The philosophical method — Meaning and Distance

We may call our technical doctrine “verisimilism”, “literary calculation”, or “an empirical mathematics of non-scientific texts”. It is a technique and not a theory. A theory is a body of rigorous demonstrations bearing on the same object, and forming as it were a system, but open to possible new discoveries. A technique is a body of certain knowledges, obtained by trial and error, on a single object. A technology is the application of a theory to the production or modification of material objects. Among techniques, some, such as the making of stone tools, issue in material objects. Others, such as the fine arts, issue in objects which suggest the question of the beautiful and the ugly, which is not very material. Others again, such as writing, give objects of which our mind makes use, in particular for the preservation of knowledges across distances and ages.

Verisimilism is a technique of analysis of texts — spoken or written — in which imagination prevails, and where verification by confrontation with facts remains very secondary. Verisimilism therefore resembles writing, since it is a technique that does not directly produce material objects, but which is useful for knowledge. Only, the difference with writing is that, instead of having been obtained solely by trial and error, verisimilism comes from the derivation of a theory towards a trial-and-error practice. The theory is the calculation of probabilities, founded by Stevin, Galileo, Fermat, Pascal, the Bernoullis, and Bayes. We do not manage to apply this theory to the interpretations of texts; we therefore make of it an empirical imitation, which is no longer theory, but a philosophically grounded technique, whose purpose is to enrich linguistic or poetic knowledge, literary analysis, or the commentary of written and oral works obtained chiefly through imagination.

Philosophical vocables

It is impossible to define rapidly the special terms used by us. We shall therefore speak here merely to the imagination of the reader, somewhat as a physicist would do who put it that the sun “burns” to express that a “combustion” takes place within it. So, in a very rough and approximate way: a “collision” relates to a paradox. An “attenuation gloss” locates a problem without resolving it. A “latch” relates to an influence exerted by the context on the formation of a paradox. A “tartan” pertains to an analogy. A “felt” touches upon a turn of phrase taking the form of a slight riddle. A “reps” connects with an onomatopoeia, with an excess of punctuation, or with a kind of pun. An “eraser” concerns a connection between meanings. For numerically expressed plausibility, the line is that of the collision for the channel; that of the gloss for the gradient; that of the latch for the acre; that of the tartan for the arch; that of the felt for the grill; that of the reps for the manse; and that of the eraser for the module. These basic clarifications will be of service in understanding the first seven parts of the book. The rest will be of easy approach, from there on, for those who have travelled the earlier stages.

Philosophical currents

David Hume's philosophy of human nature

As we need to represent the connection between the ideas of Charles Baudelaire's poem „Correspondences“, we are led to make an adaptation of the principle of David Hume — a philosopher who dared to imitate Newton in an analogical manner — according to which the greater the distance between ideas, the less associable they are. Instead of seeing this point, as David Hume did, in the mind of anyone thinking about nature or about experience, we consider the matter for the ideas expressed in the poem. In order to take logical connections into account, we admit that they reduce distance to a minimum, behaving as though the ideas were expressed in contact one with the other. «Nature is a temple…There man passes…» gives, despite the apparent distance between «Nature» and «man», a minimal Nature–man distance thanks to the logical link «passes through». In a non-demonstrative text the meanings of words are almost like masses in space — that is, the farther apart they are, the more memory neglects to connect them, and so the less they attract one another (let us not speak of the square of the distance: that is too precise). The more demonstrative a text is, the more frequent are reminders of meaning of the kind “point number 1” or “what we were speaking of above”, and the distance between the meanings of the words is by this very fact cancelled. This situation is therefore not favourable to the study we offer, which holds good only for imaginative texts. For the latter, it is sometimes very simple: the closer the meanings of the words, the more they attract one another. Furthermore, an author's provocations, paradoxes, alliances of words of contrary sense, strike the mind more strongly than ordinary meanings, and so the attraction between the meanings of the words is sharper still when they form paradoxes. This situation is in the highest degree propitious to the study being conducted — the parrot, it is said, is more inclined to repeat a word heard when accompanied by a strong emotion because it is fixed better in its “memory”, and we should be, in some respect, like that.

By imposing on ourselves the reading of the literature about literature, we set up a measurement of plausibility of the meaning posited as original, for any imaginative text that has been the subject of numerous critical investigations over the course of at least a century or so. The part of the work “Meaning and Distance 1” takes the example of the possible interpretations of Baudelaire's poem, analysing the way in which the meanings of the words composing the paradoxes presented attract one another, and the way in which the paradoxes themselves (“Nature-temple”, “living-pillars”, “incense-corrupt”, “answers between colours, perfumes and sounds”) mutually reinforce their anchoring in the mind or in memory. “Meaning and Distance 2” generalizes to non-paradoxical problems what has been seen in the preceding part. Two kinds of links not previously measured for their plausibility are now considered in this regard. First, neutral observations, or what most resembles them, such as the items of a bailiff's inventory. For example «long echoes which mingle in the distance» is close to a series of observations: “there are echoes”; “some are long”; “some are formed far from the listener”; “some mingle together”. The second category of things studied otherwise than before — that is, henceforth metrically — is constituted by the relations that may serve to locate, within the labyrinth of general ideas, the paradoxes seen in the preceding part. Thus the paradox “corrupt incense” is rendered approachable by the links “incense-sense” and “sensuality-corruption”. It is shown that, this time again, the meanings of the words attract one another all the more strongly in situations in which they are at a slight distance, temporal if one listens to the poem, or spatial and temporal if one reads it. As this attraction is less sharp than for the meanings of the words forming paradoxes, the measuring apparatus is longer, since attraction becomes negligible in more cases. The measurement made for the plausibility of what the author wanted to say is done by 1/x = 1/qepfzgj instead of being done by 1/x = 1/tsmw. There are therefore three more filters of reality, or again the 1 of the numerator has three times more opportunities to be divided — by 2 in particular — by reason of the numerous precautions to be taken in the act of attributing to the author an interpretation of his text. “Meaning and Distance 3” studies the influence of words that appear secondary, placed beside those that form a paradox.

Thus «triumphant», which is beside «corrupt» and «incense» in „Correspondences“, obliges one to set aside the “chemical“ sense of «corrupt» in favour of the ”moral“ sense. The plausibility that the author wanted the paradoxes has already been measured, and we now measure the plausibility that he wanted to favour their existence by means of words such as «triumphant», placed beside those that form them most immediately: «incense» and «corrupt» for “corrupt incense”. In passing, by ceaselessly altering Baudelaire's poem, in order better to understand texts in general, we identify facts such as the following, which is very striking. The two paradoxes “Nature-temple” and “incense-corrupt” would mutually reinforce their sense, by a reciprocal action, in “Nature is a temple and the incenses are corrupt”. But if we remove “incense”, and a plural, to obtain “Nature is a corrupted temple”, the paradox “Nature-temple” is weakened by the paradox “corrupted temple”, because a corrupted temple is no longer quite a temple, and so the relation of the temple to Nature is less shocking. It is as if “incense” protects the first paradox from the dilution that occurs when the two paradoxes are amalgamated. As there seems to be a whole set of relations of this kind to explore, we have good hopes that the method presented will be fruitful as regards the pinpointing of such precise facts. The borrowing initially made from the principles of David Hume's philosophy, on distance and the relaxation of contact between ideas, thus leads to new objects of study. But, held by other tasks, those that must be accomplished in the Parts currently following the third, we have postponed to much later the deepening of this matter.

Cournot's philosophy: calculation and probabilities

We have, to serve as the foundation of our empirical calculation of plausibility, imitated a philosophical idea of Augustin Cournot, a philosopher of scientific thought, who lived from 1801 to 1877. This remarkable intuition of Augustin Cournot's consists in representing to oneself the essential reality which emerges in the midst of the irregularities in the processes to which the calculation of probabilities is applicable. It is the famous dense central trail in the midst of the sparse cloud of disparate points in the diagrams of probability and statistics. Yet the mathematician-philosopher did not apply his conception to the study of texts. Let us move away from his time, to take the example of a 1975–80 survey on lung cancer, used to bring out variations in mood and in the diet of the patients. One will take too much coffee; another too much alcohol; the third will not eat enough; the fourth, on the contrary, will eat too much; the fifth will be ceaselessly melancholic; the sixth quick-tempered; others will be calm. Yet in the midst of this disorder, a principal tendency will appear, for almost all of them will smoke. The isolated results will be figured by points on the periphery of the main block of responses. The major character, on the contrary, will be represented as a dark trail expressing the general tendency. Laplace had elaborated probabilities while thinking that chance does not exist for a very powerful thought, but that it does exist for the one who does not know enough of the laws of nature — and of society, which prolongs it, we shall add. The calculation of probabilities is a determination by us of a determinism in things — including the things of poetic activity, it must be added. Laplace was right “grosso modo” with the idea of chance due to our ignorance, but Cournot rightly insisted on a detail of great value: the difference between the impression of determination and the impression of chance is simply a matter of scale. We shall say, trying to continue his thought, and beginning on the subjective plane, that the perception of facts is organized like water. There is water vapour; liquid water; ice. It is the same for the perception in question. There is, 1°), the unknown going in all directions for the disoriented individual who awakes in the midst of an intense action conducted around him by others; there is, 2°), chance or arrangement of events that do not show their determination unless presented in great numbers; and there is, 3°), determination — not chance — as in Archimedes' upthrust for the ship that remains afloat. The link is accentuated by the fact that, at the outset, the floating of the ship is not understood. On the objective plane now, we set aside in idea 1°), then couple 2°) and 3°) by supposing a gradation between the two, but without imagining a “Leibnizian” continuity, and so contenting ourselves with a gradation between the positions by minute discontinuities. Whether there is chance, 2°), or determination, 3°), is only a matter of scale. Determination is just the fact that the disparate irregularities surrounding the central tendency become negligible. So an absolute intelligence would perceive this matter of scale. The determining use of chance rests in any case on the “law of large numbers” or “Bernoulli's theorem”. When one watches a few coin tosses, and one has bet on a result, one has the impression that “heads” and “tails” come up by luck or bad luck. But when one sees a thousand tosses, one has the impression of regularity, with about ½ of “heads” and about ½ of “tails”. Augustin Cournot thought with such ideas to know economics, and it is not so surprising that stylistics may be viewed as a new territory to be conquered in this way. The difference is likely to be that we have allowed ourselves a great many liberties with mathematics — which doubtless harms the essay greatly — and that we do not know how to do better.

For the content of the texts, we judge that the most frequent interpretations are also the most solid. The surest meaning that criticism can reach eventually emerges over time. It has been filtered by generations of critics. It then constitutes the principal tendency of the commentaries and is due to the text. Fanciful meanings hastily supposed, by contrast, appear as disparate caprices, in the midst of which only the principal meaning remains firm, like a more pronounced trail in the middle of a “cloud” of scattered points. For „Correspondences“, one reader sees Baudelaire's «Nature» as a lover, another sees it as the magician-philosophers of the Alexandrian decadence did, a third pictures it as a wicked stepmother, a fourth identifies it with the celestial vault, but all are agreed that to call it «a temple» is a paradox. One must then imitate the theory of probabilities by playing on acceptance criteria that issue in numerical values. In doing so, we proceed to numerous empirical adaptations of the calculation, in order to fit the new object to be treated. When a signification is established, by its confirmation from critic to critic, we hold it to be the one intended by the author and we grant it maximal plausibility: 1/1. Then we look for the situation of each other interpretation, turning around the same words of the text, on a scale running from 1/1 to the negligible values <1/16. As the meaning of words is hard to treat by a true calculation of probabilities, modifications “ad hoc” are introduced as a function of the difficulties encountered, which gives indeed measurements, but in the framework of a tentative technique that does not demonstrate in the strong sense of the word. We then avoid in the exposition all terms such as “probability”, “science”, “hypothesis”, “demonstration”, and we put only “plausibility”, “knowing” or “knowledge”, “supposition”, “explanation”. Plausibilities are indeed a ratio 1/x as in probabilities, but 1/x is found in a very empirical manner and constantly with the sole example of „Correspondences“.

The measurement criteria are t, s, m, w in 1/tsmw for “Meaning and Distance 1”. They are q, e, p, f, z, g, j in 1/qepfzgj for “Meaning and Distance 2”. They are t*, s*, q*, e*, p*, f*, z*, g*, j* for 1/t*s*q*e*p*f*z*g*j* for “Meaning and Distance 3”. The filtering of abusive interpretations is permitted by these measurements. It is seen that the result shows a great numerical weakness for all “far-fetched” interpretations. The method will therefore harm those who claim to draw from a text an invented meaning, as the conjurer draws the rabbit from the hat, after having set up a rhetorical and social arrangement whose effect is to provoke illusion. We rely as far as possible on literary history in order to identify fanciful interpretations as such and to separate them from the very rare ideas which are simultaneously good and hard to find. The whole set of facts and tasks gradually takes shape. The author wanted paradoxes; he put in place means of penetrating them, and also means of stabilizing them, by micro-lockings of meaning, by way of the words neighbouring those of the paradoxes in question. The author's supposed intentions, or the interpretations, end up being measured as “highly plausible”, “scarcely plausible”, “of negligible plausibility”. Let us admit it: often the highest plausibility falls quite simply to the ideas found immediately by the public of the text. The hundreds of interpretations that pass through the filter of the critics' attacks, for a century or more, contain as the best what comes back ceaselessly, what no one manages to dismiss, because it is true — «truth is the index of itself» in the very long term. Quite simply, exegetes cannot do without it, since it comes from the text itself. Therefore from the tangle, from the “cloud” of interpretations going in every direction, the principal tendency emerges, made up of the best ideas, which are the most faithful to the text, and which are those the interpreters most need. In consulting criticism, one becomes the keeper of the “cloud” of interpretations that now come to dwell in one's own memory — and one is also, happily, the keeper of that principal tendency which runs through the “cloud”. Then a new process begins on this new scale and at a higher level. When one sees that one ceaselessly needs the same criteria to separate the illusory meanings from the principal meaning, one makes of these the means of measuring plausibility. This is the process of induction, one of the most faithful producers of substantial ideas, together with perception and deduction.

Application: literature, the study of literary texts

The interest of literary texts

Since «Correspondences» means, according to numerous exegetes, “Analogies”, we were bound to take up, sooner or later, the figures of speech of the same name, which are frequent in universal literature. “Meaning and Distance 4” thus joins the treatment of problems of rhetoric, by studying several important tropes, and among them, in order to remain within the best-known field, comparison and metaphor. Connoisseurs ordinarily wonder about the workings of these figures, and we take up this point by drawing on a rapid but illuminating observation of Aristotle's “Poetics”, whose importance Vuillemin has emphasized. This allows the development of the supposition according to which mathematical analogy, of the model 2/3 = 4/6, seems the logical basis of a family of four tropes, whose types are “old age is for life the evening of a day”, “old age is the evening of life”, “old age is like an evening”, “old age is an evening”. While characterizing this set by its internal links, we apply to the new object the central perspective of the essay, in order to ask whether some imaginative author whatsoever, bard or writer, literary glory or obscure storyteller of the oral tradition, isolated individual or spokesman of a collectivity, working for mythology or for poetry, has indeed wished to deliver such a figure of speech as is perceived in his text by an interpreter, or whether, on the contrary, the critic has invented it from too little in the work considered. Conceiving, from one of these extremes to the other, a Leibnizian or Bernoullian gradation, we put in place a measurement of certainty as to the presence, in imaginative texts, of turns belonging to one of the four kinds of analogy studied. For this, a portion of the means previously employed in the progressive sorting of the plausible from the implausible is reused.

“Meaning and Distance 5” examines turns of phrase neighbouring those above, having in particular the types “I perceive a sail”, “he has visited all the sceptres of Europe”, “how I love her bicycle”, “they will make him disappear”, «Go, I do not hate you.» The same idea concerning distance presides over this new development. Consider the text "society needs you, sounding boards, instruments of alarm, and let us not forget that in an important moment of the general crisis of morals, he too played his part, Baudelaire“. The figure ”you are a Baudelaire“ will be less plausible than with ”society needs you, Baudelaire too played his part". In short, in all the cases here forming the objects of study of Parts I, II, III, IV, V, VI and VII of the essay, memory replaces the codified connections well known in verbal usages, when they are lacking. Thus, for two words that the author has voluntarily united by a grammatical disposition, such as «corrupt» and «incense» in the poem, their distance does not prevent their relation. But for the rest, in an imaginative text, two ideas without express connection owe their connection to the memory of the first when the second is broached. It follows that their relation weakens with their distance. Masses, according to Newton, are in space mutually attracted in inverse proportion to the square of their distance. We imagine that under certain conditions and within a single text, significations attract one another all the more strongly the closer they are, and all the less the more distant they are. For this to be so, the writing must not be rigorous, which explains why the method is interesting only for imaginative texts.

The choice of „Correspondences“, Baudelaire's poem

We must adapt to our procedure a conception unequalled though halting, and so commonplace that it is attributed to a great number of different scholars: experimental method. By drawing support from it, we put to the test every numerical criterion invented by trial and error for the sole purpose of measuring an implausibility of literary interpretation, sought out on purpose or known to us for some time. In order to avoid the provisional synthesis of the criteria of implausibility being blurred, new trials are conducted with them all taken together this time, varying various quantities of multiple aspects among those studied, in order to complete the measurement. At the end of each procedure, all that remains, in order to obtain the quantity of plausibility sought, is to take the reciprocal of the implausibility, that is, the numerical reciprocal of the product of the criteria of implausibility. As great works have survived their scholastic adaptation, they should equally well withstand our trials; and one should not too eagerly insist that it would be better to write the text without ever borrowing one, for the suspicion would soon arise that it had been supplied solely for the defence of the analysis presented, and so, in the end, to shine vainly.

As for ourselves, indeed, the tastes and counsels of our parents, as well as those of our teachers, very early directed us towards Baudelaire, “Les Fleurs du mal”, and „Correspondences“, so that this poem has, for very many years, been a convenient object of mental exercise, which we frequently have in mind, in order to test what we think regarding interpretation. It then became like a portable workshop of poetic linguistics, open at any moment, and even in situations in which nothing allows one to note any idea down.