20 October 2012
Three Little Words: “Where are they?”
In The Visibility Presumption I examined some issues in relation to the response to the Fermi paradox by those who claim that a technological singularity would likely overtake any technologically advanced civilization. I don’t see how the technological singularity visited upon an alien species makes them any less visible (in the sense of “visible” relevant to SETI) nor any less likely to be interested in exploration, adventure, or the quest for scientific knowledge — and finding us would constitute a major scientific discovery for some xenobiological species that had matured into a peer industrial-technological civilization.
The more I think about the Fermi paradox — and I have been thinking a lot about it lately — and the more I contextualize the Fermi paradox in my own emerging theory of civilization — which is a theory I am attempting to formulate in the purest tradition of Russellian generality so that it is equally applicable to human civilization and to any non-human civilization — the more I have come to think that our civilization is relatively isolated in the cosmos, being perhaps one of the few civilizations, or the only civilization, in the Milky Way, and one among only a handful of civilizations in the local cluster of galaxies or our supercluster.
Having an opinion on the Fermi paradox, and even making an attempt to argue for a particular position, does not however relieve one of the intellectual responsibility of exploring all aspects of the paradox. I have also come to think, while reflecting on the Fermi paradox, that the paradox itself has been fruitful in pushing those who care to think about it toward better formulations of the nature and consequences of industrial-technological civilization and of interstellar civilization — whether that of a supposed xenocivilization, or that of ourselves now and in the future.
The human experience of economic and technological growth in the wake of the industrial revolution has made us aware that if there are other peer species in the universe, and if these peer species undergo a process of the development of civilization anything like our own, then these peer species may also have experienced or will experience the escalating exponential growth of economic organization and technological complexity that we have experienced. Looking at our own civilization, again, it seems that the natural telos of continued economic and technological development — for we see no natural or obvious impediment to such continued development — is for human civilization to extend itself beyond the confines of the Earth and the establish itself throughout the solar system and eventually throughout the galaxy and beyond. This natural teleology has been called “The Expansion Hypothesis” by John M. Smart. Smart credits the expansion hypothesis to Kardashev, and while it is implicit in Kardashev, Kardashev himself does not formulate the idea explicitly and does not use the term “expansion hypothesis.”
The natural teleology of civilization
I have taken the term “natural teleology” from contemporary philosophical expositions of Aristotle’s distinction between final causes and efficient causes. We can get something of a flavor of Aristotle’s idea of natural teleology (without going too deep into the controversy over final causes) from this paragraph from the second book of Aristotle’s Physics:
We also speak of a thing’s nature as being exhibited in the process of growth by which its nature is attained. The ‘nature’ in this sense is not like ‘doctoring’, which leads not to the art of doctoring but to health. Doctoring must start from the art, not lead to it. But it is not in this way that nature (in the one sense) is related to nature (in the other). What grows qua growing grows from something into something. Into what then does it grow? Not into that from which it arose but into that to which it tends. The shape then is nature.
Aristotle is a systematic philosopher, in which any one doctrine is related to many other doctrines, so that an excerpt really doesn’t do him justice; if the reader cares to, he or she can can look into this more deeply by reading Aristotle and his commentators. But I must say this much in elaboration: the idea of natural teleology is problematic because it suggests a teleological conception of the whole of nature and all of its parts, and ever since Darwin we have understood that many claims to natural teleology are simply the expression of anthropic bias.
Still, kittens grow into cats and puppies grow into dogs (if they live to maturity), and it is pointless to deny this. What is important here is to tightly circumscribe the idea of natural teleology so that we don’t throw out the baby with the bathwater. The difficulty comes in distinguishing the baby from the bathwater in which the baby is immersed. Unless we want to end up with the idea of a natural teleology for human beings and the lives they live — this was the “human nature” that Sartre emphatically denied — we must deny final causes to agents, or find some other principle of distinction.
Are civilizations a natural kind for which we can posit a natural teleology, i.e., a form or a nature toward which they naturally tend as they grow and develop? My answer to this is ambiguous, but it is a principled ambiguity: yes and no. Yes, because some aspects of civilization are clearly developmental, when an institution is growing toward its fulfillment, while other aspects of civilization are clearly non-developmental. But civilization is so complex a whole that there is no simple way to separate the developmental and the non-developmental aspects of any one given civilization.
When we examine high points of civilization like Athens under Pericles or Florence during the Renaissance, we can recognize after the fact the slow build up to these cultural heights, which cannot clearly be distinguished from economic, civil, urban, and military development. The natural teleology of a civilization is the attainment of excellence in its particular mode of being, just as Aristotle said that the great-souled man aims at excellence in his life, but the path to that excellence is as varied as the different lives of individuals and the difference histories of civilizations.
Now, I don’t regard this brief exposition of the natural teleology of civilization as anything like a definitive formulation, but a definitive formulation of something so complex and subtle would require years of work. I will save this for another time, rather, counting on the reader’s charity (if not indulgence) to grant me the idea that at least in some respects civilizations tend toward fulfilling an apparent telos implicit in its developmental history.
