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.]

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.

Snowfall !

Just before the Equinox,

snowflakes have parachuted out of the sky,

covering everything.

Snowbunnies race everywhere  over the lawns.

(You cannot see them, because they are the same shade as the snow.

That, plus they move at the speed of light.

They are rather unusual rabbits in certain respects.)

Professor Quine confesses himself baffled

as I point to the scene and say, “Gavagai!”

Quine on bunnies

Time for some bunny-fun  with our favoritemost ontological leporiphile -- Mr. Willard Van Orman Quine !!!

The sensible materiality of the rabbit was inessential to the example, since the prime numbers between 10 and 20  sustained the same point.

-- W.V.O.Q., “Existence and Quantification”

HMMmmmm..... !   !!

Point taken;  but the prime numbers abovementioned   are not nearly so cute and furry.

…undetached rabbit-part…

-- W.V.O.Q.,  passim.

Well we would hope so ! ! !

           

Gavagai !

-- W.V.O.Q., Word and Object

You da man !



[For more wholesome Quinefun, click here.]
[If you'd like to see a really big bunny, click here!  It depicts Quine furioso  putting ontological sybarites to flight.]


[Note:
I took logic from Quine in college.  He is a brilliant and witty writer, but in person -- at least with the undergraduates -- a singularly humorless and ponderous man.  (Randy Allen Harris refers to him, with irrefutable finality, as The Venerable Quine.)  I even suspect he didn't really like bunnies very much himself.  Whether the rabbit parts in question were detached or undetached  was, one suspects, a matter of ontological indifference to the great professor:  for, as Quine has demonstrated, in either case  the animal could be considered, like the world's sum of water, as "a single scattered whole".  Or, phrasing the matter with precision:  An intact rabbit, and a shmushed rabbit, can be safely interchanged salva veritate.  Not, however, salva cutibus.]

The illustration above pretty much captures Quine's aspect  as he made his way across the Yard.]

~

A relatively little-known aspect of the professor’s career, is his attempt to answer Dedekind’s classic question, Was sind und was sollen die Zahlen?, by means of an experiment.   Working over the holidays, in the same monastery garden where Mendel carried out his celebrated work, Quine indulged in bit of bunny husbandry:

You put seven rabbits in a pen, add five more, and  for a while  the total is twelve.

-- W.V.O. Quine, Philosophy of Logic (1970), p. 100

Subsequently, Quine was able to derive the Fibonacci series  using purely biological means.

… thus proving the theorem.

Doctor Justice’s Petting Zoo

Welcome to Dr Justice’s Petting Zoo !  Admission is free.

In the outermost circle of the petting zoo, visitors may pet bunnies in the most exoteric, empirical, agnostic sense  of temporal rabbit stages -- little whiskery ripples in phase-space -- tiny lagomorphic slices of spacetime.  “Gavagai!” the children cry, delightedly scurrying among their furry friends, asking no question of what came before, or what is to come.  Lettuce is provided;  photography permitted; various plebeian refreshments are on sale, and clowns move among the populace.

In the next-inner circle of the petting zoo, qualified visitors may pet bunnies in their paradoxical yet intimate homoousian duality:  Fully Temporal-rabbit-stage, yet fully Rabbit, existing independently or supernatantly to fleeting considerations of space or of time.

In the final, innermost circle, dimly lit, and open only to the elect, the reverent visitor may pet bunnies as incarnations of Absolute Rabbithood, in all its ultimately unknowable, inscrutable Lagomorphicity -- Yet so soft, so soft … !

Quine on bunnies

-->

Time for some bunny-fun  with our favoritemost ontological leporiphile -- Mr. Willard Van Orman Quine !!!

The sensible materiality of the rabbit was inessential to the example, since the prime numbers between 10 and 20  sustained the same point.

-- W.V.O.Q., “Existence and Quantification”

HMMmmmm..... !   !!

Point taken;  but the prime numbers abovementioned   are not nearly so cute and furry.

