Edmund Griffiths  

E d m u n d   G r i f f i t h s

Winnie-the-Pooh and dialectical three-valued logic

                              Halfway up the stairs
                              Isn’t up,
                              And isn’t down.
                              It isn’t in the nursery,
                              It isn’t in the town.
                              And all sorts of funny thoughts
                              Run round my head:
                              “It isn’t really
                              It’s somewhere else
                                  — A. A. Milne


§ 1.   One of the more unexpected sensations to thrill literary and intellectual circles in 1990s Russia was Vadim Rudnev’s book of 1994, Vinni Pukh i filosofiya obydennogo yazyka [Winnie the Pooh and Ordinary Language Philosophysic, for the time being]. Oddly enough, it included the first complete Russian-language version of A. A. Milne’s Winnie-the-Pooh and The House at Pooh Corner, newly translated by T. A. Mikhailova and by Rudnev himself: the standard (and much-loved) Soviet text, translated and lightly adapted by Boris Zakhoder, had missed certain sections that the Rudnev edition restored. But the translated texts were also accompanied—as the title may lead one to anticipate—by an extensive introduction and notes subjecting the Winnie-the-Pooh stories to analysis from a predominantly philosophical standpoint. And the majority of readers will probably find this apparatus to be the most significant part of the book. Rudnev writes with considerable vividness and charm: he is seldom dull and never genuinely obscure, although he can take the pleasure of a poet in lists of ringing foreign names.

At that time [scil. in 1990] the future commentator on Winnie the Pooh was enjoying reading Frege, Carnap, C. I. Lewis, J. L. Austin, W. V. O. Quine, Georg von Wright, Jaakko Hintikka, and Saul Kripke on logical semantics, modal logic, analytical philosophy, and speech-act theory. Leafing through the Zakhoder translation of Pooh, he suddenly realized that these things—strange as it may seem—were exactly what Winnie the Pooh was about.

He also has some good jokes.

In total, he [scil. Pooh] is the author of some 23 poems belonging to the most diverse genres: from jokey wordplay, nonsense verse, comic dialogue with his unconscious, self-praise, to meditative elegy, lullaby, and solemn ode.
      In essence, Pooh is Pushkin.

If there is any likelihood that we shall nonetheless find his book disappointing, it can only be because we were hoping that his treatment of the text would be based more specifically on ordinary language philosophy. (If we were looking forward to that prospect with as much apprehension as enthusiasm, we may find ourselves pleasantly surprised.)

§ 2.   It is not that Rudnev altogether neglects ordinary language philosophy, the tendency of thought associated with the later Wittgenstein and with the philosophers of the ‘Oxford school’. But he supplements it at every turn not only with its own forerunners and successors inside the analytical tradition but also with a wealth of ideas drawn from anthropology, literary theory, the study of myths, and above all psychoanalysis. He is boldly and delightedly eclectic, willing in almost the same breath to invoke analytical philosophy (Wittgenstein, Quine, Hintikka) and analytical psychology (Jung); the glittering Paris of the structuralists and the austere 1950s Oxford of the ordinary language philosophers; Frazer, Eliade, and Malinowski; Freud, Rank, Fromm, and Stanislav Grof. Among Soviet writers he seems to draw most readily on Lotman and Bakhtin, but he also refers with respect to Shklovsky, Olga Freidenberg, and others. And in this regard Winnie the Pooh and Ordinary Language Philosophy is a superlative product of a particular moment in Russian intellectual history. The doctrines he cites have almost nothing in common beyond the significant fact that until the late 1980s most or all of them had been rather frowned upon in official Soviet scholarship. Ideas that originally belonged to different periods and quite separate worlds of thought all reached the Russian reader at once; and Rudnev’s excitement at the horizons thus opened up is infectious. The result, for Western readers who have grown accustomed to thinking (say) of ‘analytics’ and ‘Continentals’ as distinct and mutually exclusive groups, is counterintuitive but appealing—almost like being invited into an enchanted forest where bears, rabbits, kangaroos, and piglets can all live together as friends.

