Consilience in Linguistics (neu bearbeitet)

[This note is a spin-off from our initial essay, Consilience, along with its sidekick Consilient Connections (distinguishing vertical from horizontal consilience);  and is sibling to such other special mini-studies as Consilience in Psychology, Consilience in Mathematics [currently closed for reconstruction], and the purely satirical Consilience and Cognitive Science.]

The whole notion of “Consilience [with]in …” a specific field  is skew to the Wilsonian/vertical-reductionist conception of the grand principle.  Instead we are noticing similarities in various regions of a field, which may have no analogues outside that field, nor follow synthetically as consequences of other principles outside that field.  Accordingly, the various discipline-specific mini-essays may have little in common, let alone contribute to a grand TOE of the sciences.  They are more in the spirit of the various volumes of the “Bobbsey Twins”.   I do plan to stop, though, somewhere short of “Consilience in Stamp-Collecting” and “So!  You Want 2 B a  Consilientist ”.

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First:  Where does linguistics stand in the disciplinary matrix of the sciences?  Its status has often been fragile:

Finck and Wundt tried to rob linguistics of its autonomy  by incorporating it into psychology … Croce and Vossler tried to incorporate it into aesthetics.

-- Jan Romein, The Watershed of Two Eras:  Europe in 1900 (1967, Eng. transl. 1978), p. 443

Later, much of the thrust of linguistics, over the past nigh-on one hundred years, especially in America, has been an assertion of its disciplinary autonomy -- not a branch of sociology, or history, or language studies -- even with respect to its ancestor philology, and further with regard to various components of linguistics itself, which one hoped  neatly to delineate.

Cf.

… the need felt by many  to keep linguistics an autonomous discipline, to prevent it from slopping over  into psychology, sociology, neurophysiology, etc.

-- Roger Lass, On explaining language change (1980), p. 121

This depreciatory rhetoric of “slopping over” is diametrically at variance with Wilson’s utopian holistic vision for Unified Science.

Indeed, over the past  close-on to a century, or at any rate  over a good fifty years during the heyday of the growing prestige of the field, other disciplines have looked to linguistics more than it to them.  As:

The appeal of linguistics methodologically  to anthropology  is in part because of its achievement of units at once concrete and universal.

-- D. Hymes & J. Fought, American Structuralism (1975), p. 153.

In terms of the sociology of science, this influence is reminiscent of the Physics Mesmerism earlier spawned by the pizazz of the field that invented The Bomb.

That, in fact, may explain a lot.   For the study of syntactic and semantics structures plainly finds nothing of ready use for it from current physics (“The Propositional Island Condition:  a String-Theoretic Approach”), whereas the neighboring scholarly fields of psychology, anthropology, sociology, etc., have been -- not to put it too unkindly -- not especially successful of late.  They do not, so to speak, have The Bomb;  so linguistics has been free to go its own way.

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The linguistic scene in Europe during the nineteenth century, and up to about Weimar, had a decidedly less isolated or self-sufficient feel, with the same Grimm brothers who wrote straight sound-law Germanistik and who launched the massive Wörterbuch, likewise collecting their equally-celebrated work of folklore,  Kinder- und Hausmärchen.   Saussure, with his penchant for dichotomies and abstractions, culminating in his purely cerebral reconstruction of the Indo-European laryngeals  not visible in the extant texts (a ghostly forerunner of the key notion of “empty categories” in the Chomskyan school), were atypical (notice that he published precious little in his own lifetime, his main influence being posthumous, his penchants  more to the liking of a later time).   There were, to be sure, occasional Declarations of Linguistic Independence similar to those which later characterized American structuralism and its progeny --

Linguistics must be regarded as an independent science, not to be confused with either physiology or psychology.

--  Baudouin de Courtenay (1871)

but more characteristic were the plumbing of ancient literatures, the quasi-folkloristic dialectological spelunkings in the hills and hamlets of the hinterland, and so concrete, sleeves-rolled-up a tendency as that of Wörter und Sachen.   As a Romance philologist once put it, emphasizing the Unentbehrlichkeit of the sister-disciplines for linguistics,

Man komme also nicht mit dem beliebten « ne supra crepidam »;  das gilt wirklich nur für Schuster.

-- Hugo Schuchardt, (1892), in Leo Spitzer, ed., Hugo Schuchardt-Brevier (1921; 2^nd edn. 1928), p. 105

These humanistic traditions were carried on at Berkeley by my Doktorvater Yakov Malkiel, a White Russian refugee and time-capsule of Mitteleuropäische Kultur, whose journal Romance Philology (and it really was as deeply his, as The Rambler was Doctor Johnson’s) featured both linguistic and literary articles side by side.   It was this tradition I relished, and which informed my dissertation (later published as The Semantics of Form in Arabic, in the Mirror of European Languages).   It is a Kulturgut deeply to be savored, in centuries to come, long after the squabbles of Amerian Vietnam-era linguistics shall have faded into the mists of history.

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The fiercest assertion of linguistic independence -- what we might dub the thesis of the Idiosyncrasy of Human Language (it obeys principles peculiar to itself, not generally shared among other features of animate beings) -- has come from the Chomsky camp (that bastion of the intellectually fierce and rhetorically ferocious)

The proper perspective of linguistic independence is given a trenchant formulation by Chomsky:

How can a system such as human language arise in the mind/brain, or for that matter in the organic world, in which one seems not to find anything like the basic properties of human language?  That problem has sometimes been posed as a crisit for the cognitive sciences.   The concerns are appropriate, but their locus is misplaced:  they are primarily a problem for biology  and the brain sciencies, which, as currently understood, do not provide any basis for what appear to be fairly well-established conclusions about language.

-- Noam Chomsky,  The Minimalist Program (1995), p. 2

[Sidenote:  This stance exactly parallels our own with respect to the (possibly not entirely unrelated) question of Free Will, in our diatribes against the eliminative materialists, who, failing to discover Free Will in a test-tube, declare that it must therefore not exist.  Morality they seem to have discerned cringing at the bottom of  an Erlenmeyer flask, and identify it with oxytocin, or oxycontin, or some damn thing.   Our retort:  Free Will (and with it,  possible prolegomena to morality) stands unspattered;  good luck with whatever it is you’re doing, and ever saying anything useful about these.]

Similar American declarations of disciplinary independence go back a ways:

The history of structural linguistics in the United States  can be readily interpreted in terms of three successive (and overlapping) movements:

(1) the movement for autonomous study of language, i.e., for a profession of linguistics;

(2)  the movement for autonomous study of linguistic structure;

(3) the movement for autonomous study of grammar (syntactic structure)

Chomsky’s classification of linguistics as a branch of cognitive psychology, like Hockett’s classification of linguistics as a branch of cultural anthropology, does not imply any less of autonomy.

-- D. Hymes & J. Fought, American Structuralism (1975), p. 227-8

Back when I began at university,  linguistics as a discipline  was still largely at stage (1).  At Harvard College, they didn’t allow you to major in Linguistics simpliciter -- that was apparently perceived as being too narrow, like majoring in sausages or non-Abelian groups.  It had to be a combined major, say, Linguistics and Math.  (That is not necessarily a bad thing:  such disciplinary spread virtually forces you to think ‘consiliently’.)  I actually did briefly consider doing that, owing to the personal magnetism of two visiting luminaries:  George Lakoff and Noam Chomsky.  And while this-all takes us right off the topic of Consilience,  and back to the sociology of the wacky Sixties, perhaps the anecdotes may be worth retailing for their own sake.

It was my sophomore year (in many ways, my sophomoric year).  The campus was in turmoil, partially and fitfully shut-down.  The center had not held,  and we were whirling.

