Facts and Incomplete Information

A modern notion of hard-nosed common sense is to appeal exclusively to positive facts. This is also a major basis of simplistic notions of empirical science. Serious scientific methodologies are more indirect, and quite a bit more involved.

From a broadly Kantian point of view that I think Plato and Aristotle would also endorse, all putative facts are really just assertions of facts, made by people. The validity of the corresponding assertions depends on the soundness of the reasons that lead us to believe them. Thus, regardless of whether our concern is ethical or scientific, it is always the quality of reasons that matters in assessing the validity of assertions.

The notion of a fair and objective weighing of evidence for or against an assertion presupposes that we symmetrically consider the pro and con, as Plato emphasized in his discussions of “dialectic”. But the simplistic bias for positive facts results in an inherently asymmetrical treatment any time we have to deal with incomplete information, because what putative facts we currently have in our possession is in part a matter of sheer chance.

In a fact-biased approach, if there happen to be insufficient facts in our possession to adequately support a hypothesis, the hypothesis is likely to be be dismissed out of hand as “speculation”, regardless of how inherently plausible it might otherwise be. We end up assuming something is not true merely because we cannot empirically prove it is true. This is independent of any other prejudice that may also enter into situations involving human judgment.

Once again, I want to recommend a prudent suspension or qualification of belief in cases of incomplete information, rather than active disbelief. (See also Debate on Prehistory.)

Beauty and Discursivity

Plotinus was a huge inspiration for me in my youth. Revisiting a piece of his Enneads just now, I am again struck by the majesty of his thought and writing. These days I have a much more positive view of discursive reasoning, but I first wanted to let him speak for himself.

I still agree that there is far more to knowledge and understanding than an accumulation of propositions. But as a teenager, I definitely considered step-by-step reasoning to be something inferior to the kind of holistic intellectual intuition Plotinus emphasizes when he talks about Intellect. The latter I considered to be the true source of insight — “silent mind before talking mind”.

Nowadays, I think that kind of unitary vision is achievable only as the crowning result of much patient work. I no longer take it to be the original source that discursive reasoning imitates in an inferior way. Intellect or Reason does form a relational whole, and the whole is more important than the parts. But today I would emphasize that the relational whole is an articulated whole, and it is the articulation — the making of connections — that is the real essence.

From many connections, we get larger unities. Larger unities are still the goal, but the work of making connections is what makes such fused views possible. The contemplation of well-formed wholes by the silent mind of an embodied human depends on prior work that must include open discursive questioning and reasoning, if the result is to be genuine.

Aristotle made a vitally important distinction between what is first in itself and what is first for us. To directly aim for the highest truth in itself while being dismissive of what is “first for us” is to disregard our nature as rational animals. Put another way, to directly aim for the highest truth is simply to miss it. This is the kind of illegitimate shortcut that Plotinus himself criticized the gnostics for.

We rational animals need the “long detour” of dialectic to properly grasp any kind of real truth. Otherwise, our visionary experiences will just be fever dreams of the sort that incite fanatics. The goal is not just immediacy but mediated immediacy, as Hegel would say. I think Plotinus at least partially recognized this.

To no longer regard things in the manner of “a spectator outside gazing on an outside spectacle” is to overcome naive dichotomies of subject and object. To really do this, we have to clear our minds of prejudice, not just do meditative exercises to silence internal dialogue. Clearing our minds of prejudice is what requires the long detour.

McDowell on the Space of Reasons

John McDowell’s paper “Sellars and the Space of Reasons” (2018) provides a useful discussion of this concept. Unlike Brandom, who aims to complete Sellars’ break with empiricism, McDowell ultimately wants to defend “a non-traditional empiricism, uncontaminated by the Myth of the Given” (p. 1).

McDowell begins by quoting Sellars: “in characterizing an episode or a state as that of knowing, we are not giving an empirical description of that episode or state; we are placing it in the logical space of reasons, of justifying and being able to justify what one says” (ibid; emphasis added).

For Sellars, to speak of states of knowing is to talk about “epistemic facts”. A bit later, McDowell says that Sellars’ epistemic facts also include judgments and uses of concepts that might not be considered knowledge. Not only beliefs but also desires end up as a kind of epistemic facts. McDowell uses this to argue that the space of reasons is a version of the concept of knowledge as justified true belief. I want to resist this last claim.

