Minimalism in Physics (updated)

Truth is ever to be found in simplicity,

and not in the multiplicity and confusion of things.

-- Isaac Newton

[Note: 
In using the term “minimalism” in evaluating styles of physics, I am importing  into the philosophy of science  a term mostly associated with the arts.  The move may or may not be fruitful.  But here is a well-known parallel move, from Gerald “Mr. Themata” Holton, in The scientific imagination (1978), p. 7:

I have proposed … thematic analysis (a term familiar from somewhat related uses in anthropology, art criticism, musicology, and other fields).  ]

The whole enterprise of physics, from ancient times to today, is itself  in one sense  Minimalist, in that it seeks to sweep aside the riot of epiphenomena, and to discover underlying laws, from which that riot derives.  It does not so much banish the fullness of reality, as bracket it:  we hope later to derive much of it back, in an explanatory manner.  (Note:  Not quite the same thing as Reductionism.)

To some extent, all rational inquiry ‘minimizes’ -- idealizes, works with toy models, etc.   Some more than others -- economics notoriously so, tossing out so much bathwater that sometimes the baby goes missing.   Others roll up the sleeves of their labcoats and go in elbow-deep to the mess of reality, little bothering with economy or philosophy.   Chemists, in particular, seem perfectly content to potter about in labs, to discover stuff, invent stuff, patent stuff.  They literally multiply entities, in that they invent chemicals that weren’t there before.   Whether they thereby multiply them beyond necessity (mustard gas, thalidomide,  napalm, LSD) is a matter of individual taste.  But certainly the ethos is anything but austere.

And likewise, for the most part -- biology, geology, astronomy, engineering, what have you. 

But modern physics  raises parsimony to a central tenet, almost the prime purpose of the whole enterprise as currently understood.  This development being by now taken for granted among those of the guild, it may not be apparent how odd this really is.

The goal for some time has been the “Theory of Everything”.  This certainly sounds like a Maximalist program:  but really it is not.   For the knights who pursue this grail do not actually intend to explain any of the things that real people care about   and that motivated the enterprise of physics in the first place:  why the sky is blue, why snowflakes are the way they are, why clouds are shaped that way, what lightning is all about, why airplanes can fly…  (Purported explanations of these things exist, but the ones I’ve heard seem all fallacious.)   Instead, they want to wrap their arms around a passel of abstractions, so complex as to leave the plain man -- nay, any but the professional physicist -- behind many decades ago, and show that, at a still deeper level, they are all but facets of One Big Thing.  (Hedgehog physics, we might dub this.)  This is Minimalist, and ferociously so.

It may be objected:  All that is nothing but plain reductionism, which is simply to say:  Science.  No call to drag in an arts-related term like “Minimalism”.  -- But I believe there is an aesthetic dimension -- seldom mentioned in journal articles, though over-emphasized in popular writing -- which lies outside the bare logical necessities.  As,

“There shouldn’t be laws of physics,” Strominger maintains. “There should be just one law, and it ought to be the nicest law around.”

(Quoted in Shing-Tung Yau, The Shape of Inner Space (2010), p.  14.)

Gerald Holten, characterizing the attitude of Einstein (The scientific imagination, p. 281):

At stake was nothing less than finding the most economical, simple, formal principles, the barest bones of nature’s frame, cleansed of everything that is ad hoc and redundant.

In his own personal life, the legendary simplicity of the man was an integral part of this reaching for the barest minimum on which the world rests.

*

Central to the program is the “unification” of the various fundamental forces -- meaning, showing them to be symmetry-broken castoffs of an original single Force.    An analogy in evolutionary biology is explaining various related species  as having descended under various environmental pressures  from a common progenitor.   Only -- in physics, the enterprise is far more audacious than this analogy would suggest, if all you are thinking of are the breeds of dog, or the various canine species, or even the various land-mammals.   The forces are so fundamentally different in their phenomenology, that the task is more like tracing the common descent of the penguin, the echinoderm, and the paramecium.   Or even the mastodon, the gnat-swarm (considered as a sort of collective entity), and the sand-dune.   A tall order.

