Demonstration in Spinoza

Kant and Hegel both objected to Spinoza’s unusual presentation of his Ethics in something resembling the style of Euclid’s geometry. I think of philosophy mainly as interpretation rather than simple declaration, so I am broadly sympathetic to this point. On the other hand, I think Pierre Macherey is profoundly right when he emphasizes the non-foundationalist character of Spinoza’s thought.

The unique meaning Spinoza gives to “Substance” (not to be confused with its Aristotelian, Scholastic, Cartesian, or general early modern senses) is that of a complex relational whole that encompasses everything, rather than a separate starting point for deduction of the details of the world. Because of this, the apparent linearity of his development is just that — a mere appearance.

Hegel does not seem to recognize that Spinoza’s Substance resembles the relational whole of Force that Hegel himself developed in the Phenomenology. This is inseparable from an implicit notion of process in which relations of force are exhibited.

Macherey says Spinoza sees the world in terms of an infinite process, i.e., one without beginning or end or teleological structure (Hegel or Spinoza, p. 75).

(I would argue that neither Aristotle nor Hegel actually endows the world with teleological structure, though they each give ends a significance that Spinoza would deny. For Aristotle, it is particular beings in themselves that have ends. For Hegel, teleological development is a retrospectively meaningful interpretation, not an explanatory theory that could yield truth in advance. But for Spinoza, ends are either merely subjective, or involve an external providence that he explicitly rejects.)

It seems to me that the “point of view of eternity” that Spinoza associates with truth is actually intended to be appropriate to this infinite process. Spinoza points out that eternity does not properly mean a persistence in time that lasts forever, but rather a manner of subsistence that is entirely outside of — or independent of — the linear progression and falling away that characterizes time.

(Kant’s famous assertion of the “ideality of space and time”, which means that space and time are only necessary features of our empirical experience, is not inconsistent with Spinoza’s commendation of the point of view of eternity. Though it has other features Spinoza would be unlikely to accept, Kant’s “transcendental” as distinct from the empirical is thus to be viewed from a perspective not unlike Spinoza’s “point of view of eternity”.)

Spinoza wants to maintain that the order of causes and the order of reasons are the same. Whereas Aristotle deconstructs “cause” into a rich variety of kinds of “reasons why” (none of which resembles the early modern model of an impulse between billiard balls), Spinoza narrows the scope of “cause” to “efficient causes” in a sense that seems close to that of Suárez with inflections from Galilean physics, and suggests that true reasons are causes in this narrower sense. It seems to me that Spinoza’s “order of causes” resembles the infinite field of purely relational “force” that Hegel discusses in the Force and Understanding chapter.

Spinoza wants us to focus on efficient causes of things, but to do so mainly from the “point of view of eternity”. This takes us away from the event-oriented perspective of linear time, toward a consideration of general patterns of the interrelation of different kinds of means by which things end up as they concretely tend to do. In speaking of means rather than forces, I am tacitly substituting what I think is a properly Aristotelian notion of “efficient” cause for the meaning it historically seems to have had for Spinoza.

In pursuit of this, he takes up a stance toward demonstration that is actually like the one I see in Aristotle, in that it is more about improvement of our understanding through its practical exercise in inference than about proof of some truth assumed to be already understood (see also Demonstrative “Science”?). As Macherey puts it, for Spinoza “knowledge is not simply the unfolding of some established truth but the effective genesis of an understanding that nowhere precedes its realization” (p. 50). (Unlike Macherey, though, I think this is true for Aristotle and Hegel as well.)

Demonstration in both Aristotle’s and Spinoza’s sense is intended to improve our normative understanding of concepts by “showing” their inferential uses and points of application. It is only through their inferential use in the demonstrations that Spinoza’s nominal definitions and axioms acquire a meaning Spinoza would call “adequate”.