McDowell points out that knowledge for Sellars has a normative character. Sellars also regards the foundationalist claim that epistemic facts can be explained entirely in terms of non-epistemic facts (physiology of perception and so on) as of a piece with the naturalistic fallacy in ethics.

McDowell cites Donald Davidson’s contrast between space-of-reasons intelligibility and the kind of regularity-based intelligibility that applies to a discipline like physics, but does not want to assume there is a single model for all non-space-of-reasons intelligibility.

He notes that Sellars contrasts placing something in the space of reasons with empirical description, but wants to weaken that distinction, allowing epistemic facts to be grounded in experience, and to be themselves subject to empirical description. “Epistemic facts are facts too” (p. 5). I prefer going the other direction, and saying empirical descriptions are judgments too.

The space of reasons is only occupied by speakers. Sellars is quoted saying, “all awareness of sorts, resemblances, facts, etc., in short all awareness of abstract entities — indeed, all awareness even of particulars — is a linguistic affair” (p. 7, emphasis in original). “And when Sellars connects being appropriately positioned in the space of reasons with being able to justify what one says, that is not just a matter of singling out a particularly striking instance of having a justified belief, as if that idea could apply equally well to beings that cannot give linguistic expression to what they know” (ibid).

“‘Inner’ episodes with conceptual content are to be understood on the model of overt performances in which people, for instance, say that things are thus and so” (p. 8). “What Sellars proposes is that the concept of, for instance, perceptual awareness that things are thus and so should be understood on the model of the concept of, for instance, saying that things are thus and so” (p. 10). All good so far.

To be in the space of reasons, “the subject would need to be able to step back from the fact that it is inclined in a certain direction by the circumstance. It would need to be able to raise the question whether it should be so inclined” (pp. 10-11, emphasis in original). But McDowell says — and I agree — that this is without prejudice as to whether there is still a kind of kinship between taking reasons as reasons, on the one hand, and the purposeful behaviors of animals, on the other.

McDowell acknowledges that the idea that epistemic facts can only be justified by other epistemic facts is easy to apply to inferential knowledge, but rather harder to apply to the “observational knowledge” that he claims should also be included in the space of reasons. For McDowell, observational knowledge is subject to a kind of justification by other facts.

McDowell and Brandom both recognize something called “observational knowledge”, but Brandom thinks that it necessarily involves appeal to claimed non-epistemic facts, whereas McDowell wants to broaden the concept of epistemic facts enough to be able to say that observational knowledge can be justified by appealing only to epistemic facts. I would prefer to say, observational judgments are subject to a kind of tentative justification by other judgments.

McDowell says that acquiring knowledge noninferentially is also an exercise of conceptual capacities. This clearly implies a noninferential conception of the conceptual, and seems to me to presuppose a representationalist one instead. This has huge consequences.

He says that the space of reasons must include noninferential relations of justification, which work by appeal to additional facts rather by inference. But where did those facts come from? In light of Kant, I would say that we rational animals never have direct access to facts that just are what they are. Rather, if we are being careful, we should recognize that we can only consider claims and judgments of fact, which may be relatively well-founded or not. But appeal to claims of fact for justification is just passing the buck. Claims of any sort always require justification of their own.

As an example, McDowell discusses claims to know that something is green in color. As non-inferential justification in this context, he says one might say that “This is a good light for telling the colours of things by looking” (p. 18). That is fine as a criterion for relatively well-founded belief, but that is all it is.

A bit later, he adds, “I can tell a green thing when I see one, at least in a good light, viewed head-on, and so forth. A serviceable gloss on that remark is to say that if I claim, in suitable circumstances, that something is green, then it is” (p. 19).

This is to explicitly endorse self-certification of one’s authority. It is therefore ultimately to allow the claim, it’s true because I said so. I think it was a rejection on principle of this kind of self-certification that led Plato to sharply distinguish knowledge from belief.

