road closure

In my previous post on The Finality Fallacy I discussed the fallacy of treating open matters as though closed, and quoted Hermann Weyl’s 1932 lectures The Open World as a countervailing point of view. If the world is an open world, an unfinished world, then there will always be unfinished business — no finality, no closure, no resolution, no end of anything — and no beginning either.

Bertrand Russell wonderfully described the ontology implicit in such a conception of the world:

“Academic philosophers, ever since the time of Parmenides, have believed that the world is a unity. This view has been taken over from them by clergymen and journalists, and its acceptance has been considered the touchstone of wisdom. The most fundamental of my intellectual beliefs is that this is rubbish. I think the universe is all spots and jumps, without unity, without continuity, without coherence or orderliness or any of the other properties that governesses love. Indeed, there is little but prejudice and habit to be said for the view that there is a world at all.”

Bertrand Russell, The Scientific Outlook, Part One, Chapter IV. Scientific Metaphysics

There is a subtle difference, of course, between finality and unity; the presumption of unity that Russell mocked could be finitistic or infinitistic in character, but, as I pointed out in my last post, I suspect that Russell and Weyl, whatever their differences, could have agreed that the world is open. Unity may not imply openness, but openness implies the possibility of revision, the possibility of revision implies the iteration of revision, the iteration of revision implies evolution, and evolution implies anti-realism, at least in the essentialist sense of “realism.” Anything that changes gradually over an indefinite period of time may be so transformed by its incremental and cumulative change that it can be transformed into something entirely other that what it once was. This, I have argued elsewhere, is the essence of existential viability.

By the same token, there is a subtle difference between finitude and contingency. I can imagine that someone might argue that finitude implies contingency and contingency implies finitude, but I would reject any such argument. The distinction is subtle but important, and I think that it marks that difference between a naturalistic philosophy, that is essentially a philosophy of contingency, and an anthropocentric point of view that reduces the infinitistic contingency of the world to a manageable finitude because human beings are comfortable with finitude. That is to say, I am suggesting that finitistic modes of thought constitute a cognitive bias. But let’s try to penetrate a little further into what self-described finitists have in mind, and let’s try to find an unambiguously finitistic perspective.

I remember running across the phrase “radical finitude” in some of my past reading, so I looked for the original source in which I had first encountered the term and was unable to find it, but I have found many other references to radical finitude. The name that comes up most often in relation to radical finitude is that of Martin Heidegger (on Heidegger cf. my Conduct Unbecoming a Philosopher and Ott on Heidegger). Heidegger is mentioned by Weyl as a representative of the “thesis of the categorical finiteness of man” in the quote from Weyl in my last post, The Finality Fallacy. Here, again, is an abbreviated portion of the section I previously quoted from Weyl, where Weyl singles out Heidegger:

“We reject the thesis of the categorical finiteness of man, both in the atheistic form of obdurate finiteness which is so alluringly represented today in Germany by the Freiburg philosopher Heidegger…”

Here, on the other hand, is a representative exposition of radical finitude that draws upon the Heideggerian tradition:

“Nonbeing as the principle of finitude is non-being understood in its relative and dialectical character through which it becomes a constitutive factor of human being or Dasein himself. Anxiety in its disclosure of nothingness thus brings man to an awareness of his radical finitude, and what ever else is to be said of existentialist philosophy, it must be said that existentialism is an emphatic philosophy of human finitude. The principle of finitude is central to all the existentialist thinkers, and it emerges with particular emphasis in the philosophy of Heidegger. Heidegger interprets this philosophy of human finitude to be, at least in part, a legacy of Kant’s critical philosophy. With his emphasis on the finite character of human reason and his insight into the negativities of moral striving, Kant paved the way for the development of fundamental ontology formulated in terms of finite structures.”

