Stochastic Bookmark

abstruse unfinished commentary

about correspondence


Tractatus Rationali-Exspectationem

1. The economy is all that is the case.

1.1 The economy is the totality of prices, not of values.
1.11 The economy is determined by the prices, and by their being all the prices.
1.12 For the totality of prices determines what is the case, and also whatever is not the case.
1.13 Prices in the markets are the economy.

1.2 The economy divides into prices.
1.21 Each item can be the case or not the case while everything else remains the same.

2. What is the case—pricing—is the execution of transactions.

2.01 A transaction (an exchange of values) is a combination of values.
2.011 It is essential to values that they should be possible constituents of transactions.
2.012 In markets nothing is accidental: if a value can be monetized in a transaction, the possibility of the transaction must be written into the value itself.
2.0121 It would seem to be a sort of accident, if it turned out that an asset would fit a value that could already exist entirely on its own. If values can be monetized in transactions, this possibility must be in them from the beginning. (Nothing in the province of markets can be merely possible. Markets deal with every possibility and the average of all possibilities are its prices.) Just as we are quite unable to imagine equity values outside profitability or debt values outside timely payment, so too there is no value that we can imagine excluded from the possibility of combining with others. If I can imagine values combined in transactions, I cannot imagine them excluded from the possibility of such combinations.
2.0122 Values are independent in so far as they can be monetized in all possible assets, but this form of independence is a form of connection with transactions, a form of dependence. (It is impossible for a trade to appear simultaneously in two different roles: by themselves, and in propositions.)
2.0123 If I know a value I also know all its possible monetizations in transactions. (Every one of these possibilities must be part of the nature of the value.) A new possibility cannot be discovered later.
2.01231 If I am to know a value, though I need not know its external properties, I must know all its internal properties.
2.0124 If all values are given, then at the same time all possible transactions are also given.
2.013 Each value is, as it were, in a space of possible transactions. This space I can imagine empty, but I cannot imagine the value without the space.
2.0131 An equity value must be situated in nonnegative space. (A book-value is an accounting-place.) An entry in the balance sheet, thought it need not be dollars, must have some currency: it is, so to speak, surrounded by currency-space. Notes must have some maturity, present values of the claims of loans some degree of interest, and so on.
2.014 Values contain the possibility of all assets.
2.0141 The possibility of its being monetized in transactions is the form of a value.
2.02 Values are simple.
2.0201 Every statement about derivatives can be resolved into a statement about their constituents and into the propositions that describe the derivatives completely.
2.021 Values make up the substance of the economy. That is why they cannot be composite.
2.0211 If the economy had no substance, then whether a proposition had sense would depend on whether another proposition was true.
2.0212 In that case we could not provide any estimation of the economy (valid or defective).
2.022 It is obvious that a risk-free economy, however different it may be from the real one, must have something—a form—in common with it.
2.023 Values are just what constitute this unalterable form.
2.0231 The substance of the economy can only determine a form, and not any material properties. For it is only by means of propositions that material properties are represented—only by the configuration of values that they are produced.
2.0232 In a manner of speaking, values are currency-less.
2.0233 If two values have the same market form, the only distinction between them, apart from their external properties, is that they are different.
2.02331 Either a value has properties that nothing else has, in which case we can immediately use a description to distinguish it from the others and refer to it; or, on the other hand, there are several values that have the whole set of their properties in common, in which case it is quite impossible to indicate one of them. For it there is nothing to distinguish a value, I cannot distinguish it, since otherwise it would be distinguished after all.
2.024 The substance is what subsists independently of what is the case.
2.025 It is form and content.
2.0251 Equity, debt, currency (being denominated) are forms of values.
2.026 There must be values, if the economy is to have unalterable form.
2.027 Values, the unalterable, and the subsistent are one and the same.
2.0271 Values are what is unalterable and subsistent; their configuration is what is changing and unstable.
2.0272 The configuration of values produces transactions.
2.03 In a transaction values fit into one another like the links of a chain.
2.031 In a transaction values stand in a determinate relation to one another.
2.032 The determinate way in which values are connected in a transaction is the structure of the transaction.
2.033 Form is the possibility of structure.
2.034 The structure of a price consists of the structures of transactions.
2.04 The totality of executed transactions is the economy.
2.05 The totality of executed transactions also determines which transactions are not executed.
2.06 The execution and non-execution of transactions is reality. (We call the execution of transactions a realized P&L, and their non-execution an unrealized P&L.)
2.061 Transactions are independent of one another.
2.062 From the execution or non-execution of one transaction it is impossible to infer the execution or non-execution of another.
2.063 The sum-total of reality is the economy.

2.1 We quote prices to ourselves.
2.11 A quote presents an asset in market space, the execution and non-execution of transactions.
2.12 A quote is a model of reality.
2.13 In a quote values have the elements of the quote corresponding to them.
2.131 In a quote the elements of the quote are the representatives of values.
2.14 What constitutes a quote is that its elements are related to one another in a determinate way.
2.141 A quote is a price.
2.15 The price that the elements of a quote are related to one another in a determinate way represents that values are related to one another in the same way. Let us call this connection of its elements the structure of the quote, and let us call the possibility of this structure the indicative form of the quote.
2.151 Indicative form is the possibility that values are related to one another in the same way as the elements of the quote.
2.1511 That is how a quote is attached to reality; it reaches right out to it.
2.1512 It is laid against reality like a measure.
2.15121 Only the end-points of the bid-ask spread actually touch the value that is to be measured.
2.1514 So a quote, conceived in this way, also includes the indicative relationship, which makes it into a quote.
2.1515 These correlations are, as it were, the feelers of the quote's elements, with which the quote touches reality.
2.16 If a price is to be a quote, it must have something in common with what it depicts.
2.161 There must be something identical in a quote and what it depicts, to enable the one to be a quote of the other at all.
2.17 What a quote must have in common with reality, in order to be able to depict it—at-market or off-market—in the way that it does, is its indicative form.
2.171 A quote can depict any reality whose form it has. An equity quote can depict anything profitable, a currency one anything denominated, etc.
2.172 A quote cannot, however, depict its indicative form: it displays it.
2.173 A quote represents its subject from a position outside it. (Its standpoint is its representational form.) That is why a quote represents its subject at-market or off-market.
2.174 A quote cannot, however, place itself outside its representational form.
2.18 What any quote, of whatever form, must have in common with reality, in order to be able to depict it—at-market or off-market—in any way at all, is market form, i.e. the form of reality.
2.181 A quote whose indicative form is market form is called a market quote.
2.182 Every quote is at the same time a market one. (On the other hand, not every quote is, for example, a equity one.)
2.19 Market quotes can depict the economy.

2.2 A quote has market quotation form in common with what it depicts.
2.201 A quote depicts reality by representing a possibility of execution and non-execution of transactions.
2.202 A quote contains the possibility of the asset that it represents.
2.203 A quote agrees with reality or fails to agree; it is at-market or off-market, valid or defective.
2.22 What a quote represents it represents independently of its validity or defectiveness, by means of its indicative form.
2.221 What a quote represents is its sense.
2.222 The agreement or disagreement or its sense with reality constitutes its validity or defectiveness.
2.223 In order to tell whether a quote is valid or defective we must compare it with reality.
2.224 It is impossible to tell from the quote alone whether it is valid or defective.
2.225 There are no quotes that are valid a priori.

I could continue, but it would involve the arcana of CAPM theory, financial modeling and back-office / accounting mechanics, and I’m boring us already. Sometimes even whereof one may speak, thereof it is best that one remain silent.


Waxwing philosophical: a hermeneutic interpretation of Pale Fire

Pale Fire, my favorite book, my Lit 202, its literary allusion thick as thieves; lit-critical flypaper, in which no commentator has the last word (we are all Kinbote now). By topsy-turvy coincidence it sparked blogcommentary on philosophical ruminations (the most relevant here, TheValve: Uncruel Beauty?), and a blogpost series (not intended as such to start with, just turned out that way) 3 years ago, in which I explored some of its many aspects, on Nabokov generally (1, 2) and Pale Fire specifically (3, 4, 5, 6, 7), culminating in "The Antinomy of Criticism", aligning Aunt Maud and Prof Botkin with Maud Bodkin. But now it's time to up the ante, beyond lit-critical interpretation, and to bring it full circle. Today we have the naming of parts.