Hegelian Semantics

Brandom begins his second Brentano lecture saying, “On the ground floor of Hegel’s intellectual edifice stands his non-psychological conception of the conceptual. This is the idea that to be conceptually contentful is to stand in relations of material incompatibility and consequence (his “determinate negation” and “mediation”) to other such contentful items. The relations of incompatibility and consequence are denominated “material” to indicate that they articulate the contents rather than form of what stands in those relations. This is his first and most basic semantic idea: an understanding of conceptual content in terms of modally robust relations of exclusion and inclusion” (p. 39).

I think Aristotle and even Plato would have agreed with all of this: both the nonpsychological nature of concepts and the fundamental role of modally robust relations of exclusion and inclusion in determining meaning. But the Latin medieval to European early modern mainstream was in this regard much more influenced by the Stoic explanation of meaning by representation, and by the “psychological” cast of Augustine’s thought.

Brandom goes on to characterize Hegel’s position as a “bimodal hylomorphic conceptual realism”, carefully unpacking each part of this dense formula. The two modalities in question are the two fundamental ways in which things have grip on us: the “bite” of reality and the moral “ought”. Brandom holds that there is a deep structural parallel or isomorphism between these two kinds of constraints that affect us. Further, the isomorphism is also a hylomorphism in the sense that the two modalities are not only structurally similar, but so deeply intertwined in practice as to be only analytically distinguishable. Concepts and normativity are interdependent. Finally, it is through concepts and normativity that all our notions of the solidity of reality are articulated.

This kind of conceptual realism in Hegel is complemented by what Brandom calls a conceptual idealism. “At the grossest level of structure, the objective realm of being is articulated by nomological relations, and the subjective realm of thought is articulated by norm-governed processes, activities or practices. It can be asked how things stand with the intentional nexus between these realms. Should it be construed in relational or practical-processual terms?” (p. 43). “Hegel takes there to be an explanatory asymmetry in that the semantic relations between those discursive practices and the objective relations they know about and exploit practically are instituted by the discursive practices that both articulate the subjective realm of thought and establish its relations to the objective realm of being. This asymmetry claim privileging specifically recollective discursive practices over semantic relations in understanding the intentional nexus between subjectivity and objectivity is the thesis of conceptual idealism.” (p. 44).

Plato had talked about recollection in a mythical or poetic way in relation to paradoxes of learning. Hegel’s more “historiographical” recollection is also related to a kind of learning, but Hegel specifically stresses the importance of error as the stimulus to learning. Brandom says there is both a “subjunctive sensitivity of thought to things” (ibid) and a “normative responsibility of thought to fact. What things are for consciousness ought to conform to what things are in themselves.” (p. 45). This translates into a central obligation to repair our errors, and for Hegel the specific way to do this is through a recollective account of what was right in our previous stance; how we came to realize that it went wrong; and what we did to fix it.

“The normative standard of success of intentional agency is set by how things objectively are after an action. The idea of action includes a background structural commitment to the effect that things ought to be as they are intended to be. Conceptual idealism focuses on the fact that all these alethic and normative modal relations are instituted by the recollective activity that is the final phase of the cycle of cognition and action” (ibid).

“Conceptual realism asserts the identity of conceptual content between facts and thoughts of those facts. (Compare Wittgenstein: ‘When we say, and mean, that such-and-such is the case, we—and our meaning—do not stop anywhere short of the fact; but we mean: this—is—so.’ [PI§95]) Conceptual idealism offers a pragmatic account of the practical process by which that semantic-intentional relation between what things are for consciousness and what they are in themselves is established. Pragmatics, as I am using the term, is the study of the use of concepts by subjects engaging in discursive practices. Conceptual idealism asserts a distinctive kind of explanatory priority (a kind of authority) of pragmatics over semantics. For this reason it is a pragmatist semantic explanatory strategy, and its idealism is a pragmatist idealism. The sui generis rational practical activity given pride of explanatory place by this sort of pragmatism is recollection” (pp. 45-46).

Brandom says that Hegel’s notion of experience has two levels, corresponding to two top-level kinds of concepts he distinguishes: ordinary practical and empirical concepts, and meta-level philosophical, categorial or “logical” concepts.

“The master-strategy animating this reading of Hegel (and of Kant) is semantic descent: the idea that the ultimate point of studying these metaconcepts is what their use can teach us about the semantic contentfulness of ground-level concepts, so the best way to understand the categorial metaconcepts is to use them to talk about the use and content of ordinary concepts… The pragmatic metaconcept of the process of experience is first put in play in the Introduction, at the very beginning of [Hegel’s Phenomenology], in the form of the experience of error. It is invoked to explain how the consciousness-constitutive distinction-and-relation between what things are for consciousness and what things are in themselves shows up to consciousness itself. Hegel assumes that, however vaguely understood it might be at the outset, it is a distinction-and-relation that can at least be a topic for us, the readers of the book” (pp. 47-48).

The most naive human awareness already implicitly recognizes a distinction between appearance and reality. “The question is how this crucial distinction already shows up practically for even the most metatheoretically naïve knowing subject. How are we to understand the basic fact that ‘…the difference between the in-itself and the for-itself is already present in the very fact that consciousness knows an object at all’… Hegel traces its origin to the experience of error” (p. 48).

“Hegel finds the roots of this sort of experience in our biological nature as desiring beings…. What a creature practically takes or treats as food, by eating it, can turn out not really to be food, if eating it does not satisfy the hunger that motivated it…. This sort of experience is the basis and practical form of learning” (p. 49). This is “the practical basis for the semantic distinction between representings and representeds, sense and referent” (pp, 49-50).

“[A]n essential part of the acknowledgment of error is practically taking or treating two commitments as incompatible. Such genuinely conceptual activity goes beyond what merely desiring beings engage in. The origins of Hegel’s idea here lie in Kant’s earlier broadly pragmatist account of what knowing subjects must do in order to count as apperceiving” (p. 50).

“Hegel breaks from the Kantian picture by adding a crucial constraint on what counts as successful repairs…. Successful repairs must explain and justify the changes made, in a special way” (p. 52). This takes the form of a historical recollection. “To be entitled to claim that things are as one now takes them to be, one must show how one found out that they are so. Doing that involves explaining what one’s earlier views got right, what they got wrong, and why…. This is the progressive emergence into explicitness, the ever more adequate expression, of what is retrospectively discerned as having been all along implicit as the norm governing and guiding the process by which its appearances arise and pass away” (p. 53). “Recollection… turns a past into a history” (p. 54).

All this serves as an explanation of how we come to have representations that actually refer to something, in terms of how we express our concerns. “In general Hegel thinks we can only understand what is implicit in terms of the expressive process by which it is made explicit. That is a recollective process. The underlying reality is construed as implicit in the sense of being a norm that all along governed the process of its gradual emergence into explicitness” (p. 56).

“Kant had the idea that representation is a normative concept. Something counts as a representing in virtue of being responsible to something else, which counts as represented by it in virtue of exercising authority over the representing by serving as a standard for assessments of its correctness as a representing. It is in precisely this sense that a recollective story treats the commitments it surveys as representings of the content currently treated as factual” (p. 58). Brandom says that Hegel reconstructs in expressive terms what the representationalists were right about, while strongly contrasting this way of thinking with representationalism.

“Hylomorphic conceptual realism then underwrites the idea of the categorial homogeneity of senses as graspable thoughts and their referents (what they represent) as correspondingly conceptually contentful, statable facts. This makes intelligible the idea that thoughts are the explicit expressions of facts. They make explicit… how the world is” (p. 60).

“The plight of finite knowing and acting subjects metaphysically guarantees liability to empirical error and practical failure. The experience of error is inescapable. What I earlier called the ‘false starts, wrong turns, and dead ends’ of inquiry can be retrospectively edited out of the sanitized, Whiggish vindicating recollective narrative, but they cannot be avoided going forward.

“Why not? In short because the rational, conceptual character of the world and its stubborn recalcitrance to mastery by knowledge and agency are equally fundamental primordial features of the way things are” (pp. 61-62).

“For Hegel, the experience of error requires not just the revision of beliefs… but also of meanings” (p. 62). “The manifestation of stubborn, residual immediacy in thought is the inevitability of the experience of error…. [T]he ineluctability of error and the realistic possibility of genuine knowledge [both] express valid perspectives on what is always at once both the experience of error and the way of truth. The important thing is not to seize exclusively—and so one-sidedly—on either aspect, but to understand the nature of the process as one that necessarily shows up from both perspectives” (p. 63).

“One of Hegel’s animating ideas is that the independence of immediacy (its distinctive authority over structures of mediation) is manifested in its role as a principle of instability, as providing a normative demand for change, for both rejection and further development of each constellation of determinate concepts and commitments articulated by them. The independence of mediation (its distinctive authority over immediacy) is manifested in all the retrospective recollective vindications of prior constellations of commitments as genuine knowledge, as resulting from the expressively progressive revelation of reality by prior claims to knowledge.” (pp. 64-65).

“The forward-looking obligation to repair acknowledged incompatibilities of commitment acknowledges error and the inadequacy of its conceptions. The backward-looking recollective obligation to rationalize as expressively progressive previous, now superseded, repairs and recollections institutes knowledge, truth, and determinate concepts whose incompatibilities and consequences track those articulating (in a different modal key) the objective world…. The recollective process is also what Hegel calls ‘giving contingency the form of necessity.'” (p. 65).

“The key in each case is to understand [truth and error] not as properties, states, or relations that can be instantiated at a single time, but as structural features of enduring experiential processes” (p.66).

This is to move from what Hegel calls Understanding to what he calls Reason. Understanding focuses on the fixity of concepts; Reason also has regard for their malleability. To think of experience as asymptotically approaching objective facts and relations belongs to the Understanding that disregards the mutation of meanings.

“The world as it is in itself as distinct from how it is for consciousness is not a brute other, but in that distinctive sense the product of its own recollective activity in experience” (p.72).

Beings

When I talk about beings, or us as beings, I mean this in a very ordinary, pre-philosophical way. It seems to me that to informally qualify as a “being”, something must have a degree of coherence; a degree of resilience or persistence in the face of change; and relations to other beings.

We might form a notion of something absolutely singular or self-contained, but it would not be a notion of a being. The classic notion of something absolutely singular was the One of Plotinus, which for him explicitly preceded all being. For Plotinus, we should only begin to talk about being when we have something that is “both one and many”.

If we speak of beings, it makes some sense to inquire about the being of beings. To me, though, this just means a higher-order consideration of the ordinary “being a being” of ordinary beings. It does not imply some very different “Being with a capital B” that gives being to all ordinary beings.

When Aristotle inquired about “being as being”, he reached two main conclusions. First, “being is said in many ways”. That is to say, being is not a univocal concept; it has multiple meanings. More profoundly, what we nonetheless informally call being itself is itself analogous to something that is nonunivocal rather than univocal. The non-self-containedness that seems to be characteristic of beings means that if we look closely, what we call individual beings do not have univocal identity, but rather are “identified” by a kind of family resemblance to themselves. Beings do not have sharp edges that would unambiguously separate an inside from an outside, and sometimes they change profoundly. Second, being a being nonetheless always involves being some way that is distinguishable from some other way. Calling something a being or saying it “is” in any sense thus expresses a kind of commitment on our part, and as Aristotle and Brandom would both remind us, the very nature of commitments implicitly commits us to abstain from or correct other incompatible commitments.

Being a being in whatever sense thus involves both a determinateness and an openness. Determinateness and openness in turn have to be understood in ways that permit their coexistence. (See also Equivocal Determination; Openness of Reason; Bounty of Nature.)

I want to say that everything important about being a being belongs in the register of “whatness”, or what was traditionally called essence. Contrary to the great arguments of Aquinas as well as to the 20th century mystique of existentialism, I don’t find value in an allegedly separate register of existence. Some people have argued that Aristotle did not have a proper concept of existence, as if this were a shortcoming. I find Aristotle’s direction of our attention to the “what” of being to be noninflationary in a quite salutary way. (See also Substance; Platonic Truth; Meant Realities.)

