15 January 2017
Early in the history of this blog I wrote about a snowstorm in Portland during December 2008, Snow in Portland, More Snow, and Lessons from a Snowstorm, and now Portland has had another uncharacteristically heavy snowfall eight years on. I am always fascinated to watch the rapidly changing behaviors of the population of a city as it responds to rapidly changing conditions, and I can’t help but extrapolate from these observations to other disruptions to the ordinary business of life.
The initial impact of a big snowstorm (in a temperate climate where snowstorms are infrequent) is chaos and frantic activity. After the initial chaos, the city goes quiet, and driving around a city after it has gone quiet gives an apocalyptic feeling, as though the end of the world has come. A snowstorm is, in miniature, the collapse of a complex society, such as Joseph Tainter wrote about:
“Collapse, as viewed in the present work, is a political process. It may, and often does, have consequences in such areas as economics, art, and literature, but it is fundamentally a matter of the sociopolitical sphere. A society has collapsed when it displays a rapid, significant loss of an established level of sociopolitical complexity. The term ‘established level’ is important. To qualify as an instance of collapse a society must have been at, or developing toward, a level of complexity for more than one or two generations. The demise of the Carolingian Empire, thus, is not a case of collapse — merely an unsuccessful attempt at empire building. The collapse, in turn, must be rapid — taking no more than a few decades — and must entail a substantial loss of sociopolitical structure. Losses that are less severe, or take longer to occur, are to be considered cases of weakness and decline.”
Joseph A. Tainter, The Collapse of Complex Societies, Cambridge: Cambridge University Press, 1988, p. 4
Of course, the collapse precipitated by a snowstorm is not a political collapse, but it is a rapid and significant loss of an established level of complexity, and a temporary return to a simpler way of life.
When someone abandons their car and walks away, eventually walking around their neighborhood rather than driving, this is a significant simplification of life, and the simplest level to which life can be reduced is that of mere survival, or perhaps I should say subsistence. Because the conditions of a snowstorm or a flood or some similar disruption (say, a power outage) are temporary it does not force a return to subsistence agriculture, but there are occasions when one finds oneself no longer concerned by the technical details of one’s work, and one is only fighting to stay alive, as all other considerations are thrust aside in order to deal with the immediacy of the circumstances. However, it is easy to imagine (especially with the looming specter of climate change) that a storm could be the first disruption in a series of escalating disruptions that could force society to abandon its complex institutions and way of life, returning to subsistence agriculture, or even nomadic hunting and gathering. If a large flood failed to recede after a few days because water levels had crept higher, the disruption of the the storm that caused the flood would be a mere foretaste of things to come.
There is a great deal of social momentum behind the ordinary business of life, and one can observe that people continue to go about their routines in the routine way for as along as possible — right up the moment when it becomes actually physically impossible to continue to going about things as usual. Thus one sees people setting out for work as usual even as the snow is beginning to fall, and as the snow piles up they try to continue to go about their business. It is only when, on the drive home, their car will not move forward another inch, when they abandon it and walk away. As long as a choice remains, most will choose to continue with the ordinary business of life; the routine is only abandoned when no choice remains and one is forced by circumstances to alter one’s behavior.
There is also a strong desire to return to normalcy after the disruption of a storm, so that at the first sign of conditions improving, people head out again in large numbers. In the case of the snowstorms I have seen in my years, this creates a problem because the main roads will be cleared of snow, but the secondary roads and parking lots are still icy, and many people over-confidently driving at full speed on the highways cause problems for themselves and others. The desire for the return to normalcy is a desire for the familiar normalcy, the old normal, while the conditions of the storm, strange and unfamiliar at first, dictate a new normal, and there is a tension between the old normal and the new normal as society attempt to adjust and compensate for changed conditions. As long as the conditions of the new normal are temporary, the old normal will return, but the longer the conditions persist, the longer the new normal persists, and, as the phrase implies, the new normal eventually becomes familiar if it endures for a sufficient period of time.
I imagine that in the case of the true collapse of societies, and not merely an ephemeral collapse precipitated by a weather event, that this desire to return to normalcy results in a lot of false starts, like commuters returning to the roads too soon after a snowstorm. There are probably many hopeful moments in the collapse of a society when people come out of their hiding places and venture out into the world again, hoping that they can return to their routines. When Sarajevo was under siege during the Balkan wars of the 90s, it was several years before life could return to normal. Similarly, when the First and Second World Wars began, it would be several years before normalcy would return.
When a society well and truly collapses, never to rise again, one can imagine for years or for decades people looked for a return to normalcy that would never come. Or if life seemed to return to normal for a time — for weeks or months or years — it was only a deceptive return to old ways that would soon disappear forever. When Roman cities in the west began to fail, there was probably a movement like the ebb and flow of the tide, when people would abandon their city, then go back, then abandon it again. Each time those who returned would be fewer in number, there would be fewer shops open, and fewer goods for sale, and there might be increasing lengths of time between abandonment and return, until eventually the period of abandonment stretched into years, and the city fell into disrepair, fit only for looting from the ruins.
. . . . .
. . . . .
. . . . .
. . . . .
In my recent paper “A Manifesto for the Scientific Study of Civilization” I argued that the study of civilization should be scientific, and that a scientific theory of civilization would be a formal theory. Prior to this, I argued in Rational Reconstructions of Time that a formal historiography is possible. What is the connection between these two claims? In A Metaphysical Disconnect I suggested that it is a philosophical problem that philosophies of time have not been tightly-coupled with philosophies of history. This implies that a formal theory of time could be tightly-coupled with a formal theory of history, and a formal theory of history would presumably encompass (or, at least, overlap) a theory of civilization. A formal theory of civilization, then, might ultimately follow from formal historiography.