As Aristotle pointed out in discussing the relation between what he respectively called “demonstration” and “dialectic”, we can apply the same kinds of inference both to things we take as true and to things we are examining hypothetically. We can make only hypothetical inferences (if A, then B) from claims or judgments of A; we can only legitimately make categorical inferences (A, therefore B) from full-fledged knowledge of A — which, to be such, must at minimum not beg the question or pass the buck of justification.

The great majority of our real-world reasoning is ultimately hypothetical rather than categorical, even though we routinely act as if it were categorical. One of Kant’s great contributions was to point out that — contrary to scholastic and early modern tradition — hypothetical judgement is a much better model of judgment in general than categorical judgment is. The general form of judgment is conditional, and not absolute.

I think it’s fine to include beliefs, opinions, and judgments in the space of reasons as McDowell wants to do, provided we recognize their ultimately hypothetical and tentative character. But once we recognize the hypothetical and tentative character of beliefs, I think it follows that all relations within the space of reasons can be construed as inferential.

I don’t think contemporary science has much to do with so-called observational knowledge of the “it is green” variety, either. Rather, it has to do partly with applications of mathematics, and partly with well-controlled experiments, in which the detailed conditions of the controls are far more decisive than the observational component. The prejudice that simple categorical judgments like “it is green” have anything to do with science is a holdover from old foundationalist theories of sense data.

I would also contend that all putative non-space-of-reasons intelligibility ultimately depends on space-of-reasons intelligibility.

Proclus’ Elements

The later neoplatonist Proclus (412-485 CE) was head of the Platonic Academy in Athens, at a time when the Athenian Academy was somewhat notorious as the intellectual center of resistance to the spread of Christianity in the Roman Empire. Nonetheless, his work had a profound influence on the Arabic, Byzantine, and Latin traditions. He is usually cited as the main philosophical influence on the early Christian theologian pseudo-Dionysius, who was taken very seriously by Albert the Great and Thomas Aquinas.

Proclus wrote extensive commentaries on Plato, as well as an influential commentary on book 1 of Euclid’s Elements of Geometry. Hegel called him the greatest dialectician of antiquity. Though I think Hegel by his own principles really should have given that title to Aristotle, Hegel was right to recognize Proclus as important.

Aquinas is credited with recognizing that the Latin Book of Causes — a translation of the Arabic Discourse on the Pure Good — was mostly derived from Proclus’ Elements of Theology. Aquinas treated Proclus himself with considerable respect. Dietrich of Freiberg made significant use of his work, and his student Berthold of Moosburg wrote a very long commentary interpreting the Elements of Theology in Christian terms. The Renaissance theologian Nicolas of Cusa and the maverick Giordano Bruno were much inspired by Proclus.

Along with Spinoza’s Ethics, Proclus’ Elements shares the peculiar distinction of being written in a style visibly influenced by Euclid’s Elements. Euclid’s work has often been cited as a sort of paradigm of demonstrative reasoning. Though Proclus, unlike Spinoza, did not work from explicit definitions and postulates and used a looser style of demonstration, his Elements consists of theorems and a sort of demonstrations.

Proclus defends the neoplatonic idea of a One that transcends being, but as Gwenaëlle Aubry and Laurent Lavaud point out in the introduction to the French collection Relire les Éléments de théologie de Proclus (2021), perhaps his most influential idea is that of a very strong continuity from the highest principles to the most mundane effects, which has been read as a strong assertion of immanence as well as transcendence. He is an important source for all the later theological traditions that want to argue for simultaneous immanence and transcendence.

Proclus very explicitly crystallizes what I have called the generalized “unmoved mover” model of causality in Plotinus. For Proclus, “higher” and “lower” causes cooperate in the constitution of worldly things, but the higher cause is always more of a cause than the lower cause. At the same time, he rejects Plotinus’ identification of matter with evil, while emphasizing all of Plotinus’ more positive affirmations of the goodness of manifestation and the beauty of the cosmos.

In a separate treatise On Providence, he develops a sort of epistemic analogue to the generalized unmoved mover theory. “Providence” (pronoia — literally, “forethought”) is a knowledge-like thing that is superior to knowledge in that it is supposed to be eternal and unextended, and to involve no separation of what we might call subject and object. Proclus develops a subtle and suggestive account of something metaphorically like implicit, unextended “seeds” of forms within the overflowing of the One that transcends all extended form. While the One does not “know” worldly things, it “pre-knows” their unextended “seeds”, within something like what Schelling later paradoxically called the identity of identity and nonidentity.