…undetached rabbit-part…

-- W.V.O.Q.,  passim.

Well we would hope so ! ! !

           

Gavagai !

-- W.V.O.Q., Word and Object

You da man !



[For more wholesome Quinefun, click here.]
[If you'd like to see a really big bunny, click here!  It depicts Quine furioso  putting ontological sybarites to flight.]


[Note:
I took logic from Quine in college.  He is a brilliant and witty writer, but in person -- at least with the undergraduates -- a singularly humorless and ponderous man.  (Randy Allen Harris refers to him, with irrefutable finality, as The Venerable Quine.)  I even suspect he didn't really like bunnies very much himself.  Whether the rabbit parts in question were detached or undetached  was, one suspects, a matter of ontological indifference to the great professor:  for, as Quine has demonstrated, in either case  the animal could be considered, like the world's sum of water, as "a single scattered whole".  Or, phrasing the matter with precision:  An intact rabbit, and a shmushed rabbit, can be safely interchanged salve veritate.]

-->

The illustration above pretty much captures his aspect  as he made his way across the Yard.]

Gavagai !

[Note to nonprofessional philosophers:
The following follows the classic treatment of W.V.O. Quine, in Word and Object.]

This Sunday's papers contained an interesting report from America’s premier naturalist, Mark Trail.  It offered a curious observation, of interest to linguistic analysis in the style of Quine, and to the theory of Mind generally.

According to this consummately reliable source,  our furry friends the prairie dogs, are preyed upon by coyotes.  But they are difficult to catch, since these loveable rodents dwell in gigantic underground colonies (a single one of which, in Texas,  once numbered 400 million -- now that’s a lot of prairie dogs),  with a great many escape hatches.  The instant any one of them  spots a coyote, it lets loose with “Gavagai !!!” (or squeaks to that effect), at which distress signal everybody  -- pop!  underground.   Leaving the coyote going mad with hunger.

But!  There’s a catch.  -- Let Dr. Trail himself tell it, since we can scarcely improve upon his prose:

Sharp-eyed [ed. note: and also furry]  prairie dogs [oh and -- did we neglect to mention? -- also cute]  sound the alarm when coyotes approach, but the coyote seems to know that these creatures can’t count.   With his mate he trots along in plain sight, right through the mound city.  The inhabitants all dive into their tunnels  as he continues on his way.  But his mate stops and quietly crouches among the mounds.

The first curious rodent who pops out to watch his enemy depart  suddenly becomes the coyotes’ dinner.

Alas!  frisky and adorable, the prairie dog -- like his cousin the humble woodchuck -- is entirely unfamiliar with the Peano postulates -- or in layman’s terms, with Our Friends the Integers.   Therefore they get eaten.  Gobble gobble gobble !!!  Gone!

Now, from this we may conclude, that apud the sciurideans, the vocalization “Gavagai!” does not mean “Lo, coyotes!”, but more something along the line of “Lo, undetached coyote parts!”, or “Lo, Platonic ideal of coyotehood  currently manifested locally!”.  In any event, the denotatum is a mass noun, not a count noun, and does not obey the digital rules of subtraction.

Dr. Trail goes on to report that, by such means, the prairie-dog population has declined by a whopping 98% over the past century.

Canny Darwinians will, however, already have noted the likely result of all this.  By ruthlessly culling the fluff-head innumerates of the population, generation upon generation (quite a good idea, really), Mother Nature (note to secularists:  that's Natural Selection in drag) is insuring  that  those who are eventually left  will be the mathematically most astute animals on earth.   Already we perceive the distant sound of scribbling upon chalkboards, in the M.I.T.- corridor-like  underground tunnels.

-- This just in!  Actual footage of a prairie dog suddenly conceiving the solution to the Riemann Hypothesis!   (This fellow has generally been known, in despite of taxonomy, as the “Dramatic Hamster”, for assonance’ sake.  But he’s really a prairie dog.)

Further proof that prairie dogs have already become the linguistic wizards of the animal kingdom  here.