I fully understand that these are strange claims for me to be making. What in the world do I mean by a formal theory of time, of history, or of civilization? How could a science of civilization be a formal science? What is a formal science, anyway? Despite the burgeoning growth of computer science in our time, which is the latest addition to the formal sciences, the very idea of the formal as a distinct category of thought (distinct, especially, from the material) seems odd and alien to us, and the distinction between the formal sciences and the natural sciences seems archaic. What are the formal sciences? Here is one view:
“To put it in Kantian terms, the formal sciences dealt with the Reine Anschauung as opposed to empirical data. By that they have been connected to the methodology of mathematics and logic, thereby being part of both the philosophical tradition and the newly won applications of mathematical sciences to the natural sciences and engineering. Both the object and the methods of the Formal sciences were recognized as different from the Natural and the Social sciences.”
“The Formal Sciences: Their Scope, Their Foundations, and Their Unity” by Benedikt Löwe, Synthese, Vol. 133, No. 1/2, Foundations of the Formal Sciences I (Oct.-Nov., 2002),pp. 5-11
In the same paper there is an explicit attempt to answer the question, “What are the Formal Sciences?” Two answers are given:
● Answer 1: “There is a profound duality in the classification of sciences according to their scientific approaches: some sciences are empirical, some are formal. The former deal with predictions and their falsification, the latter with the understanding of systems without empirical component, be it man-made systems (literary systems, the arts or social systems) or formal systems”.
● Answer 2: “Formal sciences are those that deal with the deductive analysis of formal systems (i.e., systems independent of direct human influence)”.
At present I am not going to analyze these differing definitions of the formal sciences, but I will leave them to percolate in the back of the mind of the reader in order to return to the question at hand: the study of civilization as a formal science, i.e., one formal science among many other formal sciences, however we choose to define them.
We can get a hint of what a formal science of civilization would look like from structuralist historians and historians of the Annales school, the chief representatives of the latter being Marc Bloch, Lucien Febvre, and Fernand Braudel. Marc Bloch’s two volume history of feudalism, in particular, stands out as a great achievement in the genre, with chapters devoted to features of feudal society rather than to great events and historical turning points. Whereas John Florio had Montaigne say that I describe not the essence but the passage, Bloch sought to describe not the passage, but the essence. (I previously quoted from Bloch in Hegel and the Overview Effect.)
There is (or, there will be) no one, single way to approach formal historiography, in the same way that there is no one, single axiomatization of set theory. Even if one agrees with Gödel that set theory describes a “well-determined reality” (a realist conception that most people today would agree describes the past, even if they would hesitate to say the same of set theory), there are, as yet, many distinct approaches to that reality. So too with formal historiography; there will be many distinct formalisms for the organization, exhibition, and exposition of the well-determined reality of history.
I reveal myself as being more of a traditionalist than Bloch by my preference for approaching a theory of civilization by way of a theory of history, and a theory of history by way of a theory of time. This is “traditional” in the sense that, as I have remarked many times in other places, it has been traditional to study civilization by studying history, rather than studying civilization as an object of knowledge in its own right. I retain the historical perspective, and indeed even many of the prejudices of historians (these come naturally to me), but I can also see beyond history sensu stricto and to a science of time, a science of history, and a science of civilization that lies beyond history even as it draws from the tradition all that that tradition has to offer.
Both the essentialist approach of Bloch and the Annales school, and my own quasi-historical approach to a formal science of civilization, may each have something to contribute to a theory of civilization. Obviously, these are not the only ways to study civilization. Civilization also can be studied as an empirical science — this is probably how most would conceive a science of civilization — and even as an adventure science. What is adventure science?
Together with Dr. Jacob Shively, I wrote an article about adventure science, Adventure Science Enters the Space Age, noting that “big science” has become the paradigm of scientific activity at the present time, but when individual human beings are able to go exploring they will be able to pluck the low-hanging fruit of exploration and discovery. Adventure science characterizes the earliest stage of a science when discoveries can be made simply by traveling to an exotic locale and being the first to describe some phenomenon never before documented by science. Such discoveries are difficult for us now, because the low-hanging fruit of terrestrial discovery has all been plucked, but once off Earth, new worlds will beckon with new discoveries waiting to be made. This will be a new Golden Age of adventure science.
Paradoxically, the science of civilization will become an adventure science (if it ever becomes one) quite late in its history, so that adventure science will characterize a science of civilization not in its earliest stages, but in its latest stages. But civilization has had a kind of early adventure science phase as well. Archaeology was once the paradigm of adventure science — as attested to by the cinematic adventures of Indiana Jones and the television adventures of Relic Hunter — when real life explorers entered jungles and deserts and swamps to search for long lost cities. Archaeology is perhaps the closest existing discipline that we have to a true science of civilization — archaeologists have many theories of civilization — so that the adventure science that archaeology once was, was at the same time (at least in part) an adventure science of civilization. And it may be so again, when xenoarchaeologists lead the way, looking for the ruins of alien civilizations.
All of the resources of contemporary big science, with its thousands of researchers and multi-generational socially-organized research programs, will be necessary in order to develop the science that will make possible the production of interstellar vessels. In my Centauri Dreams post, The Interstellar Imperative, I wrote, “A starship would be the ultimate scientific instrument produced by technological civilization, constituting both a demanding engineering challenge to build and offering the possibility of greatly expanding the scope of scientific knowledge by studying up close the stars and worlds of our universe, as well as any life and civilization these worlds may comprise.” Once starships become a reality, they will make possible the empirical study of civilizations, which will begin as an adventure science, the primary qualification for which will be a willingness to tolerate discomfort and to travel to distant places with a determination to document every new sight that one sees.
Geology will become an adventure science like this once again as soon as human beings have the freedom to travel around our solar system; biology and ecology will become adventure sciences once again as soon as we can visit other living worlds. The study of civilization will not become an adventure science until human beings are free to travel about the cosmos, so that this is a very distant prospect, but still a hopeful one. If we do not find a number of interesting civilizations to study, we will build a number of interesting civilizations, and eventually these will be studied in their turn. In this latter instance, the science of civilization will only become an adventure science after civilization has expanded throughout the cosmos, has forgotten the saga of its expansion, and then rediscovers itself across a plurality of worlds. And once again we will be forced to reckon with Hegel’s prescience for having said that the owl of Minerva takes flight only with the setting of the sun.
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
26 December 2016
In my recent Manifesto for the Study of Civilization I employed the phrase history in an extended sense. Here is a bit more context:
“One form that the transcendence of an exclusively historical study of civilization can take is that of extrapolating historical modes of thought so that these modes of thought apply to the future as well as to the past (and this could be called history in an extended sense).”
In several posts I have developed what I call concepts in an extended sense, as in Geocentrism in an Extended Sense and “biocentrism in an extended sense” in Addendum on the Technocentric Thesis and “ecology in an extended sense” in Intelligent Invasive Species.
In Developmental Temporality I wrote:
“With the advent of civilization in the most extended sense of that term, comprising organized settled agricultural societies and their urban centers, planning for the future becomes systematic.”
And in Reduction, Emergence, Supervenience I wrote:
“Philosophy today, then, is centered on the extended conceptions of ‘experience’ and ‘observation’ that science has opened up to us, and these extended senses of experience and observation go considerably beyond ordinary experience, and the prima facie intellectual intuitions available to beings like ourselves, whose minds evolved in a context in which perceptions mattered enormously while the constituents and overall structure of the cosmos mattered not at all.”
In these attempts to extrapolate, expand, and extend concepts beyond their ordinary usage — the result of which might also be called overview concepts — each traditional concept must be treated individually, as there is a limit that is demarcated by the intrinsic meaning of the concept, and these limits are different in each case. With history, the extrapolation of the concept is obvious: history has taken the past as its remit, but history in an extended sense would apply to the totality of time. This is already being done in Big History.
When I attended the second IBHA conference in 2014 I was witness to a memorable exchange that I described in 2014 IBHA Conference Day 2:
“During the question and answer session, a fellow who had spoken up in previous sessions with questions stood up and said that there were (at least) two conceptual confusions pervasive throughout discussions at this conference: 1) that something could come from nothing (presumably a reference to how the big bang is framed, though this could have been intended more generally as a critique of emergentism) and, 2) that history can say anything about the future. The same individual (whose name I did not get) said that no one had given an adequate definition of history, and then noted that the original Greek term for history meant ‘inquiry.’ Given this Grecian (or even, if you like, Herodotean) origin for the idea of history as an inquiry, I immediately asked myself, ‘If one can conduct an inquiry into the past, why cannot one also conduct an inquiry into the future?’ No doubt these inquires will be distinct because one concerns the past and the other the future, but cannot they be taken up in the same spirit?”
There was a note of frustration in the voice of the speaker who objected to any account of the future as a part of history, and while I could appreciate the source of that frustration, it reminded me of every traditionalist protest against the growth of scientific knowledge made possible by novel methods not sanctioned by tradition. In this connection I think of Isaiah Berlin’s critique of scientific historiography, which I previously discussed in Big History and Scientific Historiography.
Berlin argued that the historical method is intrinsically distinct from the scientific method, so that there can be no such thing as scientific historiography, i.e., that the intrinsic limitations of the concept of history restricts history from being scientific in the way that the natural sciences are scientific. While Berlin’s objection to scientific historiography is not stated in terms of restricting the expansion of historical modes of thought, his appeal to a nature of history intrinsically irreconcilable with science and the scientific method is parallel to an appeal to the nature of history as being intrinsically about the past (thus intrinsically not about the future), hence there can be no such thing as a history that includes within it the study of the future in addition to the study of the past.
Here is a passage in which Berlin characterizes distinctively historical modes of thought, contrasting them to scientific modes of thought:
“Historians cannot ply their trade without a considerable capacity for thinking in general terms; but they need, in addition, peculiar attributes of their own: a capacity for integration, for perceiving qualitative similarities and differences, a sense of the unique fashion in which various factors combine in the particular concrete situation, which must at once be neither so unlike any other situation as to constitute a total break with the continuous flow of human experience, nor yet so stylised and uniform as to be the obvious creature of theory and not of flesh and blood. The capacities needed are rather those of association than of dissociation, of perceiving the relation of parts to wholes, of particular sounds or colours to the many possible tunes or pictures into which they might enter, of the links that connect individuals viewed and savoured as individuals, and not primarily as instances of types or laws.”
Isaiah Berlin, “The Concept of Scientific History,” in Concepts and Categories, p. 140
Every cognitive capacity that Berlin here credits to the historian can be equally well exercised in relation to the future as to the past (I should point out that, as far as I know, Berlin did not take up the problem of the relation of the historian to the future). Indeed, one of the weaknesses of futurism has been that futurists have not immersed themselves in these distinctively historical modes of thought; our conception of the future could greatly benefit from a capacity for integration and perceiving the relation of parts to wholes. I don’t think Berlin would ever have imagined his critique of scientific historiography as advice for futurists, but it could be profitably employed in developing history in an extended sense.
It is common for historians to invoke distinctively historical modes of thought, and I believe that this is a valid concern. Indeed, I would go farther yet. Human modes of thought are primarily temporal, and non-temporal modes of thought come very late in our history as a species in comparison to the effortless way we learn to think of time in subtle and sophisticated ways. For example, when one learns a language, one finds that one spends an inordinate amount of time attempting to master past, present, and future tenses — the tenses of our mother tongue are so fixed in our minds that any other schema strikes us as counterintuitive (and, interestingly, even those who attain fluency in another language or languages usually revert to their mother tongue for counting). But in order to communicate effectively we must master the logic of time as expressed in linguistic tenses. Human beings are inveterate planners, preparers, and schemers; our present is pervasively animated by a concern for the future. We are so taken up with our plans for the future that it is considered something of a “gift” to be able to “live in the moment.”
