More on the Unfinished world

12 August 2009


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.


. . . . .


. . . . .

Grand Strategy Annex

. . . . .


Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )


Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.

%d bloggers like this: