Tullimonstrum gregarium

The past couple of years have seen a remarkable series of fossil discoveries, from Yutyrannus huali, through Pinguinus ingens, down to Protungulatum donnae.

This next creature does not represent a new fossil find -- that dates back almost half a century -- but rather a brand-new (and quite surprising) taxonomic determination.    Let the New York Times tell it:

Some thought the 300-million-year-old creature was a mollusk, like a snail. Others assumed it was an arthropod like an insect or crab. And others believed it was some sort of worm.

Now, a team of researchers from Yale University say they have figured out the monster’s identity:  It’s a vertebrate most closely related to the lamprey.

http://www.nytimes.com/2016/03/17/science/solving-the-tully-monsterscold-case.html

Scale model of the “Tully monster”

(actual length:  fifty feet)

Etymology of the Latin designator:

Tullimonstrum:  meaning, ‘monster found by Mr Tully’ (in Illinois)

gregarium: meaning, ungainly though it may have been, this creature liked to hang out with his homeys.

For a scientific summing-up of recent paleontological triumphs, click here.

Metrization, Mensuration, Measurement

We earlier treated the matter of a metric on a topological space, in a series of essays beginning here:

The Urysohn Metrization Theorem:  for real this time

Now, as lagniappe, we offer a pair of Metrization Epigrams, which the budding mathematician, stuck for an opener with that leotard-clad vision at the espresso bar, can use for a pick-up line:

 A discrete space is like the autistic atomism of the Tractatus, or Leibnizian monads.

An indiscrete space is (as one writer charmingly put it), “really quite crowded:  each point is an accumulation point of every other set.”  (One pictures the Jellyby children in Bleak House, ever tripping over one another’s legs.)

(Believe me, chicks go wild over such things.  Or at least, if you are like most gangly Adam's-apple-challenged graduate-students in math, it’s your last best shot.)

~

It is by no means only topological spaces that one might wish to subject to a metric: all kinds of things, really:    Which species lie how close to which others (and different metrics -- phenotypic, cladistic, etc. -- yield different results);  which languages are neighbors in linguistic space (again there is a phenotypic/cladistic distinction:  descent vs. Sprachbund); which people have a natural affinity with which other (seating-plans at dinner-parties; blind dates; etc.)  And more generally, what is the curvature tensor of the noösphere?

As (from a philosopher of science):

One sometimes wants to say that a theory has much more testable content than some other statement:  for instance, the Newtonian theory has much more testable content than ‘The moon orbits the earth’.  But our apparatus, as it stands, does not entitle us to say this.  We have no metric for testable content.

--John Watkins, Science and Skepticism (1984), p.  185

Compare Keynes’ critique of relative subjective probabilities.

Here a noted philologian on the notion as applied to languages:

Was nun die Sache selbst anlangt, so meine ich  daß immer Sprache und Sprache, mögen sie auch noch so weit auseinander liegen, in wissenschaftlichem Sinn  enger zusammengehören  als Sprache und Literature, seien es auch die  desselben Volkes.

-- Hugo Schuchardt, “Über die Lautgesetze”  (1885), in Leo Spitzer, ed., Hugo Schuchardt-Brevier (1921; 2^nd edn. 1928), p. 85

And here, indeed, he polemicizes against the nominalist treatment or ‘indiscrete toplogy” of diachronic linguistics:

Ist es denn nun nicht an sich ganz gleichgültig, ob rom. andare von adnare oder addare oder ambulare oder einem keltischen Verbalstamm herkommt;  ob in diesem Dialecte  l zu r  und in jenem  r zu l  wird usw.?   Welchen Sinn haben alle die Tausende etymologischer und morphologischer Korrespondenzen, die Tausende von Lautgesetzen, solange sie isoliert bleiben, solange sie nicht in höhere Ordnungen aufgelöst werden?

-- Hugo Schuchardt, “Über die Lautgesetze”  (1885), in Leo Spitzer, ed., Hugo Schuchardt-Brevier (1921; 2^nd edn. 1928), p. 84

~

This metaphor of ‘metrization’, outside the exact sciences, is very loose, as it is not strictly needed -- for taxonomic purposes, a more approximate neighborhood-system will suffice (a “Uniformity”) so to speak -- and still less is to be obtained.

