Thursday


From ‘Big Bang Discovery Opens Doors to the ‘Multiverse”

The observable/observed distinction

We can make a distinction between observable universes that are, in fact, observed, and observable universes that, while observable in principle, are not actually observed in fact. Thus, the set of all observable universes may be larger than the set of all universes actually observed, just as the set of all habitable planets is almost certainly larger than the set of all planets that are actually inhabited.

There are many parallels between the observable/observed and inhabitable/inhabited distinctions, and this is because this is, in each case, a modal distinction between potentiality and actuality. For a universe to be observable is for it to be potentially an object of perception, and for a universe to be observed is for it to be actually an object of perception. If “observation” is taken to include not only perception (which might be unknowing and unreflective, i.e., not self-aware) but also conception, we can revise these formulations so that some universe is potentially or actually both an object of perception and an object of thought.

But the observable/observed and inhabitable/inhabited distinctions are even more closely related than both being particular cases of potentiality vs. actuality; an observable universe is a habitable universe, and an observed universe is an inhabited universe. The universe (or a universe), then, is a generalization of a planet, so that in studying the habitable/inhabited distinction where it concerns planets, we are studying the question of observable/observed universes in miniature.

In the case of habitability (i.e., the habitable/inhabited distinction), we know the confusion that this routinely causes. With the increasing number of announcements of exoplanet discoveries, there have been an increasing number of confused accounts which imply that a planet of the right size found within a habitable zone is not just potentially habitable (arguably this formulation is redundant, and it should be sufficient to say “habitable”), but that it is, or must be, inhabited. Exoplanet scientists and astrobiologists are not guilty of this conflation, but accounts of their work in the legacy media make this conflation with regularity.

Perhaps because we see our near neighbors Venus and Mars, both smallish rocky planets like Earth, and both more-or-less in the habitable zone, we can easily understand that a planet that has the right conditions for life does not necessarily host life: these planets are habitable but not inhabited. We can bring the habitable/inhabited distinction home and understand it in human terms, but the observable/observed distinction, especially when applied to the universe entire, is likely to elude us. Moreover, the idea of an empty universe, that is to say, an entire universe without intelligent observers (observers who can both perceive the world and form a conception of what they perceive), is likely to strike many as a bit bizarre, if not absurd.

The Anthropic Cosmological Principle

Sometimes the idea that an empty universe is absurd is made explicit, or nearly so. John Wheeler is credited with saying, “A universe without an observer is not a universe at all.” In fact, Wheeler didn’t write these exact words, but the idea is pervasively present in his exposition of the anthropic cosmological principle. To give a sense of this, here is a comment on the weak anthropic principle (WAP) from Barrow and Tipler’s classic work (with a forward provided by John Wheeler):

“According to WAP, it is possible to contemplate the existence of many possible universes, each possessing different defining parameters and properties. Observers like ourselves obviously can exist only in that subset containing universes consistent with the evolution of carbon-based life.”

The Anthropic Cosmological Principle, John D. Barrow and Frank J. Tipler, Oxford: Oxford University Press, 1986, p. 19

Three interpretations are given of the strong anthropic principle:

(A) There exists one possible Universe ‘designed’ with the goal of generating and sustaining ‘observers’.

(B) Observers are necessary to bring the Universe into being.

(C) An ensemble of other different universes is necessary for the existence of our Universe.

Ibid., p. 22

As these ideas are given an extensive exposition in the text, I will not attempt to flesh them out, but I quote them here only for purposes of exhibition. It would be a considerably involved enterprise to give an exposition of the various formulations of the weak, strong, participatory, and final anthropic principles propounded by Barrow, Tipler, and Wheeler, and then to present them in comparison and contrast with what I have written here about empty universes, but I am not going to attempt that here. Some of these ideas are consistent with a range of universes, some of them empty, and some are not.

Empty, unobserved universes and scientific realism

There can only be two senses of “observable universe” if one is willing to countenance the possibility of empty, unobserved universes, which suggests a strongly realist position, and this interpretation takes to the limit of extrapolation the idea that something exists whether or not we see it (or anyone sees it). If we assume that the back side of the head of the person we are talking to continues to exist even when we do not see it (and if there is no one else looking at it), then we are assuming some degree of realism.

In the case of the person, it could be argued that the person in question is always viscerally conscious of their bodily integrity, and on this basis the back side of their head continues to be perceived, and hence continues to exist without the posit of realism. However, this argument cannot be made with inanimate objects without positing panpsychism. We assume that the back sides of houses, the insides of closets, and the contents of empty rooms continue to exist even when we are not looking at them. I can see no reason this intuitive realism should not be scaled up to entire universes that exist without being observed. This is, at least, consistent with scientific realism, even if it is not entailed by scientific realism.

The Principle of Plenitude

This kind of distinction I am making here between observable universes and observed universes immediately puts us in mind of the principle of plenitude (on which I previously wrote in Cosmology is the Principle of Plenitude Teaching by Example and Parsimony and Plenitude in Cosmology). The most obvious interpretation of the principle of plenitude in this context is that a universe that was habitable would eventually realize the potential of this habitability and would become inhabited. Perhaps this is why some advocates of the strong anthropic principle say that a universe that does not produce observers is a “failed” universe (not the kind of claim I would ever make, but one can understand something of this by saying that such a universe has failed to realize its potential). If we acknowledge the possibility of “failed” universes in this sense, then we would have empty, uninhabited universes, only we would attach a (negative) valuation to them (and presumably we would attach a positive valuation to successful universes that realize their potential and produce observers).

There is, however, another way to interpret the principle of plenitude in this context, and that is to argue that the principle of plenitude entails the realization of every possible kind of universe, and that the existence of an empty universe without observers is a potential that will eventually be realized, if it has not already been realized. Moreover, every kind of universe that can be observed by an observer that evolves within that universe constitutes another kind of universe that could exist in which the potential of such an observer is not realized. Thus if there are a plurality of observed universes, then this interpretation of the principle of plenitude suggests that there will be a plurality of observable but unobserved universes.

The Principle of Parsimony

The principle of plenitude as applied to worlds or to universes would imply densely inhabited worlds and intensively observed universes — what Frank Drake and Dava Sobel called, “an infinitely populated universe.” The principle of parsimony (often invoked as a counter to the principle of plenitude) as applied to worlds or the universe would limit us almost in a constructivistic sense to the world we inhabit — there is at least one observable universe that is, in fact, observed — though before or after the existence of this one known instance of an observer the universe would be empty and unobserved.

The intersection of the principle of plenitude and the principle of parsimony would yield at least one such-and-such (plenitude) and at most one such-and-such (parsimony), that is to say, this intersection would yield uniqueness, one and only one such-and-such — but whether this uniqueness should apply to each and every universe, or whether the universe itself ought to be considered unique, is another question.

A final reflection

It seems to me that the idea of an uninhabited planet, that is unobserved because it it uninhabited, has become a familiar and even a conventional idea of contemporary cosmology and astrobiology — it is, I think, widely assumed that we will eventually find other life in the universe, sprung from other origin of life events, but that intelligent life, and thus an observer that knows itself to be observing, is likely to be quite rare. This consensus view — if it is a consensus — encounters problems when it is extrapolated from habitable/inhabited planets to habitable/inhabited universes. Why this idea appears to transcend science (in the narrow sense) when extrapolated to the whole of the universe I am not yet prepared to say, but I will continue to think about this.

I began this post with the intention to make a simple and straight-forward distinction between observable universes and observed universes (my first draft was only three paragraphs), but as I worked on this I got myself entangled in a number of difficult questions that ended up entailing all-too-brief discussions of difficult ideas like the principle of plenitude and the principle of parsimony. This is admittedly unsatisfying, and I know that I have not done these ideas justice, but at some point I have to bring this to a close.

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Tuesday


William of Ockham, one of the greatest philosophers of the late Middle Ages, is remembered today primarily for his formulation of the principle of parsimony, also called Ockham's razor.

William of Ockham, one of the greatest philosophers of the late Middle Ages, is remembered today primarily for his formulation of the principle of parsimony, also called Ockham’s razor.

A medieval logician in the twenty-first century

In the discussion surrounding the unusual light curve of the star KIC 8462852, Ockham’s razor has been mentioned numerous times. I have written a couple of posts on this topic, i.e., interpreting the light curve of KIC 8462852 in light of Ockham’s razor, KIC 8462852 and Parsimony and Plenitude in Cosmology.

