Sunday, February 27, 2011

A New Proof of the Existence of Coffee-Cups

 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.

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.  (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.

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 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.

~ ~ ~

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 anyone) 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.

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 (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 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 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:  a circumstance 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 enthymatic 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.)

~ 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, 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 almost reassuring.

~ ~ ~

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.


Susan Haack, Evidence and Inquiry (1993), p. 219, meaning to challenge Descartes:

Why did God not create us with unlimited powers of reasoning … ?  And his answer:  that God’s purposes are beyond human comprehension, is completely unsatisfying.

Really… completely unsatisfying?  Completely unsatisfying as in, “How icky of Him, I demand my lollipop now” (“Why did not God create us with wings?  It would be such a lark”); or as in, “Your statement is false”?  And if the latter:  False in the usual sense of the term, so that “God’s purposes are within human comprehension” is accordingly true?  Or false in the devious Russellian present-king-of-France manner (more modernly termed, not straightforwardly false, but without truth value, or suffering from presupposition-failure), so that you will object to anything predicated or denied of God, because you don’t believe in Him in the first place, but refuse to just come out and say so?

Throughout her epistemological magnum opus, Haack plies some keen reasoning;  but confronted with God, she falls apart.   Indeed, we can with some confidence state, that if God exists, as anything like the being that is envisioned in the Abrahamic tradition, then yes indeed His purposes are beyond human comprehension:  of course they are.   Heck, most of the time, a man’s wife’s purposes seem beyond human comprehensions;  quantum mechanics is beyond human comprehension (take it from the experts who know it best); and until recently, algebraic geometry was beyond human comprehension -- Aristotle would have thrown up his hands.

Deny Him if you will (for He leaves you entirely free to do so);  but do not pretend that Descartes was here being irrational.

~  Posthumous Endorsement ~
"If I were alive today, and in the mood for a mystery,
this is what I'd be reading: "
(Je suis René Descartes, and I approved this message.)
~         ~

Saturday, February 26, 2011

The World is Too Much With us

Too much going on. -- we need relief.  The Maghreb, the Middle East… not to mention math.

Relax with this:

(You might want to set it to Mute just at first, since there’s an ad.)

Thursday, February 24, 2011

Good News for Workers!

After the Republicans are done with us -- we'll still have a job!

        "Inmates Help States Fill Budget Gaps"

And... this just in:

      "Shock Doctrine, U.S.A."

Wednesday, February 23, 2011

A Taxonomy of Nominalism

Among my favorite books in the field of logic is Susan Haack, Philosophy of Logics (1978).  The plural in the title might be surprising -- isn’t Logic simply the formalization of the way things are?  -- but it is by no means a typo.  She distinguishes no fewer than five families of logics:  traditional logic (i.e., the Aristotelian syllogistic), classical logic (what you were  taught in college, unless you spent all your time on panty raids), extended logics, deviant logics (no no, it’s not what you imagine), and inductive logics.  These each come in various flavors:  thus, under “extended logics”, we understand:

            modal logics
            tense logics
            deontic logics
            epistemic logics
            preference logics
            imperative logics
            erotetic logics  (no, that’s not what you imagine either)

Note the plurals:  These each have subflavors too.

Are we having fun yet?  We should be.  William James remarks (The Principles of Psychology (1890), vol. II)  that humanity seems to have a kind of taxonomic instinct, reveling in setting up systems of pigeon-holes:  rather like the sex instinct but even better because you don’t get AIDS.  Surely you remember the delight you felt as a ten-year-old, putting your return address on the envelope of a letter to a friend (well, that was before e-mail;  you’ll remember if you are over about eighty years old):

Timmy Thompson
322 Mulberry Street
The Midwest
The Western Hemisphere
The Planet Earth
The Solar System
The Milky Way …

Nowadays it’s even better, since you can keep going all the way up to the Multiverse.  (Only, no-one writes letters anymore, and there are no more ten-year-olds.)