The reason so hubristic a program could come into existence despite the odds, is that it had an early success:  Maxwell’s unification of electricity and magnetism, back in the nineteenth century, truly a monument of the human intellect.  Now, later analysis has suggested that this success was something of a lucky fluke:  in the four macroscopic dimensions in which we reside, electricity and magnetism are both expressed by a vector.  You can not only analogize these, the one to the other, but calculate with them in the ordinary way -- say, forming their cross-product to get the Poynting vector.  In higher dimensions, electricity would be a vector and magnetism would be a tensor, and they would not play so nicely together.

The next success along these lines was far spookier:  the unification of electromagnetism with the “weak force”, into an unassuming-sounding entity called electroweak.   Now, this is far more bizarre than it seems. Electricity and magnetism were always rather like Batman and Robin, typically showing up together in the lab.  Whereas the weak “force” seems, to my untutored mind, like a force in some Pickwickian sense, like the  “force” of a metaphor in a poem.  A thing more different than electrostatic attraction or repulsion  can scarcely be imagined:  it deals neither in repulsion nor attraction, but rather in a handful of obscure and scarcely explicable processes such as beta decay.   Even to have conceived the project of their unification  was an act of extraordinary intellectual audacity;  the eventual success is, well, beyond any but specialist comprehension.

This new composite entity, this hippogriff, the electroweak, was subsequently unified with the “strong force”, yielding the hyperweak of today’s Standard Model.   The next -- and long elusive -- step, is the unification of that with gravity.   Now, to your average toddler, the natural analogy would be rather between electrostatic and gravitation attraction -- both, in their simple nonrelativistic forms, central forces obeying an inverse-square law    But your average toddler, like your average Nobel-Prize-winner-in-anything-but-Physics, would be mistaken.   And so the torch has passed to an ever-more-esoteric brotherhood, in particular  the magi of String Theory:  pale, spectral beings, who neither eat nor defecate, and whose results -- well, they do not as yet have anything so vulgar as actual verifiable physical results, mind you, but they do have theories, and conference papers, incomprehensible to all but the magi.  That does not mean they are on the wrong track;  perhaps they, and they alone, are on the right track, in which case, the more fools we.

*

A startling development in some corners of recent physics  is an actual ‘Maximalism’ -- basically, the catastrophic breakdown of any parsimonious project, yet not taken as a reductio ad absurdum of reductionism itself, but rather embraced, by amor fati (a fancy name for making the best of a bad bargain).   No longer can one really -- nor does one aspire to -- explain anything, since everything that might exist, does exist, and the (now uninteresting) facts of the matter in our own neck of the woods  can be chalked up to Selection Effect.  (We satirized this Rabelaisian Fay ce que voudras  here).   

Templeton-Prize winner Paul Davies,  in The Goldilocks Enigma (2006), p. 264, takes rather understated notice of this:

The disadvantage of the multiverse theory is that it invokes an overabundance of entities, most of which could never be observed, even in principle.  This profligacy strikes many people as an extravagant way to explain bio-friendliness.

Likewise, though for different reasons, the earlier Many-Worlds school (or cabal) of quantum theory,  in which entities -- again, entire universes in this case -- are multiplied, not simply beyond necessity, but beyond common decency.

The ethos of all this is atheistic -- a-anything, really.  It is perhaps no accident that Hugh Everett, an early pioneer of many-worlds, was (in Wiki’s words) “a committed atheist".  Or that the thélémisme of the distinguished hexagonal/pentagonal humanist  was taken up with gusto  by the diabolist Aleister Crowley, the stench of whose cinders may occasionally bother your nostrils, whenever a high wind blows up from Hell.

[Update 27 III 12]  Freeman Dyson in the current NYRB, reviewing a book by Margaret Wertheim about eccentric amateurs:

String cosmology is different. String cosmology is a part of theoretical physics that has become detached from experiments. String cosmologists are free to imagine universes and multiverses, guided by intuition and aesthetic judgment alone. Their creations must be logically consistent and mathematically elegant, but they are otherwise unconstrained. That is why Wertheim found the official string cosmology conference disconcertingly similar to the unofficial Natural Philosophy conference. The insiders and the outsiders seem to be following the same rules. Both groups are telling stories of imagined worlds, and neither has an assured way of deciding who is right. If the title Physics on the Fringe fits the natural philosophers, the same title also fits the string cosmologists.

