Fifth Salvo: Tarski's Snow Job

Virtually a sacred text in the purlieus of analytical philosophy, (1) can hardly fail to be boringly familiar.

(1)     Snow is white, if and only if the sentence “snow is white” is true.

Whoops, more than a mere parody of (2), (1) figures as the evil twin of (2) who figures in turn as the good brother already elected early on by Alfred Tarski himself to serve as the public face of his quite technical biconditional.

(2)     The sentence “snow is white” is true iff snow is white.

Thanks to the fact that (2) is a mere platitude and featuring (2) over (1) as a pneumonic device abbreviating his biconditional, Tarski could hoodwink even hardened professionals into crediting his technical biconditional with being “more or less analytic” (Beall p. 1) as well.  How’s that for a snow job!

As the evil twin who is quite on a par with (2) when it comes to constituting Tarski’s biconditional, (1) lends itself much less readily to being viewed as a platitude if only because we expect snow to remain white even in the absence of all sentences, trading indeed on the thesis that conditionals in English are characteristically infected with modal import.

Invited by my use of the word “infect” here to protest that (1) should be allowed to be as unproblematic as (2) in so far as both alike are to be glossed in terms of “material implication”, one may need to be reminded that early in the last century one spoke of “the paradoxes of material implication” among which (1) might well be registered.

   

Actually, translating “p materially implies q” by “~ p v q” can produce “funny” business of its own.  Thus (1) supplies “Either snow is not white or the sentence ‘Snow is white’ is true.  Hardly your everyday idiomatic disjunction!  Call it a material disjunction evaluating which it will suffice to ignore the rubbish on the left, while plumping for the truth on the right, thereby extending Tarski’s snow job beyond the conditional to disjunction.

Emerging here one encounters at least a minor puzzle as to how serious a glitch figures in this informal privileging of (2) over (1) in current discussions about . . . truth.  For it may be urged that privileging (2) over (1) over wide stretches of these discussions is just the sort of simplification that advances serious research in one discipline after another.  Fair enough; an immediate case in point lies in (2)’s tacitly recognizing a truth that (1) brazenly flouts, namely that it is because snow is white that the corresponding sentence has the semantic value it does, and not the reverse. Alas, this “advance” has “all the benefits of theft over honest toil” that Bertrand Russell satirized years ago, the theft being of course at the expense of the traditional Correspondence Theory of truth, with Tarski’s own official even-handed biconditional failing to respect the critical asymmetry that is highlighted by (1) being juxtaposed with (2).

Deconstructing Tarski’s snow job in terms of how his famous biconditional combines a platitudinous (2) with a highly non-platitudinous, and even freaky-deaky, (1) that trades on worries about material implication, one comes to grasp how Tarski could have vacillated in his attitude toward the Correspondence Theory of truth.  Viewing (2) rightly as being all of a piece with it, he could hardly fail to appreciate that his originality lay rather with his biconditional taken as a whole.  And here we have learnt that what counts is how (3) semantically relates to four.

(3)     Snow is green.

(4)     The sentence “snow is green” is true.

Starting from a ‘true’ free language from which (4) is absent, the noise “true” enters in terms of a rule that takes (4) and (3) to be alike in truth value.  That (4) inherits its truth value from (3) in accordance with the Correspondence Theory one quickly, and risibly, finds to be altogether occluded in the recent discussions collected in Deflationism and Paradox, edited by J. C. Beall and Bradley Armour-Garb.

          Not that the introduction (and elimination) rules for “true” aka T-in and T-out are not expressly defined by way of first adding to ‘Snow is green’ the two words ‘is’ and ‘green’, thereby yielding “‘Snow is green’ is true’” and later eliminating them.  This second operation is especially instructive.  Knowing nothing about snow, you are given the sentence “the sentence ‘Snow is green’ is true” without, however, any hint as to its true value.  No matter.  Invoking the rule T-out, you validly deduce that snow is green, again quite aware of your ignorance as to its truth value.