In her later work, Evidence and Inquiry (1993), in the course of arriving at her new style of epistemology --- “double-aspect foundherentism”, no less -- Susan Haack coins or refines nomenclature for a great many epistemological schools and subschools, and even for individual varieties of ideas, labeling these with such tags as 
            FD1 superscript-E subscript-EXT
            FD2 superscript-P

rather reminiscent of the old joke about the comedy club, for whom the jokes were so familiar they all had numbers.  (Punchline:  “933.”  Nobody laughs.  Why not? “He didn’t tell it right.”)

*     *     *
~ Commercial break ~
Relief for beleaguered Nook lovers!
We now return you to your regularly scheduled essay.

*     *     *
~ ~ ~

In this spirit, we shall here embark upon an ambitious project of anatomizing Nominalism.  (Funded by USAF grant #586-77-E8-99999.)

(1)  On Nominalism

There are a great many individual theories beneath the big tent of Nominalism.  Since, however, they all suck, these need not detain us.

Much more rewarding is the following.

(2)  On Anti-Nominalism

There are several venerable schools in this vein.  Most familiar is Classical Anti-Nominalism, also known as Anti-Nominalism simpliciter, whose central thesis reads as follows:

(C.A-N.)  Nominalists just suck.  End of story.

Then there is Aetiological Anti-Nominalism, characterized by the following insight:

(Ae. A-N.) Nominalists were all dropped on their heads as infants;  a fact that explains, while it does not excuse, their behavior.

And lastly Pediculotic Anti-Nominalism, which maintains:

(P. A-N.)  Nominalists can best be understood as a form of body lice.

This popular view breaks into three schools, according as the insects in question be specifically head lice (Pediculosis capitis), lice infesting the armpit hair, or some even naughtier lice of which decorum forbids mention.

(This will all be on your mid-term.)

*     *     *
~ Commercial break ~
We now return you to your regularly scheduled essay.

*     *     *
~     ~     ~

[update October 2011]
I just stumbled upon this spicily-titled item:
Scientific Realism and Mathematical Nominalism:  A Marriage Made in Hell

Here we learn that “Nominalists hold that there are no numbers”;  this involves them in certain epistemological difficulties.   But en revanche (ô doulce revanche), numbers hold that there are no nominalists.  This  involves them in no difficulties at all.

~     ~     ~

Nevertheless, in that broad spirit of tolerance so characteristic of Realists, we here list those instances in which a Nominalist did (against all odds) manage to come up with something witty or interesting.  We believe this list to be complete.

Unum, verum, bonum -- the old favorites deserve their celebrity.  There is something odd about each of them.    Theoretical theology is a form of onomatolatry.
-- J. L. Austin, “Truth” (1950)

Tuesday, February 22, 2011

Tahrir and the Badger: a Logical Excursus

I do try to stay away from politics on this site, since

(1) Everything political is already blogged to death
(2) You’re more likely to ignite a flame-war than to persuade anyone
(3) Blogs need a focus -- for this one, primarily philosophy of math and science, often with a theological slant.  
(4) I don’t in general have more political wisdom than the best political commentators (one of them linked-to in the previous post, to which this is an addendum), and have necessarily less empirical grounding than does someone who does that sort of thing full-time.

There is, however, one motivation peculiar to people of my background, which might justifiably call forth comment:   the same motivation that led John Allen Paulos to publish his very useful A Mathematician Reads the Newspaper,  or Bryan Hayes and other statistically sophisticated authors  to pen essays about redistricting and measuring school performance and what have you, in that excellent periodical American Scientist  (American Scientist is now  what Scientific American used to be, decades ago, back when it was any good).  Namely, when a simple bit of logic can be applied to blow away the fog.

Now, logic is what we do, folks;  so let’s roll up our sleeves and go.  And note:  The importance of this exercise is  in one sense  quite independent of whatever degree of importance you might ascribe to what is now going on in Wisconsin.    The point is rather to demonstrate how a tiny wink of clear thinking  can show the media presentations to be internally incoherent.

So:  Consider the bill of goods that the Teabaggers are trying to sell us:

(I)  Public-sector workers are better compensated than private-sector workers.   (Of course, this is useless without statistical provisos such as “doing comparable jobs”;  but let’s bracket that.  For the sake of present argument, assume that (I) is true.)
(II) Therefore, for simple fairness, we need to abolish collective-bargaining rights for public workers.

