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 medieval illustration of the four humours: melancholic, choleric, phlegmatic, and sanguine (clockwise from upper left).

What is a definitive formulation?

Recently on my other blog I discussed the philosophical pursuit of definitive formulations. What is a definite formulation? The reader will, I am sure, immediately see that giving a concise and accurate idea of what constitutes a definitive formulation would itself require a definitive formulation of a definitive formulation.

I don’t yet have a definitive formulation of what constitutes a definitive formulation. I could simply say that it is a formulation of a concept that could serve as a definition, but this wouldn’t be very helpful. Here is how I characterized it in my other post:

“…a handful of short, clear, concise, and intuitively accessible sentences…”


“…to put this in clear and simple terms, if I have a definitive formulation, that means if you stopped me on the street and asked me to explain myself while standing on one foot, I could do it. Lacking definitive formulations, the attempted explanation would go on a little too long to be comfortable (or safely balanced) on one foot.”

Lacking a definitive formulation of an idea that is central to our thought means that we can only say what Augustine said of time in his Confessions:

What then is time? If no one asks me, I know: if I wish to explain it to one that asketh, I know not: yet I say boldly that I know, that if nothing passed away, time past were not; and if nothing were coming, a time to come were not; and if nothing were, time present were not. (11.14.17)

quid est ergo tempus? si nemo ex me quaerat, scio; si quaerenti explicare velim, nescio. fidenter tamen dico scire me quod, si nihil praeteriret, non esset praeteritum tempus, et si nihil adveniret, non esset futurum tempus, et si nihil esset, non esset praesens tempus.

In some cases, I think that we can move beyond this Augustinian limit to definition, and it is when we hit upon a definitive formulation that we are able to do this.

It seems appropriate that I should give a concrete example of something that I would identify as a definitive formulation, and since I have recently hit upon a formulation that I rather like, I will try to use this to show what a definitive formulation is.

Call it what you will… temperament, personality, disposition… but people are not all the same.

What is temperament?

I have written several posts about temperament, including Temperamental Diversity, A Third Temperament, Intellectual Personalities and Temperament and Civilization. I don’t think that philosophy, science, or socio-political thought has yet done justice to the role that temperament plays in the world.

But what is temperament? The seventh of ten definitions in the Oxford English Dictionary (which of the ten is the closest to the sense of “temperament” as I have been using the word) defines temperament as follows:

“Constitution or habit of mind, esp. as depending upon or connected with physical constitution; natural disposition”

The sixth of the OED definitions defines temperament in terms of the four humours recognized in medieval medical theory and practice:

“In mediæval physiology: The combination of the four cardinal humours (see humour n. 2b) of the body, by the relative proportion of which the physical and mental constitution were held to be determined; known spec. as animal temperament; also, The bodily habit attributed to this, as sanguine temperament, choleric temperament, phlegmatic temperament, or melancholic temperament (see the adjs.).”

In traditional philosophical parlance, a dictionary definition gives us a nominal definition, but as philosophers what we really want is a real definition. While the philosophical distinction between nominal and real definitions is ancient and widely familiar, and therefore probably ought to remain untouched, I think it is more intuitive to call these two kinds of definition formal definition and metaphysical definition. A formal definition situates the meaning of a term within a formal system, perhaps within the system of language, whereas a metaphysical definition situates the meaning of a term within the structure of the world. So I guess what I am saying here is that one function of a definitive formulation is to give a metaphysical definition — but to be able to do so without requiring the exposition of an entire metaphysical system. You can imagine why this might be difficult.

So, what would I offer as a definitive formulation of temperament, that (hopefully) goes beyond the formal (i.e., nominal) definition in the OED? I define temperament as follows:

Temperament is the intellectual expression of individual variability.

I hope that the reader doesn’t find this too anti-climactic. I’ll try to explain why I find this to be a fruitful formulation.

Ludwig Wittgenstein, former Russellian, later anti-Cantorian

The charm of an idea

A definitive formulation, as I understand it, has an aphoristic quality: it is brief, concise, sententious, and pregnant with meaning. It also has a certain indefinable “appeal” that, like most forms of appealingness, is compelling to some even while it leaves others cold.

Wittgenstein formulated this appeal by calling it the “charm” that some proofs in mathematics and the foundations of mathematics possess. The later Wittgenstein was concerned to criticize the whole Cantorian conception of set theory and transfinite numbers, and much of Wittgenstein’s later philosophical of mathematics has this purpose implicitly as the center of the exposition. (In connection with this, I have previously mentioned Brouwer’s influence on Wittgenstein in Saying, Showing, Constructing, and more recently wrote more about Brouwer in One Hundred Years of Intuitionism and Formalism.)

Here’s what Wittgenstein said about mathematical “charm” in his lectures of 1939:

“The proof has a certain charm if you like that kind of thing; but that is irrelevant. That fact that is has this charm is a very minor point and is not the reason why those calculations were made.–That is colossally important. The calculations have their use not in charm but in their practical consequences.”

“It is quite different if the main role or sole interest is this charm — if the whole interest is showing that a line does cut when it doesn’t, which sets the whole mind in a whirl, and gives the pleasant feeling of paradox. If you can show that there are numbers bigger than the infinite, your head whirls. This may be the chief reason this was invented.”

Ludwig Wittgenstein, Wittgenstein’s Lectures on the Foundations of Mathematics, Cambridge, 1939, edited by Cora Diamond, University of Chicago Press, 1989, p. 16

With this in mind, I am well aware that the “charm” that I find in my definitive formulation of temperament may well be lost on others. The fact that an idea that has a certain charm for one person has none for another is itself a function of temperament. Individuals of different temperaments will find an intellectual charm in different formulations.

Theoretical contextualization

Part of the charm that a formulation has (or fails to have) is the connections that it forges to familiar theories. A definitive formulation, among its other functions, contextualizes a less familiar or less precise concept in an established theory or theories, enabling a systematic exploration and exposition of the idea in relation to familiar and therefore more thoroughly explored theories. Well known theories provide clear parameters for an idea, which, when formerly known only in a vague and imprecise form, had no clear parameters.

In formulating temperament as the intellectual expression of individual variation I am contextualizing human temperament in evolutionary theory, and thereby suggesting an interpretation of temperament based in and drawing upon evolutionary psychology. Thus evolutionary theory provides the parameters for temperament understood as the intellectual expression of individual variability.

Individual variability is one of the drivers of natural selection. When distinct individuals have distinct properties, a selection event may favor (select for) some properties while disfavoring (select against) other properties. Usually we think of the properties of an organism as being structural features of an organism: one finch has a longer beak than another, or one ape is better at walking on two legs than another. These differences might disappear into the dustbin of natural history if no selection event comes along that favors one or the other. But if a selection event does occur, and it favors some structural attribute of an organism that varies among individuals, the favored individuals will go on to experience differential survival and reproduction.

While we usually think of selection in structural terms, a selection event can also select for behaviors. Organisms can adapt to their environment through behaviors just as certainly (and much more rapidly) than through structural changes in their bodies. Behavioral adaptation is no less significant in natural history than structural adaptation.

At very least with the emergence of human beings, and probably also with other species, both hominid precursors of homo sapiens and other large-brained mammals, mind emerged in natural history. With the emergence of mind, there emerged also a novel basis of selection. Some minds are constituted in one way, while other minds are constituted in other ways. In other words, the same individual variability we find in bodies and behaviors are also to be found in minds.

If a selection event occurs that should happen to favor (or disfavor) any one kind of mind over any other kind of mind, those possessing the favored minds will enjoy differential survival and reproduction. With individual variability of minds represented in a sentient population — individual temperaments that lead individuals to think in different ways, and value things in different ways, and deliberate over alternatives in different ways — there is the continual possibility of natural selection.

The more variety of minds that there are, the greater the number of alternatives amongst which a selection event can select, the greater the likelihood that some one temperament is more fitted to survive the particular conditions that obtain than other temperaments.