Beyond Subject-Object

Hegel famously wanted to move beyond the subject-object dichotomy he saw as typical of early modernity. In practical terms, Kant’s most famous concern to avoid “dogmatic” assumptions about direct possession of epistemic objects had seemed to accentuate the separation of subject and object, by focusing on the distinction between appearance and reality. But both Kant and Hegel wanted to assert the possibility of knowledge in a strong sense, while avoiding what Kant called dogmatism. They also had considerable common ground in a shared rejection of naive early modern notions of subjects and objects and their relations.

Kant had begun — seemingly unwittingly — to recover some neglected Aristotelian insights in these areas, and Hegel made this an explicit theme. Thus they both already questioned the dichotomous interpretation of subject-object relations. Kant had also already highlighted the inevitable involvement of concepts in experience. For Kant, there is no direct epistemic access to real-world objects, or things in themselves (or to our own subjectivity). All knowledge proceeds by way of concepts, but he retains the concept of objects (and subjects) as a sort of placeholders for new distinctions between appearance and reality that can always be wrapped around current concepts in a new iteration.

When dichotomous connotations have already been applied to a distinction in some communicative context, it can be tricky to simultaneously clarify the transcendence of the dichotomy and the preservation of the underlying distinction, but the general solution is not far to find — just ensure that the underlying distinction is expressed in terms of some finite relation, rather than A versus not-A. Then we have Hegelian determinate negation or Aristotelian difference between the terms, rather than classical negation. So in effect, the solution lies in recognizing that the previous understanding of the distinction in terms of dichotomy was wrong in the first place.

More positively, Hegel eliminates dichotomies by putting determinate relations, coherence, and mediation first in the order of explanation, before all particular terms. The Hegelian Absolute — or that which transcends the subject-object dichotomy — is just a handle for perspectives that put processes, relations, coherence, and mediation before any preconceived notion of the conceptual content of particular terms.

I think Hegel saw this sort of structure as common to Aristotelian substance or “what it was to have been” a thing on the one hand, and Kantian subjectivity or synthesis of apperception on the other.

Working in the Hegelian Absolute does not require epistemic super powers or specious Cartesian certainty, just a sustained honest effort that is still implicitly defeasible. Hegel intends the Absolute to be a kind of Aristotelian achievable perfection, not a kind of omniscience or theological perfection that could never be legitimately claimed by a rational animal. (See Substance Also Subject.)

In approaching these matters in A Spirit of Trust, Brandom characteristically focuses not directly on higher-order abstractions, but on their implications for what we do with ordinary concepts in ordinary experience. Like Aristotle and Hegel but following a distinct strategy of his own, Brandom avoids the impasse of a supposed transition from psychological to “metaphysical” terms, or from ordinary experience to something that would seemingly have to be like the mind of God, by clarifying what we implicitly mean by concepts in the first place.

With Aristotle, Hegel, and Frege and in contradistinction to the empiricist tradition, Brandom understands concepts and apperception in a nonpsychological, nonrepresentational, normative-pragmatic, inferential-semantic way. Through the discovery of counterfactually robust relations, concepts evolve toward increasing universality. Through the experience of error, synthesis of apperception comes to incorporate the recognition that not only its commitments but also its concepts are always in principle provisional, subject to reformulation when faced with a new case. Through both of these combined with the additional cross-checks provided by mutual recognition, synthesis moves toward increasing objectivity and what might be called contact with reality. Through Brandom’s “expansive” model of responsibility, the last remaining obstacle to a full resolution of subject-object separation — the lack of a normative interpretation of unintended consequences of actions — is removed.

Neither “subjects” nor “objects” as such are very prominent in an account of this sort. It is much more a story about processes, relations, coherence, and mediation. Aristotle, Hegel, and Brandom each develop their own ways of working that start in the middle, as it were, and do not need reified subjects and objects to begin with. This, again, is just what the Hegelian Absolute is — a name for the sort of perspective that emphasizes the in-principle provisional character of all finite concepts, as contrasted with the more directly practical sort of perspective that provisionally works with the current basis as a source of reasons for particular sayings and doings. (See also Aristotelian and Hegelian Dialectic; Contradiction vs Polarity; Three Logical Moments.)