The Preemption Hypothesis
What I am going to suggest here as another response to the Fermi paradox will sound to some like just another version of the technological singularity response, but I want to try to show that what I am suggesting is a more general conception than that — a potential structural failure of civilization, as it were — and as a more comprehensive concept the technological singularity response to the Fermi paradox can be subsumed under it as a particular instance of civilizational preemption.
The more general conception of a response to the silentium universi I call the preemption hypothesis. According to the preemption hypothesis, the ordinary course of development of industrial-technological civilization — which, if extrapolated, would seem to point to a nearly inevitable expansion of that civilization beyond its home planet and eventually across interstellar space as its natural teleology — is preempted by the emergence of a completely different kind of civilization, a radically different kind of civilization, or by post-civilization, so that the expected natural teleology of the preempted civilization is interrupted and never comes to fruition.
Thus “the lights go out” for a given alien civilization not because that civilization destroys itself (the Doomsday argument, Solution no. 27 in Webb’s book) and not because it collapses into permanent stagnation or even catastrophic civilizational failure (existential risks outlined by Nick Bostrum), and not because it completes a natural cycle of growth, maturity, decay, and death, but rather because it moves on to the next stage of social institution that lies beyond civilization. In simplest terms, the preemption hypothesis is that industrial-technological civilization, for which the expansion hypothesis holds, is preempted by post-civilization, for which the expansion hypothesis no longer holds. Post-civilization is a social institution derived from civilization but no longer recognizably civilization.
The idea of a technological singularity is one kind of potential preemption of industrial-technological civilization, but certainly not the only possible kind of preemption. There are many possible forms of civilizational preemption, and any attempted list of possible preemptions is limited only by our imagination and our parochial conception of civilization, the latter being informed exclusively by human civilization. It is entirely possible, as another example of preemption, that once a civilization attains a certain degree of technological development, everyone recognizes the pointlessness of the the whole endeavor, all the machines are shut down, and the entire population turns to philosophical contemplation as the only worthy undertaking in life.
Acceleration and Preemption
I have previously argued that civilizations come to maturity in an Axial Age. The Axial Age is a conception due to Karl Jaspers, but I have suggested a generalization that holds for any society that achieves a sufficient degree of development and maturity. What Jaspers postulated for agricultural civilizations, and understood to be a turning point for the world entire, I believe holds for most civilizations, and that each stage in the overall development of civilization may have such a turning point.
Also, the history of human civilization reveals an acceleration. Nomadic hunter-gatherer society required hundreds of thousands of years before it matured into a condition capable of producing the great cave paintings of the upper Paleolithic (which I call the Axialization of the Nomadic Paradigm). The agricultural civilizations that superseded Paleolithic societies with the Neolithic Agricultural Revolution required thousands of years to mature to the point of producing what Jaspers called an Axial Age (The Axial Age for Jaspers).
Industrial civilization has not yet produced an industrialized axialization (though we may look back someday and understand one to have been achieved in retrospect), but the early modern civilization that seemed to be producing a decisively different way of life than the medieval period that preceded it experienced a catastrophic preemption: it did not come to fulfillment on its own terms. In Modernism without Industrialism I argued that modern civilization was effectively overtaken by the sudden and catastrophic emergence of industrialization, which set civilization on an entirely new course.
At each stage of the development of human society the maturation of that society, measured by the ability of that society to give a coherent account of itself in a comprehensive cosmological context (also known as mythology), has come sooner than the last, with the abortive civilization of modernism, Enlightenment, and the scientific revolution derailed and suddenly superseded by a novel and unprecedented development from within civilization. Modernism was preempted by accelerating events, and, specifically, by accelerating technology. It is possible that there are other forms of accelerating development that could derail or preempt that course of development that at present appears to be the natural teleology of industrial-technological civilization.
The Dystopian Hypothesis
Because the most obvious forms of the preemption hypothesis, in terms of the prospects for civilization most widely discussed today, would include the technological singularity, transhumanism, and The Transcension Hypothesis, and also because of the human ability (probably reinforced by the survival value of optimism) to look on the bright side of things, we may lose sight of equally obvious sub-optimal forms of preemption. Sub-optimal forms of civilizational preemption, in which civilization does not pass on to developments of greater complexity more technically difficult achievement, could be separately identified as the dystopian hypothesis.
In Miserable and Unhappy Civilizations I suggested that the distinction Freud made between neurotic misery and ordinary human unhappiness can be extended to encompass a distinction between a civilization in the grip of neurotic misery as distinct from a civilization experiencing ordinary civilizational unhappiness. I cited the example of the religious wars of early modern Europe as an example of civilization experiencing neurotic misery. It is possible that neurotic misery at the civilizational level could be perpetuated across time and space so that neurotic misery became the enduring condition of civilization. (This might be considered an instance of what Nick Bostrum called “flawed realization” in his analysis of existential risk.)