Now, there has been a bit of logical sleight-of-hand here:  (II) deserves its “therefore”  only granted an unstated four-part premise,

(Ia) The superior compensation of public-sector workers is owing to the fact that
(i) collective bargaining is a powerful tool for winning compensation;
(ii) public employees have  rights to collective bargaining;
(iii) this right is not enjoyed by private-sector workers;
(iv) it is this differential access to the right of collective bargaining that results in their unfair advantage over private workers.

Syllogisms based on such smuggled assumptions are known as enthymemes.  They may still point to valid inferences, once the unstated auxiliary premises are made explicit;  but, for obvious reasons, invalid ones often show up in public rhetoric.

Now:  (Iaii) is true in part, though not generally.  (Iaiv) turns out, quite surprisingly, to be basically false -- but to know that requires a lot of specialized empirical knowledge that you will not get if your principle sources of information about the outside world are “American Idol” and “Jersey Shore”.   We are not asking anything so burdensome of the public, as that they should actually read a decent newspaper;  we wish, rather, to point out a conclusion that may reasonably be drawn by anyone with his wits about him, even if he is a quadriplegic who has been deaf and blind and confined to a vault beneath the ocean ever since 1935.

We pause to  do the math.  


All right, pause over.

We must concede that the above conundrum is not resoluble by anyone whose knowledge of the external world ended in 1934.  But if you have access to  information later than that, you know this:  that the National Labor Relations Act of 1935 (when FDR was in the White House:  Working people need to take a gander back to that administration, rather than the smoke and mirrors of Ronnie Reagan) guaranteed collective bargaining rights to workers… in the private sector.  Not to workers in the public sector:  those must be granted ad hoc, piecemeal and patchwork, by local or state governments.
Hence:  the factual picture is virtually the reverse of what the Teabaggers are peddling.   Based on their premise (quite plausible in itself) that collective bargaining is a powerful tool for gaining compensation, we would expect private sector workers to be at least as well off as public.   That is, (I) and (Iaiii) actually clash.

Thus endeth what mere, sheer logic can contribute.   All we know at this point is that something is seriously awry in the picture that is painted for us by the (con) artists, and dutifully passed on to an uncritical public  by the timid media.

To go any further involves getting down in the weeds.   Since you can do this as well as I, I’ll mention only a couple of salient points, made earlier this evening on NPR.  First, depending on the state and on the profession, many public employees are covered by collective bargaining and many are not.  Surprising fact:  Those that are are not in general better compensated than those who are not.  This is clearly counter-intuitive, and requires an explanation, which would likely involve consideration of the demonstration effect (which is vividly on display in the Maghreb  even as we speak) and of statistics concerning labor mobility between markets and so forth.   Such an explanation having been provided, (Iai) need not be false.  Indeed, it is obviously intuitively plausible; and I believe it to be true in actual fact.
Another important point, and the reason why I said that (I) is only “partly” true, is that there is a serious apples and oranges problem.   For  -- according to the report on NPR  above-referenced -- another surprising fact:  If you control for education level of the worker, the public worker is slightly undercompensated w.r.t. the private one.  And if you look just at the more highly skilled professional jobs, public workers are relatively even more undercompensated.   (Logical note!   I don’t know whether those two statements are empirically true.  But they show the kind of factor that must be taken into account, if we are not just to spout simplistic nonsense.)


Eppur’ si! “ (I can hear many of you cry).   “Many public workers enjoy grotesquely inflated pensions, phony disability payments, etc. “

Now -- did I say anything above to deny that?   In point of fact, I affirm it.

Given, however (as outlined above) that public/private disparity in collective bargaining muscle does not explain this -- what does?
The problem lies, not essentially with the workers (who all, understandably, public or private, will usually push for the best deal they can get -- those are the rules of the game), but with spineless and venal politicians who, off in the shadows, out of the limelight, strike sweetheart deals with public workers in return for financial contributions and electoral support.   This ability on the part of elected officials is in principle unrelated  to whether or not the workers in question are even unionized:  the officials just want the swag and the votes.   And the reason such deals affect public workers exclusively, relates not to the power of public workers, but to the circumscribed power of public officials, who do not have the power to grant raises and pensions to private workers.
A further supporting wrinkle:  Federal employees do have collective bargaining rights (in many agencies, though not where I work);  this right was granted in 1962 under JFK.   And yet the outragious deals we hear of  are invariably at the state and local level, not the federal.  (My own pension will apparently amount to less than ten percent of my current income.)  So trying to pin the abuses on "Washington" is way off.   Your troubles, irate locals, are home-grown.

