A Fine-Grained Overview

5 December 2016



Constructive and Non-Constructive Perspectives

Whenever I discuss methodology, I eventually come around to discussing the difference between constructive and non-constructive methods, as this is a fundamental distinction in reasoning, though often unappreciated, and especially neglected in informal thought (which is almost all human thought). After posting Ex Post Facto Eight Year Anniversary I realized that the distinction that I made in that post between detail (granularity) and overview (comprehensivity) can also be illuminated by the distinction between the constructive and the non-constructive.

Two two pairs of concepts can be juxtapositioned in order to show the four permutations yielded by them. I have done the same thing with the dual dichotomies of nomothetic/ideographic and synchonic/diachronic (in Axes of Historiography) and with weak panspermia/strong panspermia and theological/technological (in Is astrobiology discrediting the possibility of directed panspermia?). The table above gives the permutations for the juxtaposition of detail/overview and constructive/non-constructive.

In that previous post I identified my theoretical ideal as a fine-grained overview, combining digging deeply into details while also cultivating an awareness of the big picture in which the details occur. Can a fine-grained overview be attained more readily through constructive or non-constructive methods?

In P or Not-P I quoted this from Alain Connes:

“Constructivism may be compared to mountain climbers who proudly scale a peak with their bare hands, and formalists to climbers who permit themselves the luxury of hiring a helicopter to fly over the summit.”

Changeux and Connes, Conversations on Mind, Matter, and Mathematics, Princeton, 1995, p. 42

This image makes of constructivism the fine-grained, detail-oriented approach, while non-constructive methods are like the overview from on high, as though looking down from a helicopter. But it isn’t quite that simple. If we take this idea of constructivists as mountain climbers, we may extend the image with this thought from Wittgenstein:

“With my full philosophical rucksack I can climb only slowly up the mountain of mathematics.”

Ludwig Wittgenstein, Culture and Value, p. 4

And so it is with constructivism: the climbing is slow because they labor under their weight of a philosophical burden. They have an overarching vision of what logic and mathematics ought to be, and generally are not satisfied with these disciplines as they are. Thus constructivism has an overview as well — a prescriptive overview — though this overview is not always kept in mind. As Jean Largeault wrote, “The grand design has given way to technical work.” (in the original: “Les grands desseins ont cédé la place au travail technique.” L’intuitionisme, p. 118) By this Largeault meant that the formalization of intuitionistic logic had deprived intuitionism (one species of constructivism) of its overarching philosophical vision, its grand design:

“Even those who do not believe in the omnipotence of logic and who defend the rights of intuition have acceded to this movement in order to justify themselves in the eyes of their opponents. As a result we find them setting out, somewhat paradoxically, the ‘formal rules of intuitionist logic’ and establishing an ‘intuitionistic formalism’.”

…and in the original…

“Ceux-la memes qui ne croient pas a la toute-puissance de la logique et qui défendent les droits de l’intuition, ont du, eux aussi, céder au mouvement pour pouvoir se justifier aux yeux de leurs adversaires, et l’on a vu ainsi, chose passablement paradoxale, énoncer les ‘regles formelles de la logique intuitioniste’ et se constituer un ‘formalisme intuitioniste’.”

Robert Blanché, L’axioimatique, § 17

But intuitionists and constructivists return time and again to a grand design, so that the big picture is always there, though often it remains implicit. At very least, both the granular and the comprehensive conceptions of constructivism have at least a passing methodological familiarity, as we see in the table above, on the left side, granular constructivism with its typical concern for the “right” methods (which can be divorced from any overview), but also, below that, the philosophical ideas that inspired the constructivist deviation from classical eclecticism, from Kant through Hilbert and Brouwer to the constructivists of our time, such as Errett Bishop.

These two faces of methodology are not as familiar with non-constructivism. In so far as non-constructivism is classical eclecticism (a phrase I have taken from the late Torkel Frazén), a methodological “anything goes,” this is the granular conception of non-constructivism that consists of formal methods without any unifying philosophical conception. This much is familiar. Less familiar is the possibility of a non-constructive overview made systematic by some unifying conception. The idea of a non-constructive overview is familiar enough, and appears in the Connes quote above, but it this idea has had little philosophical content.

There is, however, the possibility of giving non-constructive formal methodology an overarching philosophical vision, and this follows readily enough from familiar forms of non-constructive thought. Cantor’s theory of transfinite numbers, and the proof techniques that Cantor formulated (and which remain notorious among constructivists) is a rare example of non-constructive thought pushed to its limits and beyond. Applied to a non-constructive overview, the transfinite perspective suggests that a systematically non-constructive methodology would insistently seek a total context for any idea, by always contextualizing any idea in a more comprehensive setting, and pursuing that contextualization to infinity. Thus any attempt to think a finite thought forces us to grapple with the infinite.

A fine-grained overview might be formulated by way of a systematically non-constructive methodology — not the classical eclecticism that is an accidental embrace of non-constructive methods alongside constructive methods — that digs deep and drills down into details by non-constructive methods that also furnish a sweeping, comprehensive philosophical vision of what formal methods can be, when that philosophical vision is not inspired to systematically limit formal methods (as is the case with constructivism).

Would the details that would be brought out by a systematically non-constructive method be the same fine-grained details that constructivism brings out when it insists upon finitistic proof procedures? Might there be different kinds of detail to be revealed by distinct methods of granularity in formal thought? These are elusive thoughts that I have not yet pinned down, so examples and answers will have to wait until I have achieved Cartesian clarity and distinctness about non-constructive methods. I beg the reader’s indulgence for my inadequate formulations here. Even as I write, ideas appear briefly and then disappear before I can record them, so this post is different from what I imagined as I sat down to write it.

Here again I can appeal to Wittgenstein:

“This book is written for such men as are in sympathy with its spirit. This spirit is different from the one which informs the vast stream of European and American civilization in which all of us stand. The spirit expresses itself in an onwards movement, building ever larger and more complicated structures; the other in striving after clarity and perspicuity in no matter what structure. The first tries to grasp the world by way of its periphery — in its variety; the second at its center — in its essence. And so the first adds one construction to another, moving on and up, as it were, from one stage to the next, while the other remains where it is and what it tries to grasp is always the same.”

Ludwig Wittgenstein, Philosophical Remarks, Foreword

These two movements of thought are not mutually exclusive; it is possible to build larger structures while always trying to grasp an elusive essence. It could be argued that anything built on uncertain foundations will come to naught, so that we must grasp the essence first, before we can proceed to construction. As important as it is to attempt to grasp an elusive essence, if we do this, we risk the intellectual equivalent of the waiting gambit.

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Constructivism and Non-constructivism

P or Not-P

What is the Relationship between Constructive and Non-Constructive Mathematics?

A Pop Culture Exposition of Constructivism

Intuitively Clear Slippery Concepts

Kantian Non-Constructivism

Constructivism without Constructivism

The Vacuous Identity Principle

Permutations of Infinitistic Methods

Methodological Differences

Constructivist Watersheds

Constructive Moments within Non-Constructive Thought

Gödel between Constructivism and Non-Constructivism

The Natural History of Constructivism

Cosmology: Constructive and Non-Constructive

Saying, Showing, Constructing

Arthur C. Clarke’s tertium non datur

A Non-Constructive World

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Wittgenstein wrote, “With my full philosophical rucksack I can climb only slowly up the mountain of mathematics.”

Wittgenstein wrote, “With my full philosophical rucksack I can climb only slowly up the mountain of mathematics.”

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Ludwig Wittgenstein

A Wittgensteinian Approach to Civilization

One of my most frequently accessed posts is titled following Wittgenstein’s Tractatus Logico-Philosophicus section 5.6, “The limits of my language are the limits of my world” (“Die grenzen meiner sprache sind die grenzen meiner welt”). I noted in Contextualizing Wittgenstein that this earlier post on Wittgenstein was posted on Reddit and as a result gained a large number of views — a larger number, at least, than my posts usually receive.

If there is a general principle that can be derived from Tractatus 5.6, one application of this general principle would be the idea that the limits of science are the limits of scientific civilization. In the same vein we could assert that the limits of agriculture are the limits of agrarian civilization (or even, “the limits of agriculture are the limits of biocentric civilization”), and the limits of technology are the limits of technological civilization, and so forth. Another way to express this idea would be to say, the limits of science are the limits of industrial-technological civilization, in so far as our industrial-technological civilization belongs to the genus of scientific civilizations.

Recently I have taken up the problem of scientific civilizations in Folk Concepts of Scientific Civilization, Types of Scientific Civilization, Suboptimal Civilizations, Addendum on Suboptimal Civilizations, David Hume and Scientific Civilization, The Relevance of Philosophy of Science to Scientific Civilization, and Addendum on the Stages of Civilization, inter alia. None of this, as yet, is a systematic treatment of the idea of scientific civilization, though there are many ideas here that can some day be integrated into a more comprehensive synthesis.

What does it mean to live in a scientific civilization constrained by the limits of science? One of the points that I sought to make in my earlier post on Tractatus 5.6 was a scientific interpretation of Wittgenstein’s aphorism, acknowledging that the different idioms we employ to think about the world involve different conceptions of the world. In that post I wrote, “…scientific theories often broaden our horizons and allow us to see and to understand things of which we were previously unaware. But a scientific theory, being a particular idiom as it is, may also limit us, and limit the way we see the world.” This is part of what it means to be constrained by the limits of science: our scientific idioms constrain the conceptual framework we use to understand ourselves and our civilization.

Significantly in this context, different scientific idioms are possible. Indeed, distinct sciences are possible. We have had an historical succession of scientific idioms, which could also be called a succession of distinct sciences — something that could be presented as a Wittgensteinian formulation of Thomas Kuhn — according to which one scientific paradigm has replaced another over time. There is also the unrealized possibility of different origins of science, and different developmental pathways of science, in different civilizations. This is an idea I explored in Types of Scientific Civilization.

A civilization might develop science in a different way than science emerged in terrestrial history. A civilization might begin with a different mathematical formalism or a different logic. Perhaps logic itself might begin with the kind of logical pluralism we know today, which would contrast sharply with the logical monism that has marked most of human history. Different sciences might develop in a different order. The ancient Greeks developed an axiomatic geometry, but no scientific biology. But the idea of natural selection is, in itself, no more difficult than the idea of axiomatic geometry, and could have developed first.

A civilization might fail to develop axiomatic geometry and instead develop a scientific biology in its earliest history — its equivalent of our classical antiquity — and this kind of early biological knowledge would probably take agricultural civilization in a profoundly different direction. There may be (somewhere in the universe) scientific agrarian civilizations that are qualitatively distinct from both agrarian-ecclesiastical civilization and industrial-technological civilization. Thus the developmental sequence of sciences in a civilization — which sciences are developed in what order, and to what extent — will shape the scientific civilization that eventually emerges from this sequence (if it does in fact emerge). Is this sequence an historical accident? That is a difficult question that I will not attempt to answer at present.

There are, then, many possibilities for scientific civilizations, and we have not, with the history of terrestrial civilizations, fully explored (much less exhausted) these possibilities. But scientific civilizations also come with limitations that are intrinsic to scientific knowledge. In my Centauri Dreams post, “The Scientific Imperative of Human Spaceflight,” I argued that the science of industrial-technological civilization, essentially narrowed by its participation in the STEM cycle that drives our civilization, is riddled with blind spots, and these blind spots mean that the civilization built on this science is riddled with blind spots.

This should not be a surprising conclusion, though I suspect few will agree with me. There is a comment on my Centauri Dreams post that implies I am arguing for the role of mystical experiences in civilization; this is not my purpose or my intention. This is simply a misunderstanding. But, in fact, the better I am understood probably the less likely it will be that others will agree with me. In another context, in A Fly in the Ointment, I argued that science is a particular branch of philosophy — that philosophy also known as methodological naturalism — which subverts the view (predictably prevalent in industrial-technological civilization) that if philosophy has any legitimacy at all, it is because it is a kind of marginal science in its own right. More often, philosophy is simply viewed as a kind of failed science.

Philosophy is not a kind of science. Science, on the contrary, is a kind of philosophy. This is not a common view today, but that is my framework for interpreting and understanding scientific civilization. It follows from this that a philosophical civilization would not necessarily be a kind of scientific civilization (the philosophy of such a civilization might or might not be the philosophy that we identify as science), but that our scientific civilization is a kind of philosophical civilization.

Philosophy is a much wider field of study, and it is from philosophy that we can expect to address the blind spots of science and the scientific civilization that has grown from science. So the limits both of science and scientific civilization can be addressed, but only from a more comprehensive perspective, and that more comprehensive perspective is not possible from within scientific civilization.

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The young Ludwig Wittgenstein in 1905.

The young Ludwig Wittgenstein in 1905.

This past December a link to my 2011 post The limits of my language are the limits of my world was posted on a Reddit philosophy discussion forum. I have never paid any attention to Reddit, but I guess it gets a lot of traffic, since as a result of this link I received a peak number of 12,749 hits on 22 December 2014 — most of them from Reddit, but also a substantial number from Hackernews, which had apparently re-posted the link. This is the greatest number of hits that any of my individual posts have received.

The spike in traffic encouraged me to look at my old post again, and think about what I had said in it. My past effort left much to be desired, and as a result of all the traffic I did receive one perceptive comment on the post itself (apart from all those comments on the Reddit page, where I am not registered so could not respond), and this also gave me reason to think it over again.

In retrospect what bothers me the most (but which was not a focus of any of the comments) is that I had taken this popular Wittgenstein quote out of context and discussed it without systematically relating it to the corpus of Wittgenstein’s thought from which it drawn. In defense of my former self, I can say that it was merely a blog post, and pretty much written off the top of my head. It would take a book-length study, or several book-length studies, to adequately contextualize the Wittgenstein quote that I had plucked out as an aphorism and to give it a proper textual exegesis. But my scholarly conscience bothers me a bit, as my conscience has also been bothering me about a post I wrote about a line plucked out of Einstein in Unpacking an Einstein Aphorism. I don’t repudiate what I wrote in that post, any more than I repudiate what I wrote in my brief post on Wittgenstein, but I do intend to return to this Einstein passage and write about it again in proper context.

The aphorisms taken out of the Tractatus must be understood in the context of the work from which they are taken, and the work itself much be understood in the context of the Wittgenstein’s thought — no small task, especially given the sheer volume of Wittgenstein scholarship. In the case of the Tractatus we are quite fortunate to possess two closely related posthumously published texts by Wittgenstein, Notebooks 1914-1916, edited by G.H. Von Wright and G.E.M. Anscombe, as well as Prototractatus: An Early Version of the Tractatus Logico-Philosophicus, edited by B.F. McGuinness, T. Nyberg, and G.H. Von Wright. Both of these works generously overlap with the completed text of the Tractatus and provide material not included in the published text. In addition, there are numerous personal letters between Wittgenstein, his philosophical friends, publishers, and translators, and a commentary tradition starting with Russell’s introduction written for the first English language edition and continuing up to the present day. I myself own at least a dozen commentaries on the Tractatus alone (excluding works on Wittgenstein himself or on his later work). That is a lot of context to grind one’s way through.

Some of the confusion surrounding aphorisms attributed to Wittgenstein is understandable because Wittgenstein did write some aphorisms (many of them collected in the posthumously published Culture and Value). However, the sections of the Tractatus that have been taken out of context and used as aphorisms are not aphorisms, but rather sections of a treatise that was composed in aphoristic style. This may sound like an overly-subtle distinction, but it is a distinction that makes a difference. An aphorism is intended to stand on its own; a work composed in aphoristic style is intended to be read and understood as a whole.

Wittgenstein shares this confusing character of his style with the writings of other philosophers who composed works in aphoristic form, notably Nietzsche and Kierkegaard. Walter Kaufmann, the noted Nietzsche scholar, often went out of his way to point out that Nietzsche’s aphorisms are part of books and are intended to be read as part of a text that develops an idea throughout. I think part of my scholarly conscience grows out of reading so much of Kaufmann at an early age. When Kaufmann wrote about Nietzsche the latter was still a highly controversial figure, so Kaufmann was at pains to be on his best scholarly behavior. I think that it was also Kaufmann who said that Nietzsche often wrote too well for his own good, as he is often attacked for passages that he was not himself defending, but which he formulated so concisely that his phraseology was taken as a kind of advocacy. The same might be said of Kierkegaard and Wittgenstein.

Kierkegaard, of whom I just wrote in Kierkegaard and Russell on Rigor, takes this confusion of the aphorism taken from an aphoristic work to a higher level by publishing pseudonymous works written in aphoristic style, so that any “aphorism” attributed to Kierkegaard may be be a single sentence plucked from a longer work which moreover is written under a pseudonym. Does this “aphorism” represent Kierkegaard’s views? The question is as fraught as how much of Plato’s Socrates represents the views of the historical Socrates.

Given the volume of scholarship available on a figure like Wittgenstein, is it even possible to write something like a blog post without entirely misrepresenting one’s source? In other words, is it possible to blog with intellectual integrity? A lot of my early blog posts were written off the top of my head, often from memory without bothering to consult an actual text. That seemed sufficient at the time. None of these posts would stand up to serious critical scrutiny. Since then, my posts have become longer, better researched, and much less frequent. With blog posts like this, one is likely to lose all but the most dedicated readers, but in the event that a post should receive unexpected attention (like my Wittgenstein post that was linked on Reddit), it would stand up a little better to critical scrutiny.

Aware of this, I started my second blog, Grand Strategy Annex, but this, too, has grown into something more serious and I hesitate even there to post poorly thought-out ideas — though I am still guilty of this on occasion (especially with my recent post on gray goo).

A lot of what I put in my early blog posts consisted of ideas to which I attached no great importance. My first post on civilization, for example — Today’s Thought on Civilization — was something I wrote because it wasn’t one of the ideas I was working on in my manuscripts, hence of no great importance. However, that post led to further posts, and now I have a significant tranche of posts on civilization. I also have a much clearer idea of civilization than I had six years ago, and the philosophy of civilization now constitutes a central research interest of mine. Most of what I think about civilization now goes on my blogs, with no thought of “saving” it for a manuscript because I consider it too important for a mere blog post. So my own attitude to my own writing has changed over the time I’ve been blogging on strategy, civilization, and philosophy.

In any case, I now hope to return to my post on The limits of my language are the limits of my world and to give this idea an exposition that does not treat this passage from the Tractatus like an aphorism, which it is not. Skimming though a number of Wittgenstein’s works and commentaries over the past new days I already have a idea of how I will do this, but it will take me some time to get to it. And it would take more time yet to then take the consequences of an inquiry into Wittgenstein and apply it to the interpretation of quantum theory, which was what I did my my original post. To do justice to that idea would definitely require a work of some scope. But I am not entirely ready to give up my intellectually opportunistic ways, seizing upon any idea that strikes me as interesting at the moment and writing about whatever seems related to it.

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In this picture you can clearly see the spike in my stats generated by the Reddit link to my post on Wittgenstein. You can also see that the best day ever was 12,749, which was the second day of the spike in traffic.

In this picture you can clearly see the spike in my stats generated by the Reddit link to my post on Wittgenstein. You can also see that the best day ever was 12,749, which was the second day of the spike in traffic.

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A Fly in the Ointment

11 November 2014


Wittgenstein - cartoon

Wittgenstein was not himself a positivist, but his early work, Tractatus Logico-Philosophicus, had such a profound influence on early twentieth century philosophy that the philosophy that we now identify as logical positivism was born from reading groups that got together to study Wittgenstein’s Tractatus — what I have elsewhere called The Ludwig Wittgenstein Reading Club — primarily the Vienna Circle.

Wittgenstein began his education as an engineer, and only later became interested in philosophy by way of the philosophy of mathematics then emerging from the work of Frege and Russell. It has been said that the early Wittgenstein approached philosophy like an engineer, setting out to drain the swamps of philosophy. A more familiar metaphor for Wittgenstein’s philosophy, though for the later rather than the earlier Wittgenstein, is that of philosophy as a kind of therapy:

“A philosopher is a man who has to cure many intellectual diseases in himself before he can arrive at the notions of common sense.”

Wittgenstein, Culture and Value, 1944, p. 44e

Wittgenstein does not himself use the term “therapy” or “therapeutic,” but frequently recurs to the theme in other words:

“In philosophizing we may not terminate a disease of thought. It must run its natural course, and slow cure is all important. (That is why mathematicians are such bad philosophers.)”

Wittgenstein, Zettel, 382

The idea of philosophy as therapy is not entirely new. In my Variations on the Theme of Life I noted the medieval tradition of conceiving philosophers as “doctors of the soul”:

“During late antiquity philosophers were sometimes called ‘doctors of the soul.’ Later yet, Avicenna was a practicing physician in addition to being both a logician and a philosopher, and he stands at the head of a tradition of doctor-philosophers among the Arabs. All this has a superficial resemblance to the contemporary conception of philosophy as therapy, but in reality it is the antithesis of the modern conception of philosophy as a sickness in need of therapy, of scholarship as an illness, and of the philosopher as corrupt and corrupting.”

Variations on the Theme of Life, section 767

Every age must confront the ancient and perennial questions of philosophy anew, because each age has its own, peculiar therapeutic needs. It has become a commonplace of contemporary commentary, as least since the middle of the twentieth century, that the pace and busyness of our civilization today is driving us insane, and in so far as this is true, we are more in need of therapy than previous ages.

In my previous post, Philosophy for Industrial-Technological Civilization, I suggested, contrary to Quine, that philosophy of science is not philosophy enough; that we also need philosophy of technology and philosophy of engineering, and to unify these aspects of the STEM cycle within the big picture, we need a philosophy of big history. There is only one problem with my vision for the overarching philosophy demanded by the world of today: there is no demand for it. No one is interested in my vision or, for that matter, any other vision of philosophy for the twenty-first century.

Previously I wrote three posts on contemporary anti-philosophy:

Fashionable Anti-Philosophy

Further Fashionable Anti-Philosophy

Beyond Anti-Philosophy

The most prestigious scientists of our time seem at one in their insistence upon the irrelevance of philosophy. A post on the SelfAwarePatters blog, E.O. Wilson: Science, not philosophy, will explain the meaning of existence, brought my attention to E. O. Wilson’s recent statements belittling philosophy. SelfAwarePatters has also written about Neil deGrasse Tyson’s “blanket dismissal of philosophy” in Neil deGrasse Tyson is wrong to dismiss all of philosophy, but he may have a point on some of it.

It is almost painful to watch Wilson’s oversimplifications in the above linked “Big Think” piece, though I suspect his oversimplifications will have a wide and sympathetic audience. After implying the pointlessness of studying the history of philosophy and making the claim that philosophy mostly consists of “failed models of how the brain works,” Wilson then appeals to the “full story of humanity” (without mentioning big history, though the interdisciplinary concatenation he mentions is very much in the spirit of big history), and formulates a point of view almost precisely the same as that I heard several times at the 2014 IBHA conference: once we have this big picture view of history, we no longer need to ask what the meaning of life is, because we will know it.

The inescapable reflexivity of philosophical thought means that any principled rejection of philosophy is itself a philosophical claim; unprincipled rejections, that is to say, dismissal without reason or argument, have no more standing than any other unprincipled claim. So the scientists who dismiss philosophy and give reasons for doing so are doing philosophy. The unfortunate consequence is that they are doing philosophy poorly, much like someone who dismisses science but who pontificates on matters scientific, and does so poorly. We are well familiar with this, as pseudo-science has been given a megaphone by the internet and other forms of mass media. Scientists are aware of the problem posed by pseudo-science, but seem to be blissfully unaware of the problem of pseudo-philosophy.

There is a book by Louis Althusser, Philosophy and the Spontaneous Philosophy of Scientists, that I have cited previously (in Fashionable Anti-Philosophy) since the title is so evocative, in which Althusser says, “…in every scientist there sleeps a philosopher or, to put it another way, that every scientist is affected by an ideology or a scientific philosophy which we propose to call by the conventional name: the spontaneous philosophy of the scientists…” It is this spontaneous philosophy of scientists that we see in the anti-philosophical pronouncements of E. O. Wilson and Neil deGrasse Tyson.

Not only eminent scientists, but also science popularizers share this attitude. Michio Kaku’s recent book, The Future of the Mind: The Scientific Quest to Understand, Enhance, and Empower the Mind, is essentially a speculative work in the philosophy of mind. There is a pervasive yet implicit Kantianism running through Kaku’s book of which I am sure he is unaware, because, like most scientists today who write on philosophical topics, he has not bothered to study the philosophical literature. If one knows that one is arguing a neo-Kantian position on the transcendental aesthetic, in trying to come to terms with how the barrage of sensory data is somehow translated into an apparently smooth and unitary stream of consciousness, then one can simply consult the literature to learn where state of the argument over the transcendental aesthetic stands today, what the standard arguments are for and against contemporary Kantianism, but without this basic knowledge, one does little more than repeat what has already been said — better — by others, and long ago. Even Sam Harris, who has some background in philosophy, gives his exposition of determinism in a philosophical vacuum, as though the work of philosophers such as Robert Kane, Helen Steward, and Alfred R. Mele simply did not exist, or is beneath notice.

The anti-philosophy and pseudo-philosophy of prominent scientists is an instance of the spontaneous philosophy noted by Althusser. But this spontaneous expression of uninformed philosophical speculation does not come out of nowhere; it has a basis, albeit dimly understood, in the nature of science itself. What is the nature of science itself? I have an answer to this, but it is not an answer that will be welcome to most of those in science today: science is philosophy. That is to say, science is a particular branch of philosophy, that branch once called natural philosophy, and it is natural philosophy practiced in accordance with methodological naturalism. Science is a narrow slice of a far more comprehensive conception of the world.

Scientists are philosophers without realizing they are philosophers, and when then pronounce upon philosophical questions without reference to the philosophical tradition — which is much broader and pluralistic than any one, single branch of philosophy, such as natural philosophy — they do little more than to restate their presuppositions as principles. Given the preeminent role of science within industrial-technological civilization, this willful ignorance of philosophy, and of the position of science in relation to philosophy, is not only holding back both science and philosophy, it is holding back civilization.

The next stage of development of our civilization (not to mention the macro-evolution of our civilization into another kind of civilization) will not come about until science utterly abandons the positivistic assumptions that are today the unquestioned yet implicit presuppositions of scientific inquiry, and science extends the scientific method, and the sense of responsibility to empirical evidence, beyond the confines of any one branch of philosophy to the whole of philosophy. To paraphrase Plato, until philosophers theorize as scientists or those who are now called scientists and leading thinkers genuinely and adequately philosophize, that is, until science and philosophy entirely coincide, while the many natures who at present pursue either one exclusively are forcibly prevented from doing so, civilization will have no rest from evils… nor, I think, will the human race.

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A Discourse on Center and Periphery

In a posthumously published remark Wittgenstein mentioned “the main current of European and American civilization.” (I previously quoted this in my post American Civilization.) The remark is made is passing, in the context of highlighting Wittgenstein’s own feelings of alienation from this tradition, which he employs as a caution at the beginning of one of his posthumously published works, lest the unwary denizen of this main current of European or American civilization should crack its covers and find himself challenged by a fundamentally different perspective.

If civilization has a main stream, does it also have tributaries, shallows, bends, bayous, and parallels to all the hydrological structures of riparian environments?

This passage from Wittgenstein is interesting in several respects. It assumes that there is a main current of European and American civilization, and a main current implies that there is also a periphery to civilization that it not the main current — perhaps even distant sources of the main stream, tributaries, bayous, and other topographical features of the river of time (to continue with the implied metaphor of a “current” of civilization). I find this metaphor to be highly suggestive and even fruitful. Civilization is an historico-temporal phenomenon, so that any detailed articulation we can being to our historico-temporal understanding will likely result in a more fine-grained understanding of civilization. (We could, alternatively, say that civilization consists of temporal structures.)

The “river of time” is an ancient metaphor, and like all metaphors it has its uses and abuses. One of the signal sea changes in twentieth century philosophy on which I have remarked elsewhere but receives scant attention in the literature, is the nearly complete turn-around from philosophical rejection of the reality of time to a philosophical acceptance if not embrace of the reality of time. There were, however, holdouts, even in the analytical community, and some of these holdouts went so far as to deny that there is any such thing as the “flow” of time, which is pretty much the same thing as denying the metaphor of the river of time, which is pretty much the same thing as denying the temporal reality of historico-temporal phenomenon such as civilization. (Pretty much, but not exactly.)

I will here take the reality of time and of temporal phenomena as given, thus betraying both my naturalism and my acceptance of the contemporary philosophical consensus that time is real. I won’t bother to argue for this. While some metaphors may be more apt than others, and some metaphors more intuitively perspicuous than others, I don’t see that the “river of time” metaphor does any harm, and in so far as the metaphor can be extrapolated as suggested above, it may expand our conception of temporal phenomena such as civilization.

There is a sense in which a Wittgensteinian approach to civilization is both obvious and interesting. In his The Faith of a Heretic, Walter Kaufmann writes of the application of the later Wittgenstein’s theory of family resemblances to words with complex meanings like “religion” and “civilization.” Subsequent philosophers have come to call such words “open textured,” and this applies to a great many common nouns. When we casually employ language in conversation such open-textured concepts cause little trouble, and especially so when there is a desire for mutual understanding. But when we attempt to make the open-textured concepts of ordinary language rigorous and precise we almost always run into trouble, and the contexts in which we attempt to precisify our concepts we usually cannot count on a desire to collaboratively converge upon meanings. (For this reason, among others, certain kinds of communication are possible among friends and family that are not possible with others — assuming that friends and family are sympathetic to us, which for some is a vertiginous leap.)

In any case, “civilization” would seem to be a paradigm case of an open-textured concept such that the instances that are taken to exemplify the meaning of the term display a family resemblance rather than all possessing a particular property by which all are definitively identified as being civilization. (That is to say, the legitimacy of an open-textured concept implies the rejection of essentialism for the concept in question.) Also, and as importantly, an open textured concept is open to revision. It can accommodate new permutations of meaning while abandoning old meanings. One way to revise the concept of civilization is to arrive at a more comprehensive conception by extrapolating Wittgenstein’s metaphor, and one way to do this is to leave the literalness of the metaphor aside, and instead of speaking of a mainstream of civilization and its implied branches off the main stream, to speak of the center and the periphery of civilization.

Civilization, to date, has meant those human undertakings on the surface of the earth that have included building cities, engaging in large-scale communal projects (such as agriculture and religious ceremonies), systematic application of intelligence to technology in order to solve problems, the maintenance and extension of social structures, and many other things. Because civilization is open-textured, we cannot exhaust its meanings, so we must be content with an incomplete list that simply gives a sense of what is involved in the enterprise.

Arnold Toynbee, author of A Study of History

The main stream of civilization to which Wittgenstein referred can be taken as the earliest, largest, core, and central efforts of this type. This is the center of civilization. The list of civilizations that Toynbee gives in his A Study of History — Egyptian, Andean, Sinic, Minoan, Sumerian, Mayan, Indic, Hittite, Hellenic, Western, Orthodox Christian (Russia), Far Eastern (Japan), Orthodox Christian (main body), Far Eastern (main body), Persian, Arabic, Hindu, Mexican, Yucatec, and Babylonic — constitutes a temporal-historical list of examples; the list of civilizations given by Samuel Huntington in his The Clash of Civilizations — Western, Latin, Japanese, Sinic, Hindu, Islamic, Orthodox, African — constitutes a spatio-structural list of examples. Both of these attempts at giving a comprehensive catalog of actual civilizations are imperfect and inadequate, but the intersection of both might give as a rough spatio-temporal catalog of the centers of civilization.

Samuel Huntington

The idea of the center of civilization is at once both vague and intuitive, making it difficult to precisify, but the rewards of precisification are all the greater given the potential of the concept. But we must honestly concede that the idea of civilization itself is none-too-clear, and even thinkers who worked on the idea for their entire careers, such as Toynbee and Huntington mentioned above, have done little more than point to examples — what philosophers call an “ostensive definition” — since a logical or formal characterization of civilization seems to be beyond the present conceptual infrastructure of the social sciences. But difficult as the task of formulating and formalizing the concept of a center of a civilization may be, we can gain a little bit of analytical clarity by contrasting the center of civilization with the periphery of civilization, and such an analysis has already been suggested.

The simplest model of center and periphery.

I have previously criticized the terminology of Thomas P. M. Barnett that employs the locution “credentializing.” While Mr. Barnett took the trouble to explain himself after my criticism (which clarification I have posted in Credentializing Clarified), I still find this term in particular (viz. credentializing) to lack intuitive perspicuity. However, Barnett’s influential text The Pentagon’s New Map, with its distinction between core states and gap states, is highly intuitively perspicuous, and it moreover is an exposition of the world in terms of center and periphery. (Huntington, cited above, divided the clashes between civilizations into fault line conflicts and core state conflicts, which also is a form of center/periphery distinction. I don’t know enough about Barnett’s position to know whether he was influenced in this respect by Huntington.)

A more realistic model of multiple centers and overlapping peripheries. Beyond this spatial model, one ought also to imagine multiple centers and overlapping peripheries in time.

The strategic logic of center and periphery is more fundamental than, and therefore underlies, the culture, social milieu, or civilizational context, and so we find in it a cross-cultural mode of analysis that is found in works antithetical not only to the “Washington Consensus” but even to western civilization. For example, we find this exposition of center and periphery in Abu Bakr Naji’s The Management of Savagery: The Most Critical Stage Through Which the Umma Will Pass:

“The two superpowers which used to dominate the global order controlled it through their centralized power. The meaning of “centralized power” here is: The overwhelming military power which extends from the center in order to control the areas of land that submit to each superpower, beginning from the center and reaching the utmost extremity of these lands. Submission, in its primary, simplest form, means that these lands owe the center loyalty, submission to its judgment, and responsibility for its interests.”

The Management of Savagery: The Most Critical Stage Through Which the Umma Will Pass, Abu Bakr Naji, Translated by William McCants, translation supported by the John M. Olin Institute for Strategic Studies at Harvard University

And again a few pages later, in comparing relative Russian and American proximity to Afghanistan and adjacent lands:

“The matter is different with regard to America — the remoteness of the primary center from the peripheries should help the Americans understand the difficulty of our continued submission to them, their control over us, and their pillaging of our resources if we decide to refuse; but only if we refuse and enflame opposition to its materialization.”

Part of Naji’s argument is that the nature of power, and the nature of power projection, on the periphery is distinct from the nature of power and power projection close to the center. I find Naji’s position close to my own in terms of his analysis, and if we change the specific terms of Naji’s analysis it can be seen as an alternative formulation of Barnett’s gaps (as mentioned above) and George Friedman’s borderlands (as mentioned immediately below).

Another use of the strategic logic of center and periphery is to be found in George Friedman’s discussion of borderlands. I have previously visited this in Moral Borderlands where I quoted Friedman’s The Next 100 Years as follows:

“Between two neighboring countries, there is frequently an area that has, over time, passed back and forth between them. It is an area of mixed nationalities and cultures… It has a unique mixed culture and individuals with different national loyalties… But regardless of who controls it at any given time, it is a borderland, with two cultures and an underlying tension. The world is filled with borderlands.”

If we expand and extrapolate this that Friedman attributes to countries to also include multi-state entities, ethnicities, social systems, cultures, and civilizations, then his borderlands are approximately similar to Barnett’s unstable gaps between core regions.

There is a tendency today to minimize the distinction between center and periphery because of instantaneous global communications and nearly instantaneous global travel. (I considered the social changes wrought by ease of global travel in The Space Age and Addendum to “The Space Age”.) Indeed, there is a sense in which expanding globalization is the neutralization (if not the negation) of the center/periphery dialectic that runs like a thread through human affairs from the earliest empires of west Asia to the great confrontation of the two superpowers that dominated the second half of the twentieth century, with the stability at the center and its proxy wars at the periphery.

If (and I stress if) globalization is conceived as the elimination of dialectic of center and periphery, as the closing of Barnett’s gaps and the consolidation of the functioning core, or the elimination of Friedman’s borderlands, while these developments may be approximated, they will never be fully consolidated. In this sense, and I mean in this sense narrowly conceived, globalization will either falter in some phase of its unfolding, or the same dialectic of center and periphery will be extrapolated as human civilization extends beyond the surface of the earth and the periphery is to be found in marginal communities established far from the center on a new scale of distance that outstrips that possible upon the surface of the earth, and therefore exhibits the dialectic in an even more stark form (which I have called extraterrestrialization).

Civilizational centers migrate over time, albeit slowly, almost too incrementally to notice. During classical antiquity, Western civilization was centered on the Mediterranean; during the medieval period, Western civilization was centered in Western Europe; with the discoveries of the Americas there is a sense in which Western civilization has been centered on the Atlantic. Islamic civilization has similarly shifted gradually during its history. During the medieval period Islamic Spain became sufficiently wealthy and influential that Cordoba virtually represented a second center of Islamic civilization, so that the tradition seemed to bud another iteration of itself in a very different land than that of its birth.

In Human Nature and the Human Condition I argued that the apparent fixity of human nature was due to human nature being shaped by the human condition, and the human condition changes, albeit very slowly. Civilizational change, along with the migration of the center of a civilization and the redefinition of a barbarous periphery, is part of this incremental shifting of center and periphery. Thus the main stream of Western civilization to which Wittgenstein referred in the quote that opens this post, is, like any great river, an ancient stream that has changed its bed many times as both the geology underlying the river has shifted and the inhabitants who have lived along its banks have changed their habits and domiciles over time.

While the periphery may be barbarous and not fully civilized, as well as being far from the center of things by definition, that does not mean that the periphery is not important. In many cases, the fate of the center of a civilization is determined by what occurs in and at the periphery of civilization. Certainly this was the case with the later Roman Empire. As the Roman Empire grew the periphery was forced farther and farther outward in the grand strategic ambition to secure the center from incursion and instability, as well as to keep tribute and booty flowing inward from the periphery to the center. Eventually the fate of the Empire was sealed as barbarians on the periphery, attracted by the wealth, luxury, and comfort of Mediterranean civilization, pushed inward toward the center and eventually themselves took control of the center.

When the barbarians took control of the center of Western civilization and thereby in one fell swoop (a swoop that took centuries to consolidate) brought the periphery into the center, the center was then no longer the center and the whole of Western civilization was topsy-turvy for a few hundred years. This was formerly called the “Dark Ages,” but historians no longer use this term as it implies a valuation that seems out of place in objective historiography, though the term is often justly applied. (I previously wrote about civilizational dark ages in The Phenomenon of Civilization Revisited.) It took hundreds of years for Western civilization to turn itself inside-out and in the process transition its center roughly from Rome to Paris, making the Mediterranean, once the center of civilization, into the periphery.

There is a close parallel between the frontier, as conceived in Frederick Jackson Turner’s famous essay “The Significance of the Frontier in American History,” and the periphery, or borderlands (or gaps). We could, in fact, speak in terms of the significance of the periphery in American history, and as soon as we do so we realize that, while the center is the focus of civilization, the periphery can be crucial to the development of a civilization. In this case, the Turner Thesis becomes the thesis that the periphery was of central importance in the development of American civilization, which latter Wittgenstein had called the “main stream” of civilization.

There are things that are possible at the center that are not possible on the periphery, and there are things that are possible on the periphery that are not possible at the center. This complementary facilitation is parallel to complementary obstacles: there are particular conditions for accomplishing anything at the center, and different conditions for accomplishing anything one the periphery. For example, at the center you need to the cooperation of the wealthy, the well-connected, the influential, the powerful, and the like. Without them, you accomplish nothing. On the periphery, on the other hand, you have a much freer hand in terms of those with whom you work, but the resources to which you have access will be correspondingly slight. At the periphery, infrastructure is thin on the ground or non-existent. If you want to try something controversial, this is the place to try your proof of concept.

Because of the complementary possibilities and obstacles of center and periphery, a large civilizational undertaking may require the agents of that civilization to pass back and forth between center and periphery in order to secure the resources necessary from the center and remove them to the periphery to accomplish in relative autonomy and seclusion that which cannot be easily accomplished in the center. The Manhattan Project drew the best minds from the centers of academic world, but it placed them in the isolation of the New Mexican desert. And while the focus of the Manhattan Project has been the design and testing center in New Mexico, the fissionable materials were created in the isolation of eastern Washington state at the Hanford Nuclear Reservation.

On a larger scale, it could be argued that the vitality of American civilization has been at least in part a consequence of the ongoing dialectic between center and periphery made possible by the unification, in one nation-state, of a industrially developed center along the eastern seaboard and the wilderness of the frontier in the interior of the North American continent. For the most part, these conditions were lacking in South America. The closest approximation was Argentina in the nineteenth century, which at that time was one of the wealthiest countries in the world, and Brazil, which is today rapidly improving its fortunes as its people exploit the possibilities created by the vast Amazonian interior and the enormous and wealthy cities on the coast.

Similar considerations — a dialectic of wealthy cities connected to the outside world and vast, nearly empty interior wildernesses — hold for China and Russia, except that Russia has no major ocean coastline, though it does have St. Petersburg on the Baltic. In China, the balance is tilted toward the center (the large and wealthy coastal cities), while in Russia the balance is tilted toward the periphery (the vast spaces of the Russian interior and Siberia, lacking the counterweight of cities like Shanghai, Hong Kong, and Qingdao).

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PS: This post has been in gestation longer than anything else I have made available here, since I began it just over two years ago. Thus these are perennial issues that I have had in mind for some time. Though I have been thinking about these ideas for some time, my thoughts still lack focus, but I wanted to at least sketch the idea in order to have the material available for further development.

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The Doors of Intellection

23 February 2009

“If the doors of perception were cleansed every thing would appear to man as it is, infinite. For man has closed himself up, till he sees all things through narrow chinks of his cavern.”

William Blake, The Marriage of Heaven and Hell

William Blake, The Marriage of Heaven and Hell, Plate 14

William Blake, The Marriage of Heaven and Hell, Plate 14

William Blake is the source of the famous phrase “the doors of perception” — it is from his wonderfully Faustian The Marriage of Heaven and Hell — though most readers will connect the phrase to the novel by Huxley. Huxley, of course, took his title from Blake. Since in yesterday’s Algorithms of Ecstasy I mentioned religious experiences induced, at least in part, by chemical means, it is appropriate to mention in this connection Huxley’s drug-addled visions of “Love as the primary and fundamental cosmic fact” (in a letter to Humphry Osmond). Huxley represents a dead end in the scientific pursuit of the absolute; Huxley represents science that has lost its objectivity and has ceased to operate according to methodological naturalism, and therefore ceased to be science.

What Blake has observed about the doors of perception holds good also for the doors of intellection: if the doors of intellection were cleansed every thing would appear to man as it is, infinite. For man has closed himself up, till he understands all things through narrow chinks of his cavern.

I have just finished listening to Richard Dawkins’ The God Delusion on CD. From a philosophical perspective, the book is highly problematic, but Dawkins is quite explicitly coming from a scientific perspective, and he knows it. He often has difficulty concealing his contempt for philosophical argumentation, and this makes the book problematic as he takes on many paradigmatically philosophical questions and does so from a scientific standpoint. Thus much of the book is at cross purposes with its intended subject matter.


I mention Dawkins not to criticize him, however — many others have already done so, and I genuinely enjoyed the book — but to take up some of the themes with which he closes. The book has a fine peroration, and I was pleased with this as many authors on such subjects don’t bother to craft a good closing so that the book just lurches to a halt without any sense of climax and resolution. Dawkins delivers nicely on this score.

In the last few pages Dawkins introduces a number of notions, among them the Middle World and the motif of our sense perception being like the slit of light admitted by a burka. The Middle World is the familiar world of things not too large (like the objects of cosmology), not too small (like the objects of quantum mechanics), and not too fast (like objects approaching the speed of light), so that they obey the familiar laws that seem to hold for the greater part of things of our experience. dawkins_spine

The final sentences of Dawkins’ book thus proclaim, “Could we, by training and practice, tear off our black burka, and achieve some kind of intuitive — as well as just mathematical — understanding of the very small, the very large, and the very fast? I genuinely don’t know the answer, but I am thrilled to be alive at a time when humanity is pushing against the limits of understanding. Even better, we may eventually discover that there are no limits.”

Dawkins is here suggesting the equivalent for physical science of opening the doors of intellection, as well as the doors of perception. Prior to this passage the motif of the burka is used to emphasize the narrow range of phenomena to which our senses give us access, and he rightly generalizes to the possibility of understanding that similarly throws off the limits imposed by the anthropocentric origins of our ideas about the world.

However, there are limits. We already know this, and we can prove it. Dawkins’ mention of “just mathematical” in this passage — as though to say “mere mathematical” — provides a clue as to the false hopefulness of this otherwise inspiring conclusion. There is a highly developed branch of mathematical logic that deals explicitly and systematically with what are called the “limitative theorems”, i.e., theorems of formal logic that demonstrate the logical limits of our thinking.  The formal treatment of these limits is daunting, but it has been well-put (intuitively so, no less) by Wittgenstein: “The limits of my language mean the limits of my world.” (Tractatus Logico-Philosophicus, 5.6)

The limitative theorems are especially interesting in relation to Dawkins’ book given an amusing formulation given to the most famous of the limitative theorems, viz. Gödel’s incompleteness theorems:

“Suppose we loosely define a religion as any discipline whose foundations rest on an element of faith, irrespective of any element of reason which may be present. Quantum mechanics for example would be a religion under this definition. But mathematics would hold the unique position of being the only branch of theology possessing a rigorous demonstration of the fact that it should be so classified.”

F. De Sua, “Consistency and completeness — a résumé” American Mathematical Monthly, 63 (1956)

The kind of intuitive mastery of concepts that originate in mathematics and advanced recent work in the physical sciences is difficult, but we have ample evidence that it is achievable. The concept of zero was once advanced mathematics; today it is elementary, and most people experience little difficulty in mastering the concept. The truth table method for semantic decision procedures was advanced logic when Wittgenstein wrote his Tractatus; now it is familiar fare for elementary logic textbooks.

We create intuitions through the labor of the mind, and once an adequate intuition is obtained we can let the labor fall away as though it had never existed, like the scaffolding that held Michelangelo up to the underside of the ceiling of the Sistine Chapel. That is to say, it is possible to transcend the process by which we arrive at our ideas — the ontogeny of cognition, as it were — and to grasp the idea beyond its own history. When we do this in the social context of the idea (as with the examples above of the concept of zero and the truth table method) we even transcend the phylogeny of cognition. To invoke Wittgenstein again: .

My propositions are elucidatory in this way: he who understands me finally recognizes them as senseless, when he has climbed out through them, on them, over them. (He must so to speak throw away the ladder, after he has climbed up on it.)

Wittgenstein, Tractatus Logico-Philosophicus, 6.54

This motif of throwing away the ladder after climbing up it has become widely quoted in philosophical literature. Wittgenstein gives the paradoxical tension between intuitive concept and formal surrogate in its strongest form. Even when the tension does not appear in this radically paradoxical form, it is still present, informing our conceptions of logic, mathematics, and science. Sometimes the intuitive conception comes first, and we struggle to formalize it; sometimes the formal concept comes first, and we struggle to find an intuition adequate to it. In either case, it is a philosophical labor of no mean order (and one rarely appreciated for what it is).

This notion was also given a surprising and equally paradoxical (i.e., counter-intuitive) formulation by Alfred North Whitehead:

“It is a profoundly erroneous truism, repeated by all copy-books and by eminent people when they are making speeches, that we should cultivate the habit of thinking of what we are doing. The precise opposite is the case. Civilization advances by extending the number of operations which we can perform without thinking about them. Operations of thought are like cavalry charges in a battle — they are strictly limited in number, they require fresh horses, and must only be made at decisive moments.”

Alfred North Whitehead, An Introduction to Mathematics, Chapter 5

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Epistemic Space

19 February 2009

Wittgenstein, on the left, wrote one of the masterpieces of twentieth century philosophy, the Tractatus Logico-Philosophicus

Wittgenstein, on the left, wrote one of the masterpieces of twentieth century philosophy, the Tractatus Logico-Philosophicus

Ludwig Wittgenstein, in his Tractatus Logico-Philosophicus, introduced the concept of logical space. This does not play a large role in the Tractatus, but a few other philosophers have found it to be of interest and have fleshed out the concept. Donald Davidson formulated an analogous conception of logical geography: “to give the logical form of a sentence is to give its logical location in the totality of sentences, to describe it in a way that explicitly determines what sentences it entails and what sentences it is entailed by.” (Essays on Actions and Events, “Criticism, Comment, and Defence”, p. 140)


Ultimately, all space is logical space, and all geography is logical geography, or, rather, these categories of logical space and logical geography are the most formal and abstract formulations of space as it is conceived by the intellect as an ideal form of order. Wittgenstein and Davidson present to us the most idealized and refined formulations of concepts that we employ daily in our ordinary lives in a less refined and less ideal form. But if we are to come to a theoretical understanding of space, we must master the abstract and formal conceptions. Geopolitics is ultimately incomprehensible without logical geography.

Foucault sought to map the spaces of knowledge, and called his chair that of "History of systems of thought"

Foucault sought to map the spaces of knowledge, and called his chair that of "History of systems of thought"

Our knowledge is laid out in epistemic space, so that our epistēmē (as Foucault called it; ἐπιστήμη in the original Greek) governs not only how we see and understand the world, but also how we move through it and how we construct our lives within the world, for the world is a world in space defined epistemically, that is to say, defined in terms of our knowledge.

The Tabula Peutingeriana

The Tabula Peutingeriana: this is a lesson in how differently ancient and modern peoples see (and construct) the space in which they live.

On 27 November 2007, in celebration of its inclusion in UNESCO’s Memory of the World Register, the Tabula Peutingeriana was displayed in Vienna. I should have liked to have seen this. It is a medieval copy of an ancient Roman road map. The copy is quite large, like many medieval maps, though quite long and thin, about seven meters by thirty-four centimeters. The Mediterranean Sea is stretched out like a river in this elongated space. The original is thought to date from some time in the fifth century AD.

The map mosaic at Madaba, Jordan.

The map mosaic at Madaba, Jordan.

One of the few maps to date from antiquity is perhaps a hundred or so years later than the original for the Tabula Peutingeriana, and this is the map mosaic at Mādabā, Jordan. While damaged, it survives in part because of the robust character of mosaics. Colored stone and glass set in concrete survives the centuries much better than parchment or papyrus. This map mosaic, like the Tabula Peutingeriana, and indeed as with all maps, there is a surprising combination of practical detail and ideological schematism. A map is a practice of political ideology.


A detail from the Tabula Peutingeriana, showing the city of Rome as an Emperor, with globe and sceptre, seated on a throne.

As strange as the Tabula Peutingeriana looks to modern eyes, stranger still is the map of the world by Mahmud al-Kashgari. The Tabula Peutingeriana seems stretched and distorted, but it is still recognizably a map. The map of al-Kashgari might not be recognized as a map by the modern, western eye. Its schematism of a circle within a square contrasts with the schematism of “T in O” maps mentioned below, but perhaps as intriguingly, mirror the structure of Hagia Sophia, the great church built under the rule of Justinian, but which became the model of mosques the world over after Constantinople was taken by the Turks.

A map of the world by Mahmud al-Kashgari from his Diwan Lugat at-Turk, believed to date from 1072 AD.

A map of the world by Mahmud al-Kashgari from his Diwan Lugat at-Turk, believed to date from 1072 AD.

As with most maps of late antiquity and later, Jerusalem is shown at the center of the world in the Mādabā map, a Christian-era map, whereas the focus of the Roman map was Rome itself, represented by a crowned man sitting on a throne (on the far right of the larger section of the Tabula Peutingeriana pictured above, and shown in detail immediately above). And, as we know, all roads lead to Rome. The Via Appia Antiqua is shown radiating from Rome at about 4 o’clock. That the Roman map was a road map is a sign of the role that communications networks played in Roman administration.

A medieval "T" map, also called a "T-O" map or a "T and O" map or a "T in O" map.

A medieval "T" map, also called a "T-O" map or a "T and O" map or a "T in O" map.

Even more schematic, and nearly devoid of practical detail, is the medieval “T in O” map: the very name describes its structure. In many of these maps Jerusalem in prominently in the center with Asia on top, Europe to the lower left of the “T” and Africa to the lower right of the “T”. Such a construction of the world is purely about expressing the relation of the major divisions of the world to its center, positioning the human world within the divine cosmos — marking one’s place within the totality, to borrow a term of the Davidson quote above.

The Thomas Digges chart of a Copernican solar system from 1576.

The Thomas Digges chart of a Copernican solar system from 1576.

Even as maps became more scientifically sophisticated after the scientific revolution, they remain highly schematic and their purpose is often to show the interrelation of major epistemic divisions so that man can know his place in the world. The Thomas Digges Copernican solar system (shown above) is more sophisticated than a medieval “T in O” map, but similarly schematic in conception. A map orders the world for us, and in so ordering our world, orders our lives.

Scientific realism has produced its own abstract and schematic maps, not unlike the dramatic poster art of so-called socialist realism.

Scientific realism has produced its own abstract and schematic maps, with striking color contrasts and bold graphic motifs not unlike the dramatic poster art of so-called socialist realism.

Some of the most advanced scientific maps of our time continue to be as schematic as maps of the past, highly specialized depictions of the state of our knowledge, and such that can only be meaningfully interpreted and understood by an adept of the culture so formulated. One of the most famous scientific images of our time is that of the cosmic microwave background radiation, which showed very subtle differences in the background radiation. This slight departure from a purely homogeneous background radiation is the oldest evidence we have of the natural history of the universe. Here time is shown unfolded across deep space, mapped, as it were. The order mapped in space overflows into an order in time.

Maps of the Roman Empire are inherently problematic, as almost all have been formulated according to a paradigm derived from the territorial nation-state.

Maps of the Roman Empire are inherently problematic, as almost all have been formulated according to a paradigm derived from the territorial nation-state: at the heart of the empire is not a particular territory, but the Mediterranean Sea.

The maps we draw of the migration and distribution of species, with their long, sinuous lines demarcating broad swathes of territory, are redolent of the maps historians attempt to draw for past political entities, with their long, curving lines across deserts, steppe, and forest where the territorial sovereignty of any political entity would be questionable, especially before the age of the territorially defined nation-state.

Attempts to map bird populations and migrations always remind me of attempts to map pre-nation-state political entities: both the world of the past and the avian world are alien to us.

Attempts to map bird populations and migrations always remind me of attempts to map pre-nation-state political entities: both the world of the past and the avian world are alien to us.

A map represents a special kind of knowledge, and indeed a special approach to knowledge — a bird’s eye view of knowledge in which epistemic space is plotted out in a scheme that is both abstract and synthetic, at once intuitive and non-constructive. We are all familiar with the saying that, “The map is not the territory” (credited to Alfred Korzybski), which emphasizes the abstract and schematic character of maps. Like Magritte’s picture of a pipe, which is self-evidently not a pipe and yet recognizably a pipe, a map represents, and as a representation it assumes and presupposes certain principles of representation. Maps, thus, are texts inscribed in a symbolic language.


In our bureaucratized industrial society, we live by flow charts, which are transparently maps of epistemic space. In this way we see at a glance our life mapped out, the paths we will take, the choices we must make, and even the choices that lead to other choices leave us within the well-worn schema of life reduced to an algorithm.

Medieval maps were often highly "realistic" in their use of projection and perspective, yet highly "realistic" in the one-to-one correspondence observed between objects and their representation.

Medieval maps were often highly "unrealistic" in their use of projection and perspective, yet highly "realistic" in the one-to-one correspondence observed between objects and their representation.

Today one commonly hears others say “It’s just semantics” as though semantics don’t matter, and one could equally well imagine someone saying, in the same dismissive vein, “It’s just syntactics” as though it doesn’t matter what language you happen to be speaking. But it does matter. A perspicuous symbolism can be the difference between getting your meaning across or failing to do so. In Principia Mathematica Russell and Whitehead wrote, “The terseness of the symbolism enables a whole proposition to be represented to the eyesight as one whole, or at most in two or three parts divided where the natural breaks, represented in the symbolism, occur.” (Whitehead and Russell, Principia Mathematica to *56, London and New York: Cambridge University Press, 1978, p. 2) And this was the same sort of thing that Wittgenstein was trying to do in his Tractatus, and in doing so found himself explicitly formulating a doctrine of logical space.

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The Forma Urbis Romae was a map of ancient Rome carved into marble slabs and on display in the Templum Pacis.

The Forma Urbis Romae was a map of ancient Rome carved into marble slabs, affixed to a wall, and (in antiquity) permanently on display in the Templum Pacis.

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