It would likely be the case that neurotically miserable civilization — which we might also call dystopian civilization — would be incapable of anything beyond perpetuating its miserable existence from one day to the next. The dystopian hypothesis could be assimilated to solution no. 23 in Webb’s book, “They have no desire to communicate,” but there many be many reasons that a civilization lacks a desire to communicate over interstellar distances with other civilizations, so I think that the dystopian lack of motivation deserves its own category as a response to the Fermi paradox.
Whether or not chronic and severe dystopianism could be considered a post-civilization institution and therefore a preemption of industrial-technological civilization is open to question. I will think about this.
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18 December 2011
Aristotle is famous for saying, among other things, that excellence is not an act, but a habit. The Greek word for excellence — areté, ἀρετή — is also translated as “virtue,” so the same Aristotelian quote is sometimes rendered virtue is not an act but a habit. These variant translations are justified, as they point to the close interrelationship between excellence and virtue in Aristotle.
Aristotle was a common sense philosopher before there was any such thing as common sense philosophy, and his moral psychology is equally commonsensical. Aristotle maintained that people enjoy doing the things that they are good at doing, and so people make an effort at getting good at doing certain things so that they can enjoy these activities all the more. I think that this is largely correct.
It would not be overstating the case to say that many individuals actively seek out opportunities for cultivating excellence. These opportunities can vary dramatically from place to place and time to time. Certain socio-economic systems will be richer in opportunities for certain kinds of excellence, so we find excellence unevenly distributed across history and geography.
If Aristotle’s moral psychology is more or less correct, it would then stand to reason that we will find excellence-seeking individuals at all times and places, so that these efforts toward excellence are likely to be directed into whatever channels happen to be available.
Today the news has brought word that Kim Jong-il, the North Korean despot, has died. I have written repeatedly about Kim Jong-il and North Korea, as these provide a radical example of state failure. Even while North Korea is the paradigm case of a failed state, there is a sense in which its rulers have chosen to rule over just such a failed state, though we usually think of failure as an accident. This is failure by design. But what then is the design? In a word: the military.
While the Kim family has been the despotic focus of attention in North Korea, the country is really ruled by the military. And while it is often reported that North Korea maintains an enormous military of a million men under arms, it is rarely reported how the North Korean military is not merely large, but is also an innovative, aggressive, and essentially meritocratic institution (assuming you also know to say the right thing and not say the wrong thing).
Sometimes dictators will create a bloated military of conscripts for bragging rights, but this does not accurately describe the North Korean military. People who study such things say that the North Korean military is an impressive institution in terms of its discipline, organization, and training. While they cannot count on having the most advanced technology and the most sophisticated weapons systems, they can train relentlessly and by all reports they do.
Knowing this to be the case, I would guess that one of the few opportunities to pursue excellence in North Korea would be by way of entering the military. Another opportunity would be to be a gymnast, dancer, or other performer in the enormous spectacles that were staged for the “Dear Leader.” Those are narrow options, but in the nation-state in which saying the wrong thing can mean a life sentence to the gulag for you and your family, it is best not to even try to pursue excellence in literature, art, entertainment, or anything else that might “send a message” and therefore be considered dangerous or subversive. Sports are relatively safe, and we all recall how the Eastern Bloc Warsaw Pact nation-states cultivated extensive sports training programs during the Cold War.
If the only (safe) outlets for a people’s pursuit of excellence is the military or sports, this is going to profoundly affect the cultural life of a country. It is also going to channel a lot of very clever and innovative people into the military who would not, under other circumstances, choose a career in the military. The talents of these intelligent men and women, indirectly conscripted through the suppression of other activities by which they might have pursued other forms of excellence, are in North Korea at the service of the military and therefore at the service of the state. These are the people who rule North Korea.
How will the military rule North Korea after the death of Kim Jong-il? Will they allow his inexperienced son, Kim Jong-un, to assume his place as a figurehead, and continue to rule the country to the greater glory of the DPRK military at the expense of all else? Some self-perpetuating institutions do exactly this; they have an overriding incentive to maintain the system that has put them in control and which disproportionately benefits them at the expense of their countrymen.
There are problems, however. A military establishment of more than a million soldiers is a sufficiently large organization for factions to emerge, and for those factions to be quite large. If, say, each son of Kim Jong-il could command the loyalty of a third of the army, each would still have military forces far larger than those of most nation-states. Internal power struggles have almost certainly already begun, and the issue of these struggles is not likely to be decided for months, if not years. Kim Jong-un is still quite young, and much could happen before he has any opportunity to exercise control (or for others to exercise control in his name).
Internal power struggles in the DPRK could be an opportunity for outside powers to intervene, or to use whatever levers they have available to influence the outcome in North Korea. But China and South Korea, the geographical neighbors, will be most concerned about stability and avoiding a flood of refugees should a crisis emerge. Furthermore, China will not want to take any action that might be interpreted as condoning either interference in internal affairs or questioning the legitimacy of a one-party state, since either action could be turned around and used against China in turn.