[Note:  Dyson -- a notably fair man -- has long been a fixture of the Institute for Advanced Studies in Princeton; and the IAS, in recent years,  has been premier in string theory.  So Dyson's assessment here  is by no means that of an envious outsider.]

On the extra profusion of different string theories, a mathematician remarks dryly,

It was hardly an idea calculated to appeal to a man with a taste for desert landscapes  … There are more than 10^500 versions of string theory  lounging indolently about.

-- David Berlinski,  The Deniable Darwin (2009), p. 532-3

*

It will sometimes not be obvious, which proposals are Minimalist in spirit.  Thus, imagine some wretched Nominalist, who balks at the infinite, and proposes that the numbers needed for physics  are finite -- specifically, the field of integers mod a prime p (necessarily quite large, to accord with observation).   Finite’s gotta be simpler, more minimal, than infinite, right?  Roger Penrose retorts (The Road to Reality (2004), p. 359):

A physical theory which depends fundamentally upon some absurdly enormous prime number  would be a far more complicated (and improbable) theory than one that is able to depend upon a simple notion of infinity.

More precisely:   The problem is not essentially that the number is so large, but rather, with infinitely many primes to choose from, the choice would seem arbitrary:  in much the same way that the omniscient computer in  The Hitchhiker’s Guide to the Galaxy reveals, quite disappointingly, that the Meaning of Life is … “26”.

*

Differing from a theory-wide programatic theoretical minimalism, is a kind of personal cognitive-epistemological economy, described by Gerald Holton, The scientific imagination (1978), p. 158:

Fermi ordered the overwhelming and vast amount of knowledge  into a set of very few principles and ‘cases’, which allowed him to understand almost any new problem as an example of one of about seven primitive or primary physical situations.  Fermi would return throughout his career  to a listing or digest of the chief ideas in physics, which he had made when he first organized the field for himself as a young student.

Our own thoughts about such Leading Ideas in other areas, may be surveyed here.

*

A curious philosophico-cosmogonic anticipation of the TOE vs. Landscape divide  goes back several hundred years:

Leibniz … assure que la perfection de Dieu ne lui permettait pas de procéder d’autre manière que de la meilleure … mais Thomas d’Aquin sait que, créant du fini, un Dieu infini pouvait librement créer un nombre illimité d’univers différents, tous bons  et chacun commençant de manière différente.

-- Etienne Gilson, Linguistique et philosophie (1969), p.  163

And indeed, though Leibniz coinvented the calculus, we must say that, here, from a mathematical standpoint, it is Saint Thomas who is closer to the target.

Bonus quote:

Willem de Sitter found an exact solution to Einstein’s field equation … having no matter at all. … Why should we be interested in such a universe?  Because the real universe is of rather low density …

-- J. Richard Gott, The Cosmic Web (2016), p. 16

.

Axial-gravitational anomaly experimentally verified!

From the morning’s press:

The axial–gravitational anomaly should destroy the symmetry of particular kinds of particles that usually come in mirror-image pairs. The kinds of conditions needed to prove this unusual breakdown of a fundamental ‘conservation law’ can’t be created in a laboratory. But the researchers exploited a peculiar parallel between gravity and temperature to create a lab analogue of the anomaly in niobium phosphide crystals. Inside the crystal, the effect is as if a drawerful of pairs of gloves were suddenly to acquire an excess of right-handed gloves because some of the left-handed ones had switched handedness.
https://www.scientificamerican.com/article/exotic-physics-glimpsed-for-first-time-in-lab-crystal/

But … exactly that effect has been repeatedly observed in our own household, especially over winter! 

The effect is statistically too strong to be due to chance.

It’s a nuisance, too.  I’ve tried auctioning off the extra left-hand-gloves on eBay at very reasonable prices (more than half off the price of the original pair), but no takers.

Possibly there is an excess of right-hand-gloves in, say, Australia.  Some enterprising arbitrageur could make a mitt, I meant a mint.