Such sweetheart deals were in effect a fraud perpetrated against the public (including the tax-paying workers of the private sector, who must eventually pick up the tab.  Such clever clefts dividing worker from worker, whose natural interests are one and the same, cause bankers to jiggle with mirth).  That they for the most part involve outsize pensions -- a future cost -- rather than something that must come out of the pockets of those who were taxpayers at the time such deals were struck, shows that the stain of fraud extends beyond the officials, and to some extent must touch the general public, which has been massively incurious about such deals for decades, much as they are incurious about environmental ravages that will mostly affect future generations. (This melancholy subject is discussede under the label "the tragedy of the commons".)  For:   Everyone makes out like bandits.  Politicians and public workers get a sweet deal, and for the time being the taxpayers are not out of pocket (any real-time expenses being typically funded by further borrowing), and they enjoy (for that time) smooth uninterrupted public services provided by happy campers.   The victims here are the next generation, to whom, grinning, politicians and unions both  present the bills, for services rendered to the generation before.  (And I am myself speaking as a codger;  just, a logical codger.)


Nothing to do with logic, but what is needed now:

The Rabid Right is trying to roll back, not just the LBJ Great Society, but FDR’s New Deal.  
They've been stewing in their own rancid juices, ever since 1932.

OK, let’s start all over, from square one.  Suggested reading:
John Steinback,  In Dubious Battle (1936),  The Grapes of Wrath (1939).
 And here's another voice from that era:

Solidarity forever.

We Interrupt This Blogcast …

We selflessly interrupt our annual fund drive to direct your attention to this pressing need.

Little Timmy Needs Your Help!

There he lies, on his little bed, almost totally consumed by his tragic affliction.
He moan;  he groan;  he chat with fellow-sufferers on the telephone.

Already you are probably racing to begin collecting those little aluminum pull-tab thingies – but alas!  In a tragic development, it turns out that little aluminum pull-tabs are (incredibly) *not* a cure for cancer, or almost anything else!  In fact, the only disorder this favorite remedy is actually able to address, is hematopultabopoenia – a condition so rare as to be non-existent (and which in any case responds equally well to aspirin).
No-o, the only thing that can help Timmy now  is –

 =>  Send your Social Security Number, credit card info, mother’s maiden name (if applicable), penis length (again, if applicable) and bank account numbers,
to Timmy’s personal private website:


In conclusion, here is a message from Timmy Himself,
sent personally to you and you only :

              “TH – th -     th-th-th-   ..   thththththth—
                  th-th-th-a-    -a ---    thththththaaann-k-   th     th
                            th th th ththaannnkkksssss …..”

Monday, February 21, 2011

Koans of Analytical Philosophy

 (1)  Bovine biology and geometry

Russell, bringing to bear the entire artillery of modern logic and mathematics, succeeded in proving the nonexistence of carnivorous cows.  (Scott Soames, Philosophical Analysis in the Twentieth Century (2003), vol. I, p. 96 fff.)
We, however, calmly assert  the existence of round ones.

(2)  A word on the Golden Mountain

My wife and I climbed this last year on spring break, so I speak with some authority.  The air above is fresh and cool, the skies serene, and it gives off a pleasant aureate glow.  However, actual existence does not figure among the predicates it enjoys.  On this, the philosophers were spot-on:  The Golden Mountain does not exist.

Sunday, February 20, 2011

Philosophy Not Worth Bothering With

[a.k.a., She Reads it so We Don't Have To.]