§ 3.   Even when the interpretations Rudnev offers do not seem especially convincing (‘that terrible and aggressive phallus, the Heffalump’), they gain vitality from being comparatively unfamiliar in the immediately post-Soviet context—much less familiar, at any rate, than this kind of Freudian symbol-spotting would be in the West. One factor that can create a degree of difficulty for the modern Western reader—perhaps the modern Russian reader too—who tries to appreciate even late-Soviet popular culture is how un-Freudianized (in this sense) it was. A single example will suffice: it does not seem likely that a songwriter working in English would, in any recent decade, have chosen to begin a rather gentle number about a sailor who misses a woman with Yury Vizbor’s lines

O my dear, my incomparable lady,
My icebreaker is mournful, and my navigator looks to the south...

The Interpretation of Dreams and The Psychopathology of Everyday Life and even popularizations of Freud are perhaps not so widely read today as they once were; but Freud’s achievement in shaping the way large numbers of people still find it natural to discuss their mental and emotional life remains impressive. And in 1994, in Russia although not perhaps in every country, a Freudian reading of the kind Rudnev proposes could seem new and even revelatory.

§ 4.   It is thus almost possible to argue that Winnie the Pooh and Ordinary Language Philosophy is a mistranslation, and that the title would be better rendered more naïvely as Winnie the Pooh and the Philosophy of Ordinary Language. The Russian is of course compatible with either interpretation, although it will probably be understood differently depending on how familiar the reader is with filosofiya obydennogo yazyka ‘ordinary language philosophy’ as a term of art. But the implications of the two translations are almost diametrically opposed. Ordinary language philosophy in its classical form appeals to ordinary language (meaning thereby not necessarily colloquial non-specialist language, but at least language that has not been distorted by the efforts of professional philosophers) to chasten and correct a philosophy that has putatively strayed into nonsense by canonizing its own non-ordinary ways of talking and then attempting to criticize or adjust ordinary speech. ‘The philosophy of ordinary language,’ in contrast, could sound as though it aspired less to use ordinary language to discipline philosophy than to use the tools of philosophy to extract new interest and excitement from what seem to be mere pieces of ordinary language. And this, at least in part, is what Rudnev does, relying throughout on the convenient methodological principle that

aesthetic and philosophical ideas are always in the air: they find their way into people’s minds uninvited, and direct their behaviour

and that the adventures of Winnie-the-Pooh can thus legitimately be interpreted in the light of parallels not only from the philosophy of the time but also from the classic works of modernist prose, without it being necessary to establish (or even to think it probable) that Milne had read any particular book.

§ 5.   True, on occasion Rudnev creates through a misreading of the text the very problems he then attempts to solve. (The format of his book, including as it does a complete translation embodying his understanding of the original, is particularly unforgiving to him in this regard.) One unfortunate case concerns the Introduction to Winnie-the-Pooh, in which the title character figures—as it seems to Rudnev—both as a stuffed toy and as a real bear that lives at London Zoo and is friends with Christopher Robin.

In the first chapter Pooh is just an ordinary teddy bear, a favourite toy about which a father tells stories to his little boy. The episode at the zoo [...] receives no further development of any kind in the rest of the text and is thus left hanging somewhat in the air. This ambivalence in WP’s etiology can easily be explained if we accept the hypothesis that the zoo episode takes place in a dream.

This is only one of three separate occasions on which Rudnev attempts to reconcile the apparent contradiction. If the episode is not a dream, perhaps Pooh has in some sense a double nature; or perhaps the whole problem is somehow bound up with the doubleness or contradictoriness that belongs anyway to a male character whose first name sounds feminine. It seems tolerably clear, however, that these manoeuvres are unnecessary. The relevant passage in Milne’s original reads as follows:

[A]t last we come to the special cage, and the cage is opened, and out trots something brown and furry, and with a happy cry of “Oh, Bear!” Christopher Robin rushes into its arms. Now this bear’s name is Winnie, which shows what a good name for bears it is, but the funny thing is that we can’t remember whether Winnie is called after Pooh, or Pooh after Winnie. We did know once, but we have forgotten...