            Into this maelstrom  stepped  Noam Chomsky, meeting with Harvard undergraduates,  not to lecture, but to hear us out.   Already he was better known as a political commentator than as a linguist (I had eagerly read his foresightful American Power and the New Mandarins);  a small but respectful student audience  gathered at his feet -- or rather, he at ours:  for the students had occupied the available sofas and chairs,  and he himself sat down on the floor with the rest of the overflow.  He spoke softly, when he spoke at all;  listening, thinking, listening …

What he said that day, I don’t remember (how often are our memories  wordless, alas!)  but his sense or essence of open-mindedness, yet centeredness (most of us  were neither)  powerfully remains.    I left the meeting  feeling  that we student activists were truly juvenile, even if  largely right on the central issue of the Vietnam War;  and have him to thank that, thenceforward, I may have been  marginally less of an imbecile  than would otherwise have been the case.

Where Chomsky was all calm -- Jovian -- Lakoff was all energy -- Mercurial -- and tended to create a fevered atmosphere wherever he bustled -- not unlike that at campus protests and SDS meetings.  It was attractive, in a way, to an undergraduate whose veins flowed full with the sap of the Zeitgeist. 

However, I had, before my freshman year, renounced my original intention of majoring and English with a view to becoming a writer, penitentially donning the sackclothlike labcoat of a chemistry major,  in part because I knew myself to be subject to the Siren-calls of pride and cliqueishness  that went with the literary life.  And in Lakoff and his entourage (for there is no other word for the cloud of virtual particles that surrounded him), that factor was much in evidence.  So I drew back.  (Years later, at Berkeley, our paths would once again anastomose.)

What really settled it, though, was the practical reality of what it would mean to take courses from the permanent Harvard faculty (Lakoff was just passing through, and Chomsky taught over at M.I.T.)  I lasted just two meetings of the introductory course taught by droning Professor Undertaker (as I thought of him;  the real surname lies not too distant in phonological space).

Senior year, I applied to graduate school in math at Stanford and Berkeley.   When both accepted, I asked Lynn Loomis which he would recommend.   He was very practical:  no finicky attempts at comparing this professor with that, just:  Berkeley is bigger.  That proved wise advice, for exactly the same meta-reason for which I turned down Yale (whose English department had been making beckoning advances) and chose Harvard because, well, what the hell.  Once again, I wound up pursuing a course of studies entirely different from that in which I had applied.  After dropping out of math from impecunity, I stumbled upon a much more inviting introductory lecture-series by Charles Fillmore of Berkeley linguistics, and there was a thriving department ready to take me on;  whereas Stanford, at that time, didn’t even have a full-fledged Linguistics Department, just a Program within English.   So it looked as though, providentially, I had landed in the right place.

Yet how often have I dwelt in retrospect, how different my intellectual life (and with it, life tout court) might have been, had I instead found myself across the bay at Stanford.  For, despite its shoestring beginnings, by the time I received the doctorate (1981), Stanford had burgeoned into the M.I.T. of the West, whereas the Berkely department -- like the surrounding town -- was falling victim to centrifugal forces, partly political, and partly personality-driven, but more particularly, in the case of Linguistics, because the Rota Fortunae had made another half-turn, resurrecting MIT-style linguistics to a second run of pre-eminence, and sending the fortunes of Berkeley-style Generative Semantics down, down, down…   Fuit Ilium!

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Below, a miscellany of consilient influences.

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The syntactic cycle (cyclic ordering of rules in syntax) has been called “analogous” to the phonological cycle (e.g. Noam Chomsky, Language and Mind (1968), p. 39).   This, however, is  from a disciplinary standpoint  quite a domestic affair, and need not be ‘consilient’ with anything outside linguistics.   And indeed, as Chomsky remarks later in the same pamphlet (p. 66), “One cannot expect structuralist phonology, in itself, to provide a useful model for investigation of other cultural and social systems.

A word of caution.  By saying that a theory of sense ‘breaks down’ the complex ability of linguistic productivity,  I do not mean to suggest that the explanation must be reductive, but only that the theory of sense must articulate [unpack, make plain] the structure of complex ability.  If the ability is best explained by reducing it to other abilities, the theory of sense says what these are … If the ability is best explained holistically, … then it explains how the ability functions holistically …

-- Norbert Hornstein, Logic as Grammar (1984), p. 127

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The whole thrust of modularity is that, while tout might more or less se tenir , within  a given module, the modules themselves are connected, in some cases, only the way the wheels and the engine and the windshield of a car are connected, in subserving a larger whole.

Ctr. a sort of ideological purity:

By strongly syntactic, I mean  not only that the theory is developed using syntactic notions,  but also that the principles invoked, and the distinctions advocated, have no natural semantic analogues.

… In fact, a stronger point can be made:  the natural distinctions and generalizations that a natural semantic theory of interpretation would [consiliently] make available  lead us to expect configurations of data that are simply not attested.

-- Norbert Hornstein, Logic as Grammar (1984), p. 102, 4

And,  more polemically, emphatically rejecting any extradisciplinary aid:

An extreme position was taken by Kurylowicz:  “One must explain linguistic facts by other linguistic facts, not by heterogeneous facts. … Explanation by means of social facts is a methodological derailment.” (1948).  For Kurylowicz, even the influence of other languages was irrelevant:  “the substratum theory has no importance for the linguist”.

-- U. Weinreich et al.  in W. Lehmann & Y. Malkiel, Directions for Historical Linguistics (1968), p. 177

All of this -- taken as  a program rather than a description -- is strictly unexceptionable, apart from the final “the” in front of the word “linguist”.  With that restrictive article, the passus passes over into the overweening;  as who should say,  “The wearyingly multifarious  and mostly insensate behaviors  of non-penguin species  is of no concern to The Zoologist.”

Contrast, indeed, in the very same volume, the opinion of one of its editors (Y. Malkiel, p. 28): 

In languages where “progressive” and “conservative”, “aristocratic” and “rustic” variants are suggested by differences in form, no truly satisfactory interpretation is conceivable  without an equal share of attention  granted to the social matrix.”

Along with many other stances that could be cited. (“Pike’s tagmemics  expressly linked to an analysis of cultural behavior as a whole”).

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In post-Chomskyan linguistics, hardcore practitioners have usually been at pains to distinguish concepts and processes peculiar to the human language faculty, from those obtaining elsewhere, be it in bee-langue, or the “language of flowers” or “the Brain’s Inner Language” (this, from an article in this morning’s New York Times), or neuranatomy or chemistry or physics or -- horrendo referens -- Psychology with its “general learning strategies.”  By contrast, generativists revel in any apparent structural or procedural harmony within their discipline -- striving, for example, to see how much material can be gleichgeschaltet under the sway of the Empty Category Principle -- the awe-inspiring ECP (the Great and Powerful).

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Rules relating S-Structure to LF are of the same kind that operate in the Syntax:  Move alpha.

-- Norbert Hornstein, Logic as Grammar (1984)

Outsiders are unlikely to gasp at this last, nor to marvel about the Unreasonable Effectiveness of Move-alpha.  (“alpha” here stands for:  anything at all.  A slightly more general formulation  would be Stephenson’s Rule:  Do Stuff.)

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It is desireable for the overall theory to be articulated into strata, and for certain general notions or procedures to recur at different strata, at least masking their differences in basic material, and perhaps providing a genuine generalization.    Thus:  segmentation;  compositionality; and projection.  E.g. (Hornstein):  The Projection Principle:  the Theta Criterion applies at D-structure, ((S-structure)), and LF  (these being the antiseptic rechristening of the old deep structure, surface structure, and logical form, which proved too exciting for the peasantry and had to be withdrawn from general circulation).

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The technical tools for dealing with “rule-governed creativity” [basically, a synchronic system of limitless productivity] as distinct from “rule-changing creativity” [diachronic evolution] have only become readily available during the past few decades, in the course of work in logic and foundations of mathematics.