Many of Berlin’s examples of distinctively historical thought position the historian as attempting to explain historical change. The emphasis on describing change in history results in an indirect deemphasis of continuity, though continuity is arguably the overwhelming experience of time and history. It would be almost impossible for us to delineate all of the things that we know will happen tomorrow, and which we do not even bother to think of as predictions because they fall so far near certainty on the epistemic continuum of historical knowledge. All of the laws of science that have been discovered up to the present day will continue to be in effect tomorrow, and all of the events and processes that make up the world will continue to be governed by these laws of nature tomorrow. We could exhaust ourselves describing the nomological certainties of the morrow, and still not have exhausted the predictions we might have made. Thus it is we know that the sun will rise tomorrow, and we can explain how and why the sun will rise tomorrow. If you are an anchorite living in a cave, the sun will not rise for you, but you can nevertheless be confident that Earth will continue to orbit the sun while rotating, and that this process will result in the appearance of the sun rising for everyone else not so confined.
But our sciences that describe the laws of nature that govern the world are incomplete, and they are in particular incomplete when it comes to history. I have noted elsewhere that there is (as yet) no science of time, and it is interesting to speculate that the absence of a science of time may be related to a parallel absence of a truly scientific historiography or a science of civilization. Because we have no science of time, we have no formal concepts of time — or, rather, we have no concepts of time recognized to be formal concepts. I have argued elsewhere that the idea of the punctiform present is a formal concept of time, i.e., interpreted as a formal concept it can be employed in a formal theory of time which can illuminate actual time as an ideal, simplified model. But as soon as you try to interpret the idea of the punctiform present as an empirical concept you run into difficulties. Would it be possible to measure a dimensionless instant? The punctiform present is like a pendulum with a weightless string, frictionless fulcrum, and no air drag. No such pendulum exists in actual fact, but the ideal pendulum remains a useful fiction for us. Similarly, the punctiform present is a useful fiction for a formal science of time.
A truly (perhaps exhaustively) scientific historiography would not only employ the methods of the special sciences in the exposition of history, but would also incorporate a science of time that would allow us to be as definite about history to come as we can now be definite about our predictions for the natural world as governed by laws of nature. It is not difficult to imagine what Berlin would have thought of such an idea. Here is another quote from Berlin’s essay on scientific historiography:
“…the attempt to construct a discipline which would stand to concrete history as pure to applied, no matter how successful the human sciences may grow to be — even if, as all but obscurantists must hope, they discover genuine, empirically confirmed, laws of individual and collective behaviour — seems an attempt to square the circle.”
Isaiah Berlin, “The Concept of Scientific History,” in Concepts and Categories, p. 142
What Berlin here condemns as an attempt to square the circle is precisely my ideal in history, and it is what I called formal historiography in Rational Reconstructions of Time. A formulation of history in an extended sense would be a step toward a formal historiography.
While on one level I am interested in history as an intellectual discipline in its own right — history for history’s sake — and therefore I am interested in formal historiography as a sui generis discipline, I also have an ulterior motive in the pursuit of a formal historiography that can develop history in an extended sense. Such a formal historiography will be one tool in the interdisciplinary toolkit of future scientists of civilization, who must study civilization both in terms of its past and its future.
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
7 December 2016
The full awareness of our sun being a star, and the stars being suns in their own right, was a development nearly coextensive with the entire history of science, from its earliest stirrings in ancient Greece to its modern form at the present time. During the Enlightenment there was already a growing realization of this, as can be seen in a number of scientific works of the period, but scientific proof had to wait for a few generations more until new technologies made available by the industrial revolution produced scientific instruments equal to the task.
The scientific confirmation of this understanding of cosmology, which is, in a sense, the affirmation of Copernicanism (as distinct from heliocentrism) came with two scientific discoveries of the nineteenth century: the parallax of 61 Cygni, measured by Friedrich Wilhelm Bessel and published in 1838, which was the first accurate distance measured to a star other than the sun, and the spectroscopy work of several scientists — Fraunhofer, Bunsen, Kirchhoff, Huggins, and Secchi, inter alia (cf. Spectroscopy and the Birth of Astrophysics) — which demonstrated the precise chemical composition of the stars, and therefore showed them to be made of the same chemical elements found on Earth. The stars were no longer immeasurable or unknowable; they were now open to scientific study.
The Ptolemaic conception of the universe that preceded this Copernican conception painted a very different picture of the universe, and of the place of human beings within that universe. According to the Ptolemaic cosmology, the heavens were made of a different material than the Earth and its denizens (viz. quintessence — the fifth element, i.e., the element other than earth, air, fire, and water). Everything below the sphere of the moon — sublunary — was ephemeral and subject to decay. Everything beyond the sphere of the moon — superlunary — was imperishable and perfect. Astronomical bodies were perfectly spherical, and moved in perfectly circular lines (except for the epicycles). Comets were a problem (i.e., an anomaly), because their elliptical orbits ought to send them crashing through the perfect celestial spheres.
This Ptolemaic cosmology largely satisfied the scientific, philosophical, moral, and spiritual needs of western thought from classical antiquity to the end of the Middle Ages, and this satisfaction presumably follows from a deep consonance between this conception of the cosmos and a metaphysical vision of what the world ought to be. Ptolemaic cosmology is the intellectual fulfillment of a certain kind of heart’s desire. But this was not the only metaphysical vision of the world having its origins (or, at least, its initial expression) in classical antiquity. Another intellectual tradition that pointed in a different direction was mathematics.
Mathematics was the first science to attain anything like the rigor that we demand of science today. It remains an open question to this day — an open philosophical question — whether mathematics is a science, one of the sciences (a science among sciences), or whether it is something else entirely, which happens to be useful in the sciences, as, for example, the formal propaedeutic to the empirical sciences, in need of formal structure in order to organize their empirical content. The sciences, in fact, get their rigor from mathematics, so that if there were no mathematical rigor, there would be no possibility of scientific rigor.
Mathematics has been known since antiquity as the paradigm of exact thought, of precision, the model for all sciences to follow (remembering what science meant to the ancients, which is not what it means today: a demonstrative science based on first principles), and this precision has been seen as a function of its formalism, which is to say its definiteness, it boundedness, its participation in the peras. Despite this there was yet a recognition of the infinite (apeiron) in mathematics. I would go further, and assert that, while mathematics as a rigorous science has its origins in the peras, it has its telos in the apeiron. This is a dialectical development, as we will see below in Proclus.
Proclus expresses the negative character of the infinite in his commentary on Euclid’s Elements:
“…the infinite is altogether incomprehensible to knowledge; rather it takes it hypothetically and uses only the finite for demonstration; that is, it assumes the infinite not for the sake of the infinite, but for the sake the infinite.”
Proclus, A Commentary on the First Book of Euclid’s Elements, translated, with an introduction and notes, by Glenn R. Morrow, Princeton: Princeton University Press, 1992, Propositions: Part One, XII, p. 223. This whole section is relevant, but I have quoted only a brief portion.
There is no question that the apeiron appeared on the inferior side of the Pythagorean table of opposites, but it is also interesting to note what Proclus says earlier on:
“The objects of Nous, by virtue of their inherent simplicity, are the first partakers of the Limit (περας) and the Unlimited (ἄπειρον). Their unity, their identity, and their stable and abiding existence they derive from the Limit; but for their variety, their generative fertility, and their divine otherness and progression they draw upon the Unlimited. Mathematicals are the offspring of the Limit and the Unlimited…”
Proclus, Commentary on the First Book of Euclid, Prologue: Part One, Chap. II
Here the apeiron appears on an equal footing with the peras, both being necessary to mathematical being. “Mathematicals” are born of the dialectic of the finite and the infinite. Both of these elements are also found (hundreds of years earlier) in the foundations of geometry. As the philosophers produced proofs that there could be no infinite number or infinite space, Euclid spoke of lines and planes extended “indefinitely” (as “apeiron” is usually translated in Euclid). Even later when the Stoics held that the material world was surrounded by an infinite void, this void had special properties which distinguished it from the material world, and indeed which kept the material world from having any relation with the void. The use of infinities in geometry, however, even though in an abstract context, force one to maintain that space locally, directly before one, is essentially of the same kind as space anywhere else along the infinite extent of a line, and indeed the same as space infinitely distant. All spaces are of the same kind, and all are related to each other. This constitutes a purely formal conception of the uniformity and continuity of nature. One might interpret the subsequent history of science as redeeming, through empirical evidence, this formal insight.
The infinite is the “internal horizon” (to use a Husserlian phrase) and the telos of mathematical objects. Given this conception of mathematics, the question that I find myself asking is this: what was the mathematical horizon of the Greeks? Did the idea of a line or a plane immediately suggest to them an infinite extension, and did the idea of number immediately suggest the infinite progression of the series, or were the Greeks able to contain these conceptions within the peras, using them not unlike we use them, but allowing them to remain limited? Did ancient mathematical imagination encompass the infinite, or must such a conception of mathematical objects (as embedded in the infinite) wait for the infinite to be disassociated from the apeiron?
The wait was not long. While the explicit formulation of the mathematical infinite had to wait until Cantor in the nineteenth century, Greek thought was dialectical, so regardless of the nature of mathematical concepts as initially conceived, these concepts inevitably passed into their opposite numbers and grew in depth and comprehensiveness as a result of the development of this dialectic. Greek thought may have begun with an intellectual commitment to the peras, and a desire to contain mathematics within the peras, consequently an almost ideological effort to avoid the mathematical infinite, but a commitment to dialectic confounds the demand for limitation. It is, then, this dialectical character of Greek thought that gives us the transition from purely local concepts to a formal concept of the uniformity of nature, and then the transition from a formal conception of uniformity to an empirical conception of uniformity, and this latter is the cosmological principle that is central to contemporary cosmology.
The cosmological principle brings us back to where we started: To say that the sun is a star, and every star a sun, is to say that the sun is a star among stars. Earth is a planet among planets. The Milky Way is a galaxy among galaxies. This is not only a Copernican idea, it is also a formal idea, like the formal conception of the uniformity of nature. (In A Being Among Beings I made a similar about biological beings.) To be one among others of the same kind is to be a member of a class, and to be a member of a class is to be the value of a variable. Quine, we recall, said that to be is to be the value of a variable. This is a highly abstract and formal conception of ontology, and that is precisely the importance of the formulation. This is the point beyond which we can begin to reason rigorously about our place in the universe.
We require a class of instances before we can draw inductive inferences, generalize from all members of this class, or formalize the concept represented by any individual member of that class. This is one of the formal presuppositions of scientific thought never made explicit in the methodology of science. We could not formulate the cosmological principle if we did not have a concept of “essentially the same,” because the “same” view that we see looking in any direction in the universe is not identically the same, but rather essentially the same. Of any two views of the universe, every detail is different, but the overview is the same. The cosmological principle is not a generalization, not an inductive inference from empirical evidence; it is a formal idea, a regulative idea that makes a certain kind of cosmological thought possible.