This is partly fictionalized, of course: we are not to suppose that the real child Christopher Milne was taken by special and private routes to see a special and private bear, still less to hug it. But neither are we to take this bear as being the developed fictional character, Winnie-the-Pooh. The natural reading is that Christopher Milne was fond of a bear (named Winnie) that he had seen at London Zoo, and that the Winnie-the-Pooh of the stories results from a partial conflation of his teddy bear with this real bear. (So that it is in fact Pooh who was named after Winnie, and not the other way around.) As it happens, it appears that there was a bear named Winnie—short for Winnipeg, the city in Manitoba—kept at London Zoo at the right time. If we now turn to the same passage as translated by Mikhailova and Rudnev, the nature of the misunderstanding is immediately apparent:

[F]inally we get to a special cage. And the cage opens, and somebody brown and furry rushes out, and Christopher Robin flings himself into his arms with a joyful cry of ‘Oh, Bear!’
      This bear is called Winnie now, which is itself a sign of what a suitable name it is for a bear; but at the same time it’s funny that we can no longer remember whether Winnie subsequently got the name Pooh or Pooh subsequently got the name Winnie. We used to know, but now we’ve forgotten.

(I deliberately made this translation from Mikhailova and Rudnev’s Russian without having the original in front of me—not all the divergences from Milne’s wording should therefore be taken as implying that the Russian translators have altered the sense.) The translators have overlooked the fact that Winnie here is less anthropomorphized than is Winnie-the-Pooh: she is an ‘it’, where he is always a ‘he’, and she is ‘something’ rather than ‘somebody’ [kto-to]. The phrase beginning ‘the funny thing is’, meanwhile, is not talking about which of his two names Winnie-the-Pooh had first and which he acquired ‘after’ (subsequently)—it is discussing whether (Winnie-the-)Pooh was ‘called after’ (named after) Winnie the real bear, or Winnie was named after Pooh. Nor does the ‘now’ in ‘now this bear’s name’ imply that the bear’s name was ever different. This time, at least, we can say quite in the spirit of ordinary language philosophy: attend to the ordinary use of language, and you will find that the philosophical difficulties dissolve of themselves.

§ 6.   There are other occasions, however, where what could seem to be a mistake can only really be understood as a deliberate and effective literary choice on the part of Mikhailova and Rudnev. We do not need to look further afield for an example than the name ‘Winnie-the-Pooh’ itself. As it happens, quite a few of the characters appear under different names here from the ones they are given by Zakhoder; and the revised names generally move closer to the English originals in sound, sense, or both (Tigger not Tigra, Kanga not Kenga, I-Yo not Ia-Ia, Porosyonok ‘piglet’ not Pyatachok ‘snout’). Sych ‘little owl’, unlike Zakhoder’s Sova ‘owl’, allows Owl to remain masculine. But the treatment given to the central character in this respect may seem at first glance to be slightly bizarre. The hyphen in Zakhoder’s Vinni-Pukh (corresponding to the hyphens in ‘Winnie-the-Pooh’) is suppressed without explanation. Vinni (Cyrillic Винни), supposedly because it will not be read by the Russophone audience as a girl’s name, is replaced by ‘Winnie’ (printed in Roman). But the Zakhoderian Pukh ‘down, fluff’ for Pooh—a substantial addition of meaning, especially for a character based at least in part on a soft toy, and one that probably does more than any of Zakhoder’s other adaptations to make the stories feel native and Russian-speaking—is quietly retained. The only comment Rudnev offers is manifestly inadequate:

In Russian, the name Winnie-the-Pooh would sound something like Uinni-de-Pu. Of course, no-one would recognize that as being Vinni Pukh. But the last letter in the word Pooh is in fact silent in English: that’s why it always rhymes with who or do.

This hardly seems compatible with the proclaimed goal of producing an ‘analytical translation’, one which will resemble the Brechtian as opposed to the Stanislavskian theatre, a translation that will never let the reader forget for a moment that this text originated in a foreign linguistic environment. If the worry is really over potential readers not realizing that the book is about Winnie-the-Pooh at all, it would be possible to use a more conventional spelling in the title and on the front cover—and in fact Rudnev does exactly that, writing Vinni Pukh in his title but Winnie Pukh in his text. In any event, it seems scarcely conceivable that anyone could be such a purist as to spend a paragraph straining at Vinni and yet so permissive as to swallow Pukh without feeling the need even to justify it.