Among the less-well-known philosophers whom I have especially enjoyed, is Susan Haack, the author of a bracing survey, Philosophy of Logics (1978).   Recently I have been slowly working through her principle work on epistemology:  Evidence and Inquiry (1993).  “Working through” is the mot juste, for it is sometimes tough slogging.   She carefully distinguishes more sub-subcategories of philosophical stances than there are practicing analytical philosophers who might embody them, many of these labeled with Peirce-style neologisms (“foundherentism”) or with truly inscrutable homonyms like “science” and “SCIENCE” to subindex subtle distinctions in the senses of various terms.  Leading, in the worst instances, to passages like

    FOUNDATIONALISM does not imply foundationalism, nor foundationalism foundationalism. (*)

(Imagine trying to read that aloud!  For the capitals, I supposed one could shout, or flap one's arms like a chicken;  for the italics, tilt your head to the right ...)
Still, she’s good company, with a very level head.

As the book goes on, though, and as she gets past such reliable stalwarts of earlier years as C.I. Lewis, Hans Reichenbach, and Quine, she feels herself obliged to engage with an increasingly creepy set of characters, who apparently infest the Academy these days.  She diligently expounds their positions -- truly an unpleasant task;  but then, she gets paid for it.

Thus, on page 149, she conscientiously canvasses the arguments put forward by one Goldman, and combatted by one Cohen:

In Epistemology and Cognition, he faces the objection articulated by Cohen, that reliabilism yields counter-intuitive consequences under the hypothesis of an evil demon who brings it about that our beliefs are comprehensibly false.  If there is such an evil demon, reliabilism implies that we have no justified beliefs.

Oh does it now.
Look folks -- if the universe is ruled by an evil demon, --  then we’re f*cked.   Just --  f*cked.   No epistemology, no morality, game over.  Pawn your typewriter, and join the party, looting and raping till the sun goes down.

These essays do not aim at surpassing simple theism, since that is all that Cantorian Realism has to contribute along those lines -- no implications for morality, really, that I can see.   Sticking to the intellectual arena here, not from first principles, but the way Babe Ruth stuck to baseball.  It’s what I know.   But faced with such sciamachy between hand-puppets as the epic battle of Goldman vs. Cohen…. we wish to posit one further axiom, merely for intellectual hygiene:

=>  Our cosmos is not ruled by any demon.
=>  It is ruled by God, and God is good.  Or, as Einstein put it (in a strictly philosophical/scientific context),  “Boshaft ist er nicht”.

This is not  by any means  to deny the existence of demons, nor of their Dark Prince,  who has his fat thumb in many a soup-bowl.   But those sterile beings did not lay out the Creation, nor do they rule it now.  To find them, you have to dive head-first down the moral/philosophical toilet bowl.

If that seems more an Alexandrian thwack at the Gordian knot, than a genuine untying of it, it is still preferable to the usual alternatives.  Haack mentions two of them (p. 215):  one, that the Demon Hypothesis is “covertly unintelligible”; two, that “since the deception it hypothesizes would be absolutely undetectable, it is, for us, epistemically absolutely idle”.  Now, first, the Demonic Hypothesis (as I shall re-name it, since it is not merely about demons, but is itself demonic) is perfectly intelligible;  second, what is idle is to assume that the deception need be “absolutely” undetectable.   It would only have to be largely undetectable, to reduce human life to a travesty;  in the movie “Matrix”, eventually a doughty band actually does detect it.  
But in fact, we are not in this existential pickle, since God is good -- thank God.

Oh dear… it gets worse.
Reading on a bit, we come to this:
in Evidence and Inquiry (1993), p. 153:

By the time of Epistemology and Cognition, Goldman is making much more startling claims.  The division of labour now envisaged between philosophical analysis  and empirical psychology  assigns to the former  only the task of supplying a schematic account such as Goldman’s ‘criterion schema’ for the rightness of J-rules;  according to Goldman, it is for psychology to supply a substantive theory of justification, to adjudicate between foundationalism and coherentism, to determine whether there is such a thing as a priori knowledge…

Folks … psychology is a sub-branch of zoology.   And as such, all very well in its way.  After all, to zoology falls the welcome task of displaying the wondrous ways of Our Friend the Beaver.   But its philosophical significance  is next to nil.