          By parity of reasoning then the false sentence “Snow is green” inherits or quasi-inherits its pseudo truth value from its false premise, namely (4).  Teasing apart these two senses of “inherit”, the one naturalistically oriented to the Correspondence Theory of truth, the other semantically prompted by Tarski’s snow job, one comes to grasp how one might continue, with Tarski, to sympathize with an inflationary Correspondence Theory even while deflating it on behalf of a more fundamental semantic approach to truth.

          Which is by no means to concede that fans of this fifth salvo could be expected to rest satisfied with this result.  To the contrary, they are more likely to rally around (5) even as they are prepared to relish the keen tension that sizzles when (5) is juxtaposed with (6).

(5)     It is because snow is not green that the

sentence “Snow is green” is false.

(6)     The sentence “’Snow is green’ is true’” and the sentence “Snow is green” have the same truth value.

Resolving this tension, the dominant deflationary theory of truth as sponsored by Tarski’s snow job may be expected to relax its fetishistic preoccupation with (6) in its fiercely tendentious disregard of (5).  Accordingly we may expect a mature theory of truth to plump for (5) very nearly as much as for (6).

José A. Benardete "Meaning, Ontology and Anti-Realism: New Directions" S...

Meaning, Ontology and Anti-Realism Handout

      1)     ~ ($x) x is a colored physical object.

2)     ($x) x is a colored physical object.

3)     ~ ($x) x is a chair & x is blue.

4)     There is a blue chair in the attic.

5)     We don’t know what we mean when we engage in vernacular utterances like   4).

6)     There are seven people in the room but only six chairs.

7)     There was a severe sugar-shortage in Moscow this winter.

8)     Some shapes (i.e., shape properties) are uninstantiated.

9)     There is a possibility that James will come.

10)  The statement that James will come is not certainly false.

11)  ($x) x is a possibility.

12)  ($x) x is a sugar-shortage.

13)  There is a brown cow in the barn.

14)  There is a meaning which can be given to his remarks.

15)  His remarks can be understood in a certain way.

16)  The direction of a is the same as the direction of b.           

17)  Line a is parallel to line b.

18)  The number of Fs is the same as the number of Gs.

19)  There are just as many Fs as Gs.

Fourth Salvo

Actually, this is hardly more than a promissory note advertising a book, on which I am currently dispensing finishing touches, entitled “Greatness of Soul, in Hume, Aristotle and Hobbes”, featuring a greater and a lesser “missing chapter in the history of philosophy”.

            If the greater of the two can be seen in retrospect to be already signaled in my previous post by Hume’s riveting Nietzschean Paragraph, the lesser missing chapter also recalls my earlier post, by picking up on its theme of straddling, only now a straddling as between Hume’s Treatise and his Enquiry Concerning the Principles of Morals.  The issue here turns on how we are to think in tandem about this passage launching his Paragraph – “The generality of mankind consider heroism or military glory as the most sublime kind of merit” when it is juxtaposed with the following in his chapter “Of benevolence” early in the Enquiry:  “The epithets sociable, good-natured, humane, merciful, grateful, friendly, generous, beneficent, or their equivalents, are known in all languages, and universally express the highest merit, which human nature is capable of attaining.”

            The operative word in the two passages being “merit”, it is hard if not impossible to square the most sublime variety of it, according to the generality of mankind, with the highest kind as expressed universally in all languages by Hume’s seven epithets or their equivalents.  Resolving the puzzle is the task set by the fifth chapter of my book.

            By no means altogether promissory, this post I take to supply a missing chapter in the history of philosophy in its own right, simply by focusing attention on this exegetical puzzle in Hume studies, the relevance of which to our understanding of his theory of personal merit (= ethics) I leave here largely as an open question.  That these two sorts of merit at least smack of Nietzsche’s distinction between master and slave morality is not likely to be contested. Or is it?

