13 September 2011
One of the most memorable and enduring aspects of Wittgenstein’s later work is his conception of family resemblance. Wittgenstein in his Philosophical Investigations formulates an essentially anti-essentialist position, and his account of family resemblances is an attempt to state how things resemble each other without sharing some single “essence.” He wanted to get away from the idea there there must be something in common, and to this end he urged his readers to look for themselves and see if there is anything in common — say, for example, among all games.
I have been thinking about family resemblances in Wittgenstein because I mention the idea in passing in my paper, The Moral Imperative of Human Spaceflight, which I am to present at the upcoming 100 Year Starship Symposium. (I hope you’ll show up to be in my cheering section.)
Wittgenstein described family resemblances as, “…a complicated net of similarities which overlap and intersect.” This translation is due to Walter Kaufmann (Critique of Religion and Philosophy, Princeton: Princeton University Press, 1978, p. 55), which is a rather more felicitous rendering than the familiar Anscombe translation: “a complicated network of similarities overlapping and criss-crossing,” (Ludwig Wittgenstein, Philosophical Investigations, The German Text, with a Revised English Translation, Third Edition, Malden, Oxford, and Victoria: Blackwell Publishing, 2003, section 66, p. 27e).
When I was thinking about this use of “overlapping” (“übergreifen” in the original German) I happened to watch a video by Richard Dawkins, and I thought about Dawkins’ criticism of Gould’s exposition of “non-overlapping magisteria” or NOMA for short. S. J. Gould wrote an essay on the topic which is fairly well know. Here are a few quotes taken from it:
“…each subject has a legitimate magisterium, or domain of teaching authority—and these magisteria do not overlap (the principle that I would like to designate as NOMA, or ‘nonoverlapping magisteria’).”
“The net of science covers the empirical universe: what is it made of (fact) and why does it work this way (theory). The net of religion extends over questions of moral meaning and value. These two magisteria do not overlap, nor do they encompass all inquiry (consider, for starters, the magisterium of art and the meaning of beauty). To cite the arch cliches, we get the age of rocks, and religion retains the rock of ages; we study how the heavens go, and they determine how to go to heaven.”
“This resolution might remain all neat and clean if the nonoverlapping magisteria (NOMA) of science and religion were separated by an extensive no man’s land. But, in fact, the two magisteria bump right up against each other, interdigitating in wondrously complex ways along their joint border. Many of our deepest questions call upon aspects of both for different parts of a full answer—and the sorting of legitimate domains can become quite complex and difficult. To cite just two broad questions involving both evolutionary facts and moral arguments: Since evolution made us the only earthly creatures with advanced consciousness, what responsibilities are so entailed for our relations with other species? What do our genealogical ties with other organisms imply about the meaning of human life?”
“I believe, with all my heart, in a respectful, even loving concordat between our magisteria—the NOMA solution. NOMA represents a principled position on moral and intellectua] grounds, not a mere diplomatic stance. NOMA also cuts both ways. If religion can no longer dictate the nature of factual conclusions properly under the magisterium of science, then scientists cannot claim higher insight into moral truth from any superior knowledge of the world’s empirical constitution. This mutual humility has important practical consequences in a world of such diverse passions.”
Stephen Jay Gould, “Nonoverlapping Magisteria,” Natural History 106 (March 1997): 16-22; Reprinted here with permission from Leonardo’s Mountain of Clams and the Diet of Worms, New York: Harmony Books, 1998, pp. 269-283.
Dawkins will have none of this. He devotes a section of Chapter 2 of The God delusion to criticizing the very idea of NOMA. Here is a typically Dawkinsian passage:
“The very idea is a joke. You can bet your boots that the scientific evidence, if any were to turn up, would be seized upon and trumpeted to the skies. NOMA is popular only because there is no
evidence to favour the God Hypothesis. The moment there was the smallest suggestion of any evidence in favour of religious belief,
religious apologists would lose no time in throwing NOMA out of the window. Sophisticated theologians aside (and even they are
happy to tell miracle stories to the unsophisticated in order to swell congregations), I suspect that alleged miracles provide the
strongest reason many believers have for their faith; and miracles, by definition, violate the principles of science.”
Richard Dawkins, The God Delusion, Chapter 2
Dawkins goes on for several pages in this vein, but the only reason I cite Dawkins here is that he represents the antithesis of the NOMA position outlined by Gould. What interests me in this debate between Gould and Dawkins is that the NOMA and anti-NOMA positions do not exhaustively divide the field of opinion.
In fact, however heretical to the orthodox, I think that one of the most prevalent views held today in industrialized Western nation-states is the antithesis of both Gould and Dawkins. I propose to call this position COMA, which should be understood to stand for COinciding MAgisteria.
