Substance and Subject

This is part 2 of my walk-through of the Preface to Hegel’s Phenomenology of Spirit. We’ve reached the point where he says “In my view, which must be justified by the exposition of the system itself, everything hangs on grasping and expressing the true not just as substance but just as much as subject” (Pinkard trans., p. 12).

I’ve previously written two posts (Substance Also Subject; Subject and Substance, Again) that try to bring this aspect of Hegel as close as possible to the deeper sense that Aristotle gives to “substance” in the Metaphysics. I still think this fits well with Hegel’s larger perspective, but here I want to deal with the text as it stands.

Just two sentences after the one quoted above, there is an unmistakable reference to Spinoza’s controversial view that God is the only substance there is. Spinoza defines substance as “what is in itself and is conceived through itself, i.e., that whose concept does not require the concept of another thing, from which it must be formed” (Ethics book 1 definition 3; Collected Works, Curley trans., vol. 1 p. 408). The sentences in which Hegel literally speaks of substance in the Preface appear to be consistent with this. In general, Hegel most often speaks of “substance” as something whose main attributes are self-containedness and immediate identity with itself. This is very far indeed from the Metaphysics-based notion of substance I have been concerned to develop here. But as we will see, Hegel makes up for this in other ways.

A “subject” for Hegel is always a conscious or self-conscious being. But consciousness for Hegel always comes paired with an object. Self-consciousness eventually overcomes the duality of consciousness and object, but it is constituted in irreducible relation with other rational beings.

So when Hegel says “substance is also subject”, it is a paradoxical expression saying that what is self-contained “also” has irreducible relations to objects or other beings. Language is here strained to the breaking point. Perhaps he wants to imply that the very thing that the Schellingians claimed was entirely self-contained is in reality essentially embedded in otherness.

Overall, Hegel stresses irreducible relations far more than self-containedness. In the opening quote, he just told us that in his discourse, we should not expect to find a “substance” that is only substance and nothing more. In Hegel, even the absolute is never “just” absolute. Everything for Hegel is more than it “just” is.

When he speaks of ethical substance or spiritual substance, what he seems to really want to convey is just that these have an aspect of self-containedness or simple immediacy, not that they are strictly reducible to it.

“The true is not an original unity as such, or, not an immediate unity as such. It is the coming-to-be of itself, the circle that presupposes its end as its goal and has its end for its beginning, and which is actual only through this accomplishment and its end” (pp. 12-13).

The circular relation here is importantly different from that by which Plotinus strictly identifies the end of all things with the origin of all things (for him, the One is both of these). In Hegel, the circle explicitly involves actualization of the end via coming-to-be, which escapes strict identity, whereas in Plotinus the circle is supposed to be eternal and to figuratively represent a simple identity. Directly contrary to Hegel, Plotinus would tell us that the true is both an original unity and an immediate unity.

Hegel expands his previous statement as follows:

“However much the form is said to be the same as the essence, still it is for that very reason a bald misunderstanding to suppose that cognition can be content with the in-itself, or, the essence, but can do without the form — that the absolute principle, or absolute intuition, can make do without working out the former or without the development of the latter. Precisely because the form is as essential to the essence as the essence is to itself, the essence must not be grasped as mere essence, which is to say, as immediate substance or as the pure self-intuition of the divine. Rather, it must likewise be grasped as form in the entire richness of the developed form, and only thereby is it grasped and expressed as the actual.”

“The true is the whole. However, the whole is only the essence completing itself through its own development. This much can be said of the absolute: It is essentially a result, and only at the end is it what it is in truth. Its nature consists just in this: to be actual, to be subject, or, to be the becoming-of-itself. As contradictory as it might seem, namely, that the absolute is to be comprehended essentially as a result, even a little reflection will put this mere semblance of contradiction in its rightful place. The beginning, the principle, or, the absolute as it is at first, or, as it is immediately expressed, is only the universal. But just as my saying ‘all animals’ can hardly count as an expression of zoology, it is likewise obvious that the words, ‘absolute’, ‘divine’, ‘eternal’, and so on, do not express what is contained in them; — and it is only such words which in fact express intuition as the immediate. Whatever is more than such a word, even the mere transition to a proposition, is a becoming-other which must be redeemed, or, it is a mediation” (p. 13).

“Hence, reason is misunderstood if reflection is excluded from the truth and is not taken to be a positive moment of the absolute. Reflection is what makes truth into the result, but it is likewise what sublates the opposition between the result and its coming-to-be” (p. 14).

As with “substance”, Hegel gives essence a much more restrictive meaning than I have been developing here. On the other hand, he has a lively Aristotelian notion of form that is quite unusual among modern writers.

To pay attention to mediation is to “be at home in otherness”. Here I think we are much closer to Aristotle again, perhaps in spite of what I find to be the awkward earlier words about substance and subject. Hegel seems to confirm this by explicitly comparing what he has just said to the larger scheme of Aristotelian teleology, just as I had hoped before (see Aristotle on Explanation; Nature, Ends, Normativity; Hegel’s Preface). Now that the ground is clear, I’ll apply this to the earlier point about Kant and Aristotle in a future post.

“What has just been said can also be expressed by saying that reason is purposive doing. Both the exaltation of a nature supposedly above and beyond thinking, and especially the banishment of external purposiveness have brought the form of purpose completely into disrepute. Yet, in the sense in which Aristotle also determines nature as purposive doing, purpose is the immediate, the motionless, which is self-moving, or, is subject…. For that reason, the result is the same as the beginning because the beginning is purpose — that is, the actual is the same as its concept only because the immediate, as purpose, has the self, or, pure actuality, within itself. The purpose which has been worked out, or, existing actuality, is movement and unfolded coming-to-be” (ibid).

As an added bonus, he puts an explicit caveat on the previous talk about the subject. What really matters is the actuality of the concept as self-moving, not the putative fixed point of the subject. I like this vocabulary much better.

“The subject is accepted as a fixed point on which the predicates are attached for their support through a movement belonging to what it is that can be said to know this subject and which itself is also not to be viewed as belonging to the point itself, but it is solely through this movement that the content would be portrayed as the subject. Because of the way this movement is constituted, it cannot belong to the point, but after the point has been presupposed, this movement cannot be constituted in any other way, and it can only be external. Thus, not only is the former anticipation that the absolute is subject not the actuality of the concept, but it even makes that actuality impossible, for it posits the concept as a point wholly at rest, whereas the concept is self-movement” (p. 15).

Not only does he emphasize the movement of the concept, but he even mentions the content being “portrayed” as the subject. (See also Ideas Are Not Inert.)

Associative Synthesis

We have reached the heart of Husserl’s passive synthesis lectures, a long subdivision on associative synthesis. This is Husserl’s re-visioning of the classic notion of association that empirical psychology ultimately derived from Locke and Hume. For Husserl, it will provide the key to the constitution of subjectivity overall.

Rather than treating association in terms of a notion of psycho-physical causality, he wants to explain it as as a product of synthesis. As Husserl now reminds us, he has been implicitly working under the phenomenological reduction, which puts “in brackets” all questions of external existence and natural causality. He focuses on what to my Aristotelian eye look like questions of form and of a kind of teleology immanent to the subject matter.

Here he again refers to Kant’s discussion of synthesis in the Critique of Pure Reason (see Capacity to JudgeFigurative Synthesis). Husserl claims that he will go further than Kant in explicitly discussing synthesis of immanent contents of consciousness, as well as apprehensions of objects of external perception. For both Husserl and Kant, all this is closely bound up with the constitution of our experience of time. Memory and expectation will again play a key role.

“[T]he path is cleared from here toward a universal theory of the genesis of a pure subjectivity, and in particular, initially in relation to its lower level of pure passivity. Phenomenological eidetic [form-oriented] analyses of consciousness constituting a temporal objectlike formation already led to the beginnings of a lawful regularity of genesis prevailing in subjective life. We see very quickly that the phenomenology of association is, so to speak, a higher continuation of the doctrine of original time-constitution. Through association, the constitutive accomplishment is extended to all levels of apperception” (Analyses Concerning Passive and Active Synthesis, p. 163).

“The doctrine of the genesis of reproductions and of their formations is the doctrine of association in the first and more genuine sense. But inseparably connected to this, or rather, grounded upon this is a higher level of association and doctrine of association, namely, a doctrine of the genesis of expectations, and closely related to it, the genesis of apperceptions to which belong the horizons of actual and possible expectations. All in all, it concerns the genesis of the phenomena of expectation, that is, of those specific intentions that are anticipatory” (p. 164).

Association, as Husserl analyzes it, is constituted from memories of things similar to the present object. In turn, it is from particular associations that particular expectations are constituted. Now we see memory and expectation linked together in a larger process that is precisely one of association.

“But it is precisely the analysis of associative phenomena that draws our attention to the fact that consciousness must not necessarily be a consciousness of a single object for itself, and accordingly, we touch on a new problem here: how a consciousness of something particular and how a consciousness of explicit particulars becomes possible as a consciousness of a multiplicity and a consciousness of wholeness; namely, a comparative analysis also shows the opposing possibility of many [elements], indeed, a multiplicity being continually fused into a unity within one consciousness, [implicitly], such that consciousness is not a consciousness of a multiplicity, a consciousness that becomes aware of separated particulars in a unitary and yet separate manner” (p. 165).

Here he is leading up to the central role of the experience of time, simultaneity, and streaming in the constitution of subjectivity and in turn of external experience, already foreshadowed above.

“We realize, then, that it really concerns nothing else than clarifying the fundamental problem, the basic, essential conditions of the possibility of a subjectivity itself. What must belong to it so that a subjectivity can have the essential sense without which it could not be subjectivity, [namely,] the sense of an existing subjectivity being for itself, and precisely thereby of a subjectivity constituting itself as being for itself? Certainly, a complete phenomenology of reproductive awakening concerns and exhausts this problem only with respect to the one side, namely, with respect to the constitution of one’s past, or rather, the constitution of the self-having-been in endless immanent time. But we will see that the supplementary part, the other half of the problem, is the realm of the phenomenology of inductive, anticipatory association. Here we will make clear the essential conditions of the possibility of a subjectivity that can know itself as identically one, having its inherent endless future life” (p. 169).