Thus to formulate temperament as the intellectual expression of individual variability is to place mind within natural history.

To place mind within nature is a metaphysical formulation.

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Ludwig Wittgenstein and L. E. J. Brouwer

Brouwer and Wittgenstein were contemporaries, with the whole of Wittgenstein’s years contained within those of Brouwer’s (Wittgenstein lived 1889 to 1951 while Brouwer lived the longer life from 1881 to 1966). It is mildly ironic that even as Brouwer’s followers were playing down his mysticism and trying to extract only the mathematical content from his intuitionist philosophy (even the faithful Heyting distanced himself from Brouwer’s mysticism), Wittgenstein’s writings reached a much larger public which resulted in the mystical content of Wittgenstein’s works being played up and the early Wittgenstein himself, very much the logician following in the tradition of Frege and Russell, presented as a mystic.

Not only were Brouwer and Wittgenstein contemporaries, but we also know that Brouwer played a little-known role in Wittgenstein’s return to philosophy. After having written the Tractatus Logico-Philosophicus and then disappearing into the mountains of Austria to become a village schoolmaster in Trattenbach, some of those philosophers that continued to seek out Wittgenstein in his self-imposed exile convinced him to go to a lecture in Vienna in March 1928. The lecture was delivered by Brouwer (Brouwer gave two lectures; Wittgenstein is said to have attended one of them). Wittgenstein was said to have listened to the lecture with a surprised look on his face (sort of like G. E. Moore saying that Wittgenstein was the only student that looked puzzled at this lectures). So it may be the case that Brouwer played a pivotal role in the transition from the thought of the early Wittgenstein to the thought of the later Wittgenstein. (Matthieu Marion has argued this thesis.)

Wittgenstein’s distinction between saying and showing, a doctrine that dates from the Tractatus (cf. sections 4.113 and following), is often adduced in expositions of his alleged mysticism. According to Wittgenstein’s distinction, some things can be said but cannot be shown, while other things can be shown but cannot be said. While to my knowledge Wittgenstein never used the term “ineffable,” that which can be shown but cannot be said would seem to be a paradigm case of the ineffable. And since Wittgenstein identified a substantial portion of our experience as showable although unsayable, the ineffable seems then to play a central role in his thought. This puts Wittgenstein firmly in the company of figures like, say, St. Symeon the New Theologian (also, like Wittgenstein, an ascetic), which makes the case for his mysticism.

An extract from St. Symeon on the ineffable: “The grace of the all-holy spirit is given as earnest money of the souls pledged in marriage to Christ. Just as a woman without a pledge has no certainty that the union with the groom will occur within a certain length of time, so does the soul have no firm assurance that it will be re-united to its God and Master for all eternity. The soul cannot be certain that it will achieve this mystic, ineffable union nor that it will enjoy its inaccessible beauty if it does not have the pledge of His grace and does not consciously have that grace within.” (Krivocheine, Basil and Gythiel, Anthony P., In the Light of Christ: Saint Symeon, the New Theologian 949–1022, St. Vladimir’s Seminary Press, 1986, p. 367)

Brouwer was a bit more explicit in his doctrine of ineffability than was Wittgenstein, and he repeatedly asserted that the language of mathematics was a necessary evil that approximated but never fully captured the intuitive experience of mathematics, which he understood to be a free creation of the human mind. This comes across both in his early mystical treatise Life, Art, and Mysticism, which is pervaded by a sense of pessimism over the evils of the world (which include the evils of mathematical language), and his more technical papers offering an exposition of intuitionism as a philosophy of mathematics. But, like Wittgenstein, Brouwer does not (to my limited knowledge) actually use the term “ineffable.”

There is another ellipsis common to both Brouwer and Wittgenstein, and that is despite Brouwer’s openly professed intuitionism, which can be considered a species of constructivism (this latter is a point that needs to be separately argued, but I will only pass over it here with a single mention), and despite the strict finitism of the later Wittgenstein, which can also be considered a species of constructivism, neither Brouwer nor Wittgenstein employ Kantian language or Kantian formulations. No doubt there are implicit references to Kant in both, but I am not aware of any systematic references to Kant in the work of either philosopher. This is significant. Both Brouwer and Wittgenstein were philosophers of the European continent, where the influence of Kant remains strong even as his reputation waxes and wanes over the generations.

Kant was an early constructivist, or, rather, a constructivist before constructivism was explicitly formulated, and therefore sometimes called a proto-constructivist — although I have pointed out an obvious non-constructive dimension to Kant’s thought despite his proto-constructivism (which I do not deny, notwithstanding Kant’s non-constructive arguments in the first Critique). Kant’s classic proto-constructivist formulation is that the synthetic a priori truths of mathematics must be constructed, or “exhibited in intuition.” It is this latter idea, of a concept being exhibited in intuition, that has been particularly influential. But what does it mean? Obviously, a formulation like this has invited many interpretations.

The approaches of Brouwer and the later Wittgenstein could be considered different ways of exhibiting a concept in intuition. Brouwer, by casting out the law of the excluded middle from mathematics (at least in infinitistic contexts), assured that double negation was not equivalent to the truth simpliciter, so that even if you know that it is not the case that x is false, you still don’t know that x is true. (On the law of the excluded middle cf. P or not-P.) The later Wittgenstein’s insistence upon working out how a particular term is used and not merely settling for some schematic meaning (think of slogans like “don’t ask for the meaning, ask for the use” and “back to the rough ground”) similarly forces one to consider concrete instances rather than accepting (non-constructive) arguments for the way that things putatively must be, rather than how they are in actual fact. Both Wittgenstein’s finitism and Brouwer’s intuitionism would look with equal distaste upon, for example, proving that every set can be well-ordered without actually showing (i.e., exhibiting) such an order — also, the impossibility of exhaustively showing (i.e., exhibiting in intuition) that every set can be well-ordered if one acknowledges an infinity of sets.

I give this latter example because I think it was largely the perceived excesses of set theory and Cantor’s transfinite number theory that were essentially responsible for the reaction among some mathematicians that led to constructivism. Cantor was a great mathematical innovator, and his radical contributions to mathematics spurred foundationalists like Frege (who objected to Cantor’s methods but not his results) and Russell to attempt to construct philosophico-mathematical justifications, i.e., foundations, that would legitimize that which Cantor had wrought.

The reaction against infinitistic mathematics and foundationalism continues to the present day. Michael Dummett wrote in Elements of Intuitionism, a classic textbook on basic intuitionistic logic and mathematics, that:

“From an intuitionistic standpoint, mathematics, when correctly carried on, would not need any justification from without, a buttress from the side or a foundation from below: it would wear its own justification on its face.”

Dummett, Michael, Elements of Intuitionism, Oxford University Press, 1977, p. 2

In other words, mathematics would show its justification; in contrast, the foundationalist project to assure the legitimacy of the flights of non-constructive mathematics was wrong-headed in its very conception, because nothing that we say is going to change the fact that non-constructive thought that derives its force from proof, i.e., from what is said, does not show its justification on its face. Its justification must be established because it does not show itself. This is what “foundations” are for.

Note: There is also an element of intellectual ascesis in Dummett’s idea of a conservative extension of a theory, and this corresponds to the asceticism of Wittgenstein’s character, and, by extension, to the asceticism of Wittgenstein’s thought — asceticism being one of the clear continuities between the earlier and the later Wittgenstein — like the implicit development of constructivist themes.

But it was not only the later Wittgenstein who reacted with others against Cantor. It seems to me that the saying/showing distinction of the Tractatus is a distinction not only between that which can be said and that which can be shown, but also a distinction between that which is established by argument, possibly non-constructive argument, and that which is exhibited in intuition, i.e., constructed. If this is right, Wittgenstein showed an early sensitivity to the possibility of constructivist thought, and his later development might be understood as a development of the constructivist strand within his thinking, making Wittgenstein’s development more linear than is often recognized (though there are many scholars who argue for the unity of Wittgenstein’s development on different principles). The saying/showing distinction may be the acorn from which the oak tree of the Philosophical Investigations (and the subsequently published posthumous works) grew.

For the early Wittgenstein, the distinction between saying and showing was thoroughly integrated into his idea of logic, and while in the later sections of the Tractatus the mysticism of what which can only be shown but cannot be said becomes more evident, it is impossible to say whether it was the logical impulse that prevailed, and served as the inspiration for the mysticism, or whether it was the mystic impulse that prevailed, and served as the pretext for formulating the logical doctrines. But the logical doctrines are clearly present in the Tractatus, and serve as the exposition of Wittgenstein’s ideas, even up to the famous metaphor when Wittgenstein says that the propositions of the Tractatus are like a ladder than one must cast away after having climbed up and over it.

Just as there is a mathematical content to Brouwer’s mysticism, so too there is a logical content to Wittgenstein’s mysticism. It is, in fact, likely that Wittgenstein’s distinction between saying and showing was suggested to him by what is now called the “picture theory of meaning” given an exposition in the Tractatus. Few philosophers today defend Wittgenstein’s picture theory of meaning, but it is central to the metaphysics of the Tractatus. For Wittgenstein, the logical structure of a proposition can be shown but not said. Since for Wittgenstein in his Tractarian period, “The facts in logical space are the world” (1.13), and “In the proposition the thought is expressed perceptibly through the senses” (3.1) — i.e., the proposition literally exhibits its structure in sensory intuition — thus, “The proposition is a picture of reality.” (4.01) One might even say that a proposition exhibits the world in intuition.

Today these formulations strike us as a bit odd, because we think of anything that can be formulated in logical terms as a paradigm case of something that can be said, and very possibly also something that may not be showable. For us, logic is a language is among languages, and one way among many to express the world; for the early Wittgenstein, on the contrary, logic is the structure of the world. It shows itself because the world shows itself, and after showing itself there is nothing more to be said. The only appropriate response is silence.

As we all know from the final sentence of the Tractatus, whereof one cannot speak, thereof one must remain silent. According to the Wittgenstein of the Tractatus, all scientific questions can be asked and all scientific questions can be answered (shades of Hilbert’s “Wir müssen wissen. Wir werden wissen.” — which Per Martin-Löf has called Hilbert’s solvability axiom, and which is the very antithesis of Brouwer’s rejection of the law of the excluded middle), but even when we have answered all scientific questions, the problems of life remain untouched.

As implied by the early Wittgenstein’s insistence upon the solvability of all scientific questions, the metaphysics of Brouwer and Wittgenstein were very different. Their common constructivism does not prevent their having fundamental, I might even say foundational, differences. Also, while Wittgenstein comes across in a melancholic fashion (a lot like Plotinus, another philosophical mystic), he is not fixated on the evils of the world in the same way that Brouwer was. If both Brouwer and Wittgenstein can be called mystics, they are mystics belonging to different traditions. Brouwer was a choleric mystic while Wittgenstein was melancholic mystic.

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Grand Strategy Annex

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A couple of days ago in describing my pilgrimage to Kinn I suggested that the phenomenon of pilgrimage is a Wittgensteinian “form of life,” and as a form of life we may understand it better if we confine ourselves to the material infrastructure while setting aside the formal superstructure that surrounds the form of life we call pilgrimage. But in a fine-grained account of pilgrimage we must distinguish between those forms of pilgrimage that, when taking the long view of the big picture, become conflated.

As I attempted to show, in different ways, in Epistemic Orders of Magnitude and P or not-P, both la longue durée and the fine-grained view have their place in our epistemic development — respectively, and roughly, they represent the non-constructive and the constructive perspectives on experience — and we ought to be equally diligent in exploring the consequences of each perspective, since we have something important to learn from each.

I tried to suggest a similarly comprehensive synthesis yesterday in A Meditation upon the Petroglyphs of Ausevik, when remarking that an extrapolation of a personal philosophy of history, when drawn out to a sufficient extent coincides with the history of the world entire. In other words, non-constructivism represents the furthest reach of constructivist thought, which immediately suggests the contrary perspective, i.e., that constructivism represents the furthest reach of non-constructive thought. Constructivism is non-constructivism in extremis; non-construtivism is constructivism in extremis. To translate this once again into historico-personal terms, the history of the world entire coincides with an intimately personal philosophy of history when the former is extrapolated to the greatest extent of its possible scope.

In a fine-grained account of pilgrimage (in contradistinction to pilgrimage understood in outline, in the context of la longue durée), at the level of personal experience that is constructive because every detail is of necessity immediately exhibited in intuition and nothing whatsoever is demonstrated, we can distinguish many forms of pilgrimage. There are religious pilgrimages, such as the Sunnivaleia, there are personal pilgrimages, such as my pilgrimage to Kinn, there are aesthetic pilgrimages, such as when the custom dictated the young gentlemen of good families and fortune would take the “Grand Tour” of Europe, there are political pilgrimages, as when a candidate for office visits a politically significant place — and there are even philosophical pilgrimages. I have previously made some minor philosophical pilgrimages, as when I sought out Kierkegaard’s grave in Copenhagen and similarly visited Schopenhauer’s grave in Frankfurt. Today I made another philosophical pilgrimage, by visiting the small town of Skjolden, where Wittgenstein spent time working on the ideas that would later becomes the Tractatus Logico-Philosophicus.

In the letters that Wittgenstein subsequently exchanged with his acquaintances in Skjolden (which have, of course, been published along with the rest of his correspondence), the people of Skjolden almost always close their letters by observing that Skjolden is as it always was and ever will be, essentially unchanged in the passage of time. I wrote about this previously in The Charms of Small Town Norway. It seems to be true that life changes very slowly, almost imperceptibly, in the fjord country of Norway, as life always changes slowly in isolated, mountainous regions the world over. The peoples who retreat from the onrushing advance of civilization to the margins of the world where they will not be bothered, are not the kind of peoples who wish to indulge in change for the sake of change. It is this latter attitude that typifies industrial-technological civilization, which is still largely confined to the regions of the world fully given over to agricultural civilization. The margins of the world before industrialization largely coincide with the margins of the world after industrialization.

Wittgenstein, I think, left little impact upon Skjolden. He didn’t make waves, as it were, and didn’t want to make waves. Life in Skjolden is probably little changed in essentials from when Wittgenstein isolated himself in a small, bare hut at the end of a fjord in order to think and write about logic. I think that Wittgenstein would have liked this — or, at least, that he would have preferred this near absence of influence. The fjords are unchanged since Wittgenstein lived here, even if life has been modernized, and they still provide a refuge for those who would seek a world largely untouched by what Wittgenstein in his later years would call, “the main current of European and American civilization,” from which he felt profoundly alienated.

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Grand Strategy Annex

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The boat that brought us from Florø to Kinn — six passengers total, including my sister and me.

One of the westernmost islands of Norway is Kinn, which can be reached by boat from Florø. On Kinn there is a Romanesque church, one of the oldest stone churches in Norway, and also, like the island, perhaps the westernmost church of Norway. The island and the church were the object of pilgrimage in the middle ages. There is a legend, of course, and it is the Legend of Saint Sunniva.

The Romanesque church on the island of Kinn.