-- Noam Chomsky, “Current Issues in Linguistic Theory”, repr. in Jerry Fodor & Jerrold Katz, eds., The Structure of Language (1964), p. 59

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There are books and papers that speculate about the evolution of human language while studiously ignoring all of linguistic research

-- Paul Bloom, reviewing LINGUA EX MACHINA:

Reconciling Darwin and Chomsky With the Human Brain.

By William H. Calvin and Derek Bickerton.

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Appendix: Historical references to collaboration or lack of it, between linguistics and neighboring fields:

Summing up the wide-ranging work of the philologist and etymologist Hugo Schuchardt (floruit 1864 - 1927, magnum jubilaeum), Leo Spitzer writes:

Schuchardt hat nicht nur über fast alle allgemeinen Probleme der Sprachwissenschaft  nachgedacht, sondern alle irgendwie zur Linguistik peripherisch gelegenen Gebiete des Lebens  abgesucht, von der Sprachwissenschaft als Zentrum aus  seinen Beitrag der Lösung der drängenden Lebensprobleme  gegeben.

-- Leo Spitzer, ed., Hugo Schuchardt-Brevier (1921; 2^nd edn. 1928), p.

Schuchardt himself, however, in places posits the wisdom of keeping linguistics sauber getrennt:

Hamitische Sprachen sind solche die von Hamiten gesprochen werden, oder Hamiten sind die  welche hamitische Sprachen reden.  Jenes ist die anthropologische Erklärung, dieses die linguistische … Mißverständnissen kann nur dadurch vorgebeugt werden, daß Linguistisches und Anthropologisches strengstens auseinandergehalten werde.

-- review (1912) of  C. Meinhof, Die Sprachen der Hamiten; repr. Leo Spitzer, ed., Hugo Schuchardt-Brevier (1921; 2^nd edn. 1928), p. 334

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Referring to the theoretical-semantic efforts of the pre-eminent 19^th-century psychologist Wilhelm Wundt:

Wundt’s failure seems to have discouraged others from taking up the matter in earnest, for during the last 30 years, no one has made public any system of semasiology worthy of serious consideration.  Semantic work from 1900 to 1930  has been characterized by an astonishing and highly regrettable lack of contact and collaboration between psychologists and philologists.

-- Gustav Stern, Meaning and Change of Meaning (1931)

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Contra sociological-anthropological structuralisme:

… eager souls who think they can easily borrow  and fruitfully adapt  a formal model  from simpler and perhaps more fortunate fields such as linguistics  or even phonetics.

-- Ernest Gellner, Contemporary Thought and Politics (1978), p. 122

(Here he means rather phonology;  it is phonology, and not phonetics, that is structuralist.)

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Where does linguistics fit in -- among the humanties, or the sciences?

Um die Sprachwissenschaft   haben sich bekanntlich  die Natur- und die Geistes- (order Geschichts-)wissenschaften gerissen,  wie in der mittelalterlichen Legende  die Teufel und die Engle  um die Seele des Menschen.  Jetzt pflegt man sie  ihrem Inhalt nach  zu den Geisteswissenschaften,  ihrer Methode nach  zu den Naturwissenschaften zu zählen;  mit fast dem gleichen Rechte  könnte man das Umgekehrte tun.

Ich halte an der Einheit der Wissenschaft  fest,  und vermag  beispiesweise  zwischen Biologie  und Sprachwissenschaft  keine tiefere Kluft wahrzunehmen  als zwischen Chemie und Biologie.

-- Hugo Schuchardt, (1892), in Leo Spitzer, ed., Hugo Schuchardt-Brevier (1921; 2^nd edn. 1928), p. 105

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Minimalism in Mathematics (further updated)

A disclaimer:   What follows is not a substantive proposal, but a suggestive meditation, turning over this minute but multifaceted notion of “minimalism” and seeing how the light glints off.  It is neither better nor worse than a metaphor.

A couple of years ago,  a book-length treatment was published  that similarly plays with the notion of (in this case) “modernism”  -- which, like “minimalism”, is originally a term of the arts -- in relation to math:  Plato’s Ghost:  The Modernist Transformation of Mathematics, by Jeremy Gray.   To the extent that such an enterprise is worthwhile, it is in casting a bit of light from innovative angles, rather than deepening one’s understanding of math itself (though it did manage to get published by Princeton University Press):  it is more like a bull-session than a milestone.    Reviewing the book for American Scientist (Sept 2009), the mathematician Solomon Feferman sums up by quoting a remark by the historian Leo Corry, to the effect that

Extending the appellation modernism to mathematics … is like “shooting an arrow and then tracing a bull’s eye around it.”

Our own effort, in seeking resonances with the prior notion of minimalism, in mathematics, physics, and linguistics, is open to the same remark;  but it is what it is.

In the stylistic spirit of minimalism (and of that pointilliste Wittgenstein), we shall begin with a Delphic  epigram:

Logicism:  a kind of reductionist minimalism.

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Considering that he took on the whole universe, in his methods  Newton was surprisingly Spartan.  Not only as regards “hypotheses non fingo”, but methodologically:

Newton consistently preferred Euclidean-style proofs.  He used his own calculus only where strictly necessary, and barred algebra from his treatise  entirely.

-- Leo Corry, “The Development of the Idea of Proof”, in Timothy Gowers, ed., The Princeton Companion to Mathematics (2008).

(Cf. a laborious non-analytic “elementary” proof in number theory.)

As fastidious as an Intuitionist!

*

Not a matter of method, let alone of taste, but sheer fact (albeit initially so counter-intuitive as to have been dubbed a "paradox"):

The Löwenheim-Skolem theorem: if a first-order theory has a model, then it has a countable model.

*

The attempts, lasting centuries, to do away with the Parallel Postulate by deriving it from the other Euclidean axioms, represent a remarkable early manifestation of the minimalist instinct.  Success would not have added to our fund of theorems about geometry, nor led to more perspicuous proofs.  The impulse was in part aesthetic.

A topic to explore:  the relation between abstraction in mathematics (an intellectual quality) and mathematical minimalism (which is not antecedently defined, but I have in mind the aesthetic, even spiritual side).

Contrast Finitism, Intuitionism, etc.:  Not Minimalism, but self-castration.

Zijn lange, magere  maar gespierde gestalte,  zijn scherp ascetische gelaatstrekken…

There is also a sterile sort of minimalism:  as, the replacement of the standard set of logical symbols AND, OR, NOT, by a single one --   NOR or  NAND (Sheffer’s stroke).  It led nowhere.

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A variety of the Minimalist instinct  characteristic of abstract mathematics  is the notion of elegance.   Its role in mathematical practice (it has no purchase on mathematical fact) is reminiscent of, though practically distinct from, that of beauty in the practices of physics.

This, from a man with one foot firmly in either camp, math and physics:

The development of mathematics may seem to diverge from what it had been set up to achieve, namely  simply to reflect physical behavior.  Yet, in many instances, this drive for mathematical … elegance takes us to mathematical structures and concepts  which turn out to mirror the physical world in a much deeper and more broad-ranging way…

-- Roger Penrose,  The Road to Reality (2004), p. 60

(This is the "unreasonable effectiveness" motif.)

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We earlier noticed what we called “the Dialectic of the Topological Enterprise” -- abstracting-away from rich familiar entities, extracting what seem the essentials, and seeing what happens.   The first step might seem Minimalist, but the consequence is an effusion and exfoliation of new spaces which meet the newly relaxed criteria, and which turn out to have an even richer riot of properties than we began with.   Per se, there is little in all this that might justify bringing in the aesthetically-tinged label of “Minimalist” (not a traditional term in mathematics; the closest you get is “abstract”):  but the aesthetic ethos is there, for all that.  Thus Shing-Tung Yau, The Shape of Inner Space (2010), p. 77:

 

We start with some raw topological space, which is like a bare patch of land that’s been razed for construction.  On top of that, we’d like to build some kind of geometric structure that can later be decorated in various ways.