What is Ockham’s razor exactly? Well, that is a matter of philosophical dispute (and I offer my own more precise definition below), but even if it is difficult to say that Ockham’s razor is exactly, we can say something about what it was originally. Philotheus Boehner, a noted Ockham scholar, wrote of Ockham’s razor:

“It is quite often stated by Ockham in the form: ‘Plurality is not to be posited without necessity’ (Pluralitas non est ponenda sine necessitate), and also, though seldom: ‘What can be explained by the assumption of fewer things is vainly explained by the assumption of more things’ (Frustra fit per plura quod potest fieri per pauciora). The form usually given, ‘Entities must not be multiplied without necessity’ (Entia non sunt multiplicanda sine necessitate), does not seem to have been used by Ockham.”

William of Ockham, Philosophical Writings: A Selection, translated, with an Introduction, by Philotheus Boehner, O.F.M., Indianapolis and New York: The Library of Liberal Arts, THE BOBBS-MERRILL COMPANY, INC., 1964, Introduction, p. xxi

Most references to (and even most uses of) Ockham’s razor are informal and not very precise. In Maybe It’s Time To Stop Snickering About Aliens, which I linked to in KIC 8462852 Update, Adam Frank wrote of Ockham’s razor in relation to KIC 8462852:

“…aliens are always the last hypothesis you should consider. Occam’s razor tells scientists to always go for the simplest explanation for a new phenomenon. But even as we keep Mr. Occam’s razor in mind, there is something fundamentally new happening right now that all of us, including scientists, must begin considering… the exoplanet revolution means we’re developing capacities to stare deep into the light produced by hundreds of thousands of boring, ordinary stars. And these are exactly the kind of stars where life might form on orbiting planets… So we are already going to be looking at a lot of stars to hunt for planets. And when we find those planets, we are going to look at them for basic signs that life has formed. But all that effort means we will also be looking in exactly the right places to stumble on evidence of not just life but intelligent, technology-deploying life.

Here the idea of Ockham’s razor is present, but little more than the idea. Rather than merely invoking the idea of Ockham’s razor, and merely assuming what constitutes simplicity and parsimony, if we are going to profitably employ the idea today, we need to develop it more fully in the context of contemporary scientific knowledge. In KIC 8462852 I wrote:

“One can see an emerging adaptation of Ockham’s razor, such that explanations of astrophysical phenomena are first explained by known processes of nature before they are attributed to intelligence. Intelligence, too, is a process of nature, but it seems to be rare, so one ought to exercise particular caution in employing intelligence as an explanation.”

In a recent post, Parsimony and Emergent Complexity I went a bit further and suggested that Ockham’s razor can be formulated with greater precision in terms of emergent complexity, such that no phenomenon should be explained in terms of a level of emergent complexity higher than that necessary to explain the phenomenon.

De revolutionibus orbium coelestium (On the Revolutions of the Heavenly Spheres) is the seminal work on the heliocentric theory of the Renaissance astronomer Nicolaus Copernicus (1473–1543). The book, first printed in 1543 in Nuremberg, Holy Roman Empire, offered an alternative model of the universe to Ptolemy's geocentric system, which had been widely accepted since ancient times. (Wikipedia)

De revolutionibus orbium coelestium (On the Revolutions of the Heavenly Spheres) is the seminal work on the heliocentric theory of the Renaissance astronomer Nicolaus Copernicus (1473–1543). The book, first printed in 1543 in Nuremberg, Holy Roman Empire, offered an alternative model of the universe to Ptolemy’s geocentric system, which had been widely accepted since ancient times. (Wikipedia)

De revolutionibus orbium coelestium and its textual history

Like Darwin many centuries later, Copernicus hesitated to publish his big book to explain his big idea, i.e., heliocentrism. Both men, Darwin and Copernicus, understood the impact that their ideas would have, though both probably underestimated the eventual influence of these ideas; both were to transform the world and leave as a legacy entire cosmologies. The particular details of the Copernican system are less significant than the Copernican idea, i.e., the Copernican cosmology, which, like Ockham’s razor, has gone on to a long career of continuing influence.

