Betrachtungen eines Unphilosophischen (quater)

I don’t like purely philosophical works.  I think a little philosophy should be added to life and art, by way of seasoning;  but to make it one’s specialty  seems to me  as strange as eating nothing but horseradish.

-- Boris Pasternak, Doctor Zhivago (1957) (ch. XIII.16; Lara speaking)

Nicht vom Wetter spricht sie, nicht vom Schneider,

höchstens von den Grundproblemen  beider.

-- Christian Morgenstern

[I wrote the following around twenty years ago, before I was baptised.  Just stumbled on it while cleaning up some files. 

Since that time, I’ve read a fair amount of philosophy, often with pleasure, and dabbled in composing some.  But the treatment here of the cognitive problem does not need revision or retraction.]

I must conclude, reluctantly, that I am of a  not very philosophical cast of mind.  Intellectual, yes; thoughtful, I hope so; but philosophical, in the sense of spontaneously grappling with the questions that engage those denominated philosophers, alas not.

Had I never read a line of academic philosophy, I could contentedly have walked for seven decades down the lanes of life, kicking at stones and appreciating the trees, without once wondering, let alone worrying, whether a name denotes a universal, or rather a concept, rather than (snicker snicker) a thing. Left to my own devices, I would likely never have asked whether Being even had a nature. let alone what the bugger might be.

Such questions as these have never troubled my sleep; and it is only with the greatest difficulty than I can induce them to trouble my waking hours.  Yet we read, in the letters of our betters:

"What distinguishes a man from a word?  There is a distinction, doubtless."

--C.S. Pierce, "Some Consequences of Four Incapacities".

This I no more ponder than whether a hawk may be discerned from a handsaw -- indeed, it rather recalls the grotesque title of the neurologist Oliver Sacks, The Man Who Mistook His Wife for a Hat.  Yet Peirce concludes, alarmingly, that "The word or sign which man uses  is the man himself."  Should we be troubled by this?

Doing philosophy – well, I seldom do.  But when reading philosophy – something never undertaken save after a sound night's sleep, in the company of pots of strong coffee – I have often had the horrible experience of carefully lucidly processing each phrase of a sentence as it comes along, then finding, when I reach the sentence end, that the meanings of the initial phrases have evaporated:  as were intelligence but a porthole on a passing landscape, seizing each piece clearly as it looms into view, but at the expense of losing the last.  (That was rather a long sentence itself; let us pause.)

            (Pause.)

            Herewith a specific instance, taken from a little work in paperback (Arthur Danto, What Philosophy Is) known for being a relatively clear and non-technical introduction for the layman:

            "It is demonstrable that, for any system of sentences – any theory, say – which satisfies exceedingly weak and undemanding formal criteria, just this alleged desideratum can be achieved."

            This is not a long sentence; and for the first two-thirds of it, it actually calls up to me very visual ideas.  "Any system of sentences – any theory, say": I picture these sentences as speech-balloons, dangling from a mobile, with little hand-icons pointing at other sentences which they imply or from which they derive.  "Which satisfies exceedingly weak and undemanding formal criteria":  here our hypothetical theory is embodied as a sort of Doctor Watson, waving his hand with bluff good humor, in dismissal of the trifling demands made upon him: "No trouble at all, sir!"  And as for that initial "It is demonstrable that", well, we all know that "It is demonstrable that P" means (for the plain man) just that "P", and moreover gives you license to swallow P without troubling yourself to prove it or make it plausible, or even to understand it very deeply:  just one of those solid facts that people our Watsonian society, which the tradespeople have somehow seen to.

            Then comes "just this alleged desideratum".  Alas: this sends you haring back to the previous paragraph, or previous page.  And the "alleged" is troubling:  do we desire this (whatever it is), or do we not?  This centrifugal tension makes subtly more difficult the task of going back and finding the antecedent for "this".  It's not like "she": hmm, hmm, complicated, this, -- aha, Natasha Nikolayevna.

            Now:  one fact about philosophy, which makes the subject hard to follow, is rather to its credit.  Namely:  we never know what might be called into question.  So we can't just sit back and nod  as bits of received opinion are spooned into our open mouths.

            In many non-philosophical areas of life, we can count on so much that is unchallengeable, that their arguments are like sermons in a lazy church.  We can doze; we can idly watch the fly buzzing across the stained-glass windows; and miss nothing that is essential, for we have already all that is essential, the rest is embroidery.  As, in the radical Sixties, syllogism went rather like this.

Granted:
     (1) Amerikkka is a honkey-assed imperialist pig
     (2) The righteous Vietnamese people are righteous, popular, and Vietnamese.

