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.)

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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

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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

.

The Realist Vernacular

            What follows is neither proof nor argument, nor philosophy of any sort, but rather an exercise in sociolinguistics.  [And as such, a sort of sociological preparation for the thread announced here.]  The point is simply to exhibit a common way of talking among contemporary mathematicians, as well as some physicists and philosophers -- an easy style of conversation  that you would never imagine exists, if most of your acquaintance with science and its philosophy is mediated by figures like Daniel Dennett and Richard Dawkins.

            To cite evidence of theistic talk from the learned men of history, from antiquity through the nineteenth century, would be pointless, since the mode was well-nigh universal, at all times and in all realms.  Yet in our present day, most of the habitués of faculty clubs and coffee-houses  have managed to satisfy themselves, that all those who ever lived, in history, from Pythagorus  to the Einstein of “Der Herrgott würfelt nicht”, were, without exception,  imbeciles, and simply didn’t know what they were talking about, when they talked that way.  At last mankind has seen the light (or the darkness, rather);  we speak only of what is sensible and sniffable, like Donald Trump.  And who should be so rash as to cite the testimony of a mere Plato, or Galileo, or Cantor, or Gödel, against the brass certitude of so eminent a scholar as Sir Christopher Hitchens, Ph.D?

            Therefore I shall limit myself to recent citations.  A few examples from among many, snatched at random from  recent reading.

            Again, note:   I am not implying anything about the theology, per se, of the people here quoted, let alone suggesting that they never miss Mass.  Indeed a Dennett -- a roaring atheist -- can still indulge in such turns of phrases as "we can take advantage of the God's-eye perspective we have temporarily adopted" (the Devil can quote Scripture to his purpose).   So far, this is just corpus linguistics;  but more anon.

(1) Theistic language

 (a) mathematics

Arthur Koestler, The Act of Creation (1964):

Karl Friedrich Gauss described how he finally proved a theorem on which he had worked unsuccessfully for four years:  “At last, two days ago, I succeeded, not by dint of painful effort, but so to speak  by the grace of God.”

Thomas Tymoczko, ed., New Directions in the Philosophy of Mathematics (1986, rev. 1998), p. 219:

In one of the most cited discussions in his much-quoted book, Kuhn [1962] talks of scientific decision in terms of “conversion experience” and “faith”.

Richard de Millo et al., “Social Processes and Proofs”, in Thomas Tymoczko, ed., New Directions in the Philosophy of Mathematics (1986, rev. 1998), p. 271:

The classical view does not require that an ordinary proof be accompanied by its formal counterpart; on the contrary, there are mathematically sound reasons for allowing the gods to formalize most of our arguments.

Similar language is often used in formulating the contemporary concept of a “hypertask”.  Cf. likewise

Shaughan Lavine, Understanding the Infinite (1994), p. 55:

            For Cantor … “countable” meant countable by God.

and similarly

Michael Potter, Set Theory and its Philosophy (2004), p. 250, re the plausibility of the Axiom of Choice:

… generalizing to the uncountable case  by appeal to the idea than an ideal being could achieve the choices required of him (or perhaps Him).

If we adopt some particular postulate system for abstract set theory, and agree that the criterion for accepting an intuitive set-theoretic argument  is that its analogue can be justified by the postuates, then we are  in efect  agreeing that the set of all intuitive sets  endowed with the membership relation  is a configuration satisfying the postulates.  We can have at best  intuitive reasons for believing this.  It is really an act of faith.

-- Andrew Gleason,  Fundamentals of Abstract Analysis (1966), p. 153

Gregory Chaitin, “Gödel’s Theorem and Information”, in Thomas Tymoczko, ed., New Directions in the Philosophy of Mathematics (1986, rev. 1998), p. 306:

If God tells one how many different programs of size less than N halt, this can be expressed as an N-bit base-two numeral, and from it  one could eventually deduce  which of these programs half  and which do not.  An alternative divine revelation would be knowing that program of size less than N which takes longest to halt.

