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”.

Cause of Itself

Spinoza famously begins his Ethics with a definition of “cause of itself” (causa sui). This will become the hallmark of his “Substance”, of which he says there can be only one, and which he identifies with his own heterodox conception of God. Cause of itself would be that the essence of which involves existence.

In Hegel or Spinoza (French ed. 1979), Pierre Macherey writes that “First of all we can show, as Guéroult does, that the concept of causa sui does not really have an initial foundational value for Spinoza: it does not represent a kind of first truth, a principle in the Cartesian sense, from which the entire system can be developed, as if from the starting point of a germ of truth” (p. 16).

“Here we can begin to be astonished: does Hegel ignore that this aporia of beginning — which sets his Logic in motion, this impossibility of grounding the infinite process of knowledge in a first truth which in itself as principle or foundation — is also an essential lesson of Spinozism, the principal objection that he himself opposes to the philosophy of Descartes? In such a sense that it is only… ‘so to speak’, the geometric exposition of the Ethics ‘begins’ with definitions, which for that matter do not have an effective sense, except at the moment when they function in demonstrations or they really produce the effects of truth: Spinozist thinking precisely does not have this rigidity of a construction relying on a base and pushing its analytic to an end point, which would find itself thus limited between a beginning and an end” (p. 17).

For Hegel according to Macherey, “The causa sui is based on a substantial principle that ‘lacks the principle of the personality’. It thus constitutes a substance that cannot become subject, which fails in this active reflection of self, which would permit it to undertake its own liberation in its own process…. This is an arrested and dead spirit” (p. 18).

This is supposed to be the individuality and freedom denying “Oriental” attitude that Hegel with broad brush unfortunately really does attribute to Judaism, Islam, Hinduism, Buddhism, the Roman Empire, Catholicism, the pre-Socratic philosopher Parmenides, and Spinoza, among others. This unfortunate over-the-top anti-anti-subjectivity theme of Hegel’s kept me from really appreciating his work for a long time.

On the other hand, the details of his argument about freedom and subjectivity as affirmative values actually make sense, even to the point of winning over an old sympathizer of French anti-Hegelianism like myself.

Reference, Representation

The simplest notion of reference is a kind of literal or metaphorical pointing at things. This serves as a kind of indispensable shorthand in ordinary life, but the simplicity of metaphorical pointing is illusory. It tends to tacitly presuppose that we already know what it is that is being pointed at.

More complex kinds of reference involve the idea of representation. This is another notion that is indispensable in ordinary life.

Plato and Aristotle used notions of representation informally, but gave them no privileged status or special role with respect to knowledge. They were much more inclined to view knowledge, truth, and wisdom in terms of what is reasonable. Plato tended to view representation negatively as an inferior copy of something. (See Platonic Truth; Aristotelian Dialectic; Aristotelian Semantics.)

It was the Stoics who first gave representation a key role in the theory of knowledge. The Stoics coupled a physical account of the transmission of images — bridging optics and physiology — with very strong claims of realism, certain knowledge both sensory and rational, and completeness of their system of knowledge. In my view, the Stoic theory of representation is the classic version of the “correspondence” theory of truth. The correspondence theory treats truth as a simple “correspondence” to some reality that is supposed to be known beyond question. (Such a view is sometimes misattributed to Plato and Aristotle, but was actually quite alien to their way of thinking.)

In the Latin middle ages, Aquinas developed a notion of “perfect” representation, and Duns Scotus claimed that the most general criterion of being was representability. In the 17th century, Descartes and Locke built foundationalist theories of certain knowledge in which explicitly mental representations played the central role. Descartes also explicitly treated representation in terms of mathematical isomorphism, representing geometry with algebra.

Taking putatively realistic representational reference for granted is a prime example of what Kant called dogmatism. Kant suggested that rather than claiming certainty, we should take responsibility for our claims. From the time of Kant and Hegel, a multitude of philosophers have sharply criticized claims for certain foundations of representational truth.

In the 20th century, the sophisticated relational mathematics of model theory gave representation renewed prestige. Model-theoretic semantics, which explains meaning in terms of representation understood as relational reference, continues to dominate work in semantics today, though other approaches are also used, especially in the theory of programming languages. Model-theoretic semantics is said to be an extensional rather than intensional theory of meaning. (An extensional, enumerative emphasis tends to accompany an emphasis on representation. Plato, Aristotle, Kant, and Hegel on the other hand approached meaning in a mainly intensional way, in terms of concepts and reasons.)

Philosophical criticism of representationalist theories of knowledge also continued in the 20th century. Husserl’s phenomenological method involved suspending assumptions about reference. Wittgenstein criticized the notion of meaning as a picture. All the existentialists, structuralists, and their heirs rejected Cartesian/Lockean representationalism.

Near the end of the 20th century, Robert Brandom showed that it is possible to account very comprehensively for the various dimensions of reference and representation in terms of intensionally grounded, discursive material inference and normative doing, later wrapping this in an interpretation of Hegel’s ethical and genealogical theory of mutual recognition. This is not just yet another critique of representationalism, but an actual constructive account of an alternative, meticulously developed, that can explain how effects of reference and representation are constituted through engagement in normative discursive practices — how reference and representation have the kind of grip on us that they do, while actually being results of complex normative synthesis rather than simple primitives. (See also Normative Force.)

Brandom and Hermeneutics

It’s been a while since I said much about Robert Brandom, though his work — along with my own nonstandard reading of Aristotle — continues to be one of the main inspirations behind everything I write here.

Lately I’ve been devoting a lot of energy to belatedly catching up on the hermeneutics of Paul Ricoeur. To my knowledge, Ricoeur never commented on Brandom during his lifetime, and Brandom has not specifically commented on Ricoeur.

Brandom has, however, in Tales of the Mighty Dead explicitly endorsed some of the broad perspectives of Hans-Georg Gadamer’s hermeneutics, and he has devoted much attention to a “hermeneutics of magnanimity” in Hegel’s Phenomenology. Brandom’s mentor Richard Rorty concluded his famous work Philosophy and the Mirror of Nature by recommending a general turn from foundational epistemology to nonfoundationalist hermeneutics, and I have previously suggested that Brandom’s work as a whole could be viewed as a novel sort of hermeneutics developed within the analytic tradition.

Brandom’s fundamental concept of the priority of material inference over formal inference puts meaning — and therefore the interpretation of meaning — in the driver’s seat for reasoning, so to speak. This allows for the recovery of a more historic concept of Reason, which ever since Descartes has been mostly replaced by a mathematically based kind of rationality that is more precise and invaluable in technical realms, but also much more rigid, and in fact far more limited in its applicability to general human concerns (see Kinds of Reason).

Even prior to Descartes, Latin medieval logic already moved increasingly toward formalism. Since Frege and Russell, the rigorous mathematization of logic has yielded such impressive technical results that most philosophers seem to have forgotten there is any other way to view logic.

In the 1950s Wilfrid Sellars took the first steps toward initiating a counter-trend, reaching back to the pre-Cartesian tradition to formulate the notion of material inference later taken up by Brandom.

Modern complaints against Reason strongly and wrongly presuppose that it inevitably follows or approximates a formal path. Material inference provides the basis for a fundamentally hermeneutic view not only of Reason but also of logic and logical truth.

I have further stressed the fundamentally ethical or meta-ethical character of material inference, leading to a concept of ethical reason as the most fundamental form of Reason overall in a view that puts material inference before formal logic. As I put it not too long ago, ethical reason may optionally use the more technical forms of reason as tools. Ethical reason, I want to say, has a genuinely active character, but technical reason does not. Ethical reason is fundamentally oriented toward the concrete, like Aristotle’s practical judgment.

I want to say that there is such a thing as logical or semantic reference — saying something about something is not in vain — but a prior hermeneutic inquiry is necessary to ground and explain reference. Moreover, both Aristotle and Kant recognized something like this. Such a perspective is compatible with science, while putting ethical and meta-ethical inquiry first.

A hermeneutic concept of Reason saves us from a false dilemma between formalism on the one hand and question-begging appeals to intuition, authority, or irrational “decision” on the other. (See also Dialogue.)

Aristotelian and Hegelian Dialectic

When Hegel talked about dialectic instead of just using it, he occasionally made it sound as if dialectic governed events in the world. This is a loose, popular way of speaking that should not be taken literally. Dialectic is the main tool of the forward progress of philosophical criticism, and thus indirectly helps refine our understanding of the world and events in it. It could not directly drive events.

It is actually very hard to draw a sharp line between the world “in itself” and our understanding of it, because our understanding (in the general, not the specifically Hegelian sense) is all we actually have to go on. Our sense of the world in itself is permeated by artifacts of our understanding, because it comes entirely from our understanding.

But then it turns out that our understanding is not just some private, subjective thing of ours. Our understanding participates in the world, and is part of it. The cultivation of shareable thought grounds objectivity in (our sense of) the world. Much of the content of shareable thought comes to us from outside. In a poetic manner of speaking, it could be said that the world thinks itself through us. But in a more direct way, we are the agents and stewards of the world’s thought. In particular, it advances through us. There is thus no wall between our understanding and the world. There is a meaningful distinction, but the content of shareable thought straddles the boundary, so to speak.

Aristotle’s version of dialectic is much less famous nowadays, but a great deal easier to understand, and it does not require apologetics of the sort I just provided for Hegel’s. It uses logic and semantics to analyze the meaning of things said, making no assumption whether or not they are grounded in knowledge.

Aristotle explicitly said (Topics, book 1) that this is the way to investigate first principles (i.e., starting points) of knowledge. With respect to such starting points, we have no possibility of knowledge in the strong sense (episteme) — which requires development — but only a kind of initial personal acquaintance or familiarity (gnosis), as he said in Posterior Analytics.

There has been a strong tradition of misinterpretation of this latter passage. With no textual basis, many people who wanted to read Stoic-style foundationalism back into Aristotle — or were influenced by others with this sort of motivation — have glossed Aristotelian gnosis as something like a strong intellectual intuition, and claimed Aristotle was saying first principles of knowledge were better known in a strong sense, rather than just more familiar. (See also Aristotelian Demonstration.)

Aristotle’s actual practice, however, confirms the reading of first principles of knowledge as themselves objects of mere familiarity rather than strong knowledge. (Aristotle’s loftier principles are ends, not starting points of knowledge, and he typically places discussion of them at the end of an inquiry.) His starting points for inquiries are very pragmatic. He typically begins an inquiry with logical/semantic (i.e., “dialectical”) analysis of widely known opinions on the subject. He also explicitly recommends that we begin any inquiry from what is closer to us, and then, through analysis, refine our understanding. (See also The Epistemic Modesty of Plato and Aristotle).

The development of knowledge starts from what is close to us and easier to grasp, and becomes progressively more secure through the dialectical work we do on it. Aristotelian dialectic uses the same logical forms as demonstration, but is mainly concerned with inferential semantic analysis rather than deriving conclusions. (Even Aristotelian demonstration is concerned not so much with deriving conclusions, as with perspicuously showing their basis.) Aristotle does the great majority of his actual work with dialectic rather than demonstration.

Once one becomes familiar with the profile of the Aristotelian version, it becomes possible to see something very like it at the core of Hegel’s way of working — not so much in what he says about it, as in what he does. (See also Aristotelian Dialectic; Dialogue; Scholastic Dialectic; Contradiction vs Polarity; Three Logical Moments.)

Three Logical Moments

The “Logic Defined & Divided” chapter of Hegel’s Encyclopedia Logic contains some brilliant, relatively popular aphorisms from his lectures, and provides a nice introduction to his views. Having recently treated with approval Kant’s denunciation of speculation in the usual sense, I’m turning to this now because among other riches, it contains Hegel’s recovery of an alternative, much more positive sense for “speculation”. As Aristotle would remind us, things are said in many ways, and it is wise to give heed to the differences.

Hegel says that every notion and truth involves three moments that are all essential and cannot really be separated from one another: Understanding, Dialectic, and Speculation.

In other places, Hegel frequently polemicizes against the narrowness and rigidity of mere Understanding. Here, he rounds out the picture, noting that “apart from Understanding there is no fixity or accuracy in the region of theory or of practice” and that knowledge begins “by apprehending existing objects in their specific differences”. He cites examples of how Understanding contributes to science, mathematics, law, practical life, art, religion, and philosophy.

Preparing the transition to dialectic, he notes “It is the fashion of youth to dash about in abstractions — but the man who has learnt to know life steers clear of the abstract ‘either-or’, and keeps to the concrete”. Dialectic for Hegel if viewed separately is the moment of “negative” Reason or criticism. He says that dialectic subordinated to Understanding’s mode of thought leads to skepticism, but dialectic freed from this subordination builds on distinctions developed by the Understanding, even while “the one-sidedness and limitation of the predicates of understanding is seen in its true light”. Dialectic studies things “in their own being and movement”. He goes on to expound Plato’s use of dialectic, and its difference from sophistry. (See also Contradiction vs Polarity; Aristotelian and Hegelian Dialectic.)

Speculation in Hegel’s special sense is the “positive” moment of Reason, which if considered separately begins from a kind of faith in reasonableness in the world. He implicitly connects it with a charitable reading of the long religious tradition of faith seeking understanding, construed in such a way as to be not incompatible with a charitable version of Enlightenment criticism. He notes that “the true reason-world, so far from being the exclusive property of philosophy, is the right of every human being [of] whatever grade of culture or mental growth”, adding that “experience first makes us aware of the reasonable order of things… by accepted and unreasoned belief”. Once this rational order becomes an object of thought rather than mere belief, we have speculative Reason proper.

Speculative Reason builds on both Understanding and dialectic. “A one-sided proposition… can never even give expression to a speculative truth.” He notes a connection between this and basic intuitive fairness. Starting from a simple faith in the reasonableness of the world and advancing through various stages of criticism, speculative Reason ultimately realizes substance as subject, and overcomes the dichotomy of subject and object.

Dialectic undid the abstract, atomistic, foundationalist, “either-or” tendencies of isolated Understanding. Speculative Reason in Hegel’s sense turns this into a new affirmation. In many places, Hegel talks about Reason or dialectic in ways that subsume both the dialectical and the speculative moment described here.

I read Hegelian speculative Reason — or dialectic incorporating the speculative moment — as just ordinary reason moving forward without the crutches of foundationalism and dogmatic claims of certainty. Reason without foundationalism is concerned with the very same open-ended work of interpretation I have attributed to Aristotle. Ultimately, Hegelian Reason is defeasible rational interpretation of experience, optimistically doing the best we can with the resources we have, and always on the lookout for something better. Thus, it too can be reconciled with Kantian discipline. (See also “Absolute” Knowledge?)