The Trinity (triune unity -- re-renewed)

[In observance of Maundy Thursday,  a re-post  from yesteryear.]

I spend a fair amount of time in the company of Muslims these days;  indeed, at present, by an accident of the seating-chart, I probably spend more time in close propinquity with Muslims, than with Christians, Hindus, Jainists, Jews, and Zoroastrians combined.   (Lotta LDS, though.  Plus all that could change with the next re-org, as my next podmates might be Zoroastrians.)   [Update March 2017:  And now, in fact, our branch chief is a Zoroastrian.] There is an effort of good-will on both sides;  my Sunni neighbor points eagerly to passages in the Koran, where good things are promised to ‘believers’ (mu’miniin) rather than specifically ‘Muslims’ (muslimiin).  A kind-hearted man, he hopes to be with me in Paradise, and not to gaze down on me roasting in Hell.  (`Uqbaalak, ya shaykh.)

Now, we Christians know implicitly, that the doctrine of the Trinity is no polytheism:

that Father, Son, and Holy Ghost, are not at all like Apollo, Zeus, and Hera, say, but more like le père Dupont, at once father, and Frenchman, and fireman.   But to explain this to our Muslim friends, is difficult.   I often have to fall back on saying:  the Trinity is a Christian mystery; it may be true or false (in some transcendental sense of those categories), but it is no descendent, direct or indirect, of the sort of pagan polytheism which stuffed the Kaaba with idols, and peopled the trees with dryads, and Olympus with squabbling gods.  For us as for you, God Himself -- Allah -- Yahweh -- e’en He -- is indeed One.

Yet this unity by no means necessitates or logically entails, that there could be no parts at variance within the Godhead, even to dissension.  (Of course, their absence might be a truth of the Church, and thus beyond dispute;  I am speaking here only of logic, the only subject in which I have been ordained.)  How indeed could we ever know otherwise (save by some enigmatic Revelation)?  After all:  We are made in His image, and we ourselves are a bundle of contradictions;  and He contains us, as a proper part.  (Additionally, that Eloi, eloi passage would seem to point in that direction.)

~

C. S. Lewis saw rightly when he compared the notion of the Trinity (purely as regards its intellectual coherence, rather than anything theological) with the ‘separate’ faces of a cube -- which latter is, however, nothing more nor less than the sum of all of them.  (Indeed, if you were to go with a sort of ‘projective cube’, with antipodal faces identified, our new Cube (topologically a three-torus) would even consist of exactly three parts.)

The historian of physics D’Abro offers a similar parable, along the lines of Abbot’s Flatland (A. D’Abro, The Rise of the New Physics (1939), vol. II, p. 653), his quarry being however, not the Trinity, but the (in some ways similar) “wave-particle duality”:  or, as we might term it, the wave-particle identity.  He imagines our various perceptions of something we believe to be one entity, but which sometimes seems a triangle, and at others, a circle:  eventually we realize that it is a cone, seen now this way, now that.  And, regarding the separateness/unity of electricity and magnetism:

The theory of relativity brought about the fusion of the two aspects, no longer by utilizing the background of 3-dimensional space, but by introducing the more refined background of 4-dimensional space-time.   The underlying entity, the partial aspects of which are electric and magnetic, were found to be the 4-dimensional electromagnetic tensor  situated in space-time.

-- A. D’Abro, The Rise of the New Physics (1939), vol. II, p. 653

The Trinity, we may confide, whatever in its unknowable essence it may be, is at the very least as complex as a  tensor.

~

Pascal (Pensées, 1670 [posthum]), has a very odd passage, asserting the alienating nature of God’s complexity -- or perhaps not -plexity, but monolithicness :

S’il y a un Dieu, il est infiniment incompréhensible, puisque, n’ayant ni partie ni bornes, il n’a nul rapport à nous.  Nous sommes donc incapables de connaître  ni ce qu’il est, ni s’il est.

Ni s'il est ! -- A useful first step towards an antidote  might be to drop that assertion about God's lacking any parts.

.

The Ontology of Physics (updated)

The question at issue here is, What sort of entities are fundamental in physics?  E.g., in the late nineteenth century through early twentieth centuries,

whether atoms were real objects or only mnemonic devices for coding chemical regularities.