According to the legend, Sunniva was a daughter of an Irish king and a Christian. Although the Irish were among the first Christians in Europe, they couldn’t defend themselves, so when the Vikings strong-armed their way into the kingdom of Sunniva’s father, it seemed that Sunniva was going to be forced to marry a Viking and a pagan. Horrified at the prospect, Sunniva with two sisters, a brother, and a number of followers fled. They went down to the sea in ships, and to place themselves utterly in the hands of God, they cast away their oars and sails so that their destination would be decided by God alone. Here is one telling of the legend of Saint Sunniva:

“Without oars or ship-gear they committed themselves to
the sea, and the storm and tempest carried them across the North Sea and finally landed them on the little island of Selje. The people on the mainland saw the strangers, and proceeded to attack them. Sunniva and her companions fled for refuge to a cave on the island, and prayed that death might come to deliver them from their heathen foes. The prayer was heard, and a stenskred (stone avalanche) fell and closed the entrance to the cave and all perished. Later on some merchants sailing past the island, saw a light, and going ashore found a human head, which emitted a fragrant odor. They went to Olaf Trygvesson and told the tale. The king then with Bishop Sigurd went to the island, and after searching they discovered the body of St. Sunniva perfectly preserved. A church was erected on the island and a cloister established, and from Selje later on, many teachers went out to spread the faith. It seems most probable, on the whole, that the visit of Olaf and Bishop Sigurd to Selje, took place after he had gone to Nidaros, and when his work of Christianizing the north was further advanced. Selje was subsequently the seat of a bishopric, which was transferred to Bergen at the end of the eleventh century; but it remained an important monastic center down to the sixteenth century, and may well be called the ‘holy isle’ of Norway.”


While Sunniva herself washed up on the island of Selje, her sisters came to rest on different islands. Her sister Ingeborg washed up on the island of Moster, and the other sister, Borni, came to rest on Kinn.

A symbol of a Sunnivaleia pilgrimage way on one of the buildings next to the church on Kinn.

We know from other historical accounts that Christian monks from Ireland, seeking both complete isolation from the world and to completely place their fate in God’s hands, did in fact commit themselves in primitive rafts to the icy waters of the north sea. Those who arrived alive on distant shores created monasteries where they landed. We also know that the prevailing currents will bring flotsam from Ireland to this part of the Norwegian coast. Moreover, we know that in the transitional period of Christianization that there were many stories of princesses who refused to be married to heathens, probably intended to bolster popular piety — but of course the legend is much more beautiful than the facts.

My sister with wooden carvings of St. Sunniva, St. Borni, and St. Ingeborg, but we were told that it is likely there were originally carvings of St. Barbara, St. Catarine, and Mary Magdalene, executed in a German workshop, and saved from the furies of the Reformation by their creative adaptation to local legend.

While on Kinn we were told a local legend about the life of Saint Borni after she arrived on Kinn. She contracted with a local man, perhaps a supernatural character (perhaps even a species of troll), to build the church that is the church that still stands on Kinn. He said he would do so if Borni would marry him, but Borni was as horrified of marrying him as Sunniva had been horrified at the idea of marrying a Viking. So he changed his offer: he would build the church, and if she could guess his name before he was finished, she would not have to marry him. When the church was nearly finished, Borni traveled to a neighboring island and heard the builder’s folk singing his name in honor of his presumed upcoming nuptials. So Borni returned, called the builder by his name, and so shocked him that he dropped the belfry on the ground next to the church, where it is to be seen today, instead of installing it on the top of the church.

My sister and I inside the church at Kinn. Above our heads is a very rare thirteenth century lectorium, carved by an English monk. It is nothing short of remarkable that this piece of woodcarving survived the centuries.

I have read books and heard lectures in which the writers and speakers insist that it is an anachronism to attribute to medieval pilgrims the motives of modern travelers; that medieval pilgrims were engaged in a religious duty, and that this ideological focus transformed the act of pilgrimage into something distinctive. Well, yes and no. It is right for scholars to point out what makes medieval pilgrimage distinctive, but I don’t buy the most general formulation of this thesis — not for a minute. It is impossible for me to believe, among the vast numbers of peoples who went on pilgrimage throughout the European Middle Ages, that all were solely motivated by a narrowly-conceived religious ideology, and that in visiting distant places never found themselves marveling at the sights in a way indistinguishable from the modern tourist.

Pilgrimage is what Wittgenstein would have called a “form of life.” Or, to use Marxist language, we can find in pilgrimage throughout the ages — whether ancients visiting the Oracle at Delphi or medievals visiting the relics of Saint Sunniva or moderns visiting the lands of their forefathers — an invariant material infrastructure that can be distinguished from the ideological superstructure. In other words, we are all doing pretty much the same thing, whatever we may understand ourselves to be doing.

The altar from the Kinn church has some early elements that date contemporaneously to the church — and the three female saints pictured above previously occupied the center of the altar where there is a painting today — but its appearance today mostly dates to the early eighteenth century.

I, too, was on a pilgrimage when I visited Kinn. It was a familial pilgrimage, like my first trip to Norway in 1988, also with my sister who is traveling with me now. Our father’s mother was born on Kinn and was baptized and confirmed in the church we visited today. So while I would not hesitate to identify tourism as the modern form of pilgrimage, and to identify those great symbols of civilization like the Parthenon and the Taj Mahal as places of tourist pilgrimage, my pilgrimage to Kinn was more personal. It was important for me to see Kinn in order to understand where I come from, and to understand the form of life lived by my ancestors. In that way I become less the Other to my own past, to my own history (in the sense of otherness I described in Being the Other).

Another view of the 13th century lectorium from the Kinn church.

When my father first told me about Kinn he emphasized its barrenness, that there was nothing there but fish. Today I learned that there was a lot of fish — the local guide said that in the late nineteenth century (my fraternal grandmother was born in 1891) that Kinn was so famous for its herring fisheries that there was a saying in Norway to the effect that you can go to Kinn and get rich. And the fishing boats were said to be so thick on the water that you could go from one island to the next by stepping across the boats like a bridge. This gave me a new perspective on Kinn even as at the same time it fitted in with my overall understanding of history.

The rocky and barren coast of Kinn, though at one time in its history it is said that you could have walked across the boats to the next island, seen here in the distance.

At the end of the nineteenth century a number of developments were coming together — increasing populations, increasing commerce, the growing influence of the industrial revolution, and so forth — that meant that traditional resources that had been local staples were transformed into extractive industries and cash crops for an export industry. At Kinn, herring and salmon were the cash crop; they were put on ice and sent to Bergen the same day, and then sent from Bergen to England the next day. At the same time this was shaping the lives of my father’s family in Norway, it was also affecting my mother’s ancestors half a world away at the mouth of the Columbia River, where salmon fishing became a booming industry at the same time, before the over-exploited fisheries could no longer support that level of harvesting. Fortunes were made and fortune vanished almost as quickly. That is the way of the world.

The boat that took us back to Florø from Kinn. The weather could not have been more perfect.

That is how I put it all together — at least, that is what I try to do — bringing together the big picture and the local picture, filling in the details that illuminate the whole by going to the point of my origins and finding what stories I can. In the end, all we have are our stories, and now I have part of the story of my family, with the story of Saint Sunniva and her sisters thrown in for good measure.

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Evening in Floro after our trip to Kinn and a visit to the local Kystmuseet, documenting life along the Norwegian coast.

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Grand Strategy Annex

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The thesis that epistemic space is primarily shaped and structured by geometrical intuition may be equated with Bergson’s exposition of the spatialization of the intellect. Bergson devoted much of his philosophical career to a critique of the same. Bergson’s exposition of spatialization is presented in terms of a sweeping generality as the spatialization of time, but a narrower conception of spatialization in terms of the spatialization of consciousness or of human thought follows from and constitutes a special case of spatialization.

One might well ask, in response to Bergson, how we might think of things in non-spatial terms, and the answer to this question is quite long indeed, and would take us quite far afield. Now, there is nothing wrong with going quite far afield, especially in philosophy, and much can be learned from the excursion.

There is a famous passage in Wittgenstein’s Tractatus Logico-Philosophicus about “logical space,” at once penetrating and obscure (like much in the Tractatus), and much has been read into this by other philosophers (again, like much in the Tractatus). Here is section 1.13:

“The facts in logical space are the world.”

And here is section 3.42:

“Although a proposition may only determine one place in logical space, the whole logical space must already be given by it. (Otherwise denial, the logical sum, the logical product, etc., would always introduce new elements — in co-ordination.) (The logical scaffolding round the picture determines the logical space. The proposition reaches through the whole logical space.)”