Formal principles like this are present throughout the sciences, though not often recognized for what they are. Bessel’s observations of 61 Cygni not only required industrialized technology to produce the appropriate scientific instruments, these observations also presupposed the mathematics originating in classical antiquity, so that the nineteenth century scientific work that proved the stars to be like our sun (and vice versa) was predicated upon parallel formal conceptions of universality structured into mathematical thought since its inception as a theoretical discipline (in contradistinction to the practical use of mathematics as a tool of engineering). Formal Copernicanism preceded empirical Copernicanism. Without that formal component of scientific knowledge, that scientific knowledge would never have come into being.
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
5 December 2016
Constructive and Non-Constructive Perspectives
Whenever I discuss methodology, I eventually come around to discussing the difference between constructive and non-constructive methods, as this is a fundamental distinction in reasoning, though often unappreciated, and especially neglected in informal thought (which is almost all human thought). After posting Ex Post Facto Eight Year Anniversary I realized that the distinction that I made in that post between detail (granularity) and overview (comprehensivity) can also be illuminated by the distinction between the constructive and the non-constructive.
Two two pairs of concepts can be juxtapositioned in order to show the four permutations yielded by them. I have done the same thing with the dual dichotomies of nomothetic/ideographic and synchonic/diachronic (in Axes of Historiography) and with weak panspermia/strong panspermia and theological/technological (in Is astrobiology discrediting the possibility of directed panspermia?). The table above gives the permutations for the juxtaposition of detail/overview and constructive/non-constructive.
In that previous post I identified my theoretical ideal as a fine-grained overview, combining digging deeply into details while also cultivating an awareness of the big picture in which the details occur. Can a fine-grained overview be attained more readily through constructive or non-constructive methods?
In P or Not-P I quoted this from Alain Connes:
“Constructivism may be compared to mountain climbers who proudly scale a peak with their bare hands, and formalists to climbers who permit themselves the luxury of hiring a helicopter to fly over the summit.”
Changeux and Connes, Conversations on Mind, Matter, and Mathematics, Princeton, 1995, p. 42
This image makes of constructivism the fine-grained, detail-oriented approach, while non-constructive methods are like the overview from on high, as though looking down from a helicopter. But it isn’t quite that simple. If we take this idea of constructivists as mountain climbers, we may extend the image with this thought from Wittgenstein:
“With my full philosophical rucksack I can climb only slowly up the mountain of mathematics.”
Ludwig Wittgenstein, Culture and Value, p. 4
And so it is with constructivism: the climbing is slow because they labor under their weight of a philosophical burden. They have an overarching vision of what logic and mathematics ought to be, and generally are not satisfied with these disciplines as they are. Thus constructivism has an overview as well — a prescriptive overview — though this overview is not always kept in mind. As Jean Largeault wrote, “The grand design has given way to technical work.” (in the original: “Les grands desseins ont cédé la place au travail technique.” L’intuitionisme, p. 118) By this Largeault meant that the formalization of intuitionistic logic had deprived intuitionism (one species of constructivism) of its overarching philosophical vision, its grand design:
“Even those who do not believe in the omnipotence of logic and who defend the rights of intuition have acceded to this movement in order to justify themselves in the eyes of their opponents. As a result we find them setting out, somewhat paradoxically, the ‘formal rules of intuitionist logic’ and establishing an ‘intuitionistic formalism’.”
…and in the original…
“Ceux-la memes qui ne croient pas a la toute-puissance de la logique et qui défendent les droits de l’intuition, ont du, eux aussi, céder au mouvement pour pouvoir se justifier aux yeux de leurs adversaires, et l’on a vu ainsi, chose passablement paradoxale, énoncer les ‘regles formelles de la logique intuitioniste’ et se constituer un ‘formalisme intuitioniste’.”
Robert Blanché, L’axioimatique, § 17
But intuitionists and constructivists return time and again to a grand design, so that the big picture is always there, though often it remains implicit. At very least, both the granular and the comprehensive conceptions of constructivism have at least a passing methodological familiarity, as we see in the table above, on the left side, granular constructivism with its typical concern for the “right” methods (which can be divorced from any overview), but also, below that, the philosophical ideas that inspired the constructivist deviation from classical eclecticism, from Kant through Hilbert and Brouwer to the constructivists of our time, such as Errett Bishop.
These two faces of methodology are not as familiar with non-constructivism. In so far as non-constructivism is classical eclecticism (a phrase I have taken from the late Torkel Frazén), a methodological “anything goes,” this is the granular conception of non-constructivism that consists of formal methods without any unifying philosophical conception. This much is familiar. Less familiar is the possibility of a non-constructive overview made systematic by some unifying conception. The idea of a non-constructive overview is familiar enough, and appears in the Connes quote above, but it this idea has had little philosophical content.
There is, however, the possibility of giving non-constructive formal methodology an overarching philosophical vision, and this follows readily enough from familiar forms of non-constructive thought. Cantor’s theory of transfinite numbers, and the proof techniques that Cantor formulated (and which remain notorious among constructivists) is a rare example of non-constructive thought pushed to its limits and beyond. Applied to a non-constructive overview, the transfinite perspective suggests that a systematically non-constructive methodology would insistently seek a total context for any idea, by always contextualizing any idea in a more comprehensive setting, and pursuing that contextualization to infinity. Thus any attempt to think a finite thought forces us to grapple with the infinite.
A fine-grained overview might be formulated by way of a systematically non-constructive methodology — not the classical eclecticism that is an accidental embrace of non-constructive methods alongside constructive methods — that digs deep and drills down into details by non-constructive methods that also furnish a sweeping, comprehensive philosophical vision of what formal methods can be, when that philosophical vision is not inspired to systematically limit formal methods (as is the case with constructivism).