-- Abraham Pais, Subtle is the Lord (1982), p. 80

The idea of atoms in some sense  goes back to Ancient Greece; and today, they are taken for granted.  So it is surprising to laymen, how long opposition to a Realist take on atoms lasted among some philosophers and physicists (e.g. Ernst Mach).  An opposing view, from a leading German chemist:

Ostwald’s ‘Energetik’, according to which molecules and atoms are but mathematical fictions, and energy, in its many forms, the prime physical reality.

-- ibid, p. 83

Good bluff Rutherford, by contrast, had sucked atoms with his mother’s milk, and claimed that he “could see the little buggers as plainly as a spoon”.

Oddly, the debate on this seemingly practical laboratory matter,  had elements more characteristic of political or theological controversy, in which neither side has a prayer of of convincing the other by rational argument:

The most remarkable fact about the nineteenth century debates on atoms and molecules   is the large extent to which chemists and physicists spoke at cross purposes, when they did not actually ignore each other.

-- ibid, p. 80

~

Since that time, a host of new physical building-blocks have been proposed, and in some cases observed: from the unexpected and rather unwelcome muon (I.I. Rabi: “Who ordered that?”), to the massless chargeless neutrino (rather like Bishop Berkeley’s “ghosts of departed quantities”), through quarks, gluons, gravitons & gravitinos, selectrons & electrinos, axions, preons, virtual photons, phonons … such as might make even Rutherford gag.  But several of these are now widely accepted -- not as mere bookkeeping mechanisms, but as entities with further properties to be discovered;  so that the smart money has been on Realism, so far.

Ernest Rutherford,  swallowing an atom  but straining at a quark

Footnote:

We shouldn’t be too hard on old Ostwald  for backing the wrong horse in the Atoms Affair.   Dissident voices today would declare  as epiphenomenal not only atoms, but even the elementary particles of which those are admittedly merely bundles:  demoted to excitation-states of superstrings;  or emerging from the combinatorial-automaton structure of the world. 

Additionally, his Energetik has enjoyed a bit of a revival in some quarters:

  https://de.wikipedia.org/wiki/Energetik_(Philosophie)

More recently, information (or, solemnly, “The Information” -- Wheeler's "It from Bit") has emerged among some as a skeleton-key to everything else in the physical world.

Thus, at the bottom of everything, behind and beyond the Maya of the particle zoo, lies:

Thales:  Water.
Oswald:  Energy.
John Wheeler:  Information.

Stewardess:  Coffee tea or mi-ilk?
The Milesian:   Just water, thanks.

Or, a more recherché candidate, from philosopher Hilary Putnam:

Nothing has more physical significance than spectral measure.

(That might strike the layman as rather a … spectral candidate for the role of firmest substrate of all.)

~     ~     ~

The word “ontology” is not one you are likely to overhear at the bus-stop;  nor indeed does a physics-major typically run across it.   But the more we see physics as science (Wissenschaft) rather than a special kind of engineering (the “shut up and calculate” ethos of the years around WWII), the more we meet questions traditionally treated under that rubric -- and indeed, contemporaneously, even under that very name. 

As:

My own position is that the issue of ontology is crucial to quantum mechanics.
-- Roger Penrose,  The Road to Reality (2004), p. 785

Let us now return to the ontology of the consistent-histories approach.  The theory operates with entities called coarse-grained histories.  … The ontological status of the insertion of such a projector set  is still not fully clear. …  A history from a maximally refined set seems to me to provide a strong candidate for what might be regarded as ontologially ‘real’.

-- Penrose,  The Road to Reality (2004), p. 788

Present-day quantum mechanics has no credible ontology … The importance of having an ontologically coherent quantum mechanics cannot be over-estimated.
-- Penrose,  The Road to Reality (2004), p. 860, 865

Re the notion of macroscopic quantum superposition being unproblematic:

This is taking a ‘pragmatic’ stance  that does not really address the ontological issues.

