Structure, Potentiality

I now want to say, structure — which statically captures a determinate field of potential inferences — is isomorphic to Aristotelian potentiality. These concepts are mutually illuminating.

This helps clarify how Aristotelian potentiality differs from the Platonic power referenced by the same Greek word, as well shedding light on the association I have made between potentiality and counterfactual inference.

From the other direction, the thing to notice is that for Aristotle, potentiality exists only in a pair with actuality or at-work-ness. Similarly, synchronic structure exists only in a pair with diachronic process. I always read the conspicuous lack of definition of the synchronic/diachronic interface as reflecting something like Aristotle’s principled use of underdetermination in order to focus on what is most essential and clearly justifiable.

A lot of people seem to have been very confused about this latter point during the drama over 1960s French structuralism. What passed for dialogue was often a complete disconnect. “Look at how much can be explained synchronically!” “Oh no, you’re abolishing history, free will, personality, and identity!” If the new viewpoint was forgivably one-sided in its enthusiasm, some of the reaction verged on hysteria. (See also The Dreaded Humanist Debate.)

Another source of confusion seems to be that many people apparently thought of structural causality in terms of a monolithic, complete determination. I think instead that structural causality comes in many separate blocks, in an overall context of less-than-complete determination. (See also Structural Causality, Choice; Values, Causality; The Importance of Potentiality.)

Structuralism

As a very youthful person in the 1970s, I was delighted to discover support for “my” thesis that relations are prior to things (and much else of interest) in the French writers associated with so-called structuralism. (The Anglophone comparative literature people had not yet invented “poststructuralism”.) There have been many structuralisms and attributions thereof over the years. I tend to be sympathetic to a lot of them — mathematical, linguistic, and historiographical.

From my current perspective, the unifying theme is that structure — of whatever sort —statically captures a field of potential inferences. Fields of potential inference are the basis on which diverse things such as mathematical theories, proprieties of linguistic usage, practices and practical attitudes of individuals, and large cultural formations are all constituted as determinate. I actually use a variant of the notion of static capture in my day job, at the mundane level of capturing potential inferences in a software or data model. (See also Difference; Althusser’s Hegel; Foucault; Empirical-Transcendental Doublet; Archaeology of Knowledge; 1968; Imaginary, Symbolic, Real; Immediacy, Presence; Ricoeur on Structuralism; Genealogy.)

In Aristotelian terms, in addition to structure’s connection with potentiality, what has been called structural causality is actually a good interpretation of efficient causation, and also turns out to look like the operation of an unmoved mover. (See also Structure, Potentiality; Efficient Cause, Again; Potentiality, Actuality; Values, Causality.)

Leibniz

Leibniz was one of the greatest minds ever — deeply original, vastly prolific, encyclopedic like Aristotle, but working in the ferment of early modernity. He formulated many differently detailed systems, in an exploratory and tentative way. What he published during his lifetime was only a tiny fraction of his output, and not fully representative of his thought. The critical edition of his collected works will not be completed for many decades yet to come.

Leibniz favored an ethical and political ideal of what he called wise charity. An ethical being is one who does more for others than is required to satisfy rights and responsibilities or social contract, and demands less of others than would be justified, while taking care to act in ways that are sustainable and not self-destructive. I like this very much.

An avowed Lutheran who cultivated extensive dialogue with Catholic scholars and religious leaders, Leibniz was deeply disturbed by Europe’s terrible religious wars. He sought to promote tolerance, diplomacy, and understanding.

As a Platonist in theology who stressed the importance of Plato’s Euthyphro, Leibniz said that God is first and foremost supposed to be good and reasonable, not just obeyed. His God would never say “…because I said so!” Leibniz was highly sensitive to the dangers of subordinating Reason and the Good to any kind of arbitrary Will, be it divine or political. To those who objected that this limited God’s power, he replied that attributing an arbitrary will to God would degrade God to a mere tyrant and despot rather than a good and wise ruler (see Leibniz on Justice vs Power).

Leibniz partly anticipated Einstein in saying that space and time are relations.

He held that mathematical physics of the sort he helped develop was fundamentally compatible with — and complementary to — what I have referred to as Aristotle’s semantic physics.

He argued for what I take to be the Aristotelian position that identity is just discernibility.

