The Logic of Sense

1. Sense is a Non-Existent Entity, Existing at the Surface

Sense is a nonexisting entity, and, in fact, maintains very special relations with nonsense.

Sense is not a thing. It's not a physical object, a mental state, or a concept. It's an incorporeal entity, a pure event that subsists or inheres, not exists. It's the "what is expressed" by a proposition, not the proposition itself.

Surface phenomenon. Sense isn't found in the depths of things or in the heights of ideas. It's a surface effect, like a mist rising from a prairie, a film without volume that envelops bodies. It's the boundary between things and propositions.

Paradoxical nature. Sense is inseparable from paradoxes because it's always both at once: future and past, active and passive, cause and effect. It's the affirmation of both senses or directions simultaneously, defying good sense and common sense.

2. The Stoics Discovered Surface Effects, and Language's Role

The Stoics discovered surface effects.

Two kinds of things. The Stoics distinguished between bodies (with their states of affairs) and incorporeal effects (events). Bodies exist in the present, while events subsist in the past and future, always eluding the present.

Incorporeal events. Events are not physical qualities but logical attributes, not things but results of actions and passions. They are impassive, sterile, and play out on the surface of being. Examples include "to grow," "to diminish," "to be cut."

Language and events. Language is essential to events, as events are expressed or expressible in propositions. The Stoics saw language as both establishing limits and transcending them, making paradoxes a tool for analyzing language and synthesizing events.

3. Propositions Have Four Dimensions: Denotation, Manifestation, Signification, and Sense

Sense is the fourth dimension of the proposition.

Three traditional dimensions. Propositions have three relations: denotation (relation to external states of affairs), manifestation (relation to the speaker's desires and beliefs), and signification (relation to universal concepts and implications).

Sense as the fourth dimension. Sense is not reducible to the other three. It's the "expressed" of the proposition, an incorporeal entity that inheres in the proposition but is also an attribute of the state of affairs. It's the boundary between propositions and things.

Sense is not signification. Signification is the condition of truth, but sense is the condition of signification. Signification is always a form of possibility, while sense is the ideational material or stratum that makes denotation and other dimensions possible.

4. Dualities Define Our World: Body/Language, Eat/Speak, Denotation/Expression

The duality in the proposition is not between two sorts of names . . . rather, it is between two dimensions of the proposition, that is, between denotation and expression.

Body and language. The duality of bodies and language is expressed as the alternative to eat or to speak. Eating represents the depth of bodies, their mixtures, and their actions, while speaking represents the surface, the incorporeal events.

Two kinds of words. There are two kinds of words: substantives and adjectives that denote states of affairs, and verbs that express events. Verbs are "prouder" because they carry becoming and its paradoxes.

Denotation and expression. The duality is also internal to the proposition, between denotation (relation to things) and expression (relation to sense). To pass to the other side of the mirror is to pass from denotation to expression, reaching a region where language relates only to sense.

5. Sense is Defined by Paradoxes: Regress, Division, Neutrality, Absurdity

Sense is both the expressible or the expressed of the proposition, and the attribute of the state of affairs.

Paradox of regress. Sense is always presupposed, yet it can always be taken as the object of another proposition, leading to an infinite regress. This shows both the impotence of the speaker and the power of language.

Paradox of sterile division. Sense, once extracted from the proposition, is independent of it, yet it's also its evanescent double. It suspends affirmation and negation, remaining neutral and sterile.

Paradox of neutrality. Sense is indifferent to the modes of the proposition (quality, quantity, relation, modality). It's the same for contradictory objects, for inverse relations, and for all modes of possibility.

Paradox of the absurd. Propositions that designate contradictory objects have a sense, even though their denotation cannot be fulfilled. Impossible objects are "extra-existents," outside of being, but with a precise position in this outside.

6. Serialization is Key: Heterogeneous Series Converge on a Paradoxical Element

The serial form is thus essentially multi-serial.

Homogeneous and heterogeneous series. A single series of names, for example, is homogeneous, but it subsumes two heterogeneous series: one of denotations and one of expressions. The serial form is always multi-serial.

Signifier and signified. In any two series, one is the signifier (presenting an aspect of sense) and the other is the signified (correlative to that aspect). Even when series appear homogeneous, one always plays the role of signifier.

Paradoxical element. Two series are always in disequilibrium, with one having an excess and the other a lack. They converge on a paradoxical element that circulates between them, ensuring their communication while making them diverge. This element is always displaced in relation to itself.

7. Esoteric Words Connect, Coordinate, and Ramify Series

The esoteric word in general refers at once to the empty square and to the occupant without place.

Three types of esoteric words. There are contracting words (synthesis of succession), circulating words (synthesis of coexistence), and portmanteau words (disjunctive synthesis).

Contracting words. These words contract syllabic elements of a proposition to extract its global sense (e.g., "y'reince" for "your royal highness"). They connect a single series.

Circulating words. These words coordinate two heterogeneous series, acting as a frontier between them (e.g., "Snark," "it," "thing"). They guarantee the conjunction of two series.

Portmanteau words. These words contract several words and senses, but their function is to ramify series by introducing disjunctions (e.g., "Jabberwocky"). They guarantee the disjunction of series.

8. Structure Requires Series, Singularities, and a Paradoxical Element

There is no structure without the empty square, which makes everything function.

Two heterogeneous series. A structure requires at least two series, one signifying and one signified. Each series is constituted by terms that exist only through their relations.

Singularities. Each series has singular points corresponding to the values of relations between terms. These singularities are ideal events that determine the terms of the other series.

Paradoxical element. The two series converge on a paradoxical element that circulates between them, always displaced in relation to itself. It's a two-sided entity, an empty place and an occupant without a place, ensuring communication and divergence.

9. Events are Ideal Singularities, Defined by Problems, Not Solutions

The mode of the event is the problematic.

Singularities and events. Events are ideal singularities, turning points, and points of inflection. They are pre-individual, non-personal, and a-conceptual, indifferent to all oppositions.

Problematic nature of events. Events are not solutions but problems. A problem is determined by the singular points that express its conditions. The event is problematic and problematizing.

Recreational mathematics. Mathematics can be used to problematize human events and to develop human events as conditions of a problem. Carroll's recreational mathematics explores this double aspect.

10. The Ideal Game is a Chaos-Cosmos, Played on the Surface of Time

This game is reserved then for thought and art.

Ordinary games. Ordinary games have pre-existing rules, distributing hypotheses, fixed distributions, and a clear winner or loser. They are partial and refer to other activities like labor or morality.

Ideal game. The ideal game has no pre-existing rules, affirms chance, has no numerically distinct throws, and no winner or loser. It's a game of thought and art, where chance is affirmed and ramified.

Two readings of time. Time is grasped in two ways: Chronos (the living present of bodies) and Aion (the infinitely divisible past and future of incorporeal events). The Aion is the time of the ideal game, a straight line where events are distributed.

11. Nonsense is the Co-Presence of Sense, Not Its Opposite

Paradox is initially that which destroys good sense as the only direction, but it is also that which destroys common sense as the assignation of fixed identities.

Nonsense as a double. Nonsense is not simply the absence of sense. It's a word that says its own sense, a word that is both word and thing, name and object, sense and denotatum. It's a co-presence of sense, not its opposite.

Two figures of nonsense. There are two figures of nonsense: one corresponding to infinite regress (a name saying its own sense) and one corresponding to sterile division (a portmanteau word forming an alternative).

Absurdity and nonsense. The absurd is that which is without signification, while nonsense is that which has no sense. Impossible objects are absurd, but they have a sense as "extra-existents."

12. Paradox Destroys Good Sense and Common Sense, Revealing the Surface

Paradox is initially that which destroys good sense as the only direction, but it is also that which destroys common sense as the assignation of fixed identities.

Good sense. Good sense affirms a single direction, from the most to the least differentiated. It's distributive, seeks to equalize differences, and is linked to the present and to prevision.

Common sense. Common sense is the faculty of identification, relating diversity to the unity of a subject or object. It's the basis of personal identity and the permanence of the world.

Paradox as a reversal. Paradox destroys both good sense and common sense. It affirms both directions at once, and it contests fixed identities. It reveals that everything happens at the surface, at the border between things and propositions.

Last updated: January 18, 2025