I will not attempt an exposition of these passages; I quote them here only to give the reader of flavor of Wittgenstein’s . Clearly the early Wittgenstein of the Tractatus approached the world synchronically, and a synchronic perspective easily yields itself to spatial expression, which Wittgenstein makes explicit in his formulations in terms of logical space. And here is one more quote from Wittgenstein’s Tractatus, from section 2.013:

“Every thing is, as it were, in a space of possible atomic facts. I can think of this space as empty, but not of the thing without the space.”

I find this particularly interesting because it is, essentially, a Kantian argument. I discussed just this argument of Kant’s in Kantian Non-Constructivism. It was a vertiginous leap of non-constructive thought for the proto-constructivist Kant to argue that he could imagine empty space, but not spatial objects without the space, and it is equally non-constructive for Wittgenstein to make the same assertion. But it gives us some insight into Wittgenstein’s thinking.

Understanding the space of atomic facts as logical space, we can see that logical space is driven by logical necessity to relentlessly expand until it becomes a kind of Parmenidean sphere of logical totality. This vision of logical space realizes virtually every concern Bergson had for the falsification of experience given the spatialization of the intellect. The early Wittgenstein represents the logical intellect at its furthest reach, and Wittgenstein does not disappoint on this score.

While Wittgenstein abandoned this kind of static logical totality in this later thought, others were there to pick up the torch and carry it in their own directions. An interesting example of this is Donald Davidson’s exposition of logical geography:

“…I am happy to admit that much of the interest in logical form comes from an interest in 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. The location must be given relative to a specific deductive theory; so logical form itself is relative to a theory.”

Donald Davidson, Essays on Actions and Events, pp. 139-140

In a more thorough exposition (someday, perhaps), I would also discuss Frege’s exposition of concepts in terms of spatial areas, and investigate the relationship between Frege and Wittgenstein in the light of their shared equation of logic and space. (I might even call this the principle of spatial-logical equivalence, which principle would be the key that would unlock the relationship between epistemic space and geometrical intuition.)

Certainly the language of spatiality is well-suited to an exposition of human thought — whether it is uniquely suited is an essentialist question. But we must ask at this point if human thought is specially suited to a spatial exposition, or if a spatial exposition is especially suited for an exposition of human thought. It is a question of priority — which came first, the amenability of spatiality to the mind, or the amenability of the mind to spatiality? Which came first, the chicken or the egg? Is the mind essentially spatial, or is space essentially intellectual? (The latter position might be assimilated to Kantianism.)

From the perspective of natural history, recent thought on human origins has shifted from the idea of a “smart ape” to the idea of a “bipedal ape,” the latter with hands now free to grasp and to manipulate the environment. Before this, before human beings were human, our ancestors lived in trees where spatial depth perception was crucial to survival, hence our binocular vision from two eyes placed side by side in the front of the face. Color vision additional made it possible to identify the ripeness of fruit hanging in the trees. In other words, we are a visual species from way back, predating even our minds in their present form.

With this observation it becomes obvious that the human mind emerged and evolved under strongly visual selection pressure. Moreover, visual selection pressure means spatial selection pressure, so it is no wonder that the categories native to the human mind are intrinsically spatial. Those primates with the keenest ability to process spatial information in the form of visual stimuli would have had a differential survival and reproductive advantage. This is not accidental, but follows from our natural history.

But now I have mentioned “natural history” again, and I pause. Temporal selection pressure has been no less prevasive than spatial selection pressure. All life is a race against time to survive as long as possible while producing as many viable offspring as possible. Here we come back to Bergson again. Why does the intellect spatialize, when time is as pervasive and as inescapable as space in human experience?

With this question ringing in our ears, and the notable examples of philosophical logical-spatial equivalence mentioned above, why should we not have (parallel to Wittgenstein’s exposition of logical space) logical time and (parallel to Davidson’s exposition of logical geography) logical history?

To think through the idea of logical history is so foreign that is sounds strange even to say it: logical time? Logical history? These are not phrases with intuitive self-evidence. At least, they have very little intuitive self-evidence for the spatializing intellect. But in fact a re-formulation of Davidson’s logical geography in temporal-historical terms works quite well:

…the logical form of a sentence is to give its logical position in the elapsed sequence of sentences, to describe it in a way that explicitly determines what are following sentences it entails and what previous sentences it is entailed by…

Perhaps I ought to make the effort to think things through temporally in the same way that I have previously described how I make the effort to think things through selectively when I catch myself thinking in teleological terms.

In the meantime, it seems that our geometrical intuition is a faculty of mind refined by the same forces that have selected us for our remarkable physical performance. And as with our physical performance, which is rendered instinctive, second nature, and unconscious simply through our ordinary interaction with the world (all the things we must do anyway in order to survive), our geometrical intuition is often so subtle and so unconsciously sophisticated that we do not even notice it until we are presented with some Gordian knot that forces us to think explicitly in spatial terms. Faced with such a problem, we create sciences like topology, but before we have created such a science we already have an intellect strangely suited to the formulation of such a science. And, as I have written elsewhere, we have no science of time. We have science-like measurements of time, and time as a concept in scientific theories, but no scientific theory of time as such.

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Fractals and Geometrical Intuition

1. Benoît Mandelbrot, R.I.P.

2. A Question for Philosophically Inclined Mathematicians

3. Fractals and the Banach-Tarski Paradox

4. A visceral feeling for epsilon zero

5. Adventures in Geometrical Intuition

6. A Note on Fractals and Banach-Tarski Extraction

7. Geometrical Intuition and Epistemic Space

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Grand Strategy Annex

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What is called “losing” in chess may constitute winning in another game.

Ludwig Wittgenstein, in a discussion of Gödel’s incompleteness proofs

I have for quite some time been intending to wade into the COIN debate (that’s “counter-insurgency,” for those among you without an absolute command of inherently ambiguous acronyms), and while this post is not going to be that post which takes COIN as the leitmotif, I will here approach COIN indirectly by taking a bit of the debate on the margins of COIN. To paraphrase Wittgenstein’s well known remark about Gödel — “My task is, not to talk about (e.g.), Gödel’s proof, but to pass it by.” — I can say that, in the present context, my task is not to talk about COIN, but to pass it by.

And I will pass by COIN by way of a detour through SoT. Now we have another acronym, so I must tell you that “SoT” means “strategy of tactics.” I found this on the Ink Spots blog, in a piece by Jason Fritz titled be-SoT-ted: COIN tactics and strategy through the lens of ends, ways, means. Fritz makes several interesting assertions that I would like to review. Fritz notes that Gian Gentile originated (or popularized) the notion of “COIN is the strategy of tactics,” implying that COIN has no true strategic content, and that a military force that makes COIN its central doctrine is a force essentially without a strategy.

Fritz links to several interesting pieces by Gian Gentile, who has written an excellent essay on this idea. Here are a couple of excerpts from Gentile:

Nation-building using population-centric COIN as its centerpiece should be viewed as an operation. It should not be viewed as strategy, or even policy for that matter. But what is occurring now in Afghanistan, for example, at least for the American Army, is a “strategy of tactics.” If strategy calls for nation-building as an operational method to achieve policy objectives, and it is resourced correctly, then the population-centric approach might make sense. But because the United States has “principilized” population-centric COIN into the only way of doing any kind of counterinsurgency, it dictates strategy.

…the most damaging consequence to the American Army from the new zeitgeist of COIN is that it has taken the Army’s focus off of strategy. Currently, US military strategy is really nothing more than a bunch of COIN principles, massaged into catchy commander’s talking points for the media, emphasizing winning the hearts and minds and shielding civilians. The result is a strategy of tactics and principles.