Would the details that would be brought out by a systematically non-constructive method be the same fine-grained details that constructivism brings out when it insists upon finitistic proof procedures? Might there be different kinds of detail to be revealed by distinct methods of granularity in formal thought? These are elusive thoughts that I have not yet pinned down, so examples and answers will have to wait until I have achieved Cartesian clarity and distinctness about non-constructive methods. I beg the reader’s indulgence for my inadequate formulations here. Even as I write, ideas appear briefly and then disappear before I can record them, so this post is different from what I imagined as I sat down to write it.
Here again I can appeal to Wittgenstein:
“This book is written for such men as are in sympathy with its spirit. This spirit is different from the one which informs the vast stream of European and American civilization in which all of us stand. The spirit expresses itself in an onwards movement, building ever larger and more complicated structures; the other in striving after clarity and perspicuity in no matter what structure. The first tries to grasp the world by way of its periphery — in its variety; the second at its center — in its essence. And so the first adds one construction to another, moving on and up, as it were, from one stage to the next, while the other remains where it is and what it tries to grasp is always the same.”
Ludwig Wittgenstein, Philosophical Remarks, Foreword
These two movements of thought are not mutually exclusive; it is possible to build larger structures while always trying to grasp an elusive essence. It could be argued that anything built on uncertain foundations will come to naught, so that we must grasp the essence first, before we can proceed to construction. As important as it is to attempt to grasp an elusive essence, if we do this, we risk the intellectual equivalent of the waiting gambit.
. . . . .
Constructivism and Non-constructivism
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
3 December 2016
Last month, November 2016, marked the eight year anniversary for this blog. My first post, Opening Reflection, was dated 05 November 2008. Since then I have continued to post, although less frequently of late. I have become much less interested in tossing off a post about current events, and more interested in more comprehensive and detailed analyses, though blog posts are rarely associated with comprehensivity or detail. But that’s how I roll.
It is interesting that we have two distinct and even antithetical metaphors to identify non-trivial modes of thought. I am thinking of “dig deep” or “drill down” on the one hand, and, on the other hand, “overview” or “big picture.” The two metaphors are not identical, but each implies a particular approach to non-triviality, with the former implying an immersion in a fine-grained account of anything, while the latter implies taking anything in its widest signification.
Ideally, one would like to be both detailed and comprehensive at the same time — formulating an account of anything that is, at once, both fine-grained and which takes the object of one’s thought in its widest signification. In most cases, this is not possible. Or, rather, we find this kind of scholarship only in the most massive works, like Gibbon’s Decline and Fall of the Roman Empire, or Mario Bunge’s Treatise on Basic Philosophy. Over the past hundred years or so, scholarship has been going in exactly the opposite direction. Scholars focus on a particular area of thought, and then produce papers, each one of which focuses even more narrowly on one carefully defined and delimited topic within a particular area of thought. There is, thus, a great deal of very detailed scholarship, and less comprehensive scholarship.
Previously in Is it possible to specialize in the big picture? I considered whether it is even possible to have a scholarly discipline that focuses on the big picture. This question is posed in light of the implied dichotomy above: comprehensivity usually comes at the cost of detail, and detail usually comes at the cost of comprehensivity.
Another formulation of this dichotomy that brings out other aspects of the dilemma would to ask if it is possible to be rigorous about the big picture, or whether it is possible to be give a detailed account of the big picture — a fine-grained overview, as it were? I guess this is one way to formulate my ideal: a fine-grained overview — thinking rigorously about the big picture.
While there is some satisfaction in being able to give a concise formulation of my intellectual ideal — a fine-grained overview — I cannot yet say if this is possible, or if the ambition is chimerical. And if the ambition for a fine-grained overview is chimerical, is it chimerical because finite and flawed human beings cannot rise to this level of cognitive achievement, or is it chimerical because it is an ontological impossibility?
While an overview may necessarily lack the detail of a close and careful account of anything, so that the two — overview and detail — are opposite ends of a continuum, implying the ontological impossibility of their union, I do know, on the other hand, that clear and rigorous thinking is always possible, even if it lacks detail. Clarity and rigor — or, if one prefers the canonical Cartesian formulation, clear and distinct ideas — is a function of disciplined thinking, and one can think in a disciplined way about a comprehensive overview. If one allows that a fine-grained overview can be finely grained in virtue of the fine-grained conceptual infrastructure that one employs in the exposition of that overview, then, certainly, comprehensive detail is possible in this respect (even if in no other).
I could, then, re-state my ambition as formulated in my opening reflection such that, “my intention in this forum to view geopolitics through the prism of ideas,” now becomes my intention to formulate a fine-grained overview of geopolitics through the prism of ideas. But, obviously, I now seldom post on geopolitics, and am out to bag bigger game. This is, I think, implicit in the remit of a comprehensive overview of geopolitics. F. H. Bradley famously said, “Short of the Absolute God cannot stop, and, having reached that goal, He is lost, and religion with Him.” We might similarly say, short of big history geopolitics cannot stop, and, having reached that goal, it is lost, and political economy with it.
. . . . .
. . . . .
. . . . .
. . . . .
10 November 2016
The parallels between the US presidential election and the recent Brexit vote are so numerous and so telling and it is difficult to discuss one without the other. In both cases, almost every mainstream social institution declared itself for the status quo, the polls seemed to point to the maintenance of the status quo, the narrative of the media was a relentless drumbeat for the status quo that made the alternative not so much something to be avoided as something unthinkable, and yet the status quo was upended by a popular vote. The aftermath of the Brexit vote is still unfolding, and there are sectors of the media that, even today, months later, continue the drumbeat, which indicates that they are not yet reconciled to the accepting the result of the vote. Those who voted against the status quo did so in the face of overwhelmingly negative portrayals of such a vote, and of any voters who would so vote.
