Pop ! goes the Positivist

 [This is a continuation of a thread begun here.]

Another example of fetishizing the visible (cf. now also this)  occurs in Karl Popper’s Conjectures and Refutations: the Growth of Scientific Knowledge (1962; page refs. to the Harper paperback reprint), p. 284:

In the last pages of Testability, Carnap discussed the sentence ‘If all minds should disappear from the universe, the stars would still go on in their courses.’  Lewis and Schlick asserted, correctly, that this sentence was not verifiable.

They so asserted incorrectly.  After all, we have a pretty good handle on those stars in their courses, beginning from not long after the Big Bang  through the present, during most of which there were no human minds.

And here’s a simpler experiment:  Let’s all just refrain from observing the moon for the next two weeks.  Now we open our eyes.  Surpri-ise!  Right where we expected to find it, and at a phase two weeks more mature than when we last checked (rather than the phase as last seen).

One occasionally observes a very young child shut her eyes and announce in a sing-song: “Youuu ca-han’t seee mee….!”  I doubt the child actually believes that, it’s just fun to say.  But suppose she did. She is then entertaining an erroneous optical theory, but not an erroneous ontological one.  She imagines that the lights went out for you as well; but she never entertains the thought that you yourself have been extinguished, or been transfixed into some mute deaf motionless limbo until such time as she shall be pleased to gaze again – after all, she has just shown this, by addressing you.

Incidentally, the whole Schlick-shop with its merry/morose band of logical positivists, appear to have created enormous problems for themselves, and come up with completely counter-intuitive results, from the basic motivation of wishing to exclude all metaphysical propositions from the outset as strictly meaningless.   (The story here is in line with our overarching defense of theism.)  In other words, it wasn’t enough to denounce as wholly unconvincing,  all purported metaphysical statements hitherto; nor to brand it a particularly uninteresting language-game; nor to marginalize the enterprise with the derision usually reserved for circle-squarers.  Metaphysics as such, and for all time, had to have a stake driven through its heart, the stake itself consisting in pure reasoning from selbstverständlich  (metaphysically a-priori? God-given? -- oops, NOT) first principles.  For a demonstration of the absurdities that apparently resulted, cf. Popper, passim.  As (p. 281, op.cit.)

My criticism of the verifiability criterion has always been this: against the intention of its defenders, it did not exclude obvious metaphysical statements, but it did exclude the most important … of all scientific statements … the universal laws of nature.

Why even go near such a disaster, for the sake of excluding-in-principle all metaphysical statements – which they were ignoring anyway?  Popper goes so far as to hazard a guess in a footnote to p. 175:  “One not need believe in the ‘scientific’ character of psycho-analysis (which, I think, is in a metaphysical phase) in order to diagnose the anti-metaphysical fervour of positivism as a form of Father-killing.”  (Note, b.t.w., the capital initial of “Father”.)

*

Since we were obliged, a moment ago, to deprecate Popper, let us hasten to another example, in which we find him on the side of the angels.  First let us note:

             * Our conduct is guided by moral laws.

             * Our scientific activity is guided by metaphysical principles.

             * Both categories are philosophically vexed, and any concrete application of these laws and principles may prove problematic; but we cannot do without them.

            Here is Popper (p. 287) characterizing the logical positivists: “They implicitly accept the rule: ‘Always chose the most probable hypothesis!’  He goes on:

Now it can be easily shown that this rule is equivalent to…’Always choose the hypothesis which goes as little beyond the evidence as possible!’  And this, in turn [amounts to] ‘Always choose the hypothesis which has the highest degree of ad hoc character!’

an undesirable result for science.   (Cf. Chomsky, passim, re the extraordinarily abstract and roundabout way you may have to proceed  to get valid results, by no means simply tip-toeing a bit beyond “the evidence”.)

            The principles which we require instead  may be best illustrated by an old joke (presented here in a slightly revised form):

     A zoologist, a mathematician, and a positivist  are touring the hinterlands of Bohemia by train.  Through the window they spot, standing motionless at some distance, a purple cow.

     “Fancy that!” exclaims the zoologist. “There are purple cows in Bohemia.”

     The mathematician, in a low voice, amends: “There is at least one purple cow in Bohemia.”

     The positivist, raising his finger, crisply corrects to:  “In Bohemia there is at least one cow, purple on one side.”

            The joke is that the positivist has the most precise view of the evidence; and of the three statements, only his own is certainly true (interpreting an unmodified “purple cow” in the natural way, as “purple more or less all over”); yet his scruples are absurd.  Science would not progress, were it bound by such fragmented literalism.  (Indeed, we should have to replace “cow” with “an apparently bovine organism”, and always assuming that we can rule out a mirage, or a collective hallucination, or some effect of swamp gas; or for that matter an analogue to one of Hilary Putnam’s pet entities, the Mechanical Cat from Mars.)  And we would have to gloss Quine’s celebrated interjection, gavagai!, as possibly:  “Lo, a rabbit-stage, seen from the east.”

(For more on bovine mathematics, see "How Now, Round Cow".)

A gathering of Positivists

Note:  Occasionally one meets with such unilateral positivist agnosticism  in a non-jocular context:

Franz Ferdinand rode erect, his visible foot deep in the stirrup, a saber at his side.

-- Robert D. Kaplan, Balkan Ghosts (1993), p. xxvi

The above scenario has been much discussed among epistemologists, under the rubric “Henry and the barn façades”.   However, the cow version is much funnier.