In the Elements, Proclus argues for an interdependence of being, life, and intellect. While one obvious reading of this would emphasize a foundational role of spiritual beings in Proclus’ metaphysics, I am intrigued that it can also be interpreted as a somewhat “deflationary” account of being, closer to Aristotle, and far removed from later notions of pure abstract existence. We can’t begin to have an account of being, without also having an account of life and intellect. With his endorsement of a One beyond “being”, Proclus had no need for a commitment to a notion of pure “being”.

Hegel on Skepticism

The next shape of self-consciousness after “Stoicism” in Hegel’s Phenomenology is “Skepticism”. H. S. Harris in his commentary thinks some of Hegel’s remarks apply specifically to Carneades, perhaps the best known “Academic” Skeptic, who shocked the Romans by arguing for opposite theses on alternating days, as an exercise on Platonic dialectic. Carneades also wrote a work arguing in detail against the great early Stoic Chryssipus. Although I like to stress the less textually obvious role of Aristotelian dialectic in Hegel’s work, Hegel’s explicit remarks emphasize a kind of Platonic dialectic with Skeptical inflections (see Three Logical Moments).

For Hegel, neither pure Understanding — which excels in clarity, utility, and systematic development but tends toward dogmatism — nor a skeptically inclined Dialectic, whose movement undoes everything that is apparently solid — is adequate to characterize what he wants to call Thought. Thought ought to involve a sort of Aristotelian mean that combines the insights of both.

Hegel writes, “Skepticism is the realization of that of which Stoicism is merely the notion, and is the actual experience of what freedom of thought is…. [I]ndependent existence or permanent determinateness has, in contrast to that reflexion, dropped as a matter of fact out of the infinitude of thought” (Baillie trans., p. 246). “Skeptical self-consciousness thus discovers, in the flux and alternation of all that would stand secure in its presence, its own freedom, as given by and received from its own self…. [This] consciousness itself is thoroughgoing dialectical restlessness, this melée of presentations derived from sense and thought, whose differences collapse into oneness, and whose identity is similarly again resolved and dissolved…. This consciousness, however, as a matter of fact, instead of being a self-same consciousness, is here neither more nor less than an entirely fortuitous embroglio, the giddy whirl of a perpetually self-creating disorder” (pp. 248-249).

Harris comments, “[T]he Stoics had to be taught by the Sceptics that no Vorstellung [representation] (not even that of the great cosmic cycle) could comprehend Erscheinung [appearance]” (Hegel’s Ladder I, p. 393). “[Skepticism] knows that ‘language is truer’… than the simple assumption that truth is the name of an extralinguistic Sache [thing or content]” (ibid).

“The Sceptic ideal is to be untroubled in the face of the sensory flux. Sceptical reason tells us not to worry about what we cannot help” (ibid). But “Far from behaving like one who is undisturbed, [Carneades] enjoys being an active disturber; and on the practical side his life has to be controlled by the felt motive actually present at a given moment” (p. 394). “Achieving ‘suspension of judgment’, by setting whatever contingent arguments one can discern in the whirl against those that someone else offers, is a cheat. The Sceptic lives in the world, and allows himself to be guided by senses which he says we ought not to trust” (ibid).

“Every effort the Stoic makes to realize his freedom is tantamount to a serf’s fantasy that he really owns the land” (p. 395). “The Sceptic is a laughing sage because he has the Stoic to laugh at. We laugh at both of them” (ibid).

“[The Skeptic] has not recognized that the [self] he identifies with is only a formal ideal by which the concretely actual self can measure itself. Nobody is that ideal self. No finite consciousness can be that self (by definition). There is no Lord walking the earth: not the one that the serf fears; not the Stoic who thinks he is free; and not the Sceptic who knows what thinking is, and what it is not” (p. 396).

The Ladder Metaphor

Hegel’s figure of a “ladder”, adopted by H.S. Harris in the title of his commentary on the Phenomenology, stands in contrast to the notion of a metaphorically life-risking intuitive leap of faith or salto mortale that had been popularized by the fideistic proto-existentialist German literary figure F. H. Jacobi. Harris has not said it yet and I don’t recall whether he will, but it seems clear to me that the ladder is a metaphor for dialectic.

He emphasizes that for Hegel, except in his very early period, “knowledge is actual only as system” (Hegel’s Ladder I, p. 63) and “Only a community of knowers can constitute the presence of the Spirit to itself as science” (p. 64).

What will turn out to be essential to Hegel’s notions of “system” and “Science” is neither a foundationalist construction nor some kind of closure, but the much more modest idea that (as Brandom might say) meaning has its basis in mutual recognition and shareable inferential articulation.

Harris’ abstract of paragraph 26 reads in part, “The element of Wissen [knowledge] is self-cognition in otherness. This conceptual soil is the substance of spirit. So Science presupposes that we self-consciously exist in this element; but we have a good right to ask for the ladder by which to get into heaven where it is” (ibid).

He comments that “from 1797 onwards, Hegel was explicating the religious experience of ‘love’…. [H]e expounded religion philosophically because he regarded the intuitive leap to the awareness of living, moving, and having one’s being in God as the sin qua non of all speculative insight…. It was through long meditation upon Greek religion, and upon the experience of the religious founders Moses and Jesus, that Hegel’s concept of philosophic science was shaped. But from about the middle of 1803 onwards, he had begun to believe that the leap could be replaced by a ladder of explanatory discourse” (p. 65). For the mature Hegel, religion gives an accessible imaginative representation to what philosophy develops in thought.

In the course of this exposition, Harris notes that “The ‘antithesis’ between consciousness and its objects arises from the concern with controlling or being controlled; no matter how much ‘self-control’ we have, or how much control we are consequently able to exercise over our environment, what we desire and what we fear controls us. ‘Science’ transcends this relationship; it inverts control into freedom. When Jesus claimed identity with ‘the Father’…, he was not claiming to control anything. He was not even claiming to control his own thinking…. Rather, he was adopting a noncontrolling attitude towards experience; and in so doing he ceased to be controlled by it in any practical sense” (ibid).

Form, Substance

Faced with questions like what the world is “made of”, modern people have generally assumed that it must be some kind of “stuff”. The usual presumed answer is some sort of matter-stuff, or less commonly some sort of mind-stuff.

Plato and Aristotle already suggested a radical alternative to this way of thinking that takes the accent away from “stuff” altogether. Aristotle especially developed a rich account of how we think about these kinds of things, by looking at how we express these kinds of questions, and what we are implicitly trying to get at when we ask them.

The most obvious simple answer attributed to Plato and Aristotle is form. In Aristotle’s case, one should also mention what has been traditionally called substance.

Etymologically, eidos — the Greek word we translate as “form” — seems to begin from a notion of visual appearance, with an emphasis on shape. It acquired a more abstract sense related to geometrical figure. Plato attributed great significance to the practice of geometry as an especially clear and perspicuous kind of reasoning, but he also recognized a broader kind of reasoning associated with a dialectic of question and answer, which comes into play especially where questions of value are concerned. From a point of view of ethical practice and human life generally, questions about what something really is and why this rather than that are more important than what things are made of (see What and Why). Already with Plato, “form” came to be inseparable from meaning.

Aristotle’s classic discussion of substance (ousia) in the Metaphysics starts from the idea of a substrate in which properties inhere. This most superficial level later inspired the Greek grammarians to articulate the notion of a grammatical subject of predicates. In what I think is the single greatest example of ancient dialectic, Aristotle gradually steps back from the simple notion of a substrate. Substance becomes “what it was finally to have been” a thing, at the end of the day so to speak. But then this is further interrogated to disclose the level of actuality, or what is effectively operative in a process. But it turns out that actuality is not complete in itself. What is effectively operative does not form a self-contained whole that explains everything. A fuller understanding must take into account potentiality, which leads to a transition away from simple actuality to a larger perspective of processes and degrees of actualization, in which nothing is simply given just as it is. Aristotle was especially concerned with the forms of living things, which have this character.

The more interesting senses of form for Plato and Aristotle do not refer to something that could be simply given. In line with this but in a more speculative mode, Plotinus suggested that every form somehow in a way “contains” all other forms. The poetic truth in this is that the articulation of one form depends on the articulation of other forms, and while everything in some sense coheres, we have no unconditional starting point. We always begin in the middle somewhere, in a context that has yet to be fully elaborated. The work of elaboration is itself the answer. (See also Interpretation.)

Searching for a Middle Term

“But nothing, I think, prevents one from in a sense understanding and in a sense being ignorant of what one is learning” (Aristotle, Posterior Analytics; Complete Works revised Oxford edition vol. 1, p. 115). The kind of understanding spoken of here involves awareness “both that the explanation because of which the object is is its explanation, and that it is not possible for this to be otherwise” (ibid). To speak of the “explanation because of which” something is suggests that the concern is with states of affairs being some way, and the “not… otherwise” language further confirms this.

Following this is the famous criterion that demonstrative understanding depends on “things that are true and primitive and immediate and more familiar than and prior to and explanatory of the conclusion…. [T]here will be deduction even without these conditions, but there will not be demonstration, for it will not produce understanding” (ibid). The “more familiar than” part has sometimes been mistranslated as “better known than”, confusing what Aristotle carefully distinguishes as gnosis (personal acquaintance) and episteme (knowledge in a strong sense). I think this phrase is the key to the whole larger clause, giving it a pragmatic rather than foundationalist meaning. (Foundationalist claims only emerged later, with the Stoics and Descartes.) The pedagogical aim of demonstration is to use things that are more familiar to us — which for practical purposes we take to be true and primitive and immediate and prior and explanatory — to showcase reasons for things that are slightly less obvious.

Independent of these criteria for demonstration, the whole point of the syllogistic form is that the conclusion very “obviously” and necessarily follows, by a simple operation of composition on the premises (A => B and B => C, so A=> C). Once we have accepted both premises of a syllogism, the conclusion is already implicit, and that in an especially clear way. We will not reach any novel or unexpected conclusions by syllogism. It is a kind of canonical minimal inferential step, intended not to be profound but to be as simple and clear as possible.

(Contemporary category theory grounds all of mathematics on the notion of composable abstract dependencies, expressing complex dependencies as compositions of simpler ones. Its power depends on the fact that under a few carefully specified conditions expressing the properties of good composition, the composition of higher-order functions with internal conditional logic — and other even more general constructions — works in exactly the same way as composition of simple predications like “A is B“.)

Since a syllogism is designed to be a minimal inferential step, there is never a question of “searching” for the right conclusion. Rather, Aristotle speaks of searching for a “middle term” before an appropriate pair of premises is identified for syllogistic use. A middle term like B in the example above is the key ingredient in a syllogism, appearing both in the syntactically dependent position in one premise, and in the syntactically depended-upon position in the other premise, thus allowing the two to be composed together. This is a very simple example of mediation. Existence of a middle term B is what makes composition of the premises possible, and is therefore what makes pairings of premises appropriate for syllogistic use.

In many contexts, searching for a middle term can be understood as inventing an appropriate intermediate abstraction from available materials. If an existing abstraction is too broad to fit the case, we can add specifications until it does, and then optionally give the result a new name. All Aristotelian terms essentially are implied specifications; the names are just for convenience. Aristotle sometimes uses pure specifications as “nameless terms”.

Named abstractions function as shorthand for the potential inferences that they embody, enabling simple common-sense reasoning in ordinary language. We can become more clear about our thinking by using dialectic to unpack the implications of the abstractions embodied in our use of words. (See also Free Play; Practical Judgment.)

Dialectic Bootstraps Itself

Here is a subtle but vital point. I’ve just reiterated that dialectic assumes no prior truth. Dialectic approaches coherence in an iterative and incremental way, sometimes backing up and trying a new path. As a philosopher in what I take to be the genuine spirit of Plato and Aristotle, I think seriously taking up such a work is the very best we mortals can honestly do to achieve high levels of practical confidence about the things that matter most in life. No, it does not have the precision or definitiveness of mathematics, but mathematics is like Aristotelian demonstration in that all it tells us with certainty is that certain conclusions follow from certain premises, so the conclusions are only as applicable to life as the premises and their assumed mapping to the real world.