And make no mistake that this was a vote against the status quo. This was not a vote of left vs. right, or liberal vs. conservative, or even Democrat vs. Republican. This was a vote of insider vs. outsider, establishment vs. non-establishment, status quo vs. change (or even the media haves vs. the media have-nots). It is true that Trump ran as a Republican, but he did so in the face of many if not most of the party leadership explicitly in opposition to him. Indeed, the Republican leadership was every bit as bitter in its condemnation of Trump hijacking their party for his purposes as the Democratic leadership was bitter in denouncing Trump.
Perhaps the most telling headline I noticed was this: World media shock and dismay at Trump win. The media was not impartial in this presidential fight; they had a stake in the outcome, and, when the outcome failed to confirm their narrative, there was indeed shock and dismay. There was also this from the New York Times, indicating the first signs of soul searching on the part of the media: How Did the Media — How Did We — Get This Wrong? by Michael Barbaro. A surprisingly candid BBC piece from Rod Dreher, Senior editor of The American Conservative, US election 2016: America’s front-porch revolt, acknowledged that he, too, had been drawn into the media narrative — though, as I noted above, the presidential election was not about liberal vs. conservatives, so the conservative élites were just as likely to misread the election as were liberal élites.
In the wake of the surprise result, it will widely said that the polls cannot be trusted, and this will be used to imply that polling methodology is fatally flawed. But it is not the polls, but the pollsters, that cannot be trusted. Pollsters, like the media, have come to constitute their own political class — or, rather, pollsters belong to the same political class as journalists and pundits, and, sharing the assumptions of this class, they shared the idea that anything other than a Clinton victory was unthinkable. They formulated their polls on this basis, and so their methods dutifully repeated back to them the only message they were capable of hearing. There is a name for this in the study of cognitive bias: availability cascade.
It certainly isn’t rocket science to understand why the polls failed. Many people told me privately that they planned to vote for Trump, but no one who told me privately that they would vote for Trump said publicly that they would do so. (Yes, I understand that this is merely anecdotal evidence, but when statistical evidence has been compromised by statisticians in the grip of an availability cascade, telling personal anecdotes can provide a window into events that has been missed by the statistics.) Why was this the case? Why would individuals privately discuss their vote, but not discuss their vote publicly? Because to publicly state your support for Trump prior to the election was to be subject to a torrent of abuse (cf. the experience of Peter Thiel, alone among Silicon Valley notables supporting Trump, and who found his business interests threatened by this support). Not surprisingly, individuals do not wish to be subject to a torrent of abuse, so they simply choose to remain silent. I would not be at all surprised if Trump supporters intentionally misled pollsters, not out of any sense of malice, but simply knowing that they were talking to someone who had completely bought into the availability cascade of a Clinton victory, they may have found it easier to tell the pollsters what the pollsters expected to hear. This kind of thing cannot even be captured in the language of the questions of the poll: it may be the tone of voice or the attitude of the pollster that communicated the message.
The issue of subjecting those who differ from the establishment narrative to personal abuse and denigration is more important than is usually recognized. The phenomenon has been evolving in American political life since the tumult of the 1960s, first with the Civil Rights movement, and then with Vietnam war protests. With these issues it was widely felt that the establishment was not acting upon moral imperatives viewed as central at the time. Because no results were being had by traditional means of political participation, a culture of organized civil disobedience came into being. Traditional politicians told young people during their messianic stage (also known as youthful idealism) that the proper way to express themselves politically was to vote. But voting was not felt to be sufficient to address the evil at hand, so protest became an additional avenue of political participation.
The rise of protest as a form of political participation — and the observed efficacy of well-staged protests — resulted in what I will call the dialectic of activism and electoral politics. Activism has been so effective as a political tactic that some political pressure groups have entirely abandoned electoral politics (i.e., seeking a vote on an issue) in favor of activism. Activists do not need an electoral majority in order to realize their political ends; they merely need to be effective activists. The emergence of activist politics changed the political landscape of the US, allowing small minorities to advance their agenda in a way that electoral politics would not have allowed. One might say that it is the business of successful activism to create an availability cascade and so give the appearance that their cause represents the electoral consensus. But the success of activist politics that serves minority viewpoints means that electoral politics then becomes the opposite swing of the pendulum, and society is moved back and forth between votes that express an actual majority of the electorate, and activism that expresses the views of the most motivated and most effective activists.
With the Brexit vote and the US presidential election, the élites of their respective societies — political élites, policy élites, journalist élites, celebrity élites, business and financial élites, and even activist élites — not only created an availability cascade that was at odds with the electoral majority, they moreover believed the narrative that they themselves had created. Thus the shock at the electoral correction. And this dialectic of electoral and activist politics should be expected to continue. The most motivated and passionate activists will continue to press for political change unrelated to electoral politics, and electoral politics will repeatedly place politicians in office unrelated to the political demands of activists.
It is often noted that the US political system is gridlocked and incapable of functioning effectively (I wrote about this in Checks, Balances, and Gridlock, and a recent Harvard study, Problems Unsolved & A Nation Divided by Michael E. Porter, Jan W. Rivkin, and Mihir A. Desai, with Manjari Raman, focused on political paralysis; also cf. an article on this study at Geopolitical Monitor by Oscar Silva-Valladares, American Decline and the Limits of Academic Thinking). On the one hand, activism is a response to political paralysis, since it promises results outside the usual mechanisms of political influence, but, on the other hand, the dialectic of activism and electoral politics is itself a source of gridlock and stagnation. In order for democracy and popular sovereignty to have a future in the twenty-first century, it may be necessary to find a way around the traditional mechanisms of electoral politics that is nevertheless responsive to the electorate. Consider this a research question in the future of democracy.
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .