Simulated Annealing and the Art of Detection

“My way of learning  is to heave a wild & unpredictable monkey-wrench  into the machinery.”
-- shamus Sam Spade, in The Maltese Falcon (1929)

Dashiel Hammett’s P.I.’s find themselves in large, chaotic situations, in which the methodical self-discipline of, say, Dragnet, won’t get you anywhere.   Joe Friday is scrupulous, professional, polite;  Hammett’s guys  are none of those things.

Nor do they follow the cool, cold-blooded approach of what we might dub “Newton’s method “of successive triangulations and approximations.  Instead it’s: stir up the pot. Stir and observe, stir and observe;  add bullets to taste, p.r.n.

cf. Newton’s method of repeatedly refining an initial guess.

~

The police want to grill a man they suspect of having abused and murdered his step-daughter, but have no tangible evidence.

“I don’t know.  What are we going to ask him?”
“If he reads the Evening News. … Christ, Tommy, we can ask him what his favourite colour is.  I just want him in here, under pressure, so we can see what happens.”

-- Val McDermid, A Place of Execution (1999), p. 205

~

And thus it is with Murphy, Private Eye.  He is no master of empirics nor of ratiocination, like Holmes;  nor of intuition into souls, like Father Brown;  but he’s got heart, and he can take a punch, and he’s got a gun;  plus what’s a fella to do?  He’s got a Mission.

So Murphy has what starts out as yet another hopeless case:  His so-called “client” is a ditsy dame with no simoleons to pay him;  plus she gets bumped off practically at the outset;  but he soldiers on.  Because that’s what soldiers do, when they’re on a Mission.

And so it looks hopeless but, he stirs the pot a little, tries this and that, and the next thing you know …

To follow this sobering  yet inspiriting  adventure, simply click here.

For more from Murphy -- philosopher and P.I. -- check out his blog:

=>   http://murphybros.blogspot.com/

~

In sum:   Jiggle the system, let it settle into a local equilibrium;  then jiggle again.  Repeat (with decreasing strength of perturbations as the ideal is neared).

Related to this is an epistemological principle, valid for scientists and detectives alike:   Don’t jump to conclusions.   Or, in a quantum-computing metaphor, don’t provoke a premature collapse of the wave-function.  Keep the various possibilities  juggling in the air, until one or more can be definitively ruled out.

 

Veracity, Verifiability, Vindication

[That is an ascending series.  Some things that are true, may yet be inaccessible to us -- temporarily, or forever;  a veracious person is someone who asserts only what he sincerely believes to be true (and -- for this quality to have any practical value -- has reasonable warrant for so believing, reasonable relative to the contemporaneous state of the art.)

Verifiable means that the assertion is ‘in the running’ for being experimentally (or proof-theoretically) confirmed, even though these happy results have not yet eventuated.

Vindicated means that the result has been supported, whether by (theory-supported) experiment, formal proof, or revelation.]

[Original post from 7 VI 2015]

A crisp, concise op-ed, in this morning’s NYTimes, “A Crisis at the Edge of Physics” by Adam Frank and Marcelo Gleiser (both professors of physics), states the case against (over-cantilevered or under-buttressed) speculation, not only for string theory (which has notoriously come in from a lot of pushback;  see Lee Smolin, The Trouble with Physics), but for supersymmetry generally.  The authors note that, as of even date, “no supersymmetric particles have been found” (perhaps they are hiding out in a back room, playing poker with the Higgs boson).  So far as that goes, not a problem;  plenty of propositions in math and science took centuries or even millennia to settle.  What disturbs the authors is that some champions of supersymmetry -- the jusqu’au-boutistes, we might call them -- may simply move the verificationist goalposts.

Some may choose to simply retune their models to predict supersymmetric particles at masses beyond the reach of the Large Hadron Collider’s power of detection -- and that of any foreseeable substitute.

Exactly the same concerns were voiced, a good decade earlier, by the mathematician-physicist Roger Penrose, in the section “Can a wrong theory be experimentally refuted?” (p. 1020 ff.), in The Road to Reality (2004), concerning “un-Popperian” practices in physics.

If that were only a problem for one avenue at the forward fringes of physics, that would not be a problem for most of us  as we bustle about our daily chores.  Yet the authors further suggest that certain well-traveled avenues  are actually cul-de-sacs:

The standard model, despite the glory of its vindication, is also a dead end.  It offers no path forward to unite its vision of nature’s tiny building-blocks with … gravity.

