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
principles 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
~
~ ~ ~
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