We begin with Brian Boyd, in Vladimir Nabokov: The American Years:

It is Shade who points out that Kinbote is "the author of a remarkable book on surnames”—a hint if there ever was one. According to Nabokov's dictionary, Webster's Second, a kinbote is a bote or compensation "given by a homicide to the kin of his victim." Jack Grey, the man who kills Shade, certainly does not give Kinbote to Sybil, nor would she want him. The only way the name make the sense that Nabokov indicates it ought to have is if Shade, in compensation for the shock of fictively killing himself off, presents Sybil with the maddening but supremely colorful Kinbote, whose attacks on Sybil, if reflected through one more mirror so that we can read them the right way around, are of course a tribute to her staunch loyalty. And "Botkin" is just as apt. Webster's Second records one meaning of bodkin—or as Kinbote insists, "botkin”—as "a person closely wedged between two other persons," like Kinbote trying to thrust himself between John and Sybil Shade. Its main meaning, of course, is a stiletto, and in this sense it evokes Hamlet's "When he himself might his quietus make / With a bare bodkin" and the suicide that will remove the figmentary interloper between the two Shades as soon as he has finished his commentary and index.

In the service of identifying Kinbote with Botkin, and Shade as sole author of Pale Fire (a judgment subsequently revised), Boyd is echoing Kinbote's technique of argumentation as seen in a digression in the commentary to line 71 [C71]:

[of Shade's parents] ...a bird had been named for him: Bombycilla Shadei (this should be "shadei," of course). The poet's mother, nee Caroline Lukin, assisted him in his work and drew the admirable figures of his Birds of Mexico, which I remember having seen in my friend's house. What the obituarist does not know is that Lukin comes from Luke, as also do Locock and Luxon and Lukashevich. It represents one of the many instances when the amorphous-looking but live and personal hereditary patronymic grows, sometimes in fantastic shapes, around the common pebble of a Christian name. The Lukins are an old Essex family. Other names derive from professions such as Rymer, Scrivener, Limner (one who illuminates parchments), Botkin (one who makes bottekins, fancy footwear) and thousands of others. My tutor, a Scotsman, used to call any old tumble-down buildings a "hurley-house." But enough of this.

Professor Hurley, English department head at Wordsmith, who opened C71, is a rival commentator enlisted by Sybil Shade, one of two that she proposes to assist in the editing of the poem "Pale Fire"; per the Foreword:

Instead of answering a month-old letter from my cave in Cedarn, listing some of my most desperate queries, such as the real name of "Jim Coates," etc., she suddenly shot me a wire, requesting me to accept Prof. H. (!) and Prof. C. (!!) as co-editors of her husband's poem. How deeply this surprised and pained me! Naturally, it precluded collaboration with my friend's misguided widow.

I propose that Profs. H. & C. correspond to Hermogenes and Cratylus in Plato's dialogue of the latter name. Need I mention that the point of this dialogue is the making of names, and that Pale Fire is set at Wordsmith University? The above are sidebars to the crux, C894, the rock upon which theories of ultimate authorship and of the novel's "reality" founder, seeming to cede Kinbote's objective existence among witnesses—and if skepticism about Kinbote's reportage is to reject this evidence, where doe it end? But aside from this, its function within the matrix of the novel has been a tough nut to crack; Cratylus sheds light upon much of what's going on here.