GIAN P. GENTILE, “A Strategy of Tactics: Population-centric COIN and the Army,” Parameters, Autumn 2009

Of Gentile’s dismissal of COIN as a “strategy of tactics” Fritz has this to say:

My main beef with COIN as a strategy of tactics (I’m going to go ahead and call it SoT from now on) is that all military strategy is made up in part as a summation of its tactics. In the ends-ways-means calculus of strategy, a large chunk of the “ways” section is the aggregation of tactical actions based on operational concepts and/or TTPs… This is an elegant way of saying it, but all military strategies are in part SoT, in a non-pejorative sense. You can’t have strategic success without tactical successes. COIN, IW, UW, maneuver warfare are all common in this regard.


…for now I disagree that COIN is inherently a strategy of tactics any more than any category of tactics can be labeled a strategy. Those tactics may be part of a military strategy that logically connects ends, ways, and means. On the other hand, COIN tactics may be the commander’s ways in an illogical or inaccurate strategic equation and thus we may see COIN as a SoT.

While I am in complete agreement that you cannot have strategic success without tactical successes, it is important to point out that tactical objectives can be antithetical to strategic objectives, so much so that a “successful” tactical move may involve a local defeat in the interest of a global strategic victory (and here I mean “global” not as “worldwide” but simply as a contrast to “local”). If your skirmishers can flush out an ambush before that ambush can be sprung on the main body of your troops, the skirmishers may lose this engagement but in so losing they may have saved the day for the force on the whole. What is called “losing” in tactics may be called “winning” in another game, namely, the game of strategy.

Still, both Gentile and Fritz are on to something (though they seem to take distinct positions) in the analysis of a collection of tactical methods and principles that are thrown together as an ad hoc strategy without the benefit of what might be called strategic vision (for lack of a better term). Gentile is somewhat dismissive of a “strategy of tactics” cobbled together on the local level, while Fritz seems to suggest that all strategies are ultimately strategies of tactics, since, “all military strategy is made up in part as a summation of its tactics.”

The problem here (if there is a problem) can be neatly illuminated by interpolating a distinction into this discussion, so I am going to make a distinction between formal and informal strategy, or formal and material strategy (either set of terms will do). Although I am introducing my own terminology, the idea is not at all new.

Actually, I’m going to make two distinctions. Among strategies of tactics we can distinguish those that add up to more than the sum of their parts, and those that fail to add up to anything. A number of tactics thrown together in an operational context may only apparently have little or nothing to do with each other, but it emerges in time that they do in fact function coherently as a whole. This whole turns out to be a strategic whole. This is when tactics add up to more than the sum of their parts, and this is what Adam Smith called the “invisible hand” and what Hegel called the “cunning of reason.” Sometimes, things get done quite without our knowing how they get done.

Fritz, in suggesting that all strategies may be strategies of tactics comes close to this idea that strategy is emergent from a coherent body of tactics. But this, as we know, is not the only possibility. A number of tactics thrown together for an operation may reveal their essential incoherence by ignominiously falling to pieces under the extraordinary stresses of combat. Tactics combined without any overarching idea of what is to be accomplished may be pursued at cross-purposes to each other and become self-defeating. This would be an instance of tactics turning out to be less than the sum of their parts (what I have elsewhere called negative organicism and submergent properties). This seems to be Gentile’s primary concern.

History provides adequate examples both of strategy emergent from tactics and strategy failing to emerge from tactics, so we can’t really say that Gentile is right or Fritz is right, because they are both right — just in different circumstances. So here’s where we come to formal strategy and material strategy.

A formal strategy is an explicitly formulated doctrine of strategic objectives distinct from the tactical objectives that may be employed to achieve the aims of the strategy. When a formal strategy is formulated, those who are formulating it know that they are formulating it, they know what they want to accomplish, and if any time lines are given for the strategy they will be able to say eventually whether that strategy was successful or a failure.

An informal or material strategy is that strategy that emerges in the absence of a formal strategy. A material strategy may be grasped intuitively or instinctively by military commanders on the ground or by politicians in their negotiations in smoke-filled rooms. It is probably the case that most US strategies are informal strategies, which is why US military forces must so often get by with strategies of tactics, because no one can explicitly formulate exactly what is going on. Even when such an explicit statement of a strategy is lacking, however, we should not sell informal strategy short, because in some cases everyone understands, from the Commander-in-Chief to the foot soldiers slogging through the mud, what it is all about. When men die for freedom and democracy without being able to define either freedom or democracy (or the tactics that are consistent with a free and democratic society) they are dying for an informal strategy.

Given this distinction, then, between formal and informal strategy, the distinction between strategy and tactics is maintained; in other words, it is not the case that all strategies are strategies of tactics, but rather that informal strategies are strategies of tactics when these tactics do turn out to be coherent and to accomplish something. When strategies of tactics fall apart and a fiasco ensues, then there was no strategy at all — not even an informal one.

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Grand Strategy Annex

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Radical Rigor

18 September 2011


The Legacy of Wittgenstein and the

last section of his Philosophical Investigations

Not long ago in Beyond Anti-Philosophy I introduced the idea of conceptual naturalism:

“…science is a philosophical research program, and it is based upon a small set of philosophical principles that have proved themselves remarkably fruitful in the investigation of the natural world. Scientific concepts are amenable to exposition by methodological naturalism. We might call this conceptual naturalism. Failures of conceptual naturalism — like investigating past lives as past lives, rather than as reports and descriptions of lives — result in conceptual confusion, and no amount of observation or experiment will clarify conceptual confusion.”

There is, as I see it, a reciprocity between methodological naturalism and conceptual naturalism: each is necessary to the exposition of the other; each is clarified by the clarity of the other. Methodological naturalism converges on conceptual naturalism; conceptual naturalism enlarges the sphere of phenomenon to which we can bring the resources of methodological naturalism. Both stop short of naturalism simpliciter, and a fortiori of ontological naturalism. This is the province of philosophy rather than of science, and it is perhaps one of the sources of anti-philosophy in science that science is ultimately bounded by philosophy.

In any case, since I explicitly mentioned conceptual confusion in this passage it was my intention to cite Wittgenstein in this connection. There very last section of Wittgenstein’s Philosophical Investigations includes this:

“The confusion and barrenness of psychology is not to be explained by its being a ‘young science’; its state is not comparable with that of physics, for instance, in its beginnings. (Rather, with that of certain branches of mathematics. Set theory.) For in psychology, there are experimental methods and conceptual confusion. (As in the other case, conceptual confusion and methods of proof.)”

“The existence of the experimental method makes us think that we have the means of getting rid of the problems which trouble us; but problem and method pass one another by.”

“An investigation is possible in connection with mathematics that is entirely analogous to our investigation of psychology. It is just as little a mathematical investigation as the other is a psychological one. It will not contain calculations, so it is not for example logistic. It might deserve the name of the ‘foundations of mathematics’.”

Ludwig Wittgenstein, Philosophical Investigations, Blackwell, 2003, p. 197e (translation modified)

It is interesting to note in this section how Wittgenstein approaches the philosophy of mathematics almost gingerly in this passage. While the Philosophical Investigations touches upon the philosophy of mathematics in places, elsewhere in Wittgenstein’s oeuvre the philosophy of mathematics is central, the fons et origo of Wittgenstein’s thought. Here Wittgenstein seems to be coming at it again, although from a new angle: as though after the experience of formulating ordinary language linguistic philosophy he had passed through to the other side of thought and was prepared to return to the source of his thought, older and now wiser.

Wittgenstein’s Tractatus Logico-Philosophicus — the only book-length work published during this lifetime — is through and through concerned with the philosophy of mathematics. The only contemporary philosophers Wittgenstein cited in this work were Frege and Russell, who had pioneered the doctrine of logicism, which is the position that mathematics is simply a highly developed form of logic, which amounts to the claim that there are no uniquely mathematical ideas, only logical ideas.