What really bothers the authors is something that goes well beyond physics:  “the specter of an evidence-independent science”.   And that specter has been haunting the West for some time, and increasingly reaches into the headlines, as witness the countermovements to the theses of natural selection or of global climate change.

Not being a physicist, I have no right to comment;  but, at the margins, this:

(1) The larger cultural worry, is the dissociation of the notion of Truth überhaupt  from that of Evidence and Argument. In that perspective, we would deplore the demand to dissociate theory from experiment.

(2)  Yet -- Do not forget  Einstein’s classic crack in 1919, anent the possible negative results of an experiment purporting to validate or refute General Relativity:  “Da könnt’ mir halt der liebe Gott leid tun.  Die Theorie stimmt doch.”  (Informal translation:  "I'm right.  Bite me.")

Die Theorie stimmt doch!

The consensus of scientific history (for right reasons or wrong)  has been to applaud  those cheeky remarks .

~

Einstein was speaking of his theory of gravitation.  But similarly for particle physics.

Compare, re Feynman and Gell-mann’s joint article “Theory of the Fermi Interaction” (written in 1957, and subsequently published in Physical Review):

The V - A theory was in disagreement with more than a half dozen experimental results on beta-decay,  but it was so beautiful  that the authors proposed it anyway, suggesting that all those results were wrong.

-- Harald Fritzsch, introduction to Murray Gell-Mann: Selected Papers (2010), p. 5

And:

The Standard Model … has been driven largely by certain powerful consistency requirements, hard to satisfy in such theories.  In order to appreciate something of the force behind these consistency requirements (which continue to drive the more modern speculative theories, such as string theory), we shall need to look at the structure of quantum field theory. … The theoretical requirements appear to be so tight  that it might seem almost incidental that these answers are actually in excellent agreement with experiment!

-- Roger Penrose,  The Road to Reality (2004), p. 655-6

And more generally:

Polanyi delighted in drawing attention to cases where the scientific community ignored or waved aside or explained away  seeming counter-evidence to accepted theories.  He seems to have felt that a scientist would abrogate his personal responsibility for his beliefs  if he allowed them to be at the beck and call of experimental results.

-- John Watkins, Science and Skepticism (1984), p. 29

Nor must we wait until our own extravagant age of post-modernism and M-theory, to find ourselves confronted with an “All is Permitted” ethos in the realm of physics.

Karl Pearson, as a pioneer of statistical thinking in a wide range of fields, is in that respect  a representative of a hard-headed, just-the-facts-ma’am, shut-up-and-calculate approach to messy realities.  But when doing (what he thought of as) physics, his Romanticism, which early on was a major strain of his make-up, got the better of him.   In the years around 1890, he theorized about atoms in terms of the then-regnant ether theory:

He spoke  not of causation  but of analogy, indeed “analogies … of the vaguest description”, and in the context of this paper, his doubts about the human capacity to get at real objects or real causes  functioned as a license to invent … Since his ether model  so far  had strange, almost inconceivable properties, he discarded physical plausibility as a criterion of a good theory.

-- Theodore Porter, Karl Pearson (2004), p. 187

"You see it's all simply a matter of ether-squirts ..."

~

Working the equations of physics to their long-reaching logical conclusions, continually leads to apparent absurdities:  negative energies or frequencies, unobserved particles, particles moving backwards in time, a Hobson’s choice between acausality or indefinitely-proliferating alternate universes, and miscellaneous infinities.  Some physicists shudder at such;  others grin and say “Bring ‘em on.”  (Unfortunately, the latter are the ones favored in the popular media -- the phenomenon of Physics Porn.)  The problem is deciding when that is just the way Nature (inscrutably) actually works (in which case you have made a major discovery), and when it is merely absurd.  Will the Higgs boson turn out to have been more like the positron (born from the forehead of Dirac’s mathematics) and the pion (brain-born from Yukawa), eventually found in everyday space, or  instead  like the cute-sounding but still-missing photinos, squarks, and pentaquarks?

[Update July 2015]  Bzzt!  No sooner had I posted that, than experiments claim to have spotted one of the elusive critters:

http://www.nature.com/news/forsaken-pentaquark-particle-spotted-at-cern-1.17968

So here is the larger temptation -- the intellectual Occasion of Sin:

Beginning several decades ago, comparing the results of experimentally well-verified physics  with the predictions of the equations, scientists marveled at what was memorably dubbed “the unreasonable effectiveness of mathematics”, summed up by the epigram “the equations seem to give us more than we put into them;  they seem to be wiser than ourselves”.   But The Edge beckons when we start to conclude, that if our favorite equations predict something, then that something must be so (if only in the Multiverse) -- even if, to the guys in the lab, it doesn’t seem physically reasonable.

As Penrose puts it:

What is the physical justification in allowing oneself to be carried along by the elegance of some mathematical description  and then trying to regard that description as describing a ‘reality’?

-- Roger Penrose,  The Road to Reality (2004), p. 670

That question takes us back  to a very old debate -- as old as poetry :  What is the relation between Beauty and Truth?

In that essay, we concluded that, in a sense, ‘beauty’ (in a rather austere sense of crisp symmetric elegance, having more to do with the Parthenon than with a Miss America pageant or a Turnerian sunset) does characterize any deep theory in the mathematicized sciences -- but only in retrospect, after years and decades of its practitioners coming to appreciate its depth; the theory does not wear its beauty on its sleeve.

Thus, even in the case of the (relatively) well-behaved, now-long-familiar poster child of particle physics, QED:  Paul Dirac, the pioneer of QFT, wasn’t buying it.   In response to a 1936 experiment (by Shankland) which suggested (incorrectly, as it turns out) that energy need not be microscopically preserved,

Dirac immediately jumped at this opportunity to disown QED, claiming “because of its extreme complexity, most physicists will be glad to see the end of it."

-- Matthew Schwartz, Quantum Field Theory and the Standard Model (2014), p. 247

~

Taking physics on faith

Penrose again, concerning a couple of signature contributions by Richard Feynman -- probably the educated public’s favorite hip physicist since Einstein:

The path-integral approach is, it seems, almost wholly dependent upon a faith that the wildly divergent expressions that we are presented with (like the divergent series above) actually have a deeper ‘Platonic’ meaning  that we may not yet properly perceive.

-- Roger Penrose,  The Road to Reality (2004), p. 670

Theophysical note:  Here we see a reference to “faith”;  its truth-functional content may be roughly equivalent to “working assumption”, but since we are indeed dealing with such deep and ultimate matters of Platonism, the theological overtone is not actually out of place. 

Similarly, my casual reference to “revelation” above, as denoting one of various routes to knowledge, was not flip.  Compare, from our hard-headed flinty-eyed philosopher of science:

If  we had a hot line to the Author of Nature, and if we had a clearly formulated IP [for which see below], an excellent question to put to him would be:  Is our IP true?  If he answered ‘Yes’, we could happily set a computer to work to print out all those h[ypothese]s that are singled out by our evidence  in conjunction with this authoritatively endorsed IP.
-- John Watkins, Science and Skepticism (1984), p. 93

And if that strikes anyone as credulous, note that most of us largely treat computers as oracles as well (e.g. in the proof of the Four-Color Theorem, or any of innumerable unsurveyable and possibly preposterous simulations).

Back to the sadder-but-wiser Penrose:

Even that archetypal renormalizable theory, QED, is not actually a finite theory, even after renormalization.  How can this be?  Renormalization refers to the removal of infinities from finite collections of Feynman graphs.  It does not tell us that the summation of all these resulting finite quantities is actually convergent. … In fact it is not finite, but has a ‘logarithmic divergence’.

-- Roger Penrose,  The Road to Reality (2004), p. 680

(Logarithmic divergence is comparatively mild, but it still gets where it's going -- an unphysical infinity -- in the end.)

As for the next step beyond QED (which is part of the Standard Model), QFT:

Strictly speaking, quantum field theory … is mathematically inconsistent.

-- Roger Penrose,  The Road to Reality (2004), p. 610

~

But let us set aside quantum mechanics, that known maze of paradox, along with its ever-more-speculative successors.  Surely matters stand better in the case of classical mechanics and electromagnetism, along with their tool-of-all-work, the venerable Lagrangian, which dates back to the eighteenth century. 

Yet even here, Penrose demurs:

In modern attempts at fundamental physics, when some suggested new theory is put forward, it is almost invariably given in the form of some Lagrangian functional. … However, I must confess my unease … The choice of Lagrangian is often not unique, and sometimes rather contrived … Even the Lagrangian for free Maxwell theory … has no obvious physical significance. … Moreover, the ‘Maxwell Lagrangian’ does not work as a Lagrangian unless it is expressed in terms of a potential, although the actual value of the potential, A, is not a directly observable quantity. … In most situations, the Lagrangian density does not itself seem to have clear physical meaning.

-- Roger Penrose,  The Road to Reality (2004), p. 491

Nor is Penrose a professional maverick or skeptic.   After all, the book we’ve been quoting from clocks in at over a thousand pages, and is subtitled “A Complete Guide to the Laws of the Universe”;  you wouldn’t do that if you thought physics was a crock.

~

Simply as an assertion, the Weyl curvature hypothesis  is perhaps more like a claim for ‘an act of God’  than a physical theory.

-- Roger Penrose,  The Road to Reality (2004), p. 769

Rule of Thumb:

Physics advances by dint of Physicists’ Encyclicals.

These are almost never arrived at purely deductively;  nor as the result of conclusive, slam-dunk experiment, leaving no leeway for doubt of validity nor variation in interpretation(**); yet neither do they come out of nowhere.

[**:   That classic 1919 experiment, about which Einstein was so dismissively cocksure, was not actually so probative as the newspapers made out.  Worse yet, that alltime- irreproachable über-icon of experimental virtuosity, the Michaelson-Morley experiment, traditionally cited as crucial for Special Relativity, did not really quite have the widely-advertised null result.  Lindsay and Margenau, in their history of physics, note this fact with some embarrassment, since so much of what they have to recount -- and which they do recount -- rests upon that pedestal;  they keep mentioning it with a proviso.  And at an even more elementary level in cosmology, the experimental results that led to the Red Shift principle: when Steven Weinberg painstakingly went over the actual original data, he pronounced himself baffled as to how Hubble ever extracted his famous monotonic relation from them.]

Schrödinger’s equation -- Feynman’s path-integrals -- the laws of thermodynamics:  inspired guesses, which awaited the mathematicians to tidy things up.

-- Not trying to debunk, here;  simply being historical.

(Feyerabend, too, was long  historical  in this sense, before he went over to the dark side.)

~

Donning our old lexicographer’s hat, let us look a bit more into the matter of vocabulary, the Wortfeld of terms for justification. 

Our negative result so far, entirely in line with Hume’s, is that, without an inductive principle, there can be no legitimate ascent from level-0  [i.e., things like “yellow patch, for me, here, now”] to level-1, or from level-1 to level-2, and that any inductive principle strong enough to “legitimise” the ascent  could not itself be legitimised.   If that is so, then it is obvious that there can be no legitimate ascent to still higher levels.

-- John Watkins, Science and Skepticism (1984), p. 105

In the following, we see a fine distinction drawn between justification and “vindication”.

The philosopher John Watkins imagines a principle, call it the Inductive Principle, which would answer Hume’s objections, to the satisfaction of inductivists.  What would then be the status of the IP?   He distinguishes several possible theses :  that it is “synthetic and true a-priori”, “synthetic and provable by a transcendental argument” (which latter turns out to be little more than “Well, it seems to work”), and:

*  IP is synthetic and empirically justified.

*  IP is synthetic, and, although it cannot be justified either a priori or a posteriori, it can be vindicated.

-- John Watkins, Science and Skepticism (1984), p. 93

The verb vindicate is slightly odd here;  usually it has moral overtones, of someone having been right against opposition or against the odds.   You verify someone’s age on his driver’s-license;  you validate a parking-stub; you vindicate a statesman’s course of conduct.

The term justification also has a richly complex ethico-theological usage in Christianity, quite opaque to an outsider.

~

More fine distinctions, this one semi-defined on the fly:

One’s degree of rational assent to a hypothesis should be controlled by its degree of confirmation (‘confirmation’ being understood in some quasi-verificationist or probabilist sense).

-- John Watkins, Science and Skepticism (1984), p. 118

Watkins then spins off into the world of proofs-and-refutations, abduction, and the like:

The sought-for relation between e[vidence] and h[ypothesis] is now inverted:  instead of an upward, quasi-verifying inference from e to h, we have a downward, explanatory derivation of e from h.

-- John Watkins, Science and Skepticism (1984), p. 119

Note those squirrely “quasi”s, by the way.  For all the wealth of the verificatory Wortfeld, no term seems quite to fit.

~

We have been focusing on physics;  but analytic philosophers have long discussed these matters in great depth.  A few representative teaser-quotes, giving some extra vocabulary, and the flavor of the debates:

The great contribution of [Quine’s “Two Dogmas of Empiricism”] was that it offered an essentially verificationist account of language  without committing the logical-positivist error of supposing that the verification of every sentence could be represented as the mere occurrence of sense-experiences. … Proof, which is verification by inference alone, thus becomes a limiting case, or a distinct species.

-- Michael Dummett, “What is a Theory of Meaning? (II)”, in: Evans & McDowell, eds., Truth and Meaning (1976), p. 111

… notorious problems about the connection between corroboration and verisimilitude …

-- Susan Haack, Evidence and Inquiry (1993), p. 105

Note here that, within the genus of positive instances, the term “confirming instance” is disastrously ambiguous  as between a supportive  and a nonsupportive species of positive instances.  By the same token, logical mischief has been wrought by the weasel word “verification”  and the equivocal verb “verify”.

-- “Is Falsifiability the Touchstone of Scientific Rationality”, in: Adolf Grünbaum, Collected Works, vol. I (2013), p. 15

[Update Dec 2015]  Physicists are beginning to get seriously perturbed by all this.

A Fight for the Soul of Science

https://www.quantamagazine.org/20151216-physicists-and-philosophers-debate-the-boundaries-of-science/

String theory is at the heart of a debate over the integrity of the scientific method itself.

http://www.nature.com/news/feuding-physicists-turn-to-philosophy-for-help-1.19076

[Update 19 Jan 2017] Philosophically on a more modest level than any of these "V's", is simple reproducibility of experiments --a minimum requirement for verifiability.  But there are problems even with that.  A new study of reproducibility released its results for the first five classic cancer-related experiments whose re-performance was attempted:  five experiments, five failures.   Background:

Cancer reproducibility project releases first results

The Reproducibility Project: Cancer Biology launched in 2013 as an ambitious effort to scrutinize key findings in 50 cancer papers published in Nature, Science, Cell and other high-impact journals. It aims to determine what fraction of influential cancer biology studies are probably sound — a pressing question for the field. In 2012, researchers at the biotechnology firm Amgen in Thousand Oaks, California, announced that they had failed to replicate 47 of 53 landmark cancer papers2. That was widely reported, but Amgen has not identified the studies involved.

Perhaps the clearest finding from the project is that many papers include too few details about their methods, says Errington. Replication teams spent many hours working with the original authors to chase down protocols and reagents, in many cases because they had been developed by students and postdocs who were no longer with the lab. Even so, the final reports include long lists of reasons why the replication studies might have turned out differently — from laboratory temperatures to tiny variations in how a drug was delivered.

http://www.nature.com/news/cancer-reproducibility-project-releases-first-results-1.21304?WT.ec_id=NATURE-20170119&spMailingID=53225513&spUserID=MjA1NjgwMjUyOAS2&spJobID=1083504884&spReportId=MTA4MzUwNDg4NAS2

Stochastic Rabbit Chromodynamics

I was sitting at ease on the back porch, in the gathering dusk, with a drink at my left hand, and a pencil in my right;  reading, as it happens, about Quantum Field Theory.  I mention this detail  merely by way of explaining how it came to be that I was wearing only my reading, and not my distance glasses.   Thus I was instrumentally impaired as regards the strange events that soon ensued,  rather like Particle Physicists before the advent of the Large Hadron Collider.

All at once, as if out of nowhere (in the image, as it were, of the quantum-mechanical Creation-Operator; though more specifically, through a hole in the hedge), there appeared a rabbit -- or rather, given the limitations of our equipment, a soft beige bunny-blur.   (Sort of a Heisenberg hare.)  "Gavagai!" I said to myself (**);  and stared.  -- On the other side (unseen), a mean dog is making horrible barking noises.  Bad, bad dog!

[**:  The translation of this manifold-ambiguous ejaculation, in these field-conditions, would indeed be, not “Lo! Rabbithood again”, but something like “Lo! A rabbit-instanton” or even “Behold, a rabbity-patch!”.]

Given these initial conditions, one would have predicted that the frightened rabbit would have continued to accelerate, streaking off out of view;  but no.  The bunny did not scuttle-and-run, but settled down peacefully on the spot.  Somehow, she seems to feel safe, here within the nice man’s hedged perimeter. 

The textbook, meanwhile, has yielded to the force of gravity, and subsided lifeless upon my lap.   I stare in the direction of the location of the bunny (to within experimental error).

Omigosh!  The bunny is washing her face with her furry pawsies!  Amid other cutenesses.

(Mind you, I can’t precisely see that, owing to the crude granularity of my present electro-optical apparatus, but can deduce it from certain fluctuations in the hare’s Hamiltonian, together with various interference-effects.

In much the same sense, our perception and positing of coffee-cups  is epistemologically inferential, and ultimately based on faith.

Since my vision of QFT is even dimmer than my myopic perception of distant objects, the bunny-blur is perfectly satisfying.)

Eventually the dog stops barking (go bury a bone, Fido), yet the bunny still placidly remains in place.  Contented, feeling secure.  The bunny can pick up my love-waves with her special tall antenna-ears.

Bunny, picking up signals

Eventually, having errands elsewhere, Miss Bunny goes hip-hoppity off,  leaving behind  a friend for life.

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

Ontological Epigrams

Okhamians like Quine (for so I shall refer to him, out of deference to my former professor, so as to avoid the loathsome connotations of Nominalist) are concerned not to clutter up the ontology with extra entities like facts or meanings which parallel and move in unison with statements  without really adding anything useful.  Strawson (a reliable nutshell-stuffer) puts it in a nutshell  thus:

Facts are what statements (when true) state;  they are not what statements are about.

-- P.F.Strawson, “Truth” (1950; often anthologized)

~     ~     ~

Quantum superposition is ontological, not epistemological.  It is not that we don’t know what state the cat is in.

(Unfortunately I have forgotten who said this.  Mark Twain?)

~     ~     ~

The ontological touchstone for British analytic philosophy, whether of the Idealist or the Empiricist inclination, has ever been the Tree in the Quad.    For several thousand years, this noble oak has been under uninterrupted observation by a rota of pre-Chalcolithic druids, lest it pop out of being, unobserved.  What a shame that would be!  It was such a nice tree!

~     ~     ~

The first question of ontology is:  What is there?

The answer to this, as Quine put it: Everything.
(Yet adds the stern proviso:  But no more than that.)

The second is, of each thing:  What is it?

To answer this, we may revise good Bishop Butler thus.

=>  Everything is, what it is  --  along with several other things as well.

Thus: a diamond is:

* A costly gem, proverbial for hardness

* A face-centered cubic crystaline allotrope of carbon

* A girl’s best friend

* Forever.

Given this, the question, What is Being? (überhaupt or tout court), must be categorized as meta-ontological.

~     ~     ~

Meinong’s bizarre deviation(**) … was … jenseits von Sein und Nichtsein.  Oddly enough, I find this idea a good one, provided that we bolster it with Bentham’s theory of fictions.  Contextual definition, or what Bentham called paraphrasis, can enable us to talk very considerably and conveniently about putative objects  without footing an ontological bill.  It is a strictly legitimate way of making theories in which there is less than meets the eye.

--- Quine, “Existence and Quantification”

The concluding epigram of that paragraph  is particularly relished by Minimalists.

(** Note:  The reference is to that philosopher’s ontological exuberence,  and not to any possible undue familiarities with capybaras during off-hours.)

~     ~     ~

Thus far the apophthegmatic epitome.  If these have whetted your appetite, click here.

[Orthoepic update]  Since folks keep clicking on this post, I'll add this:
The fifty-dollar first word of this essay  refers to the Nominalist, William of Okham.  That last word is pronounced OCK-um.  But the adjective, Okhamian (which I possibly just made up, but on a proper model) would be pronounced ock-HAY-mee-an.
Try to work this into your next singles-bar conversation.  It's guaranteed.

~     ~     ~

« Ontology can be saved  with a sufficient ideology. »

-- Saul Kripke, “Is There a Problem about Substitutional Quantification?”,

in: Evans & McDowell, eds., Truth and Meaning (1976), p. 343

Not sure what that means, exactly;  but it has a lilt to it, like “Die Welt ist alles, was der Fall ist”;  of which, perhaps, it is a paraphrase.