C894 recounts the episode in which a German lecturer visiting Wordsmith from Oxford remarks upon Kinbote's likeness to King Charles, the deposed monarch of Zembla, Kinbote's denials leading to consideration of etymologies of resemblances and names, and is the first indication of Botkin, another prospective double. The whole episode, largely reported dialogue, mirrors Socrates' arguments:

Soc. [...] I should say rather that the image, if expressing in every point the entire reality, would no longer be an image. Let us suppose the existence of two objects: one of them shall be Cratylus, and the other the image of Cratylus; and we will suppose, further, that some God makes not only a representation such as a painter would make of your outward form and colour, but also creates an inward organization like yours, having the same warmth and softness; and into this infuses motion, and soul, and mind, such as you have, in a word copies all your qualities, and places them by you in another form; would you say that this was Cratylus and the image of Cratylus, or that there were two Cratyluses?
Crat. I should say that there were two Cratyluses.
Soc. Then you see, my friend, that we must find some other principle of truth in images, and also in names; and not insist that an image is no longer an image when something is added or subtracted. Do you not perceive that images are very far from having qualities which are the exact counterpart of the realities which they represent?
Crat. Yes, I see.
Soc. But then how ridiculous would be the effect of names on things, if they were exactly the same with them! For they would be the doubles of them, and no one would be able to determine which were the names and which were the realities.

Beyond this, though, we have larger implications regarding the source for the name of the poem itself, Shakespeare's Timon of Athens: "The sun's a thief, and with his great attraction / Robs the vast sea; The moon's an arrant thief, / And her pale fire she snatches from the sun ..." (gender-mangled in Zemblan translation; cf the introduction of images in Cratylus: Soc. First look at the matter thus : you may attribute the likeness of the man to the man, and of the woman to the woman ; and so on? ... And conversely you may attribute the likeness of the man to the woman, and of the woman to the man?). But thievery is not the sole point to be taken from this:

Soc. I should imagine that the name Hermes has to do with speech, and signifies that he is the interpreter (ermeneus), or messenger, or thief, or liar, or bargainer; all that sort of thing has a great deal to do with language; as I was telling you the word eirein is expressive of the use of speech, and there is an often-recurring Homeric word emesato, which means “he contrived”—out of these two words, eirein and mesasthai, the legislator formed the name of the God who invented language and speech; and we may imagine him dictating to us the use of this name: “O my friends,” says he to us, “seeing that he is the contriver of tales or speeches, you may rightly call him Eirhemes.” And this has been improved by us, as we think, into Hermes. Iris also appears to have been called from the verb “to tell” (eirein), because she was a messenger.

Note that this also expands and folds in the part played by Iris Acht (King Alfin's flame) in the proceedings. But the list of Hermes' referents—interpreter, messenger, thief, liar, bargainer, contriver—all have resonance within Pale Fire.

To return to Boyd's quote above, a hint if there ever was one:
Shade [addressing the German visitor]: "Professor Kinbote is the author of a remarkable book on surnames. I believe [to me] there exists an English translation?"
"Oxford, 1956," I replied.

The excerpts from Cratylus above are taken from the translation of Benjamin Jowett, in Dialogues of Plato, Oxford 1953; the only contemporaneous reference I've found (but not seen) is Richard Robinson (of Oxford), ‘A Criticism of Plato’s Cratylus’, The Philosophical Review LXV:3, July 1956. (For an overview of the dialogue, see Stanford's Encyclopedia.)

Cratylus is an ur-text of hermeneutics (Aristotle refers to it, though as being suspect, and not in On Interpretation). Kinbote seems to cast himself as Plato to Shade's Socrates (in the latter case there may be a physical resemblance). It leads me to wonder to what extent Nabokov was addressing the evolution of hermeneutics; for example, in his writings of this period St. Augustine seems a pervasive influence in other ways, but also had something to say about rules of interpretation in On Christian Doctrine. Does our visiting German lecturer stand in for Herder-Schleiermacher-Heidigger-Gadamer?


The Purloined Letter: a note on what's missing

I was enjoying the luxury of meditation, in profound silence; intently and exclusively occupied with mentally discussing certain topics which had formed matter for conversation at an earlier period of the evening; I had been sitting in the dark, and now arose for the purpose of lighting a lamp, but sat down again, without doing so, requiring reflection to better purpose in the dark. That the difficulty now, I hope, is very simple indeed, and I can manage it sufficiently well; but I thought the details of it odd. Simple and odd, and not exactly that, either. The very simplicity of the thing which puts at fault such an idea. And what, after all, is the matter on hand?