“Awakening” seems to be Husserl’s preferred term for the activation of memory that is somehow relevant to what is present. This may relate to a distinction I have found obscure so far, between memory as “empty” intention and “intuitive” memory. My difficulty has been that no memory, insofar as it is of the past, concerns a present object, so it seems to me as though all memory then would be what he calls empty intention. But perhaps the “intuitive” memory is a memory of a past object insofar as it is related to an intuited present object.

“Clearly, what is presupposed is the synthesis that is continually accomplished in original time-consciousness. In the concretely full, streaming living present we have present, past, and future life already united in a certain mode of givenness. But this manner in which subjectivity becomes conscious of its past and future life along with its inherent intentional contents is an incomplete one. The aforementioned manner would be meaningless for the ego if there were no awakening, for the retentions are empty and even sink into the undifferentiated retentional background. Our consciousness of the protentional future is especially empty. On the other hand, there would be no progress at all without this beginning. In the ABCs of the constitution of all objectivity given to consciousness and of subjectivity as existing for itself, here is the ‘A’. It consists, we might say, in a universal, formal framework, in a synthetically constituted form in which all other possible syntheses must participate.”

As in Kant, the experience of time for Husserl is a synthetic construct that anchors things like identities of objects, as well as the overall shape of consciousness.

“Still many other types of syntheses are transcendental in the special sense, as apodictically [demonstrably] necessary for the genesis of a subjectivity (which is indeed only conceivable in genesis). As we said, these syntheses run their course together with the synthesis constituting the temporal form of all objects, and thus must co-relate to the temporal content, the temporally formed content of the object” (pp. 170-171).

“Since the spatial world is constituted through consciousness, since it can only be there for us as existing and can only be conceived at all by virtue of certain syntheses carried out in immanence, it is clear that the constitutive problems of the world presuppose the doctrine of the necessary, most general structures and the synthetic shapes of immanence that are possible in general” (p. 171).

Working under the phenomenological reduction, he is not concerned with the transcendent existence of external objects, but only with the more particular ways in which they are immanently determined or determinable as meanings for us.

“What is constituted universally through these syntheses is known under the rubric of coexistence and succession of all immanent objects in relation to one another” (p. 172).

The universality here has to do with the generality of the form of the experience of the flow of time.

“Accordingly, corresponding to every Now is a universal synthesis. Through this synthesis, a universal concrete present is constituted, a present into which all particulars that are set off from one another are integrated. Further, the fact that the Now streams in and through temporal orientations implies at the same time another universal synthesis in constituting life whereby we are conscious of the presents coursing as a sequential unity” (p. 173).

The integral Now and the streaming sequence of Nows are in effect the outermost frames in which all concrete experience is constituted as coherent.

“This is the most general and the most primary synthesis that necessarily connects all particular objects of which we become conscious…. But naturally, the synthesis of time-consciousness also contains (and already as a presupposition for possible coexistences and succession) that synthesis in which one object is constituted as identically one or (what amounts to the same thing) as enduringly one in streaming manifolds…. [T]ime-consciousness is the primordial place of the constitution of the unity of identity or of an objectlike formation, and then of the forms of connection of coexistence and succession of all objectlike formations” (ibid).

“But what gives unity to the particular object with respect to content, what makes up the differences between each of them with respect to content…, what makes division possible and the relation between parts in consciousness, and so forth — the analysis of time alone cannot tell us, for it abstracts precisely from content. Thus, it does not give us any idea of the necessary synthetic structures of the steaming present and of the unitary stream of the presents — which in some way concerns the particularity of content” (p. 174).

The implicit distinction between the constitution of identities of objects in the quotation before last, on the one hand, and that of their unities with respect to content in the quotation immediately above, on the other, is not yet clear to me. It makes sense that the general forms of time, coexistence, and succession do not tell us the whole story about particular concrete objects. I do not see, however, how it would be possible to constitute the identities of concrete objects — in Aristotelian terms, their surface status as “substances” in the sense of things persisting through change — without taking into account their content, or their deeper substantiality in the sense of “what it was to have been” the things in question. I expect that he will have more to say about the content in what follows, so hopefully this will be clarified.

The very idea of treating subjectivity as something constituted opens up a huge new territory that later authors like Foucault, Ricoeur, and de Libera have substantially developed, and in which I have been tremendously interested. The works that Husserl published in his lifetime seemed to me mainly to focus on the constitution of objects by a subjectivity that was somewhat taken for granted. That Husserl in fact went beyond this is important to recognize. (See also Passive Synthesis: Conclusion.)

Intuition, Presentation, Time

The first part of the detailed discussion of “evidence” in Husserl’s passive synthesis lectures expands on his previous remarks about the interrelations between present intuitions and “presentifications” of what he calls “empty” intentions, which seem to be those pertaining to things that are non-present, but somehow relevant to what is present. It somewhat clarifies what he means by intuition; begins to develop important ideas about the role of time in the synthesis of experience that have some analogy to similar themes in Kant; and introduces Husserl’s reinterpretation of association, which will probably turn out to be the centerpiece of these lectures overall.

There seems to be a two-sided character to Husserl’s development here. On the one hand, he starts with a strong bias in favor of presence and immediacy. On the other, he quickly and repeatedly points out that every present intuition “points beyond its own content” by means of a related horizon of “empty” intentions of contents that are not directly present, but are implied in or by what is directly present. It is this latter aspect that I find especially interesting.

Another term he uses, which seems to subsume both present intuitions and “presentifications”, is “presentation”. Husserl says “Thus there are intuitive presentations of something present that are surely not perceptions of that present something” (Analyses Concerning Passive and Active Synthesis, p. 110), and these are the presentifications of empty intentions, as in memory and expectation. The suggestion seems to be that no presentation is self-sufficient; as was said above about present intuitions, every presentation also intrinsically points beyond itself. This I would wholeheartedly endorse.

I note here that Husserl says we have intuitive presentifications of memories and expectations that are not themselves present intuitions. I think the idea is that these are synthetically joined together with present intuitions that point to them, and this is what explains the “intuitive but not intuition” status he attributes to them. So far at least, I am not aware that Kant ever spoke of concrete memories or expectations as “intuitive”. Kant did say that general intuitions of space and time are presupposed by our intuitions of the sensible manifold.

Does Husserl think we have intuitions of objects? Does Kant? I think that in both cases, positive answers involve equivocation on what an “object” is. We saw that Husserl speaks of loosely of “objects given to consciousness” by the senses, and refers to an object “in the flesh” that we always have, before quickly pointing out that what we definitely have in the flesh is highly indeterminate. Similarly, I see commentators on Kant sometimes referring to objects being “given” in intuition, but only in an indeterminate way.

It has been pointed out that German has two words that get translated as “object”: the cognate Objekt, and Gegenstand, which literally means “something standing against”. The “standing against” one seems well suited to the indeterminate case, and this would be helpful in resolving this kind of ambiguity about objects.

I think that at least in the context of Kant, it would be wrong to say that intuition gives us proper objects, because I don’t think we have a proper object in Kant until a concept (a universal) is applied. What Kantian intuition gives us is a raw manifold of particulars that can potentially be discriminated into proper objects once concepts are applied.

Husserl says, “[W]hat is past extends unaltered into the future in the manner of an object for consciousness. This future proceeds from the reproduced past and does so in such a way that this future is at the same time co-present, relative to our current perceptual present to which these things here in our current perceptual field belong…. Obviously, expectations are not always like this, merely extending the perceptual moment continuously into the future. Something unknown, something singular never yet experienced can also be fore-seen, like an event that is indeed expected, but yet is singularly new” (p. 111).

“The problem of evidence led us back to the distinctive syntheses of coinciding that forms identities, namely to such syntheses in which intuitions and empty presentations (or intuitions and intuitions) are synthetically united, but whereby empty presentations and their fulfillment once again play an essential role” (ibid).

Here we have the vital point that identities of things are not given to us; as we experience them, they are results of passive synthesis.

“[T]he primary task becomes elucidating the founding level of the passive syntheses of ‘verification’ lying at the basis of all active verification. To do this, however, one must gain deeper insights into the structures of the intuitions and empty presentations that may be functional here…. We will be led to insights into the most universal lawful regularities of essences, to the most universal lawful regularities of structure concerning the unity of transcendental inner life, but also to the most universal lawful regularities of genesis” (p. 112).

“In all of this we find internal structural intertwinings…. Only when we understand them in their structural interrelatedness can we also understand how they function in synthetic interrelatedness, including here, as well, how they can function as confirming or confirmed” (pp. 112-113).

Again, every presentation points beyond itself.

“[I]n the synthesis, we gain an evidence-consciousness, a consciousness that exactly the same [object] that was meant in an empty manner is there in intuition in a genuine way, as the same [object] actually presented…. This is certainly the first aspect of the fundamental lawfulness of the constitution of original time-consciousness: that every lived-experience, speaking most basically, every Now-phase that arises in a primordially impressional manner is continually modified in retention” (p. 114, brackets in original).

Now we have explicit mention of the “constitution of original time-consciousness”. This was an extraordinary idea of Kant that Husserl took up, that our experience of time itself is not something given to us, but is the product of a passive synthesis.

“In our analysis of perception, which was in this regard an analysis of the temporal modes of givenness, we have already touched upon the essentially new role of protentions over against the role of retentions. The rubric, protention, designates the second aspect of genetic primordial lawfulness that strictly governs the life of consciousness as the time-constituting unitary stream” (p. 115).

“In spite of its pure passivity, we spoke of protention as an expectation, with the colorful image of the present meeting the future with open arms. Accordingly, we already speak this way in pure passivity, which is to say, even prior to [actively] grasping and viewing the perceptual object. We did not use such expressions, and we could not use such expressions with respect to retention. In this connection, there is a difference in the way protention and retention function in mindful perception, when we take note [of something] and grasp it. We are mindfully directed, purely and simply, toward the present object, toward the ever new Now that emerges as fulfilling the expectation; and in and through it, it is directed further toward the approaching object. Mindful perceiving follows the protentional continuity. The directedness-ahead, which already lies in passive perception itself, becomes patent in mindful perceiving. On the other hand, there is however not a directedness in the retentional continuity; there is not a directedness that would follow the trail of pasts being pushed back further and further” (p. 116).

This assymmetry between protention and retention tracks with the distinction that we experience time as moving continuously forward, but never backward.

“In order to clarify all this it will do us well initially to go beyond protentions as intentions of expectation, and to draw upon other empty presentations that are structurally related to them, and that are at the same time different from all mere retentions. We have in mind making co-present, memories of the present as forms of intuitive presentations, alongside memories of the past and memories of the future” (pp. 116-117).

He doesn’t explain the reference to “memories of the future”. I can only suppose that what is meant is something like a reproduction of an expectation.

“If we now consider the genetically more original modes of making co-present, then at issue, e.g., for every perceptual object, are its entire horizons that are constitutive of it, horizons that belong immediately to it…. We recognize this peculiar feature with respect to all such presentations: that they exist with other presentations in a synthetic nexus of a special kind, namely, in a synthetic nexus that lies entirely outside of the genre of identifying syntheses or syntheses of coinciding” (p. 117).

He speaks of horizons and pointings-beyond as constitituting the object. They are not some sort of optional decorations that we could choose to ignore, and still have the object. This is vitally important.

“If, from the very beginning, we remain focused most simply on the realm that already has our exclusive interest now, the realm of passive presentations as the material for passively emerging syntheses, then we will be concerned generally speaking with such syntheses in which a presentation points beyond itself to another presentation. The latter gains a new inner character that it otherwise could not have. It is the character of the specific ‘intention’, that is, of teleological directedness, of being-intended, of meantness” (p. 118).

Here we have a genesis in passive synthesis of the famous Husserlian intentionality.

“For want of terms at our disposal, we will avail ourselves of the apposition, ‘passive’, passive intention. And from here on we will speak only of passively intending presentations. At the outset we also want to name the synthesis in which this intention arises: associative synthesis” (pp. 118-119).

I am not greatly enamored of this use of “passive” for something that is really only relatively more passive than something else, but for this exposition I’ll continue following Husserl and use it. I prefer “preconscious”.

We’ll hear much more about the associative synthesis associated with directedness and intentionality later on. For now, it’s worth remarking that its very characterization as a form of synthesis separates it from the more common psycho-physical causal notion of association.

“Indeed, even retentions, those emerging originally, synthetically cohere with one another and with the primordial impression, but this synthesis proper to original time-consciousness is not a synthesis of association; retentions do not arise through an associative awakening directed backward from the impression, and thus, they do not have in themselves a directedness radiating out from there toward the emptily presented past” (p. 119).

Here we have a sharp distinction between the synthesis responsible for our experience of the flow of time and the associative synthesis that generates intentionality.

“I said that retentions, as they arise in their originality, have no intentional character. This does not rule out that in certain circumstances and in their own way they can assume this intentional character later…. Now, how does a retention get this oriented structure? By a subsequent association, of course” (p. 120).

Neoplatonic Critique of Identity?

A common theme of much 20th century continental philosophy was criticism of presumed identities of people and things. Writers like Theodor Adorno and Michel Foucault, to name but two, systematically questioned the role of identity in our understanding of the world. Edmund Husserl had recommended suspending judgments of existence in favor of the concrete description of essences; starting especially from a historiographical point of view, Foucault recommended suspension of judgments of pre-existing unity in favor of a concrete description of differences.

Later neoplatonism like that of Proclus (412-485 CE) is commonly associated with an extreme “realist” multiplication of metaphysical entities that implicitly had their own presupposed identities. The positive side of this is a rich view of differentiation metaphysically underpinning the diversity of concrete being. But the neoplatonic technical term hypostasis is the etymological source of our verb “to hypostasize”, which basically means to attempt to artificially impose more unity on something than it really has.

But especially if we go back to Plotinus (204/5 – 270 CE), and also in later authors, there is a strong strand of what might be called “negative henology” in neoplatonism. Plotinus was the main originator of so-called negative theology in the West. Negative theology indirectly gives meaning to the notion of transcendence by pointing out how every definite description falls short of adequately characterizing God. Hen is Greek for “one”, so by analogy with negative theology, a negative henology would be an account of how everything falls short of the pure unity of the One — in other words, how things that we think of as pre-existing unities are less unified than we suppose.

Hand in hand with this perspective comes the recognition that unity has many degrees. There are a few strong unities and many weak ones, and many degrees in between. As Plotinus recognized, nothing real has the pure unity of the One. (See also Power of the One?Plotinus Against the Gnostics; Subjectivity in Plotinus.)

Logic for People

Leading programming language theorist Robert Harper refers to so-called constructive or intuitionistic logic as “logic as if people mattered”. There is a fascinating convergence of ideas here. In the early 20th century, Dutch mathematician L. E. J. Brouwer developed a philosophy of mathematics called intuitionism. He emphasized that mathematics is a human activity, and held that every proof step should involve actual evidence discernible to a human. By contrast, mathematical Platonists hold that mathematical objects exist independent of any thought; formalists hold that mathematics is a meaningless game based on following rules; and logicists argue that mathematics is reducible to formal logic.

For Brouwer, a mathematical theorem is true if and only if we have a proof of it that we can exhibit, and each step of that proof can also be exhibited. In the later 19th century, many new results about infinity — and infinities of infinities — had been proved by what came to be called “classical” means, using proof by contradiction and the law of excluded middle. But from the time of Euclid, mathematicians have always regarded reproducible constructions as a better kind of proof. The law of excluded middle is a provable theorem in any finite context. When the law of excluded middle applies, you can conclude that if something is not false it must be true, and vice versa. But it is not possible to construct any infinite object.

The only infinity we actually experience is what Aristotle called “potential” infinity. We can, say, count a star and another and another, and continue as long as you like, but no actually infinite number or magnitude or thing is ever available for inspection. Aristotle famously defended the law of excluded middle, but in practice only applied it to finite cases.

In mathematics there are conjectures that are not known to be true or false. Brouwer would say, they are neither true nor false, until they are proved or disproved in a humanly verifiable way.

The fascinating convergence is that Brouwer’s humanly verifiable proofs turn out also to exactly characterize the part of mathematics that is computable, in the sense in which computer scientists use that term. Notwithstanding lingering 20th century prejudices, intuitionistic math actually turns out to be a perfect fit for computer science. I use this in my day job.

I am especially intrigued by what is called intuitionistic type theory, developed by Swedish mathematician-philosopher Per Martin-Löf. This is offered simultaneously as a foundation for mathematics, a higher-order intuitionistic logic, and a programming language. One might say it is concerned with explaining ultimate bases for abstraction and generalization, without any presuppositions. One of its distinctive features is that it uses no axioms, only inference rules. Truth is something emergent, rather than something presupposed. Type theory has deep connections with category theory, another truly marvelous area of abstract mathematics, concerned with how different kinds of things map to one another.

What especially fascinates me about this work are its implications for what logic actually is. On the one hand, it puts math before mathematical logic– rather than after it, as in the classic early 20th century program of Russell and Whitehead — and on the other, it provides opportunities to reconnect with logic in the different and broader, less formal senses of Aristotle and Kant, as still having something to say to us today.

Homotopy type theory (HoTT) is a leading-edge development that combines intuitionistic type theory with homotopy theory, which explores higher-order paths through topological spaces. Here my ignorance is vast, but it seems tantalizingly close to a grand unification of constructive principles with Cantor’s infinities of infinities. My interest is especially in what it says about the notion of identity, basically vindicating Leibniz’ thesis that what is identical is equivalent to what is practically indistinguishable. This is reflected in mathematician Vladimir Voevodsky’s emblematic axiom of univalence, “equivalence is equivalent to equality”, which legitimizes much actual mathematical practice.

So anyway, Robert Harper is working on a variant of this that actually works computationally, and uses some kind of more specific mapping through n-dimensional cubes to make univalence into a provable theorem. At the cost of some mathematical elegance, this avoids the need for the univalence axiom, saving Martin-Löf’s goal to avoid depending on any axioms. But again — finally getting to the point of this post — in a 2018 lecture, Harper says his current interest is in a type theory that is in the first instance computational rather than formal, and semantic rather than syntactic. Most people treat intuitionistic type theory as a theory that is both formal and syntactic. Harper recommends that we avoid strictly equating constructible types with formal propositions, arguing that types are more primitive than propositions, and semantics is more primitive than syntax.

Harper disavows any deep philosophy, but I find this idea of starting from a type theory and then treating it as first of all informal and semantic rather than formal and syntactic to be highly provocative. In real life, we experience types as accessibly evidenced semantic distinctions before they become posited syntactic ones. Types are first of all implicit specifications of real behavior, in terms of distinctions and entailments between things that are more primitive than identities of things.

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.

Taking “Things” as True

The second standpoint examined by Hegel in the Phenomenology is Perception, or in the literal etymological sense of the German word for it, “true-taking”. This etymology has an intriguing but probably accidental resonance with the notion of taking things as thus-and-such that Brandom emphasizes in Kant. In Perception, emphasis is more on the things than on the taking.

Harris in his commentary associates Perception with the philosophy of healthy common sense. Even the peasant woman of the previous chapter “must follow the ‘leading’ of language at least one step beyond the naming of [things]. She identifies her cows not just by their names, but by their color-patterns; and she knows her apple trees from her plum trees or her neighbor’s peach, etc. Hers is a world not just of singular [things], but of perceptible types; but for her, the process of classification with its universal names is an instrumental shorthand for dealing with the ‘real things’ that can be identified and pointed to. She does not want to take the leading of language seriously, but only to get back to her life, and to get on with it” (Hegel’s Ladder I, p. 238).

Perception at least begins to take up the nuances of how things interrelate that are ignored by sense certainty. “Sense-Certainty is rich only in positive things to be certain of…. Only perception can say what is, because it names universal things that are perceived through the changing sequence and variety of their properties”(p. 239). “Perception is the being grasped together of the moments that unfold in perceiving as process…. The perceiving we are concerned with is a process in which the universal self takes itself to be a rational being, and the truth of its object to be a universal truth” (p. 238). By “universal self” he means an individual self taken as an instance of a rational self, not anything like a world soul.

Harris continues, “Our situation as philosophical observers is different in its ‘object’ from the perceiving consciousness. Our object has been logically determined for us, whereas the object of the perceiving consciousness simply ‘falls out of the world of Sense-Certainty’ for it… It knows that the object is a universal essence; but it does not know that ‘universality’ is an activity of the perceiving mind” (pp. 238-239).

