language acquistion -- take leave of philosophy altogether, and glance at actual acquisition,  in all its oddity.

There was a time, I am told, by one in a position to know (I myself have no memory of it), when I uttered “Daddy” in the presence of any bald man.  What did I mean by this?   Did I actually mistake the gentlemen in question for my own father?  Was the word used as a metonym or simile -- “Lo, a man who reminds me of my father!”   Was it a way of saying (the word bald not yet being in my young vocabulary) “Behold, a bald man!”  Or is the reality behind the reference  truly inscrutable, my infantile mind not being yet up to the task of distinguishing among these variant interpretations.  (Such, indeed, was some of the thrust of my “Petting Zoo” parable:  Quine’s sophisticated picture of temporal rabbit-slices competing with Rabbithood and the Rabbit Fusion  for primacy, is comically at variance with his scenario of savages in the bush.)

The first hypothesis (debility in recognizing my own father) seems unlikely (certainly I blush to imagine it), and yet a somewhat similar situation occurred involving a friend of mine, who at the time was eight years old -- not eight months.  The lad was somewhat familiar with a friend of mine named Nick;  and one day, spotting a fellow who sported a sandy moustache like Nick’s, referred to him as “Nick”.   I said No, that’s not Nick, they just look somewhat alike.   To my surprise, the boy insisted that he was not mistaken, and was quite upset that I continued to contradict him.

Now, such anecdotes have a curious attraction, as offering rare insights into the no-longer-accessible logic of our own young minds.  (For another such, click here: Temps et durée chez une enfant de quatre ans.) But more significant -- and more disturbing -- are referential inscrutabilities that persist (often undetected) into our adult life.

The clearest examples are provided by the shifting, mixed figures of our own dreams.   Very often an individual in your dream is a sort of quantum superposition of a number of people you have known (and some, perhaps, that you have not precisely known personally, but are archetypes or something of the sort).  You seldom get “Daddy” in a pure state.  -- In film, such ambiguities were classically depicted in “Persona”.

By now we are on the boggy ground, not of Frege and Quine, but of Freud.   And the latter’s analysis of the Psychopathologie des Alltaglebens  is relevant here as well.  We can see this in standard-issue misspeakings (Versprechen).  One my wife spotted just an hour ago, when, referring to a phone conversation she had had with our son Steven concerning the Shakespeare course he’s now taking, I said, “Did you mention that you and Steven used to attend the Ashland Shakespeare festival?” -- but I should have said, “You and I”.  And this was indeed no mere unmotivated “slip of the tongue”; its psychological grounding was immediately apparent to analysis (for I live an examined life).   What was surprising was simply that the mixed quantum state here involved a melding of myself with my son, whereas the usual melding in my mind (originally pre-conscious, now familiar) is between my son and my younger brother.

Again, such blends are not restricted to persons.  Freud discovers many examples in Die Traumdeutung, under such designations as Mischbildung, Mischgebild, and Mittelding.  In extreme pathological cases, such blending can involve the rational and the inanimate, as in The Man who Mistook his Wife for a Hat.  (The most nightmarish title  in the history of literature.)

*

Back to Quine.

His radical-translation fable was framed as a tale of linguistic anthropology; of rabbit-hunting, but really he was after bigger game.  As he later stated (“Ontological Relativity”):  referential inscrutability begins at home.

I was reminded of this earlier today, while perusing Scott Soames’ account of Kripke’s Naming and Necessity and its aftermath.  All sorts of ingenuity has been applied to the case, to try to tame its oddities and paradox (problems with Peano, Thales, etc.):  actuality operators, neo-descriptivism …  And I couldn’t help thinking:  quelle besogne ingrate.   Here some highly trained minds are applying techniques appropriate to philosophy and mathematics, largely with a view to constructing abstract semantic castles in the air, yet in part to model actual human linguistic behavior, at least in the sense of being inspired and corrected and tethered to the same -- much as the theoretical physicist, spinning his gossamer webs of Strings, must occasionally glance at the actual facts of the cosmos, to justify his departmental affiliation.  But human linguistic behavior -- human any behavior -- is simply too messy and defective to admit of such austere systematic description.  (Kripke’s point was indeed partly just that, and he left his lecture informal.)   Certainly mathematicians, when asking foundational questions, do not worry about what Joe Sixpack thinks about Zorn’s lemma.