The above is extracted from the opening to "The Purloined Letter", steganographically (i.e. by process of elimination, preserving word order); I had thought to devise a full first-person narrative in this manner but found that task too difficult, so it will serve instead to introduce consideration of an aspect of this short story (my favorite) which I have not seen remarked upon.

There's a hole in the story, but not the one that the critical commentary I've seen addresses (taken in by the nullity that is the contents of the letter). Instead, I mean a hole in the logic, something said which is contradicted by something left unsaid. Dupin's reasoning seems perfect, but one extrapolation appears to be unwarranted, at odds with everything that led up to it:

" [...] But I had an object apart from these considerations. You know my political prepossessions. In this matter, I act as a partisan of the lady concerned. For eighteen months the Minister has had her in his power. She has now him in hers; since, being unaware that the letter is not in his possession, he will proceed with his exactions as if it was. Thus will he inevitably commit himself, at once, to his political destruction. His downfall, too, will not be more precipitate than awkward. [...]"

Contexting this (renowned verbifier Alexander Haig's abusage), the letter came into the Minister's possession in full view of the lady concerned, and his knowledge of her knowledge of this conferred its power. But the repossession of the letter, unbeknownst to the Minister, is not accompanied with the information that the Minister remains in the dark about its loss:

"In that case," replied Dupin, opening a drawer, and producing a check-book, "you may as well fill me up a check for the amount mentioned. When you have signed it, I will hand you the letter."

I was astounded. The Prefect appeared absolutely thunderstricken. For some minutes he remained speechless and motionless, less, looking incredulously at my friend with open mouth, and eyes that seemed starting from their sockets; then, apparently in some measure, he seized a pen, and after several pauses and vacant stares, finally filled up and signed a check for fifty thousand francs, and handed it across the table to Dupin. The latter examined it carefully and deposited it in his pocket-book; then, unlocking an escritoire, took thence a letter and gave it to the Prefect. This functionary grasped it in a perfect agony of joy, opened it with a trembling hand, cast a rapid glance at its contents, and then, scrambling and struggling to the door, rushed at length unceremoniously from the room and from the house, without having uttered a syllable since Dupin had requested him to fill up the check.

When he had gone, my friend entered into some explanations.

So the Prefect departs without any notion that the Minister still believes himself in possession of the letter; the Prefect, and by extension that exalted personage for whom he is agent, does not know that the Minister does not know. The question is, who will first discover this state of affairs? Every indication would seem to favor the Minister in this regard: his powers of discernment already having been demonstrated in the original theft, supported by the digression on games (an identification of the reasoner's intellect with that of his opponent. [...] And the identification [...] of the reasoner's intellect with that of his opponent, depends, if I understand you aright upon the accuracy with which the opponent's intellect is admeasured. [NB: I particularly like the interpolation of "if I understand you aright"]) and the following adumbration of the false duality between poet and mathematician (with another nice touch: Bryant, in his very learned 'Mythology,' mentions an analogous source of error, when he says that 'although the Pagan fables are not believed, yet we forget ourselves continually, and make inferences from them as existing realities.'). The repossession of the letter will change the behavior of both the Prefect and of the exalted lady in response to and even prior to any attempted continued usage of the Minister's supposed but now non-existent power. The Prefect's diligence in tracking the Minister will relent; any subsequent audience with the lady will evince changed circumstances by her newly-found confidence in dealings with the Minister. So Dupin's supposition that the Minister "will proceed with his exactions" is flawed, and so too the consequent "political destruction ... not ... more precipitate than awkward." While this course of events is indeed possible, it presupposes an unlikely blind spot in the Minister's dealings, and suggests a blind spot in Dupin's. But I do not think that this is a point that Poe overlooked in his composition of this tale, but rather something hidden in plain view for the astute reader (who, me?) to discover.