We know that the ‘thing’ is a result of this process…. Our perceiving is the process, of which the object is the result. Perception… is an interpretation of sense-certainty in which the knowing consciousness is no longer concerned about the truth of the copula ‘is’, but about what is…. Sense-Certainty was already implicitly perception in its examples” (p. 239).

He quotes Hegel saying “Being is a universal in virtue of having mediation or the negative in it” (p. 240). As Harris says a bit later, “There is no nameable property of anything that is not part of a range of alternative properties. Some variations of properties are consistent with the thing continuing to count as the ‘same thing’ — and some are not” (ibid).

“[T]he singular property of ‘being salt’ is known to us as immediate sensation only when we taste it (and that is when the salt itself is necessarily dissolved back into the flux of sense-immediacy). Thus, in the white cube that is the ‘thing’ I perceive, the character of being salt is a not-this; it is not immediately sensed, but it is stably preserved for the sensation whenever I want to sense it…. It is a potentiality for sensation…. As this potentiality, this ‘otherness’ than what it is (the cubical whiteness etc.), it is a universal” (pp. 240-241).

(I am delighted to see Harris stressing the importance of potentiality in this crucial transition out of immediacy in Hegel. I don’t recall Hegel using the word “potentiality” much, but thought he ought to have.)

“What is ‘truly taken’ is an essence that is the negative ‘property’ which determines and holds together all the positive ones. But it is also truly taken as the positive property of filling a certain space. All of the properties cohere together in the space that the thing occupies…. ‘Thinghood’ as directly given for perceiving is the persisting spatial togetherness of many independent qualities…. The ‘thing’ is not just a loose collection of properties inhering somehow in the same identifiable region of space at the given time. It is a thing because of what it excludes; and its exclusiveness is what particularizes each of its properties” (p. 241).

“I know that I do not passively perceive what is true, in the way that I seem to apprehend the fact that ‘this is Lisa, and this is Ursel’ passively. My reflective capacities are involved. Perceiving is an activity of consciousness” (p. 245). “But it ought to be consistent” (p. 246).

“The attempt to claim that the manifold of sensation is simply subjective ignores its interpersonal objectivity. Every identifiable property is an objective essence…. Not just the oneness of the thing is objectively real, but its ‘difference’ from everything else” (p. 247).

“The essence of being a thing is to be ‘for another'” (p. 249). “Everything is specified by its difference from others” (p. 250). “The determinacy which is the ‘essential’ or ‘absolute’ character of a thing on its own account is essentially a relation to others (which negates the thing’s independence)” (p. 251).

Here we begin to see the limits of Perception. “The standpoint of Perception presupposes an absolute community of ‘things’. But the definition of ‘thinghood’ that the perceptual consciousness set up for itself contains no necessary reference from one thing to another for its being. The independent being of the thing is what makes it the ‘object’ that can be ‘truly taken’…. We have now seen that in any consistent formulation of the perceptual standpoint, this is logically impossible. It is the independence that is a sham” (p. 252).

“What is ‘essential’ and what is not ‘essential’ is a function of our supposedly external observation” (p. 253).

“Hegel… aims to show us that the naive empiricism which wants to conceive of perception causally (as analogous to mirror-reflection) cannot succeed.”

“We have already seen how we could not stand still at the concept of the ‘one thing’ with ‘many properties’. We had to admit that the multiplicity was founded in the ‘thing’, and not simply generated by the perceiving mind; and on the other hand, the ‘unity’ was an actively negative exclusion, which could not be simply contributed by the mind as it sorted the perceived ‘properties’ into things” (p. 254).

The standpoint of perception treats logic and philosophy as mere “game[s] with verbal counters” (p. 256). Its mistake is “to assume that ‘cognition’ is an activity that supervenes on an object that is already there; but actually it is the construction of ‘the object’ in a process of interpretation” (p. 257).

Ricoeur on Locke on Personal Identity

“John Locke is the inventor of the following three notions and the sequence that they form together: identity, consciousness, self…. Locke’s invention of consciousness will become the acknowledged or unacknowledged reference for theories of consciousness in Western philosophy” (Ricoeur, Memory, History, Forgetting, p. 102).  The English word “consciousness” was actually coined by Locke’s friend the Cambridge Platonist Ralph Cudworth in a work inspired by Plotinus, but it is Locke’s systematic use of it that was spread throughout the modern world by his famous Essay Concerning Human Understanding.  Ricoeur’s account significantly draws on that of Etienne Balibar in Identity and Difference: Locke’s Invention of Consciousness.

Chapter 27 of book 2 of Locke’s Essay, “Of Identity and Diversity”, lays out his unprecedented new theory of personal identity as grounded purely in a continuity of memory, rather than any underlying substance.  We tend to forget that Descartes’ cogito, as Ricoeur says, “is not a person….  It bursts forth in the lightning flash of an instant.  Always thinking does not imply remembering having thought.  Continual creation alone confers duration on it” (p. 103).  Ricoeur says that whereas Descartes had sought to conquer doubt with certainty, Locke sought to conquer diversity and difference with an unprecedented concept of pure reflexive identity.