Ceci n’est pas une grange 

~

To move from this to an outlook useful for science, we need these metaphysical principles:

   (1) a certain uniformity or self-cohesion to nature

   (2) the reliability (not in a logical, but in a practical sense) of induction.

(There are others, of course, such as the usefulness of deduction;  but that applies in every world, not just in this contingent one.)

            Now, both these principles are of vexed and delicate application; as are, indeed, the Commandments.   Just as it is difficult to avoid situation ethics, I see no way around a kind of “situation metaphysics”.   The zoologist, using these principles, together with his discipline-specific knowledge (to the effect that animals generally come in species, not as singletons), concludes the presence of purple cows.  But here I must side with the formulation of the mathematician: there is at least one such cow, but perhaps no more.  For, nature’s uniformity depends on the domain.  Were an experiment ever to identify, say, a Higgs boson, we should conclude the existence of an emphatic plurality of Higgs bosons; that there should only be one in the universe, is inconceivable.  But biology is more mottled than that.  Given our collective prior acquaintance with hundreds of thousands of cows, none of which was ever purple, we would hypothesize here an extremely rare mutation for (bilateral) purple (bilateral because bilaterally symmetric animals generally continue to evolve with bilateral symmetry, pace the occasional narwhal).  Since a cow delivers but a single calf at a time, this one has no identical siblings, so it is probably unique.  Moreover, the bulls will likely shun her for her color, and she shall have no offspring.  The mutation dies with her.

Carnap attempts to avoid the assumption of a metaphysical principle, by declaring (1) to be “analytic” (i.e., more like “2+2 = 4” than like “animals tend to come in species” or “each elementary particle is invariable within its class”).  Popper comments (p.289) that “no such principle of uniformity can be analytic (except in a Pickwickian sense of ‘analytic’)."  In fact, we noticed, the principle is nothing remotely like analytic, having always constraints on its application, which in some domains may be severe.  And as for (2), I concur with Popper (p.292) that it is “a principle of a priori metaphysics.”  And none the worse for that.

[For further notes on ineluctable metaphysical underpinnings of the scientific enterprise, see here.]

A New Proof of the Existence of Coffee-Cups

But the math had not clarified one basic question:  what the hell did it all mean?  How could the world of atoms be nothing but a puff of probabilities, and yet conglomerations of those atoms could create something as strong and unbending as the  chair on which he sat?

-- David Kaiser, How the Hippies Saved Physics (2011), p.  54

[Update to an earlier essay.  For the original, with readers’ comments, click here.]

Re the authors of “The Stability of Many-Particle Systems” (1966):

They couldn’t explain why it was  that ordinary everyday objects wouldn’t just go up in smoke.  It was quite anomalous.  Inert matter just lies there in a kind of steady state, ticking over silently in a metaphysical sort of way, but this ordinary and plain fact of experience  was incomprehensible to physics.

-- Ed Regis, Who Got Einstein’s Office? (1987), p. 185

There comes a time in the life of every young person, when they doubt the existence of coffee-cups.  So here comes jolly old Doctor J, to prove it for you;  and more importantly, to reassure you that, even should you someday forget the details of the proof, you may continue  to place entire faith in the existence of these useful objects, asking no questions for conscience’ sake.

(We earlier sketched the idea of the proof, but there the argumentation was informal.)

So!  It’s a quiet Sunday, the desk and the mind are clear, let us pour out a generous helping of this fresh-ground, new-brewed, steaming darkling French roast, into the convenient receptacle which (to all appearances, at any rate) sits within easy arm’s reach upon the solid oaken desktop, to stimulate the grey cells, and set ourselves to this great task  of confounding the nominalists and solipsists.

[Excursus:  Historique du problème

Dr Johnson famously proved the existence of stones  by kicking one (a martyr to science -- he reckoned without his gout).  The Cambridge philosopher of banality, G. E. Moore, satisfied himself (I choose the verb with care) of the existence of physical reality, by noticing his own hands.  (The choice was not a happy one, being potentially seen as solipsistically self-centered, not to say onanistic;  further, the phenomenon of phantom limbs complicates the picture in irrelevant ways.)
Accordingly, we shall proceed by proving the existence of coffee-cups:  both because they form the prototypical physical object for philosophers (apart from mats, which are ignored unless they have cats on them), and because, for mathematicians, who in general care not a fig for the physical, do care crucially about this one concrete object, since coffee is their essential fuel.]

But before embarking upon the abstract part of this argument (since some folks are uncomfortable with abstractions -- though really, they need not be;  what follows makes a lot more sense than most of what gets uttered around the water-cooler), I shall offer what critics have called the objective correlative:  a description of the actual coffee-cup whose space-time coordinates are My-Here and My-Now [** But now see below!].  (Rather than the ambiguous “here and now”;  for such coordinates must indeed be relativized to some observer, though not necessarily a mortal observer.)  After all, we wouldn’t want you to wonder whether we might not be just making the whole thing up.

[**Horrified update, August 2019:  Testing the link, I clicked, winding up  indeed at the sales-site for the "Catholic Attitude" mug;  but -- It has been censored!  Shorn of its knight, along with his attitude! -- Fortunately I -- Fahrenheit-451-fashion -- saved the original image, and included it in this essay; vid. inf.]

From the standpoint of the chemist, the object in question would appear to consist in some sort of ceramic, whatever that may be, though I really couldn’t say -- anyhow, something sturdily non-porous.  In general outline, it forms a cylinder, sealed off at the bottom and evacuated at the top.  Somewhat spoiling this sleek Platonic profile, a handle protrudes from the side, a concession to the physical infirmities of hominoidal incarnation.

It is thus strictly speaking a ‘mug’ rather than a cup;  but still I say “coffee-cup” because, for philosophers (who don’t get out much), that is the prototypical object in the cosmos.  (At least this is true for hypercaffeinated Americans; more leisurely Oxonians look to "the tree in the Quad").  In similar fashion, the propotypical Contingent Truth for the Oxbridge set is:  “The cat is on the mat.”  (That last one is not true at the moment, b.t.w.;  she seems to have wandered off.)

That is pretty much all you need to be  to call yourself a coffee-cup.  But these days, most cups are not quite so minimalist:  most of them sport some wacky slogan of office lore, or the logo of a sports team.  This particular specimen displays the image of a medieval knight, standing in contrapposto, his tabard emblazened with a cross pommée.  On his face is an expression difficult to read, some blend of troubled arrière-pensées and manly determination.  He is set largely within a blue circle, which his mailed headgear slightly overtops; at the bottom -- a detail I just noticed only now -- the end of his belt (bulging slightly at the tip) laps down and over, in a way that, hm,  might be misinterpreted.  And written boldly above him, the words:

Catholic  Attitude

Well.  So much for the objective correlative.  Now for the proof, deo volente -- while mindful of the strictures of Kant:

It remains a scandal for philosophy  and for human reason in general, that the existence of things outside us  must be taken only on faith,
and that, if it occurs to someone to doubt it,
we can produce no counter-argument  sufficient to prove it.

-- Kant, Critique of Pure Reason

~ ~ ~

We must confess at the outset (well, it’s a bit late for that) that we cannot actually prove the existence of coffee-cups, by the lofty standards of proof first intuited by Euclid, and refined  in our own day  to a high sheen.   Outside indeed of mathematics, such a capability appears not to exist:  Whenever I try to read a physics article reporting recent research, it always appears at some point to be hand-waving, “You’ll just have to trust us on this.”   And within mathematics itself (trade secret; don’t whisper this to Muggles) we seldom explicitly set out all the steps, even in the final published results.   As for the actual process of mathematical discovery, it normally bears no relation at all to Hilbert’s formalist program;  at its deepest and most mysterious, it is more like…. (and here we’ll have to whisper very softly) … Revelation…

Anyhow, we obviously can’t actually prove the existence of coffee-cups, because logically, strictly speaking, they might not exist:  We might all be just brains in a vat, hallucinating the whole thing.   So to clear the air, we frankly state our Auxiliary Assumption:

(AUX)  We’re not just brains in a vat.

If you personally reject that assumption -- well, happy marinating.  For the rest of us -- to proceed.

[Excursus:  Among the merits of d’Abro’s history The Rise of the New Physics (1939), is that he repeatedly points out the (sometimes unacknowledged) auxiliary assumptions that were required in the development of even the most successful programs in the physical sciences, by the most celebrated researchers, during physics’ Golden Age.

Almost nothing we do in everyday life  is free of unspoken assumptions, sheer force of habit, and random whims.  So, simply by listing such propositions as (AUX), we are making some modest progress.]

The principal premises of the proof, and the only ones that would occur to most people, are evidential.   This is where the hard work of science is done.  Fortunately, in the case of perceptions of ordinary middle-size objects, Nature does it for us, that we need not continually trouble our little heads:  all sorts of cross-connections and epistemological assumptions are hard-wired into our brains.  (These brains, b.t.w., reside in a cranium, vice a vat.)  We shall nevertheless lay out some of the perceptions and observations that serve to buttress the conclusion to objectual existence -- not so much to convince you yet further that your mug is real, but rather, virtually the contrary:  by such explicit exposure of our evidential grounds, to make plain their essential poverty, absent certain grounding metaphysical principles, along the lines of (AUX) though more substantial -- or rather again, more abstract and as it might be insubstantial, since (AUX), though it has the look of a metaphysical assumption, might in some circumstances be actually demonstrable, and thus empirical, as happens in the movie “The Matrix”.

(PE) Perceptual Evidence

(1) I seem to see before me a colour-patch (Note to the lay reader: These colour-patches compose the whole of the world for the positivist empiricists, who never quite manage to convince themselves that coffee-cups are real, and therefore cannot drink the coffee, and die of thirst), roughly cylindrical in outline -- though the exact projection upon the retina depends on the viewing-angle in complex ways (blah blah blah; insert usual empiricist verbiage here).

(2) When I reach out with my hand (for reassurance as to the existence of your own hands, consult the works of G. E. Moore), groping in the general direction of the above-named coloured patch, I abruptly encounter what seems to be a solid object -- a bit too abruptly, it turns out, as some sort of dark hot liquid is now pouring into my lap.

(3) (Insert more such evidence here -- crucially, cross-modally, involving the sound of the mug as you strike it with your pen; the smell and the taste of the coffee within).

(4)  When I pour a small amount of coffee into this apparent container, it does not quantum-tunnel out:  thus recalling, by uniformity and analogy, such similar objectual posits as the Water-Glass.

(5)  Jones here -- a stout fellow of sound mind -- affirms that, egads, he too perceives a coloured patch in what, calculating the parallax by triangulations, dum-de-dum, doing the math, appears to correspond to the same space-time locus that I myself have identified.

(6)  (etc. etc. etc.)

(C ) Conclusion

Coffee-cups really do exist.

(They do, but this one's just an image of such a cup)

Now:   The thoughtful reader will already have noticed how grotesquely speckled with gaps  such reasoning is -- why, it shouldn’t convince a child.  For, though it pretends to consist of but simple reports of perceptions -- “observation sentences” in the lingo -- rather than any abstract reasoning that might be open to critique, it actually smuggles in a great deal of unbuttressed assumptions.  Thus -- what ties (1) and (2) into any sort of connection with each other?  Why,  the unexamined assumption that the visual coordinates of (1) map smoothly and without controversy to the kinesthetic coordinates of (2):  a fact by no means obvious  -- intellectually, that is;  of course, the identity is more or less hard-wired, though it may take baby a certain amount of groping and spoon-dropping to get the respective ordinates and abscissae to finally match up.  Nor is the correlation in any sense necessary -- indeed, it can be easily overturned in simple experiments involving funny spectacles.

And as for that “Jones” there -- you are assuming the existence of Other Minds, about which great vats of ink have been spilled!  (There is, in fact, one sense in which philosophers at any rate  are brains-in-a-vat.)  And indeed you need vastly more than that -- for the Other Minds projected by mere analogy, might be only Other Monads, and incommunicable among themselves.  All right, wire them one to another -- still not enough:  you are assuming that you each mean ‘the same thing’ when you utter the same (or: “similar”) syllables:  an assumption demonstrably false in every political summit or marital argument.  All right, plow ahead and assume that:  you’re still not there.  With all the intelligence and good-will in the world, your private knowledge might not be transmissable intact: witness the celebrated case of determining whether or not your extragalactic pen-pal resides in a world made of matter or of anti-matter, or whether he is right- or left-handed.  -- And here my grey-cells throw in the towel; but were you (younger, and keener) to pursue this line of speculation further, things would probably only get worse.

No, for the various clauses of (PE) to have any cohesion and probative force at all, we require a vast apparatus of non-evidential, metaphysical assumptions, almost never made plain.  The above syllogism,  (PE) => (C ), is thus in reality an enthymeme .  Suppressed is what we might dub the enthymematic assumption, which we now state here:

(EA -- full version)  Background metaphysical premises

(Insert the entire body of philosophy here, along with the whole of science.  Do not omit to mention the Assumption of Cosmic Uniformity (spatial; temporal; spatio-temporal), the Problem of Induction, the Reliability of Deduction, along with some still-unnamed rules of thumb concerning our right to ignore pesky quantum-mechanical paradoxes when speaking of mid-level objects, etc. etc.)

Now, that is rather a tall order, and even were it somehow to be accomplished for this particular case (which might or might not "go over" towards founding the existence of pickles, say), no individual mind could survey the results and verify their correctness and inter-consistency.   And yet, this is the heavy machinery that we need to conclude to so modest a proposition as the existence of coffee-cups.  So let us superadd, as a concession to our feeble powers of ratiocination and memory, the following Concise Version:

(EA -- concise version)  God is Good.

This one works for me;  but if you’re an epistemological stickler, you can probably get by with this weaker assumption, as stated by Einstein, and applied, not only in his life, but in the practice of his physics:

(EA -- weakened version)  Boshaft ist er Nicht.

Which is to say, anglicê:  at least He is not plain mean.   By which he meant:  The cosmos is not just some vast joke, jerry-rigged to baffle our senses.  Overall, it ultimately makes sense -- even if what we perceive here below, is but the thread-gnarly underside of the grand patterned carpet.

(Note:  The basic point is more logical than theological;  still, the realms do tend to intertwine.)

Historical footnote:

Descartes derived the principle of inertia from two premises:

* the homogeneity of the straight line, and

* the immutability of God, of which the constant quantity of motion in the world is an expression.

-- Charles Gillispie, The Edge of Objectivity (1960), p. 90

Note incidentally that the first of these Cartesian premises  is at least as fraught as the second (the problems and paradoxes of The Continuum).

~

~ For a theo-philosophical fantasia, try this:

Murphy and the Magic Pawnshop

[Kindle] [Nook]

~

~ ~ ~

To add some punch to our insistence on the Importance of the Enthymeme, with all its tacit metaphysical assumptions, let us instance another, less familiar syllogism.

(P) Evidential Premises:

1. Something funny’s going on here.

2. What’s that smell?

3.  I can’t find my car keys -- probably somebody swiped them.

4.  What’s that noise?!

5.  So where does Jones get the money for a fancy car like that?

6. No way I’m letting that bastard merge into my lane.

7. Why are all those people staring at me?

8. Ouch!

9. It’s a conspiracy.

(C ) Conclusion:  The world is ruled by giant lizards.

That conclusion is an actual doctrine, firmly held by some people:  non-institutionalized people, actual citizens who have the right to vote (and who seemingly exercise that right with disproportionate frequency).  I’d provide a link to the relevant Web sites, but fear lest these poison your computer.

What, though, must be the missing enthymeme, which licenses this deduction?  Apparently something like this:

(E)  The cosmos is ruled by Satan.

Compared with (E), (C) begins to look relatively inviting.

~  ~  ~

But enough of such stuffy studies!   The sun, renewed, has broken through the clouds, the bird-sounds rise in chorus, and a breeze bestirs itself among the leaves.   Let us then fare forth, into the wide world, whose splendor bears the imprint of its Maker, as plainly as had He signed it, John-Hancock-style, with His celestial pen.

~  ~  ~

[Afterthought]  But what then, of the java, that flows from the mug whose reality we have just proved???  Why, it flows to fuel the brains of mathematicians! 

[Appendix, Jan 2015]  Having at length satisfied ourselves as to the reality, or at least reliability, of coffee-cups, would should not  on that account sink back into an attitude of Moorean complacency (“I’m all right, Jack;  I’ve got hands”).  For our commitment to these  suggests yet further commitments, which we had not realized were there to assess.  Such as :  Realism with regard to quantum state vectors.

The question of ‘reality’ must be addressed in quantum mechanics -- especially if you takes the view that the quantum formalism applies universally to the whole of physics -- for then, if there is no quantum reality, there can be no reality at any level.

-- Roger Penrose,  The Road to Reality (2004), p. 508

And:

The question of the objective existence of the objects of mathematics … is an exact replica of the question of the objective existence of the outer world.

-- Kurt Gödel, “What is Cantor’s continuum problem?”, in American Mathematical Monthly, 1947.

In for a penny, in for a pound.

~

This notion of ‘enthymeme’ deserves further comment, and here is not really the place;  yet I can find no other home for it, among these essays.  Thus:

This is characteristic of ancient informal logic -- that is, of the logic of proof or of thought-experiment …. ; we regard it as enthymematic  only through hindsight:  it was only later that an increase in content  became a sign, not of the power, but of the weakness, of an inference.

-- Imre Lakatos, Proofs and Refutations (1976), p. 81

For more from this pen, try this:
http://www.linguasacrapublishing.com/justice.html

A Minimum Axiomatization for Reality (Part IV)

[continued from this]

So:  Having further motivated our positing of the new ZFC, as an essentially modest and conservative move,  we inquire, what further potential axioms  might attract our attention?

The first thing that springs to anybody’s mind  is “the existence of God”; but here I must be a spoilsport.  Simply by its bare wording, it yields us almost nothing – no more than a positing of “the Great Pumpkin”.  But then, almost everyone who subscribes to the statement  means a heck of a lot more by it than they let on;  that lot-more differs, from person to person; what it is, is inexplicit, at least until some War of Religion breaks out; and is mostly unconscious in each one of us.  It’s about as useful as, in set theory, the proposition that  “Sets exist”; or, in the Theory of Everyday Life, “Sh*t happens”.  Both doubtless true, but not fruitful.

Thus:  What conjecture might be worthy of being accorded provisional axiomatic status, by the Regressive Gambit (“By their fruits ye shall know them”)?

One we have already met.

(Axiom I) Der Herrgott ist rafiniert,  aber boshaft ist er nicht.

Remarkably, this principle is tacitly assumed  in enterprises as widely separated as the Theory of Everyday Life, and theoretical physics.  Our Olympic judges are holding up a unanimous “10-out-of-10” on the score of Fruitfulness.

Specifically:

(A) In the former, it serves for such essential tasks  as allowing us to accept, without qualms,

(i) the Existence of Other Minds; and for refuting that vile devil’s-spawn,

(ii) the falsity of the Myth of the Brains in a Vat, along with the ravings of Berkeley.

Note:  The Man in the Street already accepts (i) without qualms, having fortunately been spared contact with the corrosive hyperscepticism of the tenured diabolists (excuse me – eliminative materialists); and has probably never heard of (ii), unless he has watched “The Matrix”.  So who needs another axiom already? -- But here he simply joins the otherwise honorable ranks of those early mathematicians, who made implicit use of the Axiom of Choice in their proofs, without knowing it.  (I) is indeed necessary for the deduction of (Ai) and (Aii) – trust me on this. If you deny it – well, if you lead the Unexamined Life, I can’t argue with you.

(B) In physics, it undergirds (though it does not establish) such covertly metaphysical principles as Uniformity, Symmetry, Analyzability … 

Again:  the Lad in the Classroom imagines, between toothsome chomps on his chewing-gum, that these are affordances of Science itself, along with the opposite Coulomb charge of electrons and protons, and the curious mating habits of the mantis; for he has met these ideas in no other setting.  But again:  They are prior principles guiding the practice of science, not something we discovered in a lab.

A merely autobiographical aside, of no philosophical import whatsoever:

I tend instinctively to accept (I), though on very little evidence.  If pressed, I defend it – lest Reason flee her throne.  But in the matter of physics, I tend to think its reach is less than one might suppose.  Already the paradoxes of quantum theory seem to infirm it to some extent.

(I), then, though some deem it crucial, is not comparable to the seemingly intuitive Axiom of Choice, but is more like one of the ambitious axioms for Large Cardinals, with which, in recent years, theoreticians have attempted to trick out Set Theory. 

And here is another one, a classic – an axiom with the gloves off, comparable in overvaulting ambition   to the hypothesis of full-bore Measurable Cardinals, GCH, Surreal Numbers, you name it.  Its implications are absolutely incredible (and I mean that, alas, in both senses of the word), so please be sitting down before it is stated.  Ready?  Here goes:

(Axiom II) God cares about each one of us, individually.

This proposition is central to the theology, and even moreso to the psychology, of almost every Christian congregation.  It is in bad odor with most contemporary philosophers – but leave these aside.  We have each, in our own lives, experiences that make us contemplate (II), and either nod -- or wring our hands.

I’ll neither publically doubt that proposition, nor defend it, not being privy to any arguments beyond those already long-since trotted out on either side, nor to any personal experiences that might change the game..  But let us note that, largely from within the ranks of scientists, there has arisen a conjecture  intermediate in strength  between (I) and (II) –

            (Axiom AP) the Anthropic Principle

in any of its forms, concentrations, or dilutions.

