Negation and Negativity

“Hegel is willing to say some extraordinary things about the concept he sometimes calls ‘negation’, sometimes ‘negativity’. What he has been taken to mean has been the source of most of the criticism of Hegel: that he confused logical negation with actual opposition, as in the oppositions of forces or magnitudes in general in the world; that he thought everything in the world contradicted itself, and so believed that pairs of contradictory judgments could both be affirmed; or simply that what he said about negation and contradiction cannot be coherently understood. And any commentator must face the fact that he invoked the notion of negation in many different contexts in many different ways. So the first task is to have in view that variety of contexts before we can understand what they all might have in common (if anything)” (Pippin, Hegel’s Realm of Shadows, p. 139).

Some time ago I touched on the most elementary parts of this thorny issue in Contradiction vs Polarity. My basic sense at this point is that Hegel does indeed have very worthwhile things to say on this very distinctive theme of his, but that the standard connotations of his core vocabulary for talking about it — negation, negativity, contradiction — are so impoverished relative to what he really means in his extensive and varied metaphorical uses of it that the vocabulary does not communicate well.

Pippin identifies five somewhat overlapping contexts that ought to be taken into account in a serious interpretation of Hegelian negation: the nature of thinking; the talk about freedom; the nature of intelligibility; the notion of speculative truth; and the talk about contradiction.

In the context of the nature of thinking, he says “In the simplest sense, we are talking about the logical structure of apperceptive intentional knowledge, as well as the ontological status of agency. What it means to claim that the intelligibility of any content of empirical knowledge is not… wholly ‘positive’… is best understood by contrast. If it were not so and were wholly positive, subjectivity would be something like a mere complex registering and responding device (of the same ontological status as a thermometer) ” (p. 141).

“As we have seen, one is not simply wholly absorbed in the presence of the world to one, not wholly and merely reactive to the stimulation of sensibility, and that ‘not’ is the beginning (but certainly not the end) of all the logical issues of negation that emerge in Hegel’s philosophy, at both the phenomenological and the logical level. In making such a judgment I ‘negate’ the mere immediacy or givenness of perceptual content, negate it as immediate and putatively given, and take up, am always taking up, a position of sorts about what is there, what is the case” (p. 142).

The suggestion is that all “taking” of things to be thus-and-such for Hegel implicitly involves a negation of immediacy.

“What thinking is is such a ‘negation’ of one’s immediate ‘positive’ state. (One can say: this negation of mere immediacy is ‘taking a stand’, rather than being put into a state.) Any thinking could be a seeming-to-be-the-case, not what is the case, and that possibility is constitutive of the act’s being a judging in the first place…. The constitutive feature attended to in a Hegelian philosophical logic is the fact that judgments are potentially responsive to reasons and revisions just qua judgments” (ibid).

Pippin thus cites responsiveness to reasons as another non-obvious instance of negation for Hegel.

“And in being an agent, I am not simply causally responsive to inclinations and desires; there is no ‘fullness of positive being’ here either. I interrupt or negate positive being (what I feel inclined to do, experience as wanting to do) by deliberating and resolving what to do” (p. 143).

Deliberation is another non-obvious instance.

“As noted before, the closest first and general approximation of what he means is Aristotelian: subjectivity (thinking and acting according to norms) is the distinct being-at-work… of the biological life form that is the human, reason-responsive substance; this in the same sense in which Aristotle says, if the eye were body, seeing would be its form, its distinctive being-at work” (ibid).

Subjectivity in general is another.

“Instead of thinking of the fundamental act of understanding as a synthesis of independent, originally unrelated elements, either by subsuming an individual under a concept, or by including one concept under another, we should understand ourselves, both in experience and in logical reflection, beginning with ‘wholes’, never with experiential or logical subsentential simples [individual words] or atoms” (pp. 143-144).

Hegel presents this last point as a sort of inversion of Kant, and it does speak to some of Kant’s language. But I would argue that the true starting point of Kantian synthesis is not experiential or logical atoms, but rather the sensible manifold in intuition, which is only potentially differentiable. This brings Kant closer to Hegel. True, the manifold has such a loose unity that arguably it might have trouble qualifying as a “whole”, but even less does it consist in already predifferentiated “atoms”. In Kant I think we have no basis for identifying putative atoms in experience until “after” the figurative synthesis of imagination has done its work. (It is the preconscious, in a non-Kantian sense “spontaneous” figurative synthesis that for Kant creates an inevitable gap between being and thinking, and that for Hegel gives us the fixed representations relied upon by common sense.)

