LOGIC BY OTHER MEANS
Already in the preface to LOGIC OF SENSE Deleuze is situating his investigation in the element of logic, but of a logic that can be formalised by other means than that of mathematical logic. He does not exclude the formalisations of Symbolic Logic but his affair is elsewhere. It consists in following the relative autonomy of different contemporary practices of thinking (literature, science, politics, mathematics, art, psychoanalysis, philosophy) in order to make explicit the new logic immanent to these practices.
Thus in order to create a book and an intellectual project of manageable proportions Deleuze initially limits his logical investigation to literary formalisations such as those of Lewis Carroll and to conceptual formalisms such as those he finds in Stoicism. Deleuze never gets round to a consideration of the conceptual revolution inaugurated by the creation of non-classical logics, and this is a weak point in his logical project, and in his system more generally, leaving it open to charges of vagueness, ambiguity, irrationality, mere « poetry », or incomprehensibility.
Despite all his conceptual formalism, key aspects of Deleuze’s logic remain unacknowledged or under-developed, insisting in his text without being elevated to formal existence. In particular Deleuze has not created a concept of negation adequate to the radical negativity that is clearly perceptible in his conceptual practice, and omni-present in his texts.
Deleuze’s method is one of deconstruction-transformation. He will examine existing categories that are caught within metaphysical structures that function as obstacles to thought (such as rigid binary oppositions), deconstruct the system of oppositions governing it by elevating one of the marginal terms to the status of privileged term (deconstructive phase), then proceed to incorporate the « lower » term inside a new problematic where not only its status but its content and meaning are radically revised (transformative phase).
PARADOX OF INFINITE IDENTITY: logic of contradiction
The transformed term can either keep its old name or be given a new one. It is interesting to note the first example of this method as it unfolds in the first series of LOGIC OF SENSE. The concept of becoming is elevated from its inferior status within the Platonist problematic and given a new sense as embodying the « infinite identity…of future and past, of the day before and the day after, of more and less, of too much and not enough, of active and passive, and of cause and effect ». Because Deleuze refuses the Hegelian model, as he imagines it, of synthesis he does not choose to call his revised concept the identity of opposites (which is clearly what it is) but rather « infinite identity ». Rather than calling this infinite identity a contradiction Deleuze prefers to call it a « paradox ».
This act of renaming is motivated by Deleuze’s practice of transformative re-conceptualisation. It has the disadvantage in this context of obfuscating the role of negativity and negation within Deleuze’s system.
THE PLAY OF INTUITION AND FORMALISATION
Deleuze’s own logic is implicit in his explicitations of the logic of sense that he encounters in the novels of Lewis Carroll and in the semiotics of the Ancient Stoics. This is in accord with his paradox of infinite regress of sense:
« I never say the sense of what I am saying. But on the other hand I can always take the sense of what I am saying as the object of another proposition, whose sense in turn I cannot say » (page 31, translation modified).
Thus Deleuze can say, make explicit, the logic of sense of Carroll and the Stoics, but he cannot at the same time make explicit his own logic – which remains immanent in his analyses, present in intuitive form, awaiting future explicitation, which never fully comes. Necessarily, viewed in comparison with the explicit formalisations of Symbolic Logic Deleuze’s logic to come remains intuitive. The « intuitive » presentation of logic in Deleuze’s work means the creation of concepts to make explicit, philosophically explicit, the non-standard content that he finds in the diverse works he considers.
However, it is Deleuze’s argument that non-mathematical intuition, whether artistic, literary or philosophical, contains its own formalisation. A further implication would be that Symbolic Logic contains its own sense, and that it is a separate task to formulate that sense, one in which philosophy can participate.
SENSE IS THE PRINCIPLE OF VARIANCE
One can readily see that the logic of sense is also a logic of creation. By freeing the sense that is imprisoned within the proposition, inside its stabilised significations, one allows it to express itself in quite different propositions, with different or even incommensurable significations. So, beginning the book with the example of Alice’s becoming, and then extracting the paradoxical concept of becoming in general, is no arbitrary starting point nor indifferent example. Sense is a principle of variance at work inside, always ready to undermine and to transform the stability that is the principle of signification.
Deleuze’s book LOGIC OF SENSE does indeed fulfil the promise of its title in that it moves and develops entirely within the element of logic, of a conceptual logic appropriate to philosophy. One is entitled to reply Okay, but how does this « new » logic compare with the standard logic that we are familiar with? Deleuze clarifies his answer from the very beginning, his logic is non-Aristotelian, it does not respect the law of non-contradiction:
« We present here series of paradoxes which form the theory of sense. It is easy to explain why this theory is inseparable from paradoxes: sense is a non-existent entity » (xi, translation modified).
PARADOXICAL CONSTITUTION AND CONSTITUTIVE PARADOX
In other words, paradoxes are not encountered, formulated, examined, and then resolved or eliminated. Deleuze’s logic is not about paradoxes, it is formed of, constituted by paradoxes. This logic does not aim at the elimination of paradoxes, but at giving them new life and force, and at extending scope.
Deleuze’s rendering paradox ineliminable by including it in the enunciative form of the theory, rather than treating it as an undesirable content of enunciation to be eliminated is in contrast to the whole tradition of Aristotelian logic and its successors, whose over-riding imperative is to eliminate paradoxes, to prevent the very possibility of their formation. In this spirit, Deleuze praises the Stoics’ logic as « closely linked to the paradoxical constitution of a theory of sense » (xi, emphasis mine).
SENSE OF DELEUZE’S LOGIC (OF SENSE): the logic to come
As we begin to get clear on the sense of Deleuze’s logic we come to see its incompleteness. He has created the concepts necessary to a logic of sense, but necessarily he has not created the concepts adequate to explicating the logic of that logic.
This further step is to be taken up by Deleuze’s readers in their task of creative explicitation.
My own analyses on this point are convergent with the important and interesting new book by Corry Shores THE LOGIC OF GILLES DELEUZE.