As, a pair of British linguists comments:

One recent attempt by French researchers  has given us the term dialectometry, which describes a formula for indexing the dialect ‘distance’ of any two speakers in a survey.  So far, the utility of the index has not been demonstrated.

--J.K. Chambers & Peter Trudgill, Dialectology (1980), p. 112

This, in the synchronic arena, is reminiscent of the glottochronology of Morris Swadesh, who attempted a sort of carbon-dating of linguistic evolution, based on an assumed universal rate of lexical decay, in the absence of direct evidence.

[Update 17 January 2016]  Another cautionary tale about the fetishization of metrics:

Two of our most vital industries, health care and education, have become increasingly subjected to metrics and measurements. Of course, we need to hold professionals accountable. But the focus on numbers has gone too far. We’re hitting the targets, but missing the point.

http://www.nytimes.com/2016/01/17/opinion/sunday/how-measurement-fails-doctors-and-teachers.html?ref=international

Philologisches:

Whether, in that opening paragraph, the author wrote “metrics and measurements” intending to refer to two distinct though related concepts, or whether it was just an idle bit of synonymic accumulation like “bequeath and bestow” for those who might be unfamiliar with the somewhat technical word metric, is there unclear.  But it does raise a linguistic point.

The word metric, and its close kin meter, metrical, metrization, derive from Greek.

Mensuration and commensurable  go back to Latin mensura.

Measure comes ultimately from that Latin word as well, but via the phonetics of medieval French.

The same Indo-European root  is said to lie at the base of all of them.

English, an etymological patchwork, has some tendency to layer its vocabulary by origin, Greek roots being reserved for the most technical, followed by Latin,  with the Saxon vocabulary as jack of all work.  In this, it contrasts with German:  to Graeco-English oxygen, hydrogen, nitrogen  correspond homely-sounding Germanic compounds Sauerstoff (‘sour-stuff’), Wasserstoff, Stickstoff.   And Freud’s German originals for the English ego and id, were nothing but nominalizations of the ordinary pronouns, das Ich & das Es.

Roughly such tiering is at work in our Wortfeld of ‘measure’. 

Measure sounds reasonably English (though partly just because it chimes with pleasure and leisure, which are likewise French words in disguise), and is in everyday use for all purposes (though it also has technical specializations, as in mathematical measure theory).

Latinate mensuration (little used) is scarcely more than a stuffy synonym for ‘measuring’;  commensurate has everyday though businesslike uses (“a salary commensurate with the job responsibilities”); while commensurable is mostly technical, whether in its mathematical sense, or its more recent philosophic sense (“commensurable discourses”).

Metric is kind of a green-eyeshade/clipboard sort of word at best.  It becomes fully technical in mathematical uses like metric space and semi-metric,  finally soaring off into the intellectual empyrean with metrizable.

~

Still wearing our lexicographer’s hat, here is an attestation for a word with which I had previously been unfamiliar, used by a philosopher of science.  After a rather confusing Gedankenexperiment judging the verifiability of a physical geometric hypothesis, involving all sorts of skulduggery with measuring rods, and “tampering with the semantic anchorage of the word congruent”  (that’ll get you two weeks in the clinky  without the option), and in which Albert Einstein (from beyond the grave) plays a role like that of Fantomas, battling the equally post-mortem shade of Pierre Duhem,  our professor writes:

The required resort to the introduction of a spatial dependence of the thermal coefficients  might well not be open to Einstein.  Hence, in order to retain Euclideanism, it would then be necessary to remetrize the space.  ….  Einstein’s geometric articulation of that thesis  does not leave room for saving it by resorting to a remetrization in the sense of making the length of the rod vary with position or orientation  even after it has been corrected for idiosyncratic distortions.  But why saddle the Duhemian thesis as such  with a restriction peculiar to Einstein’s particular version of it?  And thus why not allow Duhem to save his thesis by countenancing those alterations in the congruence definition which are remetrizations?