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17 December 2010
I have never thought of myself as a person who takes risks. On the contrary, I view my actions as cautious and calculated, since I am not likely to engage in some activity until I judge it to be a sure thing. But others see things otherwise. Some years ago I was talking to a financial adviser and I was taken up short when he characterized me as a risk taker. I think this was primarily because of my attitude to insurance. I have a personal distaste for insurance, probably from a mixture of instinct and experience. This may sound odd, but it is accurate.
As I see it, the attempt to manage risk is illusory. I act upon this view by minimizing my insurance coverage. (This is what struck my financial adviser as risky.) About the only regrets I have in life are when I paid for an insurance policy when I didn’t strictly have to do so under legal compulsion. It felt a lot like flushing money down a toilet, and this latter exercise would probably be more fun than sending a check to an insurance company. Buying insurance does not give me peace of mind, it only makes me angry.
One of the reasons I view the attempt to manage risk as illusory is because of my personal experiences with insurance policies that do not pay when you most need them. There are countless stories in the news, some of them tragic, about people who thought they were covered for some eventuality but found out in their hour of need that they were not. Whether it is someone who lost their home to a flood and later found a waiver in the homeowner’s policy for flood damage, or someone who cannot convince their HMO to pay for some particular medical procedure and who is dying as a result, there is almost always something in the fine print that makes it possible for an insurance company to deny coverage. These episodes are not accidental. Insurance companies have many lawyers who write up policies precisely to minimize the losses of the insurance companies for whom they work, and insurance adjusters can be even more creative in their interpretation of events.
The state of Oregon requires that Oregon residents maintain insurance on their motor vehicles. I always buy the legal minimum, which means that I get liability insurance, but no collision or comprehensive coverage. I have no life insurance policy, but I have no wife or children so the only beneficiaries could be my sisters or parents or a charity. Also, life insurance feels like blood money to me. I wouldn’t want to receive a payoff, and I wouldn’t want someone to profit from my demise. I think it is a good policy to be worth more alive than dead; it gives others an incentive to keep you around. The moorage where I live requires residents to have fire insurance, and this seems reasonable to me as a fire could easily spread, so again I get the minimum coverage required, which is to say that I have the structure covered but not the contents. How could one replace the contents of one’s home? If you have picked up irreplaceable items throughout your life, and received gifts from family and friends, your possessions are more the widgets that can be replaced. Being paid for their loss would, to me, feel like getting blood money for objects.
I also have no health insurance. That’s right, I’m one of those people who make up the statistic of 47 million Americans without health insurance. And I am fully prepared to accept the consequences of my actions (and inaction). I have emergency instructions in my mobile phone that state that I have no health insurance and that no special measures are to be taken to preserve my life, because I can’t afford them. I suppose if I were taken to an emergency room contrary to my wishes, and I died despite any efforts made to save my life, that a diligent collector for the hospital might come after my assets to pay the bill, so they might eventually get their pound of flesh.
What would I do if I were diagnosed with a serious condition that required major surgery or some expensive treatment like chemotherapy? One thing I can tell you is what I would not do, and what I would definitely not do is to seek treatment in the US. Policies and litigation have so distorted the market for health care that no ordinary working class person in the US can afford to be sick, but this is not the case everywhere in the world. Since I know people all over the world, if I required major medical treatment, I would send out e-mails to friends in other countries and ask them to find a doctor who speaks English and to get an estimate for the procedure needed. I would without hesitation seek treatment in Korea or Peru, Indonesia or Argentina, before I would seek treatment in the US.
Perhaps you think this is odd, and perhaps even odd enough to be pathological. I have had many disagreements with others over insurance. None of the arguments that have been advanced to try to convince me of the folly of my position have changed my mind; they certainly have not changed how I feel about insurance. Then could we at least, at the very minimum, agree that it is rational to minimize risk, and to not take any unnecessary risks? Alas, we cannot even agree on the rational minimization of risk. As I see it, risk (like pain) is a good thing that forces us to think through our course of action carefully, so that the minimization of risk by way of insurance is a moral hazard that lures people unnecessarily into braving risks they would otherwise avoid.
Allow me to relate a little story about the philosophical dimensions of risk. Contemporary legal and political philosophy is dominated (utterly dominated) by the work of John Rawls. Rawls’ claim to fame is a thought experiment. According to Rawls, a just society is a society that would be chosen behind a “veil of ignorance,” that is to say, if we would choose a social system not knowing what place we would be born into it, then that is a just social system (by our lights). The assumption here is that, if you don’t know the position in which you will be born into in a society, you will choose a thoroughly egalitarian system so that the birth lottery does not relegate you to a irremediably marginal role. It has been observed that this thought experiment and its presumed outcome assumes that the individual choosing a society from behind a veil of ignorance is risk averse. Of course, not everyone is risk averse, and there may be individuals — perhaps many of them — who might prefer inequitable social arrangements and be willing to take the risk that they will either end up in a privileged position or that they can manipulate the social system in question sufficiently to their benefit that the initial inequity will not be a liability that they cannot overcome.
I don’t take the Rawlsian thought experiment too seriously, partly because almost no one believes in their own impoverishment and immiserization before they have hit rock bottom, and partly because the Rawlsian emphasis upon fairness seems so vulgar that it might have been explicitly conceived in contradistinction to the Aristotelian conception of areté. How would Aristotle’s Great Souled Man judge a society from behind a veil of ignorance? He would value most highly that society in which the highest virtues would attain their highest development. This would not necessarily be an egalitarian society, and it would not be a society without risk.
Great accomplishments, great deeds, and great undertakings are all won in the face of adversity and risk. To eliminate risk from the world would be to eliminate the possibility of greatness and excellence (areté); to minimize risk would be to minimize the possibility of greatness and excellence (areté). There is a sense, then — an Aristotelian sense — in which virtue is predicated upon risk. Even the great works of art, literature, poetry, science, mathematics, and philosophy all enjoin risk and entail risk. It is a risk to entertain a radical new idea or to present a radically new vision to the world. One risks one’s career, one’s reputation, one’s ability to make a living, one’s friends — in a word, one risks everything in attempting any authentic innovation. And yet almost everything of value in the world comes from such efforts, and from such willingness to court risk, all in the pursuit of being true to oneself.
This is perhaps a somewhat grandiose if not histrionic characterization of risk, but even if we reduce our scope and scale to the most intimate and personal perspective, risk cannot be eradicated from life. To be alive is to be at risk of dying. Whether we choose to think in terms of our legacy we leave in the world or our immediate personal circumstances, in remains true that we cannot control the world, we cannot control our circumstances, we cannot control what others say, think, do, or feel, and sometimes we cannot even control ourselves. The world is an unpredictable place, and, as I have argued many times in several posts, we ought to expect to be blindsided by history. And if we are blindsided by history to our misfortune, we ought also expect that our insurance policy is not going to cover the loss or make us whole again.
I hope that this personal view of risk management has managed to convince you of one thing. I do not expect to have convinced you that the attempt to manage risk is illusory, but I may have been able to successfully make the point that an individual’s attitude to risk management is deeply embedded in the way that a given individual sees the world. A conception of risk management is predicated upon a particular Weltanschauung. Two individuals with distinct outlooks on life are also likely to have distinct ideas on how to best manage risk — or, as the case may be, to live with risk and not attempt to wish it away. The point is that there is not a single rational and pragmatic way to manage risk, but that the management of risk will be relative to the criteria of reasonableness and pragmatism that follows from a given Weltanschauung.
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Note added 03 March 2011: There was a great article in Financial Times by John Kay, Don’t blame luck when your models misfire, which includes the following:
“Like practitioners of alchemy and quack medicine, these modellers thrive on our desire to believe impossible things. But the search for objective means of controlling risks that can reliably be monitored externally is as fruitless as the quest to turn base metal into gold. Like the alchemists and the quacks, the risk modellers have created an industry whose intense technical debates with each other lead gullible outsiders to believe that this is a profession with genuine expertise.”
What can I say other than that I agree? This isn’t quite as blunt as my contention that, “the attempt to manage risk is illusory,” but it is not far from it. If the technical debates of risk modellers constitute a profession without genuine expertise, as implied by Kay, it is high time that we declared our independence from technocrats who would presume to control us all for our own good.
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3 August 2010
Aristotle claimed that mathematics has no ethos (Metaphysics, Book III, Chap. 2, 996a). Aristotle, of course, was more interested in the empirical sciences than his master Plato, whose Academy presumed and demanded familiarity with geometry — and we must understand that for the ancients, long before the emergence of analytical geometry in the work of Descartes (allowing us to formulate geometry algebraically, hence arithmetically), that geometry was always axiomatic thought, rigorously conceived in terms of demonstration. For the Greeks, this was the model and exemplar of all rigorous thought, and for Aristotle this was a mode of thought that lacked an ethos.
In this, I think, Aristotle was wrong, and I think that Plato would have agree on this point. But the intuition behind Aristotle’s denial of a mathematical ethos is, I think, a common one. And indeed it has even become a rhetorical trope to appeal to rigorous mathematics as an objective standard free from axiological accretions.
Our human, all-too-human faculties conspire to confuse us, to addle our wits, when we begin talking about morality, so that the purity and rigor of mathematical and logical thought seem to be called into question if we acknowledge that there is an ethos of formal thought. We easily confuse ourselves with religious, mystical, and ethical ideas, and since the great monument of mathematical thought has been mostly free of this particular species of confusion, to deny an ethos of formal thought can be understood as a strategy to protect and defend of the honor of mathematics and logic by preserving it from the morass that envelops most human attempts to think clearly, however heroically undertaken.
Kant famously stated in the Critique of Pure Reason that, “I have found it necessary to deny knowledge in order to make room for faith.” I should rather limit faith to make room for rigorous reasoning. Indeed, I would squeeze out faith altogether, and find myself among the most rigorous of the intuitionists, one of whom has said: “The aim of this program is to banish faith from the foundations of mathematics, faith being defined as any violation of the law of sufficient reason (for sentences). This law is defined as the identification (by definition) of truth with the result of a (present or feasible) proof…”
Though here again, with intuitionism (and various species of constructivism generally), we have rigor, denial, asceticism — intuitionistic logic is no joyful wisdom. (An ethos of formal thought need not be an inspiring and edifying ethos.) It is logic with a frown, disapproving, censorious — a bitter medicine justified only because it offers hope of curing the disease of contradiction, contracted when mathematics was shown to be reducible to set theory, and the latter shown to be infected with paradox (as if the infinite hubris of set theory were not alone enough for its condemnation). Is the intuitionist’s hope justified? In so far as it is hope — i.e., hope and not proof, the expectation that things will go better for the intuitionistic program than for logicism — it is not justified.
Dummett has said that intuitionistic logic and mathematics are to wear their justification on their face:
“From an intuitionistic standpoint, mathematics, when correctly carried on, would not need any justification from without, a buttress from the side or a foundation from below: it would wear its own justification on its face.”
Dummett, Michael, Elements of Intuitionism, Oxford University Press, 1977, p. 2
The hope that contradiction will not arise from intuitionistic methods clearly is no such evident justification. As a matter of fact, empirically and historically verifiable, we know that intuitionism has resulted in no contradictions, but this could change tomorrow. Intuitionism stands in need of a consistency proof even more than formalism. There is, in its approach, a faith invested in the assumption that infinite totalities caused the paradoxes, and once we have disallowed reference to them all will go well. This is a perfectly reasonable assumption, but one, in so far as it is an article of faith, which is at variance with the aims and methods of intuitionism.
And what is a feasible proof, which our ultra-intuitionist would allow? Have we not with “feasible proof” abandoned proof altogether in favor of probability? Again, we will allow them their inconsistencies and meet them on their own ground. But we shall note that the critics of the logicist paradigm fix their gaze only upon consistency, and in so doing reveal again their stingy, miserly conception of the whole enterprise.
“The Ultra-Intuitionistic Criticism and the Antitraditional program for the foundations of Mathematics” by A. S. Yessenin-Volpin (who was arguing for intellectual freedom in the Soviet Union at the same time that he was arguing for a censorious conception of reason), in Intuitionism and Proof Theory, quoted briefly above, is worth quoting more fully:
The aim of this program is to banish faith from the foundations of mathematics, faith being defined as any violation of the law of sufficient reason (for sentences). This law is defined as the identification (by definition) of truth with the result of a (present or feasible) proof, in spite of the traditional incompleteness theorem, which deals only with a very narrow kinds [sic] of proofs (which I call ‘formal proofs’). I define proof as any fair way of making a sentence incontestable. Of course this explication is related to ethics — the notion fair means ‘free from any coercion or fraud’ — and to the theory of disputes, indicating the cases in which a sentence is to be considered as incontestable. Of course the methods of traditional mathematical logic are not sufficient for this program: and I have to enlarge the domain of means explicitly studied in logic. I shall work in a domain wherein are to be found only special notions of proof satisfying the mentioned explication. In this domain I shall allow as a means of proof only the strict following of definitions and other rules or principles of using signs.
Intuitionism and proof theory: Proceedings of the summer conference at Buffalo, N.Y., 1968, p. 3
What is coercion or fraud in argumentation? We find something of an illustration of this in Gregory Vlastos’ portrait of Socrates: “Plato’s Socrates is not persuasive at all. He wins every argument, but never manages to win over an opponent. He has to fight every inch of the way for any assent he gets, and gets it, so to speak, at the point of a dagger.” (The Philosophy of Socrates, Ed. by Gregory Vlastos, page 2)
What appeal to logic does not invoke logical compulsion? Is logical compulsion unique to non-constructive mathematical thought? Is there not an element of logical compulsion present also in constructivism? Might it not indeed be the more coercive form of compulsion that is recognized alike by constructivists and non-constructivists?
The breadth of the conception outlined by Yessenin-Volpin is impressive, but the essay goes on to stipulate the harshest measures of finitude and constructivism. One can imagine these Goldwaterite logicians proclaiming: “Extremism in the defense of intuition is no vice, and moderation in the pursuit of constructivist rigor is no virtue.” Brouwer, the spiritual father of intuitionism, even appeals to the Law-and-Order mentality, saying that a criminal who has not been caught is still a criminal. Logic and mathematics, it seems, must be brought into line. They verge on criminality, deviancy, perversion.
The same righteous, narrow, anathamatizing attitude is at work among the defenders of what is sometimes called the “first-order thesis” in logic. Quine sees a similar deviancy in modal logic (which can be shown to be equivalent to intuitionistic logic), which he says was “conceived in sin” — the sin of confusing use and mention. These accusations do little to help us understand logic. We would do well to adopt Foucault’s attitude on these matters: “leave it to our bureaucrats and our police to see that our papers are in order. At least spare us their morality when we write.” (The Archaeology of Knowledge, p. 17)
The philosophical legacy of intuitionism has been profound yet mixed; its influence has been deeply ambiguous. (Far from the intuitive certainty, immediacy, clarity, and evident justification that it would like to propagate.) There is in inuitionism much in harmony with contemporary philosophy of mathematics and its emphasis on practices, the demand for finite constructivity, its anti-philosophical tenor, its opposition to platonism. The Father of Intuitionism, Brouwer, was, like many philosophers, anti-philosophical even while propounding a philosophy. No doubt his quasi-Kantianism put his conscience at rest in the Kantian tradition of decrying metaphysics while practicing it, and his mysticism gave a comforting halo (which softens and obscures the hard edges of intuitionist rigor in proof theory) to mathematics which some have found in the excesses of platonism.
In any case, few followers of Brouwer followed him in his Kantianism and mysticism. The constructivist tradition which grew from intuitionism has proved to be philosophically rich, begetting a variety of constructive techniques and as many justifications for them. Even if few mathematicians actually do intuitionistic mathematics, controversies over the significance of constructivism have a great deal of currency in philosophy. And Dummett is explicit about the place of philosophy in intuitionistic logic and mathematics.
Intuitionism and constructivism command our respect in the same way that Euclidean geometry commanded the respect of the ancients: we might not demand that all reasoning conform to this model, but it is valuable to know that rigorous standards can be formulated, as an ideal to which we might aspire if nothing else. And and ideal of reason is itself an ethos of reason, a norm to which formal thought aspires, and which it hopes to approximate even if it cannot always live up the the most exacting standard that it can recognize for itself.
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19 November 2009
Yesterday’s meditation upon The Fungibility of the Biome led me to think in very general terms about scientific knowledge. It is one of the remarkable things about contemporary natural science — following rigorously, as it does, the methodological naturalism toward which it has struggled over the past several hundred years since the advent of the Scientific Revolution — that the more complex and sophisticated it becomes, the more closely science is in touch with the details of ordinary experience. This is almost precisely the opposite of what one finds with most intellectual traditions. As an intellectual tradition develops it often becomes involuted and self-involved, veering off in oddball directions and taking unpredictable tangents that take us away from the world and our immediate experience of it, not closer to it. The history of human reason is mostly a history of wild goose chases.
In fact, Western science began exactly in this way, and in so doing gave us the most obvious example of an involuted, self-referential intellectual tradition that was more interested in building on a particular cluster of ideas than of learning about the world. This we now know as scholasticism, when the clerics and monks of medieval Europe read and re-read, studied and commented upon, the works of Aristotle. For a thousand years, Aristotle was synonymous with natural science.
Aristotle is not to be held responsible for the non-science that was done in his name and, to add insult to injury, was called science. If Aristotle had been treated as a point of departure rather than as dogma to be defended and upheld as doctrine, medieval history would have been very different. But at that time Western history was not yet prepared for the wrenching change that science, when properly pursued, forces upon us, both in terms of our understanding of the world and the technology it makes possible (and the industry made possible in turn by technology).
Science forces wrenching change upon us because it plays havoc with some of the more absurd notions that we have inherited from our earlier, pre-scientific history. Pre-scientific beliefs suffer catastrophic failure when confronted with their scientific alternatives, however gently the science is presented in the attempt to spare the feelings of those still wedded to the beliefs of the past.
Once we get past our inherited absurdities, as I implied above, we can see the world for what it is, and science puts us always more closely in touch with what the world it is. Allow me to mention two examples of things that I have recently learned:
Example 1) We know now that not only does the earth circle the sun, and the sun spins with the Milky Way, but we know that this circling and spinning is irregular and imperfect. The earth wobbles in its orbit, and in fact the sun bobs up and down in the plane of the Milky Way as the galaxy spins. This wobbling and bobbing has consequences for life on earth because it changes the climate, sometimes predictably and sometimes unpredictably. But regularity is at least partly a function of the length of time we consider. The impact of extraterrestrial objects on the earth seems like a paradigmatic instance of catastrophism, and the asteroid impact that likely contributed to the demise of the dinosaurs is thought of as a catastrophic punctuation in the history of life, but we now also know that the earth is subject to periods of greater bombardment by extraterrestrial bodies when it is passing through the galactic plane. Viewed from a perspective of cosmological time, asteroid impacts and regular and statistically predictable. And it happens that about 65 million years ago we were passing through the galactic plane and we caught a collision as a result. All of this makes eminently good sense. Matter is present at greater density in the galactic plane, so we are far more likely to experience collisions at this time. All of this accords with ordinary experience.
Example 2) We have had several decades to get used to the idea that the continents and oceans of the earth are not static and unchanging, but dynamic and dramatically different over time. A great many things that remain consistent during the course of one human lifetime have been mistakenly thought to be eternal and unchanging. Now we know that the earth changes and in fact the whole cosmos changes. Even Einstein had to correct himself on this account. His first formulation of general relativity included the cosmological constant in order to maintain the cosmos according to its presently visible structure. Now cosmological evolution is recognized and we detail the lives of stars as carefully as we detail the natural history of a species. Now that we know something of the natural history of our planet, and we know that it changes, we find that it changes according to our ordinary experience. In the midst of an ice age, when much of the world’s water is frozen as ice and is burdening the continental plates as ice, it turns out that the weight of the ice forces the continents lower as they float in the magma beneath them. During the interglacial periods, when much or most of the ice melts, unburdened of the weight the continents bob up again and rise relative to the oceanic plates that have not been been weighted down with ice. And, in fact, this is how things behave in our ordinary experience. It is perhaps also possible (though I don’t know if this is the case) that the weight of ice, melted and now run into the oceans, becomes additional water weight pressing down on the oceanic plates, which could sink a little as a result.
Last night I was reading A Historical Introduction to the Philosophy of Science by John Losee (an excellent book, by the way, that I heartily recommend) and happened across this quote from Larry Laudan (p. 213):
…the degree of adequacy of any theory of scientific appraisal is proportional to how many of the [preferred intuitions] it can do justice to. The more of our deep intuitions a model of rationality can reconstruct, the more confident we will be that it is a sound explication of what we mean by ‘rationality’.
Contemporary Anglo-American analytical philosophers seem to love to employ the locution “deep intuitions” and similar formulations in the way that a few years ago (or a few decades ago) phenomenologists never tired of writing about the “richness of experience.” Certainly experience is rich, and certainly there are deep intuitions, but to have to call attention to either by way of awkward locutions like these points to a weakness in formulating exactly what it is that is rich about experience, and exactly what it is that is deep about a deep intuition.
And this, of course, is the whole problem in a nutshell: what exactly is a deep intuition? What intuitions ought to be considered to be preferred intuitions? I suggest that our preferred intuitions ought to be those most common and ordinary intuitions that we derive from our common and ordinary experience, things like the fact that floating bodies, when weighted down, float a little lower in the water, or whatever medium in which they happen to float. It is in this spirit that we recall the words that Robert Green Ingersoll attributed to Ferdinand Magellan:
“The church says the earth is flat, but I know that it is round, for I have seen the shadow on the moon, and I have more faith in a shadow than in the church”
The quote bears exposition. Almost certainly Magellan never said it, or even anything like it. Nevertheless, we ought to be skeptical for reasons other than those cited by the most familiar skeptics, who like to point out that the church never argued for the flatness of the earth. We ought to be skeptical because Magellan was a deeply pious man, who lost his life before the completion of his circumnavigation by his crew because Magellan was so intent upon the conversion to Catholicism of the many peoples he encountered. Eventually he encountered peoples who did not want to be converted, and they eventually took up arms and killed him in an entirely unnecessary engagement. But what remains interesting in the quote, and its implied reference to Galileo’s early observations of the moon, is not so much about flatness as about perfection. Aristotle in particular, and ancient Greek philosophy in general, held that the heavens were a realm of perfection in which all bodies were perfectly spherical and moved in perfectly circular motions through the sky. We now know this to be false, and Galileo was among the first to graphically demonstrate this with his sketches of superlunary mountains.
What does the word “superlunary” refer to? It is a term that derives from pre-Copernican (or, if you will, Ptolemaic) astronomy. When it was believed that the earth was the center of the universe, the closest extraterrestrial body was believed to be the moon (this happened to be correct, even if much in Ptolemaic astronomy was not correct). Everything below the moon, i.e., everything sublunary, was believed to be tainted and imperfect, contaminated with the dirt of lowly things and the stain of Original Sin, while everything above the moon, i.e., everything superlunary, including all other known extraterrestrial bodies, were believed to be free of this taint and therefore to be perfect, therefore unblemished. Thus it was deeply radical to observe an “imperfection” on the supposedly perfect spheres beyond the earth, as it was equally radical to discover “new” extraterrestrial bodies that had never been seen before, like the moons of Jupiter.
Both of these heresies point to our previous tendency to attribute an eternal and unchanging status to things beyond the earth. It was believed impossible to discover “new” extraterrestrial bodies because the heavens, after all, were complete, perfect, and unchanging. For the same reason, one should not be able to view anything as irregular as mountains or shadows on extraterrestrial bodies. Once we get beyond the absurd postulate of extraterrestrial perfection, we can see the world with our own eyes, and for what it is. And when we begin to do so, we do not negate the properties of perfection once attributed to the superlunary world as much as we find them to be simply irrelevant. The heavens, like the earth, are neither perfect nor imperfect. They simply are, and they are what they are. To attribute evaluative or normative content or significance to them, such as believing in their perfection, is only to send us off on one of those oddball directions or unpredictable tangents that I mentioned in the first paragraph.
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