Friday, September 30, 2011

“Res ipsa loquitur”

In the pilot for “NYPD Blue”, the DA, a woman in the reigning TV mode (beautiful, dressed-for-success, smarter than the men) says to the main guy in the show, a beat cop who has just been humiliated on the witness-stand:  “I’d say ‘Res ipsa loquitur’, if I thought you knew what it meant.”
OK -- pretty snide, pretty snarky.  But still.  Don’t you be caught out -- at a cocktail party, or between the sheets -- not knowing this phrase !   Here you go !

[Update, 1 second later]
OK so -- Press Pause, then Play, and the guy says, grabbing his privates (you'd think he'd be a grease-spot by this point, but what a comeback):
        "HEY!  Ipse this, you pissy little bitch !"

(And so, in the battle of the sexes -- 40-All.)

I understand that, later in the series, the two have an affair.  Still, neither debuted with a very good pickup line.  You're better off learning Latin.

So, next time you're in a singles bar and spot some hot broad [memo to self:  be sure to find a more-PC description before posting], simply sidle up to her, drink (not privates) in hand, and intone suavely:

"Vivamus, mea pulchra, atque amemus."

(That's Latin for 'Howdy, my hottie, let's get it on."  Only, in Latin it's in very good taste.)

Chances are she will coyly/archly/demurely reply (her ripe lips sensuously molding the classical vowels):

"Res ipsa loquitur, big guy."

Now you know you have a playmate for the night.

For a cool dude
and a hot dame,
check this out:


monostich (XXIX -- resartus)

~          ~

word    /less     /  
                               l y     .   .     .

~           ~

[For an interpretation of this deceptively simple-seeming poem, click here.]

Thursday, September 29, 2011


Just kidding.  (They weren’t really Senators, just Congressmen.)

NEW !!

For hot hard-hitting detective fiction, click here:

For dames-a-million, click here:

For hot curvaceous dames, click here:

[Warning !  Banned in Pakistan !!]

Enjoy !


Anyhow, you arrived here by mistake.  This here is a math & philosophy site.  We discuss things like:


            Category theory.
            The continuum hypothesis.

            History of mathematics.

            Topology, and in particular  The Urysohn Metrization Theorem.

Especially recommended:

            Consilience in mathematics.

If you’re more interested in thrilling yet cerebral detective fiction, check this out:


Wednesday, September 28, 2011

On What There Is

Existence is -- what existential quantification expresses.
       -- W.V.O. Quine, “Existence and Quantification”  (epigrammatic punctuation added) 

And, contra a couple of celebrated slogans of Quine:

The locution ‘ontological commitment’ is not one I have any use for, and neither do I care to ask or to answer the curious question “What is there?”  I say “There are chairs in the room,” and if someone wants to say “Therefore there are chairs”, tout court, it sounds odd… If this is ontology, then ontology is a mouthful of air.
-- Paul Ziff, Semantic Analysis (1960)

The subject of this essay is ontology; we gave a foretaste of the subject here.

By its dictionary definition, ontology is the study of Being.   Now, for me, “What is Being?” is the ultimate conversation-stopper;  that question, like Being itself in so bald an encounter, is like a diffuse and vaguely repugnant blancmange, filling all space.   It is questions like that which persuaded me early on that I was not interested in Philosophy.   And at that level, I still am not.

(Similarly, this:
The meaning of a remark in any language.
-- section-heading in: Jonathan Cohen, The Diversity of Meaning (1963), p. 154 )

Quine, it turns out, is of like mind, for he remarks, of the epigram above, “This is as unhelpful as it is undebatable, since it is how one explains the symbolic notation of quantification to begin with.  The fact is that it is unreasonable to ask for an explication of existence in simpler terms. … Explication of general existence  is a forlorn cause.”

At only one level down of abstraction, philosophers have traditionally brooded upon the ontological status of abstractions -- “whether concepts have a supramundane, or only a psychological existence;  whether they are transcendent intuitables or only private instrospectibles.” (Gilbert Ryle, “Ordinary Language” (1953).) 
For hardcore Realists like Meinong and even early Russell, “Consistently with the assumed equation of signifying with naming, they maintained the objective existence of all sorts of abstract and fictional entia rationis.” (id., “The Theory of Meaning” (1957).)

The question becomes more compelling in the context of the philosophy of quantification (“To be is to be the value of a variable,” quoth the Quine); and shapelier still in the context of what counts as an ‘item’ for, say, physics.
(Incidentally… I have borrowed the title of this post from a well-known work (1948) of the eminent Harvard philosopher, who taught me logic when I was but a wee lad.  Quine, having passed to a different realm of quantification, will doubtless not object.)
(Sudden update:  Just browsing around, I notice that this is actually the second time I stole  the title -- Shakespearian in its simplicity -- of my former magister;  earlier effort here.)

Thus, the focus shall be now  not on Being, but on beings -- on what counts, for us, as entities, when we pursue science, and why.   As Quine nicely puts it:  “Ontology … is a generalization of somatology.” (Roots of Reference (1973), p. 88).  The top-down approach to ontology -- “What is Being?” -- is baffling;  but starting from what we understand, we might build upwards.

Thus, we confront more tractable matters of hypostasis (reification) and individuation.  
By getting down in the weeds concerning what choices have been hit upon by the various scientific enterprises that have had to deal practically with such matters, we might in time return refreshed to the general question.

Consider this analogy.  The ancient Greeks asked themselves, “What is motion?”, and discovered that, once you dig into the matter, it’s more puzzling than it looks  -- cf. St. Augustine’s celebrated quip about the meaning of Time:  If you don’t pose the question, I know perfectly well;  if you ask me point-blank, I am flummoxed.  Some philosophers even came to feel that the very notion of motion was paradoxical, or impossible : compare more contemporary thinkers with similar doubts about Free Will.  (Eppur’, in both cases, si muove.)  Once one has studied the matter, however, in classical dynamics and in special relativity, and understood how (Achilles and the tortoise) an infinite series may yet sum to a finite value, you return to the matter with new confidence.

~     ~     ~

We must concede at the outset that ontological quandaries seldom arise in daily life.  Only very occasionally, and that not systematically, do you pose What-There-Is questions.  Things like:  Does Bigfoot exist?  Does Dark Energy?  (Everyday life if you’re a physicist, that is.)   True, a questing undergraduate may once in a while trouble himself with questions such as the Existence of Other Minds, and Is the Universe an Illusion;  but such queries cease once he gets himself a proper girlfriend.
~     ~     ~

The atomists, in their purest and here somewhat idealized form, imagined a world in which indivisible particles were the basic Things, all else being combinations of these, and thus, in the most parsimonious view, ontologically subaltern.   (Leibniz imagined something rather like this for the noösphere, with his ineffable monads.)  And indeed, we can well imagine a world, in which such entities entered into but fleeting congeries, without definite or lasting outline, and crucially, with no emergent properties for the ensembles (thus, in particular, no reproduction of atomic ‘clouds’).   Such a world would have an essentially unambiguous, monolevel ontology.

Now, however, consider a different world:  a pool table.  And -- for this is necessary too, and we rather finessed the question in the fable immediately above -- consider that we have been given a task:  viz, to characterize the perambulations of matter atop it.   In this scenario, it is the billiard balls themselves we must consider, and in no wise the atoms that constitute these.
Consider now Euclidean geometry.  Here, fundamental ontological status was posited for just two entities:  the point, and the line.   (Notoriously,  one can present this geometry in a ‘substrate-neutral’ way that professes agnosticism as to the nature of these posited ‘points’ and ‘lines’ -- beer-mugs and beer-mats, we could call them just as well.  And, more tellingly, styles of geometry in which the point and the line are dual to each other, thus interchangeable.  But to consider this further, were to sail afield.)
No higher figures were distinguished as fundamental -- neither the triangle nor the ten-million-and-seventeen-gon  enjoy axiomatic status as part of the furniture of the Euclidean universe.  And indeed, in the broader perspective (the Erlangen Program) which sorts out and makes sense of a variety of geometries, it is not the individual figures  on which all things hinge, but their transformations -- their symmetries, and the way these form an algebraic Group.

~     ~     ~

The prototypical example of an indisputably extant entity is you.  You are physically coherent, you have purposes and plans, you are self-aware from moment to moment; ontologically, it doesn’t get better than this.  And if you’re Donald Trump, you’re done:  end of ontology.  You slide through life like a bubble down the duodenum, a blob of solipsism.
For the rest of us, we embrace the existence of Other Minds, and indeed quite on a par with our own.  
And now comes (as Blessed Pope John Paul II put it ) an ontic discontinuity or  “ontological gap” between ourselves and the beasts.   There is a spiritual truth to this, but biologically, it does not cut nature at the joints.

(Note:  That gap itself should not be over-emphasized, since, in the grand mediaeval vision of the scala naturae, it is just one of several such.  Roughly:
archangels -- seraphim -- cherubim -- penguins -- mankind -- critters -- Protista -- sludge.)

[Click that image for more exciting details!]

So we admit the biosphere -- only, just where to draw the lines among individuals gets murky, the more you learn about what-all is out there.  Herd animals, species all of whose members are genetically identical, parasites, incorporated former parasites such as plasmids and mitochondria, slime mold, elm forests (one giant subterraneanly-connected plant), and even such exotica as the cast-off arm of a male cuttlefish:  as Darwin put it, “So completely does the cast-off arm resemble a separate animal, that it was described by Cuvier as a parasitic worm”.
There is no fact-of-the-matter about such cases; their intershadings show that our question, Which are the functional individuals?, must be more sharply posed.

~  Posthumous Endorsement ~
"Were I alive today, and in the mood for a mystery,
this is what I would be reading: "
(I am Quine, the great and powerful;
and I approved this message.)
~         ~

Let us revisit the examples of the pool table, and the geometries.   Here the basic entities were identified relative to certain transformations of the roster of potential entities:  the billiard balls caroming about, rebounding, never blending, proved to be the units to reckon with here.   And in modern mathematics, the symmetry transformations of the individual geometries proved more important that the various squiggles and shapes (or collections of squiggles and shapes) that undergo them.    So perhaps the way forward is to consider the kinematics of life. Ecology, that is, and Evolution.

When the theory of Natural Selection was introduced to the world in 1859, species rose to prominence in our conception of the way the world really is, right in the title of that great work, The Origin of Species.  Individuation can be problematic when we contemplate such things as animals undergoing complete metamorphosis, sessile vs. vagile stages,  and so forth:  but at each moment the species are (in the somewhat idealized classic view) sharp in outline, non-interbreeding, reliable entities.  (From a NeoPlatonist perspective, the species may even be more real than any of the variously imperfect and misshapen individuals that instantiate that ideal.)  For a time, Nature red in tooth and claw was conceived as a battle among these  supra-individual entities, competing, going extinct -- tyrannosaur versus triceratops. predator and prey, the early mammals peering out discretely from the prehistoric underbrush, waiting their chance.

Yet no sooner had we managed to wrap our heads around the notion of the species   as the fundamental unit of biological accounting (which in particular, delightfully,  cleared up the mystery of sex), than a pot of cold water was flung in our face:

Why should a female  produce offspring carrying only half her genes, when by parthenogenesis … she could produce clones…?  The simple answer, that the variability produced by sexual recombination makes for greater adaptability, and is therefore ‘for the good of the species’, will not serve.  Darwinian natural selection … has to do … with individuals,  and selection for group characteristics  has no simple place.
John Bonner & Robert May, introduction (1981) to a reprint of Darwin’s Descent of Man.

The next step (and the consensus of current thinking) settles neither on individuals nor on groups, but on a unit which, in Darwin’s day, was not even known specifically to exist:  the gene.  The argument has been superbly laid out for the general public in Richard Dawkins The Selfish Gene, so we needn’t walk through the reasoning here.  The upshot is as follows:
Richard Dawkins, The Selfish Gene (1976; 2nd edn. 1989), p. 34:

In sexually reproducing species, the individual is too large and too temporary a genetic unit  to qualify as a significant unit of natural selection.  The group of individuals is an even larger unit.  Genetically speaking, individuals and groups are like clouds in the sky or dust-storms in the desert.  They are temporary aggregations or federations.

(This reminded me curiously of a suggestive passage from a historical-espionage novel by Tim Powers, Declare:
You know what the djinn tend to be made of, from moment to moment -- wind, dust, snow, sand, agitated water, swarms of bugs, hysterical mobs. )

Anyhow, Dawkins goes on to make clear that his definition is functional not anatomical:

The largest practical unit of natural selection -- the gene -- will usually be found to lie somewhere on the scale between cistron and chromosome.

This functional/structural rather than physical definition  is reminiscent of the notion of phoneme, as opposed to a phone or sound.

Edward Wilson concurs:

The average differences between people in different localities … are narrowing.  Genetic homogenization has similarities to the stirring together of liquid ingredients.  … But the most elemental units, the genes, remain unperturbed.  They stay about the same  in both kind and relative abundance.
-- E.O. Wilson, Consilience (1998), p. 273

Now we feel we are back on familiar ground.  These genes are rather like biological analogs of atoms, in the old Greek well-behaved, billiard-ball-like conception of these.  They just take some getting used to.

Yet even after the first ontological question has been answered (What is there?) in favor of the gene, there is still the second (What is it?).  As.

Should we think of a gene … as a structure that is replicated, or as information that is copied and translated?
J. Maynard Smith & E. Szathmáry, The Origins of Life (1999), p. 10

Actually, Dawkins makes a much simpler and apparently unanswerable argument for thus privileging the gene as a unit of accounting:

The true unit of natural selection has to be a unit of which you can say it has a frequency.

(Individuals and groupings obviously don’t fit the bill.)   This argument is completely general, and is independent of the details of biology.   Thus in particular, it should apply (if it is valid) mutatis mutandis  outside of biology.
For the style of thought, though not the detailed content, cf. Quine (“On What There Is”), maintaining that quantification is “the only way we can involve ourselves in ontological commitments”.

Further, compare this:
Gerd Gigerenzer et al, The Empire of Chance (1989), p. 246, quoting Read Tuddenham:
To the statistician's dictum that whatever exists can be measured, the factorist had added that whatever can be 'measured' must exist 

[For a brief and untendentious survey of the various candidates for status as a Unit of Selection, click here.]
~     ~     ~

Having persuaded us that the gene, rather than the individual or the herd or the species, is the fundamental reckoning-unit of life, Dawkins then complicates matters in a way reminiscent of those extended and ill-individuated entities like elm forests and slime molds, or even Bertrand Russel’s definition of the number ‘four’ as the set of all foursomes:

What is the selfish gene?  It is not just one single physical bit of DNA, it is all replicas of a particular bit of DNA.  … ‘It’ is a distributed agency, existing in many different individuals at once.

By this time it is clear that, the more you look into it, the ontology of biology looks more like biology and less like Ontology -- in that original maximally abstract metaphysical program to whose allurements we confessed ourselves deaf.

Still, this business of the gene, defined as a functional rather than a spatiotemporal unit, does get us back to old-fashioned ontology as practiced by philosophers.   Quine sparkles at this.   He wastes no time on “What is the Nature of Being?”, but rather rolls up his sleeves, and, in the chapter “The Ontogenesis of Reference”, constructs a plausible, insightful, and wittily-told fable of how we acquire our notions of objects, and what it is that we acquire.   (A wry tribute to the style of mind involved in such exercises  can be appreciated here.)   By page 98 of Word & Object (1960), he has made a case for the ontological respectability of “a single sprawling object”, and admonishes:

There is no reason to boggle at water as a single though scattered object, the aqueous part of the world.  Even the tightest object, short of an elementary particle, has a scattered substructure  when the physical facts are in.

To which, Amen;  adding only that, when even more surprising physical facts are in, concerning indistinguishable elementary particles (bosons, at any rate), there is a sense in which these too could be considered a single scattered object.

The genes (or bosons), as thus conceived, are only, so to speak, accidentally scattered;  things empirically might have been otherwise.  Consider now rather entities that are scattered by construction, by definition:  higher-level entities, sets or collections of lower ones.

Questions about the ontological status of such things can arise even in the everyday pre-philosophical world.  In what way can we say that the following are genuine entities, with lasting contours and cross-temporal identification, despite the changing roster of the individuals that make them up? -- Your (nuclear/extended/….) family; the Boy Scouts; the nation-state to which you belong.   This is a moral and practical matter, not simply ontological:  having pledged allegiance to any one of these at t=0, are we likewise bound at a later time, despite their ever-shifting membership (and foreign policy)?  (I address such questions in a projected essay, “Continuity of Identity”.)
So, we have noticed an actual ontological question within the cares of daily life.  Still, it is not to a metaphysician that you would turn for clarification, should your eighth cousin thrice removed suddenly show up on your doorstep, claiming ties of kin that give him the right to move in with you and to borrow your car,  nor to an ontologist, were the Boy Scouts ever to get the Bomb.

In Biology -- the fons et origo of structured higher-level objects in scientific practice -- such entities include:  species (made up of conspecific individuals);  genus (made up of species); family (made up of genera); order; class; and so on up.  Here the ‘atom’ is the individual animal or plant;  there is no place in the traditional taxonomy of considering an individual as a congeries of genes -- and indeed the set-theoretical structure is completely different, the gene-sets in question being radically non-disjoint, whereas an animal is either in one species or another, not both.

In the nature of the case, it is clear that the higher taxa of biology are not ontologically given as such, but are confections of convenience, based  to be sure  upon what’s out there, and proceeding via sound and defensible principles.  Thus in particular, whereas a species as a whole does pretty much hang together or hang separately (say, in a sexually reproducing species, if the survivors are too sparsely scattered to hook up), there is no such selective linkage among the various n-level groupings in a taxon at level n+1.  Should the echidna ever bite the dust, ‘twill be a sad day for all lovers of monotremes; but the valiant platypus  still will soldier on.
There have also been major revisions in higher-order taxa;  even some quite familiar ones (reptiles, insectivores, puffballs) have  upon closer inspection  been dismissed as polyphyletic.

~     ~     ~

So much for the entities of biology.  What of Chemistry -- which is “the next level down” in terms of the agenda of Consilience?

Here we are in for a pleasant surprise.  No such agonizing and backtracking will be necessary as it was before.  The answer is:  atoms.   And not just atoms, in a row as it were, but, stacked, structurally stacked, in a most revealing way.  This is the Periodic Table of the Elements, first unveiled to a grateful world by Mendeleev, of blessed memory.  It is possibly the single most satisfactory scientific object on the planet.  Moreover its elements and its structure reach directly, consiliently, straight down to basic physics.  It is a wonder to behold.

There is even a loose analogy between atoms-and-molecules, on the one hand, and genes-and-individuals, on the other.  Loose, but better than most of those cited by Wilson in his ambitious book.
~     ~     ~

Physics, by contrast, is in no such happy case.  Such subjects as cosmology or thermodynamics or hydrodynamics don’t seem to have ‘basic-level objects’ in any obvious way.   There are, to be sure, the “elementary” particles, but these have been as troublesome as they are helpful, referred to distastefully as the “particle zoo”.   What with quarks and various subtle symmetries, these have now been regimented into something more satisfactory, though still nothing like as self-explanatory as the Periodic Chart.  Further, they do not span the whole of physics, but only of Particle Physics, a subfield.

There are, nonetheless, deep ontological questions within physics, with still-tentative but sophisticated answers.   I am not currently competent to comment on these, but a selection of intriguing quotations may be consulted here.

~     ~     ~

Astronomy affords relatively little by way of ontological interest; but consider this wise observation by astronomer  Mike Brown (quoted in The New Yorker for 24 July 2006):

Planets are like continents. ‘Continent’ is a good geological word, but, like ‘planet’, it has no scientific meaning whatsoever.

This is an epigram, and thus permits itself a breezy way with words; meaning here really means ‘ontological status’.
The point is of course lost on the layman;  witness the heavy coverage of Pluto’s “dethronement” by the latest Kuiper-belt detritus, as though this were of the least importance for the understanding of our cosmos.  But far more important, the opposite assumption seriously misled some of the finest minds of the Middle Ages.  For Galileo’s misadventure with circular planetary orbits, click here.  For Kepler’s fine failed vision of the planetary distances reflecting nested Platonic solids, here.  Their basic insights were sound, even brilliant; but planets (i.e., floating lumps of dirt) simply don’t have the ontological status to deserve such angelical constructions.

~     ~     ~

In Mathematics, the conundrum concerns, not so much the existence of thís (class of) object versus that (class of) object, let alone which are the ‘basic-level’ objects (I know of none), but the existence of any objects überhaupt.  That is, we have retreated from the question of beings, and are back at the bad old topic of Being.   At best:  for in fact, the question is probably not best posed in terms of “the existence of mathematical objects”, which threatens to involve us in fruitless discussions of what they are exactly (e.g. the integers as really sets of one sort or another, including Russell’s extravagant suggestion), whereas in fact,  mathematical objects or entities or thingums or whatever they are, are the very plume and prototype of substrate-neutrality;  a less contentious formulation would be “the transcendence (epistemological independence) of mathematical truths”.  (One is less likely to wonder whether a “truth” is, say, pink, than whether an object is.)

Let us consider a specific question, with an at least superficially ontological aspect, that is more localized than that vast barely-answerable question about the ontological status of mathematics as a whole.  (My attempt at a Realist answer to that one begins here.)
For example:  Does there exist a topological object of the following description:  It is regular, second-countable, yet could never be assigned a metric?   Urysohn looked into the matter, and concluded that none exist.  But it wasn’t by looking around, or by exhaustive search, that he reached this conclusion, the way you might drag every inch of Loch Ness and finally conclude that it contains no monster.  Never quitting his armchair, he deduced the result, in a way in which things were never really serially considered.
Indeed we had to strain a bit to cast the problem in the form of a question about ‘existence’ at all:  it’s not like finding Bigfoot, or failing to find him.   If biology were like mathematics, then we could infer the existence or non-existence of Bigfoot, without ever actually spotting him, nor searching the wooded hills, based upon abstract patterns elsewhere in the system.  This is one of the very many ways in which biology and mathematics are not the least bit alike (I mention this only because of the counter-program of consilience - a nice idea, but a will-o’-the-wisp.)

Mathematics does nonetheless afford good grist for the ontology-mill, indeed more clearly ontological than anything we have yet seen.  Namely, the entities posited by what are known as “existence proofs”.    There is no properly (intra)mathematical doubt about these purported objects -- they uncontroversially have such&such properties, if indeed they are there to bear properties at all.  The problem is with the special sort of purported demonstration that says, although we may never see such a thing, yea verily, it doth exist.  Such proofs can be purely deductive, non-constructive; so that, although we are assured of the existence of something fitting a given description, we are given no hint as to how to find the item in question.  Understandable ontological qualms about such spectral beings led to the founding of a school of mathematics that rejects such non-constructive proofs:  Intuitionism.  This dog-in-the-manger school gets vastly less play in actual day-to-day mathematical practice, than it does in philosophy books.

The one place within mathematics where ontology is definitely at home is Set theory.  A typical credo:

I have written this book from an uncompromisingly realist or platonist position; that is, I have taken the viewpoint that  in some sense  sets do exist,  as objects to be studied, and that set theory is just as much about fixed objects as is number theory.
Frank Drake, Set Theory (1974), p. 18

Indeed, this subject is often practiced by ontologically-inclined philosophers (such as Quine) and taught in the philosophy department.  (That other mathematical outlier -- logic -- is likewise often so housed.  I took Intro Logic -- “Phil 140” -- from Quine.)  It is from this milieu that we got the slogan “To be is to be the value of a variable.”
Quine’s quip, suitable for recital to the babe in the cradle, is actually trickier than it sounds, owing to his notion of substitutional quantification, which does not express existence, vs. objectual quantification, which does.  There is a grey area of entities which, like most nonalgebraic real numbers, are assumed to lead just as robust an existence as the algebraic irrationals, but which are not finitely specificable.
(Further remarks on the ontology of logic and set theory  here.)
Note, incidentally, a certain resonance between this last distinction, and the notion in physics of observables -- an attempt to get a firm handle on What There (Really) Is, amid the welter of mathematical abstractions.
~     ~     ~

Linguistics and Anthropology come each in two flavors: traditional mostly-European philology and Völkerkunde, and a present-day, typically American scientistical approach.  The former fall under the Humanties.  They were not much concerned with positing abstract analytical entities;  the “parts of speech” go back to ancient times, and were defined intuitively, largely morphologically, which is something you can get away with in the highly inflected classical languages like Latin or Sanskrit or Greek.   The latter, by contrast, strive (or, in the case of Anthropology, strove; now it strives only to be politically correct) to be honest-to-goodness sciences like physics or anything else.   Many intricate and closely-argued entities were posited and fought over, for phonology and syntax (some in morphology and semantics too, of course, but those weren’t worth fighting over);  and anthropological got algebraically structural in its analysis of kinship systems.  Both fields were self-aware of what they were up to, and there was a running discussion of the ontology of the theories, under the rubric “God’s Truth vs. Hocus-Pocus”.  The God’s Truth faction took a Realist stance towards the posited analytic entities; the Hocus Pocus faction, a Nominalist.

~     ~     ~

Somewhat surprisingly, the study of Folklore is also distinguished by the positing of abstract analytic entities, known as motifs; and this, already in the early years of the twentieth century.  These were carefully and exhaustively catalogued in the Stith-Thompson Motif Index.  Their combinatorics determine the tale-types around the world.   They are reminiscent, not really of atoms (since the characteristics of molecules are so wildly ‘emergent’ above anything visible in the atoms that make them up;  cf. H2O, I rest my case), but rather of genes.   Okay, the analogy is loose, but no worse than that of genes & memes.  Indeed, motifs were the forerunners of the meme idea, and already much better thought out.  There is even a sort of folkloristic analogue of the allele:  the oikotype.

There is no reason to boggle at water as a single though scattered object,  the aqueous part of the world.  Even the tightest object, short of an elementary particle, has scattered substructure  when the physical facts are in.
-- W.V.O. Quine, Word and Object (1960), p. 98

In support of this:

(1) “the aqueous part of the world”:  cf. “empty space”, an anything but simply-connected entity (object).
(2) “scattered substructure”:   Unsure quite what he meant by this -- quarks are substructure of hadrons, but were unknown -- nay, unhypothesized -- in 1960, the publication-date of Quine’s classic.   However, a “smeared-out” (not really ‘substructural’)  nature of something so tiny-tight as the electron (still regarded as truly elementary) was suggested already

~     ~     ~     ~     ~

Postscript:   These are the posts so far that have touched on ontology. These largely concern mathematical Platonism, which we won’t focus on here,  other than to say that Quine’s quip ("To be is to be the value of a variable"), suitable for recital to the babe in the cradle, is trickier than it sounds, owing to his notion of substitutional quantification, which does not express existence, vs. objectual quantification, which does.

Tuesday, September 27, 2011

Epistemological Apophthegms

(1) Die Löwen aber sprechen doch;  nur verstehen wir sie nicht.

(2) A question often posed by philosophers:
Suppose I tell Donald Trump to go stuff himself.  He then goes, and stuffs himself accordingly.  But-- how do we know that he was following a rule?

(3)  Epistemologists have at last determined, what it is like to be a bat:   You get to fly, and insects taste yummy.  Not so bad as some people had supposed.

~     ~     ~

Knowledge Explained

Q:   Can we, to some degree of accuracy, and with any certainty of our success, know the external world?
A:  Yes.

Q: Yet how can this be so?
A:  Because God has so ordered and appointed the world in which we live, and the minds of us who live in it, that we, by His grace  and by our own inborn propensities, supplemented by investigative efforts undertaken of our own Free Will, may come to learn the broad outlines of the Creation.

[Technical note:  There exist other answers, but no better answers.]

[More such profound insights here.]

Monday, September 26, 2011

Penguin funporn

What is it about you all?  People keep searching on the term "funporn" and somehow finding this site.  Sheesh!  That's not what we're about!  Topology, ontology, these we got!  Funporn, schmunporn, what's with that?

Still, vox populi, vox dei, so, here is some penguin funporn:

Note that all penguins in these videos  are duly married and care for their babies
Not like some folks one could mention!
See you in church.

Sunday, September 25, 2011

Is There a Linguist in the House ?

Hamlet:  Do you see yonder cloud that's almost in shape of a camel?
Polonius:   By the mass, and 'tis like a camel, indeed.
Hamlet:  Methinks it is like a weasel.
Polonius:   It is backed like a weasel
Hamlet:  Or like a whale?  
Polonius:   Very like a whale.

Our friend Snarla has alerted us to one of the most brain-damaged and brain-damaging stories ever to be perpetrated by the Murdoch mouthpiece known as Fox “News”:
Bizarrely, the “news”cast does not even display the “Arabic” “messages” in any clear way -- you would think people would at least be curious. 
Gawker, however, does display them (see link chez Snarla).   Using my profound knowledge of ancient Arabian dialects, I was able to decipher them.   They read:

       f y thnk y cn rd ths, thn y r a fggng m*r*n.

[Another case where it helps to have a linguist handy  documented here.]


The broadcast was disturbing in another way as well.

For many decades, broadcast journalism, though not nearly as searching as print, did try to put a serious face on things.   Anchors like Murrow, Huntley, Brinkley, and Cronkite projected a sense of responsibility and intelligence.  Though they were personally no investigative or analytic giants, the subtext was that responsibility and intelligence were good things.

You see none of that on the Fox team.  An airhead prattles for a bit; then the anchor, equally clueless, raises no questions and elicits no details, but simply dumps on a bit of his own emotion.   They seem to be descended, not from the line of Murrow, but from game-show hosts:  dolts, and happy to be so.    Dan Rather always struck me as insecure:  aware that he was not all that bright, and bothered by it, trying harder.  Whereas the Fox bobbleheads are smug, and with cause;  as who should say,  We elected Dubya, and re-elected him, and with broadcasts like this one, we may just go and elect someone even dumber, like Perry.  How’ll y’all like that, pointy-heads?

Want a woodchuck with that?


Simply add


as a search-term to any Google search, and watch your results hugely improve !

Try it !

            mathematics woodchuck
            theology woodchuck
            topology woodchuck
            Urysohn woodchuck
            grommet-top curtains woodchuck
            sexxx woodchuck sexxx woodchuck sexxx sexxx sexxx
Sadly, the following do not work:

            a woodchuck and a rabbi walk into a bar
            now is the woodchuck of our discontent
            O woodchuck my woodchuck
            in the beginning was the woodchuck

nor, amazingly, does this:

            a woodchuck and a rabbi walk into a bar grommet grommet grommet

Our R&D department is working this issue.

Meanwhile, here is a fun phrase for G*g*l to index:

            A woodchuck by any other name would be a groundhog

[This message brought to you by the International Marmotic Society.
All rights prohibited.]

Saturday, September 24, 2011

Faster than Light

Updated here:

Quine on Motherhood

Mother’s day should be coming ‘round in about eight months or so;  and to celebrate this glorious occasion, we offer the following heartwarming tribute to Motherhood, from the pen of Professor Dr. Willard “Van” Orman Quine.  This one goes out to all mothers everywhere, wherever and whoever and whatever you may be !!

We in our maturity
have come to look upon the child’s mother
as an integral body  who,
in an irregular closed orbit,
revisits the child from time to time.
-- “Speaking of Objects”, reprinted in Ontological Relativity, p. 7

“Mama”, in particular,
gets set up retroactively
as the name of a broad …
-- ibid, p. 12
[Note:  In quoting this, we have adhered faithfully to the 140-character maximum on modern communications]

More mama !
More water !
More red !
[-- This cri de cœur occurs in Word & Object (1960), p. 92.  I have been obliged to re-arrange the word-order somewhat, so as to observe the metre.]

~     ~     ~

From the mailbag

Here follows a selection of reader responses:

So, I suppose you think that’s funny.  Well let me tell you something.  When you have reached my age, you will realize that it is not.
Humph, I am in a huff over this.
-- Ticked-off in Tulsa

There’s like a typo round about the middle line.
-- Nerd in Nebraska

Thank you, dear, that is lovely.  We mothers are so underappreciated.
Just loved that bit about mothers in orbit -- just like a shining moon!
-- Grateful in Georgia

Sunday, September 18, 2011

Physics funporn

Here’s a worthwhile article by another non-fan of all the foofaraw surrounding the Freaking Higgs Boson.   Evidently desperate for a journalistic hook, he somehow ties the whole thing in to the ultraworthwhile subject of … girl-bands.  Just how he does it, I have no idea, since the article is profusely illustrated with large photographs of these ultra-hot Rising-Sun girlbands,  and I like  couldn’t keep my mind on the subject.  What was the subject again?