It is difficult for me to give a good formulation of COMA, partly because the idea, while ancient, is new to me, and it is not my own position. So I have no definitive formulation. I will rely upon my reader’s sympathy and indulgence to provide what I leave out in my account of COMA.
COMA is simply this: that religion and science are simply alternative formulations of one and the same truth. The dogmatically religious insist upon putting everything in religious terms and denying the contributions of science, while the dogmatically scientific insist upon putting everything in scientific terms and denying the contributions of religion, but ultimately there is only one truth of the world, which is studied from the varying perspectives of science and religion (inter alia).
I have had many people say things like this to me personally. While I can’t cite any locus classicus, but I’m sure that someone, somewhere, has written down this obvious point of view.
I will go further, however, and state that even among NOMA, anti-NOMA, COMA, and whatever anti-COMA might be, that these positions still do not exhaust the field of opinion. What lies beyond NOMA and COMA? Wittgenstein.
Wittgenstein’s conception of family resemblances takes another step with possible magisteria, which is that step beyond either wholly overlapping (as with COMA) or being mutually exclusive (as with NOMA), such that that magisteria may intersect (which Anscombe translates as “criss-cross”). I’m sure you get the idea. Gould and Dawkins, NOMA and SOMA, present regions of thought as spatial areas (much as Frege does in his exposition of tertium non datur in the Foundations of Arithmetic). Well, concepts as we usually find them in the real world only present these kind of ideal boundaries in the abstract. In actual fact, the boundaries of a given concept interpenetrate related concepts, often to the point that it is difficult to distinguish them. This, I think — family resemblances that overlap and intersect — is the proper way to understand the relationship between religious and scientific concepts.
Though I will, again, go one step further. I mention in my “The Moral Imperative of Human Spaceflight” paper that Wittgenstein has left an item off the relationships of family resemblance: conflict. The individual variation that both lies at the basis of natural selection and which gives each of us our unique features, is that element of conflict in family resemblance, which is never total or absolute.
Despite all the talk about so-called “militant atheists” like Dawkins (and Dennett, and others), it has in fact become quite trendy to downplay the conflict between science and religion. I listened to a set of lectures from The Teaching Company, Science and Religion — a pure exemplification of the spirit of revisionist history — in which the lecturer, Professor Lawrence M. Principe, Ph.D., ridicules what he calls the “The Warfare Thesis” and attempts to show that, because many eminent scientists were in fact deeply pious and religious, there really hasn’t been any conflict between science and religion. While I enjoyed the lectures, I didn’t agree with them, and this was one of those clear-cut cases in which historical revisionism seems to be carried to its own self-fulfilling prophecy.
But this is merely an aside in the point I wish to make today, and that point is that NOMA is really not all that common a view, that COMA is probably more prevalent, but that neither NOMA or COMA sufficiently capture the relations between science and religion, which might better be described in terms of Wittgensteinian family resemblances. Not that science and religion resemble each other, but that their relations are like the relations that hold between things that do resemble each other. This is an obviously imperfect exposition. Perhaps with time I can frame my point with greater clarity.
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14 August 2011
Dated futurism is one of my guilty pleasures, and I have written about this previously in A Hundred Years of Futurism. Recently I’ve been reading a number of mid-twentieth century futurist works for some research I am doing. These are not the wide-eyed adolescent takes on the future, but intended to be sober analyses of what one book calls The Most Probable World. This is a project in the spirit of George Friedman’s The Next 100 Years, which I have discussed several times (cf. Ecological Succession in Cultural Geography).
The wide-eyed enthusiasm for possible futures is pure fun, but the serious attempts to try to understand a likely future constitute futurism of another order, and it deserves to be treated separately, if only because of the intentions of the author. While the science fiction scenarios have sometimes come closer to the truth than some overly-serious attempts to futurism (the latter at times approaching self-parody), this kind of nearly-chance correspondence bears some resemblance to the Gettier paradox, which can be intuitively understood as the fact that a non-functioning clock is precisely correct twice a day, but when a stopped clock is correct in indicating the time, it is not correct for the right reason.
Some of these “serious” (for lack of a better term) works of futurism are more sociological than futurist in character, and can only be called futurist in virtue of their discussion of present trends with a strong implication that the trend under discussion will be a central thread in the developments of the immediate future. In this sense, the sort of sober “futurist” works to which I am here referring needn’t even mention the future or prediction. The future is understood to be embodied in the pregnant present, if only we can recognize the inchoate future in embryo.
