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complexity and analysisThose of our alumni who had really good Republic seminars won’t have forgotten the spectacularly innocuous beginning of all philosophizing that Socrates sets out in the seventh book. He is talking to Plato’s brother Glaucon about an education not so unlike ours. Where and how does reflection begin? With arithmetic. Take the one finger on your hand that doesn’t even have an ordinary name, the fourth. It sends an odd message: It’s always a finger, but it is long in respect to the pinkie, short compared to the middle finger. The attentive soul summons calculative thought to examine whether the eye’s vision is announcing one or two things. If two, then each is other and one. And yet they are together a Twosome; is this Two itself a unity, a one? Now the soul is forced by its perplexity to inquire whatever One Itself might be. Counting and calculation is thus the “winch” to Being, and thoughtful arithmetic turns the soul around to that invisible Being. In another dialogue, the Phaedrus, quite another, an erotically ecstatic beginning of the ascent to Being will be set out.

Stewart Umphrey’s book is the working out, meticulously reasoned and unflinchingly self-critical, of this humble finger problem and its relation to the second beginning in the ecstasy of love. But it is not a commentary on Platonic dialogues or on any of the writers—Hegel, Kant and a slew of moderns—that the author calls on. Though he puts to good use considerable philosophical learning, especially training in logic, it is an instrumental use. He wields the precision tools developed over two and a half millennia in the service of Socrates’ great last care in the Phaedo: that the logos, thoughtful conversation, should live and not die with him. I used to think that commenting on major texts was by and large the most respectable kind of philosophizing, since it kept one honest, in the sense of preventing the inventive kind of originality that substitutes fascinating novelties for the same old truth. Stewart Umphrey’s book, however, proves that there is honest originality—the kind that makes straight for the origin but by a unique route. It shows an independence of mind whose distinctiveness verges on eccentricity—the kind that reaches the center by leaving the mainstream, whose perspective rouses thought by being a little askew, by shifting the world by a few degrees.

41JkgXIXfAL._SY344_BO1,204,203,200_Stewart Umphrey’s distinctive mode is a sort of faithful skepticism. His first book was in fact called Zetetic Skepticism, a title alluding to the hypothesis that searching inquiry (zetesis) can never be complete, that it is the indefeasible human condition not to be perfect in knowledge—and that this is absolutely no reason not to carry on; not despair but the energizing exercise of the intellect is the proper response. Complexity and Analysis is, among other things, a demonstration of the intellectual gymnastics that is at once a preparation for and an expression of this illusion-stripped faith. Of course, the reasons why it is best to keep inquiring are detailed along the way.

The Law of Contradiction with the divisions and branchings it induces is what this author lives by—to begin with, when the differentiations of analysis are wanted (“this is not that”) and also later when distinctions in truth or falsity of statements about complex entities are to be made (“either this holds or that”). Some sections consist of very close reasoning, but the purpose is not to deconstruct polemically but to discover peacefully what is the case; it never gets irritating. At worst it is a sweaty workout, at best an illuminating high. Sometimes a long argument ends in misgivings after all; often the author, like a reasonable human being, admits to as-yet-unreasoned preferences.

If readers may quail a little before the logic (yet—no pain, no gain), they will be enchanted with the distinctive flavor of the style, the underhanded wit, the anomalous vocabulary, the dry logic that supports as it contains the soaring of thought. Did you ever think of newsstands as an exemplification of “the truthvalueless things we make,” or use “obvelation” as the obverse of revelation, or see a rational flow chart of philosophic madness? And then there is occasional lyricism—If you thought you knew your tutor, read the last couple of pages of his book.

So far I’ve talked round about the book, but I want to give some notion of its contents. Since, for Stewart Umphrey the good of philosophy is more (though not only) in the thinking than in the thought, in the doing rather than the having done, the text is practically beyond summary. Though it is full of passionate belief, it contains no thesis that won’t be denatured by being baldly stated. So I’ll be picking small samples, those that twang my logical funny bone or that speak to my philosophical preoccupations.

The book has three parts: The first is about analysis and its limits, thus about ways of knowing, epistemology. The second is about complexity, about the constitution of things that are discernible in thought (here called “entities”), thus about the inside workings of beings. (I have no idea why the order of the complementary parts is reversed in the title of the book, but have perfect faith that there is an interesting reason.) The last part draws the practical, the life-affecting consequences of the theoretical insights gained; it is thus about human wholeness and what lies beyond.

“Analysis” in this book is a way of trying to know some given whole by breaking it up into its constituents, be they themselves entities or something else, something central to the argument, namely “subentities,” “parts” that are not independently countable or even discernible in analytic thought, yet somehow in evidence. Analysis deals comfortably only with fairly independent countable components. Analysts are clear and precise but not always deep and comprehensive. They can capture complexity but have trouble with unity. (They know that the finger contains two ideas, but not how two comes to be one.) Some of the darkness of our day is due to a case of bad analysis, to “analysitis” (“Things fall apart; the centre cannot hold”), but reflectively used it is the beginning of understanding. Stewart Umphrey reviews the tensions that arise in mathematics and the natural sciences between analytic precision and comprehensiveness; the notes provide helpful sketches of several formalizations of this dilemma, two of which our seniors study: Gödel’s incompleteness proof, showing that there is more in mathematics than proofs can reach, and the Einstein-Podolski-Rosen argument that the Heisenberg indeterminacy principle taken as a description of the physical world is incomplete. One principal aspect of what turns out to be the inherent paradox of analysis is thus the Socratic problem: If you analyze an entity into, say, two constituents, you’ve lost the one whole you were trying to understand.

timthumb.phpIn the second chapter of this part, Aristotle’s metaphysics is considered as a model display of the insufficiency of analysis. This presentation not only advances the agenda of the book, it also enacts it: While showing why Aristotle has to become “transanalytic” it attempts to understand his several approaches (often made perspicuous in diagrams), and to comprehend in one understanding his notion of natural beings, of form and matter, essence and accidents, actuality and potentiality, and of divine being—unsuccessfully, of course. Anyone—all of us—who has ever wondered how these perspectives jibe will find this exposition independently illuminating.

“Complexity” describes the character of all thinkable and interesting entities. (Recall the trouble Plato’s Parmenides runs into in trying to think simple unity, the One.) The types of entities are set out with respect to their constitution, from the extremes of mere pluralities or heaps to undifferentiated unities. In between are found the ones that matter: those with definite components that are nevertheless real unities and those that are real unities but with parts—subentities—not discernible in analysis.

Entities are now inventoried; facts, for instance, which include relations or properties that seem to require a transanalytic “ontological glue” to hold them together with the entity itself. Living individuals are particularly complex entities, and with respect to them we can’t help asking about their center or essence, what each being really is. But the familiar difficulty arises: The essence is what the individual is, but is it one and the same with or other than the individual? In the former case, knowing the essence adds nothing new to our understanding; in the latter it yields nothing true about the entity.

Individuals take up or partake in space, and so space must be analyzed. Is it itself an entity, a whole? Are points its “parts”? They certainly belong to the understanding of space, but they are not its components. They are almost model subentities; space is thus a complex entity with constituents inseparable by analysis. The chapter on space is especially interesting, not just as an acute dissection of the spatial features, but because space is the field of display for the non-analytic thinking that is needed to understand the subentitive complexity which characterizes the wholes we most care about. This kind of thinking is analogical. Analysis should, at the least, give us clear and distinct components to go on with. But while clarity belongs to the content of an entity, to its own internal nature, distinctness pertains to its location, its externally delimited place in “conceptual space.” Now the discernible components of a complex entity are particularly clearly and distinctly expressed in spatial representations (such as the author draws in the Aristotle chapter and throughout the book). But such spatial images also make visible indiscernible subentitive parts, for example points (see below).

Why is spatial representation so illuminating? Because we naturally analogize the mind itself to space—our spatial imagination is so close a neighbor to our intellect—and space is the most potent field there is. Moreover, being itself transanalytic, space is particularly apt for representing that kind of complex entity.

Individuals also partake in universals through their species. And universals in turn have similar problems: How is the species a part of the universal? Is the universal genus composed of species? Then where’s the universal? So we again have Socrates’ “One-out-of, or -over, or -beyond Many” perplexity. The author proposes yet another non-analytic kind of understanding which he calls dialectical prismatics: If we think of individuals (or species) as refractions of the universal, as white light is refracted into the color spectrum, then we might, by looking through the prism backwards, so to speak, sight the unitary source. Anyone trying to squint through appearances at what is thinkable in them will recognize the experience of reverse prismatics.

In the section on universals (part of the chapter on entities) we may, moreover, discover that this member of our community inclines toward “metaphysical realms of the ante rem sort,” a fancy way of saying that ideas not only exist, but exist both separately and before the world. But that’s Platonic, glory be!

Next God is viewed prismatically and then negatively. Like the reverse prism, the via negativa, seeing God through what he’s not, is not analytic. The chapter on entities ends with a section called “Everything,” for wisdom—which is what philosophy is for—is the comprehensive understanding of everything: whether all things form a whole and how, and if not, why not. Extreme analysts, such as the logician Quine, eliminate whatever it is that might make wholes of parts, such as universals. They slash away whatever isn’t countable, as the ultimate comprehensive unity certainly can’t be. They wield what is here wittily called “Quine’s machete,” the crude counterpart to “Ockham’s razor,” which deftly excises only the truly unnecessary. Extreme “haplists” (from Greek haplous, “simple”), believers in a simply single being, like Parmenides (though I don’t know another), think that there is one non-complex entity. Neither of their accounts is sufficiently accountable for what there is.

There follow three chapters on the ways of gaining understanding that can supplement analysis. The chapter on analogy, already mentioned, contains a sensible inquiry into “likeness,” since analogy involves likeness; it is so much the more welcome because some recent estheticians have pretty much analyzed imitative resemblance away. The chapter ends with precepts for the safe use of analogies. The one I take most to heart is that philosophical analogies should be carefully framed as similes (“this is like that”) rather than metaphor (“this is that”), and that some of the dead metaphors of our daily speech should be resurrected as instructive similes. (My favorite is the contrastive pair “eidos,” that which is like something seen, and “concept,” that which is like something grasped.)

Dialectic is a second transanalytic way. Dialectic is a term that has lived through many meanings. The author begins with Hegelian dialectic. Again, here, apart from this book’s agenda, is a good account of the main moments of this developmental logic, whose chief feature is that all the analytic components are synthesized and reabsorbed into each other and the whole. It is complemented by a critique, an inventory of the “myths” underlying its beginning, its progression, its culmination, its very possibility for our thinking. A while ago, Stewart Umphrey, Chester Burke, and I together read our way—it took several years—through Hegel’s Science of Logic, a great dialectical experience for all of us (which Stewart kindly acknowledges); this critique revived for me our perplexities of long ago—now neatly marshaled.

The author then turns to the dialectic best known here at the college: dialogue, conversation. “The soul of dialectic,” he says, “is philosophy. Only secondarily are dialecticians elenctic [refutational] wizards.” This kind of philosophical reasoning does not dwell in beginnings or completions but the in-between. It is both its own end (as a healthy activity) and for a purpose (as the search for wisdom). He says much more, of course, but the point is that dialectic implicitly affirms the philosophic condition of incompleteness.

Finally there are the ways of negation. “Is it possible to combine the metaphysical splendor of infinitistic realism [faith in vague beings] with the epistemological refinement of finitistic irrealism [unbelief in any imprecisely delimited entity]?” asks the author. “No,” he answers. “We’re caught then between two opposing views, one of which appears decidedly pinched, the other decidedly vain.” Then follows a critique of Kant’s transcendental dialectic, insofar as it means to show that our deepest philosophic desires must remain forever unmet because the dilemmas we burden ourselves with are based on an illusion—that we can know things in themselves apart from the constructions of our understanding. The author shows precisely something that is eventually divined by every student of Kant: the Critique of Pure Reason is perforce shot through with the very transcendence Kant wants to cure. It is a book far more self-refuting and thus far more suggestive than the first laborious reading reveals.

Kantian naysaying having been analyzed, a praise of wonder and perplexity (carefully distinguished, of course) is mounted in a final section on intuition. Here the impersonal “one” gives way for some reason to the politically correct “she”—an object lesson in the trickiness of that business, since the attribution of intuition to women is, as it happens, quite politically incorrect. I had to grin.

The third part consists of three enticing chapters, Integrity, Ecstasy, and Community: how human beings become whole and how they transcend themselves as persons and also as social beings.

Alan_Watts___Presence_Of_Mind__31597The chapter on integrity culminates in a section about “presence of mind,” a kind of undefined summary virtue capping the qualities of “reason, choice, character,” to which are opposed “will, commitment, appetite, freedom.” I find Stewart Umphrey’s preference for unity and integrity over plurality and disorder deeply agreeable; others may find it usefully provocative. In any case presence of mind is the oldest intellectual virtue known to the West: wise Athena once calls her darling Odysseus angchinoos, “present-of-mind.”

The chapter on ecstasy presents a sober analysis of ways of going beyond oneself, especially in love; its conclusion presents the union of integrity (wholeness) with transcendence (going beyond) in the “sober madness of philosophy.” What is remarkable is that the careful descriptions and distinctions of these human chapters really are applications. They are the practical consequences of the preceding pure theoretical thinking when brought to bear on living experience; they trace out incompleteness as a human condition.

The final chapter, on community, begins with the political, the “most authoritative,” human community. Within it we work ourselves into integrity, out of it we pass beyond ourselves. Careful consideration shows that although it is the basic ground of our well-being, it is imperfect as a community. Friendship appears to be the realization of a paradigmatic community. So an analysis of friendship is in order: “Friendship is complex. It involves a relation that is usually dyadic and always symmetrical”—so this ultimate topic is broached with the formal precision and logical perspicuity of the inveterate analyst who relishes his human reserve; I have to smile even as I’m thinking along. But the logic eventually yields to love, and, as I’ve said, the last two pages of this book speak of the most intimate of human experiences.

Books by Eva Brann may be found in The Imaginative Conservative Bookstore.  This essay originally appeared in The St. John’s Review (Volume XLVI, Number three, 2002) and is republished here with gracious permission. Miss Brann welcomes questions/comments via mail: Dr. Eva Brann, St. John’s College, 60 College Avenue, Annapolis, MD, 21401-1655 (she does not use computers).

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