[Footnote 2026:  

> like a bare patch of land that’s been razed for construction

 

Terrain vague, quand tu nous tiens!

More here: 

http://worldofdrjustice.blogspot.com/2026/08/une-promenade-aux-terrains-vagues.html  ]

*

In the arts, Minimalism is a preference:  which, once adopted, is striven for.  In mathematics, you might like to keep things as simple as can possibly be:  but the mathematical facts seem to have a will of their own, at times.   Roger Penrose gives several instances of this, in The Road to Reality (2004).  For instance, with real functions, you can do pretty well as you like; but complex functions have a built-in naturalness.  You can try to define one on a given domain, but they have a mind of their own, and expand to their natural maximal domain by analytic continuation.   Thus, the larger set of numbers, the complex, spanned by the reals and the imaginaries, turn out to be in some sense more ‘real’ -- more round, more natural -- than the “reals” themselves.

Or again:   Suppose, once-bitten by the set-theoretic antinomies, you become twice-shy, and (p. 373)

adopt a rigidly conservative ‘constructivist’ approach, according to which a set is permitted only if there is a direct construction for enabling us to tell when an element belongs to the set.

(I picture this hypothetical constructivist as being played by Graham Chapman doing his officer’s shtick.)   But alas!  Penrose runs through the Turing/Cantor diagonal arguments and concludes (p. 376):

What this ultimately tells us is that, despite the hopes that one might have had for a position of ‘extreme conservatism’, in which the only acceptable sets would be the ones -- the recursive ones -- whose membership is determined by clear-cut computational rules, this viewpoint immediately drives us into having to consider sets that are non-recursive. … We are always driven to consider classes that do not belong to our previously allowed family of sets.

This is either a baffling, even a provoking mystery, or a simple consequence of what the Cantorian Realist indeed believes:  that these things are Out There, independent of ourselves (this might remind you of a certain Deity), and you can’t just methodologically sweep them away.   U B the judge.

(For a similar example applied to physics, click here.)

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Pedagogical observation from a wise observer, who has been around the block:

Instead of the principle of maximal generality that is usual in mathematical books, the author has attempted to adhere to the principle of minimal generality,  according to which  every idea should first be clearly understood in the simplest situation;  only then can the method developed  be extended to more complicated cases.

-- Vladimir I. Arnold, Lectures on Partial Differential Equations (Russian edition 1997; English translation 2004), Preface to the second Russian edition

*

The nec plus ultra  of mathematical minimalism  is probably Category Theory -- which, however, I cannot elucidate, since I do not understand it.  It contains such things as the Forgetful Functor (this pops up in several introductory treatments, so it’s not as though I’m grasping at straws), which, given an algebraic group, “forgets” the group structure, leaving you with just a set  (excuse me: an element of the Category of Sets.)   Great -- die Gruppe ohne Eigenschaften.   The only way this even begins to seem to have a point  is if you then consider the adjoint functor, from sets to… free groups (these being a desolate Last Year at Marienbad landscape, again groups with the flavor removed).   Category theory looks at the bare bones common to many a different area of mathematics -- rather as though one were to study portraiture by looking at stick-figures.
(Actually, there is an analogy with the motif-index in folklore.  So, not knocking it here...)

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On Ramanujan’s notebooks:

There were thousands of theorems, corollaries, and examples.  For page after page, they stretched on, rarely watered down by proof or explanation, almost aphoristic in their compression, all their mathematical truths  boiled down to a line or two.

-- Robert Kanigel, The Man who Knew Infinity, p. 204

The reasons for this were twofold.  Ramanujan himself was not particularly aphoristic.   But he had never absorbed the modern notion of proof, which would take up so much more space;  and as a poor man in India, he suffered from a shortage of paper.

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From a logician:

The power-set operation has been interpreted  in the constructible hierarchy  as thinly as possible … We might be tempted to think of [the minimal model] as realizing a sort of contrary of the principle of plenitude -- a principle of paucity, if you will.   …  The principle of ontological parsimony … encourages some authors to eliminate individuals and un-well-founded classes.

-- Michael Potter, Set Theory and its Philosophy (2004) , p. 254

(All so difficult.  Why not relax with a mystery story instead?  Cool ones here: )

http://www.linguasacrapublishing.com/justice.html

Genetics Porn

The reliably acute H. Allen Orr has published a trenchant review of A Troublesome Inheritance: Genes, Race and Human History, by Nicholas Wade, which we link to without comment:

http://www.nybooks.com/articles/archives/2014/jun/05/stretch-genes/?insrc=hpma

Longtime readers of this blog will know that our salute of this article (in the still-solid New York Review of Books) owes nothing to political correctness.  We are perfectly open to the possibility that the thesis championed by Wade in the second part of his book, may have some validity.   But, being explosive, it needs much more backing than he has given it.  (Such is the identical reason for our chiding the "Universe as simulation" hypothesis.)

For our own polemic against ultra-Darwinist excess (well, "polemic";  actually it's pretty funny), try this:

http://worldofdrjustice.blogspot.com/2013/03/the-urysohn-metrization-theorem.html

~

Another recent example of Darwinian academic overreach, though much less incendiary as its implications are confined within linguistics, is Language in a Darwinian perspective, by Bernard Bichakjian, which maintains that “every linguistics feature, be it a speech sound, a grammatical marker, or a syntactic strategy, interfaces with a neuro-muscular algorithm, and that selection pressures have steadily guided languages …”.   (Credit where credit is due, though:  the man gets full marks from a Popperian perspective, in which “a theory needs to stick its neck out.”   This one sticks out like an ostrich.)  The level-headed Fred Newmeyer dismisses it as “bizarre” (his one-word summary) in the Sept 2003 issue of Language, p. 583ff.   And since, unlike a potential best-seller by a New York Times science writer, which could well influence public debate on sensitive issues, along with such semipopular works as On Aggression, African Genesis, and The Naked Ape, Bichakjian’s influence if any  will remain confined to pockets of academia, there is no need to comment further in this place, other than to quote Newmeyer’s witticism (one of several in the review):

A lot can be said against Chinese writing [he means, the writing system -- the logograms] as ‘evolutionarily primitive’, but one must agree that it has allowed its users to develop at least as vibrant an intellectual and creative life  as that of their alphabetic neighbors.

~

Orr remarks in a footnote, citing just one example from a fund of hundreds,

Geneticists have had an extraordinarily hard time finding genes that make substantive contributions to complex diseases like Type 2 diabetes. This doesn’t bode well, to put it mildly, for finding the genes that allegedly underlie subtle differences in predisposition to middle-class behavioral traits.

Such overreach is bad enough;  worse, is when the nihilistically inclined among neurophilosophers, conclude from a bit of petri-dish handwaving, that free will is an illusion, and morality with it.   Such views have the potential to wreak real mischief;  and we have polemicized against them here:  Eliminative Materialism

Note:  That essay does not specifically address linguistics, though the problems with reductionism of minds to neurons  are similar in several disciplines, and go back a ways in each.  Thus, Uriel Weinreich, contra the behaviorist simplifications of Leonard Bloomfield: 

Bloomfield’s neurological reductionism  depends on discoveries  that may never be made.

Bloomfield was the dean of American linguistics before WWII;  his introductory textbook Language (1933) was long standard, and contains much of lasting value; yet the early, pseudo-foundational chapter about Stimulus-and-Response, with its feeble fable about Jack and Jill, falls far below the standards of the rest of the book, and indeed feels perfunctory, contributing nothing even on its own terms:  like those Stalin-era exordiums in praise of the great leader, in Soviet texts about physics or what have you;  having made the needful obeissance, we move right along.

Rulon Wells had a nice line about all this (in “Meaning and Use”, in Word 1954):

In diagnosing the conflict between mentalism and mechanism, [Bloomfield] mislocates the issue, and thus plants his germ of truth  in the sand of confusion.