The vital point is that dialectic — the development of richer meaning — can make real progress, without ever assuming a foundation. No, we’ll never say the last word, but we can iteratively and incrementally build cumulative results. With iterative and incremental development of coherent articulations of what we care about and an openness to acknowledging error, we can progressively improve interpretive confidence.

I think this is what is behind Hegel’s somewhat mystifying talk about spirit producing itself. (See also Interpretation; Dialogue; Ethical Reason; Practical Reason; The Autonomy of Reason; Openness of Reason; Reason, Feeling.)

Demonstrative “Science”?

The “historiographical” notes on the history of philosophy I offer here from time to time are a sort of compromise. For much of my life, I’ve been very concerned with the fine grain of such history, and with casting a broad net encompassing many historical figures. Here, I made a strategic decision to focus instead on a mere handful of philosophers I consider most important.

Discussion of actualization in Hegel led to actualization in Aristotle, which led me to indulge my fascination with the Aristotelian commentary tradition. To the extent that it is possible to generalize about the historic readings discussed in the Greek, Arabic, Hebrew, and Latin commentaries, my own view of Aristotle is quite different on a number of key points, having more in common with some modern readings. Nonetheless, I am enormously impressed by the levels of sophistication shown by very many writers in this tradition.

I just mentioned al-Farabi again. As previously noted, al-Farabi (10th century CE) played a great historic role in the formulation of Arabic (and consequently, Hebrew and Latin) views of Aristotle. The Syrian Christians who did the majority of the translating of Aristotle to Arabic from Syriac had access to most of Aristotle’s works, but publicly only taught from the logical treatises. It was al-Farabi who initiated public teaching of the full range of Aristotelian philosophy in the Islamic world. He flourished during the so-called Islamic golden age, a time of tremendous interest in ancient learning not only by aristocrats but by many literate skilled crafts people. The political climate of the Islamic world at the time was much more embracing of secular learning than it came to be between the 13th and 19th centuries CE.

One unfortunate aspect of al-Farabi’s reading was a very strong privileging of a notion of demonstrative “science” over Aristotle’s own predominant use of dialectic in philosophical development. This was based on a reading of Aristotle’s Posterior Analytics as propounding a model of “science” as a deductive enterprise expected to result in certain knowledge, which is still dominant today, but which I (following a number of modern interpreters) think involves a misreading of the basic aims of Aristotelian demonstration.

The idea that Aristotle was fundamentally concerned to develop “sciences” yielding certain knowledge gave a more dogmatic cast to his whole work, which has been a contributing factor in common negative stereotypes of Aristotle. Many modern commentators who still accept this reading of Posterior Analytics have been puzzled by the huge gap between this and Aristotle’s actual practice throughout his works, which in fact is mainly dialectical. I think a careful reading of the Topics (on dialectic) and Posterior Analytics (on demonstration) with consultation of the Greek text on the originals of some key phrases yields a view that is far more consistent with Aristotle’s actual practice.

Demonstration is a pedagogical way of showing very clear reasons for certain kinds of conclusions. It works by assuming some premises are true, whereas dialectic makes no such assumption. Thus the only necessity that results from demonstration is the “hypothetical” one that if the premises are true, then the conclusion is also true. But the more important point in regard to the classic syllogistic form is that the common “middle term” that allows the major and minor premises to be both formally and materially composed together illuminates why we ought to consider it appropriate to assume the conclusion is true if we believe the premises are true.

Dialectic, as I have said, is cumulative, exploratory discursive reasoning about meanings in the absence of initial certainty. This is how Aristotle mainly approaches things. Dialectic implicitly relies on the same logical form of syllogistic argument explicitly used in demonstration, but Aristotle distinguishes dialectic and demonstration by whether premises are treated as hypotheses to be evaluated, or as hypothetically assumed “truths” to be interpreted.

It is also important to note that in the Latin scholastic tradition, the dogmatic trend resulting from wide acceptance of claims about demonstrative science was significantly mitigated by a strong counter-trend of evenhandedly analyzing arguments pro and con, which effectively revived a form of dialectic. (See also Foundations?; Fortunes of Aristotle; Scholastic Dialectic.)