The Finality Fallacy

11 January 2014


fallacy taxonomy

One of my pet peeves is when a matter is treated as though settled and final when there is in fact no finality at all in a given formulation or in the circumstances that the formulation seeks to capture. I am going to call this attribution of finality to matters remaining unsettled the “finality fallacy” (it would more accurate to call this the “false finality fallacy” but this is too long and alliterative to boot). This is an informal rather than a formal fallacy, so an individual might be impeccable in their logic while still committing the finality fallacy. Another way to understand informal fallacies is that they concern the premisses of reasoning rather than the reasoning itself (another term for this is material fallacy), and it is one of the premisses of any finality fallacy that a given matter is closed to discussion and nothing more need be said.

Like many fallacies, the finality fallacy is related to recognized fallacies, although it is difficult to classify exactly. One could compare the finality fallacy to ignoratio elenchi or begging the question or the moralistic fallacy — all of these are present in some degree or other in the finality fallacy in its various manifestations.

Preparing for a cosmic journey -- but one trip settles nothing.

Preparing for a cosmic journey — but one trip settles nothing.

Allow me to begin with an example from popular culture. Although it has been several years since I have seen the film Contact (written by Carl Sagan and loosely based on the life of Jill Tartar, famous for her work in SETI) I can remember how irritated I was by the ending, which treated the celestial journey made by the main character as a unique, one-off effort, despite the fact that an enormous apparatus was built to make the journey possible. If I had made the film I would have finished with a waiting line of people queued up to use the machine next, to make it clear that nothing is finished by the fact of a disputed first journey.

It is routine for films to end with a false sense of finality, as filmmakers assume that the audience requires resolution, or “closure.” We hear a lot about closure, but it is rare to see a clear definition of what exactly constitutes closure. Perhaps it is the desire for closure, generally speaking, that is the primary motivation for the finality fallacy. When the psychological need for closure leaks over into an intellectual need for closure, then we find rationalizations of a false finality; perhaps it would be better to call the finality fallacy a cognitive bias rather, or this might be the point at which material fallacy overlaps with cognitive bias.

Closure sign

The cultivation of a false finality is also prevalent among contemporary Marxists, especially those who focus on Marx’s economic doctrines rather than his wider social and philosophical critique. Marx’s economics was already antiquated by the time he published Das Kapital, but because of Marx’s influence, and because of the ongoing revolutionary tradition that rightly claims Marx as a founding father, Marx’s dictates on the labor theory of value are taken as final by Marxists, who must now, more than 150 years later, pretend as though no advances had been made in economics in the meantime. Strangely, this attitude is also taken for granted among ideological foes of Darwin, who, again more then 150 years later, continue to raise the same objections as though nothing had happened in biology since before 1859. This carefully studied ignorance takes a particular development in intellectual history and treats it as final, as the last word, as definitive, as Gospel.

Wherever there is a dogma, there is a finality fallacy waiting to be committed when the adherents of the dogma in question treat that dogma as final and must thereafter perpetuate the ruse that nothing essential changes after the dogma establishes the last word. In Islam, we have the notorious historical development of ‘closing the gate of ijtihad’ — ijtihad being individual rational inquiry. This is now a contested idea — i.e., whether there ever was a closing of the gate of ijtihad — as there seems to have been no official proclamation or definitive text, but there can be no question that the idea of closing the gate of ijtihad played an important role is Islamic civilization in discouraging inquiry and independent thought (what we would today call a “chilling” effect, much like the condemnations of 1277 in Western history).

Bertrand Russell evinced a certain irritation when his eponymous paradox was dismissed or treated as final before any satisfactory treatment had been formulated.

Bertrand Russell evinced a certain irritation when his eponymous paradox was dismissed or treated as final before any satisfactory treatment had been formulated.

Bertrand Russell evinced an obvious irritation and impatience with the response to his paradox, which reveals an attitude not unlike my impatience with false finality:

“Poincaré, who disliked mathematical logic and had accused it of being sterile, exclaimed with glee, ‘it is no longer sterile, it begets contradiction’. This was all very well, but it did nothing towards the solution of the problem. Some other mathematicians, who disapproved of Georg Cantor, adopted the March Hare’s solution: ‘I’m tired of this. Let’s change the subject.’ This, also, appeared to me inadequate.”

Bertrand Russell, My Philosophical Development, Chapter VII, “Principia Mathematica: Philosophical Aspects”

Russell knew that nothing was settled by dismissing mathematical logic, as Poincaré did, or by simply changing the subject, as others were content to do. But some were satisfied with these evasions; Russell would have none of it, and persisted until he satisfied himself with a solution (which was his theory of types). Most mathematicians rejected Russell’s solution, and it was Zermelo’s axiomatization of set theory that ultimately became the consensus choice among mathematicians for employing set theory without running into the contradiction discovered by Russell.

Now I will turn to the contemporary example that prompted this post — as I said above, the finality fallacy is a pet peeve, but this particular instance was the trigger for this particular post — in the work of contemporary philosopher John Gray.

John Gray is not a philosopher who writes intentionally inflammatory pieces in order to grab headlines. He regularly has short essays on the BBC (I have commented on his A Point Of View: Leaving Gormenghast; his A Point of View: Two cheers for human rights also appeared on the BBC). He has written a sober book on Mill’s On Liberty, Mill on Liberty: A Defence, and a study of the thought of Isaiah Berlin (Isaiah Berlin) — in no sense radical topics for a contemporary philosopher.


Among Gray’s many books is The Immortalization Commission: Science and the Strange Quest to Cheat Death, in which we find the following:

“Echoing the Russian rocket scientist Konstantin Tsiolkovsky, there are some who think humans should escape the planet they have gutted by migrating into outer space. Happily, there is no prospect of the human animal extending its destructive career in this way. The cost of sending a single human being to another planet is prohibitive, and planets in the solar system are more inhospitable than the desolated Earth from which humans would be escaping.”

John Gray, The Immortalization Commission: Science and the Strange Quest to Cheat Death, New York: Farrar, Straus and Giroux, 2011, p. 212

There is a lot going on in this brief passage, and I would like to try to gloss some of this implicit content. Gray is here counting on his reader nodding along with him, since human beings have indeed had a destructive career on Earth, and I can easily imagine someone agreeing to this also agreeing to the undesirability of this destructive career being extended beyond the Earth. Gray also throws in a sense of gross irresponsibility by speaking of human beings having “gutted” the planet, and presumably moving on to “gut” the next one, with the clear implication that this would be worse than arresting the destructive career of human beings on their homeworld. Then Gray moves on to the expense of space travel at the present moment and the inhospitableness of other planets in our solar system. He treats as though final the present expense of space travel and the need to live on the surface of a planet, but more importantly he does so in a moral context that is intended to give the impression that any attempt to go beyond the Earth is unspeakable folly and morally disastrous.

Eunapius and Philostratus

This may sound like a stretch, but I am reminded of a passage from Eunapius (b. 347 A.D.), where Eunapius described the kind of atmosphere that made the condemnation of Socrates possible in Athens:

“…no one of all the Athenians, even though they were a democracy, would have ventured on that accusation and indictment of one whom all the Athenians regarded as a walking image of wisdom, had it not been that in the drunkenness, insanity, and license of the Dionysia and the night festival, when light laughter and careless and dangerous emotions are discovered among men, Aristophanes first introduced ridicule into their corrupted minds, and by setting dances upon the stage won over the audience to his views…”

Philostratus and Eunapius, Lives of the Sophists, Cambridge and London: Harvard, 1921, p. 381

Though a sober philosopher in his own right, Gray here trades upon the light laughter and careless and dangerous emotions when he engages in the ridicule of a human future beyond the Earth, which he implies is not only unlikely (if not impossible) but also morally wrong. But to demonstrate his intellectual sobriety he next turns serious and has this to say on the next page:

“The pursuit of immortality through science is only incidentally a project aiming to defeat death. At bottom it is an attempt to escape contingency and mystery. Contingency means humans will always be subject to fate and chance, mystery that they will always be surrounded by the unknowable. For many this state of affairs is intolerable, even unthinkable. Using advancing knowledge, they insist, the human animal can transcend the human condition.”

John Gray, The Immortalization Commission: Science and the Strange Quest to Cheat Death, New York: Farrar, Straus and Giroux, 2011, p. 213

Gray’s certainty and confidence of expression here mask the sheer absurdity of his claims; the expansion of a scientific civilization will by no means prejudice our relationship to contingency and mystery. On the contrary, it is a scientific understanding of the world that reminds us of contingency on levels that far exceed human capacity. The universe itself is a contingency, and all that it holds is contingency; science reminds us of this at every turn, and for the same reason, no matter how distantly human civilization travels beyond Earth, scientific mystery will be there to remind us of all that we still do not know.

But this is not my topic today (though it makes me angry to read it, and that is why I have quoted it). It is the previously quoted passage from Gray that truly bothers me because of its pose of finality in his pithy remarks about the human future beyond Earth. Gray is utterly dismissive of such prospects, and it is ultimately the dismissiveness that is the problem, not the view he holds.

I don’t mean to single out John Gray as especially guilty in this respect, though as a philosopher he is more guilty than others because he ought to know better, just as Russell knew better when it came to his paradox. In fact, there is some similarity here, because both mathematicians and philosophers were dismissive either of Russell’s paradox or of the formal methods that led to the paradox. We should not be dismissive. We need to confront these problems on their merits, and not turn it into a joke or an excuse to condemn human folly. We recall that a great many dismissed Cantor’s work as folly — after all, how can human beings know the infinite? — and Russell’s extension of Cantor’s work drew similar judgments. This, again, is closely connected to what we are talking about here, because the idea that human beings, finite as they are, can never know anything of the infinite (i.e., human beings cannot escape their legacy of intellectual finitude) is closely related to the idea that human beings can never escape their biological legacy of finitude, which is the topic of Gray’s book.

Hermann Weyl said that we live in an open world.

Hermann Weyl said that we live in an open world.

Anyone who views the world as an ongoing process of natural history, as I do, must see it as an open world. That the world is open, that it is neither closed nor final, neither finished nor complete, means that unprecedented events occur and that there always remains the possibility of evolution, by which we transcend a previous form of being and attain to a new form of being. The world’s openness is an idea that Hermann Weyl took as the title of three lectures from 1932, which end on this note:

“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, and in the theistic, specifically Lutheran-Protestant form, where it serves as a background for the violent drama of contrition, revelation, and grace. On the contrary, mind is freedom within the limitations of existence; it is open toward the infinite. Indeed, God as the completed infinite cannot and will not be comprehended by it; neither can God penetrate into man by revelation, nor man penetrate to him by mystical perception. The completed infinite we can only represent in symbols. From this relationship every creative act of man receives its deep consecration and dignity. But only in mathematics and physics, as far as I can see, has symbolical-theoretical construction acquired sufficient solidity to be convincing for everyone whose mind is open to these sciences.”

Hermann Weyl, Mind and Nature: Selected Writings on Philosophy, Mathematics, and Physics, edited by Peter Pesic, Princeton University Press, 2009, Chapter 4, “The Open World: Three Lectures on the Metaphysical Implications of Science,” 1932

Weyl gave his own peculiar theological and constructivist spin to the conception of an open world — Weyl, in fact, represents one of those mathematicians “who disapproved of Georg Cantor” about which I quoted Bertrand Russell above — but in the main I am in agreement with Weyl, and Weyl and Russell could have agreed on the openness of the world. To commit the finality fallacy is to presume some aspect of the world closed, and if the world is indeed open, it is a fallacy to represent it as being closed.

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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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work in progress2

Yesterday in The Unfinished World I attempted, however awkwardly, to draw a distinction between a common conception of the world becoming more rigid, inflexible, and closed as mature institutions dominate progressively greater areas of life, and the world becoming more unpredictable, changeable, and open as novel developments open new possibilities to us. I am not denying that the mature institutions of contemporary civilization do indeed conspire to confine us within ossified categories, but exclusively interpreting the world in this way does an injustice to the world.

I was bothered by the fact that my exposition of yesterday was as awkward as it was, because this is an issue of paramount importance. Whether one conceives of the world as finite, closed, bounded, finished, and completed on the one hand, or as infinite, open, unbounded, unfinished, and incomplete on the other hand, is one of those frighteningly clear points where one’s Weltanschauung — and not merely any aspect of one’s world-picture, but one’s intellectual world-picture, one’s ontological orientation, one’s personal metaphysic — comes into direct if not poignant contact with life. How one acts, and how one understands that action — with hope or fear, optimism or fatalism — will depend crucially on one’s conception of the world: what it is, how it is, and whether there is any “why” behind it.

Traditional institutions that are as old as civilization itself — law, economic organization, political hierarchy, privilege and subordination, hold before our eyes the image of a world that, if not eternal, is as close to eternal as anything sublunary can be. Even the sciences constructed to study these institutions — the social sciences — while often critical nevertheless end up recapitulating and regurgitating the society that they study, whatever shortcomings are found in it. It is this sort of attitude that must have inspired Marx to write in the last of his Theses on Feuerbach (which also appears on his tombstone), “The philosophers have only interpreted the world in various ways; the point is to change it.”

What shows us a very different world, a transient world in which all things solid melt into air, and what ought to excite us, are those institutions that have emerged since the advent of modernity: modern science, modern industry, modernism in the arts, the city as megalopolis, and all the things that are condemned by moralists and self-appointed defenders of the old order.

Hermann Weyl

Hermann Weyl

As Hermann Weyl formulated it in his Yale lectures of 1932 subsequently published as The Open World:

Modern science, in so far as I am familiar with it through my own scientific work, mathematics and physics make the world appear more and more as an open one, as a world not closed but pointing beyond itself.

Weyl was not the only one inspired by contemporary science to imagine a world no longer subject to the dead weight of tradition. Bertrand Russell, one of the greatest logicians of the nineteenth and twentieth centuries, turned his later career to expressing his skepticism about traditional society that he had earlier expressed regarding traditional logic. Russell was an iconic iconoclast and was often unsparing in his attacks on traditional institutions.

Bertrand Russell lecturing at University of California Los Angeles in 1939; Russell was one of the great iconoclasts of recent philosophy, and he often expressed his iconoclasm in compelling prose.

Bertrand Russell lecturing at University of California Los Angeles in 1939; Russell was one of the great iconoclasts of recent philosophy, and he often expressed his iconoclasm in compelling prose.

Not precisely describing an open world, but definitely a modern and non-classical world view (perhaps we could call it a quantum world view), Russell, in one of my favorite passages from his writings painted this picture of the world for us:

“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

While I am ready to countenance “the view that there is a world at all” (though with the caveat, as I wrote in my Variations on the Theme of Life, that the world is a metaphor for a concept that cannot be made literal), of which Russell here appears skeptical, on the whole I enthusiastically approve and applaud the world-picture that Russell draws in this passage.

In this semi-popular work by Russell he criticizes the idea of the unity of the world in clever and immediately comprehensible terms, but unlike much that Russell wrote for a popular audience this radical criticism of the unity of the world was also something that he developed in his technical philosophical writings. There is one particular passage in his lecture “On Scientific Method in Philosophy” that always strikes me as incredible each time I read it, though it is not widely quoted:

The philosophy which I wish to advocate may be called logical atomism or absolute pluralism, because, while maintaining that there are many things, it denies that there is a whole composed of those things.

The whole composed of logical atoms would presumably be the world, hence Russell’s skepticism about the world mentioned above. Russell’s “logical atomism” went on to enjoy a stellar career within philosophy, spawning one of the great movements of twentieth century thought. Unfortunately, the idea of absolute pluralism got lost in the logical shuffle that led to what we may call orthodox analytical philosophy. If Russell’s technical work in the philosophy of logic and mathematics had come to be called absolute pluralism instead of his other moniker, logical atomism, the history of twentieth century though might have been different.

One of the classics of intellectual history of the twentieth century is Alexander Koyre’s From the Closed World to the Infinite Universe, which characterizes the emergence of modernity in history as precisely the opening up of the closed conception of the world that dominated ancient and medieval thought into the infinite universe of modern science.

Alexander Koyre

Alexander Koyre

Instead of imagining the world as described in the passage I quoted yesterday from Tamim Ansary — “…over the centuries, even those cracks [in established precedent] grew narrower, because once an eminently qualified scholar weighed in on some subject his pronouncements also joined the canon. ” — in which novelty is being squeezed out and the scope of human action narrowed to insignificance, we ought to make an effort to imagine the world as opening up ever greater vistas, so that history shows us a widening human future that only gets larger the closer we approach it.

Ernst Friedrich Ferdinand Zermelo

Ernst Friedrich Ferdinand Zermelo

Even if one conceives of the world as an open world — and according to Koyre, most Westerners since the renaissance so conceive of it — that does not settle all questions and leave us all in agreement. The world, open by consensus, remains a complex and mysterious place, and it will still be variously conceived by different persons. Weyl, for example, as a constructivist, conceives of the infinitude of the world differently than someone like Ernst Zermelo, who was an unabashed advocate of the actual infinite. Zermelo wrote:

Purely “finitistic” mathematics in which, as a matter of fact, nothing has been left to be proved because everything could be verified already by a finite model, would no longer be mathematics in the true sense. Rather, a true mathematics is genuinely infinitistic and based on the assumption of infinite domains; it can directly be called the “logic of the infinite.”

The open and infinite world of Zermelo is distinct from the open and infinite world of Weyl. Thus even if we can agree with Weyl’s elevated statement near the end of his lectures that, “…mind is freedom within the limitations of existence; it is open toward the infinite” (and I do agree), the infinite recognized by Weyl is not necessarily the infinite we recognize, and therefore the quality of freedom is distinct as well. Again, this is important, though it sounds like mere scholasticism to point out the importance of something that will be dismissed by most as overly-subtle and without human interest or personal relevance.

Zermelo built upon the work of Georg Cantor, who was one of the great intellectual revolutionaries of all time.

Zermelo built upon the work of Georg Cantor, who was one of the great intellectual revolutionaries of all time.

I find Zermelo’s uncompromising defense of infinitistic domains and infinitistic reasoning to be refreshing. Cantor, of course, preceded Zermelo and made Zermelo possible, but it is interesting to notice the analogy between the response of the scientific establishment to Darwin and Cantor, both of whom put forward a radical and simple idea and changed history. In both cases, after the initial shock wore off, the research program initiated by each took off and rapidly bore fruit, but not long after Darwin many distanced themselves from the mechanism of natural selection, while after Cantor many distanced themselves from Cantor’s realism and his more imaginative use of infinitistic methods.

Darwin, like Cantor, was an intellectual revolutionary because he formulated an idea that changed all subsequent thought and opened up new domains of inquiry.

Darwin, like Cantor, was an intellectual revolutionary because he formulated an idea that changed all subsequent thought and opened up new domains of inquiry.

Radical innovations like those of Cantor and Darwin made the mind of the mind immeasurably larger than they were before. The world of man is expanding, and it is expanding at a faster rate than ever before in history.

We know now that the universe is not only expanding, but that its expansion is accelerating.

We know now that the universe is not only expanding, but that its expansion is accelerating: the world is getting bigger faster.

It was not until the twentieth century that Hubble proved the existence of galaxies outside the Milky Way. Up until that time, the world was quite small. Now we know better. Subsequent discoveries in astronomy have forced us to repeatedly expand our conception of the world. And only at the end of the twentieth century did we learn that the expansion of the universe is speeding up. From the first formulation of the big bang theory, that assumption had been that the expansion of the universe was slowing down. now we know that is not the case. There is not yet any satisfactory explanation for this. We have more than ever to learn, and more than ever before to explain.

The world is more unfinished than ever.


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Grand Strategy Annex

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