Abstract
A logic is a normative theory, which states not how people do reason but how they should reason; so, in further articulating the differences among the three logics, it is best to start by considering how differently necessity plays out in them.
In analytic logic, the necessity that sanctions an inference is derived from the one by which contraries exclude one another: if “mortal” and “immortal” are contraries, then once Socrates is subsumed under mortal humans, its link with mortality can never be severed. An analytic proof may require tremendous ingenuity; but if the right premises are found and the right inferential steps are made, this outcome appears set in stone (and independent of the heuristics of it).
The necessity ruling dialectical logic is the narrative kind: it amounts to redescribing a concept (say, being) so that it is shown to coincide with a contrary one (say, nothing), much like a good narrator redescribes a character, an event, or a situation so as to make it look natural that a momentous change would occur in them while they remain the same thing. This necessity seems looser than the analytic one but that impression is based on a misunderstanding: analytic logicians divide up the problem of providing logical accounts of ordinary arguments by first offering arguments in artificial languages which, being artificial, can be defined with total accuracy and then translating from the artificial languages into the ordinary one—at which point all the looseness that was first put aside resurfaces. Dialectical logic, not being formalizable, cannot divide up the problem in this way, so the looseness is obvious throughout.
Whereas the necessity current in both analytic and dialectical logics is brought out by attention to detail, the one current in oceanic logic blurs detail and indeed makes us think of detail as confusing: as making us miss the forest for the trees. Similarly, the identity current in this logic undervalues intellectual, conceptual qualifications and stresses the undifferentiated, material stuff that is to be found at the basis of every alleged distinction.
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- 1.
This is Section A of Self-Consciousness, pp. 111–119. The following passages are especially relevant for the discussion that follows: “The lord is the consciousness that exists for itself, but no longer merely the concept of such a consciousness. Rather, it is a consciousness existing for itself which is mediated with itself through another consciousness, i.e. through a consciousness whose nature it is to be bound up with an existence that is independent, or thinghood in general…. The lord relates himself mediately to the bondsman through a being [a thing] that is independent, for it is just this which holds the bondsman in bondage; it is his chain from which he could not break free in the struggle, thus proving himself to be dependent, to possess his independence in thinghood…. [T]he lord achieves his recognition through another consciousness…. Here, therefore, is present this moment of recognition, viz. that the other consciousness sets aside its own being-for-self, and in so doing itself does what the first does to it. Similarly, … this action of the second is the first’s own action; for what the bondsman does is really the action of the lord…. [W]hat the lord does to the other he also does to himself, and what the bondsman does to himself he should also do to the other…. But just as lordship showed that its essential nature is the reverse of what it wants to be, so too servitude in its consummation will really turn into the opposite of what it immediately is; as a consciousness forced back into itself, it will withdraw into itself and be transformed into a truly independent consciousness” (translation modified).
- 2.
This is the sense in which a strike, whatever the negative economic, legal, or even physical consequences of it for the participants, shows the workers acquiring consciousness of their power.
- 3.
“[C]onclusions which embrace more than we can grasp in a single intuition depend for their certainty on memory, and since memory is weak and unstable, it must be refreshed and strengthened through this continuous and repeated movement of thought. Say, for instance, in virtue of several operations, I have discovered the relation between the first and the second magnitude of a series, then the relation between the second and the third and the third and the fourth, and lastly the fourth and fifth: that does not necessarily enable me to see what the relation is between the first and the fifth, and I cannot deduce it from the relations I already know unless I remember all of them. That is why it is necessary that I run over them again and again in my mind until I can pass from the first to the last so quickly that memory is left with practically no role to play, and I seem to be intuiting the whole thing at once” (p. 38).
- 4.
“My propositions serve as elucidations in the following way: anyone who understands me eventually recognizes them as nonsensical, when he has used them—as steps—to climb up beyond them. (He must, so to speak, throw away the ladder after he has climbed up it)” (1961, p. 151).
- 5.
The role of a supplement, Derrida would say; see his (1974), pp. 141ff. For example, on p. 145, he writes: “But the supplement supplements. It adds only to replace. It intervenes or insinuates itself in-the-place-of; if it fills, it is as if one fills a void. If it represents and makes an image, it is by the anterior default of a presence. Compensatory and vicarious, the supplement is an adjunct, a subaltern instance which takes-(the)-place. As substitute, it is not simply added to the positivity of a presence, it produces no relief, its place is assigned in the structure by the mark of an emptiness. Somewhere, something can be filled up of itself, can accomplish itself, only by allowing itself to be filled through sign and proxy. The sign is always the supplement of the thing itself.”
- 6.
And also taught by Socrates in that play (not quite effectively, as it turns out). Here is, for example, how poor Strepsiades practices what he has just learned: “SOCRATES: What would you do if a lawsuit was written up against you for five talents in damages? How would you go about having the case removed from the record? STREPSIADES: Er, I’ve no idea, let me have a think about it. SOCRATES: Be sure not to constrict your imagination by keeping your thoughts wrapped up. Let your mind fly through the air, but not too much. Think of your creativity as a beetle on a string, airborne, but connected, flying, but not too high. STREPSIADES: I’ve got it! A brilliant way of removing the lawsuit! You’re going to love this one. SOCRATES: Tell me more. STREPSIADES: Have you seen those pretty, see-through stones that the healers sell? You know, the ones they use to start fires. SOCRATES: You mean glass. STREPSIADES: That’s the stuff! If I had some glass, I could secretly position myself behind the bailiff as he writes up the case on his wax tablet. Then I could aim the sun rays at his docket and melt away the writing so there would be no record of my case! SOCRATES: Sweet charity! How ‘ingenious.’ STREPSIADES: Great! I’ve managed to erase a five-talent lawsuit. SOCRATES Come on, then, chew this one over. STREPSIADES: I’m ready. SOCRATES: You’re in court, defending a suit, and it looks like you will surely lose. It’s your turn to present your defense, and you have absolutely no witnesses. How would you effectively contest the case and, moreover, win the suit itself? STREPSIADES: Easy! SOCRATES: Let’s hear it then. STREPSIADES: During the case for the prosecution, I would run off and hang myself! SOCRATES: What are you talking about? STREPSIADES: By all the gods, it’s foolproof! How can anybody sue me when I’m dead? SOCRATES: This is preposterous! I’ve had just about enough of this! You’ll get no more instruction from me” (pp. 53–55). No question about it: a lot of redescription is going on here.