Epigram:  The enterprise of linguistic philosophy is like that of “Consider a spherical cow” -- good mathematics, bad biology.

The larger problem that confronts us (and it is a perspective I have been brought to only reluctantly) is the truth of the following two factual complexes, either surprising in itself, but jointly infuriating:

(a)  the Unreasonable Effectiveness of Human Communication

(b)  the Utter Impotence of Human Communication

[More to come, if reader interest warrants]

Realism: What (continued)

Scott Soames, Philosophical Analysis in the Twentieth Century (2003), p. 95, summarizes the realist commitments:

(1)  To the existence of everyday objects.

(2) To the existence of abstract objects (numbers and such).

(3) To every object of thought, which “must possess some kind of being, since otherwise we couldn’t think about it.”

Herewith our assessment of these commitments.

(1) To reject these would be churlish: a universe whose apparent bunnies and gumdrops, were but phantoms, would be the work of a devil, not of God.   We embrace the phenomenal world (beginning with the breast)  with the same uncomprehending acceptance with which we receive the Host.  We believe in the Real Presence of this chair in this room.

(2)  These are the most certain; only these survive the catastrophe of Brains-in-a-Vat.

(3)  These are much more problematic than numbers, or even differentiable 4-manifolds. The zoo of correspondents to every idea (already one is somewhat begging the question,  speaking of an “object of thought”) threatens to devolve into Meinongism – an ontological slum. 

            Certainly a mere expression – a string of words – does not in general denote or connote or (as Amos ‘n’ Andy might put it) jinote  anything at all.  “The square root of the present Pope of Islam’s antigravity mushroom non-unicorn”, though evocative enough, is referentially mere flatus vocis.  But there is no clear dichotomy.  Whether or not a thought corresponds to an expression (without which assurance we cannot even open the question of the expression’s potential reference or denotation) is not an all-or-nothing question.  Take the case of the much-maligned “present King of France”.  The expression suggests a clear idea; we know what sort of thing would fill the bill; upon enquiry we learn, with some disappointment, that as it happens, nothing does.  So far so good.

            Now take the equally widely execrated expression, “a round square”.  To the average man, this probably suggests nothing at all; it may even repel him, like a bad omelette;  and philosophers never tire of pronouncing it impossible, nay incoherent; but it did suggest something to me.  The idea was dim at first, but not vacuous for all that:  whatever object might fit the description, if any, would be round, for one thing, in some reasonable sense of this elastic term. And, it turns out, round squares do exist – not on our cul-de-sac, granted, but in R x R provided with the sup norm (║  ║∞).  Place four points equidistant from the origin, symmetric about both coordinate axes, and join with geodesics: the analogue of a square in this non-Euclidean space.  But in the sup norm, every point of that figure is equidistant from the origin, which is therefore the center of a circle (again in the relevant sense).  So now the image corresponding to the expression is quite precise; the object of thought, as real as a rocks.

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In the chapter “On Realisms”, in An Experiment in Criticism (1961), C.S. Lewis writes:

The word realism has one meaning in logic, where its opposite is nominalism; and another in metaphysics, where its opposite is idealism.  In political language it has a third and somewhat debased meaning:  the attitudes we should call ‘cynical’ in our opponents  are called ‘realistic’ when our own side adopts them.  At present we are concerned with none of these, but only with realism and realistic  as terms of literary criticism.

(His discussion of this topic is bracing;  realistic, as commonly used, turns out to be something of a misnomer.

*

We close with a refreshingly clear and concise  thumbnail definition by Quine:

Unregenerate realism, the robust state of mind of the natural scientist.

Yo -- he means us!  --  Waiter, another beer!