Why, then, does this professional philosopher  yield to such abdication/self-abnegation?  The move does not seem to have anything to do with anything we have hitherto discussed (deficient commitment to theism or what not).  But Haack herself weighs in with a perceptive … psychological suggestion (ibid, p. 156):

I suspect that his aspirations to found a new interdisciplinary enterprise  in which psychology supplies the straw  and philosophy makes the bricks, since it has no very cogent motivation, may be explained in part by the hope that epistemology might come to share something of the prestige and intellectual excitement that the booming fields of AI and cognitive psychology enjoy.

Astute, that.


Uh-oh… Another page, another outrage.
We are used to philosophers, and scientists masquerading as such, attacking Faith, and believers;  well and good.  And debunking this or that belief as false or confused.   But now we find some wiseacres maintaining, not merely that many of our beliefs are epistemically shaky,  nor even that we may have no justified beliefs whatever (a point with some truth to it, if you’re a real stickler for justification, but one which should not be put in the hands of adolescents), but that we have no… beliefs…. tout court.   Such a position (admittedly attention-getting, like a flasher or a  flagpole-sitter) is espoused by the ineffable Paul Churchland, as well as by one Stich, whom we’ll not further identify.  (Nor could I tell you whether the surname rhymes with sick or with bitch.)  Evidence and Inquiry, p. 159:

Churchland holds that beliefs are mythical because not ‘smoothly reducible’ to neurophysiological states.  Stich, that beliefs are mythical because their content … violates the ‘autonomy principle’ to which psychological explanations supposedly conform.

She comments:

Churchland’s and Stich’s thesis that there are no beliefs  rests, at bottom, on misconceptions about what beliefs are.

This is to give them too much credit.   It’s not as though a bit more contact with actual people (rather than the pithed specimens they apparently surround themselves with) would set them straight.   Their attack on common sense is psychologically more akin to that supersceptic (there is one in every freshman dorm) who denies the existence of the external world:  taking him to some corner of the external world, say a playground, is not going to change his mind.
But in fact the Stich-Churchland position is logically in much worse case.  For, there is indeed a logical possibility that this coffee-cup I seem to be sipping from  does not exist.  It is an illusion, and we are all just brains in a vat (like in “The Matrix”).  In which case the evil demon above-mentioned is indeed at the helm.   It is possible.  Logically.   But even in that drastic case, we still have beliefs.  I still believe that I am sipping this coffee, though  alas  I am sadly mistaken.
( I’m pretty sure the Churchlands are an illusion -- possible an effect of swamp-gas -- but our beliefs are not an illusion.  They may well be mistaken, but they -- are.)
Indeed, the existence of beliefs is as solid as the Cogito.  I believe I have beliefs -- tiens, there's one right there!  For the attempt to impugn such things, cf. Wiki's article on "Self-Refuting Ideas".


Compare further:

Vico’s defense of the Geisteswissenschaften  against the claims of scientific naturalism  relied essentially on the principle that inner access to the products of our minds … yields a degree of certainty  unattainable in the natural sciences.
-- Noam Chomsky,  Rules and Representations (1980), p. 242

Giambattista Vico : filosofo, storico e giurista

Nor is it enough for these gentlemen   thus to reduce our view of humanity to that of sea-slugs -- a species about whom Churchland rhapsodizes.  Not only the comparitively intellectual notion of belief (somewhat problematic apud the sea-slug) but even that of desire (sea-slug: Must ... eat ... slime ....)  should be abolished:  we are merely and simply  automata -- albeit “connectionist” automata, a buzz-word that has snagged a lot of funding in recent decades.   “Beliefs and desires are of a piece with phlogiston,” he intones.

And what do we have in its place, to describe the wide world?  Why,  “vector-to-vector transformation, effected by a matrix of differently weighted synapses”.

The lay reader is expected to be stunned into silence before such big words.   (Hint:  They are trivial.)   And it is was partly to inoculate myself against such sciolist-scientistical flimflam that, having been accepted to college as an English major, but spent a year before entering  immersed in the nonsense of literary France, I abruptly changed my major to Chemistry (switching later to Physics and then Math) -- sheer intellectual prophylaxis.   For you need the confidence that comes with a certain background, to stand firm in the face of such faddish blasts, as issue from the fundaments  of the gentlemen above-referenced.   A splendid example of such unflappable phronesis   is provided by John Maynard Keynes, who, in his  Treatise on Probability (1921), performs a valuable civic service in exposing the crippling conceptual deficiences that can hide behind a gauze of mathematical formalism.