In the context of freedom, Pippin says that “In the same way that judging, insofar as it is genuine, holds open the possibility of its negation or disconfirmation, just by being judging, not by virtue of any second, reflective act…, a deliberation about action, if it is to be a deliberation, is open to the force of reasons the agent has already accepted by deliberating at all, a possibility criterial for his acting at all…. [Hegel] is insisting on the logical or categorical requirements of the normative, and in that sense (the sense in which freedom is normatively constrained judgment and rational action), the negative (here only the possibility of not doing what I am powerfully inclined to do) is ‘that by which a person is free’. (And he does not mean any uncaused causality, but that which counts to the subject as a reason” (p. 147).

Normativity in general thus counts as depending on a kind of negation.

“In terms of the structure of the Logic, what Hegel will want to argue is that we cannot adequately explain freedom if we consider just a determinate property that some beings happen to have…, and we cannot explain it either as a kind of essential ideal, manifest in but never adequately expressed in its appearances, in concrete individual actions…. We need the logic of the Concept, in which concepts are said to ‘give themselves their own content’ and be ‘self-determining’ in a way indebted to [the] Kantian claim on self-legislation…. Any philosophical determination of actuality must be understood as ‘self-legislating’ in the broad sense [that] reason relies only on itself in determining such a normative structure. These are not empirical questions. There is no flash of ‘essence intuition’ (Wesenschau) giving access to a world of abstract immaterial objects, essences” (p. 148).

Self-legislation too involves some subtle kind of negation.

In the context of the nature of intelligibility, Pippin says “Every determination of every sort of content in the Logic is a negation of some insufficient determinacy that must be able to be conceived positively” (p. 153). This is another way of characterizing the basis of the notorious “movement” in Hegel’s logic.

The determination of content for sure involves negation.

In the context of speculative truth, he mentions that “[E]valuative judgments, like ‘this action is good’, or our familiar ‘this is a bad house’, will be paradigmatic examples of judgment in the logic of the Concept. They do not qualitatively specify a thing by distinguishing it from other things; they do not identify the appearances that show the ‘essence’ of the thing; they understand the content ‘in terms of its concept'” (p. 154).

Evaluation of anything against its concept is another subtle variety.

In the context of the notorious “contradiction”, Pippin says “So in a general sense, one has to say that a thing… ‘includes’ its contrary, or more precisely its relation to its contrary, in order to be, and be known to be, what it is. Neither of these ‘moments’ of negation involves contradiction in the Aristotelian sense because ‘is’ and ‘is not’, while said of the same thing and at the same time, are not meant in the same sense. But Hegel wants for various reasons to call such an analyzed state a ‘contradiction’, and there is some ground in the use of the term for saying that…. In the simplest sense, personifying the process, what someone intends to say, means to say, can be ‘contradicted’ by what is actually said, what he finds he has to or can say” (p. 156).

Evaluation of any outcome against intent is another.

Pippin notes that Hegel says retrospectively at the end of the Logic that the abstract treatment typical of the logic of being and the logic of essence is due to “mere opinion” or lack of awareness of what it is actually treating. “It cannot say what it means to say” (p. 157). This is yet another way of characterizing the Logic‘s “movement”.

Logical “movement” is another.

“Hegel’s speculative notion of contradiction is not predicate or sentence negation…. [H]e means to focus attention on concept negation…. Now concepts, understood as rules, have content by being understood to have the content that they have. To understand a rule is to know how to use it, and in using it, to know one is following it…. So understanding… is not… ‘grasping a content’ but understanding what the rule instructs us to think. That is, the concept is always already a moment of discursive activity, a thinking through of its implications” (pp. 158-159).

“[T]he considerations discussed so far should not be understood to be matters of formal clarity…. As Hegel insisted, we are not studying how we think about (or talk about) matters (or even how we ‘must’ think). The question is a question about ‘any possible intelligibility’, and so about being in its intelligibility, … not ‘our ways’ of rendering intelligible” (p. 160).

All the above varieties of “negation” involve normativity in one way or another. Here Pippin again emphasizes the universality of criteria of intelligibility that Hegel counterposes to the Kantian gap between thinking and being.

“The forms of intelligibility are the forms of what could be true, although they do not settle the question of what, in particular, is true” (p. 175).

“[O]ur first orientation in trying to understand Hegelian negation should be not the logical operation of predicate or sentence negation, but real opposition…. [Michael] Wolff also thinks that the controversy in the eighteenth century about positive and negative magnitudes, especially as it surfaced in Kant, as well as the emerging clarity about negative numbers, played a far larger role in the development of Hegel’s thinking about negation and contradiction than did a reflection on the logic of the formal operator” (pp. 177-178).

Real opposition is an instance of contrariety, which is actually much more relevant to Hegel than formal logical contradiction.

“Hegel’s category of becoming, so important at the beginning of the logic of being, owes much to Hegel’s defense of Newton and the latter’s doctrine of the becoming equal of magnitudes” (pp. 178-179).

“Critics like Crusius were aghast at the idea of forces having positive and negative values. But Kant understood that such ‘values’ (and here again an important precedent for Hegel) had those values in relation to each other, not absolutely, that they were relative values, arbitrarily reversible even” (pp. 179-180).

Negative magnitudes are another instance of contrariety.

“This is not the sense of contradiction throughout the Logic, but it gives us enough background… to appreciate that Hegel is neither a lunatic for saying that ‘everything is contradictory’, nor a mystical Heraclitean” (p. 180).

Pippin devotes nearly half of this chapter to critical remarks about Brandom’s interpretation of Hegelian negation as material incompatibility, which involves a more nuanced form of contrariety. He says Brandom’s reading very well captures the meaning of negation in Hegel’s logic of being, but is inadequate for what Hegel goes on to do in the logic of essence and the logic of the concept. For example, material incompatibility alone is insufficient to explain things like the “self-legislation” of the concept or the idea of the good, but Hegel at least claims that these have something to do with the concept of negation.

Brandom’s interpretation of Hegelian negation seemed to me incomparably clearer than Hegel himself, so until now I have adopted it enthusiastically as a charitable rendering of what Hegel ought to have said to better express his meaning. This is the first of many counter-arguments to Brandom I have seen that really seems to me to at least raise a serious question, but for now I will forego another lengthy tangent.

Next in this series: Deeper Truth

Logic for Expression

In recent times, Robert Brandom has pioneered the idea that the role of logic is primarily expressive. In his 2018 essay “From Logical Expressivism to Expressivist Logic”, he says this means its purpose is “to make explicit the inferential relations that articulate the semantic contents of the concepts expressed by the use of ordinary, nonlogical vocabulary” (p. 70).

In my humble opinion, this is what logic was really supposed to be about in Aristotle, but the tradition did not follow Aristotle. Aristotle insisted that logic is a “tool” not a science, but most later authors have assumed the contrary — that logic was the “science” of correct reasoning, or perhaps the science of consequence relations. Several scholars have nonetheless rediscovered the idea that the purpose of logical demonstration in Aristotle is not to prove truths, but to express reasoned arguments as clearly as possible.

Brandom says that “the task of logic is to provide mathematical tools for articulating the structure of reasoning” (p. 71). People were reasoning in ordinary life long before logic was invented, and continue to do so. But the immensely fertile further development of logic in the late 19th and early 20th centuries was mostly geared toward the formalization of mathematics. Reasoning in most specialized disciplines — such as the empirical sciences, medicine, and law — actually resembles reasoning in ordinary life more than it does specifically mathematical reasoning.

According to Brandom, “The normative center of reasoning is the practice of assessing reasons for and against conclusions. Reasons for conclusions are normatively governed by relations of consequence or implication. Reasons against conclusions are normatively governed by relations of incompatibility. These relations of implication and incompatibility, which constrain normative assessment of giving reasons for and against claims, amount to the first significant level of structure of the practice of giving reasons for and against claims.”

“These are, in the first instance, what Sellars called ‘material’ relations of implication and incompatibility. That is, they do not depend on the presence of logical vocabulary or concepts, but only on the contents of non- or prelogical concepts. According to semantic inferentialism, these are the relations that articulate the conceptual contents expressed by the prelogical vocabulary that plays an essential role in formulating the premises and conclusions of inferences” (pp. 71-72).

“Material” relations of consequence and incompatibility have a different structure from formal ones. Formal consequence is monotonic, which means that adding new premises does not change the consequences of existing premises. Formal contradiction is “explosive”, in the sense that any contradiction whatsoever makes it possible to “prove” anything whatsoever (both true statements and their negations), thereby invalidating the very applicability of proof. But as Brandom reminds us, “outside of mathematics, almost all our actual reasoning is defeasible” (p. 72). Material consequence is nonmonotonic, which means that adding new premises could change the consequences of existing ones. Material incompatibilities can often be “fixed” by adding new, specialized premises. (As I somewhere heard Aquinas was supposed to have said, “When faced with a contradiction, introduce a distinction”.)

Brandom notes that “Ceteris paribus [“other things being equal”] clauses do not magically turn nonmonotonic implications into monotonic ones. (The proper term for a Latin phrase whose recitation can do that is ‘magic spell’.) The expressive function characteristic of ceteris paribus clauses is rather explicitly to mark and acknowledge the defeasibility, hence nonmonotonicity, of an implication codified in a conditional, not to cure it by fiat” (p. 73).

“There is no good reason to restrict the expressive ambitions with which we introduce logical vocabulary to making explicit the rare material relations of implication and incompatibility that are monotonic. Comfort with such impoverished ambition is a historical artifact of the contingent origins of modern logic in logicist and formalist programs aimed at codifying specifically mathematical reasoning. It is to be explained by appeal to historical causes, not good philosophical reasons” (ibid). On the other hand, making things explicit should be conservative in the sense of not changing existing implications.

“…[W]e should not emulate the drunk who looks for his lost keys under the lamp-post rather than where he actually dropped them, just because the light is better there. We should look to shine light where we need it most” (ibid).

For relations of material consequence, the classical principle of “explosion” should be replaced with the weaker one that “if [something] is not only materially incoherent (in the sense of explicitly containing incompatible premises) but persistently so, that is incurably, indefeasibly
incoherent, in that all of its supersets are also incoherent, then it implies everything” (p. 77).

“The logic of nonmonotonic consequence relations is itself monotonic. Yet it can express, in the logically extended object language, the nonmonotonic relations of implication and incompatibility that structure both the material, prelogical base language, and the logically compound sentences formed from them” (p. 82).

Material consequence relations themselves may or may not be monotonic. Instead of requiring monotonicity globally, it can be declared locally by means of a modal operator. “Logical expressivists want to introduce logical vocabulary that explicitly marks the difference between those implications and incompatibilities that are persistent under the addition of arbitrary auxiliary hypotheses or collateral commitments, and those that are not. Such vocabulary lets us draw explicit boundaries around the islands of monotonicity to be found surrounded by the sea of nonmonotonic material consequences and incompatibilities” (p. 83).

Ranges of subjunctive robustness can also be explicitly declared. “The underlying thought is that the most important information about a material implication is not whether or not it is monotonic — though that is something we indeed might want to know. It is rather under what circumstances it is robust and under what collateral circumstances it would be defeated” (p. 85).

“The space of material implications that articulates the contents of the nonlogical concepts those implications essentially depend upon has an intricate localized structure of subjunctive robustness and defeasibility. That is the structure we want our logical expressive tools to help us characterize. It is obscured by commitment to global structural monotonicity—however appropriate such a commitment might be for purely logical relations of implication and incompatibility” (pp. 85-86).

“Logic does not supply a canon of right reasoning, nor a standard of rationality. Rather, logic takes its place in the context of an already up-and-running rational enterprise of making claims and giving reasons for and against claims. Logic provides a distinctive organ of self-consciousness for such a rational practice. It provides expressive tools for talking and thinking, making claims, about the relations of implication and incompatibility that structure the giving of reasons for and against claims” (p. 87).

Pure Difference?

A common theme here is the conceptual priority of difference over identity. I think that identity is a derived concept, and not a primitive one (see also Aristotelian Identity).

The French philosopher Gilles Deleuze (1925-1995) in Difference and Repetition and other works argued that a pure notion of difference is by itself sufficient for a general account of things. In information theory, information is explained as expressing difference. In Saussurean structural linguistics, we are said to recognize spoken words by recognizing elementary differences between sounds. In both cases, the idea is that we get to meaning by distinguishing and relating.

Deleuze initially cites both of these notions of difference, but goes on to develop arguments grounded largely in Nietzsche and Kierkegaard, whom he uses to argue against Plato and Hegel. His very interesting early work Nietzsche and Philosophy was marred by a rather extreme polemic against Hegel, and in Difference and Repetition he announces a program of “anti-Platonism” that reproduces Nietzsche’s intemperate hostility to Plato. Nietzsche blamed Plato for what I regard as later developments. Neither Plato nor Aristotle made the kind of overly strong assertions about identity that became common later on.

In The Sophist and elsewhere, Plato had his characters speak of Same, Other, and the mixing of the two as equally primordial. Hegel took great pains to elaborate the notion of a “difference that makes a difference”. But Deleuze wants to argue that Plato and Hegel both illegitimately subordinate difference to identity. His alternative is to argue that what is truly fundamental is a primitive notion of difference that does not necessarily “make a difference”, and that come before any “making a difference”. (I prefer the thesis of Leibniz that indiscernibility of any difference is just what identity consists in.)