-- Roger Penrose,  The Road to Reality (2004), p. 812

And, full-bore:

Many contemporary thinkers seem to have supposed that, in discarding its mechanist ontology, physics had discarded its ontology:  matter had been dematerialized … The very progress of physics itself  seemed to them to call for the renunciation of mechanism and materialism  in favour of the de-ontologised view of science presented by Mach.

-- John Watkins, Science and Skepticism (1984), p. 138

 

In philosophy proper, ontology is fundamental, being prior to anything else.   In its application to or rather analogue within  physics, by contrast, it historically comes behindhand, as a setting in order of what-all several centuries of reflection and experiment have come up with:  We may think of it as a kind of cast of characters, not fully drawn-up until the play has been written:  in the course of writing it, you find out you need a ladies-maid, and so eventually she is placed upon the prefatory page of Dramatis personae, that typographically precedes the play itself -- and as a nice afterthought, you name her Lisette.  Similarly, particle physics did not begin by being defined, a priori, as (back among the Greeks) the Science of Atoms, or (later) as the Science of the Proton, the Neutron, and the Electron, or (later still-- the Barock Age) as the Menagerie-management of the Particle-zoo (with a fixed given roster of inmates), nor as the Curating of the Wiggling of Strings.  There is a thematic continuity throughout all these stages, but the staffage keeps changing.

As for the role of this Ontology, or Cast of Characters, it is not (despite the spectral example of traditional metaphysics per se) just something to admire from afar, like Mount Rushmore, but rather, as Goedel said pragmatically re which axioms we should adopt for math and logic, they should themselves possess generative potential -- by their fruits ye shall know them.  Thus, hard-headedly:

Kepler’s theoretical ontology, unlike Gilbert’s, was not organically related to his laws;  even if it could be squared with the latter, which seems doubtful, it failed to make any contribution to the testable content of his system.

-- John Watkins, Science and Skepticism (1984), p. 197

~     ~     ~     ~     ~

As remarked earlier, I may well go to my grave without ever grasping the concept of an observable, much less physical ontology in general.   Still, it is helpful towards organizing my thoughts, to have an online scribble-space, so that the matter is, so to speak, officially a topic, a project under way.   For now, this is just a whiteboard on which to stow some juicy quotes.  Your own juicy contributions are more than welcome.
For a more general surview of the ontology of the various sciences, click here.

~     ~     ~     ~     ~

Physics may be defined as the art of saying things about stuff (or stuff about things -- predications concerning entities, for the fastidious).  But what are these entities, whereof we predicate?  In the first place -- observables.

P.A.M. Dirac, The Principles of Quantum Mechanics (1930; 4^th edn. 1958), p. 116:

From our assumption that the energy is an observable, there are sufficient stationary states for an arbitrary state to be dependent on them.

For a layman, this is bemusing.  The assumption that it’s an observable?   Can you observe it, or can’t you?  -- Evidently there is much more to qualifying as  “an observable” than merely being … observable.
(Compare Einstein, in one of his Zen moments: "It is the theory that decides what we can observe.")

P.A.M. Dirac, The Principles of Quantum Mechanics (4^th edn. 1958), p. 458 (re certain eigenstates):

Science contains many examples of theoretical concepts which are limits of things met with in practice  and are useful for the precise formulation of laws of nature, although they are not realizable experimentally, and this is just one more of them.

Emphasis added.  “Limits” in the mathematical sense.

Note that “not realizable experimentally” does not constitute much of a disability.  What, after all, is?  “Carthage lost the Punic Wars”; “I love you”; “E8 is a 248-dimensional rotation-space”:  no, almost nothing is.

Robert Lindsay & Henry Margenau, Foundations of Physics (1936), p.402:

Quantities such as position, energy, momentum, and the like, capable of measurement… will be called observables,  although it is not intended to imply that they are observable directly.

The caveat is troubling enough;  but now this:

In quantum mechanics, the state of a system is no longer defined by means of a number of variables having an immediate intuitive appeal … In fact, it is not defined in terms of observables at all;  it is simply a function in configuration space.

Carl Hempel, “Problems and Changes in the Empiricist Criterion of Meaning” (1950):

Green, soft, liquid, longer than  designate observable characteristics, while bivalent, radioactive, better electric conductor, and introvert do not.