Indeed, quite apart from its genesis, it is mainly scientists who pay attention to this hypothesis (and employ it in concrete calculations).  To the average believer, who already accepts (II),  (AP) is hardly news, since (II) entails it.

[completed here]

Metaphysical Infrastructure

The widest postulate of rationality is that the world is rationally intelligible throughout… The whole war of the philosophies is over that point of faith.

-- William James,  The Principles of Psychology (1890)

… unverifiable, unfalsifiable, and yet not arbitrary conceptions or hypotheses -- a class to which I have referred as thematic presuppositions … necessary for scientific work

-- Gerald Holton, The scientific imagination (1978), p. 99

[Postmodernism uses] a technique of metatheory (theory about theories), by which scholars analyze  not so much the subject-matter of the scientific discipline  as the cultural and psychological reasons  particular scientists  think the way they do.  The analyst places emphasis on “root metaphors”, those ruling images in the thinker’s mind  by which he designs theory and experiement.

-- Edward O. Wilson, Consilience (1998), p. 42

There is no such thing as philosophy-free science;  there is only science whose philosophical baggage is taken on board without examination.

-- Daniel Dennett, Darwin’s Dangerous Idea (1995)

… Whewell’s views about latent axioms, things which  at first  are not even credible, but which settle down into first principles.

-- Augustus de Morgan

Metaphysics (what we think reality is fundamentally like) can affect our ethics.

-- Edward Craig,  Philosophy: A Very Short Introduction (2002), p.  43

Awhile back, in a ground-breaking article, I proved the existence of coffee-cups.  But before the International Philosophic Society officially crowns this achievement with the name  of Justice’s Theorem (or even Justice’s Great Theorem, in contradistinction to Justice’s Little Theorem, to appear), we must confess that the proof was made possible only by the use of certain major metaphysical assumptions, up to and including the existence of God.  (Indeed, in a slightly strengthened version, known as  “Boshaft-ist-Er-Nicht” -- which still falls well short of God as conceived by Christianity.  So, you can still believe in coffee-cups without being Christian, though it helps.)  Given these assumptions, the actual deduction could have simply been “left as an exercise for the reader.”  So perhaps it should be demoted to, say, Justice’s Corollary, or even David’s Afterthought.

That was, of course, the whole point of the exercise:  to argue that many things we take for granted, and ought to take for granted, are not in fact straightforwardly empirically given, but must be derived with the aid of fundamental metaphysical principles,  which we seldom explicitly acknowledge in daily life, and which it has become the fashion  to deny.

Thus, Paul Davies, a physicist and a Christian, in The Goldilocks Enigma (2006), p. 262:

If there is no coherent scheme of things, then the success of the scientific enterprise to date  is rendered totally enigmatic, and science can be pursued only with a completely unjustified faith  that the methods used hitherto  will continue to uncover reasonlessly existing order  beneath the surface appearance of things.

A “coherent scheme of things” is basically a metaphysical notion.

He goes on to characterize the adaptationist fantasy (which we satirized here), that

brains have evolved to recognize patterns, and that -- again for no reason -- the deep patterns of physics and cosmology  resemble the patterns of the everyday world on our planet (which in fact they mostly don’t).

This all seems rock-solid.  In the satire, I wrenched it up a notch, noting the even greater implausibility of far-flung mathematicians from many different times and cultures  unanimously agreeing on the truth of such things as the Urysohn Metrization Theorem, which are farther from our experience even than quasars or quarks. 

On the other hand, where Davies, a believer, nonetheless has recourse to the phrase “unjustified faith” to belittle a credulous embrace of the scientific endeavor, Cohen & Nagel (secularists) use the same word “faith” (in the sense of naïve faith) to belittle a belief in something very like a “coherent scheme of things”:

The reader may perhaps believe that the inference from the observed conjunction of factors  to an invariable conjunction  is legitimate in virtue of the “uniformity of nature”.  We shall not disturb the reader’s faith in this familiar doctrine  at this point.  But, as we shall see presently, such a faith has no evidential value  in demonstrating the existence of invariable connections.

-- Morris Cohen & Ernest Nagel,  An Introduction to Logic and Scientific Method (1934), p. 254

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Philosophers by profession attempt to dig behind the appearance of things, and to uncover unsuspected incoherencies and hidden assumptions.  People just mowing their lawn, do not.   Midway between these  lie the scientists.

Since the scientific investigation of nature ipso facto strives to get behind the phenomena, its practitioners -- even if not otherwise philosophically inclined -- may be led to confront such assumptions.   Thus, going way back, and down almost to our day (until atomism, Mendelism, and quantum theory put something of a kink in it), is the Principle of Continuity.   Thus Wikipedia (I quote from the German, since the English in this case is a bit lame):

„Natura non facit saltus“ (lateinisch für „Die Natur macht keine Sprünge“) ist eine Grundannahme der antiken Philosophie und Naturwissenschaft seit Aristoteles (bzw. schon seit den Eleaten: altgr. Ἡ φύσις οὐδὲν ποιεῖ ἅλματα.). In dieser Form stammt das Axiom von Carl von Linné (1707-1778) aus seinem Werk Philosophia Botanica (Stockholm, 1751). Der Gedanke wurde später im biologischen und geologischen Gradualismus aufgegriffen.

Mit dem Satz wird ausgedrückt, dass sich Prozesse bzw. Veränderungen in der Natur nicht sprunghaft und plötzlich - diskontinuierlich - vollziehen, sondern prinzipiell kontinuierlich bzw. stetig.

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A magnificent expression of this view was the Great Chain of Being, stretching up from the paramecia, through the Humble Woodchuck, mankind, and the mighty penguin, up to cherubim and archangels and beyond.

This notion is closely related to the Principle of Plenitude, likewise of ancient date:  and likewise leading to startling modern updatings, in the Many-Worlds fantasy of quantum theory, or the Multiverse (currently all the rage.)  Edward Harrison (Cosmology, 2000, p. 268) characterizes it thus:

The principle of plenitude:  everything that is not forbidden is compulsory.  Whatever is possible, must exist.  In science we see that nature is plenitudinous rather than parsimonious.

A stark contrast, then, between the (plenitudinous) objects of inquiry, and our (parsimonious) ideal of explanation.  (More on parsimony here.)

 

Or again,  “Nature abhors a vacuum”.   In the universe of our forefathers, what would otherwise have been the vacuum  was filled up with the ether;  now it is clogged with quantum foam.

Or:  Occam's razor (" lex parsimoniae"), the implement of choice for those seeking Unification.

And, 

According to the rationalistic doctrine, the causal principle is a necessity of thought (Denknotwendigkeit), an a priori regulative principle, hence a presupposition rather than a result of science.  This is the opinion of the Leibnizians, for whom the causal principle is nothing but a form of the principle of sufficient reason.

Mario Bunge, Causality and Modern Science (1959, 1963)

Nonlinear systems do not 'obey' the 'principle' (theorem) of superposition (of forces, displacements, and so forth) ... The 'principle' of superposition may be regarded as the specific form taken in physics  by the hypothesis of the independence of causes.

Mario Bunge, Causality and Modern Science (1959, 1963)

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Note, though:  metaphysical infrastructure, not metaphysical foundations.   Metaphorically, these principles are like the skeleton in the body, which, though fundamental, is not more important than the blood or the flesh.

It is difficult, indeed, to come up with metaphysical foundations for science out of metaphysics itself.  Thus, consider Kant.  After thinking long and hard, abstractly (none of us could have done any better, within those limits), he managed to convince himself that having extension was of the very essence of physical objects, thus “All bodies are extended” is analytic.   Musing further, he concluded that having weight lay outside of what it meant to be a body, hence “All bodies have weight” is synthetic.

Presumably this last hunch was not a prescient anticipation of massless particles like photons and (perhaps) neutrinos.   In any event, the same arena furnishes examples of bodies that do indeed have rest-mass, but (if indeed they are point-particles) no extension:  electrons.

Reductionism, when its status is not that merely of a convenient method, but of a tenet or article of faith, might be deemed a metaphysical principle.

Edward Wilson, in Consilience (1998), rather stands the matter on its head, since he refers to science itself as metaphysical: “Science offers the boldest metaphysics of the age.”   He would seem to be using the word in some different sense. -- In any event he is not consistent in such use, as he later goes on to warn, more conventionally, against "the pitfalls of metaphysics".

Anyhow:

The prototype of a body is a coffee-cup, with extention, mass, hardness, etc. etc.   Kant’s musings really added nothing to our understanding of these.   Subsequent scientific results did add something:  an object can lack mass, or lack extension, or both, or neither.  Tiens, tiens.   To what extent we assimilate such items to our prototype of a "body", is more a matter of metaphor than of science or philosophy.  How is an electron like a coffee-cup?  like the old riddles of childhood and thereafter (“How is a blonde like a bottle?” -- “They’re both empty from the neck up.”)

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I'm not particularly wedded to this term "metaphysical", b.t.w.; mostly it is just nicely provocative.  What I'm talking about here is related to what Gerald Holton discussed using his favorite terminology of themata.  (I once visited Holton in his office one summer;  he grabbed my lapel and launched into the topic of themata, like the Ancient Mariner.)  Thus ( The scientific imagination (1978), p.20):

This prototype for explanation (classical causal sequences  account for observed accident or disorder) is a thematic commitment.  It is not an experimental or logical necessity.

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Now for some more recent methodological/metaphysical assumptions of physics.

Edward Harrison, Cosmology (2^nd edn. 2000), p. 454:

We are unable to obtain a model of the universe without some specifically cosmological assumptions that are completely unverifiable. (George Ellis, “Cosmology and Verifiability”, 1975).  The problem is that we observe isotropy, which we cannot explain,  and we assume homogeneity, which we cannot verify.

As you see, working scientists are sometimes acutely aware of such epistemologically awkward states of affairs.   But here’s another one I’ve noticed, and am not too sure that it is widely recognized as a tacit working assumption:

~ Do I contradict myself?  Very well then, I contradict myself.

It’ll all work out in the end. ~

Gerald Holton, in his detailed investigations of the rival Ehrenfest/Millikan experiments in verifying and quantifying the hypothized granularity of electricity ("Subelectrons and Presuppositions", reprinted in The scientific imagination, 1978), refers to the "suspension of disbelief" on the part of an experimenter, faced with the blooming buzzing confusion of his contradictory daily results.  But this epistemological grace period was envisioned as lasting over the course of a series of experiments, not for decades or centuries.

Thus, classical physics predicted that orbiting electrons would continuously radiate away energy -- and thus collapse into the nucleus.  Hence, atoms could not exist.  Nor was there a glimmer of a solution on the horizon.  Physicists just lived with it.  When a solution of sorts did come, with quantum mechanics, it was of an utterly strange and unforeseen sort.

The history of science -- of physics in particular -- is riddled with such intellectually scandalous states of affairs.   And yet the trustful, What-me-worry stance of the everyday scientist  is wise in its way -- it’s that or quit physics (or discover quantum mechanics).    Perhaps, without explicitly saying so, they inwardly believe that the universe is an orderly and rational place, and that our fumbling steps are somehow guided, and that the Plan unfolds in time.   Perhaps they believe  (in their heart of hearts) … in Him.  For if not -- whence the assurance of (A) ?

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Brian Greene, The Fabric of the Cosmos (2004), p. 224:

Physicists have elevated  symmetry principles  to the highest rung on the explanatory ladder. …. Physicists believe these theories are on the right track because, in some hard-to-describe way, they feel right, and ideas of symmetry are essential to this feeling.   … Symmetries are the foundations  from which  laws  spring.”

The manly admission of the role of (most unmanly) “feeling” here, is well in point.  But it is not really subjectivism -- the personal equation -- that is in play here.  Rather, a level of explanation  deeper than that of laws,  which we cannot grasp  with our intellect.

He goes on (p. 243):

Symmetry is the essential consideration  allowing us to comprehend space and time when applied to the unuiverse as a whole.  Without invoking the power of symmetry, we’d be stuck at square one.

Well I recall, many years before, a lecture by Steven Weinberg, in which he mentioned Galileo’s sticking to circular planetary orbit, despite Kepler’s having previously demonstrated their elliptic shape.   The occasion, in most settings, of indignant Whiggish sniffs; but Weinberg wisely -- like a bolt it was -- demurred:

Galileo was perfectly within his rights to privilege such symmetry, it lies at the heart of all subsequent physics.  His error, merely, lay in mistaking the planets, those -- not godlings, as for the pagans, but -- dull lumps of earth, as lying near the center of things.

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The principles lying perdu behind our practice, need not be recondite, but they are metaphysical (as opposed to empirical) nonetheless.  Thus the charming simplicity of the complicated Quine:

The so-called scientific method is a matter of being guided by sensory stimuli, a taste for simplicity in some sense, and a taste for old things.

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I do not intend to suggest a disjunctive dichotomy between “metaphysical” assumptions on the one hand, and empirical matters on the other.  Rather, there is a sort of hierarchy (not necessarily linear) of relatively-specific facts or principles, and relatively more general.  The former will be at the front of consciousness, in practical work;  the point of the present essay is to point to the latter, lest they be forgot.  But often, both levels will clearly lie within (say) physics.

Thus:

The only reason for introducing probabilities in the study of gases  is to obviate the insuperable mathematical difficulties which a direct application of the mechanical laws would involve.  The mechanical laws, however, are utilized indirectly, for it is by their means (and also by accepting the ergodic hypothesis) that the probabilities are computed.

-- A. D’Abro, The Rise of the New Physics (1939), vol. II, p. 945

And, concerning the alleged correlation of disorder and frequency of macrostates, Georgescu-Roegen comments (in The Entropy Law... 1971):

The proposition comes very close to being a metaphysical principle. ... It is this metaphysical essence which accounts for the insuperable difficulties encountered in justifying the new Entropy Law,  either experimentally,  or analytically by derivation from other basic laws.

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Edward O. Wilson, Consilience (1998), p. 198, lists the four metascientific desiderata for any scientific theory:  parsimony; generality; consilience; predictiveness.

It is in point of consilience that he finds Creationism wanting.  “God may exist, He may be delighted with what we are up to on this minor planet, but His fine hand  is not needed to explain the biosphere.”

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Unlike considerations of symmetry or simplicity, ideas of causality do not, I believe, generally guide research as (examined or unexamined) metaphysical assumptions behind the scenes.   Rather, research proceeds on its own terms, and periodically is discovered to have implications for our notions of causality.  So, I will not here comment on that.

In the public and legal arena, by contrast, very practical decisions are influenced by our hazy ideas of causality.  A stab at clarifying a couple of these: here  and  here.

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Miscellaneous quotations on the matter of metaphysical underpinnings (with attendant vocabulary):

Unity of science” … “physical forces”  were not merely directing ideas or hypothesis of scientific endeavor:  they became almost objects of worship.  They were more than methods of research -- they became a Weltanschauung.

-- Ernest Jones, Freud: the Formative Years (1953), p. 43

Gauge invariance is not a physical principle, but a logical principle.

-- Russell Standish, Theory of Nothing (2006; 2nd edn. 2011), p. 121

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The tacit ideational underpinnings need not be strictly metaphysical;  it can be straightforwardly practical:

The real issue in this connection is not the one commonly debated, “What are the criteria for the selection of patients?”, but the underlying, usually unstated assumption, “Criteria for selection are good”.  There are strong theoretical and practical reasons … for saying that  “Selection of patients is not good” … The best policy is to pick patients at random … to increase the heterogeneity of the group.

-- Eric Berne, Group Treatment (1966)

“Tacit principle” cf. “pious assumption/lip-service”:

At present, the only statement that can be made is that it is helpful for a group therapist to have had personal experience as a patient in a therapy group.  But even that   is only a pious assumption, since  in fact  it has never been critically evaluated, and so still remains part of the lore of institutional group therapy.

-- Eric Berne, Group Treatment (1966)

[Bonus quotes]

Fundamental to knowledge are certain “analytical hypotheses” that go beyond the evidence.

-- Noam Chomsky, “Quine’s Empirical Assumptions”,  in:  D. Davidson & J. Hintikka, eds. Words and Objections (1969, 1975), p. 60

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