~

The situation in genetics has an analogue in the field of linguistics:  quite apart from the difficulty of accounting for language development, or for the sort of intricate syntactic phenomena highlighted by Chomsky and his successors, from outside linguistics proper (height of the ancestral esophagus inferred from shards of crania; Bloomfieldian behaviorism; connectionism; …), progress has been discouraging even within the field, and the Chomsky current in particular.  In that same Review Article, discussing On Nature and Language by Chomsky (et, actually, alia, as Newmeyer points out), the one-word summary is:  “disappointing”.  The reviewer reluctantly concludes that, if anything, the Minimalist Program represents a step backward.

~

Just a final word on the project of reducing genius to genes, or spirit to spit:
The eliminativists may prove  to their own satisfaction  that (say)  literature, and literary criticism, are nothing but secretions of the pineal gland (or however that hoary idea is tricked-out nowadays, in the latest scientific raiments), or that it evolved in the Jurassic for the purposes of attracting a mate (or more subtly -- like those initial pre-weight-bearing nubbins of wings -- simply to regulate body temperature),

but they will never produce any literature or criticism worth reading.

Eliminative materialism (expanded update)

…those bright and breezy Americans  who call themselves Behaviourists.  They declare with some warmth that there is really nothing in their minds, and that they only think with their muscles.

-- G.K. Chesterton,  Robert Louis Stevenson (1927)

Biology is only the Fascist substitute for sociology.

-- Arthur Koestler, Scum of the Earth (1940)

… that faulty inference  from the plausible view of the cognitive sovereignty of sense, to the absurd conclusion that explanatory models of human conduct must be in terms of elements similar to ‘sensation’ or ‘stimulus’.  The inference is quite fallacious, though an entire movement in psychology (Behaviourism) is based on the failure to see this.

-- Ernest Gellner, The Psychoanalytic Movement (1985; 2^nd edn. 1993), p. 16

Abstract:   The psycholytic style of current neuroscience-invoking reductionism  is intellectually and philosophically unilluminating;   and the social and political effects to which it is often put  are morally debilitating.   Taking ever-more-microscopic tallies of the goings-on in neural tissues  is of interest only to a histologist.   The attempt to press such observations into service as solvents of long-standing noëtic questions  is unsuccessful, probably in principle so. 

As Freud put it in the first paragraph of his final summary of his own work, the Abriss der Psychoanalyse (1938), we know about the brain on one side, and consciousness on the other, but

Alles dazwischen ist uns unbekannt;  eine direkte Beziehung zwischen beiden Endpunkten  ist nicht gegeben.  Wenn sie bestünde, würde sie höchstens eine genaue Lokalisation der Bewusstseinsvorgänge liefern  und für deren Verständis  nichts leisten.

That is to say such correlations amount to a higher phrenology.

~ ~ ~ ~ ~

[Prefatory note:  An earlier nineteenth-century forerunner]

Köhlerglaube der Wissenschaftler

In the course of the Materialismusstreit …, the German Darwinist Karl Vogt  published a widely read essay entitled Köhlerglaube und Wissenschaft (1855), in which he tried  with cynical witticism  to dispense with the problem of the human soul [NB: and mind].  According to Vogt, thought is a secretion of the brain  just as the digestive juices are secretions of the stomach, bile a secretion of the liver, and urine a secretion of the kidneys.

-- Kurt Reinhardt, Germany: 2000 Years (1950, 2^nd edn. 1961), p. 594

By now, the man in the street has become acclimated to the notion of secretions, and is unlikely to be swayed by that account.  He will notice that, somehow, the liver never secretes anything but bile, the kidneys, urine;  whereas the brain ‘secretes’ such unexpected and unprecedented and mutually contradictory things as:  Catholicism, Communism, situation comedies, and the Urysohn Metrization Theorem.

But the underlying atheist-nihilist idea, that of wave-of-the-wand eliminativism (it does not even deserve the name of reductionism), whereby you eliminate the problem from consideration, rather than doing anything to actually solve it,  ever and again resurrects itself, morphing into a semblance of life, from some discarded afterbith.

~      ~      ~      ~      ~

[Herewith our original essay  from a couple of years ago]

We did not have to wait for the tribe of those laboratory nihilists known as neuroscientists, to behold an academic school dedicated to reducing free will and cogitation to the level of meat.  The behaviorists were there first.    And it is our great good fortune that we are spared the chore of actually reading and refuting their earlier and generally gratingly ill-written output, since their fifteen minutes have expired(*), the quietus marked by a famous and scathing review of B. F. Skinner’s Verbal Behavior, by Noam Chomsky, way back in 1959 (a good year -- aye, a vintage year).

 

Skinner himself, and others of his spawn, continued to “engage in writing behavior”.(**)   And like the dragon’s-teeth of Cadmus, the doctrine springs up ever anew, in this or that contorted form.

Maxfield Parrish:  Cadmus

[(*)  I spoke too soon.  Savor my groveling retraction here.]

[(**)  The phrase was made famous by a journalist who, to test the nature of asylum-based therapy in general  and involuntary commitment in particular, had himself commited, and immediately began acting perfectly normal, and telling the doctors he’d like to go home.  He kept a journal of his experiences.   This latter fact did not go unnoticed by the keenly observant psychiatric nurses, who wrote in his chart, “Patient engages in writing behavior.”  An immortal and dactylic line.]

Skinner, apart from his paid occupation of making life miserable for rats, is best known as the author of Beyond Freedom and Dignity (1971 -- not such a good year).  The title echoes that of Jenseits von Gut und Böse,  by that other evil troll, Nietzsche:   beyond, not in the sense of uplift, but of, “Get O-o-o-vah-rit!” -- A similar bit of titular legerdemain (sugar-coated in the title, rat poison on the inside) was perpetrated by Patricia Churchland, in Neurophilosophy: Toward a Unified Science of the Mind/Brain (1986).  What is really being proposed there is not Unity, but Anschluss, with the mind playing the hapless role of Austria.

Professor Skinner, hard at work in the lab

Again, prior to contemporary neuroscientists, there were philosophers who ground much the same axe.   Wikipedia (s.v. “Self-refuting idea”), re eliminative materialism, speaks of identity theorists like the philosophers Boring and Smart, who “claim that ideas exist materially as patterns of neural structure and activity.”  Now, that is one unilluminating and bone-headed idea.  By which I mean, of course, no more than that it is an unilluminating and bone-headed pattern of neural structure and activity.  Owing possibly to an excess of calcium at one of the synapses.

And why, indeed, stop short at the level of the cells, themselves already doubtless epiphenomenal?  Take it right down to quantum mechanics!   Let some gaggle of labcoats come up with the Schrödinger equation for the Bible, and another for “Paradise Lost”, and show us how certain passages -- excuse us, certain Hermitian forms -- of the former, lead directly to the eigenkets of the latter.  Put literary critics  plumb out of work.
(Something more than just a joke:  Cf. entomologist/ultrareductionist Edward Wilson donning the robe of a Milton scholar here.)

-- A further word about this scenario of ideas as “patterns of neural structures and activity".  It really is little more than ye olde idea of Ideas as Pictures-in-the-head, but dressed up in a modern labcoat (the sort worn by actors playing doctors on TV); and this is one subterranean source of  plausibility of a doctrine that  on logical (and indeed theological) grounds  is a tissue of absurdity.

~

What gives the “thought is a physical pattern” account some specious plausibility, is our modern picture of vision:  which, to be sure, is vastly more complex than the everyman’s pre-theoretical account, whereby the vision of an apple is like a little apple in my eye.  (Compare, indeed, the etymology of the word pupil.)  -- Actually, the completely pre-theoretical account doesn’t even involve vision at all;  it’s just, “Behold! an apple!”  (or, holophrastically:  Gavagai!)

In that account, we begin with the beheld object.  

  (a)  It is, as a ding-an-sich, as hopelessly unknowable in its totality as a black hole;  yet like those reticent celestial bodies -- the veiled houris of the stellar harem -- by their corona ye may know them (that, and a bit of math).

  (b)  From this object -- let us take it to be specifically a coffee-cup, since we have proved the existence of these -- photons and phonons and perhaps even an occasional Higgs boson, bounce and boing and go-or-do-not-go through visual slits, in some inextricable and inexplicable quantum fashion, to wind up

  (c ) landing on, and lighting up, this or that spot on the retina.  From there,

  (d) ganglia shiver and synapses thrill, and eventually

  (e) the visual cortex receives various rude jolts, after which

  (f) the rest of the brain somehow sorts it all out, until finally

  (g) the mind says, “Aha!  There it is!  Time for a spot of java!”

Unfortunately, this comparatively simple scenario won’t do for the generality of ideation.  It would seem that, when these reductionist gentlemen contemplate an “Idea”, they go no farther than an analogue of (f) or at best (g), for an object of thought as simple as a coffee-cup (or, in their own case, their own endlessly contemplated navel) -- the ‘idea’ of one, rather than the image of one.  -- One is reminded of Hadamard’s plaint, in The Psychology of Mathematical Invention, that previous researchers into thought-processes had restricted themselves to the elementary thumb-sucking mental-motions of the Beoetians, which simply do not display the richness of thought-processes of research mathematicians, so that his own researches had to start from scratch.
(Similarly, generative linguistics would not have gotten far, had it never considered sentences more complex than "John is fat.")

For consider:

What the cognitive eliminativists are proposing, is not that a thought consists of some pattern of little electrochemical twitches and irritations plus ideation (the thinker contemplating the canvas of his own neuroprocesses, as it were);  their explicandum cannot involve the explicans.  No, it is really just -- splat -- that.

Now consider the following ideas:

  (a)  A topological space T is regular.

  (b)  T has a countable basis for its topology.

To each of these corresponds -- in Henry’s head -- a cortical panorama (A, B) not unlike a TV test-pattern plus static, or a Jackson Pollock painting on a bad day.

And consider that, as we all know by now, (a) and (b) imply

  (c)  T is metrizable.

which in turn duly corresponds to some porridge of pixels (C) on Henry's cortex.  Fine, we grant that.
But how  by all that is holy  do (A) and (B) imply (C)?  The moreso as Henry’s cortical idiosyncrasies  differ from those of Hector (A’, B’,C’), let alone those of the silicon-based mathematicians of the planet Gnorf:  who, whatever their physiological differences from ourselves, must reach exactly the same conclusion as did Urysohn, since that conclusion is, in fact, a fact (laid up in heaven, where Churchlands do not penetrate, and the worm corrupteth not).

[An attempt from an entirely different direction, to reduce the complexly interrelated richness of mathematics to triviality, by translating it into a non-mathematical world of discourse  entirely unsuited to it (in this case, the mushy one of metaphor), is  Where mathematics comes from:  How the embodied mind brings mathematics into being (2000), by   George Lakoff and Rafael Núñez.  You can tell already by the subtitle, that the authors are no Platonists.   I did coursework with George, briefly at Harvard and later at Berkeley, where at one point I TA’d for him;  so I shall not criticize him here, lest I fall into the crime of magistricide.   Yet I must sadly concur with the verdict of the reviewer, Terence Langendoen, in the March 2002 issue of the refereed journal Language.]

~     ~      ~

Ethicists should likewise soon be out of a job.  The latest in the public press:

The End of Evil?
Neuroscientists suggest there is no such thing.
Are they right? 

A word:  I have no quarrel at all with the reductionist program as propounded and practiced by, say, Steven Weinberg (who embraces the term).  The problem comes in with the eliminativists who do not really mean to explain things, but to explain them away.

For remarks on the ontology of attributes, and their vulnerability to the eliminativist attack, click here.

~     ~      ~

What tends to get eliminated, in these proceedings, are things like consciousness and free will -- features of which we had grown rather fond.   Their very familiarity (as “folk theory”), for these gentlemen,  somehow tells against them.  As though a good rule of thumb were, If the ancient Greeks believed it, it must be wrong.  An eternal verity gets rechristened a “stagnant theory”. 

(Extraordinary idea, that, in any case: that to be any good, a theory must, like a fashion-slut, annually change the length of her skirts.  By that measure, the truths of numbers known to Diaphantos must be positively mildewed.)

Here  phlogiston plays ever and again the useful role of whipping-boy.  (Indeed, given the continued prominence of this ethereal etwas in philosophical debate, it must count as one of the most fruitful scientific hypotheses ever.  If it didn’t not-exist, someone would have to uninvent it.)  

The line of reasoning, reduced to its essentials, runs:  Well if that thing turned out not to exist, maybe freedom and God and all that lot   are just illusions too.

One problem with this angle of attack is that there's more to physics than phlogiston.  Also on the roster of theoretic posits  we find:  acceleration, force, electromagnetism, atoms, protons …  Phlogiston went out on a limb, which broke;  atoms & co. went out on a limb, and so far it seems to have held.   The eliminativists are being rather choosy in what to highlight.

Another problem with their reasoning  is that it’s nonsense.   Shooting down this or that hypothesis of theoretical physics, or even the whole lot of them, is not at all the same thing as denying what every mother has been telling her children since the beginning of time.   We are rather more certain of our own consciousness and free will, than we are of protons.

Let us examine another favorite butt of their mirthless hilarity.  Your great-great-grandsires believed in God, and that the sun set in the west.  The more fools they!   We New Atheists proclaim triumphantly that the earth circles the sun, and not the other way about.  Therefore, everything else you believe is false as well.

But in point of fact, you haven’t got much further along by taking the sun as the rest-point of your dynamical system, than when you stood firm on the earth.  For now you may be held to depict a system in which the entire galaxy whirls lumbrously around the axis of a single, peripheral, faint star.

In reality, none of these choices of a reference frame intend the absurdities ascribed to them.   Each has its use for some purpose or other.  Grandpa was well within his rights, both cosmologically and theologically.

~     ~      ~

~   Commercial break  ~            

http://www.youtube.com/watch?v=FwzOXzZWUik

We now return you to your regularly scheduled essay.

*     *     *

All biochemists and molecular biologists today are ‘mechanical materialists’.

J. Maynard Smith & E. Szathmáry, The Origins of Life (1999), p. 11

Probably no harm in that, so long as the molecularists  stick to their last, and don't go sounding off in the Sunday supplements about matters that concern them not;  indeed, it would be more concerning, were they all Cantorian Realists, or Presbyterians.   But the day when all musicologists, or mathematicians, or literary critics, take mechanical materialism for their lodestar and touchstone, is the day when we shall cease to learn anything of interest about music, math, or literature.

~     ~      ~

 

We earlier glanced at the program of consilience, which (speaking somewhat informally) depicts the sciences stacking up one atop the other, like proverbial pancakes, while the life-giving maple syrup of shared method and ontology, seeping from one to the next, unites them.   (That summary, while not perfect, is both more concise and somewhat clearer than what you may glean from scattered passages in Wilson’s book.)  Eliminative materialism takes all this a step further:  the whole stack is squashed flatter than flat (again, the individual pancake has passed into legend for this very quality) into an inedible paste: the which, however, is declared to be the sole reality, things like syrup and pats of butter being just figments of your imagination (which itself does not exist).  Understandably, this philosophy was quite popular among the guards at Belsen-Belsen.

That may sound harsh, but truly, the often creepy frisson of the behaviorist/neuroscientific mindset does recall certain experiments during that unlamented Reich which were better left undone.  Steven Pinker, The Blank Slate, p. 19, on the founder of American Behaviorism:

Watson presented a baby with a white rat, and then clanged a hammer against an iron bar, alledgedly making the baby associate fear with fur.