Now, I’m not being very nice about this.  Bounds of academic discourse and all that.  But the fact is, these clowns have adolescents under their intellectual care;  it would not be too much of a stretch to haul them up on charges of interfering with the morals of a minor.

And -- wonderful to relate -- the sober, analytical, sometimes even plodding Susan Haack, hitherto always scrupulously fair to all sides, seems suddenly to have had enough.  P. 170:

Rather than call them ‘anti-realists’ about intentional states, as Fodor does, I shall call them ‘atheists’.

You said it, sister!  Off come the gloves, and down come the masks!

[Stay tuned as the saga further unfolds.  The next chapter, “Vulgar Pragmatism:  an Unedifying Prospect”, promises to make thine each particular hair to stand on end, like quills upon the fretful porpentine.]

(*) The barbs above are meant as gentle, well-intentioned.  I have nothing but sympathy for any thinker whose intricately reticulate conceptualizations  outrun the resources of our everyday streetspeak.   As it happens, Ms. Haack, though an excellent analyst, is not much of a wordsmith, and her coinages drop like lead.  And she herself is baffled by similar abortive coinages (p. 198):
All Stich offers to persuade us that truth is not intrinsically valuable  is the observation that truth is just one of a whole range of semantic properties a belief might have (truth, TRUTH*, TRUTH**, .. etc.)[…].  Frankly, I have no idea even what it might mean to say that another culture picked out,say, TRUTH* instead of truth.

Don’t Know Whether to Laugh or Cry

I try, I really do try to steer clear of politics on this site;  but this story is beyond weird.

Back in 2009, a remarkable article appeared, in Playboy of all places:

The rest of the media mostly ignored the story, and it seemed to have died.  The public doesn’t care unless you poke it with a stick.  No-one was ever held accountable.

This morning, the NYTimes finally catches up to Playboy:

Note the detail that senior Bush administration officials considered shooting down American passenger planes, based on a fabrication.

Let’s not let this story die a second time.

[Update, 2 June 2012] ...

 ...    ....      .....     (crickets)  .....   ....    ...

[Update, 6 April 2014] ...    ...

 ...    ....      .....     (dead crickets)  .....   ....    ...

Saturday, February 19, 2011

Jumping for Joy

Actual Footage of the World Congress of Australarctic Number Theoreticians.
Can you spot the one who has just proved the Riemann Hypothesis?

The Badger State meets Tahrir Square

"...spittle-flecked screaming matches..." (now there's a well-crafted phrase):

[Update VI 2012] The LATimes has taken down that article, so here is what it said:]

State workers and pro-labor activists have filled the streets of downtown Madison to oppose Republican Gov. Scott Walker's attempt to force many Wisconsin employees to contribute more for their healthcare and pensions and to strip them of most of their collective bargaining rights.

With activists flying in from around the country, those protests were countered Saturday by a smaller but equally strident crowd of supporters of Walker's state budget measure.

The Capitol rotunda echoed with drums and voices while pro-labor protesters outside chanted, "Kill the bill." "Tea party"-led activists responded with chants of their own: "Do your job!"

What started out as a local political fight has spread to neighboring states hit hard by the recession, with newly elected Republican governors and legislators trying to control costs by muscling concessions from government workers unions.

Measures almost identical to the one in Wisconsin are advancing in Ohio and Iowa, while Michigan and Indiana are exploring other ways of limiting protections for unionized government workers.

"This is where we're going to start," said tea party organizer Melvin Timm of Neenah, Wis. "This is going to set the tone."

Some opposing activists could be seen locked in levelheaded conversations, while others engaged in spittle-flecked screaming matches before being encouraged by police to move along.

"This is an existential battle," said conservative blogger Andrew Breitbart as he took the stage before the pro-Walker demonstrators. "It's the battle of our times."