I would like to suggest that these works of sober futurism are distinct from works of enthusiasm because they are based on a method, however imperfectly put into practice, and this is the method of the historical a priori imagination. In several previous posts I have had occasion to refer to R. G. Collingwood’s conception of the historical a priori imagination. This is given in the Epilogomena to his The Idea of History, as follows:
“I have already remarked that, in addition to selecting from among his authorities’ statements those which he regards as important, the historian must in two ways go beyond what his authorities tell him. One is the critical way, and this is what Bradley has attempted to analyse. The other is the constructive way. Of this he has said nothing, and to this I now propose to return. I described constructive history as interpolating, between the statements borrowed from our authorities, other statements implied by them. Thus our authorities tell us that on one day Caesar was in Rome and on a later day in Gaul ; they tell us nothing about his journey from one place to the other, but we interpolate this with a perfectly good conscience.”
“This act of interpolation has two significant characteristics. First, it is in no way arbitrary or merely fanciful: it is necessary or, in Kantian language, a priori. If we filled up the narrative of Caesar’s doings with fanciful details such as the names of the persons he met on the way, and what he said to them, the construction would be arbitrary: it would be in fact the kind of construction which is done by an historical novelist. But if our construction involves nothing that is not necessitated by the evidence, it is a legitimate historical construction of a kind without which there can be no history at all.”
“Secondly, what is in this way inferred is essentially something imagined. If we look out over the sea and perceive a ship, and five minutes later look again and perceive it in a different place, we find ourselves obliged to imagine it as having occupied intermediate positions when we were not looking. That is already an example of historical thinking ; and it is not otherwise that we find ourselves obliged to imagine Caesar as having travelled from Rome to Gaul when we are told that he was in these different places at these successive times.”
“This activity, with this double character, I shall call a priori imagination; and, though I shall have more to say of it hereafter, for the present I shall be content to remark that, however unconscious we may be of its operation, it is this activity which, bridging the gaps between what our authorities tell us, gives the historical narrative or description its continuity. That the historian must use his imagination is a commonplace; to quote Macaulay’s Essay on History, ‘a perfect historian must possess an imagination sufficiently powerful to make his narrative affecting and picturesque’; but this is to underestimate the part played by the historical imagination, which is properly not ornamental but structural. Without it the historian would have no narrative to adorn. The imagination, that ‘blind but indispensable faculty’ without which, as Kant has shown, we could never perceive the world around us, is indispensable in the same way to history: it is this which, operating not capriciously as fancy but in its a priori form, does the entire work of historical construction.”
The Idea of History, Epilegomena: 2: The Historical Imagination, R. G. Collingwood, Oxford: Oxford University Press (1946)
This is more than I have quoted from Collingwood previously, because I wanted to give a better sense of his exposition. Collingwood calls his method “constructive” (in contradistinction to being “analytic”), but from a formal point of view it is the antithesis of constructive, it is a non-constructive inference of what must be, made on the basis of what is known to be the case.
But I think that Collingwood wanted to call his method “constructive” because he wanted to bring attention to the essentially conservative and traditional aspect of historical thought that he felt himself to be describing. It is one of the remarkable aspects of Collingwood’s conception that it is both metaphysically bold and methodologically conservative. As Collingwood notes, we have no scruples in deducing that when Caesar traveled from Rome to Gaul that he covered the intervening geographical region. This is, in a sense, a necessary truth, and in so far as it is a necessary truth, it is an a priori truth — furnished by imagination.
In works of history, we can make logical deductions as to what must have happened on the basis of connecting two points in history separated by the discrete period of time. In works of futurism, we cannot do this. We have only one point at which the facts are know, and this is the present. And often the present is known far more imperfectly than we would like to admit. As time passes, and we learn more and more about the past, we realize how little we knew of the present when it was in fact present.
Thus futurism labors under a double burden of knowing only half of what is needed to logically extrapolate the historical a priori imaginative narrative, as well as knowing this half highly imperfectly. Despite these substantial handicaps, we can still stand on the firm ground of methodological naturalism in making necessary deductions about the future.
We know that the future must follow from the present as the present has followed from the past. We know furthermore that there will be some future, and that it will be filled with some content, even if we don’t know what that content is. This makes futurism profoundly non-constructive.
Beyond these logical deductions from the very structure of time itself, we know empirically and inductively that things never quite develop as we expect things to develop, meaning that trends that seem to be important in the present often come to nothing, while world-historical events often seem to emerge suddenly if not violently from subtle trends in the present that are often evident only in hindsight.
A better appreciation of non-constructivism as a method of formal reasoning, as well as of subtle trends in the present that are neglected in favor of more obvious trends, would give us a better picture of the content of history that will shape the future. Both of these are highly difficult intellectual undertakings. Despite the fact (which you will know if you are familiar with the literature of formal reasoning) that constructivism is considered a marginal if not ideological mode of thought, I find it remarkable that constructivism has been given several systematic expositions, for example, in the work of Brouwer, Heyting, Dummett, and Beeson, among many others, while non-constructivism, the default form of formal reasoning that makes no special stipulations, has been given no explicit formulation. This is an ellipsis that not only is felt in formal thought, but as we can see here is also felt in historical thought.
As for the empirical and inductive dimension of futurism, a thorough and dispassionate survey of the present, undertaken in a frame of mind informed by parallels with past neglected trends, might reveal a number of threads of historical trends in the present which might hold the key to unexpected developments in the future.
While futurism remains marginal, it is not beyond hope in being given a firmer intellectual basis than it has enjoyed to date. What I have suggested above may be taken as a research program for putting futurism on a more solid footing.
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6 August 2011
The cover story on this month’s issue of Scientific American is Does the Multiverse Really Exist?, and the BBC has also had a story on the same, ‘Multiverse’ theory suggested by microwave background. Here is the opening paragraph of the Scientific American story:
“In the past decade an extraordinary claim has captivated cosmologists: that the expanding universe we see around us is not the only one; that billions of other universes are out there, too. There is not one universe—there is a multiverse. In Scientific American articles and books such as Brian Greene’s latest, The Hidden Reality, leading scientists have spoken of a super-Copernican revolution. In this view, not only is our planet one among many, but even our entire universe is insignificant on the cosmic scale of things. It is just one of countless universes, each doing its own thing”
It is typical for contemporary scientific thought to present this as a new idea, notwithstanding several thousand years of philosophical tradition investigating the infinity of worlds, as it is equally typical to cite a recent book on the topic rather than to acknowledge the theoretical underpinnings of the idea that go back to the earliest works of the Western tradition. I mentioned similar considerations not long ago in a post about Conformal Cyclic Cosmology.
The BBC story ‘Multiverse’ theory suggested by microwave background by Jason Palmer references the paper First Observational Tests of Eternal Inflation by Feeney, Johnson, Mortlock, and Peiris. Here’s the abstract of the paper:
The eternal inflation scenario predicts that our observable universe resides inside a single bubble embedded in a vast inflating multiverse. We present the first observational tests of eternal inflation, performing a search for cosmological signatures of collisions with other bubble universes in cosmic microwave background data from the WMAP satellite. We conclude that the WMAP 7-year data do not warrant augmenting ACDM with bubble collisions, constraining the average number of detectable bubble collisions on the full sky Ns < 1:6 at 68% CL. Data from the Planck satellite can be used to more definitively test the bubble collision hypothesis.
First Observational Tests of Eternal Inflation by Feeney, Johnson, Mortlock, and Peiris
This is from the second paragraph of the paper:
Eternal inflation is ubiquitous in theories with extra dimensions (string theory being the primary example) and positive vacuum energy. However, testing this scenario is extremely difficult since eternal inflation is a pre-inflationary epoch: any signals from outside of our bubble would naively appear to be stretched to unobservable super-horizon scales. While this is in general true, one prospect for probing this epoch lies in the observation of the collisions between vacuum bubbles. These collisions produce inhomogeneities in the inner-bubble cosmology, raising the possibility that their effects are imprinted in the cosmic microwave background
I find these recent developments in cosmology both welcome and troubling. It is welcome because the time in long overdue to give serious consideration to theories that do not limit the universe to that generated from the Big Bang (as cosmologists once limited the universe only to the Milky Way galaxy, and before that to our solar system), and it is troubling because the way in which these developments are presented confirms much that I have written recently about Fashionable Anti-Philosophy in science.
From the origins of the Big Bang model up until very recently, it was commonplace among scientists to assert that space and time began with the big bang, and that it was meaningless to speak of the big bang singularity as existing in space or time (this was called the “container theory” of space and time), since space and time (actually, spacetime) was generated by the big bang. To insist upon any other account marked you out as a philosopher and a fool who simply couldn’t understand the scientific concepts involved and the mathematics behind them.
Truly enough, from the point of view of observational cosmology it is meaningless to develop theories of things that can’t be observed, like the interior of singularities, what lies outside the light cone, or what happened before the big bang. But cosmology is not limited to observational cosmology, and physicists routinely theorize about things that can’t be observed, on the hope that they might someday be observed. The “standard model” of particle physics has been looking for the Higgs boson for years, and is hopeful that it will be found soon. But this is why we formulate hypotheses: so we have a research program that can focus on finding mechanisms that might explain the things that we can see.
The great scientific and mathematical revolution that supposedly made all this both possible and rational was the idea of the finite and unbounded universe that was bent around on itself, like the surface of the earth, so that even though there is no edge to the cosmos, that does not mean that it is infinite. There is no edge because there is no boundary, and there is no boundary because the universe is finite and unbounded. The elliptical geometry of Riemann, adapted by Einstein as the setting for General Relativity, gave a precise mathematical expression to this idea. But the advocates of the finite and unbounded universe carefully avoided explaining the distinction between intrinsic and extrinsic curvature, and with a little bit of ambiguity they were able to pretend that the universe was expanding into nothingness without giving an account of this nothingness.