So this early period of Wittgenstein’s thought was brought into being and sustained by philosophical reflection on mathematics. We know that this was true of the later period of Wittgenstein’s thought also. After revolutionizing contemporary philosophy with his Tractatus, Wittgenstein returned to Austria and hid out in the Alps as a village schoolmaster, where a few Anglo-American philosophers made the pilgrimage to seek him out and question him about the Tractatus. One of them managed to persuade him to travel to Vienna to attend a lecture by L. E. J. Brouwer, the father of intuitionism, then the most influential form of constructivist philosophy of mathematics. After this lecture, Wittgenstein began his slow, incremental return to philosophy. But it was a different philosophy.

The works that Wittgenstein wrote in this period, which have been published posthumously, are sometimes called his Middle Period, to mark them off from the better known Early Wittgenstein (the Tractatus) and Late Wittgenstein (the Philosophical Investigations). These middle period works, too, are pervasively concerned with the philosophy of mathematics. Last February in Nothing contrasts with the form of the world I commented on one of these middle period works, the Philosophical Remarks. Though not nearly as well known as the Tractatus or the Philosophical Investigations, the middle period works are intriguing and fruitful in their own way. They have been an influence on my own thought.

While Wittgenstein was writing the works of his later period he delved deeply into philosophical psychology. Several works of this nature have been published posthumously. The Philosophical Investigations is in a sense both the culmination of these efforts in philosophical psychology and a response to them. The response comes in the final section quoted above. Wittgenstein, in delving deeply into psychology, found psychology to be infected with conceptual confusions that would not, he thought, be ameliorated by workman-like progress based on the experimental method. Something more was needed, something different was needed, to deliver psychology from its conceptual confusions.

Wittgenstein put much of contemporary mathematics in the same basket by comparing the conceptual confusion of set theory to the conceptual confusion of psychology. Here I decisively part ways with Wittgenstein, since I agree about the conceptual confusion of psychology, but I am hesitant over the conceptual confusions of set theory. It is not that I deny these latter confusions, but rather than I am hopeful about them (and, I guess, I’m not that hopeful about the former). Of course, many people are and were hopeful about what might be called the set theorization of mathematics. In many of Gödel’s later posthumously published essays (those that make up the contents of Volume III of his collected papers) we can see Gödel consciously groping toward a better conceptual formulation of the foundations of set theory. He saw the need and attempted to fill it, but the conceptual infrastructure needed for the decisive breakthrough (the kind of conceptual breakthrough that make it possible for Cantor to formulate set theory in the first place) wasn’t there yet. But Gödel was headed in the right direction.

Although Gödel wasn’t influenced by the thought of the later Wittgenstein, the direction he was headed in was the direction that Wittgenstein outlined in the last section of his Philosophical Investigations, quoted above. That is to say, Gödel was doing conceptual work in the foundations of mathematics. This has been the exception rather than the rule. Since the time of Gödel and Wittgenstein the field has been dominated by technical work, work of the highest formal rigor, and also work of conceptual rigor, but not, it must be said, radical conceptual work.

It is very difficult to characterize radical philosophy. Husserl spent a career trying to do so, and in his last years took pride in being able to call himself a genuine beginner in philosophy. But Husserl’s legacy (very much like the legacy of Wittgenstein and Gödel) has been dominated by philosophers who have done work of technical and conceptual rigor, but not radical work. Another problem stems from the political connotations of “radical,” which are connected to the Marxist tradition, which retains a vital connection to contemporary philosophy. So if you talk about radical philosophical thought, many people will assume that you’re talking about Marxism or some species of far left anarcho-syndicalism, and that is not at all what I have in mind.

I made a first attempt to get at my conception of radical philosophical thought — which I see as following in the tradition of the later Husserl, the later Wittgenstein, and the later Gödel — in my post Jacob Bronowski and Radical Relflection. I haven’t returned to thus much, partly because of other work on which I have been engaged, and partly due to the intrinsic difficulty to radical philosophical thinking. But I want to note it in connection with the last section of the Philosophical Investigations quoted above.

Radical thought, as I conceive of it, would not only be philosophically radical, but also scientifically radical. That is why I wrote the above post on Jacob Bronowski, who most philosophers would not recognize as having made any contribution to philosophy. But Bronowski, as I attempted to describe, did engage in radical scientific thought (and even attempted to popularize it) and this in itself constitutes a contribution to radical philosophical thought. We must learn from this radicalism wherever and whenever we find it.

For a time it seemed that philosophical thought had been overtaken by science, and much of twentieth century philosophical thought seems like a self-parody as philosophers try to mimic the success of the physical sciences. This is what twentieth century logical empiricism and logical positivism is all about. But these philosophers learned the wrong lesson. Contemporary philosophers are starting to learn the right lessons. I have written several posts about the emerging school of philosophical thought called Object Oriented Philosophy (or object oriented ontology – “OOO”). One of the best things about this movement is the attempt to take science seriously as a source of insight for philosophical thought. A lot of analytical philosophers wouldn’t recognize this even to be the case, since OOO is largely formulated in the language of continental philosophy, though a close reading will make this obvious.

Radical philosophy, however, cannot rest with accepting the insights of science or even accepting scientific knowledge or the scientific method as its point of departure. This is an important point of departure, but it is only the beginning. As I have attempted to point out in several posts (most recently in An Aristotelian Definition of Science), science is part of philosophy, and philosophy must then take responsibility for science.

And for mathematics as well. You see, if philosophy must take science seriously, and science take mathematics seriously, then philosophy also must take mathematics seriously. Science, philosophy, and mathematics are all caught up in the same dilemma of needing radical conceptual clarification, even while each as it progresses adds more and more to the accumulated total based on a confused conceptual foundation.

Of course, Wittgenstein took mathematics seriously, which is one reason he devoted the better part of his philosophical career to the philosophy of mathematics. But while Wittgenstein mentions the conceptual confusions of psychology in the same section that he mentions the possibility of a foundational inquiry into mathematics parallel to his foundational inquiry into psychology, he doesn’t seem to have quite seen the full relationship between the two. But, then again, science and and especially psychology of that time was not mathematicized to the extent that it is today. All of the rigorous technical work that I mentioned above has had the consequence of accelerating the mathematization of the sciences (think of economics today, or even branches of biology like theoretical ecology).

Mathematics provides the framework whereby other bodies of knowledge are rendered scientific, but is mathematics itself scientific, or is it rather part of the structure of science itself, and therefore neither scientific nor non-scientific?

If mathematics is an assumption of and part of the structure of science, then it is to be put on a par with parsimony, induction, uniformitarianism, and methodological naturalism. If, on the other hand, mathematics is science, is a part of science, then it is not on the same level of the philosophical principles of science that I have just mentioned, but is subject to them just as is the rest of science.

It could be argued that the principles of mathematics make themselves manifest in science through the medium of mathematics, so that mathematical principles are ultimately also scientific principles, and they are to be understood as being on a level with the other principles of science (such as those I mentioned above). This is an interesting idea, and it is, in fact, my first reaction to this as I begin to think about it. There is even a sense in which this is parallel to logicism, in which logic and mathematics ultimately share the same principles. However, I want to immediately point out that I do not regard this as anything even approaching a definitive formulation. It is only a first, instinctive, intuitive response to the question I am attempting to pose to myself.

I have my conceptual work cut out for me: I need to systematically think through the relation of mathematics to the sciences from the perspective of the philosophical principles of science. In other words, I know that I need to think through the relation of mathematics to parsimony, uniformitarianism, induction, and methodological naturalism. This will be an unfamiliar and therefore difficult exercise of thought, because these philosophical principles of science are usually formulated in empirical terms, so they must be re-formulated in a priori terms in order to understand their consequences for mathematics (either that, or re-formulate mathematics in terms of the a posteriori, which some philosophers prefer to do). This is a tall order, and I won’t be finishing it any time soon. In fact, I have yet to begin. In any case, I leave you with this reflection and exhortation:

We need radical philosophical thought, but it is difficult to do, requiring a real conceptual effort above and beyond the norm — the “norm” of which might be called the norm of normal philosophy, conceived in parallel with what Kuhn called normal science — and so it is rare. We need technical and conceptual rigor as well. These are also difficult, but slightly less rare. Ultimately what we need is both: we need radical rigor.