Calvin O. Schrag, Existence and Freedom: Towards an Ontology of Human Finitude, pp. 73-74

According to Schrag, then, it seems that existentialism can be defined in terms of Weyl’s thesis of the categorical finiteness of man. If this is so, and existentialism is, “an emphatic philosophy of human finitude,” as Schrag said it was, it might still be possible to define another philosophical position, entirely parallel to existentialism, but which would reject the thesis of the categorical finiteness of man. What would we call this logical complement of existentialism? It doesn’t really matter what we call it, but I’m sure there must be a clever moniker that eludes me at the moment.

Although it doesn’t really matter what we would call the infinitistic complement of existentialism, it does matter that such a philosophy would reject finitism (and its tendency to commit the finality fallacy). With a slight change to Schrag’s formulation, we could say that the complement of existentialism imagined above would be an emphatic philosophy of human contingency. This is a position that I could endorse, even while I would continue to reject a philosophy of human finitude. And this formulation in terms of contingency is not necessarily at odds with non-Heideggerian existentialism.

Sartre’s formulation of existentialism — existence precedes essence — is in no sense intrinsically finitistic. I can imagine that someone might argue that existence is intrinsically finite — that the existential is existential in virtue of being marked out by the boundaries that define its finitude — but I would reject that argument. That same argument could made for essence (i.e., that essence is intrinsically finite), and thus for the whole idealistic tradition that preceded Sartre, and which Sartre and others saw themselves as overturning. (Heidegger, it should be noted, categorically rejected Sartre’s categorical formulation of existentialism.) The existence that precedes essence may well be an infinitistic existence, just as the essence that precedes existence in the idealistic tradition may well be an infinitistic essence.

To return to one of the roots of existential thought, we find in Nietzsche that it is contingency rather than finitude that is at stake. In a note from 1873 Nietzsche wrote:

“That my life has no aim is evident even from the accidental nature of its origin; that I can posit an aim for myself is another matter.”

Friedrich Nietzsche, The Portable Nietzsche, edited and translated by Walter Kaufmann, New York: Viking, p. 40

Recognition of the contingency of life, and especially (given the anthropocentrism of our human minds) the contingency of human life, is a touchstone of existential thought. Some, as I have noted above, frame contingency in finitistic terms, but as I see it contingency is the infinite context of all existents, stretching out into space and time without end. From this point of view, any finitude is an arbitrary division within the Heraclitean flux of the world, the concordia discors that precedes us, follows us, and surrounds us.

What is the relationship between Nietzschean contingency and Weyl’s openness? I would argue that the open world implies an open life. It was one of the central literary conceits of Plato’s Republic that it is easier to see justice in the large — i.e., in the just state — than to see justice in the small — i.e., in the just man — and this is how Socrates shifts the conversation to an investigation of the ideal state, which, once defined, will give us the image that we need in order to understand the ideally proportioned man. If Plato (and Socrates) are right this this, one might hold that Weyl’s open world can be a guide to the open life.

What would an open life look like? One vision of the open life is described in Charles Dickens’ classic A Christmas Carol, from the mouth of Jacob Marley:

“It is required of every man,” the Ghost returned, “that the spirit within him should walk abroad among his fellowmen, and travel far and wide; and if that spirit goes not forth in life, it is condemned to do so after death. It is doomed to wander through the world — oh, woe is me! — and witness what it cannot share, but might have shared on earth, and turned to happiness!”

Charles Dickens, A Christmas Carol, “Marley’s Ghost”

This is the open life of the individual — to walk abroad, literally and metaphorically — and to share what can be shared. The open life of the species is again another question — a question mid-way between the open world and the individual open life — and one that might simply be answered by asserting that an open humanity is the sum total of open human lives, if one regards humanity as nothing in itself and reducible to its individual instances.

This is the point at which I may perhaps lose my reader, because what I would like to suggest is that the open life for humanity is another way to understand transhumanism. Transhumanism is the openness of humanity to revision, and openness to revision implies iterated revision, iterated revision implies evolution, and the evolution of humanity implies an essentially different humanity in the future than humanity today.

What I have come to realize since writing my last post is that human finitude is one manifestation of human contingency, and, like any contingency, it is subject to revision by future contingencies. Again, our finitude, so far as it extends, is a contingency, and therefore, like any contingency, is subject to change.

