"Great Question"

Two flatulent practices relating to the posing of questions  have characterized political discourse in recent years, to the disbenefit of the polity.

(1)  Particularly associated with Donald Rumsfeld, though the maneuver antedates him, is posing ‘questions’ to oneself and immediately answering them.  Thus, let P and Q be propositions:  instead of saying simply

P.  Not-Q

the rhetorician draws it out into a monologue masquerading as a dialogue:

Is P true?  Sure it is!  Is Q true?   Absolutely not!

The advantages to the speaker are:

(a)  He gets to choose the ‘questions’, irrespective of whether anyone is interested in them or whether anyone would phrase the question in that manner.   As a result, they are invariably softball ‘questions’.

(b)  He gets to dwell in a bubble of his own voice.  Reporters, voters, maiden aunts, all fade into a kind of Meinongian subsistence;  and the Dialectic collapses to a trivial instantiation in the palaver of a single man.

Disadvantages to the audience include:

(c)  There is usually a substantive concern whether some proposition P be true, or what to do about it, or the like.   Yet by this slight-of-tongue, the bloviator poses instead some verbally related but substantively etiolated variant P-prime, and addresses that instead, thereby providing no real information or analysis, but leaving the impression that he has addressed P.

(d)  You have to listen to twice as much verbiage as for a straightforward “P” -- ten pounds of rhetoric in a five-pound bag.  And in time it gets freaking annoying.

(2)   In politically pre-sanitized settings like “town-halls” and related social Spectacles, an array of voters, carefully selected to represent each of the pressure groups to be pandered to, is permitted to pose a simple-minded, vaguely worded question, thus pushing a given button on the candidate’s library of prerecorded on-message speechlets.   But in a new development, the politician moves to snuggle-up to said Potemkin voter, with an enthusastic

   “Great question !!”

before launching in to her canned response.

The practice, repeated ad nauseam  (cf. SNL’s parody of Hillary Clinton’s use of this and similar maneuvers, in their satire of the Presidential ‘debates’), is distressing  even apart from its smarminess.    For the sort of low-info voter who most needs to be buttered-up and flattered, is least in position to actually pose a “great question”, or even a probing or pointed one.    Nor will, say, a scientist giving carefully-prepared, expert testimony on a complex subject  be patronized from the Congressional panel with a “Great question!”   The domains of “Great question!” and great questions, are virtually mutually exclusive.

Note:  The catchphrase “Great question!” is characteristically contemporary;  but the maneuvre is of longer date.   Speaking to a group,

Nixon would react to the most elementary question  as if he was hearing it for the first time.  He would ponder a bit, congratulate the questioner on his originality,  then give the answer he had given  hundreds of times before,  complete with some figures and a quotation,  as the citizen listened  in utter awe.
-- Stephen Ambrose, Nixon: the Triumph of a Politician 1962-1972 (1989), p. 139

~

And now, by an unhallowed congressus of these two tricks -- by Beelzebub out of Medusa -- comes the Great Rhetorical Question.  One came up this morning on NPR.

A Republican senator was touting Trump’s intention to

(i)  Increase spending (e.g. on infrastructure and defense)

and

(ii) Decrease taxes,

while

(iii) Holding down the deficit.

Now, this nation has been down that road many times before, both in speechifying and in practice;  so apart from the apparent logical incompatibility among those three desiderata, there is a track-record here, for anyone who cares to examine it.   That, however, is beyond the capacity of most pop journalists practicing today, as well as the attention-span of the average voter.    The substitute for critical inquiry, is a mere statement of undifferentiated unwillingness to be convinced -- the lazy-man’s lo-cal substitute for genuine skepticism (anatomized here).   In this case, the reporter’s Clarence-Darrow move was simply to ask, again, how (i)-(iii) might cohere.   But the politician was ready for it:

“Yes -- How can we address the problem of doing the things that need to be done, while holding the line on the deficit, without addressing the question of Entitlements? -- Great question!”

That may or may not be a Great Question, but the reporter had not posed it;  the rhetorician was congratulating himself.   And in so doing, bait-and-switched the subject from the incompatibility of (i)-(iii) to the problem of those pesky Entitlements.  A perfectly legitimate subject of debate, but here snuck-in via a side door.

~

The considerations above  recall to mind  what, for Europeans, must be the original Potemkin-“question” scam:  to wit, the Socratic dialogue.

The scenario has been solemnly sanctified,  countless times  over many years decades centuries.  The method has been dignified with the title  maieutic (etymologically relating to widwifery), whereby the savant or solon, by adroit interrogation, draws forth from the naïve listener (like a tapeworm from the bowel) innate knowledge  such that all might marvel that he hath.

As a build-up, this is terrific, only… You actually read the texts, and what you see is Socrates holding forth, more or less commendably, and harvesting the plaudits of uncomprehending minions or yes-men.

Thus, a demonstration of the Urysohn Metrization Theorem, via the Socratic method.

Socrates:  Let us, therefore, consider any topological space whatsoever, so that it have a countable basis.  You agree?

Minion: Sho’ nuff, boss!

Socrates: And may we not further stipulate, that said space be regular?  -- Surely that is not too much to ask!

Minion: True dat, Socrates!!