Third Salvo

Contrasting the count noun materialism of our own time with the mass noun materialism of the early Meilesians, one might suppose that just such straddling of ancient and modern might come to be a familiar feature in “missing chapters.”  At any rate I dare to scout a peculiarly unpromising venture along that line if only to indicate early on how, in pursuing my program, I shall not be content with easy pickings.  Flaunting indeed bravado, I aim to project a modern counterpart of Aristotle’s much maligned great souled man who must not fail of being quite as problematic as him.

            At the same time, the problematic greatness of mind of this modern counterpart is designed to invite us to rethink our alienation from Aristotle’s original a salient characteristic of whom lies in his . . . disdain that Aristotle feels free to liken to how the vulgar rich throw their weight around in contempt of the rest of us who are so much less well heeled than they.

            Excelling in his exercise of all the moral virtues, Aristotle’s great souled man’s disdain can only be said at 1124B 1-5 to be grotesquely aped by the vulgar rich, rather in the mode of a caricature of him in Aristophanes.  Alas, caricatures even in their monstrous exaggerations can be very revealing of the truth, and one may thus even credit the many classical scholars of the last century, not least those who were otherwise fans of the Nicomachean Ethics, for deploring NEIV, 3.  Flat-footed enough in its valorization of folk ethics in the absence of this egregious chapter, which can really be felt to stand out like the proverbial sore thumb, Aristotle’s doctrine of the mean, as between too much and too little, hardly squares with a disdain that even invites parody. 

            How then explain my own eagerness to project a modern replay of this highly infelicitous material?  Well, no such eagerness ever crossed my mind.  One very external factor, rather, comes into play, namely the following paragraph very late in Hume’s Treatise of Human Nature, from a chapter entitled “Of greatness of mind”.

Heroism, or military glory, is much admired by the generality of mankind.  They consider it as the most sublime kind of merit.  Men of cool reflection are not so sanguine in their praises of it.  The infinite confusions and disorder, which it has caused in the world, diminish much of its merit in their eyes.  When they would oppose the popular notions on this head, they always paint out the evils, which this supposed virtue has produced in human society; the subversion of empires, the devastation of provinces, the sack of cities.  As long as these are present to us, we are more inclined to hate than admire the ambition of heroes.  But when we fix our view on the person himself, who is the author of all this mischief, there is something so dazzling in his character, the mere contemplation of it so elevates the mind, that we cannot refuse it our admiration.  The pain, which we receive from its tendency to the prejudice of society, is over-powered by a stronger and more immediate sympathy. 

            So there you have it, without any coaching from me, a “missing chapter” in the history of ethics, credited solely to Hume, whereby greatness of mind is found to straddle ancient and modern thanks to Hume’s rather more candid Nietzschean trope already anticipated by Aristotle.  Equally committed to providing a philosophic rationale for folk ethics, they are also at one by jointly disrupting the scheme with a Nietzschean add-on.

            Actually, there are two “missing chapters” in ethics that come into play here, only one of which features this add-on in Hume and Aristotle alike, with the other, quite novel “missing chapter” undertaking to combine Aristotle’s ethics with Hume’s sans the Nietzschean add-on in each of them.  In projecting this novel Humeo-Aristotelian version of folk ethics, it may be almost enough for me to fixate on how the Greek word kalon, commonly translated as “noble” or “fine”, which is what Aristotle’s ethics is all about, goes much more compellingly into “meritorious”, once one registers the fact that “personal merit” plays precisely the role for Hume that the kalon plays for Aristotle.  But it is not merely “meritorious” that enriches our grasp of Aristotle’s kalon.  There is in Hume something else, though for this – “what elevates the mind” – we must not hesitate to plunder Hume’s Nietzschean add-on.

            Finally, Hume supplies a third factor – “disinterested approbation” – that trades on the distinction between what we desire and what we admire, where the kalon figures principally as regards the latter, with Aristotle’s akrasia thus kicking in at long last.  Arguably, there is even a fourth factor – Hume’s even handed treatment of self-regarding vs. other regarding considerations in his four-fold scheme of personal merit = the kalon, namely (a) conduct useful to others, (b) conduct useful to oneself, (c) conduct immediately agreeable to others and (d) conduct immediately agreeable to oneself, where (d) figures directly in what elevates the mind of the hero while (c) characterizes our vicarious participation in that elevation by way of “sympathy”.