-- “The Falsifiability of Theories”, in: Adolf Grünbaum, Collected Works, vol. I (2013), p. 72-3

As indicated, I couldn’t really follow the dialectical taffy-pull in that conterfactual-strewn discussion, but simply cite the passage as though on one of those “citation slips” we used to rely on at Merriam-Webster.

~

I just now happened upon a passage which we quoted earlier in another context (here):  a use, by a mathematician (or if you prefer, a logician) of the in-itself-not-expressly-mathematical term measurement,  not in a technical mathematical sense such as measure zero or measure theory,  but sliding mathwards towards concepts very far from any plain man’s conception of “measurement” (as: wholly non-numerical, non-quantitative   fundamental group):

Mathematics is, as it has always been, largely the science of measurement.  But “measurement” must here be understood as referring to more than the meter stick.  The genus of a topological figure  measures one of its aspects;  objects of genus zero  are in a sense simpler than those of higher genus. 

There are many dimensions of measurement ….:  characteristic, transcendence degree, cardinality, fundamental group … Occasionally we are so successful in the science of measurement  that we can completely characterize an object … by giving, as it were, its latitude and longitude:  its measurements in the relevant dimensions.

-- Herbert Enderton, “Elements of Recursion Theory”, in:  Jon Barwise, ed. Handbook of Mathematical Logic (1977), p. 554

I originally cited that as a not-especially-successful attempt (in its first sentence) at a one-line characterization of What Mathematics Is.    Measurement, in the usual sense, is common to a great many studious activities, from chemistry to engineering to dressmaking.   He only manages, in what follows, to make that characterization  more or less work, by moving the goalposts  and re-defining measurement in his own Pickwickian sense.
 

~

A philosophically alert historian of physics  calls attention to a linguistico-philosophical subtlety in the word measurement as it is used in quantum theory:

In all cases, an observation is accompanied by a measurement.  The converse is not true, however, for we may quite well perform a measurement and yet fail to observe the result.  [ndlr:  That much is true but trifling, but then he goes on to make his point.]  Now in considering the disturbance generated by an observation, we must make clear that the disturbance is caused by the physical measurement, and not by the cognitive act whereby the result of the measurement is comprehended by the percipient. … The observation is rendered possible by the collision of the photon with the particle, and hence it is this collision which constitutes the measurement.

-- A. D’Abro, The Rise of the New Physics (1939), vol. II, p. 667

Here he is not making an actio/actum distinction in the term measurement (though one exists; for the actum, “Her measurements are 36, 28, 36”), for we are still dealing with actio here:  but he is at pains to remove the connotation of a (human) action -- a human act, which one foggy school of thought has deemed central and essential  to all of quantum physics.  Observation, D’Abro is saying, is a human action;  measurement is whatever triggers the collapse of the wave-function.

~

This whole question of measurement  is, for the man meditating over brandy, frankly pretty annoying.    We want to know the scheme of things -- if equations be at the base of it, well and good, the more general the better.  (As:  Hamiltonian dynamics;  Set Theory; Topology.)  Beholding Saint Peter’s or the Taj Mahal, we wish to savor the whole, and perhaps to penetrate to the aesthetic and formal ideas behind them;  but we do not wish to know the length or this or that member in centimenters, nor how much the materials cost, etc. Such matters are distinctly hypo-ouranian.

In latterday musings upon quantum theory, measurement has been lifted to a role rather like that of (in earlier days) action, or conservation of energy -- or rather, like that of the Demiurge, bringing entities (or the values of their parameters) into existence.  Yet in practice, they don’t always even tell you much about what you are trying to measure.

Measurements on the force of attraction between two electric charges  will not  in general  verify Coulomb’s law.  We observe that the force depends  in some peculiar way  upon the position of external charges, which suggests to us that the measured effects  are not entirely due to the system in question, namely, the two test charges.

-- Robert Lindsay & Henry Margenau, Foundations of Physics (1936), p. 524

On What There Is (expanded)

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.

Quine, it turns out, is of like mind, for he remarks, of his 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.”

(Similarly, this, self-stultified by its own generality:

      The meaning of a remark in any language.