Robin Wilson, Four Colors Suffice (2002), p. 214, recounting a mathematician’s reaction to the immensely long and repetitive, unsurveyable, computer-aided proof of the Four Color Conjecture:

God wouldn’t let the theorem be proved by a method as terrible as that!

 (b) physics

Hermann Weyl, Symmetry (1952):

Contingency is an essential feature of the world.   Clarke  in his controversy with Leibniz  admitted the latter’s principle of sufficient reason, but added that the sufficient reason often lies in the mere will of God.  I think, here Leibniz the rationalist is definitely wrong, and Clarke [the theist] on the right track.  But it would have been more sincere to deny the principle of sufficient reason altogether, instead of making God responsible for all that is unreason in the world.

Abdus Salam (1988):

God created just two dimensions -- one of space and one of time. … At a later epoch, there was a phase transition to four dimensions, plus six internal ones.

Stephen Hawking, A Brief History of Time (1988; 2^nd edn. 1996) p. 91, alludes to Roger Penrose’s paraphrase of cosmic censorship:  “God abhors a naked singularity.”   The (jocularly) theistic language is especially odd and noteworthy, since the epigram here being echoed -- “Nature abhors a vacuum” (Latin:  horror vacui) does not use it.

Stephen Hawking, A Brief History of Time (1988; 2^nd edn. 1996) p. 126f.:

These laws [of physics] may have originally been decreed by God, but it appears that he has since left the universe to evolve according to them  and does not now intervene…

That, then (for that author) leaves only the explanation of the settings of the parameters for initial conditions:

One possible answer is to say that God chose the initial configuration of the universe for reasons that we cannot hope to understand.  This would certainly have been within the power of an omnipotent being, but if he had started it off in such an incomprehensible way, why did he choose to let it evolve according to laws that we could understand?

Simon Blackburn, Think (1999), p. 69, in a section called “A Scientific Model”:

Classical physics identifies the temperature of a gas with the mean kinetic energies of the molecules that compose it.  So in making hot gases, God has only one thing to fix…

Blackburn is a philosopher, not a physicist; as commonly in that community, he is writing in an “as if” mode;  but still, the choice of words is noteworthy.

John Gribbin & Martin Rees, quoted in Edward Harrison, Cosmology (2^nd edn. 2000), p. 489:  Absent the strong anthropic principle,

If there is a unique ‘theory of everything’, then … we would have to accept it as genuinely coincidental, or even providential, that the constants determined by high-energy physics happen to lie in the narrowly restricted range that allows complexity and consciousness to evolve…

(“Providential”… a lovely word…)

Paul Davies, The Goldilocks Enigma (2006), p. 3:

It appeared to Hoyle as if a superintellect had been ‘monkeying’ with the laws of physics. … Like the porridge in the tale of Goldilocks … the universe seems to be ‘just right’ for life.

Paul Davies, The Goldilocks Enigma (2006), p. 236:

Most theoretical physicists are Platonists in the way they conceptualize the laws of physics as precise mathematical relationships  possessing a real, independent existence…

Shing-Tung Yau, The Shape of Inner Space (2010), p. 101:

As Robert Greene puts it, “you’re trying to find the one metric given you by God.”

Michael Atiyah re string theory, quoted in Shing-Tung Yau, The Shape of Inner Space (2010), p. 292:

They’re onto something, obviously.  Whether that something is what God’s created for the universe  remains to be seen.  But if He didn’t do it for the universe, it must have been for something.

This statement is reminiscent of the Principle of Plenitude; and recalls Einstein’s celebrated quip, anent the possible failure of an experiment to confirm his prediction: "Da täte mir halt der liebe Gott leid; die Theorie stimmt doch."

Less seriously, but using a religious metaphor: J. L. Synge, Relativity:  The General Theory (1960), p.  ix:

It is to support Minkowski’s way of looking at relativity that I find myself pursuing the hard path of a missionary.

More serious is the following.  The author is discussing the vexed question of the Collapse of the Wave-Packet upon observation (related to:  If a tree falls in a forest, and no-one’s around, does it make a sound?  -- here rewritten in Oxford terms, replacing the forest by a quad), and quotes the old limerick:

Dear Sir, Your astonishment’s odd;

I am always about in the Quad.

And that’s why the tree

Will continue to be,

Since observed by Yours faithfully, God.

He comments (J. C. Polkinghorne, The Quantum World (1984), p. 67):

Divine reduction of wavepackets would be an overkill, since it would operate everywhere and always, forcing the electron each time to go through a definite slit.  The point about measurement is that it only occurs spasmodically.

Note the predicted empirical consequences of God in the Quad!   Then, between square brackets, the author adds:

This observation is in accord with the classic theological understanding of creation, which sees God as the ground and support of all that is (in our terms, the guarantor of the Schrödinger equation), but not as an object among objects (no collapser of wavepackets).

This aside is in fact central:  by the time he wrote this, Polkinghorne had quit his endowed Chair in physics to become a village vicar.

(c ) analytical philosophy

Michael Dummett, Truth and other enigmas (1978), p. 15, discussing character as (it may be, untested) hidden propensities:

If B still wishes to maintain the necessity of ‘Either Jones was brave or he was not’, he will have to old  either that there must be some fact of the sort to which we usually appeal … or else that there is some fact of an extraordinary kind, perhaps known only to God.

Dummett’s use of the term, to characterise the viewpoint of a hypothetical philosopher inclined to Realism, is so to speak opaque, not representing his own view, which is rather (id, p. 150) that “only a philosophically quite naïve person would adopt  realist view of statements about character”.  Only such, or Saint Peter.

(2) Realist language

Arthur Koestler, The Act of Creation (1964):

Gauss is reported to have said: “I have had my solutions for a long time, but I do not yet know how I am to arrive at them.”

Klaus Jänich,  Topology (1980; Eng. trans. 1984), p. 35:

When topological groups are found in nature [emphasis added], they  are generally not given abstractly as a set G with a composition law and a topology, but concretely, as a group of transformations…

This is not really anymore outrageously realist than saying “When a set of six objects is found in nature…”   (say, the familiar six-pack; although the one at my side is already down to five, and it’s not even noon).

And again, p. 157:

Covering spaces very often “occur in nature”:  that is, one comes across them spontaneously, while studying entirely different problems.

Shaughan Lavine, Understanding the Infinite (1994), p. 160: 

We seem to have nontrivial intuitions concerning the infinite, going far beyond simple things like Extensionality, Pairing, or even Power Set.

Shing-Tung Yau, The Shape of Inner Space (2010), p. ix:

The strength of this discipline [i.e., mathematics] lies not simply in its ability to explain physical reality…, because to a mathematician, mathematics is reality.

If all you know of math is elementary arithmetic, this statement may lack punch.   But in the upper reaches of set theory, topology and so on, it embraces a world of miracles and of monsters.

~ ~ ~

It is important to note, that this is the way Realists talk en famille.  The talk is casual, often not literal, yet is meant in some serious sense.  It is not to be compared with the tawdry pseudo-theological, pseudo-mystical sort of gibberish that popular authors (and even some serious ones, yielding no doubt to the Satanic promptings of the marketing department) use to gin up their pap for the masses -- like “God particle” for the freaking Higgs boson.

It may be objected (it will be objected;  it has been objected) that such expressions, in a modern mouth, are a mere façon de parler.  To which we reply (with Whorf), that a façon de parler tends to cohere with a façon de penser. 

Nor is it a refutation of the point here made, to adduce agnostic pseudepigrapha from any of the gentlemen here quoted.   We are each a walking contradiction;  we contain multitudes.   C.S. Lewis himself  confessed that he tended to be a cranky agnostic at dawn, but a theist later, when he’d had tea and was more himself.

Once again:   The point here is not to assert that so-and-so among our near contemporaries  is or is not a believer.  Indeed it will strengthen my eventual case, if many of them are not in fact believers, yet find themselves attracted, or guided, or driven, to Realist or Theistic language, whether for convenience, or (in the case of Cantor, Gödel, and Einstein) something deeper.

So, a very modest initial move, a sort of pawn to king’s four.  (Only later -- much later -- shall we see if we can capture Satan’s Queen.)   So far we hold simply, that occasional use of Realist or Theist language, in serious discourse, is not  in and of itself  diagnostic for Trisomy 21.

A Proof of God’s Point-lessness (Not)

 Stephen Hawking, in A Brief History of Time (1988; 2^nd edn. 1996) p. 146, attempts to wave away the otherwise lurking Big-Bang singularity  by an appeal to Heisenberg Uncertainty.  Well, fine;  actually the whole enterprise of physics around that moment strikes me as eminently Uncertain -- but fine;  passe encore.  Instead of a pointy sugar-cone, you have one of those paper cones with a rounded bottom.  Fine.

Only -- from this he leaps to:

If the universe is really completely self-contained, having no boundary or edge, it would have neither beginning nor end:  it would simply be.  What place, then, for a creator?

“Simply be”:  as though that were self-explanatory.   -- On the contrary:  philosophical-theological wonder has focussed on, “Why is there something, rather than nothing?”, and in no way on “Yipes!  There’s a singularity!  Ergo God!”

If Hawking is an atheist, fine, no problem.  What is bothersome is rather the chance that an ignorant and mesmerized public might fancy that, with such pronouncements from a media star, he has brought some startling new scientific insight into play, that would make Aquinas slap his forehead and say “Oops, you win!  K sry -- my-bad.  No God after all.”

(For an alternate proof of the non-existence of God, click here.)

Further updates

[update to  this ]

I confessed that perceptual/imaginative disability with burning cheeks;  but am somewhat comforted to come across this testimony from a fellow-sufferer:

It is impossible to imagine a four-dimensional space.  I personally find it hard enough to visualize three-dimensional space.

-- Stephen Hawking, A Brief History of Time (1988; 2^nd edn. 1996) p. 24

And now this, from William James, The Principles of Psychology (1890), vol. II, p. 275, re our apprehension of space:

It is a notion, if ever there was one;  and no intuition.  Most of us apprehend it in the barest symbolic abridgement;  and if  perchance  we ever do try to make it more adequate, we just add one image of sensible extension to another  until we are tired.  Most of us are obliged to turn round  and drop the thought of the space in front of us  when we think of that behind.

Alas, only too true!  Indeed (confiteor), I myself cannot simultaneously chew gum and conceive either.

[and to this]

P.A.M. Dirac, The Principles of Quantum Mechanics (4^th edn. 1958), p. 311:

The Schrödinger picture is unsuited for dealing with quantum electrodynamics, because the vacuum fluctuations play such a dominant role in it. … They get bypassed when one uses the Heisenberg picture, and one is then able to concentrate on qualities that are of physical importance.

“Why is there Something rather than Nothing, Grandpa?”

            That there is Something rather than Nothing, is possibly Necessary, if only in a philosophically rather trivial or anyhow tricky sense: If there were nothing, we wouldn’t be here to observe the nada (this is the Weak Anthropic Principle). But that there is This Something, rather than Some Other Something,  is quite possibly contingent (though the Strong Anthropic Principle would deny that).

            Take for instance the puzzling asymmetry of matter & anti-matter. It would be nice to have a principled explanation of this -- certainly we have heard special-pleading unprincipled ones --  but maybe there isn’t any.  Maybe God just got a little careless with the safety scissors that day, when he was cutting the cosmic cardboard.  He’d meant to slice it straight down the middle but --- oh well… And on to other projects. 

            (Physicists dignify this phenomenon with a poignant designator: “broken symmetry”.  Sounds so sad.  In layman’s terms, that means:  a coin-flip.)

            The concrete, particular cosmos in which we temporarily find ourselves, need no more directly or insightfully reflect the creative, ontological ultimate ground thereof, than the particular grit and consistency of the wafer, gives a hint of the Real Presence.  C.S. Lewis [and others before him? Aquinas?  References please!] compares our worm’s-eye view here below  to looking at a woven carpet from the wrong side.  There is some correlation (in all the wretched hernia-like loops and stitches) with the true pattern, but not much, and you’ll never figure out which bits give a hint and which are noise.  The force of the metaphor only grows, when you consider that reality’s carpet is not flat, but fills all of Hilbert space (at the very least; we are ignoring gravity), and with patterns not specifically tailored to the cerebral convolutions or lack thereof, of this species or that:  the human, the simian, the humble woodchuck.

            Indeed, we ourselves (for all our pathetic stupidity)  may perchance be one of the more Necessary things about it.  With so much Mind on the loose in the multiverse, it may be but natural that some of it would, so to speak, condense out here and there, into rational creatures.  We are like droplets on God’s windowpane.

            There is a popular industry of spewing out books for the general reader, focusing on black holes, or big bang, or the ill-named Theory of Everything, and deducing – well, not actually deducing anything, but sort of gasping in front of the black backdrop, then putting in a plug for God.  As though He cared more for black holes than for blackheads.  We may call this “physics porn”.

            Lately, the situation in physics has got even worse, with the dreadful possibility (and it is a possibility) of a ‘multiverse’ in any of several senses.   There has been some loose talk about “the Landscape”, as though that  were a neat discovery rather than the reduction of the reductionist program to near nullity -- and recent loose talk from Stephen Hawking to the effect that the new Phlabby Physics, as we shall call it (anything can happen anywhere, the basic constants set randomly differently in each separate universe) shows that “science makes God unnecessary”.   The danger is rather that Landscape physics will make physics unnecessary, or pointless.   As physicist Burton Richter said recently, the  Landscape approach means that physicists have “given up.  Since that is what they believe, I can’t understand why they don’t take up something else -- macramé, for example.” 

-- This just in, a useful corrective:

http://www.nytimes.com/reuters/2011/01/06/world/europe/news-us-pope-bigbang.html?_r=1&ref=global-home&pagewanted=print

On this Landscape question, Hawking notwithstanding, I’ll go with the Pope.

What is particularly irksome is that these New Nihilists are attempting to dress up what is essentially an impasse in physics (see our post below, “Truth Decay”), into some new advance, that solves the old problems of Being and God.   Let us satirize the situation with a parable:

            It was observed that a certain bird, known as the Woodpecker, pecks wood.  No-one knew why this was so.  Perhaps it needs to keep its bill from getting too long, the way pet rodents will gnaw and gnaw for dental hygiene.  Perhaps it likes the sound this makes, and is attempting to stake out territory or attract a mate.  Or maybe it just hates trees.

            Scientists took two different routes to a solution.

            (1) The Naturalist, by patient observation over many years, discovered that tiny creatures live hidden beneath the bark.  By pecking, the bird can reach these and eat them.

            (2)  The Landscape Biologist, with a grand wave of the hand, explains that while, locally, Woodpeckers peck, in the next forest over, he imagines they do not, but rather roller-skate; and in the next, they play the ukele.  Problem solved.   Oh and plus -- bonus result -- there is no Creator, because who would create anything so stupid.

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Addendum:

Re broken symmetry:

Such, in effect, is Hume's fantasy, in Dialogues Concerning Natural Religion (1779).

[continued here]

[Update]  A rather mournful meditation on the multiverse (by Alan Lightman)  here.

[Update 7 April 2012]  For the views on the subject, by physicist Lawrence Krauss, click here:
http://worldofdrjustice.blogspot.com/2012/03/too-much-of-nothing-updated.html

[Update April 2014]  Jim Holt has written a whole book upon the subject.  We examine it here:
http://worldofdrjustice.blogspot.com/2014/04/minimalism-vs-nihilism.html