This odd assertion, by a well-known philosopher of science, seems more psychological than scientific.  It is reminiscent of Locke’s distinction between simple and composite ideas.

Eugen Merzbacher, Quantum Mechanics (1961, 2^nd edn. 1970), p. 153:

Following Dirac, we call observable any Hermitian operator which possesses a complete set of eigenfunctions.

This might sound opaque to some, but for a math guy it’s the clearest statement yet, by far.  Of course, what it amounts to physically, intuitively, is something else…

Gerald Holton, The scientific imagination (1978), p. 202:

The idea of making quantitative indicators of anything at all  fascinates some persons, and repels others as dangerous or absurd.  This difference is caused largely by thematically incompatible -- and therefore often unresolvable -- personal views concerning the ability of quantifiables to lead to … the deepest reality.

Note the silly dichotomy -- as though failing to lead to "the deepest reality" (a deeply suspect term) meant that they couldn't be "indicators of anything at all".

~

I had some fun above, playing with a rumpled old word like stuff, shoving it before the microphone of science.  Here a gifted popularizer  makes similar play  with pronouns:

[In its] Einsteinian reframing … is spacetime a something?

-- Brian Greene, The Fabric of the Cosmos (2004), p. 39

In that historical context, the question concerned the ontological status of (the novelty) ‘spacetime’, as opposed to the traditional notions of the independent entities, space, and time.

(More recently, spacetime has been demoted in some theories -- not returning to a Cartesian product of space and time, but being derived as an epiphenomenon of more fundamental items.  Thus, twistor theory, among others.)

If there is no aether to provide the standard of rest, what is the what  with respect to which this speed is to be interpreted?

-- Brian Greene, The Fabric of the Cosmos (2004), p. 45

If an individual electron is also a wave, what is it that is waving?

-- Brian Greene, The Fabric of the Cosmos (2004), p. 88

(Here the wordplay inheres not in the pronoun what, but in the verb.  He could more conventionally have written, “What is the medium for the wave?”, but the startling verbal formulation ‘makes it strange’, confronting us with something more fundamental.)

~

Stephen Hawking, A Brief History of Time (1988; 2^nd edn. 1996) p. 75:

The fact that confinement prevents one from observing an isolated quark or gluon  might seem to make the whole notion of quarks and gluons as particles   somewhat metaphysical.  However, there is another property of the strong nuclear force, called asymptotic freedom.  The concept of these entities  was already well-defined, or not, as the case may be:  certainly well-defined as bookkeeping conventions, if nothing more.   Asymptotic freedom -- “at high energies, the strong force becomes much weaker, and the quarks and gluons behave almost like free particles” -- simply adds a further mode of observing their effects:  and in this case, their effects when they are relatively ineffectual -- quarks on holiday.

Failure to be observable in isolation certainly doesn't make a thing "metaphysical" (in the colloquial bad sense intended here).  You cannot observe a "brother" in isolation:  dissect him down to his last tissues, nothing will reveal his brotherhood but the historical context.  Nor, perhaps, can you observe Coulomb attraction in a single isolated particle -- it takes two to tangle.  (I might be wrong on this -- the photon cloud and all that.  But how does the cloud tell you whether you've got an attraction or a repulsion?)

Steven Weinberg, Dreams of a Final Theory (1992),  p. 181:

The positivist concentration on observables like particle positions and momenta  has stood in the way of a “realist” interpretation of quantum mechanics, in which the wave function is the representation of physical reality.

Wiki, "Quantum field theory" (excellent article, btw):

In quantum field theory, unlike in quantum mechanics, position is not an observable.

From the point of view of quantum field theory, particles are identical if and only if they are excitations of the same underlying quantum field.  Thus, the question ‘Why are all electrons identical?” arises from mistakenly regarding individual electrons as fundamental objects, when in fact it is only the electron field that is fundamental.

The global phase of the wave function  is arbitrary, and does not represent something physical.

Wiki, "Implicate and explicate order" (of interest only to those who are already devotees of guru-physicist David Bohm):

 Bohm’s paradigm is inherently antithetical to reductionism … and can be regarded as a form of ontological holism.