A typical expression of this attitude, in the form of an aside, comes from J. J. Callahan, in discussing his motivation for writing his frequently cited paper, “The Curvature of Space in a Finite Universe” (Scientific American, Volume 235, Number 2, August, 1976). Callahan said the paper grew:
“…out of an attempt to explain Einstein’s concept of a finite but unbounded space to my nonscientific colleagues at Smith. They found it tough going, and some simply dismissed a finite universe as impossible, because Kant had done so when he studied the question 300 years ago.”
Apart from a misrepresentation of Kant, Callahan’s “non-scientific colleagues” are caricatured as mere simpletons who can’t hack mathematical and scientific ideas (it was “tough going” for them), and not people who had genuine intuitions of the how the universe is put together but were unable to express them with the same blinding simplicity of the big bang model producing a finite and unbounded universe.
I am not the only one to have noticed this systematic ambiguity in recent cosmology. I found this amusingly acerbic quote in The Ontology and Cosmology of Non-Euclidean Geometry:
“The closest we seem to have come to a more open consideration of these matters is when both Stephen Hawking and Karl Popper [Karl Popper, Unended Quest, Open Court, 1990; p.16] point out that Einstein, whether or not he successfully answered Kant’s Antinomy of Space, did not answer the Antinomy of Time: despite decades of everyone glorifying in the philosophical revelation of a finite but unbounded universe, they simply didn’t notice that the solution proposed for space didn’t work with time. It is to Hawking’s great philosophical credit that he faces this question squarely.”
The author here has been more charitable to Hawking than I would be, as Hawking has been prominent among those who have ridiculed what he sees as the simple-mindedness of philosophers in insisting upon answers to their questions about a universe with this geometrical structure. Morevoer, I would maintain that the “philosophical revelation of a finite but unbounded universe” doesn’t even offer a solution to the problem of space, much less time, much less spacetime.
So I am happy to see cosmologists extending their scope and trying to get outside the confines of the big bang model, but I continue to be distressed that they continue to ridicule the philosophical underpinnings of their own ideas, and that they will go through a lot of needless duplication of labor in coming up with ideas that have been worked through time and again. But, if you’re aiming at research dollars to build the latest, greatest superconducting supercollider, or the biggest and most sensitive radio telescope, it isn’t going to pull much weight with the grant writing committees or the grant granting institutions themselves to tell them you’ll be spending the next few years in a library reading old books in order to refine your concepts to the point that they might suggest a research program.
Physicists and cosmologists seem to belong to the Field of Dreams school of thought, pursuing a “if we build it, they will come” strategy in research, with “they” being discoveries, suitably celebrated in the headlines of newspapers.
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19 June 2011
A few days ago in The Truth is Out There I twice made reference to anti-philosophy among scientists. I wrote, for example, the following:
“While Ferris frequently invokes the kind of anti-philosophy that I have become accustomed to encountering in the writings of scientists, he also cites philosophers has diverse as Hegel and Wittgenstein…”
“…despite the fashionable anti-philosophy of many scientists, that often leads them to say unkind things about purely philosophical inquiry, I see the enterprises of science and philosophy as parallel undertakings…”
What do I mean by the “anti-philosophy” of many scientists? Usually, and unfortunately, it simply takes the form of ad hominem abuse of philosophers while cribbing ideas that the scientists don’t understand, and often don’t even realize that they are cribbing. I will give two examples. Here is Leonard Susskind:
“…many physicists throughout the second half of the twentieth century considered the pursuit of such a unifying theory to be worthless, fit only for crackpots and philosophers.”
Leonard Susskind, The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics, 2009
And here is Stephen Hawking:
“We have known for twenty-five years that Einstein’s general theory of relativity predicts that time must have had a beginning in a singularity fifteen billion years ago. But the philosophers have not yet caught up with the idea.”
Stephen W. Hawking, Black Holes and Baby Universes and Other Essays, 1994
It would be relatively easy to multiply quotes of this character; they are regrettably common, and one must wonder why, because philosophers do not even register on the radar of the popular mind. Why should we find denunciations of philosophers and philosophy in popularizations of science by eminent physicists? I have a hard time imagining that either Susskind or Hawking would make comments like these about, say, novelists or biologists.
I have chosen the quotes from Susskind and Hawking strategically, since each represents a different side of a long-running scientific controversy, a controversy that is related in Susskind’s book cited above. Though these two physicists found themselves on opposite sides of a scientific controversy, they apparently have common ground in their use of philosophers as straw men.