From this it follows:
     (3) Blah de blah de blah de blah (rahht ohwn!) 

Everyone goes home satisfied.

What does it mean, to be "unphilosophical"?  It cannot spring simply from stupidity – which is a general term; too much counter-evidence in collateral fields.  Nor ignorance – not after having sat at the feet of the philosophical:  for, failure to absorb their wise lessons would have to be due either to stupidity (already ruled out of court) or "unphilosophicality" : quite possibly present, but this is the quality to be explained.  (I recall a case from some years ago, in which some Brazilian peasants, or Indians, were brought to trial for having killed quite a number of people: and were acquitted, on the grounds of "invincible ignorance".  A charming verdict; egomet etiam, nolo contendere; but again, this is the explicandum, not the explicans.)

            One possible partial explanation is that, apparently, despite gross this that and the other thing, I do actually, more or less, in some sense, believe in God.  This may even be largely unconscious, but it does determine things.  As:  Good heavens!  Here He went and made Eden for our grandsires to saunter in, and angels to attend our fallen birth – and you're worried about the existence of tables??!??!*  Get a life, man!  Get an afterlife!

[*On page 100 of Danto's booklet, we have an image of the philosophically inclined scientist  swallowing an atom  but straining at a table.]

It is a stylistic characteristic of the philosophic genre, that its reported combatants are generally abstract and shadowy, unnamed figures.  Not Gould vs Dawkins, or Quine vs Chomsky, but: the Realist; the Representationalist; the Phenomenalist, each with his separate agenda; curiously dispassionate partisans, like players in a masque. 

            In one sense, this should make for clarity.  As, I may know a whole bunch about Chomsky, or Chesterton, or Orwell, but it is different from the bunch of things known by disputant P., and different still from the sub-bunch of things that have caught P's attention in the present case.  Hence, when P. says: "….(Orwell)….", a million bells go off in my head, which may obscure his message.  Whereas, when the don refers to the Realist, there is no clanging, nothing to refer to but the Realist's résumé.

            And yet and yet… It is with this as with the medieval allegories, where ((Danger)) orates to ((Faithful)) anent ((Beauty)), and the eyes turn to glass.  These creatures have no form – no warts – no tits – it is difficult to attend, hard to become engaged.

            This lack of philosophical engagement has few consequences for the practical matters of life, such as renewing a driver's license.  Still, it bothers me.  For, philosophy is reputedly fundamental – indeed, is so virtually by definition.  Smart people are presumably interested in problems of ontology, while stupid people are interested in football scores.  [A surprisingly large number of smart people are interested in baseball.  This cannot, then, be an intellectual failing; but it may be a perversion.  The question remains open.]

*     *     *

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We now return you to your regularly scheduled essay.

*     *     *

Yet I am troubled by questions of epistemology, for the good and simple reason that certain people whom I know  (those notorious Other Minds, in whose complete integrity I believe implicitly) seem to know (or say that they know) what I don't know; nor know I  how (or whether) they do know it.

As:

CEO (cigar clenched in right mouth-corner, speaking laconically out of the left):  Nyaahh… Dis noo magneddic-stawritch standid, it'll nevah catch on, da mahhkit'll riject it.

Me (thinks): How the F*** does he know that?!?!?

~

On a good day, then, and with a good book, I can – granted, not do, but at least – read philosophy, and engage with it:  an EKG would reveal busy little blips and bumps, I'm not just flatlining with the book open, the mental equivalent of an all-day sucker.  And admittedly, most of the enjoyment comes from the crackling style (as with Quine) or the apt examples (Strawson, Geach), rather than from any genuine penetration into the delicious mysteries of what it means, what it really means, to say that x equals (wait for it) x.  So the author of the book need not feel that his labor is wasted:  here is John Q. Public with his engine turning over and that author's very book in his hands (those hands which might equally as well have held a breast, or a beer).  And yet – the book once laid upon the night-table, all its arguments and all its concerns  go out like a light.

            It is not so with, say, poetry.  To read poetry before retiring is as dangerous as drinking espresso for a nightcap: I toss and turn, the lingering rhythms like a hot blanket, which cannot be cast off till I drag myself out of bed, snatch a bathrobe, and WRITE - WRITE - INDITE!  Whereas philosophical propositions  spark no further fever.  I lay down the volume, fall into a dreamless sleep, and perhaps the next day have some vague lingering recollection – "Yes, that 'x' thing, it was equal to, let me see, was it 'y'? -- no!  'x', that's it!  x = x.  My, the things one learns."  Or:  “Is it true, that snow is white?  Mmmm..mmyes!”