Darwin eventually published in his lifetime, prompted by the “Ternate essay” that Wallace sent him, but Copernicus put off publishing until the end of his life. It is said that Copernicus was shown a copy of the first edition of De revolutionibus on his deathbed (though this is probably apocryphal). Copernicus, of course, lived much closer to the medieval world than did Darwin — one could well argue that Toruń and Frombork in the fifteenth and sixteenth centuries was the medieval world — so we can readily understand Copernicus’ hesitation to publish. Darwin published in a world already transformed by industrialization, already wrenched by unprecedented social change; Copernicus eventually published in a world that, while on the brink of profound change, had not appreciably changed in a thousand years.

Copernicus’ hesitation meant that he did not directly supervise the publication of his manuscript, that he was not able to correct or revise subsequent editions (Darwin revised On the Origin of Species repeatedly for six distinct editions in his lifetime, not including translations), and that he was not able to respond to the reception of his book. All of these conditions were to prove significant in the reception and propagation of the Copernican heliocentric cosmology.

Copernicus, after long hesitation, was stimulated to pursue the publication of De revolutionibus by his contact with Georg Joachim Rheticus, who traveled to Frombork for the purpose of meeting Copernicus. Rheticus, who had great respect for Copernicus’ achievement, came from the hotbed of renaissance and Protestant scholarship that was Nuremberg. He took Copernicus’ manuscript to Nuremberg to be published by a noted scientific publisher of the day, but Rheticus did not stay to oversee the entire publication of the work. This job was handed down to Andreas Osiander, a Protestant theologian who sought to water down the potential impact of De Revolutionibus by adding a preface that suggested that Copernicus’ theory should be accepted in the spirit of an hypothesis employed for the convenience of calculation. Osiander did not sign this preface, and many readers of the book, when it eventually came out, thought that this preface was the authentic Copernican interpretation of the text.

Osiander’s preface, and Osiander’s intentions in writing the preface (and changing the title of the book) continue to be debated to the present day. This debate cannot be cleanly separated from the tumult surrounding the Protestant Reformation. Luther and the Lutherans were critical of Copernicus — they had staked the legitimacy of their movement on Biblical literalism — but one would have thought that Protestantism would have been friendly to the work of Ockham, given Ockham’s conflict with the Papacy, Ockham’s fideism, and his implicit position as a critic of Thomism. (I had intended to read up on the Protestant interpretation of Ockham prior to writing this post, but I haven’t yet gotten to this.) The parsimony of Copernicus’ formulation of cosmology, then, was a mixed message to the early scientific revolution in the context of the Protestant Reformation.

Both Rheticus and Copernicus’ friend Tiedemann Giese were indignant over the unsigned and unauthorized preface by Osiander. Rheticus, by some accounts, was furious, and felt that the book and Copernicus had been betrayed. He pursued legal action against the printer, but it is not clear that it was the printer who was at fault for the preface. While Rheticus suspected Osiander as the author of the preface, this was not confirmed until some time later, when Rheticus had moved on to other matters, so Osiander was never pursued legally over the preface.

Nicolaus Copernicus (1473–1543) -- Mikołaj Kopernik in Polish, and Nikolaus Kopernikus in German

Nicolaus Copernicus (1473–1543) — Mikołaj Kopernik in Polish, and Nikolaus Kopernikus in German

Copernicus’ Ockham

The most common reason adduced to preferring Copernican cosmology to Ptolematic cosmology is not that one is true and the other is false (though this certainly is a reason to prefer Copernicus) but rather that the Copernican cosmology is the simpler and more straight-forward explanation for the observed movements of the stars and the planets. The Ptolemaic system can predict the movements of stars, planets, and the moon (within errors of margin relevant to its time), but it does so by way of a much more complex and cumbersome method than that of Copernicus. Copernicus was radical in the disestablishment of traditional cosmological thought, but once beyond that first radical step of displacing the Earth of the center of the universe (a process we continue to iterate today), the solar system fell into place according to a marvelously simple plan that anyone could understand once it was explained: the sun at the center, and all the planets revolving around it. From the perspective of our rotating and orbiting Earth, the other planets also orbiting the sun appear to reverse in their course, but this is a mere artifact due to our position as observers. Once Copernicus can convince the reader that, despite the apparent solidity of the Earth, it is in fact moving through space, everything else falls into place.