-- section-heading in: Jonathan Cohen, The Diversity of Meaning (1963), p. 154 )

A pre-philosophical, psychosociological observation:  The opportunity of waffling-on about Being with a capital B, seems to bring out the worst in writers.  As, Emerson (well, not quite fair to ontologists, since it doesn’t take much to bring out the worst in Emerson -- an ordinary pen-nib will do), in his celebrated essay “Compensation” (1841):

There is a deeper fact in the soul than compensation, to wit, its own nature.  The sould is not a compensation, but a life.  The soul  is.   ….  Being is the vast affirmative, excluding negation, self-balanced, and swallowing up all relations, parts and times  within itself.

Now that is ten pounds of horse-doody  in a five-pound bag.

~

At only one level down of abstraction, philosophers have traditionally brooded upon the ontological status of qualities or attributes or essences -- “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 Don't Do Divorce Cases

Murphy on the Mount.

(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; 2^nd 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.

That 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: on the one hand, traditional mostly-European philology and Völkerkunde; and on the other, 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, strives (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 anthropology became 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 genial 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.

[Footnote] Contra-Quine:

It is not true that ideas face the bar of reality as corporate bodies:  rather, in the past, they evaded reality  as corporate bodies.  …  This word has, so to speak, a turnover ontology.  The “objects” (ie. the terms in which we classify the continuum of experience  into “things”), are not there for keeps.  In trying to handle … the continuum of experience, it is … proper to experiment with … diverse ways of clustering the flux into “objects”.

-- Ernest Gellner, Plough, Sword, and Book (1998), p. 64f.

Where does linguistics fit in?

[Our essay  Consilience in linguistics has been considerably updated, including this latest addition:]

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.

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

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.)

[For the full essay, click here.
For linguistics-internal constitutive factors, this:
http://worldofdrjustice.blogspot.com/2014/06/the-ontology-of-linguistics.html ]

Mathematical and Natural Definition compared

[This is the latest update to this essay, q.v. ]

Another parallel between mathematics and (e.g.) biology, as regards a certain type of ‘definition’.

Sometimes you are not trying to focus on a new concept in splendid independence, giving necessary and sufficient conditions to ‘be an X’, de-fining (demarcating) its boundaries between what-all is inside and what-else is out;  but, rather, starting from some homely, antecedently-familiar item Y, to define this new X as being similar to that Y.    Sometimes you say they’re similar, and leave it at that:

            A hare is like a rabbit.

            A coot is kind of like a duck.

Sometimes you add differentia:

            A zebra is like a horse with stripes.

Or, you may say that the new concept X generalizes Y, without giving necessary or sufficient conditions for membership in the generalization, with or without further examples of members of X:

            Amphibians form a taxon of animals that includes frogs.  (They ‘generalize’ the frog.)

            Amphibians form a taxon of animals that includes frogs and salamanders.

All these strategies are (so to speak) topologically distinct, the one from the other.

Compare, in math (an actual textbook example):

Locally convex spaces are topological vector spaces that generalize normed spaces.

Here the relatively exotic new concept “locally convex spaces” plays the role of amphibians in the example above, with the normed spaces (familiar from the nursery) filling that of our friends the frogs;  with an additional delimiter, topological vector spaces, basically saying:  “generalize, but not too far”.   Thus, if we said

Vertebrates form a taxon of animals that includes frogs.

that would still be a true statement, but the belt would have been let out too many notches to hold up the conceptual trousers.

Definition, Description, Delimitation

One of the signal developments in semantic theory during my lifetime  has been an increased appreciation for the role of prototypes in organizing our knowledge.  To introduce or elucidate a concept, don’t try to define -- to delimit -- the whole domain, which can get fuzzy around the periphery:  give a central, typical, illuminating example.  Thus

sparrows, and animals like that

clams and the like

are not-half-bad characterizations of the idea of ‘bird’ or ‘mollusc’.  You might need to learn a bit more become earning your doctorate in zoology, but for ordinary folks, for everyday purposes, that is pretty much what we mean by bird and mollusc. 

There are tons of such structures in mathematics, where the prototype literally came first and then was generalized.   Thus, the integers are the prototype for ring theory;  although, as a matter of idiom, mathematicians usually do not say “prototype”, but motivating example.  