I am listening to Susskind’s book now, and while I enjoy it, I can feel the limitations that arise from anti-philosophy. What happens when you reject Western civilization’s storehouse of carefully thought out ideas? You end up citing science fiction authors to make your point, as Susskind employs Heinlein’s “grok” in the opening pages of his book. There is a vast philosophical literature on intuitive knowledge and understanding, but Susskind prefers to neglect this and employs “grok” instead. No doubt he believes this to be clearer.
There is a sense in which the Susskind reference to Heinlein is appropriate, since I recall that Heinlein himself was anti-philosophical. When I was a child I read a great many science fiction novels, a great quantity in fact, and Heinlein was among my favorites, but I can remember even then, thirty years ago and before I discovered philosophy, I wondered why Heinlein had bothered to malign philosophy. In fact, it was just this attitude, garnered from many diverse sources, that eventually made me sufficiently curious that I began to read philosophy myself. I discovered something else, something unexpected, when I began to read philosophy: I found that I was thinking for myself, and that I felt no particular obligation to follow the thoughts of others unless they gave me good reason to do so.
It has become a commonplace in contemporary intellectual discourse to note (and to bemoan the fact) that intelligent and educated people see no stigma attached to saying that they know nothing of mathematics. Even here we can cite Heinlein again: “Anyone who cannot cope with mathematics is not fully human. At best he is a tolerable subhuman who has learned to wear shoes, bathe, and not make messes in the house.” Well, it also seems to be true that many scientists not only attach no stigma to ignorance of philosophy, but many of them take a perverse pride in their science being “uncontaminated” by philosophy, not realizing that this ignorance means that they make elementary philosophical errors based on elementary philosophical presuppositions and never seem to notice or be the least bit troubled by it.
The problem is not that scientists make philosophical errors and philosophical assumptions; the problem is that they fail to acknowledge that they do so. Mathematicians make a particular effort to make their assumptions explicit. This is called axiomatization. But philosophical assumptions lie even deeper than mathematical assumptions, and are therefore all the more difficult to make explicit. An effort is required. But without the effort, we literally don’t know what we’re doing.
Louis Althusser wrote a book about the spontaneous philosophy of scientists, and I have always thought that this was a particularly apt phrase. Scientists come up with a theory on the spot, as it were, and such theories are as easily discarded. It is easy to see how this serves scientific practice. Too careful and studied a reliance on a research program dictated by a philosophical theory would probably quickly turn sterile. This does not, however, excuse either ignorance or ad hominem attacks.
Scientists are instinctive phenomenologists, in so far as they share with Husserl a desire to formulate their knowledge utterly free from presuppositions, and, at very least, free from philosophical presuppositions. But this ideal of presuppositionless knowledge is a philosophical undertaking, so that it becomes a problematic enterprise for scientists. The alternative to making one’s presuppositions explicit is to leave them implicit, and when we add anti-philosophy to implicit presuppositions we have a situation in which it becomes unacceptable to acknowledge a presupposition even if, in the back of one’s mind one begins to be dimly conscious of the fact that there is more going on in scientific experiment and theory than pure observation. Thus the scientist who denies the role of philosophy in knowledge is put in a position antithetical to that of the mathematician, being committed, as he is, to denying and obscuring his presuppositions. Thus there is a sense in which fashionable anti-philosophy is a rejection of the very idea of rigorous axiomatic thinking.
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One of the many famous aphorisms that have been plucked out of Wittgenstein’s Tractatus Logico-Philosophicus is, “The limits of my language are the limits of my world” (“Die grenzen meiner sprache sind die grenzen meiner welt” section 5.6). Like much in the Tractatus, this gnomic aphorism invites interpretation and can never be exhausted.
One way to construe this Wittgensteinism very broadly would be to think of it as the limits of my idiom are the limits of my world, with “idiom” construed broadly to include any way of talking about the world, and not merely a particular language. If you’re of a continental persuasion, you could say the limits of my discourse are the limits of my world. It amounts to pretty much the same thing.
Particular theories about the world are idioms for talking about the world, forms of discourse, if you will. Scientific theories are scientific idioms for talking about the world. Now, scientific theories often broaden our horizons and allow us to see and to understand things of which we were previously unaware. But a scientific theory, being a particular idiom as it is, may also limit us, and limit the way we see the world.
The limitations we take upon ourselves by thinking in terms of particular theories or speaking in particular ways are human limits that we have chosen for ourselves; they are not intrinsic limitations imposed upon us by the world, and this, of course, is something that Wittgenstein wanted to bring to our explicit attention.