“Proposing to define in new terms the principle of individuation… ‘so much inquired after’…, Locke takes as his first example an atom, ‘a continued body under one immutable superficies’, and reiterates his formula of self-identity: ‘For being at that instant what it is, and nothing else, it is the same, and so must continue as long as its existence is continued; for so long it will be the same, and no other’” (p. 104).

“It is consciousness that constitutes the difference between the idea of the same man and that of a self, also termed person…. The knowledge of this self-identity is consciousness” (ibid).  Locke is quoted saying “as far as this consciousness can be extended backwards to any past action or thought, so far reaches the identity of that person; it is the same self now as it was then; and it is by the same self with this present one that now reflects on it, that that action was done” (p. 105).  

Ricoeur continues, “Personal identity is a temporal identity.  It is here that the objection drawn from forgetting and from sleep, considered as interruptions of consciousness, suggests the invigorated return of the idea of substance: is not the continuity of a substance required to overcome the intermittence of consciousness? Locke replies bravely that, whatever may be the status of the substantial ground, consciousness alone ‘makes’ personal identity….  Identity and consciousness form a circle.  As Balibar observes, this circle is not a logical fallacy of the theory: it is Locke’s own invention, supported by the reduction of substance…. It is not the soul that makes the man but the same consciousness.  With regard to our inquiry, the matter has been decided: consciousness and memory are one and the same thing, irrespective of any substantial basis.  In short, in the matter of personal identity, sameness equals memory” (ibid).

The word “self” is used by Locke in both generic and singular senses, with “no discussion concerning the status of the nominalized pronoun….  Locke had decided to disconnect ideas from names.  Yet, ‘Person, as I take it, is the name for this self’” (p. 106). “The shift to a judicial vocabulary is not far off.  The transitional concept is that of ‘person’, the other ‘name for this self’…. What makes it a synonym for the self, despite its ‘forensic’ character?  The fact that it signifies that the self ‘reconciles’ and ‘appropriates’, that is to say, assigns, allocates to consciousness the ownership of its acts” (p. 107).

Locke thus not only completely rethought the notion of persons in terms of a pure logical identity in consciousness and an analogy with atoms in a void, but also formulated a radically new notion of ethical agency and responsibility, based on an analogy with the exclusive ownership associated with private property.  The ownership model of agency and responsibility leaves no room for more subtle considerations of “power to”.  Indeed, Ricoeur notes that Locke’s approach to politics is entirely grounded in “power over”.

From a purely logical standpoint, Locke successfully avoids many arguments against the putative total self-transparency of consciousness, by making its self-transparency a matter of definition rather than an empirical claim.  Locke’s position is internally consistent.  From a practical standpoint, however, any claim that total self-transparency actually applies to real life is, to say the least, fraught with difficulty.  Total self-transparency seems to me to be more extravagantly supernatural than the Latin medieval notion of a substantial intellectual soul that it replaced.  Also, real people are not atomic unities. From the point of view of more recent physical science, even atoms are not atomic unities. (See also Ego; Personhood; Meaning, Consciousness; Mind Without Mentalism; Aristotelian Identity; Narrative Identity, Substance; Ricoeur on Memory: Orientation; Ricoeur on Augustine on Memory.)

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.)

Narrative Identity, Substance

Narrative identity for Ricoeur is intended as a kind of mean between ordinary logical identity or sameness, which he calls idem identity, and a kind of mediated reflexivity, which he calls ipse identity. Ordinary logical identity is rigid and static, but worse than that, it is often taken for granted. On the cutting edge of its home ground of mathematics, however, it has become recognized that criteria for logical identity of each type of thing need to be explicitly defined. Logical identity then effectively reduces to isomorphism. Sameness effectively reduces to sameness of form, and Leibniz’s thesis of the indiscernability of indiscernability and identity is vindicated.

I have argued, however, that Aristotle’s notion of identity as applied to so-called “substance” not only implicitly anticipates this thesis of Leibniz, but also ultimately circumscribes it with a further processual dimension accommodating continuity through change over time. Independent of the considerations of narrative developed by Ricoeur but potentially interpretable in similar terms, the “identity” of a “substance” for Aristotle is already extended to continuity through change. This kind of situationally appropriate, delimited relaxation of identity criteria allows Aristotle to accommodate “realistic” nuances in the application of common-sense reasoning or material inference that cannot be justified by purely formal logic. Judgments of real-world “identity” are practical judgments, with all the usual caveats.

While Aristotle was very process-oriented, the processes with which he was concerned were short- and medium-term processes, generally not extending beyond the scope of a life. History for Aristotle is mainly an accumulation of accidents, and thus in Aristotle’s sense intelligible mainly in the register of materiality. To the extent that he thinks about history, he treats it in terms of delimited “histories” rather than an enveloping “History”.

Within that accumulation of accidents, however, we can potentially explicate other levels Aristotle left unexplored, like Ricoeur’s historical explanation or Foucault’s “archaeology”. Foucault developed a meta-level account aimed at articulating underlying forms implicit in something like Aristotle’s delimited accumulations of accidents, while I think that after the detour of historical explanation, Ricoeur ultimately wanted to cultivate signposts for an enveloping “History” as metaphors expressing a broader “meaning of life”. In a very general way, Ricoeur’s aim thus resembles Brandom’s “Hegelian genealogy”.