Leibniz defended the principle of sufficient reason (cleverly phrased by the scholastics as “nothing comes from nothing”). At the same time, he held that all necessity is of the hypothetical (if-then) variety, which means that nothing is unconditionally necessary, either.

The famous monads apply his pioneering work on infinite series to an inspiration from his friend Leeuwenhoek’s discovery of microscopic organisms. On the one hand, each monad is supposed to be a self-contained microcosm of the entire universe; on the other hand, each monad contains many others that each contain many others that are also such microcosms (each with its own unique point of view on the whole), and so on to infinity. (See also Unity of Apperception.) Leibniz also had a fascinating theory of unconscious microperceptions.

Monads are said not to causally interact, but instead to mutually reflect one another in a purely synchronic way. For Leibniz, it is as though in reality everything has always already happened. It all comes down to one eternal act of God selecting the best of all possible already completely formed worlds. His thesis of the unreality of interaction seems bizarre and was never widely accepted, but the idea of synchronic mutual reflection is fascinating. (This is quite different from the pattern of determination in Hegelian mutual recognition, which has a substantial synchronic dimension but is based on interaction and has an irreducible diachronic component.) (See also Things In Themselves; Redding on Morals and Modality.)

I think Leibniz’s preformationism may be intended as a kind of edifying Platonic myth, but that is a side issue. Its practical consequence is a vision of determination and explanation by synchronic structure rather than sequential causality. Like most people, I think we also need a diachronic, interactive dimension. However, the possibilities of synchronic structural explanation are huge.

Leibniz controversially argued that we live in the best of all possible worlds. Whether or not we adopt such a view, it is important to understand that it was not nearly as naive as Voltaire’s famous satire made it out to be. For Leibniz, the criteria for a possible world are rather rigorous. A possible world is certainly not just any world we might idly imagine. All its details and all their realistic consequences must be able to coherently coexist.

Brandom has characterized Leibniz as an early inferentialist. In English, recent secondary literature is far better than most older accounts. In French, I was impressed by Yvon Belaval’s Leibniz, critique de Descartes (1960) and his student Michel Serres’ dissertation Le Système de Leibniz et ses modèles mathémathiques (1968).

Categorical “Evil”

If we are aiming at any kind of true unity of apperception, then in any given logical moment we should aim to reason in ways that are invariant under isomorphism. Over time our practical and theoretical reasoning may and will iteratively change, but synchronically we should aim to ensure that reasoning about equivalent things will be invariant within the scope of each iteration.

In higher mathematics, difficulties arise when one structure is represented by or in another structure that has a different associated notion of equivalence. This requires maintaining a careful distinction of levels. The expected consequence relation for the represented notion may not work well with the representation. Such failures of reasoning to be invariant under isomorphism are informally, half-jokingly referred to by practitioners of higher category theory as “evil”. This is a mathematical idea with a clear normative aspect and a very high relevance to philosophy.

The serious slogan implied by the half-joke is that evil should be avoided. More positively, a principle of equivalence-invariance has been articulated for this purpose. One version states that all grammatically correct properties of objects in a fixed category should be invariant under isomorphism. Another states that isomorphic structures should have the same structural properties. On the additional assumption that the only properties of objects we are concerned with are structural properties, this is said to be equivalent to the first.

There are numerous examples of such “evil”, usually associated with uncareful use of equality (identity) between things of different sorts. A significant foundational one is that material set theories such as ZFC allow arbitrary sets to be putatively compared for equality, without providing any means to effect the comparison. Comparison of completely arbitrary things is of course is not computable, so it cannot be implemented in any programming language. It is also said to violate equivalence invariance, which means that material set theories allow evil. The root of this evil is that such theories inappropriately privilege pre-given, arbitrary elements over definable structural properties. (This issue is another reason I think definition needs to be dialectically preserved or uplifted in our more sophisticated reflections, rather than relegated to the dustbin in favor of a sole emphasis on recollective genealogy. A concern to define structures and structural properties of things appears in this context as the determinate negation of the effective privileging of putatively pre-given elements over any and all rational considerations.) ZFC set theory offers a nice illustration of the more general evil of Cartesian-style bottom-up foundationalism.