            Perhaps a policy of not asking overmany fundamental questions too often, is not so much intellectual laziness, as the better part of epistemological valor.  For, truly to nail down the simplest everyday phenomenon, is largely beyond the reach of science.
(Physics is really good at addressing problems that it invented itself, like muons;  not so much when it comes to snowflakes, or lightning, or wind.)

            In addition, when you go to the scientist, thou sluggard, you find him not exactly bent over the philosophy-of-science books either.   And this, not only among those sooty alley-dwellers the chemists, with their practical pots, but even those austere, unstained – theoretical physicists, nay, mathematicians.  Mathematics does not need metamathematics to go about its business, whether devising formulae that will predict the stresses of actual bridges, or proving theorems about ideal manifolds in n-space.  (We may define pure mathematics as the subject in which Bertrand Russell does not know what he is talking about, though what he says is none the less true.)

~     ~     ~

~  Posthumous Endorsement ~

"If I were alive today, and in the mood for a mystery,

this is what I'd be reading: "

I Don't Do Divorce Cases

Murphy on the Mount.

(Ich bin Thomas Mann, and I approved this message.)

~        

Other  tragic examples:

Valéry était atteint  de cécité philosophique.

-- Etienne Gilson, Linguistique et philosophie (1969), p. 234

Freud himself  confessed to an insensitivity to philosophy -- or at any rate, to academic philosophizing -- after reading a book a colleague had recommended:

“You cannot imagine how alien all those philosophical convolutions  seem to me.   The only feeling of satisfaction they give me  is that I take no part in this pitiable waste of intellectual powers.  Philosophers no doubt believe that  in such studies  they are contributing to the development of human thought;  but every time, there is a psychological  or even a psychopathological problem  behind them.”

-- quoted in Ernest Jones, Freud: The Last Phase (1957), p. 140.

(Assignment:  How do these observations apply to the case of Wittgenstein?  Discuss)

Latest update:  
"Even when I have moved away from observation,  I have carefully avoided any contact with philosophy proper.  This avoidance  has been greatly facilitated  by my constitutional incapacity."
--  quoted in Ernest Jones, Freud: The Last Phase (1957), p.335

Words of the Day: sublunary, postlapsarian, …

Re Melanesians:

“When a native says that he is a man, he means that he is a man and not a ghost; not that he is a man and not a beast.”

-- Robert Louis Stevenson, In the South Seas (1896)

~

Perhaps the first word we heard, ourselves still children, which, rather than simply denoting something new (like a previously unencountered animal), designated something old in a new way, and thus reframed us, was:   Earthling.   In terms of reference, the word is synonymous with people;  but its intension  (with an -s-, not -t-; a term of art among linguistic philosophers, referring to the way it picks its referent out) is different.  (Thus likewise morning star and evening star, both referring -- though from different lookouts -- to Venus.) 

We meet this first in science fiction, and it permanently expands the mind.   When the exploits of the spacemen are forgotten  along with other tales of the nursery, we yet retain the spaciousness of the new view.  “I went to the mall with three of my friends”;  “I went to the mall with three…. fellow Earthlings”:  we sense the wider world beyond our plankboard stage.

(We just came across a mirror-term to earthling:

Suppose that an archaeologist who had visited us from outer space  were trying to explain human history to his fellow spacelings.

-- Jared Diamond, The Rise and Fall of the Third Chimpanzee (1991), p. 172 )

Another take on the same referents (namely, our earthly selves) is human.  Though the word is of course by now quite common, it was not always so, being a scientific word, borrowed from Latin (humanus, from homo; if there be a further relation to humus, then we have an interesting parallel -- again ‘earthling’, but now in the sense of ‘sons of the soil’).   By this term we are distinguished from animals;  but as everyone learns that perfectly well from an infant age, we do not need this word to teach us the species perspective.

Rather otherwise is mortal -- again from Latin, from the word for ‘death’.  In this secularized age, the average reader might think of this as a kind of moldy Sunday-school word, but the original sense among the pagan Greeks and Romans  was as opposed, not to God, but to the immortals -- the gods.  This is the sense that survives in the phrase “What fools we mortals be” (in Shakespeare’s most robustly pagan play).
An unexpected limitation in this word immortal  is evidenced by the following splendid epigram:

The actual infinity of a Platonist  is as seen by a mathematician who is eternal;

The potential infinity of the Intuitionists  is as seen by a mathematican who is merely immortal.

This is brilliant.  We expect the distinction to be between an idealized immortal mathematician, with all the time in the world to count to infinity, and a mortal one, who feels time’s wingèd chariot hurrying near, though he might make do with Supertasks:  accordingly, we initially take eternal simply as a stylistic synonym for immortal, before the second strophe brings us up short.  The Cumaean sibyl was merely immortal -- and consequently longed for easeful death.   Whereas the Platonist beholds the world of Forms  sub specie aeternitatis.  