We very frequently mistake the idioms we employ, and the particular ways in which we understand these idioms, to constitute the very fabric of the world. When in this frame of mind we make claims for our theories that are not supported by the theories themselves, but rather reflect our particular, limited understanding of very difficult matters. This has been the case with the general theory of relativity and quantum theory, both of which are very young sciences, but which now dominate physics. Because of the dominant position of these theories, and of particular interpretations of these theories, we forget how young they are, and how far we have to go in really coming to an adequate understanding of them.
Our inadequate understanding of quantum theory, in particular, has been glossed so many times by physicists seeking to give a popular account of quantum theory that one might be forgiven for supposing that quantum theory is a form of mysticism rather than of science. (For example: “For those who are not shocked when they first come across quantum theory cannot possibly have understood it.” Niels Bohr) It is inevitable that, as our understanding of the world gradually and incrementally improves, much in quantum theory that now seems inscrutable will eventually make sense to us, rather than the theory being a mere systematization of a mystery.
A recent paper in Science by Sacha Kocsis, Boris Braverman, Sylvain Ravets, Martin J. Stevens, Richard P. Mirin, L. Krister Shalm, and Aephraim M. Steinberg, Observing the Average Trajectories of Single Photons in a Two-Slit Interferometer, points to new ways of thinking and talking about quantum theory. Here is the abstract of the paper:
“A consequence of the quantum mechanical uncertainty principle is that one may not discuss the path or “trajectory” that a quantum particle takes, because any measurement of position irrevocably disturbs the momentum, and vice versa. Using weak measurements, however, it is possible to operationally define a set of trajectories for an ensemble of quantum particles. We sent single photons emitted by a quantum dot through a double-slit interferometer and reconstructed these trajectories by performing a weak measurement of the photon momentum, postselected according to the result of a strong measurement of photon position in a series of planes. The results provide an observationally grounded description of the propagation of subensembles of quantum particles in a two-slit interferometer.”
There is a good article by Jason Palmer of the BBC, Quantum mechanics rule ‘bent’ in classic experiment, about the paper and its ramifications. Palmer writes that researchers, “say the feat ‘pulls back the veil’ on quantum reality in a way that was thought to be prohibited by theory.” If one wanted to go seeking headlines, one could say something dramatic like “Scientists break the laws of quantum physics” — you get the idea.
But what has been thought to be prohibited is in large measure a limitation upon the current language of quantum theory and, to a certain extent, an artifact of particular experiments. As more sophisticated experiments are conceived and conducted, we may someday know quite a bit more about quantum theory than has been thought possible to date.
In Palmer’s BBC story there is an excellent quote from Marlan Scully of Texas A&M University:
“The trouble with quantum mechanics is that while we’ve learned to calculate the outcomes of all sorts of experiments, we’ve lost much of our ability to describe what is really happening in any natural language.”
“I think that this has really hampered our ability to make progress, to come up with new ideas and see intuitively how new systems ought to behave.”
Progress in understanding quantum theory will, as implied by Scully, ultimately take the form of being able to discuss it in natural language and to formulate the theory in an intuitively perspicuous manner. We do not yet have the language or the concepts to do this, but each advance like the recent results reported in Science bring us a little closer, chipping away at the limits of our language that currently constitute the limits on our world.
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Since writing the above I have learned that the method used in the experiment described is called “weak measurement” (as mentioned in the abstract quoted above) and has been employed in other recent experiments (as well as having been criticized quite harshly). I have written further on weak measurement in some comments on the paper Observation of a quantum Cheshire Cat in a matter-wave interferometer experiment.
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Philosophical thought is often believed to be remote from the concerns of quotidian life. One of the reasons that I created this particular forum was to attempt to show the deep and systematic way that philosophical ideas penetrate even the most mundane and ordinary concerns of our daily lives.
Personally I don’t believe that a person can get out of bed in the morning without implicitly having formulated a philosophical judgment that life is worth living and therefore there is a reason to get out of bed, and not merely to lie there and do nothing. When people do lie in their bed all day and do nothing they are diagnosed with a mental illness, because science is today the paradigm for dealing with such matters. However, we are under no obligation to participate in this paradigm, and we can recognize the possibility of an existential malaise that is the visceral corollary of a philosophical position. This is only one of many ways in which a theoretical attitude can have practical consequences.
If philosophical ideas often seem distant from ordinary concerns, philosophical argument must seem an order of magnitude further removed from life, with its remarkable subtleties and its complex details that demand our careful attention, but I want to try to show how philosophical reasoning and argumentation have a basis in matters familiar to almost everyone.
There is a passage from Carl Sagan’s book The Demon-Haunted World in which he gently makes fun of those who presume to offer up, as authoritative arguments, their gut feelings:
Often, I’m asked next, “What do you really think?”
I say, “I just told you what I really think.”
“Yes, but what’s your gut feeling?”