§ 7.   In fact, it is not conceivable at all. Rather than an inexplicable failure of ‘analytical translation’, this apparent lapse is much more plausibly understood as the supreme example of it. Suspending our disbelief is terribly easy; remembering the levels of artifice that interpose between us and the adventures of Pooh Bear and Piglet is hard; but, if anything has a chance of reminding us that what we are experiencing has been mediated through the unforced choices of fallible translators, then the mingled superiority and exasperation we feel from seeing an obvious and often-repeated mistake is likely to be the thing to do it. Rudnev tells us enough to make sure we spot the blunder, just in case we were unaware that ‘Pooh’ in English is not pronounced with a final fricative—and he then leaves us to imagine that we have outsmarted him.

§ 8.   This is all the more important, assuming that ‘analytical translation’ is something we value, because it is not only the characters and the plots that risk distracting the reader from the specifics of the translated text. Rudnev’s assertion that the central issues of logical and analytical philosophy are ‘exactly what Winnie the Pooh [is] about’ may initially seem extravagant: but, once our attention is drawn to the matter, there do turn out to be several rather puzzling aspects of these stories’ language and logic—including issues that Rudnev’s apparatus touches on only briefly or not at all. Readers of the Pooh books will perhaps have noticed, for instance, that there is something peculiar going on in them with regard to individuality and class membership. Winnie-the-Pooh himself is ‘a Bear of Very Little Brain’—but there are no other bears with which (or with whom) he can be compared. Piglet is not a piglet, a member of a class of piglets: ‘Piglet’ is his unique personal name. Kanga and Roo are never identified as two kangaroos. Tigger, to be sure, is a member of a species of Tiggers; but he is the sole member. The only group that has more than one individual as members (Alexander Beetle, Henry Rush) is ‘Rabbit’s Friends-and-Relations,’ and this group is no species; the very idea that Rabbit, together with his Relations but perhaps not his Friends, might form a species of rabbits is scrupulously avoided. I think the word ‘rabbits’ never occurs in the text at all. And on the other hand there are species (bees, Heffalumps, Woozles, Jagulars) that contain no identifiable individuals. It will further be noted that these classes-without-individual-members include, although they are not limited to, all the creatures that are not real even within the terms of the fiction: Rabbit is a real person whose name is ‘Rabbit’, but Heffalumps are made up and they are only discussed as a class. Once we have noticed this, we can hardly avoid realizing that the characters’ reaction to what they take as the appearance of a new kind of animal in the Forest differs markedly depending precisely on whether the animal in question actually exists (within the world of the stories). With a new animal that does exist, they ask questions: ‘Does Christopher Robin know about you? [...] Do Tiggers like honey?’ With a new animal that they only imagine exists, they ask questions and proceed to make up the answers (Heffalumps eat honey; Jagulars don’t hurt themselves when they drop out of trees because ‘[t]hey’re such very good droppers’). A full analytical account of the Winnie-the-Pooh stories, one feels, must describe the logical workings behind this cluster of oddities. And such an account is not out of reach; but the search for it may oblige us to supplement Rudnev’s reading in the philosophy of logic with another book that was also published in Moscow in 1994, under the perhaps less than promising title Principles of Informatics.


§ 9.   For Nikolai Brusentsov (1925–2014), the 1990s came as a certain kind of culmination to a career that shows a remarkably consistent progression from the concrete to the abstract. Evacuated from his native Ukraine ahead of the German advance, he was called up as a teenager in 1943 and served as a radio operator for the latter part of the Second World War. The experience he acquired in that capacity presumably stood him in good stead after the war when he became a student of electronics, eventually joining the faculty at Moscow State University—where, inspired by the mathematician Sergei Sobolev, he designed a small but usable computer. Setun (named for a tributary of the river Moskva) was manufactured between 1961 and 1965 at the Kazan Mathematical Machines Plant and saw service with public and research institutions from Dushanbe to Yakutsk. Brusentsov spent the late 1960s working on a revised and more theoretically perfect model, Setun 70, which he hoped would be released in 1970 to mark the centenary of Lenin’s birth; but only a single prototype was ever built. In the 1970s and 1980s he studied the application of digital technology to education—the prototype Setun 70 was converted into the first version of the teaching system Nastavnik—and devised the programming language DSSP (Dialogue System for Structured Programming); but he also became increasingly interested in the arithmetical and logical foundations of computer science and indeed in logic tout court. This interest found expression during the 1990s and 2000s in a stream of books, articles, and pamphlets where Brusentsov defends what he sees as true logic—natural, commonsensical, and dialectical, the logic of Aristotle and of Lewis Carroll—against the distortions introduced by Stoics, Schoolmen, and modern formal logicians. Whatever conclusions one may reach as to how far he succeeds in this objective, his polemical style (sharp but never abusive, as angry with Chrysippus as he is with Frege) is always refreshing to read; and his willingness to criticize or abandon the most firmly-established commitments of the fields in which he worked must attract our admiration.