The critics of transhumanism who have tried to find ways to praise suffering and death, and who go out of their way to argue that human life only has meaning and value in virtue of its limitation, overlook the role of contingency in human life. They pretend that human life is final, and that its contingent features are essential to humanity, if not necessary to the definition of what it means to be human — which is to say, they commit the finality fallacy. For the prophets of wholesome loss, humanity is finished.

Human being is no more final than any other form of being. The openness of human being means that human viability is predicated upon contingency, and that we must evolve or perish.

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Grand Strategy Annex

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In what style should we think? It sounds like an odd question. I will attempt to make it sound like a reasonable one.

It would, of course, be preferable (or maybe I should say, “more natural”) to ask, “In what manner should we think?” or simply, “How should we think?” But I have formulated my question as I have in order to refer to Heinrich Hübsch’s essay, “In what style should we build?” (In welchem Style sollen wir bauen? 1828)

Building and thinking are both human activities, and thus both can be assimilated to the formulation of Weyl that I quoted in The Clausewitzean Conception of Civilization:

“The ultimate foundations and the ultimate meaning of mathematics remain an open problem; we do not know in what direction it will find its solution, nor even whether a final objective answer can be expected at all. ‘Mathematizing’ may well be a creative activity of man, like music, the products of which not only in form but also in substance are conditioned by the decisions of history and therefore defy complete objective rationalization.”

Hermann Weyl, Philosophy of Mathematics and Natural Science, Appendix A, “The Structure of Mathematics”

What Weyl here refers to as “mathematizing” can be generalized to human cognition generally speaking, and, if we like, we can generalize all the way to a comprehensive Cartesian conception of thought:

By the word ‘thought’, I mean everything which happens in us while we are conscious, in so far as there is consciousness of it in us. So in this context, thinking includes sensing as well as understanding, willing, and imagining. If I say, ‘I see therefore I am,’ or ‘I walk therefore I am,’ and mean by that the seeing or walking which is performed by the body, the conclusion is not absolutely certain. After all, when I am asleep I can often think I am seeing or walking, but without opening my eyes or moving, — and perhaps even without my having any body at all. On the other hand, the conclusion is obviously certain if I mean the sensing itself, or the consciousness that I am seeing or walking, since the conclusion then refers to the mind. And it is only the mind which senses, or thinks about its seeing or walking.

Descartes, Principles of Philosophy, section 9

Do thinking and building have anything in common beyond both being human activities? Is there not something essentially constructive in both activities? (This question is surprisingly apt, because we need to understand what constructive thinking is, but I will return to that later.) Did not Kant refer to the “architectonic” of pure reason, and has it not become commonplace among contemporary cognitive scientists and philosophers of mind to speak of our “cognitive architecture.”

Just taking the term “constructive” in its naïve and intuitive signification, we know that thought is not always constructive. Indeed, it is often said that thought, and especially philosophical thought, must be analytical and critical. Critical thought is not always or invariably destructive, and most of us know the difference between constructive criticism and destructive criticism. Still, thought can be quite destructive. William of Ockham, for example, is often credited with bringing down the Scholastic philosophical synthesis that reached its apogee in Aquinas.

Similar observations can be made about the building trades. While we usually do not include demolition crews among the construction trades, there is a sense in which demolition and construction are both phases in the building process. Combat engineers must be equally trained in the building and demolition of bridges, for example, which demonstrates both the constructive and the destructive aspects of construction engineering.

Just as we have a choice not only what to build, but in what style we will build, so too we have a choice, not only in what we think, but also how we think. As a matter of historical fact, I think you will find that the thinking of most individuals is not much more than a reaction, or a reflex. People think in the way that comes naturally to them, and they do not realize that they are thinking in a certain style unless they pause to think about their thinking. Well, this would be one way to characterize philosophy: thinking about thinking.

The unthinking way in which most of us think has the consequence of fostering what may be called cognitive monoculture. Individuals rarely step outside the parameters of thought with which they are comfortable, and so they allow their thoughts to follow in the ruts and the grooves left by their ancestors, much as architects, for many generations, reiterated classical building styles for lack of imagination of anything different.

It is probably very nearly impossible that I should write about building and thinking without citing Heidegger, so here is my nearly obligatory Heidegger citation, which, despite my general dislike of Heideggerian thought, suits my purposes quite perfectly:

“We come to know what it means to think when we ourselves try to think. If the attempt is to be successful, we must be ready to learn thinking.”

Martin Heidegger, What is called thinking? Lecture I

I agree with this: a serious attempt at thinking entails that we come to know what it means to think, and moreover we must be ready to learn thinking, and not merely take it for granted. But I find that I do not agree with the very next paragraph in Heidegger:

“As soon as we allow ourselves to become involved in such learning, we have admitted that we are not yet capable of thinking.”

Martin Heidegger, What is called thinking? Lecture I

In fact, we are capable of thinking, though the problem is that we do not really know whether we are thinking well or thinking poorly. When we think about thinking, when we reflect on what we are doing when we are thinking, we will discover that we have been thinking in a particular style, even if we were not aware that we were doing so — much like the physician in Moliere who did not know that he had been speaking prose his entire life.

If we pay attention to our thinking, and think critically about our thinking, we stumble across a number of distinctions that we realize can be used to classify the style of thought in which we have been engaged: formal or informal, constructive or non-constructive, abstract or concrete, objective or subjective, theoretical or practical, a priori or a posteriori, empirical or rational. These distinction define styles of thought, and it is only in reflection that we realize that one or another of these terms has applied to our thought, and thus we have been thinking in this particular style.

Ideally one would be aware of how one was thinking, and be able to shift gears in the middle of thinking and adopt a different mode of thought as the need or desire arose. The value of knowing how one has been thinking, and realizing the unconscious distinctions one has been making, is that one is now in a position to provide counter-examples to one’s own thought, and one is therefore no longer strictly reliant upon the objections of others who think otherwise than ourselves.

The cognitive monoculture that we uncritically accept before we learn to reflect on our own thinking is more often than not borrowed from the world, and not the product of our own initiative. Are we living, intellectually, so to speak, in a structure built by others? If so, ought we to question or to accept that structure?

This is a theme to which Merleau-Ponty often returned:

“…it is by borrowing from the world structure that the universe of truth and of thought is constructed for us. When we want to express strongly the consciousness we have of a truth, we find nothing better than to invoke a topos noetos that would be common to minds or to men, as the sensible world is common to the sensible bodies. And this is not only an analogy: it is the same world that contains our bodies and our minds, provided that we understand by world not only the sum of things that fall or could fall under our eyes, but also the locus of their compossibility, the invariable style they observe, which connects our perspectives, permits transition from one to the other, and — whether in describing a detail of the landscape or in coming to agreement about an invisible truth — makes us feel we are two witnesses capable of hovering over the same true object, or at least of exchanging out situations relative to it, as we can exchange out standpoints in the visible world in the strict sense.”

Maurice Merleau-Ponty, The Visible and the Invisible,

I trust Merleau-Ponty with this idea, but, to put it bluntly, there are many that I would not trust with this idea, since the idea that our cognitive architecture is borrowed from the world that we inhabit can be employed as a strategy to dilute and perhaps even to deny the individual. One could make the case on this basis that we are owned by the past, and certainly there are those who believe that inter-generational moral duties flow in only one direction, from the present to the past, but merely to formulate it in these terms suggests the possibility of inter-generational moral duties that flow from the past to the present.

Certainly by being born into the world we are born into a linguistic and intellectual context at the same time as we are born into an existential context, and this fact has profound consequences. As in the passage from Marx that I have quoted many times:

“Men make their own history, but they do not make it as they please; they do not make it under self-selected circumstances, but under circumstances existing already, given and transmitted from the past.”