The evil-generating supposition that utterly arbitrary things can be compared (and that we don’t need to care that we can’t even say how this would be accomplished) implicitly presupposes that all things whatsoever have a pre-given “Identity” that is independent of their structural properties, but mysteriously nonetheless somehow contentful and somehow magically immediately epistemically available as such. This is a mathematical version of the overly strong but still common notion of Identity that I and many others have been concerned to reject. Such bad notions of Identity are deeply involved with the ills of Mastery diagnosed by Hegel and Brandom.

We should not allow evil in foundations, so many leading mathematicians interested in foundations are now looking for an alternative to the 20th century default of ZFC. Some combination of dependent type theory for syntax with higher category theory for semantics seems most promising as an alternative. The recent development of homotopy type theory (HoTT) is perhaps the most vigorous candidate.

Another way to broadly characterize this mathematical “evil” is that it results from treating representation as prior to inference in the order of explanation, as Brandom might say, which means treating correspondence to something merely assumed as given as taking precedence over coherence of reasoning. This is a variant of what Sellars famously called the Myth of the Given. It is a philosophical evil as well as a mathematical one. Besides their intrinsic importance, these mathematical issues make more explicit some of the logical damage done by the Myth of the Given.

Another broad characterization has to do with mainstream 20th century privileging of classical logic over constructive logic, of first-order logic over higher-order logic, and of model theory over proof theory. Prior to the late 19th century, nearly all mathematics was constructive. Cantor’s development of transfinite mathematics was the main motivation for mathematicians to begin working in a nonconstructive style. Gödel’s proof that first-order logic was the richest logic for which all propositions that are true in all models are also true was thought to make it better for foundational use. Logical completeness and even soundness are standardly defined in ways that privilege model theory, which is the formal theory of representation.

It is now known, however, that there are several ways of embedding and representing classical logic — with no loss of fidelity — on a constructive foundation, so the old claim that constructive logic was less powerful has been refuted. Going in the other direction, however, classical logic has no way of recovering the computability that is built into constructive logic once it has been violated, so it is increasingly recognized that a constructive logic provides the more flexible and comprehensive starting point. (Also, transfinite mathematics can reportedly now be given a constructive foundation under HoTT.)

Since the mid-20th century there has been an immense development of higher-order concepts in formal domains, including mathematical foundations; the theory of programming languages; and the implementation of theorem-proving software. Higher-order formalisms offer a huge improvement in expressive power. (As a hand-waving analogy, imagine how hard it would be to do physics with only first-order equations.)

Type theory, proof theory, and the theory of programming languages are kinds of formalism that put inference before pre-given representations. Category theory seems to take an even-handed approach.

Although I noted some interest in Brandom on the part of people working in a higher-order constructive context, Brandom himself seems much more interested in things that would be described by paraconsistent logics, such as processes of belief revision or of the evolution of case law or common law, or of normativity writ large. (In the past, he engaged significantly with Michael Dummett’s work, while to my knowledge remaining silent on Dummet’s arguments in favor of the philosophical value of constructive logic.)

Paraconsistency is a property of some consequence relations, such that in absence of an explicit assumption that from a contradiction anything follows, not everything can in fact be proven to follow from a given contradiction, so the consequence relation does not “explode” (collapse into triviality).

In view of the vast proliferation of alternative formalisms of all sorts since the mid-20th century, it may very well be inappropriate to presume that we will ever get back to one formalism to rule them all. I do expect that homotopy type theory or something like it will eventually come to dominate work on mathematical foundations and related aspects of computer science (and everything else that falls under Hegelian Understanding, taken as a positive moment in the larger process); but as hugely important as I think these are, I am also sympathetic to Brandom’s Kantian/Hegelian idea that considerations of normativity form an outer frame around everything else, as well as to the Aristotelian view that considerations of normativity tend to resist formalization.

On the formal side, it seems it is not possible to synchronically reconcile HoTT with paraconsistency, which would seem to be a problem. (At the opposite, simple end of the scale, my other favorite logical mechanism — Aristotelian syllogism interpreted as function composition — apparently can be shown to have a paraconsistency property, since it syntactically constrains conclusions to be semantically relevant to the premises.)

Diachronically, though, perhaps we could paraconsistently evolve from one synchronically non-evil, HoTT-expressible view of the world to a dialectically better one, while the synchronic/diachronic distinction could save us from a conflict of requirements between the respective logics.

I think the same logical structure needed to wrap a paraconsistent recollective genealogy around a formal development would also account for iterative development of HoTT-expressible formal specifications, where each iteration would be internally consistent, but assumptions or requirements may change between iterations.

Actuality

Aristotelian energeia — traditionally translated as actuality — captures the status of being active or effectively operative in a process. I have somewhat awkwardly rendered it as “at-work-ness”. “Being-at-work” sounds like better English, but might wrongly be taken to refer to a kind of Being in the intransitive sense qualified by a predicate of at-work-ness. (I think Aristotle was in fact very little interested in Being in an intransitive sense. He devotes much more attention to several transitive senses.) There is no “being” at all in the Greek. Energeia is most literally “in-work-ness”, but I and others have preferred to substitute “at” for “in”, as better conveying the intended connotation in English.

Contrary to Plato’s doubts about the possibility of understanding becoming, Aristotle is committed to eliciting its intelligibility. Rather than looking for generative powers behind things as Plato had obscurely suggested might be our best hope, part of Aristotle’s strategy is to draw our attention to what is immanently at work in a process as a kind of methodological starting point. The discernment of what it was to have been such and such a thing begins from the indistinct apprehension of something we merely take to have been effectively operative. (That something would be a mediated immediacy in Hegelian terms.) It is eventually constituted with greater precision and a degree of universality through inferential elaboration of the counterfactual potentiality of what we initially took to have been effectively operative, as well as through the implicit correction over time of errors that become apparent in the course of this elaboration.

Worlds away from the dry stereotype of “essentialism”, Aristotle is if anything more of a process thinker or pragmatist. He directs our attention to the concrete actualization of things, which “essentially” involves the interweaving of effectively operative actuality with both counterfactual potentiality and material contingency. Hegel makes large use of this Aristotelian concept. Brandom associates Hegelian actualization with expression and making explicit.

There is a very interesting distinction suggested by Aristotle and developed by later writers between a “first” and “second” actuality. Whereas the first actuality of an organic body is not too far from the later Stoic conatus as an internal source of primitive desiring activity, second actuality applies to things associated with evolved practice like habit, character, and intellect.

Aristotle also speaks about the “First” cause as pure at-work-ness, with no admixture of potentiality. I take this to mean that the “First” cause — just as the higher-order goal at which everything indirectly aims — is effectively operative in things, but unlike other effectively operative things, it has no counterfactual aspect (because it has no factual aspect, because it exactly is a pure aim rather than something having an aim). It functions as an ideal of normativity that we can retroactively see to have been at work, as a sort of virtual, uplifting attractor of purely natural desire, and also more speculatively as a posited virtual attractor for the directionality in material tendencies. (See also Aristotelian Actualization; Moved, Unmoved.)

Identity, Isomorphism

Many strands of Western thought — from Augustinian theology to Cartesianism to set theory — have suffered from overly strong notions of what amounts to a privileged, originary, self-evident, contentful Identity of things. (There are also many significant exceptions. With their emphasis on distinctions of form, Plato and Aristotle only needed a weak identity. Spinoza’s emphasis on relations; Leibniz’s identity of indiscernibles; Hume’s dispersive empiricism; and Kant’s critical perspective are all closer to Plato and Aristotle in this regard. Hegel makes identity derivative from a Difference associated with Aristotelian contrariety or Brandomian material incompatibility. Nietzsche, Wittgenstein, and many 20th century continentals explicitly criticized the overly strong concept.)

21st century mathematics has seen tremendously exciting new work on foundations that bears on this question. Homotopy type theory very strongly suggests among other things that the identity needed to develop all of mathematics is no stronger than isomorphism. This provides a formal justification of the common practical attitude of mathematicians that isomorphic structures can be substituted for one another in a proof by an acceptable “abuse of notation”.

More generally, type theory and category theory provide an independent basis in contemporary mathematics for reaffirming the priority of form as difference over identity. I am tempted to say that they exemplify a kind of inferentialism in mathematics. (To those who say mathematics holds no lessons for philosophy, I would say that generalization disregards the specific character of these developments. nLab, the website for higher category theory, even has a page on Hegel’s logic as a modal type theory that explicitly refers to Brandom’s interpretation of Hegel!)