But I try not to think with my gut. If I’m serious about understanding the world, thinking with anything besides my brain, as tempting as that might be, is likely to get me into trouble. Really, it’s okay to reserve judgment until the evidence is in.
Carl Sagan and Ann Druyan, The Demon-Haunted World: Science as a Candle in the Dark, 1997, p. 180
While I am not without sympathy for Sagan’s point here, it strikes me as inadequate from a philosophical point of view. Sagan, whatever his reputation as a sage, was ultimately and spiritually a scientist. His thoughts are formulated like a scientist, and science-like observations (which presumably exclude gut feelings) are as crucial to science as science-like reasoning, science-like theories, and science-like predictions.
However, as philosophers we are not limited to science-like observations, any more than we are obligated to participate in the scientific paradigm of existential malaise as mental illness. In fact, as philosophers we not only have the intellectual right to pursue matters on the cusp of the ineffable, but in fact we have an intellectual duty and obligation to do so. We must go farther and test every possibility of evidence or we will fall short of full possibilities of theoretical thought.
Obviously, Sagan did not think that gut instincts constituted “evidence.” Certainly untutored instincts do not constitute scientific evidence, but they are nevertheless evidence of something, and this evidence is of the greatest philosophical interest. The point here is not whether or not our intuitions are evidence, but what the value of what evidence is, what that evidence means, and what place it ought to hold in a given body of knowledge.
There would probably be a way to formulate this in terms of Bayesianism (and hopefully some day I will take the time to work out this formulation), but I won’t pursue that at present. I will, however, pursue an alternative method to doing justice to our intuitions, instincts, and feelings.
Therefore, and without further ado, my sure-fire, quick-and-easy, step-by-step method for formulating a cogent philosophical argument merely on the basis of one’s gut instincts is as follows:
● Step 1: Review the current positions and arguments in any area of philosophy that strikes your interest.
● Step 2: Search your feelings for your visceral reactions to these ideas and arguments. (If you have no visceral reaction whatsoever to ideas, you probably aren’t cut out to be a philosopher.) You will notice that some of your visceral reactions to ideas will be sympathetic, and some will be antipathetic. That is to say, you will like some ideas, and other ideas you will dislike.
● Step 3: Turn your attention to your viscerally negative reactions to some ideas. Examine these reactions carefully. Ask yourself, “Why do I react strongly against this idea?” Inquire carefully into your intellectual likes and dislikes.
● Step 4: If you can bring your feelings to a level of explicit consciousness, you will notice that your antipathetic responses to some ideas usually follow from the fact that the ideas in question have ignored or contradicted something that you intuitively know to be the case, and perhaps also to be important. Ask yourself, “What is the intuition to which this idea has not done justice?”
● Step 5: Bring your neglected or contradicted intuition to full and explicit consciousness. Develop a theoretical exposition of this intuition (or these intuitions, if there are several) on its own terms.
● Step 6: Compare this exposition of your neglected intuition with ideas and arguments to which you felt an immediate sympathy. Does it tally with them? If yes, you can develop your exposition of your intuition in the context of known theories.
● Step 7: If your neglected idea does not tally with existing ideas with which you are sympathetic, you will need to go up to a higher level of generality to find a systematic theoretical context in which you can formulate an exposition of your intuitions.
● Step 8: If you can’t find any systematic theoretical context within which you can fit the exposition of your neglected intuition, then you will have to construct an entire metaphysics from scratch, and you’re in for a long, hard slog. Enjoy it.
● Step 9: Once you have an exposition in a fully developed metaphysical context of some gut instinct to which current philosophical ideas and arguments do not do justice, confront those ideas and arguments with your now powerfully formulated exposition of their ellipses. Wait for the sparks to fly.
● Step 10: If no sparks fly, and your powerful formulation of an ellipsis in contemporary philosophical thought falls dead-born from the press (or, rather, falls too low in Google rankings to ever be seen or read by anyone), prepare to die gracefully and await posthumous discovery and fame. For a philosopher, patience is a virtue and death is the least of considerations when it comes to the value of an idea.
So, there you have it — ten easy steps to philosophical wisdom, and a method for doing justice to matters of the intellect that the intellect sometimes neglects, to do justice to that which we know in our bones. Of course, if you know something in your bones that doesn’t mean that it’s true, only that it has a place in our thought. The next step is to determine what the proper place is in out thought for our instincts, intuitions, and feelings. That will require a further method.
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Studies in Mathematical Intuition
3. Fractal Intuitions: Benoît Mandelbrot, R.I.P.
5. Fractal Intuitions: Fractals and the Banach-Tarski Paradox
6. Fractal Intuitions: A visceral feeling for epsilon zero
8. Fractal Intuitions: A Note on Fractals and Banach-Tarski Extraction
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