(The epigram above comes not from a treatise of theology, but from a book of set theory and its logic.  I am quoting from memory, and possibly amiss, since Google finds, not that, but mostly philosophical and theological works.

-- Ha!  wait, found it, nestling on my shelves.   It is from Understanding the Infinite, by Shaughan Lavine.  He states it thus:

The idealization of experience that yields the actual infinite of classical mathematics  is that of the Eternal Mathematician, while the one that yields the potential infinite of intuitionistic mathematics  is that of the Immortal Mathematician.

But I like my misquotation rather better, and so shall leave it.)

~

A particularly delightful word,  containing, as were it a microcosm, a whole philosophy, is the word sublunary:  meaning, in the old cosmology, all that is to be found beneath the Sphere of the Moon.   (The allusion is not to the Moon’s own sphericity, wonderful though that be,  but to the celestial shell whereon that glowing queen is constrained to move  in regal splendour.)  Which is simply to say:  our everyday world;  except that now, instead of moving about in it like a tadpole in a pond, taking it all for granted, our thoughts now float upwards, and our hearts do yearn.

A simple swain -- yet fain to peer, beyond the sphere

The sublunary world is, in other words, this life Here Below.  And this brings us to a curious etymological fact:  for in Arabic, there are two common words meaning ‘world’:   al-`âlam, which is neutral, like world;  and al-dunyâ, which adds the notion of a contrast:  though now, not to any physical supralunary realm, but to al-âxirah ‘the hereafter’.   Morphologically, dunyâ is a feminine elative adjective, meaning ‘lower, nearer’:  thus precisely encapsulating the notions expressed by sublunary and Here Below, but in a single morpheme.

(The term sublunary has joined its age-mates in the medieval museum;  yet we still retain a kindred metaphor, "everything under the sun".)

~

At last we arrive at the final word of our title, postlapsarian :  a word that contains multitudes.  It refers to life subsequent to the Disaster in the Garden -- the only life that any of us ordinary folks have ever known.

In Adam’s Fall

we sinned all.

Our earliest ancestors, rueing the day

*

For a portrait of Grace and Reprobation,

try this:

The Penitent and the Impenitent Thief

 *

Once again, it is a word that picks us out, every one of us (for even Eve and Adam were postlapsarian at the end), but in a new way, thus differing most starkly from the bland philosophical agnosticism of the coreferential but non-synonymous term human.   It bears within it a deep and stark perspective -- one which we are inclined to disregard, as we scramble for sales at the mall, or lounge back glassy-eyed before the goggle-box (the behavior, however, belying the complacency).  

Yet in a better age, it was borne well in mind;  as when Condillac, in the preface to his L’art de penser (1780), though that work is seen in retrospect as having paved the way to atheism, yet was careful to remark,  that his analyses apply only to the postlapsarian soul:  much as a myrmecologist  (one more modest than Edward Wilson), should preface his monograph with the caveat that the generalizations made therein  might not apply to the world outside the termitary.   Our favorite Neothomist speaks of

… la précaution qu’il prend,  au début de son Art de penser, de rappeler qu’il va décrire l’âme telle qu’elle est à présent, après le péché originel.  Avant le péché, elle avait des idées  antérieures à l’usage qu’elle fait des sens,

«mais les choses ont changé  depuis sa désobéissance».

-- Etienne Gilson, Linguistique et philosophie (1969), p. 28

 Condillac, perhaps having second thoughts about what he unleashed 

We are, thus, all of us, earthlings, mortals, sublunary and postlapsarian.   Each of these words picks us out from among all else in the Creation, yet each from a different angle, in a way that enlarges our humanity.

~

Linguistic footnote:  We have chosen these philosophically rich words for the fun of it; but the basic phenomena here under discussion  occur more widely.  Thus cordate and nephrophoric (in their somewhat specialized use among philosophers) ‘having a heart’ and ‘having kidneys”:  non-synonymous but co-referential.

Or, to take an example quite similar to that of sublunary:

The expression dry land evokes the ocean in a way that land itself does not,  and by this very fact seems filled with sea breezes -- or rather, tempests, since the particular light in which the land is thereby set, is as a place of safety, reached at last after perilous voyages.  "Earthling"-style designation of the denizens of this default environment, from the salty perspective of the mariner: landlubbers.
Likewise terra firma:  it’s a place where you can finally find your foothold, after your return -- O Earthling -- from your voyage to outer space.

~

[update July 2020]

 

Mensch is a rather friendly-sounding German for any human being;  in Yiddish-English, a mensch is a solid, kind-hearted guy.   In the following, the word is contrasted invidiously with ‘policemen’, who thus are delimited outside the circle of humanity:

“ein Mensch schwer und vier Polizisten leicht verletzt. „ https://www.welt.de/vermischtes/article211457365/Stuttgart-Festnahmen-wegen-Auseinandersetzungen-vier-Polizisten-verletzt.html#Comments

Reader comments:

“ein Mensch schwer und vier Polizisten leicht verletzt. „ So klingt linker Sprachgebrauch. Macht ihr Journalisten schon unterbewusst. Als ob Polizisten keine Menschen sind.

-

Ein Mensch und 4 Polizisten- habt ihr das aus Versehen aus einem linksextremen Kampfblatt übernommen??

.

Truth and Provability (expanded)

[A footnote to this.]

Trying to suss out the nature of Truth by staring straight at it  is like attempting heliology by staring at the Sun.   In both cases, more assimilable enlightenment  comes from the corona.

Thus the related but distinct notion of Provability. Gödel was the first to neatly delineate the two notions:  the Propositional Calculus is deductively complete (i.e., all truths may be derived via the defining rules of the system), whereas anything as robust as the integers is deductively incomplete :  one can, within that more expressive system, formulate statements that are true but (intra-systemically) unprovable .  Previously, the Formalists (Hilbert et al.) had seen provability as an analytic explanation of what is meant by ‘truth’ itself.

Kurt Gödel
("I'm looking throuuuugh you...!")

Pre-scientifically, and indeed theologically, we are not surprised that the two notions should not be equivalent (though of course we had no notion of the precision afforded by Gödel’s results).  Some things, existing from before we were born, and lasting ever after,  just are true;  why should they be logically derivable, or even humanly comprehensible?

~     ~     ~

There is a perhaps related notion within the philosophy of language:

~ Whatever can be meant,  can be expressed.  ~

(Intended-meaning : truth  ::  expression : provability)

Yet the very existence of our word ineffable, suggests that we at least entertain the possibility that this may not be so.

In the words of a Neothomist philosopher:

La communicabilité de la pensée  est un fait immense, incontestable  et elle n'est possible que par le langage;  mais tout suggère que, dans le langage, la pensée reste  par nature  essentiellement autre que son moyen de communication.

-- Etienne Gilson, Linguistique et philosophie (1969), p.  39

Taking this in a maximalist sense  would imply, not merely that certain thoughts are ineffable, but that no thought is quite equivalent to its verbal expression.

A further discussion of this topic may be consulted here:
The "idea" idea.

~

It is clear that we need a notion of truth independent (or partially independent) of provability (however vexed and vague that notion must necessarily be, without such buttress), else how to assess the validity of what purportedly is proved.   In the Awful Warning against dividing by zero, delivered to pupils in their tender years, the young scholars meet a Falsidical Paradox:  an impressive display of mathematical handwaving, purporting to show -- there it is on the blackboard, plain as day --  that zero is equal to one.  Yet even a lad in short-pants surely resists such demonstration, if only with an incoherent “Uh, no, it’s not.”

Compare the smoke and mirrors with which philosophers and neuroscientists demonstrate that consciousness is an illusion, and free will  a will-o’-the-wisp.  Equally we reply: “Uh, no, it’s not.”

~

Relativist conceptions of truth  are familiar.  As the Harvard philosopher wittily put it, mimicking the cant of the post-‘60’s undergraduates:

“You may not be coming from where I’m coming from, but I know relativism isn’t true for me.”

-- Hilary Putnam,  Reason, Truth, and History (1981), p. 119

Less familiar is a relativist conception of provability.   Here, Ernest Gellner comments on the position of fellow-philosopher Michael Oakeshott:

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

-- Ernest Gellner, Contemporary Thought and Politics (1978), p. 180

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

The “Idea” Idea (with an excursus on ideation and subvocalisation)

Much of the most important and vital work done in the last half-century  depends [not upon experiment or brute calculation, but] upon new ideas;  and new ideas are notoriously exceedingly difficult to grasp.

-- Louis J. Mordell, Reflections of a Mathematician (1959), p. 11

We previously stated that mathematics is best characterized as the science, not of number, but of structure (or of pattern -- at this level of generality, either term will do).   As MacLane phrases it:

This chapter introduces the idea of the formal  in terms of certain basic structures:  Set, transformation, group, order, and topology.  With Bourbaki, we hold that Mathematics deals with such “mother structures”.  Against the historical order, we hold that they arise directly from the basic stuff of Mathematics.

Saunders MacLane,  Mathematics:  Form and Function (1986), p. 7

That last bit, you will note, is unabashedly Platonist, counterposing contingent human praxis  to transcendent time-independent Truth.  (We discuss this contraposition here.)

Voilà  le hic

But beyond that, or rather as an animating force within it,  and distinguishing mathematics from such structure- or pattern-centered enterprises as architecture or the plastic arts, is the central role of ideas. 

MacLane puts the matter well.  Re the derivation of Hamilton’s equations from Lagrange’s:

What appears as a trick is in fact an idea -- an idea which must have been clear to Hamilton when he did it.  But we claim that in general  most of the formal tricks appearing in Mathematics  are really ideas in disguise -- ideas presented as manipulations  because the manipulations can be made explicit, while the ideas are a bit nebulous.

-- Saunders MacLane,  Mathematics:  Form and Function (1986), p. 284

In a previous series of essays, we put forward certain particular “mother ideas”.  Here we reserve a meditation-space  for musing about “Ideas -- the very idea”.

~

Hadamard comments on Rodin’s testimony that, throughout the process of sculpting, he must keep the “global idea” in mind, even while working on the smallest details;  and that “this cannot be done without a very severe strain of thought.”

I do not feel that I have understood [a mathematical argument] as long as I do not succeed in grasping it in one global idea; and, unhappily, as with Rodin, this often requires a more or less painful exertion of thought.

-- Jacques Hadamard, The Psychology of Invention in the Mathematical Field (1945), p. 65

Hadamard scoffs at the account given by Souriau in his Théorie de l’Invention:  “Does the algebraist know what becomes of his ideas when he introduces them, in the form of signs, into his formulae?  Undoubtedly not,”  but just turns the crank of mechanical calculation.  Apparently Souriau never consulted an actual mathematician, says Hadamard:  the mathematician trusts his idea, his insight, his intuition, more than he does his calculations, which after all are not infrequently in error  (Hadamard confesses that he, like Poincaré, was but an indifferent numerical calculator):  If these clash, you first redo the calculations, before tossing overboard the Idea that motivated the whole thing.

~

Ideation and subvocalisation

Hadamard then makes an excursus  rather off the path our our principle inquiry;  yet we shall follow him a little ways.  He confronts the question of whether language be the key to thought;   and waxes indignant at those who, like Max Müller, dogmatically assert that, without language, thought itself must needs collapse:

I had a first hint of this when I read in Le Temps (1911):  “The idea cannot be conceived otherwise than through the word, and only exists by the word.”  My feeling was that the ideas of the man who wrote that  were of a poor quality.

-- -- Jacques Hadamard, The Psychology of Invention in the Mathematical Field (1945), p. 66

Likewise, the behaviorist J.B. Watson says somewhere that “thinking is nothing but our talking to ourselves”.

The devotees of this position  point to the dual meaning of the early Greek word logos -- ‘word, language’ and ‘reason, thought’;  and would by implication deny that our diminutive and prickly friend, the humble hedgehog, could really know One Big Thing or even a little weentsy one.

Hadamard, by contrast, is virtually a militant in the opposite camp:  “I fully agree with Schopenhauer when he writes, ‘Thoughts die  the moment they are embodied in words.”  This even applies to algebraic symbolism:  too cumbersome to actually think with;  you mostly only use them when checking your work.

The Dutch Intuitionist mathematician L.E.J. Brouwer is of similar mind:

De woorden van uw wiskundig  betoog zijn slechts de begeleiding van een woordloos wiskundig bouwen …

 

(Caption quotation from Dennis Hesseling, Gnomes in the Fog:  The Reception of Brower’s Intuitionism in the 1920s (2003), p. 38.)

The Neothomist philosopher Etienne Gilson  seconds the opinion of his countryman:

Si un linguiste me dit que c’est notre langue qui modèle d’abord  le monde que nous pensons,  je sais qu’il ne me parle pas en linguiste, mais en philosophe, qui se dispenserait d’ailleurs de me donner aucune justification philosophique de son opinion.  Non seulement je ne sais pas si elle est vraie, mais je ne sais même pas pourquoi elle lui semble vraie.

-- Etienne Gilson, Linguistique et philosophie (1969), p. 51

A noted Freudian psychiatrist agrees:

Every single thought, before formulation, has gone through a prior wordless state.

-- Otto Fenichel,  The Psychoanalytic Theory of Neurosis (1945), p. 46

A contemporary philosopher goes even further:  some ideas may be not only pre-linguistic, but even pre-conscious:

We may not be aware of our ideas.  An idea  in this sense  is a tendency to accept routes of thought .. that we may not recognize in ourselves, or even be able to articulate.

-- Simon Blackburn, Being Good (2001), p. 3.

The epigram "We may not be aware of our ideas" is deliberately paradoxical.  Blackburn means "idea", not in the sense of the completely conscious  "I have an idea, let's...", but of something like the often tacit metaphysical underpinnings of mentation and investigation, which we treated of earlier.  -- Blackburn extends this notion (in a way reminiscent of, but antedating, Freud):  "A permanent strand in Christian thought  is that we have no insight, or even lie to ourselves, about our heart's desires." (id., p. 30)

We close this excursus with an epigram of William Hamilton  which Hadamard quotes:

Speech is thus not the mother,

but the godmother of knowledge.

~

The reason such musings lie off our main track, is that we are largely uninterested in psychology, or thought-processes, or any of the hunches & hiccups that fallen Man is heir to  as he struggles to comprehend all that His hand hath made.  With Hadamard, we conceive that there are cognitive activities for which vocalization is neither required nor especially helpful:  say, playing Go, or basketball.  

There is an epigram, variously ascribed, that has always fascinated me:

“How can I know what I think

 until I see what I say ?”

On the face of it, this would appear to be anecdotal evidence for the thought-needs-language thesis.  But upon nearer inspection, it might argue rather the opposite:  That thought rose from some wordless region of the self, and only became an object to critical consciousness after having been concretized by transformation into words.

For us, the key question is to what extent an Idea -- one worthy of the majuscule -- can even be adequately expressed in our language.   Certainly the higher mathematics cannot be expressed in ordinary human language.  It has invented for itself a more or less arcane system of signs, obeying no human syntax;  you may, if you like, par abus de langage, call that too a “language”, but it is no natural human language, but rather an aide-mémoire cobbled together to express ideas that observe their own semantics, call that language or not.   Hadamard himself attests that human language does not serve him especially well, when he must express mathematical ideas.  Whenever he must hold forth on a mathematical topic, even one of his own devising and thus, to him, abstractly clear as a bell, he must write out the text of his lecture beforehand, lest he be left gasping and groping for words.

There is another old adage, current among linguistic philosophers:

“Whatever can be meant

can be expressed.”

At this point we hear the shade of that crusty critic of Le Temps, growling:  All that you mean, maybe. 

~

Let us put the point even more starkly.  Ask Not  (we channel Kennedy here) whether our (necessarily human versions of) ideas  could be adequately communicated to some other rational species.  Ask whether the Idea, as pre-existent in Platonic paradise, has been adequately incarnated in us.

(There now swims within my vision  the image of a category-theoretic Universal Object, with arrows slanting downwards  this way and that, as in Blake’s great painting.)

~

This is becoming interesting.  Hoping that your appetite has been whetted as well, we link to a couple of math-related installments of the “Any Ideas?” series:

Induction

The free invention of structures

Actual Infinity

~

We have tried to outline a capitalized or pregnant sense of the everyday word idea, which in most contexts certainly does not bear such freight.  (“I’ve got an idea, let’s go get pizza.”)  There is, however, another sense, which is still scientific/intellectual, yet which bears no Platonic or foundational flavor:  what is sometimes called a “bright idea”.   A bright idea is what causes a light-bulb to appear over the cartoon character’s head.  And it does represent some genuine cleverness, though its success is by no means guaranteed (and in the case of Donald Duck, will almost certainly come to grief.)

This more powerful form of inductive construction  can be deduced rather simply from the older form.  The trick is to construct, not the sequence of values, but the sequence of partial functions…

-- Andrew Gleason,  Fundamentals of Abstract Analysis (1966), p. 145

A “trick” is to an idea  as tactics is to strategy. 

Similarly:

We could prove the inequality by a limit argument from the known inequality for finite sums, but the following reasoning involves a very interesting technical device.

-- Andrew Gleason,  Fundamentals of Abstract Analysis (1966), p. 195

~

We have noted before  that, once you set out to focus on Ideas per se, you keep winding up back in mathematics -- if only because there are so many of them there.  Yet more:  In our own lifetime, math itself has spawned a subfield  whose task, it would seem, is precisely the study and development of Ideas -- for their own sake, almost, and beyond such practicalities as computing the area of the field of Farmer Brown (or rather, Farmer Enkidu, since this concern goes back to Babylonia and beyond) or even its offspring, geometry, or the handmaiden of that, the calculus, or …  This field is called Category Theory, which (as faithful readers of this tragic blog will already know)  I do not personally understand:  but do note, that a recent introduction to same (subtitled “A first introduction to categories” -- the style of the title is that of children’s books;  and God willing, someday toddlers will study this stuff), by Lawvere & Schanuel, is titled:

Conceptual Mathematics

C’est un titre astutieux.  For again (this is a phenomenon which we have treated, in these essays, under the label “faux-naïf”), on the surface this might seem to be one of those liberal-feelgood substitutions for the actual hard work of thought, meant to bolster the self-esteem of slow-learners;  whereas in actual fact, it points at concepts -- what underlies such relatively superficial activities as real analysis, point-set topology, algebraic geometry (you with me, kids?), and all the rest.

[Excelsior]   There is a vast philosophical literature (and a smaller, but still substantial, linguistic literature) concerning the relations between language and thought.   To rehearse this would be pointless;  to attempt to enrich it, quixotic.   Still we may feel our way forwards, and conceivably (eventually) contribute some minim of value, by taking as our paradigm area of Thought -- mathematics, rather than cats being on mats, and that sort of thing.   And Language as comprising, not only natural human languages, but any attempt at symbolic and communicable representation of Thought. 

(For this quest, I request:  God’s guidance and Grace.  Since, sine qua, non.)

An initial linguistic bridge is provided by our remarks above about the notion idea in the sense of ‘bright idea’.   A bright idea is no mere clothing of a perception;  it is closer to an invention.   And the key term it brings us up next to is:  insight.

[TBC?  Solâ gratiâ … ]

Ein Bericht für eine Akademie

http://www.lefigaro.fr/sciences/2012/04/13/01008-20120413ARTFIG00524-les-babouins-capables-de-lire.php

OK, OK, so apes can read.  Big deal.  How is their taste in literature?

As Etienne Gilson puts it, rather frostily:

Les bêtes ont une imagination, on comprend donc qu’elles aient de la voix  parce qu’elle ont quelque chose à exprimer, mais il semble que l’homme seul ait quelque chose à dire.

-- Etienne Gilson, Linguistique et philosophie (1969), p. 96

 

On ne connaît pas d’animal dialecticien, sophiste, rhétoricien, orateur,  qu’il s’agisse de l’éloquence judiciaire, politique, ou d’apparat.

-- Linguistique et philosophie (1969), p. 220

Plus what -- Apes absolutely suck at algebraic geometry.

(For our earlier essay prompted by animal prodigies, click here:

http://worldofdrjustice.blogspot.com/2010/12/riemann-chomsky-fido.html )

Introduction to Dialectics

Une langue est un moment particulier, sur un territoire particulier, de l’évolution du langage humain.

-- Pierre Guiraud, L’Etymologie (1964)

This ponderous epigram is difficult to translate into English, since we lack a distinction equivalent to langue/langage (or for that matter to the Saussurian langue/parole -- plain “speech” won’t suffice, because there is also le parler).   Speaking somewhat archaically, we might say:  Each tongue is but the instantiation in time and space of the evolution of human language.   Or, in Chomsky-speak, and with the vague term language now switching rhetorically to the other pan of the balance:  Each (particular, and almost epiphenomenal) language instantiates the (innate, invariable) universal language faculty.

It sounds rather grander in French.

Anyhow -- your appetite for dialectics is doubtless whetted by such grand Gallic apophthegmatic legerdemain (or legerdelangue, as it were).  And as a service to our readers, the World of Dr Justice here offers some comparable nifties of our own invention, so that, taking instruction from these, You Too can be a dialectician, and fashion fashionable quotables in your own home.

=>  A coffee-cup is just the antichiral doppelgänger of its own mirror image

=> The soupstain on your necktie is simply a concrete hypostasis of the Second Law of Thermodynamics.

=> A chamberpot is but a momentary stadial synthesis of the dialectical self-development of the historical world-spirit of Indoor Plumbing.

~

Now here is another bold Gallic sally, of which, inexplicably, I am rather more fond:  perhaps because filtered through the sense and sensibility of our favorite NeoThomist:

Ce « petit cartésien », Géraud de Cordemoy, exposa ses vues … dans un écrit  dont l’importance n’a pas échappé à Noam Chomsky, et qui, peut-être grâce à l’influence de ce qu’en avait dit cet éminent linguiste, vient d’être réédité. …

[L’arbitraire du signe] est  pour Cordemoy  un sujet de vive satisfaction, car l’absence totale de ressemblance  entre les signes et leurs significations  lui prouve  que des choses aussi dissemblables  que le corps et l’âme  peuvent être pourtant unies.

-- Etienne Gilson, Linguistique et philosophie (1969), p. 75-6

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Si cela vous parle,

savourez la série noire

en argot authentique d’Amérique :

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

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