Matter, Potentiality

I’ve suggested nonstandard readings of both Aristotelian matter and Aristotelian potentiality. While traditionally there is thought to be a loose analogy such that matter is to form as potentiality is to actuality, the two concepts as I am reading them are sharply distinct. Matter captures the accumulation of contingent fact. Potentiality captures counterfactually robust inference. Matter particularizes, while potentiality universalizes.

Potentiality seems to me to be a kind of form. This is a bit tricky, because an important classical sense of Aristotelian matter that I have not been emphasizing is associated with a disposition to respond in certain ways when acted upon. This, however, sounds like counterfactual potentiality to me.

Objectivity

“Objectivity” is said primarily of some shapes of subjectivity that have a high degree of universality. It could not mean simple passive assimilation of an object just as it was supposed to be. The path to universality lies through a robustness or resilience of inferences across counterfactual cases. Universality and objectivity are closely tied to considerations of all kinds of appropriateness in particular cases.

Universality is inherently a journey through many things, not a destination. The objectivity of objects is derivative from such an open, free process of interaction with material contingency, governed by an end of unity of apperception and mutual recognition. (See also Truth, Beauty.)

Instances of consideration of objectivity in particular contexts appear throughout the Ethics; Reason; Semantics; Historiography; Philosophy of Math etc. sections here.

Historically, there has been a near reversal of the meaning of the term “objective”.

Definition

The deeper Hegelian truth of a conceptual content can only be approached diachronically, via a historical recollective expressive genealogy. But in passing in the course of his world-historically groundbreaking interpretation, Brandom says Hegel rejects the very possibility of conveying a conceptual content by defining it, without saying what definition is or elaborating on what this denial means for the status of definition (Spirit of Trust, p.7). I find this to be ambiguous, and potentially a little misleading. At least within any given synchronic context and to some extent even more broadly, I believe definition in the sense of an Aristotelian “what it is” still has a positive role to play. It would not be reasonable to suppose that Brandom really means to ban the philosophical use of definitions; otherwise, we would have an extreme nominalism incompatible with his stated goals, which include what he calls conceptual realism. (See also Abstract and Concrete.)

The ambiguity in the passage has to do with how strong a sense we give to “conveying”. We should not expect a run-of-the-mill definitional representation to literally convey conceptual (inferential) content in its explicit form. But such a representation absolutely does address or concern conceptual content, and therefore can still “convey” that content in the weaker sense of referring to it or reliably picking it out. (We could also atypically construct definitions in terms of explicit material incompatibilities and consequences. These would presumably in a stronger sense convey the conceptual content isomorphic to them. We could even atypically construct definitions in terms of the current best expressive genealogy, so I don’t really see these as counterposed.)

I do not think Hegel would go so far as to deny the high pragmatic value of definition in synchronic contexts. This is part of the necessary moment(s) of determinacy (and Understanding) in the larger process of the development of Spirit. He just wants to make the larger point that diachronically, any realized ground-level definition is ultimately just a stopping point along the way. That does not mean we should not attempt to sum up the best understanding we have achieved at each moment. I think we are deontically obligated to do just that. Every ground-level definition is contextualized by its historical situation and therefore subject to change, but at every moment we should still strive to speak and act in accordance with the best definitions we can achieve. Representational clarity is imperfect and always dependent on other considerations in the background, but it is still a moment to be preserved.

We should distinguish the conceptual-content-related doing associated with developing a definition from the representation produced. Further, I find it difficult to separate a concern for definition from a methodological concern for problems of definition, as evinced by Plato and Aristotle for instance. From this perspective, definition has more to do with a line of questioning than a putative answer. The question of the “what” or conceptual content of things is actually far more substantial and interesting than those of mere fact or abstract existence. Even if it aims at a representation, definition as a practical task is all about inquiry into that whatness of things. The norm to which synchronic representation of whatness is responsible comes down to the best achievable view of the relevant difference and mediation, or material incompatibility and material consequence (as Brandom would put it) in the circumstances of that logical moment. This I think is actually independent of the diachronic moves of expressive genealogy.

Hegel’s “Substance that is also Subject” is explicitly presented as an extension of Aristotle’s (expressive meta) concept of ousia, and I think Aristotle anticipates even more than Hegel recognizes. (Expressive genealogy is distinctively Hegelian, but Substance certainly not, and Hegel himself notes in the History of Philosophy lectures that the concerns he groups under “Subject” were significantly addressed by Socrates, Plato, and Aristotle.)