§ 10.   It is for his rejection of binary arithmetic, which came as early as the 1950s, that Brusentsov is probably best remembered today. Unlike every other computer that has ever been put into production, Setun stored and manipulated numbers using a version of base three: specifically, a version that Brusentsov called the ‘ternary symmetric system’. (In the English-speaking world it is customarily referred to as ‘balanced ternary.’) Where a binary digit can hold one of the two values ‘one’ and ‘zero’, a Brusentsovian ternary digit can take any of the three values ‘one’, ‘zero’, and ‘minus one’. The number ‘six’ is expressed in binary as 110: one four, one two, and no ones. In balanced ternary it becomes 11̄0: one nine, minus one three, and no ones. Any natural number can be expressed about equally easily in either form, assuming there is space for enough digits. Where ternary shows a certain advantage is that it can deal with negative numbers as straightforwardly as it can with positive numbers, whereas arithmeticians working in binary have to resort to tricks of which two’s complement is the best known. The tricks work, in that they permit computations involving negative magnitudes reliably to produce the expected results; but they create opportunities for awkward mistakes if they are used carelessly, and they complicate some operations that could in principle be easy. Donald E. Knuth, one of the great names of United States computer science, has acknowledged balanced ternary’s ‘symmetric properties and simple arithmetic’—while suggesting in another place that it might nonetheless be most attractive to ‘[p]rogrammers from another planet’. (It is doubtful, in fact, whether ternary is really any less natural—as opposed to merely less familiar—than binary: long exposure to positive powers of two has made us comfortable with 32 or 128, while 27 or -243 can still seem prickly and unexpected.)

§ 11.   It seems to have been the purely practical and arithmetic advantages that initially attracted Brusentsov to the idea of working with three values rather than two. Indeed, Setun—despite its status as the only ternary computer to date to have been used for practical purposes—was only really ternary in the way it represented numbers. Its conditional operations were all based on a strictly binary, true-or-false logic. This characteristic was partially remedied in the prototype Setun 70, where the BRT instruction would cause the computer to execute one of three subroutines depending on whether the result of the last computation was negative, zero, or positive—a properly ternary choice, albeit no more so than FORTRAN had implemented back in 1957 with the arithmetic IF statement. But Brusentsov’s conviction that logic needed to be reconstructed on a dialectical and three-valued basis grew considerably in radicalism after the Setun 70 period: where writers such as Łukasiewicz or Kleene had experimented with extending classical mathematical logic to include more than two truth values, Brusentsov felt impelled to abandon it altogether and return to a three-valued interpretation of the Aristotelian syllogism and the ‘symbolic’ (diagrammatic, rather than algebraic) syllogistic logic of Lewis Carroll. It may be objected that neither Aristotle nor Carroll deals, at least explicitly, with three truth values. Brusentsov’s answer is that the blank segments in Carroll’s diagrams can only be interpreted as an ‘indeterminate’ value, while Aristotle’s συμβεβηκός ‘accidental’ represents a third value that is distinct from both ‘necessarily true’ and ‘necessarily false’. It is in tribute to this Aristotelian usage that he sometimes employs a Greek sigma as a symbol to indicate that a proposition may or may not be true, that its truth or falsity is inessential. For example, if we know that ( x ∨ y ) ∧ y [at least one of x and y is true, and also y is true], we cannot conclude either that x is necessarily true or that x is necessarily false: so we write σx, meaning thereby that the truth of x is inessential or undetermined.