Wiki, “Introduction to Gauge Theory”:

The electric field and the magnetic field are observable, while the more fundamental electromagnetic potentials V and A  are not.

~

In this ontological context, it is far from clear how the phrase ‘more like’ is to be applied.  Comparison of historical theories gives no sense that their ontologies are approaching a limit:  in some fundamental ways, Einstein’s general relativity resembles Aristotle’s physics more than Newton’s.

-- Thomas Kuhn, in I. Lakatos & A. Musgrave, eds., Criticism and the Growth of Knowledge (1970), p. 265

Cf. too Dirac’s remarks (1951) that the aether concept was ripe for resuscitation.

[Update 8 May 2012] And now this:

http://www.nature.com/news/a-boost-for-quantum-reality-1.10602

The philosophical status of the wavefunction — the entity that determines the probability of different outcomes of measurements on quantum-mechanical particles — would seem to be an unlikely subject for emotional debate. Yet online discussion of a paper claiming to show mathematically that the wavefunction is real has ranged from ardently star-struck to downright vitriolic since the article was first released as a preprint in November 2011.

The paper, thought by some to be one of the most important in quantum foundations in decades, was finally published last week in Nature Physics

They say that the mathematics leaves no doubt that the wavefunction is not just a statistical tool, but rather, a real, objective state of a quantum system.

I told you so...

Physicists reify space-time. They elevate it from a four-dimensional diagram used to record their experience into the kind of “real essence” that Bohr warned us not to seek.
-- David Mermin (March 2014), at:

http://www.nature.com/news/physics-qbism-puts-the-scientist-back-into-science-1.14912?WT.ec_id=NATURE-20140327

~

Not the same as the question of the building-blocks (ontological bricks) of physics, but related to it, is that of the Boundaries of Disciplines:  between physics and neighboring fields (chemistry, mathematics, …) and within physics itself (mechanics, astronomy, electromagnetism, condensed-matter, nucleonics, quantum theory, …).   In one sense, the question is idle -- you are working on whatever project you are working on, with methods appropriate thereto, however outsiders might classify them.  But it also has practical consequences, e.g. in the writing of textbooks.  As:

The traditional teaching of thermodynamics and statistical mechanics  as distinct subjects,  has often left students with their knowledge  compartmentalized, and has left them ill-prepared to accept newer ideas such as spin temperature or negative temperature  as legitimate and natural.

-- F. Reif, Fundamentals of statistical and thermal physics (1965), p. viii

That, from the textbook we used in stat mech at Harvard -- in the physics department, though previously I had only met notions of enthalpy, temperature, free energy, and entropy, in a chemistry course.

Similarly, Lindsay & Margenau remark, in their historical overview Foundations of Physics (1936), that they are moving away from treating optics and electrodynamics as distinct disciplines, “the former being, since Mawell’s time, really a branch of the latter.”

~

God’s-truth vs Hocus-pocus:

It is tempting to dismiss these quantum waves  as mathematical contrivances … but in the laboratory these “probability waves” can be manipulated with mirrors …

-- George Johnson,  A Shortcut Through Time (2003), p. 38

~

The prototypical example of an ontological ‘bit’ of chemistry and physics, is the atom (the ‘indivisible’ in its Greek etymology).  But later perspectives can get quite unprototypical:

A neutron star … is basically a giant atomic nucleus, stabilized by gravity.

-- J. Richard Gott, The Cosmic Web (2016), p. 29

.

Zen Physics

A wristwatch worn

by a particle of light

would  not  tick     a-tall.

(-- after Brian Greene; slightly modified, to please the Muse)

Dr. Greene delivers himself of this epigram, in the course of explaining that we

 each of us, all of us,

 even Achilles and the tortoise,

move equally at the speed of light.

To be sure, in a Pickwickian sense (dividing our motion between space and time).

~

Clocks on Earth    tick

a tiny bit

s l o w l y

relative to those in interstellar space.

[ -- Richard Gott, The Cosmic Web (2016), p. 16 ]

The Big Bang itself   is at the bottom

where all the worldlines  converge.

There is no time

before    that …

-- ibid, p. 81

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

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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.