Thus, to all our weightier indictments against Nominalism in all its forms, we add this slogan:   

“Behaviorists Hate Bunnies.”

(Our own favorite behaviorist, jolly Dr. Quine, does suffer from a certain lagomorphobia,  in his obsession with "undetached rabbit parts", documented here.)

Wilson pens a highly entertaining parable of the termite ethical code, extoling:

…the deep, saprophytic, basidiomycetic penetralia of the soil …. the sanctity of the physiological caste system; the evil of personal rights (the colony is ALL!); … the aesthetic pleasure of eating feces from nestmates’ anuses  after the shedding of our skins; and the ecstasy of cannibialism … (it is more blessed to be eaten than to eat).

Edward O. Wilson, Consilience (1998), p.  148

This is jolly stuff, skillfully done; probably give Donald Trump a stiffie.  Yet one senses a sour note,  as the (“consilient”) goal of the eliminative materialists   is to provide a similar account of human morality, decency, caring, flights of fancy, love …. Ever again and inevitably, these proctoscopists return to the anus, the central life-ring (Lebenszirkel) of their Weltanschauung.

~     ~      ~

To be fair to the reductionist program, let us briefly consider a proposal narrated by Wilson, who is both a much more graceful writer  and a more congenial companion than Skinner or the Churchlands.

Wilson offers one worked-out example of  basically eliminative reduction (or ‘consilient’ explanation): from oneirology straight down to biochemistry.  Here is a sketch of the bad old days of Freud:

Mysticism and science meet in dreams.  … When we sleep, the ego releases its grip on the id…  Freud … -- to put it as kindly as possible -- guessed wrong.

Edward O. Wilson, Consilience (1998), p. 74

Wilson is in fact a kind and temperate man; that mild rebuke is as strongly-worded as anything in the book.  (He is even able to discuss the Postmodernists without resorting to scatological invective, a task far beyond my own capacities.)

But now (p. 75) for the good news:

The competing and more modern hypothesis of the basic nature of dreaming  is the activation-synthesis model of biology.  … Sleep descends upon the brain when chemical nerve cell transmitters … such as norepinephrine and serotonin, decline in amount… Simultaneously a transmitter of a second kind, acetylcholine, rises in amount.  …

Etc., etc.; we skip to the exciting climax on the next page:

The electrical membrane activity, still mediated by acetylcholine at the nerve junctions, moves from the pons (the P of PGO), a bulbous mass of nerve centers located at the top of the brain stem, upward to the lower center of the brain mass, where it enteres the geniculate nuclei (G) of the thalamus, which are major switching centers in the visual neuronal pathways.  The PGO waves then pass on to the occipital cortex (O), at the rear of the brain, where integration of visual information takes place.

Voilà ! Any questions?  No?  We're done then.

Oh dear -- did I type all that up aright?  Was it not perhaps the serotonin that flows into the thingummy, thereby (de)activating the thalamo-geniculo-pataphysico reaction?  Well, no matter;  for you will notice that we have so far learned absolutely nothing about actual dreams.(*)

(*  Don’t misunderstand:  this is sound, painstaking work, and it is excellent that someone is doing it.  No doubt it will prove crucial to some hyperspecialists in the approriate microcompartment of biochemistry.  For the general man of science and letters, on the other hand, it is precisely as fascinating as the mysteries of the pancreas.)

This lacuna Wilson hastens to remedy by rushing in with his own broad-brush description, eclipsing that of that bungler Freud:

We fly through the air, swim in the deep sea, walk on a distant planet, converse with a long-dead parent … In dreams we are insane.  We wander across our limitless dreamscapes as madmen.

Hm.   Doesn’t ring a bell, either with my own experience or that of friends with whom I have discussed such things.    In my own dreams, I tend to be at work, or in a classroom, or (oddly) at some sprawling party on the grounds of a great country house.   No flying through the air;  more like, irksome difficulties catching the right bus.  But let that pass.   No doubt spending your days as a reductionist  means you must compensate with florid fantasies at night.

But the real killer is that last line.   It is, I believe, wildly and crucially false.   The real mind-set of the typical dreamer was captured perfectly by Louis Carroll:  Alice retains her level-headedness, while all around her are acting fantastically, and she rather taxes them for their behavior.  (A similar depiction occurs in the long-running comic strip, "The Strange World of Mr Mum".  The eponymous everyman wanders bemused through the strangest situations.)  What the dreamer beholds  may resemble the visions of psychotics:  yet the dreamer is not psychotic. In our dreams we remain our real selves:  we retain, in particular, our unbanishable morality, not doing in dreams what we would not do or at least fantasize doing in waking life. (Morality: a word anathema to some of these gentlemen -- though here Wilson himself is sound enough -- yet it survives the oneiric lysis, as it shall survive their nihilism.)  We remain perfectly rational, only…. just not at our best.   For instance, in dreams I often work out etymologies, or expound mathematical ideas.  These are without exception in error -- hey, happens to the best of us -- but that is what I do, I don’t imagine I’m a prophet, or a giant cockroach, or that everyone is out to get me, or what not.

Freud may not have nailed it, but you’ll learn more about actual dreaming from Die Traumdeutung than from this ultrareductionist stuff.

[Update]  I am currently re-reading Die Traumdeutung;  some actual reflections might follow.
Preliminary musings here:
http://worldofdrjustice.blogspot.com/2012/10/appendix-to-appendix-on-oneiric.html
And now this;
http://worldofdrjustice.blogspot.com/2012/12/die-traumdeutung-still-further-updated.html

~     ~      ~

That only somewhat facetious polemic brings me to another point.   While specialists of this or that stripe  may want to drill down to the last detail, what most of us require -- expressing this somewhat provocatively -- is an explanation that is as shallow as possible, in that it digs down only as far as it needs to, to clear things up a bit.  (Compare Quine's "Maxim of shallow analysis:  Where it doesn't itch, don't scratch.")  And even if you wind up doing a deep-dive yourself, what you intellectually retain is likely to be an explanatory skeleton. 

Thus, take mathematics.  When a proof is truly “irreducibly reductionist” (to coin a phrase), like that of the Four-Color Theorem,  where intermediate guiding Ideas, of general application, do not emerge, but everything is tediously and computationally broken down into a bad-infinity of special cases, mathematicians are disappointed and frustrated.   What we want ultimately is an agencement of Leading Ideas.  We might dutifully check the details of the proof, but these we shall probably not retain.

(Keynes, whose Treatise on Probability  brims with Leading Ideas, charmingly prefaces one particularly symbol-ridden chapter with absolution for any reader who wishes to skip it.  “We do it, to show that the thing can be done;  the exercise is more for the benefit of the writer, than the reader.” [Quoting from memory, so you might not be able to Google that.])

So, suppose we wish to know what launches birds or butterflies on their migrations.  What we hope to hear about is an account in terms of concepts antecedently familiar or at least learnable without too much fuss -- things like average temperature, extremal (trigger) temperature, average length of daylight, or depletion of ambient foliage.  Or, how do they find their way.   We are prepared for an explanation in terms of magnetism, starlight, or even “an instinct, varying in its details from species to species, whose guiding factors are as yet unknown”.   In the first-named case, we are open to talk about iron molecules in the inner ear;  but if the account in inextricably entangled in the details of the cross-effects between the ornithoboson cycle and the L-dextro-retro-feniculation mechanism, it’s TMI, and we tune out.  A ‘molar’ elucidation suffices for the general public and for the general zoologist   (and indeed, even this much is often too much to ask in practice;  apparently major mysteries remain about many migration-patterns, including the celebrated case of the Monarch butterfly).  An avian histologist might want to know more about those iron particles and their interaction with the inner ear.  But at some point even he is satified to call it a day, content to say, of levels yet further down, The Thing Can Be Done.

[Update 26 April 2012]  And now, for pigeons, it has been:
http://www.nytimes.com/2012/04/27/science/study-sheds-light-on-how-pigeons-navigate-by-magnetic-field.html?hpw

[Update 14 July 2012]  And trout:
http://www.latimes.com/news/science/la-sci-magnetic-sensing-cells-20120714,0,828028,print.story
And sharks (a segment this morning on NPR).

Now, sometimes, perhaps usually, no such shallow-draught explanation will be forthcoming.  Thus, the saga of individual animals gets you only so far towards the understanding the appearance and disappearance of species; a lower-level unit, the gene, turns out to be quite handy; and to further understand the behavior of these, we occasionally have to get down among the DNA.

Consider further,  the symmetries of snowflakes.  The usual explanation is straightforwardly intuitive, local and deterministic.  But somehow I don’t buy it.   It just feels as though such endlessly varied detail, with symmetries nonetheless rigidly enforced, brewed in a whirling cauldron of stochastic accident, must have some energy-minimizing post-editing -- something global (or “holistic”, if you like that word) along the lines of surface tension, or of standing waves on tympani.  In which case you’ll be dragging in Bessel functions, or calculus of  variations, or quantum mechanics.   And in that case  snowflakes will be one of those phenomena that can barely be intuitively understood.  In this, it would join ranks with what may be a host of questions that Homo sapiens will never really understand.  -- This is the Mysterian stance.  Believe it or not, this is also the orthodox Judeo-Christian-Muslim position towards the ultimate unknowability of the mind of God -- certain TV preachers and football coaches to the contrary.

So:  Reduce as you can and as you must, but not for its own sake.  Practically, cognitively, there is a price to pay.   The naturalist tracking an ecosystem knows he may need to have recourse to natural selection, perhaps to geology, a bit of statistics -- but it’s not as though he can’t wait to get his hand on the string theory of the thing. 

Or consider the case of generative syntax, which over the years has dug ever deeper, and become increasingly abstract in its ontology of explanation, drifting further and further from categories familiar to Jespersen.  Yet it did this, not out of any fetishism for abstraction, nor reductionism for its own sake, but rather because earlier, more traditional and intuitive attempts just did not work.  Indeed, the principle figure behind this sweep of developments has also consistently been in the forefront of debunking popular but vacuous styles of reductionism.

~     ~      ~

Again, to be fair, let us quote a man whose mind we entirely admire, whose prose sparkles like dew-bedecked blooms at break of dawn.  None other than -- but you have already guessed -- the master himself, Mr. Willard (“Van”) Orman Quine:

Corresponding to every mental state … the dualist is bound to admit the existence of a bodily state  that obtains when and only when the mental one obtains..  The bodily state is trivially specifiable in the dualist’s own terms, simply as the state of accompanying a mind that is in that mental state.  Instead of ascribing the one state to the mind, then, we may equivalently ascribe the other to the body.  The mind goes by the board, and will not be missed.(*)

(*In fairness to Quine, let us hasten to add, that his core concern here is quite abstractly ontological, even quantificational, as befits a symbolic logician.   It may even be compared to the notion, not of dualism, but of duality, in mathematics, being related rather like the positive and the negative of a photograph, where either one will do.  --  Still, his chosen periscopic viewpoint leads to some no very edifying reflections: “Mental states, construed as states of nerves, are like diseases.”  And such reasonings spawned venomous afterbirths  with Dennett and the Churchlands.)

This nifty epiphany casts our Quine into something of a Little-Jack-Horner state (= excitation of synapse #5328b), for (coming to his senses) he straightly confesses that “this effortless physicalism smacks of trickery”.   Yet what he says is true enough. --  True… enough, for sake of argument; that no such isometric reduction has ever actually been made and perhaps never will, is beside the present point.  Let us grandly grant it done;  Nobels all round, lads!  What then?  Well, then, nothing.  We are back where we were.

For: every carpet has an underside.  We may even concede (perhaps over-generously) that both sides are interderivable:  given the one, you can work out the other.  Now, you and I prefer the upper side, where green birds are depicted in an azure sky, and the prince urges his huntsmen  forward in the chase.  Equally -- and it is their right, -- the proctoscopic philosophers prefer to ogle the underside, an unintuitive tangle of knots and loose ends.  You and I can observe why the green beings  appear on a background of blue;  whereas the proctoscopists can only stare miserably at their welter of circumanal shorthairs.

Such, indeed, is the case most favorable to the proctoscopists, where we are concerned only with a single static pattern.  Consider now -- well, our old friend, the Urysohn Metrization Theorem.  All the proctoscopists can do, in trying to wrangle with that, is to examine the brains (not, note:  the thought processes) of actual people trying to wrangle with it, since the theorem itself is incorporeal.  (Compare the Competence:Performance  distinction, in linguistics. Recall as well the unprofitability of obsession with the latter.)  And granting our epistemological vivisectionists  superhuman abilities  far beyond the offing of likelihood, they will be able to peer into everybody's brain-pan  and inspect the various chemical blurps, electric fizz, and meandering fat-globules  of the would-be topologists.  Yet worse, far worse for their case -- even granted their ability to somehow read off, from this mephitic brew, such messages as “SMITH - NOW - CONSIDERING - FIRST-COUNTABILITY.  UH-OH, SMITH SAD.   MEBBE FIRST-COUNTABILITY NOT ENOUGH. OH NOES!!”, -- they will be not a whit closer to understanding the theorem.  For their data-set consists of all the various blunderers of the earth, barging about, running into dead-ends, committing fallacies, thinking they’ve proved it whereas in reality (victims of a misfolded protein) they did not -- really one would like to see Monty Python work this one up into a skit.  (They did the complete works of Marcel Proust;  why not Urysohn?)  For the truth of the theorem resides, not in the cloaca which these gentlemen are pleasured to inspect, but in the realm of Invisibilia, the kingdom of the Lord of Hosts.  And the valid mathematical moves made by this or that fallible incarnated creature, in their groping attempts to approach the truth, gain their validity, not from thermodynamic or statistical considerations, but from our miraculous harmony with such abstract truth itself, which stems, we know not whence;  though some of us have an inkling.

That, technically, one might perform such fundamental (or rather fundament-level) analyses or rather catalyses,  shows only that it is possible, by the wrong sort of reduction, to reduce meaningful phenomena to the meaningless.  We may dub this excretory reduction, as opposed to explanatory reduction.  And the craft practiced by these proctoscopic coprophiles, we may dub stercochemistry.  (Not a typo, that:  sterco-, not stereo-.)  Indeed, in this perspective, we notice that the doctrine of -- eliminative materialism, is singularly well-named.

Envoi:

… grob geredet, wie gesagt:

womit noch keineswegs  der Wunsch  ausgedrückt ist,

auch grob gehört,

grob verstanden zu werden …

-- Nietzsche, Zur Genealogie der Moral

[Update 10 III 2012]   For a briefer, parallel argument, in a lighter vein, click here:
Eliminative Immaterialism

[Update 28 III 2012] Roger Scruton weighs in:
http://www.spectator.co.uk/essays/all/7714533/brain-drain.thtml

*

Für psychologisch tiefgreifende Krimis,

in pikanter amerikanischer Mundart,

und christlich gesinnt,

klicken Sie bitte hier:

http://www.linguasacrapublishing.com/justice.html

*

[Update 13 April 2012]  This particular post keeps receiving a disproportionate number of pageviews.  Since the Comments are virtually nonexistent, I am at a loss to know why.

If you have been enjoying it for its sober philosophical content, and want more, click here:

http://worldofdrjustice.blogspot.com/search/label/Realism

If, on the other hand, you rather relish the invective, trouncing the nihilists, then you might further appreciate this:

http://worldofdrjustice.blogspot.com/2011/09/philosophy-porn.html