§ 12.   At least part of the motivation for this drastic step comes from Brusentsov’s dissatisfaction with the paradoxes that can arise from the formal logical notion of material implication, paradoxes from which he argues that his neo-Aristotelian ‘necessary consequence’ [neobkhodimoe sledovanie] is free. The nature of the question can most easily be developed through an analysis of the Aristotelian ‘universal affirmative’ statement, the statement that takes the form ‘All Heffalumps are Fierce Animals’. It is clear that this statement must be false if there are any Heffalumps that are placid and amiable. But what are we to say about the case in which there are no Heffalumps at all? Is it then true, false, or something else to assert that all of them (all zero of them) are Fierce Animals?

§ 13.   Hilbert and Ackermann’s Grundzüge der theoretischen Logik—a foundational text in first-order mathematical logic and one that happens to have appeared in 1928, just two years after Winnie-the-Pooh and one year before The House at Pooh Corner—opts forthrightly for the orthodox (but non-Aristotelian) position, which is that it is true:

[T]he meaning of the universal affirmative statement (“All A is B”), traditional since Aristotle, is not fully consistent with our interpretation of the formula |  ∨ Y |. According to Aristotle the sentence “All A is B” is true only when there are objects which are A. Our deviation from Aristotle in this respect is justified by the mathematical applications of logic, in which the Aristotelian interpretation would not be useful.
(Principles of Mathematical Logic, tr. Hammond, Leckie, and Steinhardt)

 ∨ Y | may be read here as ‘either not-X, or Y, or both’: to say that ‘All Heffalumps are Fierce Animals,’ in other words, is to say that any given thing either is not a Heffalump, or is a Fierce Animal, or perhaps both, but that in any event it cannot be both a Heffalump and not a Fierce Animal. From this it follows that the statement ‘All Heffalumps are P’ is equivalent to ‘There are no non-P Heffalumps’—which, if there are in fact no Heffalumps, is true for any P we care to imagine. Ex falso quodlibet.

§ 14.   The decision to interpret ‘All A is B’ this way may appear peculiar, and it is not my present purpose to provide a full justification for it; but it will perhaps come to seem less unnatural if we transcribe the problem into the terms of rudimentary set theory. Aristotle’s logic is, after all, well known to be preeminently a tool for grouping and classifying and sub-classifying, best adapted to working with species and with the attributes that can be used to define them (differentiae specificae); and all of that fits rather neatly into the language of sets. The proposition that ‘All A is B’ becomes, on this reading, a statement about two sets A and B (the set of all things having the attribute A and the set of all things having the attribute B) to the effect that ‘A ⊆ B’, or ‘A is a subset of B’. The relation of ‘being a subset’ is defined so that A is a subset of B if and only if every member of A is also a member of B (whether or not B has any additional members that are not in A). It thus seems inescapable that the empty set { } is a subset of any set whatsoever, because it contains no members at all and therefore cannot contain any members that any other set does not. Even if the set B is also empty—if we are asking, say, whether the set { Jagulars } is a subset of the set { animals that drop out of trees onto people’s heads } (assuming that no such animals actually exist), we are forced to conclude that it is once again a subset by the definition we have adopted. It is not, in this case, a proper subset—but it is common ground that the universal affirmative is true whether all of the A are all of the B or only some of them.

§ 15.   This reasoning is entirely unacceptable to Brusentsov. In the notation he favours, the universal affirmation ‘All Heffalumps are Fierce Animals’ becomes h 'hf    ' f    ' [at least one thing exists that is a Heffalump; and things that are Heffalumps and are not Fierce Animals do not exist; and at least one thing exists that is not a Fierce Animal]. The first two members of this conjunction do not pose a particular problem: they could in fact quite straightforwardly be translated back into set notation as saying once again that { Heffalumps } is a subset of { Fierce Animals }, with the additional requirement—to ward off the unwelcome results of material implication—that the set of Heffalumps is not empty. We may wonder, however, why Brusentsov should regard the universal affirmation ‘All H are F ’ as only being true in the case where there is at least some non-F thing within the universe we are discussing. He has characterized this element of ‘necessary consequence’ as the principle, or law, of the coexistence of opposites [sosushchestvovanie protivopolozhnostei ], and naturally he regards it as Aristotelian in origin. The proximate source, however, is more likely to be the motto that Hegel slightly misquotes from Spinoza: omnis determinatio est negatio. To define something, in other words, is to set limits to it, to say not just what it is but inevitably also what it is not. An attempted definition that fails to set any boundaries to the thing it defines thus fails to define it: it leaves it merely indeterminate, like the pure Being at the start of the Science of Logic that turns out to be indistinguishable from pure Nothing.

§ 16.   We can therefore return to the Forest and the animals with the realization that their manner of reasoning and talking is consistently mathematical, Hilbertian, and formalist, rather than dialectical and Brusentsovian. All the assertions they make about empty classes of imaginary animals are, on the orthodox view, true—it is only Brusentsov, a neglected figure on the margins of philosophical logic, who maintains that they are false. But it is by no means obvious that the freedom to make arbitrary true assertions about classes of non-existent animals can be extended to individual animals, even imaginary individuals. Writers in the analytical tradition have devoted considerable effort and ingenuity to the matter of proper names, and any attempt to survey the resulting debates would take us too far afield; but many have concluded with Bertrand Russell (‘On Denoting’, 1905) that the use of a name, or another term that serves to pick out an individual, presupposes that the individual exists.

The whole realm of non-entities, such as ‘the round square’, ‘the even prime number other than 2’, ‘Apollo’, ‘Hamlet’, etc., can now be satisfactorily dealt with. All these are denoting phrases which do not denote anything. [...] If ‘Apollo’ has a primary occurrence, then the proposition containing the occurrence is false.

This difference between what we can say about empty classes and about non-existent individuals is brought out with exceptional clarity in the case of Backson. Owl tries to convert the proper name ‘Backson’ into ‘a Backson’, a member of an imaginary class of Backsons about which it will then be possible to speak in general; but, having already admitted that ‘Backson’ is the name of an individual, he finds himself unable to make any assertions at all:

“Christopher Robin has gone somewhere with Backson. He and Backson are busy together. Have you seen a Backson anywhere about in the Forest lately?”
    “I don’t know,” said Rabbit. “That’s what I came to ask you. What are they like?”
    “Well,” said Owl, “the Spotted or Herbaceous Backson is just a—”
    “At least,” he said, “it’s really more of a—”
    “Of course,” he said, “it depends on the—”
    “Well,” said Owl, “the fact is,” he said, “I don’t know what they’re like.”

§ 17.   Only two further conclusions need to be drawn. The first is a slightly unexpected vindication of Brusentsov’s repeated claim that his logic corresponds to ‘common sense’ [zdravyi smysl ] and the logic of the formalists does not: in the world of the Forest it is the eccentric dialectician who finds himself reiterating that anything you say about Heffalumps is false and anything you say about Jagulars is false, while the conventional mathematicians are happy to let the game continue. ‘Actually,’ as Brusentsov remarks in a slightly different context in The Principles of Informatics, ‘the genuine formalists don’t seem to see anything wrong with collisions of this sort; there are even some who find them fun.’ And the second is that our analysis seems to require Pooh, Piglet, and the rest of them to have a possibly surprising degree of awareness that Heffalumps and Jagulars do not actually exist, that their status as Animals About Which You Can Make Things Up And They Will Be True is sharply distinct from the status enjoyed by Tigger and Kanga and Rabbit and Owl (for the characters, though not entirely for the author). But of course it is not surprising in the least: they do know. That is what makes hunting Heffalumps or tracking Woozles or being scared of Jagulars a game. The point of these animals is to be almost real, so real you can almost believe in them, and yet not in fact real. Wittgenstein, the greatest of the ordinary language philosophers, writes that ‘[p]hilosophy is a battle against the bewitchment of our intelligence by means of language’ (Philosophical Investigations §109, tr. Anscombe)—but perhaps that is a battle that few of us are willing to win quite always.

Principal sources

BRUSENTSOV, N. P. Nachala informatiki.

—— . Iskusstvo dostovernogo rassuzhdeniya. Neformal’naya rekonstruktsiya aristotelevoi sillogistiki i bulevoi matematiki mysli.

—— . ‘Neadekvatnost’ dvoichnoi informatiki.’

—— and Ramil Alvarez. ‘Troichnaya EVM «Setun’ 70».’

MILNE, A. A. Winnie-the-Pooh.
—— . The House at Pooh Corner.
—— . When We Were Very Young.
—— . Vinni-Pukh i vse-vse-vse, tr. Boris Zakhoder.

RUDNEV, Vadim. Vinni Pukh i filosofiya obydennogo yazyka.