            This even-handedness is all the more striking for those who have accessed in Aristotle’s Rhetoric his extended account of the kalon strongly emphasizing altruism.  Not that any such emphasis is evident to modern readers of the Nicomachean Ethics.  To the contrary, we are apt to fault Aristotle for contaminating what affects to be a rationale for folk ethics with an excess of self-regardingness.

            That the kalon comes fully into its own very belatedly, only in Hume, I take to be an astonishing “missing chapter” in the history of ethics.  How’s that for straddling ancient and modern!

Second Salvo

Fearful of the near pariah status of history of philosophy in the hard-core precincts of analytical philosophy today, I hastened in my first salvo to project an almost futuristic version of it that allows me now to relax a bit in the longuedurée of the past in which history of philosophy has been widely felt to be most at home.  Going then to the opposite extreme, it will be not some putative end of philosophy but rather its presumed beginning of it, in Thales, to which I now turn, meekly following Aristotle in the first Book of his Metaphysics.  So here at least history of philosophy figures, superbly, as all of apiece with systematic philosophy as such?

            Maybe not, though it can certainly seem so on a casual reading of his text.  However attractive, in its own right, as a history of philosophy replay of Aristotle’s discussion of his “four causes” – material, formal, efficient and final – earlier in his Physics, he is quite explicit as to the immediate rationale for undertaking this replay, “for we shall either find another kind of cause, or be more convinced of the correctness of those which we now maintain” (983B 5).  Only more convinced, thereby allowing even in this case for there being a fifth cause that continues to elude him?  Although resolving this issue could not fail to supply a missing chapter in the history of philosophy that lies at any rate beyond those few readily at hand for me now, I am in rather a position to supply a friendly amendment to Aristotle in his effort to explain why Thales settled on water as being “that of which all things consist, the first from which they come to be, the last into which they are resolved (the substance remaining but changing its modifications)”, 183B 8-9.

            Invoking a possible worlds approach to a pre-Socratic hermeneutics that aims only to secure a more or less close approximation to what the historical Thales had in mind, conceding of course that the closest possible world is always the actual world, I cannot but notice how the most immediately relevant “modifications” of water – liquid, solid and vapor – fail to feature in Aristotle’s account.  If one’s first thought, still more Aristotle’s first thought, might be that liquidity, far from being on a par with the “other” modification of water, smacks rather of being an essential property of it, “smacks” is the word that alerts us to a puzzle with which I propose to view Thales as having profoundly struggled but in vain.  Well, not in vain, seeing that a still missing chapter in the history of how philosophy and science fatefully come to go their separate ways, I take to lie encoded in that heroic struggle.

            Even allowing Thales to be in a position to distinguish water l from water s and water v, one hesitates to find him content with Aristotle’s “substance (ousia) remaining but changing its modifications”, quite as if this ousia were a Lockean “I know not what”, though once one allows ice and steam or vapor to supply such diverse Fregean modes of presentation for water, the further inductive leap to the rest of nature need not fall afoul of familiar hypothetico-deductive canons.

            Distinguish now the historical Thales, whoever he might be, from my own Thales one and Thales two who figure as Lewisian counterparts in very close possible worlds an implicit struggle between which turns on how Thales two continues to insist that, as an especially perspicuous mode of presentation of water simpliciter, water l must finally be found to trump both water s and water v.

            Mere anachronistic mention of Frege and Lewis should be enough to verify how my own take on Thales is as futuristic as Aristotle’s, only much more so, at this still greater remove from him.  Add the name of Quine, and a still deeper theme emerges, in connection with ontological commitment.  Taking Thales to be ontologically committed only to . . . water, “(x) x is water” strikes one as a highly jejune formulation of his position in Quine’s canonical notation of first-order predicate logic if only because “(x) x = water & (y) y = x” is no less acceptable, albeit appealing now to an enhanced first-order predicate logic with identity in which Quine is still more at home.