If Brandom is right that Hegel intended to exclude such expressive metaconcepts from the general prognosis that all (ground-level) concepts eventually elicit their own negation, then it is at least logically possible that Aristotle’s metaconcept had already achieved the requisite stability to be incorporated by Hegel without negating the subordinate aspect of ousia that for Aristotle corresponds to a definition.

Without prejudice to claims about what Hegel added, I would argue that Hegel did in this way intend to incorporate all the multiple nuances of Aristotelian ousia, including the definitional one. With due respect for Brandom’s distinction between determination as Hegelian process and determinateness as Kantian/Fregean property (and the importance of the process as a superior point of view), I also think we need to forgivingly recollect all best attempts at determinateness. (See also Classification.)

I wonder what Brandom would say about the role of definitions in the articulation of mathematical conceptual content. The doing of mathematics seems to join the doing of history as problematic for simple subsumption under a genealogical approach as Brandom has described it. Mathematics needs definitions, and history needs to evaluate data without Whiggish filtering. (But Brandom does not exactly disallow either, and I can’t imagine that he would want to. The meaning of mathematical theorems can certainly be expressed in terms of material incompatibility and consequence, and the concepts used in non-Whiggish historiography could themselves be Whiggishly genealogically grounded.)

We should think about the functional inferential role of stipulative definitions, as well as the definitions of empirical concepts that I expect Brandom has foremost in mind. We could say that in both cases, the meaning sought by definition — as distinct from the definiens — is actually constituted through material incompatibility and material consequence. But a stipulative definition is a making rather than a taking. It in a sense starts a whole course of reasoning, whereas empirical concepts implicitly summarize results of reasoning.

Also, mathematical definition is mostly concerned with structures and structural properties. I believe a case could be made that in general, such structures and structural properties are expressive metaconcepts in much the same sense that logical concepts are.

I don’t think it’s historically right that expressive metaconcepts are a “discovery or invention” of German Idealism (p.5). Aristotle already had quite a few expressive metaconcepts, as at least partially exhibited in this blog. I believe Hegel himself recognized this.

Potentiality

Potentiality (dynamis) is yet another great Aristotelian expressive metaconcept. Plato had the intriguing idea of explaining things and states of affairs in terms of power (also dynamis), but left power as an unexplained explainer, and required it to be postulated as pre-existent. Aristotle thoroughly reconceptualized the term to eliminate these weaknesses. Every Aristotelian potentiality begins from actuality or at-work-ness.

Instead of referring to postulated powers behind things or abstract logical possibility, Aristotelian potentiality is a way of talking about the aspects of a conceptual content captured by what Brandom would call modally robust counterfactual inference. Such robustness of inference across counterfactual cases is implicitly central to the most elementary meaning of Aristotelian substance or “what it was to have been” a thing (ousia), as what grounds the weak unity that allows us to talk about the same “thing” persisting through time even though something about it changed.

The semantic importance of counterfactual inference in determining the sense of what things are is a thesis shared by Aristotle, Hegel, and Brandom. It is explicit in Brandom and Brandom’s Hegel, and implicit in Aristotle. We cannot even really form a view of any thing as a thing of a certain kind unless we at least implicitly consider its potentiality.

Aristotle was clear that potentiality is an irreducible ingredient in things, and potentiality clearly captures counterfactuals. Brandom has made the role of counterfactuals in the development of universality more explicit. Facts alone give us at best a very brittle structure of assertions with no real conceptual articulation or interpretation, so perspectives that try to ground things on facts alone are doomed to ultimate failure. (In this light, Nietzsche‘s elimination of potentiality also turns out to have been a very serious error.) Overly strong, question-begging notions of the Identity of things have helped obscure the vital role of counterfactual inference in stabilizing our experience of the world. (See also Modality and Variation.)

Tentatively mapping this to Brandom’s Fregean terminology, I think Aristotle would intend the relation of potentiality to actuality to be one of reciprocal sense dependence paired with asymmetrical reference dependence. That is to say, at a level of determination of meaning, potentiality and actuality are interdependent and equally important, but in the order of logical truth about representations, actuality or the concrete is the starting point in terms of which potentiality is evaluated. Potentialities are potentialities of some actuality. (See also The Importance of Potentiality; Potentiality, Actuality; Structure, Potentiality; Matter, Potentiality.)