- 7.
Two significant passages among many: “Later developments … have shown more and more clearly that in mathematics a mere moral conviction, supported by a mass of successful applications, is not good enough. Proof is now demanded of many things that formerly passed as self-evident” (1980, p. 1). “To this day, scarcely one single proof has ever been conducted on these lines; the mathematician rests content if every transition to a fresh judgment is self-evidently correct, without enquiring into the nature of this self-evidence, whether it is logical or intuitive. A single such step is often really a whole compendium, equivalent to several simple inferences, and into it there can still creep along with these some element from intuition. In proofs as we know them, progress is by jumps, which is why the variety of types of inference in mathematics appears to be so excessively rich; for the bigger the jump, the more diverse are the combinations it can represent of simple inferences with axioms derived from intuition. Often, nevertheless, the correctness of such a transition is immediately self-evident to us, without our ever becoming conscious of the subordinate steps condensed within it; whereupon, since it does not obviously conform to any of the recognized types of logical inference, we are prepared to accept its self-evidence forthwith as intuitive, and the conclusion itself as a synthetic truth—and this even when obviously it holds good of much more than merely what can be intuited” (ibid., pp. 102–103).
- 8.
The recurrence of the word “intuition” here, after the previous discussion of Frege, is significant and must be noted. For another way of phrasing the commitment to given principles that I considered crucial for subscribing to a step in a(an analytic) proof would be to say that one feels (or has an intuition) that the principles are right. Therefore, intuition never becomes irrelevant to the correctness of such a proof: whatever “laws of thought” we might reduce the proof to, they must be warranted for each of us by the normative intuitions (or feelings) I described in footnotes 5 and 7 in Chap. 2 and the attending text. This point is typically obscured by the maneuver I describe later: by dividing the issue of carrying a formal proof in an artificial calculus from the one of showing the relevance of that proof to ordinary contexts (and ordinary proofs) and then downplaying the significance of the second issue. Which explains, among other things, why the most difficult logic courses to teach are the most elementary ones, the ones in “informal logic,” where logical intuitions are the very subject matter of the course and hence must be constantly referred to.
- 9.
Again, notice that a constraint is something we feel and, if we do not feel it, there is nothing that a formal system can do to make us feel it. But, again, in this case, it is a normative feeling (and constraint): a feeling that certain things should be done, and often will not be done, in a certain way—as opposed to the constraint that we feel, say, when we are chained to a wall.
- 10.
I addressed some of it many years ago, within a debate with Gerald J. Massey, in my (1979).
- 11.
That the operation be conducted after the fact is crucial for conveying the sense of such inevitability; later in the text, I illustrate this point by telling a personal anecdote. Also, note that, by adopting a dialectical attitude, we could reconceptualize what is going on in the previous proof relative to Euclidean triangles as also demanding a particular redescription that makes our expectations shift and our sense of necessity evolve accordingly. Then the logic of the proof would incorporate its heuristics and necessity would pertain to the whole process, inclusive of the redescription. Which shows that, despite the prevalence of analytic logic in mathematics, dialectical logic may also be present there. I will show other elements of this presence in Chap. 9.
- 12.
“‘Shall we, then, casually allow our children to listen to any old stories, made up by just anyone, and to take into their minds views which, on the whole, contradict those we’ll want them to have as adults?’ ‘No, we won’t allow that at all.’ ‘So our first job, apparently, is to oversee the work of the story-writers, and to accept any good story they write, but reject the others. We’ll let nurses and mothers tell their children the acceptable ones, and we’ll have them devote themselves far more to using these stories to form their children’s minds than they do using their hands to form their bodies’” (1993, 377a–c). “Left to ourselves, … with benefit as our goal, we would employ harsher, less entertaining poets and story-tellers, to speak in the style of a good man and to keep in their stories to the principles we originally established as lawful, when our task was the education of our militia” (ibid., 398a–b).
- 13.
C. P. Snow’s distinction of two cultures may have its basis in this logical difference. Though (as I mentioned in footnote 11 above) we will see that dialectical logic is not absent from even mathematics itself, it is certainly the case that analytic logic prevails in the ordinary practice of mathematicians and other scientists, and dialectical logic in the ordinary practice of humanists.
- 14.
See my (1978).
- 15.
There are no concepts in the plural in Hegel, just as there is no plurality of things: all the distinct concepts of the (analytic) tradition are but phases of the same intellectual structure.
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Bencivenga, E. (2017). Necessity. In: Theories of the Logos. Historical-Analytical Studies on Nature, Mind and Action, vol 4. Springer, Cham. https://doi.org/10.1007/978-3-319-63396-1_5
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