            If this distinction between predicate logic with and without identity will doubtless be felt to be surely at least one technical nuance too many, at any rate by those of my fans who are rooting above all for a reactivated history of philosophy, it is precisely Quine and his commitment to philosophy “from a logical point of view” on whom I am principally relying in undertaking that very reactivation.  A two-way street, however, in my juxtaposing, incongruously, Thales and Quine, I venture to shed almost as much light on the latter as I do on the former, starting with his focusing “on what there is” from a logical point of view.  A putative counter-example to Quine’s purportedly neutral – as regards competing ontologies – first-order scheme that implicitly provides only for count nouns, the early philosophers plumped for mass nouns, water for Thales, air for Anaximander and fire for Heraclitus.

            As to whether Quine would allow for a purely aqueous ontology or proto-ontology according to which “all there is is water and only water”, I believe he would refer us to his doctrine of “indeterminacy of radical translation”, insisting only that a Whigish approach that takes Thales’ mass noun quasi-ontology to be applauded as baby steps on the way to a proper count noun ontology would register for him as among his less favored translations.

            As to whether Williamson would stick in this context to his epistemic theory of vagueness I am much less confident.

            Finally, pressing into further service Davidson’s doctrine of “charity” as a talisman for dispelling Quinean indeterminacy, no less than five major figures in analytical philosophy have been called upon to discharge this “missing chapter” on poor old Thales.  How absurd now, my worries about an impending end of philosophy, when these five almost equally riveting figures pass before us in review!

First Salvo

Focusing at the outset on their immediate bearing, my program comes now to be launched by a hitherto missing chapter – featuring a three-fold “incredulous stare” extending beyond David Lewis to Graham Priest and Timothy Williamson – that could hardly be closer to home.  So much closer in fact that, far from harking back to what we conventionally call “history of philosophy”, this incredulous stare on steroids might well be felt to challenge us with hot off the press “philosophy proper”, sticking with the convention.

            With the original incredulous stare seen to be addressed to Lewis’s modal realism, it must surely be elicited at least as much by Priest’s insistence that the Liar Paradox succeeds in delivering a sentence that is at once true and false.  Ditto for Williamson’s insistence that, absent a single penny, a rich man can cease to qualify as rich.  Even without any precipitous decline in the nation’s currency.

            As to whether we might combine our three philosophers into something more than a mere potpourri, distinguish between the varying extension of “rich” in all relevant worlds and its constant intension pegged to its single-penny sharp line dividing non-rich from rich.  Although Lewis insists, tendentiously, on singling out our world as the only “actual” one, anyway relative to us, this proves to be hardly more than a verbal distraction when elucidating how Humphrey would have won the presidential election over Nixon, by calling him out for his behind-the-scenes, illegal approaches to the Viet Cong.  Relying on “Actuality entails possibility” as the only substantive, uncontroversial principle of modality, a very real duplicate of Humphrey but for the fact that he really does call out a duplicate Nixon for approaching a duplicate Viet Cong, in a world the laws of nature of which duplicate our own, Lewis does succeed in providing plausible truth conditions for this “would have”.  Even Quine, despite his famous misgivings over modality, might concede as much, even while protesting that in the absence of any independent, robust evidence for the “actual”, temporally as well as spatially disconnected existence of these duplicates.  Lewis’s rationale for contrary-to-fact modality must wither in the face of . . . an incredulous stare.

            That an omnibus three fold version of this stare threatens to undermine the logico-linguistic core of analytical philosophy itself, only goes to show how, even now, we might understand what it would be like for someone to be actively engaged in writing a first draft of “The Last Chapter in the history of philosophy”.  In a quite personal vein, let me just add that I should be very surprised to learn that I have written this first draft.  To the contrary, I look forward to fighting in the trenches, keeping that outcome at bay.