Socrates:  Whence it follows that, our space being regular, for any point thereof, we may define a continuous function  positive at that point, but vanishing outside of a neighborhood of that point. -- You agree?

Minion: Word up dawg, Socrates !!!!

Socrates: Whereupon we may plainly see, that by defining an infinite series of functions from said space, to …

(Socrates drones on;  the minion dozes, but his snores are taken as assent.)

Socrates: Whereupon we may plainly see, that our original space may be smoothly embedded into the countably-infinite Cartesian-product of the cube, which we earlier (you do recall this, don’t you, minion?) proved to be metrizable.  This metric is inherited by our embedded space in the subspace topology, thus proving the theorem.

Minion:  U da man, Socrates !!!

Socrates (beaming upon the evidently innate insight of his pupil):  Great answer !!!

Note:   We have it on good authority from the memoirs of Oxford dons, that any tutor who attempts to apply the Socratic “method” to draw wisdom out of the maws of wool-gathering undergraduates, comes up empty.

Phrase of the Day: “I’m from Missouri”

The English writer Rebecca West, in her Balkan travelogue:

There has been  in America  a wave of cynicism, entirely mindless, destitute of all content, save “Oh, year” and “So what”, which, by a strange twist, results in a bland acceptance of the whole universe  that has never been surprassed by Christian Scientists.  An automatic skepticism regarding stories of atrocities  leads to a rosy belief that every member of an invading army  behaves with the courtesy of a cinema theatre usher.

-- Rebecca West, Black Lamb and Grey Falcon (1941), p. 773

 

“You can always tell a genuine Piedmontese  immediately  by his skepticism.”

“I’m a skeptic.”

“No, you’re only incredulous, a doubter, and that’s different.”

-- Umberto Eco, Foucault’s Pendulum (1988)

[below: repost of an essay from Feb 2016]

Throughout most of my lifetime,  the American two-party system has met little serious challenge.  (“Third parties are like bees:  they sting, and then they die.”)  That hasn’t yet really changed (anyone seen the Tea Party of late?):  even the floridly contrarian candidates Trump and Sanders  chose a major-party banner to run under (or in Trump’s case, perhaps to trample underfoot).   Yet the public mood is indeed evolving -- souring, mostly -- even if not in a way that so far has managed to embody itself in an organized party with a positive platform.  The movement is essentially negative, or rather a congeries of semi-related negatives.

The phenomenon is not unexampled in our nation’s history.  In the early years of the nineteenth century, Andrew Jackson came, for a time, to be the seed around which contrarian sentiments nucleated:

Jacksonianism was … a “persuasion”, a set of attitudes  united by little save discontent.

-- Wilson McWilliams, The Idea of Fraternity in America (1973)

A prominent feature of the present mood, is simply not believing what the government tells you (nor indeed anyone perceived as somehow working for the government, such as climate scientists).   And alas there has been much matter, indicative of the wisdom of examining their statements from this angle and that, and reserving judgment --  though surely politicians are no more egregiously peccant in this respect, than beleaguered generals, gossipy neighbors, ex-wives, and anyone trying to sell you something.

Again we notice widespread nineteenth-century precedents:

Missouri's nickname is The Show Me State. There are several stories concerning the origin of the "Show Me" slogan. The most widely known story gives credit to Missouri's U.S. Congressman Willard Duncan Vandiver for coining the phrase in 1899. During a speech in Philadelphia, he said:

"I come from a state that raises corn and cotton and cockleburs and Democrats, and frothy eloquence neither convinces nor satisfies me. I am from Missouri. You have got to show me."

http://www.statesymbolsusa.org/symbol-official-item/missouri/state-nickname/show-me-state

(Melville features a relatively hard-to-bamboozle character called the “Man from Missouri”  in his enigmatic 1857 sotie The Confidence Man.)

He's from Missouri

So far as that goes, it is an expression of healthy skepticism.   The implication is that the speaker is open to being shown, given well-marshalled evidence.

A rung lower than this, this classic expression of popular disbelief:

“Sez you” became the cry of millions.

-- D. W. Brogan, The American Character (1944), p. 92

(Mostly among men.   For women, a couple of generations later, the catchphrase was a less chin-out pugnacious, but even more utterly dismissive “What-ev-vahh…”)

Or again, the Studs Lonigans of the day:

He may fall back on “Oh, yeah” or the more adequate “however you slice it, it’s still baloney.”

-- D. W. Brogan, The American Character (1944), p. 164

(Cf. the classic cartoon caption  “I say it’s broccoli, and I say the hell with it.”)

Such folks are, unlike the Missourian, not inviting you to “show them” anything;  but in many such cases, attitudes are still subject to change,  not perhaps via reasoned argument, but by such dramatic images as may eventuate.

Rungs below that  is the attitude of systematic disbelief  that scarcely deserves the name of “skepticism” at all, for it simply does not engage in the practice of evidence-and-argument.  Birthers, alien-abductionists, conspiracy-theorists of various stripes, are no progeny of Diogenes;  and their abstraction from the world of fact  would have baffled Aristotle.

~

For more on genuine skepticism versus lazy know-nothingism:
http://worldofdrjustice.blogspot.com/2013/05/chaos-coincidence-conspiracy.html

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