This is related to Deleuze’s very questionable use of Duns Scotus’ notion of the univocity of being, both in general and more particularly in his interpretation of Spinoza. For Deleuze, pure difference interprets Scotist univocal being.

I frankly have no idea what led to Deleuze’s valorization of Scotus. Deleuze is quite extreme in his opposition to any kind of representationalism, while Scotus made representability the defining criterion of his newly invented univocal being. It is hard to imagine views that are further apart. I can only speculate that Deleuze too hastily picked out Scotus because he wanted to provocatively oppose the 20th century neo-Thomism that had considerable prominence in France, and Scotus is a leading medieval figure standing outside the Thomist tradition.

For Deleuze, univocal being is pure difference without any identity. Difference that doesn’t make a difference seems to take over the functional role that identity has in theories that treat it as something underlying that exceeds any discernibility based on criteria. I don’t see why we need either of these.

I think Deleuze’s bête noir Hegel actually did a better job of articulating the priority of difference over identity. Hegel did this not by appealing to a putative monism of difference and nothing else, but by developing correlative notions of “difference that makes a difference”, and a kind of logical consequence or entailment that we attribute to real things as we interpret them, independent of and prior to any elaboration of logic in a formal sense.

In Hegel’s analysis as explicated by Brandom, any difference that makes a difference expresses a kind of “material” incompatibility of meaning that rules out some possible assertions. This is just what “making a difference” means. Meanwhile, all positive assertions can be more specifically analyzed as assertions of some consequence or entailment or other at the level of meaning (see Material Consequence). Every predication is analyzable as an assertion of consequence or entailment between subject and predicate, as Leibniz might remind us. It is always valid to interpret, e.g., “a cat is a mammal” as an inference rule for generating conclusions like if Garfield is a cat, then Garfield is a mammal.

What is missing from Deleuze’s account is anything like entailment, the idea of something following from something else. This notion of “following”, I am convinced, is prior to any notion of identity applicable to real things. Without presupposing any pre-existing identities of things, we can build up an account of the world based on the combination of differences that make a difference, on the one hand, and real-world entailments, on the other. Identity is then a result rather than an assumption. Meanings (and anything like identity) emerge from the interplay of practical real-world entailments and distinctions. It is their interplay that gives them definition in terms of one another.

Deleuze was a sort of ontological anarchist, who wanted being to be free of any pre-existing principles. While I agree that we can’t legitimately just assume such principles, I think this is very far from meaning that principles are irrelevant, or actually harmful. On the contrary, as Kant might remind us, principles are all-important. They aren’t just “given”. We have to do actual work to develop them. But if we have no principles — if nothing truly follows from anything else, or is ruled out by anything else — then we cannot meaningfully say anything at all.

Contradiction vs Polarity

The simple term “day” does not contradict the simple term “night”, although they may be conventionally treated as polar opposites. If we agree to treat them that way, then the proposition “It is day” contradicts the proposition “It is night”.

Hegel developed idiosyncratic shorthand ways of talking that may have the misleading appearance of suggesting that he ignored this distinction. In popular references to Hegelian dialectic, it is very common to hear about “contradictions” between so-called opposites. This can lead to massive misunderstanding of what Hegel was really trying to say, especially if one does not realize how concerned he was to deconstruct so-called polarities.

Polarities involve pairs of terms related by classical negation. A is the opposite of B if A = not-B, where “not” satisfies not-not-X = X. In fact, Hegel routinely criticized so-called Understanding for taking such polarities at face value.

In another piece of idiosyncratic shorthand, he talked about a “unity of opposites”. This refers to a sort of conceptual interdependence, not identity in the strict sense.

A single term may be taken as shorthand for many judgments characterizing a thing. Then “contradiction” between two terms actually refers to some contradiction between implications of the associated judgments.

Platonic dialectic in its most canonical form considered in turn the implications of pairs of contradictory propositions, in order to canvas all possibilities. The important part was really the examination of implications. Hegel, too, was far more interested in analyzing extended implications of things than in some dance of polarities.

Hegel’s dialectic — like Aristotle’s — is fundamentally about improving the subtlety of our distinctions, and thus the quality of our reasoning. If we begin with a polar opposition, the intent is to supersede it. As I previously noted, the standard method for superseding a polar opposition for Hegel is to move toward the concrete — i.e., to replace the abstract, “infinite”, classical negation of polar opposition with some suitable finite difference or specific material incompatibility or “determinate negation”, as he liked to call it. (See also Aristotelian and Hegelian Dialectic; Three Logical Moments.)