Studies in Continental Thought

The Expanse of the Elemental

John Sallis

• Publisher: Indiana University Press
• Year: 2012
• ISBN:
  9780253013644
• Topic: Philosophy
• Subtopic: Phenomenology in Philosophy

The Shakespearean image of a tempest and its aftermath forms the beginning as well as a major guiding thread of Logic of Imagination. Moving beyond the horizons of his earlier work, Force of Imagination, John Sallis sets out to unsettle the traditional conception of logic, to mark its limits, and, beyond these limits, to launch another, exorbitant logic—a logic of imagination. Drawing on a vast range of sources, including Plato, Aristotle, Kant, Hegel, Nietzsche, and Freud, as well as developments in modern logic and modern mathematics, Sallis shows how a logic of imagination can disclose the most elemental dimensions of nature and of human existence and how, through dialogue with contemporary astrophysics, it can reopen the project of a philosophical cosmology.

1 THE LOGIC OF CONTRADICTION

A. ONES

In Plato’s dialogues there is no logic. Assuredly, it is possible retrospectively—that is, anachronistically—to identify passages in the dialogues that carry out procedures similar to those that will later be characterized as logical inferences; it is even possible to find formulations similar to those that will later be identified as logical principles. For instance, the principle of noncontradiction—or at least something closely resembling it—puts in numerous appearances in the dialogues. And yet, in these texts there is no logic, no coherent discourse to which the later title logic or the Aristotelian term analytics can properly be applied. Because there is no Platonic logic, there are also no purely logical principles. Recognizing and acknowledging that the operation of these texts is anterior to the formation of logic is imperative if they are to be addressed in their own right and allowed to effect their proper manifestation; for there is nothing that more obstructs access to the Platonic texts and distorts their sense than the practice of projecting back upon them subsequent developments that they themselves first make possible but from which they remain withdrawn in a way that may draw them toward other, archaic possibilities.

A formulation resembling the principle by which subsequently contradiction will be prohibited appears in Book 4 of the Republic. The context is the discussion between Socrates and Glaucon concerning the soul and its partition. The passage in question initiates the portion of the discussion that leads to the distinction between the calculating part of the soul (τὸ λογιστικóν) and the noncalculating and desiring part (ἀλογιστικóν τε καὶ ἐπιθυμητικóν). In order to set up this distinction, Socrates gives an analysis of thirst. Once he has established that the man who is thirsty wants nothing other than to drink and is impelled toward drink, then it must be granted that a counteraction is sometimes operative, for there are cases in which men are thirsty but not willing to drink. Thus the formulation, the protoprinciple, on which the entire discussion turns is the following: “For of course, we say, the same thing would not perform opposed actions [τἀναντία πράττει] concerning the same thing with the same part of itself at the same time.”¹ Since there are in fact opposed actions performed by the soul, the soul must be partitioned, must include at least two distinct parts that are themselves sufficiently opposed to bring about opposed actions. It remains, then, only to name these parts in accord with the action that each performs.

The generality of this protoprinciple and its explicit declaration of limiting conditions (“concerning the same thing,” “with the same part of itself,” “at the same time”) anticipate the Aristotelian formulation. On the other hand, it is a pronouncement about action, not about being; and the opposition (τἀναντία = τὰ ἐναντία) to which it refers is not contradiction (ἀντίϕασις). While both opposed actions cannot be performed by the same thing (under the declared conditions), it is of course possible for the soul to perform neither of the actions, neither thirsting nor checking the impulse to drink. This opposition comes closer to what, from Aristotle on, will be distinguished, as contrariety, from contradiction.

In Book 5 of the Republic, there are several passages that display affinities with the future principle, yet in every case retaining a certain distance that heralds other possibilities. What is especially striking is that in these passages contradiction is not submitted to outright prohibition, that it is not simply banished to an outside, as it were, from which the citadel of sense and truth would be closed off and protected. Rather, in the very opening of the philosophical center of the entire dialogue, there is an affirmation of contradiction. For what is taken to differentiate the sensible from the intelligible is that it sustains contradiction, that it both is and is not. Hence, the affirmation of contradiction plays a decisive role in posing the distinction between intelligible and sensible, the distinction that will command virtually the entire history of what will be called metaphysics.

This relation to contradiction is perhaps most transparent in the passage in which, having posed the paradox of the philosopher-ruler, Socrates and Glaucon set out in search of the philosopher. In order to discover the philosopher, they undertake to determine what knowledge (γνῶσις, ἐπιστήμη) is and to distinguish it from opinion, from a mere view as to what or how something is (δóξα). To this end, Socrates introduces—for the very first time in the dialogue—explicit discourse about εἴδη, calling attention to this move with his remark to Glaucon: “It would not be at all easy to explain it to another; but you, I suppose, will grant [ὁμολογέω] me this.” In this discourse Socrates declares then that εἴδη that are opposite to one another are set utterly apart. Socrates says: “Since beautiful is the opposite [ἐναντίον] of ugly, they are two.” When Glaucon expresses his agreement, Socrates continues: “Then since they are two, isn’t each also one?”² The point is not just that εἴδη such as beautiful and ugly are countable but, more significantly, that their relation has a structure like that of numbers. Just as the number two, which in Greek mathematics is the smallest number, results from counting off two distinct ones, so likewise the dyad of beautiful and ugly is such that each is a distinct one, opposed to and apart from the other. Just as two ones must be distinct in order to be countable as two, so beautiful and ugly, or, more pointedly, being-beautiful and not-being-beautiful, admit of no mixing or blending. The arithmetic-like structure excludes all mixing of being and not-being, of is and is not. It thus prohibits or at least denounces discourse that would say, at once, both is and is not, all discourse that in what it says on the one side takes away what it says on the other, and conversely, speaking thus against itself. It is precisely this noncontradiction and the correlative demand for noncontradictory discourse that are distinctive of that to which knowledge is directed. Opinion, on the other hand, is directed precisely at that which both is and is not, at that which is such as to be and not to be (εἶναί τε καὶ μὴ εἶναι),³ at that which mixes being and not-being, so that contradiction holds sway. The discourse of opinion is such that it cannot for long avoid contradiction. Therefore, the differentiation between knowledge and opinion and correlatively between what comes to be called the intelligible (τὰ νοητóν) and the sensible (τὰ αἰσθητóν) is linked closely to the difference between an arithmetic-like structure that prohibits contradiction and a mixing of being and not-being that cannot be said otherwise than by way of contradiction.⁴

If there were a Platonic logic of the intelligible ones, it would prohibit contradiction, would be a logic of noncontradiction. If there were a Platonic logic of the sensible, it would prescribe contradiction, would be a logic of contradiction.

Yet in one of the final moves in Book 5, the contradictory many prove even less stable than the simple conjunction of being and not-being suggests. Socrates ascertains, first of all, that each of the many beautiful things will also look ugly—hence will look both beautiful and ugly. Then, decisively, Socrates makes a transition from the way things look to the names by which they are called. This transition is decisive because, in posing the names by which things are called, one sets out what is named in the name, sets out, for instance, beautiful itself, the beautiful as such, this one being over against the many apparently beautiful things. It is a matter, as Socrates mentioned earlier, of being “able to consider what is said by separating according to εἴδη.”⁵ It is a matter of turning from the way things merely appear, of having recourse to λóγος so as to address them by name, venturing the second sailing. With each name the question is whether the thing is addressed any more by this name than by its opposite. A beautiful thing, called beautiful, will also look ugly, so that it can with equal justification be called ugly. Socrates states the result as a question: “Then is each of the several manys what one asserts it to be any more than it is not what one asserts it to be?” But then, finally, Glaucon takes still another step, advancing the entire discussion to its most radical conclusion. He refers to ambiguous jokes and riddles as a way of introducing this conclusion: “For the manys are also ambiguous, and it is not possible to think of them fixedly [παγίως νοῆσαι] as either being or not being, or as both or neither.”⁶ Something called beautiful appears ugly and so is not beautiful, cannot be called beautiful, for the beautiful excludes the ugly. The same holds, conversely, if it is called ugly, and thus it is not possible to think of it fixedly as either being (beautiful) or not being (beautiful). Furthermore, it cannot be both, since the beautiful and the ugly—as they are two and each is one—exclude one another. And, finally, it cannot be neither, since it looks beautiful and ugly.

The result is that sensible things cannot be regarded as stable conjunctions of being and not-being, as lesser beings, so to speak, that have been compromised by an admixture of not-being. Rather, the mixing of being and not-being has the effect of dissolving all determinacy as such, as becomes evident when, instead of considering only how things look, recourse is had to λóγος and things are addressed by name. Yet in this final move the contradiction of being and not-being is not so much undermined as it is, rather, enacted; that is, the dissolution of determinacy enacts the self-vitiating character of speech that takes away, on the one side, what it declares, on the other.

From this discussion it perhaps becomes more evident why, despite the fact that λóγος is a constant theme—and recourse—in the dialogues, there is nonetheless no Platonic logic. It is not simply that Plato failed to project such a discipline and to distinguish it from the rest of philosophy. Rather, what is decisive in this regard is that the interrogation of λóγος in the dialogues is always also an interrogation of being; that is, the questioning is carried out as a movement between being and λóγος. In the confrontation with sophistry, for instance, it is primarily λóγος that is at issue, that is, the self-serving misuse to which the sophists put λóγος; yet the most effective defense against the sophistic distortion of λóγος lies precisely in letting things themselves refute what is said. Even when, as in the etymological comedy in the Cratylus, λóγος is analyzed solely in relation to itself, the very abstraction from being is what renders the discourse comedic, so that in the end, what the comedy brings to light is precisely the necessity of referring λóγος beyond itself to being. In every case, however indirectly, it is a question either of the demand that being places on the λóγος in which it would be said or of the way in which the λóγος prearticulates and opens upon the moments of being.

If there were a Platonic logic, it would be a logic of being, a circulation between being and λóγος, virtually indistinguishable, it seems, from Socrates’ second sailing, taken in its full import.

B. A PRINCIPLE MOST FIRM, STEADFAST, SURE

Aristotle retains the double movement of interrogation between being and λóγος. Two of his most fundamental interrogations, those of Book 4 and of Book 7 of the Metaphysics, are introduced by the sentence: “Being is said in many ways [τὰ ὂν λέγεται πολλαχῶς].”⁷ In another key passage, in Book 5, Aristotle identifies the four general ways in which being is said: in terms of the accidental (κατὰ συμβεβηκóς), according to the schemata of the categories (τὰ σχήματα τῆς κατηγορίας), as true (ἀληθές), and in terms of possibility and actuality (δύναμις and ἐντελεχία or ἐνέργεια).⁸ Within these broad senses of being as it is said, there are further, structured articulations, more specific ways in which being is said. When said, for instance, according to the categories, being can be said as some kind of thing (οὐσία), as quality, as quantity, as relation, etc.—that is, it can be said of a thing that it is of a certain quality, that it is of a certain quantity, that it is in a certain relatedness, each of these categorial senses being referred back to the primary categorial sense, that of being some kind of thing. Such ways of saying being provide a decisive clue for interrogating being. One does not simply come upon these modalities in things themselves; being does not simply announce itself and open up to interrogation. Rather, one must follow the opening offered by λóγος if one would discover and articulate the modes of being as such.

Aristotle’s questioning proceeds also in the other direction, from being to λóγος. Such directionality is nowhere more evident than in Aristotle’s extended discussion of contradiction. In one passage, for instance, he considers the problem whether the same thing can at once be and not be a man. He says that the problem is not whether the expression, the saying (τὰ ὄνομα), is possible but rather whether the thing (τὰ πρᾶγμα) is possible.⁹ It is indeed possible in some manner to say of something that it both is and is not a man; but what counts is that something cannot itself both be and not be a man and that this impossibility be brought to bear on what is said.

While thus...

Table of contents

• Cover
• Title
• Copyright
• Contents
• List of Plates
• Acknowledgments
• Precursions
• 1. The Logic of Contradiction
• 2. Formal Logic and Beyond
• 3. Exorbitant Logics
• 4. The Look of Things
• 5. Schematism
• 6. Proper Elementals
• 7. Elemental Cosmology
• Index