(For further examples, and a vigorous defense in principle, from some leading Russian mathematicians, of the wisdom of motivating-examples for mathematical pedagogy -- and indeed, even for mature cognition -- try this:  Abstraction and Generality.)

Now, this procedure works only if the prototype is antecedently known.  Thus, to revert to zoology, suppose you run across the term Chelicerata and ask your naturalist friend what that means.  Casually he replies, “Oh, that’s like harvestmen and solifugae, and all that sort of thing.”  You’d probably be pretty much where you started out.

Such was my experience, while trying to learn what is meant by "vertex operator algebra", upon meeting this helpful hint:

“Chiral algebras are the prototypical examples of a vertex operator algebra.”

So profound is my ignorance of anything touching on the subject,  so stygian is the blackness of my nescience, that it got me no further forward.

~

The status of “What is …?” questions  differs pragmatically -- subtly but importantly -- depending upon circumstances, in particular what field fills in the blank.   Thus, suppose you ask, “What is exobiology?”, already knowing the sense of exo- and biology but being unclear as to what these parts mean in conjunction (sort of like the opposite of “internal medicine”, perhaps?  Like dermatology, or the study of scales and fur?).  Upon being told that, no, it means the study of extraterrestrial life (should any such exist), you have been told all you need to know. 

Take it a step further:  “What is etymology, as opposed to entomology?”  (a question which, as a licensed etymologist, I have indeed many times met).   In this case you’ll be enlightened merely by “Word-origins versus insects”.  For here your semantic Wissbegierde is probably minimal, and may be actually zero as regards one or other of the paronyms:  you simply want to be set straight about an easily confusable pair.  In this case, clarification happened via verbal signs;  but it need not.  The case shades into those in which no intension is involved at all, but merely extension -- reference.    As, “Which of the Wilson twins is Bobby?”   A satisfactory answer might be simply pointing;  the questioner is not asking, “Who is Bobby Wilson really -- as a person?”

We may say that, in this case, we have definition not as description, but as delimitation.   Such a style of defining is called ostensive definition.

(Note:  Such a duality between interior/intension and boundary/delimitation  may remind adepts  of that jewel in the crown of the higher calculus, the generalized Stokes Theorem, displayed in all its refulgence here.   However, the analogy is superficial.)

A similar case from the vocabulary of mathematics.   I ask, “What is a semigroup, as opposed to a quasigroup?”  Without the second phrase, I might be asking for a concise but contentful thumbnail, such as “like a group but lacking inverses”.  But perhaps I simply stumbled across both terms on the back of a cereal box.   Now my friend admonishes:  “Semigroups are the things we met briefly back in undergraduate algebra, remember?  Quasigroups are fancy new items which, if you can’t even recall the definition of a semigroup, you really oughtn’t to go bothering your head about.”

O-oh, so-o-o … Do we feel patronized by that?  Okay, here you go, an actual definition, quoted from Wikipedia:

A quasigroup (Q, *, \, /) is a type (2,2,2) algebra satisfying the identities:

• y = x * (x \ y) ;
• y = x \ (x * y) ;
• y = (y / x) * x ;
• y = (y * x) / x .

Nun, alles klar?

~

Sometimes to be met with in the practice of math (the praxis, rather than the pre-existing body of truth), and scarcely outside it, is the dialectical definition:  Posit, analyze, refute, sublate;  repeat until golden brown.    Lakatos’ Proofs and Refutations illustrates the process.  (For an example of such a “working, preliminary definition”, click here.)

~

Further illustration of the vocabulary, with concrete examples:

Just as Euclidean space can be thought of as the model Riemannian manifold, Minkowski space  with the flat Minkowski metric is the model Lorentzian manifold.

-- http://en.wikipedia.org/wiki/Pseudo-Riemannian_manifold

This is not “model” in the sense of mathematical “model theory”;  it is an informal term equivalent to the linguists’ prototypical.   The latter is occasionally also used;  as here, by algebraic topologist Raoul Bott, speaking pedagogically in the introduction to a text:

We use the de Rham theory as the prototype of all cohomology.

~

For further considerations, focusing mainly on math, try this:

    Mathematical and Natural Definition

For the lexicography of mathematics proper, this:

    “What is Mathematics?”