~   ~   ~

Some background (in a widely-read commentary):

Meanwhile on Mars:

~   ~   ~

And now this (pre-)op-ed, titled in the print edition "Wisconsin's Gov. Hooligan":

~   ~   ~

And this:

[update 12 March 2011]:,0,6835437,print.story

[Update 19 III 11]:

[Update 2 IV 11]:


Miscellaneous Wisconsin factoid:

In Wisconsin, even before the turn of the century, there was an intimate union between the La Follette regime  and the state university at Madison, that foreshadowed all later brain trusts.
-- Richard Hofstadter, The Age of Reform (1955)

[Update 26 Feb 2012] Mutt "Mitt" Romney in the upper midwest, gleefully baiting labor:,0,7725322.story

Friday, February 18, 2011

On Gödel himself

We have seen, throughout history, and perhaps especially of late, the phenomenon of the monomaniac, the homo unius notionis, with his One Big Idea.  He rides it through all the talk shows, he remolds it and reworks it, and sends it out to do battle with the issues of the day, as they crop up; however distant they might be to his central conception.  (“`Soft power’, anyone?  ‘Soft power’?”)
            Had Gödel been a small man, he might have become Mr. Undecidability, after his most famous result.  “So, professor, what about this Iraq business?” “Y’know, Bob, it’s like I said in my famous paper.  The situation on the ground is like, just plain --undecidable!”  (Chuckles all around;  cut to commercial break.)  But instead, Gödel maintained (as summarized in HaoWang ,  Reflections on Kurt Gödel (1987), p. 193), that “there exist no number-theoretical questions undecidable for the human mind.  Hence, the human mind surpasses all machines.”
            That stance is part of what Wang calls Gödel’s optimism.  Again, given Gödel’s status as the discoverer of mathematics’ most celebrated negative result, and the slayer of the Hilbert program, one might intellectually expect the opposite; and, given the dreadful psychological cross he had to bear, which eventually led to his death by inanition, a more Kierckegaardian view might have been anticipated. Yet he embraces an intellectual optimism, not because of his intensely reticulated logical constitution, but to some extent despite it. As Wang puts it (op.cit, p. 193): “I find these propitious projections   a strange piece of inductive generalization … mov[ing] from accidental successes in very limited areas  to an anticipation of universal success.”

God rest his soul.

Thursday, February 17, 2011

Penguins & Politics


And like the lady says, at the very end:

-- A line which, until a few years ago, would have evoked little but nods and smiles.

But now this simple fact  is everywhere under attack.  Cf., just yesterday:

The problem addressed above is but a tiny slice (and largely the result) of a more general problem:  rampant single-motherhood.   The core of who we are, as human society,  is crumbling  -- savage rats ravaging  the fragments from without.

Fortunately, most of us still believe in this, even though it becomes ever less politically correct to say so.  From this morning’s Post:

La Manif pour tous, le 13 janvier, sur le Champ-de-Mars.

This is serious, folks.   This blog was created to explore Cantorian Realism, and to show forth its ties with theism:  because that’s a little something I happen to know.  But it pales in importance  to these basic truths:

=>  Marry in faith.
=>  Nurse your babies.
=>  Stay loyal to the day you die.

[Post-script:  Plaudits to the First Lady: ]

[Post-postscript, as the story refuses to die:
(The egregious Palin and Bachman  parade their pointlessness and ignorance.)
It began with a modest remark during a roundtable discussion with reporters: First lady Michelle Obama said she supports making it easier for mothers to breast-feed their babies, because "kids who are breast-fed longer have a lower tendency to be obese."
Within days, the sentence - and a new Internal Revenue Service policy offering tax deductions for breast pumps - had touched off a political firestorm. Rep. Michelle Bachmann (R-Minn.) blasted the Obama administration for trying to impose a "nanny state" on mothers. Another potential 2012 presidential candidate, former Alaska governor Sarah Palin, mockingly said the first lady was trying to compensate for high milk prices.

Careful readers between the lines might have gathered that I am -- when not contemplating Hilbert Space -- something of a social conservative.  But I would not vote for these Tea-Party types  if you boiled me in oil.   That they are ignorant of science is for them practically a badge;  but you'd think they'd at least get this right.]