Karl Marx, The Eighteenth Brumaire of Louis Napoleon, first paragraph

Marx gives us a particular perspective on this idea, but we can turn it around and by reformulating Marx attain to a different perspective on the same idea. Marx takes the making of history to be a unidirectional process, but it goes both ways, men make history and history makes men:

“Men begin under circumstances existing already, given and transmitted from the past, and make their own history as they please from what they select of the past. The past has not reality but that which men give to it.”

The circumstances transmitted to us from the past are not arbitrary; these circumstances are the sum total of the efforts of previous generations to re-make the world during their lives according to their vision. We live with the consequences of this vision. Moreover, the circumstances we then create are then transmitted to the past; this is our legacy, and future generations will do with it as they will.

The architect, too, begins with circumstances existing already, given and transmitted from the past. For Hübsch this is the problem. Hübsch begins his brief treatise with a ringing assertion that architectural thought is dominated to an archaic paradigm:

“Painting and sculpture have long since abandoned the lifeless imitation of antiquity. Architecture has yet to come of age and continues to imitate the antique style. Although nearly everyone recognizes the inadequacy of that style in meeting today’s needs and is dissatisfied with the buildings recently erected in it, almost all architects still adhere to it.”

Heinrich Hübsch, In what style should we build? 1828

In the twenty-first century this is no longer true. Building has been substantially liberated from classical forms. In fact, since Hübsch’s time, a new classicism — international modern — rose, dominated for a short time, and now has been displaced by a bewildering plethora of styles, from an ornately decorative post-modernism to outlandish structures that would have been impossible without contemporary materials technology. There are, to be sure, architectural conventions that remain to be challenge, and in the sphere of urban planning these conventions can be quite rigid because they become embodied in legal codes.

For our time, the most forceful way to understand Hübsch’s question would be, “In what style should we build our cities?” Another way in which Hübsch’s question retains its poignant appeal is in the form that I suggested above: in what style should we think?

Are we intellectually owned by the past? Is there a moral obligation for us to think in the style of our grandfathers? A semi-humorous definition attributed to Benjamin Disraeli has it that, “A realist is a man who insists on making the same mistakes his grandfather did.” Are we obliged to be realists?

Here we see the clear connection between building and thinking. Just as we might think like our grandfathers, so too we might build like our grandfathers. This latter was the concern of Hübsch. That is to say, we can as well inhabit (and restore, and reconstruct) the intellectual constructions of our forefathers as well as the material constructions of our forefathers.

It would be entirely possible for us today to construct classical cities on the Greco-Roman model; it is even possible to imagine a traditional Roman house with hot and cold running water, electric kitchen appliances, and wired for WiFi. That is to say, we could have our modern conveniences and still continue to build as the past built. We could choose to literally inhabit the structure of the past, as civilization did in fact choose to do for almost a thousand years when classical cities were built to essentially the same plan throughout the ancient world. (See my remarks on this in The Iterative Conception of Civilization.)

A perfectly comfortable dwelling with modern plumbing and electrical appliances added. Why not? Why not build in the style of the past?

We can take the Middle Ages as the intellectual analogy for thinking that the modernized Roman house is for living: the role of intellectual authority in medieval thinking was unprecedented and unparalleled. If experience contradicted authority, so much the worse for experience. If a classical text stated that something was the case, and the world seemed at variance with the text, the world was assumed to be in error. As classical antiquity lived with the same buildings for a thousand years, so the Middle Ages lived with the same thoughts for a thousand years. There is no reason that we could not take medieval scholarship, as we might update a Roman house, and add a few modern conveniences — like names for chemical elements, etc. — and have this perfectly serviceable intellectual context as our own.

A perfectly comfortable way of thinking with a few modern ideas and distinctions added. Why not? Why not think in the style of the past?

Thus the two previous macro-historical stages of Western civilization prior to modernism — namely, classicism and medievalism — represent, respectively, the attempt to build in the style of the past and the attempt to think in the style of the past. It has been the rude character of modernism to focus on the future and to be dismissive of the past. While this attitude can be nihilistic, we can now clearly see how it came about: the other alternatives were tried and found wanting.

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Grand Strategy Annex

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A Formulation of Naturalism

16 November 2009


Hallett Cantorian Set Theory

One of my favorite books on set theory is Michael Hallett’s Cantorian Set Theory and Limitation of Size. While I have read some rather critical notices of the book, I am not the only one who appreciates it. I found a customer review at Amazon by William D. Fusfield that reads, “This is BY FAR the best and most INTERESTING book available on how Cantor developed his key ideas about transfinite sets, large cardinals, ordinals etc.”

Since Cantor is remembered for legitimizing the infinite as a mathematical concept, it might be a little surprising to hear that Hallett attributes “finitism” to Cantor, but by finitism Hallett does not mean any of the range of constructivist or strict finitist positions staked out by those who deny the legitimacy of the actual infinite and set theory, but rather it describes what we may call the methodological finitism of Cantor’s approach to the transfinite numbers he defined by way of set theory.

Finite mathematics is largely uncontroversial and commands the consensus of almost all who take an interest in the matter, however much they disagree on other parts of mathematics. Thus Hallett formulates what he calls Cantor’s principle of finitism thus:

“The transfinite is on a par with the finite and mathematically is to be treated as far as possible like the finite.” (p. 7)

This I would call methodological finitism. A little further on, on page 32, Hallett quotes Weyl thus:

“…for set theory, there is no difference in principle between the finite and the infinite.”

Hallett then comments:

“…the unity which Weyl points to is so much a fundamental part of Cantorianism (at least when we substitute ‘transfinite’ for ‘infinite’) that I have called it Cantor’s principle of finitism.”

A week ago I was musing about naturalism while making a longish drive and it occurred to me that something parallel to this approach could be used in a formulation of naturalism. “Parallel” is the key term here as were are talking about very different things with naturalism and the transfinite. What strikes me about Hallett’s formulation is the innate good sense of “as far as possible.” This stands in contrast to polarizing and absolutist definitions that employ formulations like “nothing but” or some equivalent of an extremal clause.

In contemporary science, scientific materialism is largely uncontroversial and commands the consensus of almost all interested parties. But from a philosophical standpoint materialism is as dissatisfying as finitism. If you can focus on the science and not think much about the materialism, you’ll be fine. But if the whole object of your interest in science is to illuminate the world and to come to a better understanding of it over all (as is my own interest), then one cannot only not avoid thinking about scientific materialism, one is obligated to think about it carefully.

At this point, then, I would suggest a methodological naturalism parallel to Hallett’s formulation of methodological finitism in Cantor: “Naturalism is on a par with materialism, and philosophically is to be treated as far as possible like materialism.” Or one could formulate it thus: “The natural is on a par with the material and scientifically is to be treated as far as possible like the material.”

Such a formulation would acknowledge both the success and the limitations of classical materialism that views the world entire as “nothing but” matter in motion — Democritean atoms whirling in the void — a classically reductionist formulation. Methodological naturalism as I have formulated it above, parallel to Hallett, would follow classical materialism as far as possible, and would only depart from materialism when that materialism was unsustainable in light of the evidence. And at this point I do not mean to suggest that one makes a transition from matter in motion to a non-naturalistic account of the world. On the contrary, it is at this point that naturalism shows itself to be as distinct from materialism as the infinite is distinct from the finite. Naturalism takes the spirit of materialistic explanation forward into areas that patently cannot be treated in terms of matter in motion.

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Naturalism: a Series

1. A Formulation of Naturalism

2. Two Thoughts on Naturalism

3. Naturalism: Yet Another Formulation

4. Joseph Campbell and Kenneth Clark: Bifurcating Naturalisms

5. Naturalism and Object Oriented Ontology

6. Naturalism and Suffering

7. Transcendental Non-Naturalism

8. Methodological Naturalism and the Eerie Silence

9. Some Formulations of Methodological Naturalism

10. Darwin’s Cosmology: A Naturalistic World

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Grand Strategy Annex

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