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Grand Strategy Annex

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Wittgensteinian Magisteria

13 September 2011


One of the most memorable and enduring aspects of Wittgenstein’s later work is his conception of family resemblance. Wittgenstein in his Philosophical Investigations formulates an essentially anti-essentialist position, and his account of family resemblances is an attempt to state how things resemble each other without sharing some single “essence.” He wanted to get away from the idea there there must be something in common, and to this end he urged his readers to look for themselves and see if there is anything in common — say, for example, among all games.

I have been thinking about family resemblances in Wittgenstein because I mention the idea in passing in my paper, The Moral Imperative of Human Spaceflight, which I am to present at the upcoming 100 Year Starship Symposium. (I hope you’ll show up to be in my cheering section.)

Wittgenstein described family resemblances as, “…a complicated net of similarities which overlap and intersect.” This translation is due to Walter Kaufmann (Critique of Religion and Philosophy, Princeton: Princeton University Press, 1978, p. 55), which is a rather more felicitous rendering than the familiar Anscombe translation: “a complicated network of similarities overlapping and criss-crossing,” (Ludwig Wittgenstein, Philosophical Investigations, The German Text, with a Revised English Translation, Third Edition, Malden, Oxford, and Victoria: Blackwell Publishing, 2003, section 66, p. 27e).

When I was thinking about this use of “overlapping” (“übergreifen” in the original German) I happened to watch a video by Richard Dawkins, and I thought about Dawkins’ criticism of Gould’s exposition of “non-overlapping magisteria” or NOMA for short. S. J. Gould wrote an essay on the topic which is fairly well know. Here are a few quotes taken from it:

“…each subject has a legitimate magisterium, or domain of teaching authority—and these magisteria do not overlap (the principle that I would like to designate as NOMA, or ‘nonoverlapping magisteria’).”

“The net of science covers the empirical universe: what is it made of (fact) and why does it work this way (theory). The net of religion extends over questions of moral meaning and value. These two magisteria do not overlap, nor do they encompass all inquiry (consider, for starters, the magisterium of art and the meaning of beauty). To cite the arch cliches, we get the age of rocks, and religion retains the rock of ages; we study how the heavens go, and they determine how to go to heaven.”

“This resolution might remain all neat and clean if the nonoverlapping magisteria (NOMA) of science and religion were separated by an extensive no man’s land. But, in fact, the two magisteria bump right up against each other, interdigitating in wondrously complex ways along their joint border. Many of our deepest questions call upon aspects of both for different parts of a full answer—and the sorting of legitimate domains can become quite complex and difficult. To cite just two broad questions involving both evolutionary facts and moral arguments: Since evolution made us the only earthly creatures with advanced consciousness, what responsibilities are so entailed for our relations with other species? What do our genealogical ties with other organisms imply about the meaning of human life?”

“I believe, with all my heart, in a respectful, even loving concordat between our magisteria—the NOMA solution. NOMA represents a principled position on moral and intellectua] grounds, not a mere diplomatic stance. NOMA also cuts both ways. If religion can no longer dictate the nature of factual conclusions properly under the magisterium of science, then scientists cannot claim higher insight into moral truth from any superior knowledge of the world’s empirical constitution. This mutual humility has important practical consequences in a world of such diverse passions.”

Stephen Jay Gould, “Nonoverlapping Magisteria,” Natural History 106 (March 1997): 16-22; Reprinted here with permission from Leonardo’s Mountain of Clams and the Diet of Worms, New York: Harmony Books, 1998, pp. 269-283.

Dawkins will have none of this. He devotes a section of Chapter 2 of The God delusion to criticizing the very idea of NOMA. Here is a typically Dawkinsian passage:

“The very idea is a joke. You can bet your boots that the scientific evidence, if any were to turn up, would be seized upon and trumpeted to the skies. NOMA is popular only because there is no
evidence to favour the God Hypothesis. The moment there was the smallest suggestion of any evidence in favour of religious belief,
religious apologists would lose no time in throwing NOMA out of the window. Sophisticated theologians aside (and even they are
happy to tell miracle stories to the unsophisticated in order to swell congregations), I suspect that alleged miracles provide the
strongest reason many believers have for their faith; and miracles, by definition, violate the principles of science.”

Richard Dawkins, The God Delusion, Chapter 2

Dawkins goes on for several pages in this vein, but the only reason I cite Dawkins here is that he represents the antithesis of the NOMA position outlined by Gould. What interests me in this debate between Gould and Dawkins is that the NOMA and anti-NOMA positions do not exhaustively divide the field of opinion.

In fact, however heretical to the orthodox, I think that one of the most prevalent views held today in industrialized Western nation-states is the antithesis of both Gould and Dawkins. I propose to call this position COMA, which should be understood to stand for COinciding MAgisteria.

It is difficult for me to give a good formulation of COMA, partly because the idea, while ancient, is new to me, and it is not my own position. So I have no definitive formulation. I will rely upon my reader’s sympathy and indulgence to provide what I leave out in my account of COMA.

COMA is simply this: that religion and science are simply alternative formulations of one and the same truth. The dogmatically religious insist upon putting everything in religious terms and denying the contributions of science, while the dogmatically scientific insist upon putting everything in scientific terms and denying the contributions of religion, but ultimately there is only one truth of the world, which is studied from the varying perspectives of science and religion (inter alia).

I have had many people say things like this to me personally. While I can’t cite any locus classicus, but I’m sure that someone, somewhere, has written down this obvious point of view.

I will go further, however, and state that even among NOMA, anti-NOMA, COMA, and whatever anti-COMA might be, that these positions still do not exhaust the field of opinion. What lies beyond NOMA and COMA? Wittgenstein.

Wittgenstein’s conception of family resemblances takes another step with possible magisteria, which is that step beyond either wholly overlapping (as with COMA) or being mutually exclusive (as with NOMA), such that that magisteria may intersect (which Anscombe translates as “criss-cross”). I’m sure you get the idea. Gould and Dawkins, NOMA and SOMA, present regions of thought as spatial areas (much as Frege does in his exposition of tertium non datur in the Foundations of Arithmetic). Well, concepts as we usually find them in the real world only present these kind of ideal boundaries in the abstract. In actual fact, the boundaries of a given concept interpenetrate related concepts, often to the point that it is difficult to distinguish them. This, I think — family resemblances that overlap and intersect — is the proper way to understand the relationship between religious and scientific concepts.

Though I will, again, go one step further. I mention in my “The Moral Imperative of Human Spaceflight” paper that Wittgenstein has left an item off the relationships of family resemblance: conflict. The individual variation that both lies at the basis of natural selection and which gives each of us our unique features, is that element of conflict in family resemblance, which is never total or absolute.

Despite all the talk about so-called “militant atheists” like Dawkins (and Dennett, and others), it has in fact become quite trendy to downplay the conflict between science and religion. I listened to a set of lectures from The Teaching Company, Science and Religion — a pure exemplification of the spirit of revisionist history — in which the lecturer, Professor Lawrence M. Principe, Ph.D., ridicules what he calls the “The Warfare Thesis” and attempts to show that, because many eminent scientists were in fact deeply pious and religious, there really hasn’t been any conflict between science and religion. While I enjoyed the lectures, I didn’t agree with them, and this was one of those clear-cut cases in which historical revisionism seems to be carried to its own self-fulfilling prophecy.

But this is merely an aside in the point I wish to make today, and that point is that NOMA is really not all that common a view, that COMA is probably more prevalent, but that neither NOMA or COMA sufficiently capture the relations between science and religion, which might better be described in terms of Wittgensteinian family resemblances. Not that science and religion resemble each other, but that their relations are like the relations that hold between things that do resemble each other. This is an obviously imperfect exposition. Perhaps with time I can frame my point with greater clarity.

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Grand Strategy Annex

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