One of the reasons that theoretical parsimony and elegance played such a significant role in the reception of Copernicus — and even the theologians who rejected his cosmology employed his calculations to clarify the calendar, so powerful was Copernicus’ work — was that the evidence given for the Copernican system was indirect. Even today, only a handful of the entire human population has ever left the planet Earth and looked down on it from above — seeing Earth from the perspective of the overview effect — and so acquired direct evidence of the Earth in space. No one, no single human being, has hovered above the solar system entire and looked down upon it and so obtained the most direct evidence of the Copernican theory — this is an overview affect that we have not yet attained. (NB: in The Scientific Imperative of Human Spaceflight I suggested the possibility of a hierarchy of overview effects as one moved further out from Earth.)

The knowledge that we have of our solar system, and indeed of the universe entire, is derived from observations and deduction from observations. Moreover, seeing the truth of Copernican heliocentrism would not only require an overview in space, but an overview in time, i.e., one would need to hover over our solar system for hundreds of years to see all the planets rotating around the common center of the sun, and one would have to, all the while, remain focused on observing the solar system in order to be able to have “seen” the entire process — a feat beyond the limitations of the human lifetime, not to mention human consciousness.

Copernicus himself did not mention the principle of parsimony or Ockham’s razor, and certainly did not mention William of Ockham, though Ockham was widely read in Copernicus’ time. The principle of parsimony is implicit, even pervasive, in Copernicus, as it is in all good science. We don’t want to account for the universe with Rube Goldberg-like contraptions as our explanations.

In a much later era of scientific thought — in the scientific thought of our own time — Stephen J. Gould wrote an essay titled “Is uniformitarianism necessary?” in which he argued for the view that uniformitarianism in geology had simply come to mean that geology follows the scientific method. Similarly, one might well argued that parsimony is no more necessary than uniformitarianism, and that what content of parsimony remains is simply coextenisve with the scientific method. To practice science is to reason in accordance with Ockham’s razor, but we need not explicitly invoke or apply Ockham’s razor, because its prescriptions are assimilated into the scientific method. And indeed this idea fits in quite well with the casual references to Ockham’s razor such as that I quoted above. Most scientists do not need to think long and hard about parsimony, because parsimonious formulations are already a feature of the scientific method. If you follow the scientific method, you will practice parsimony as a matter of course.

Copernicus’ Ockham, then, was already the Ockham already absorbed into nascent scientific thought. Perhaps it would be better to say that parsimony is implicit in the scientific method, and Copernicus, in implicitly following a scientific method that had not yet, in his time, been made explicit, was following the internal logic of the scientific method and its parsimonious demands for simplicity.

Andreas Osiander (19 December 1498 – 17 October 1552) was a German Lutheran theologian who oversaw the publication of Copernicus' De revolutionibus and added an unsigned preface that many attributed to Copernicus.

Andreas Osiander (19 December 1498 – 17 October 1552) was a German Lutheran theologian who oversaw the publication of Copernicus’ De revolutionibus and added an unsigned preface that many attributed to Copernicus.

Osiander’s Ockham

Osiander was bitterly criticized in his own time for his unauthorized preface to Copernicus, though many immediately recognized it as a gambit to allow for the reception of Copernicus’ work to involve the least amount of controversy. As I noted above, the Protestant Reformation was in full swing, and the events that would lead up the Thirty Years’ War were beginning to unfold. Europe was a powder keg, and many felt that it was the better part of valor not to touch a match to any issue that might explode. All the while, others were doing everything in their power to provoke a conflict that would settle matters once and for all.

Osiander not only added the unsigned and unauthorized preface, but also changed the title of the whole work from De revolutionibus to De revolutionibus orbium coelestium, adding a reference to the heavenly spheres that was not in Copernicus. This, too, can be understood as a concession to the intellectually conservative establishment — or it can be seen as a capitulation. But it was the preface, and what the preface claimed as the proper way to understand the work, that was the nub of the complaint against Osiander.

Here is a long extract of Osiander’s unsigned and unauthorized preface to De revolutionibus, not quite the whole thing, but most of it:

“…it is the duty of an astronomer to compose the history of the celestial motions through careful and expert study. Then he must conceive and devise the causes of these motions or hypotheses about them. Since he cannot in any way attain to the true causes, he will adopt whatever suppositions enable the motions to be computed correctly from the principles of geometry for the future as well as for the past. The present author has performed both these duties excellently. For these hypotheses need not be true nor even probable. On the contrary, if they provide a calculus consistent with the observations, that alone is enough. Perhaps there is someone who is so ignorant of geometry and optics that he regards the epicyclc of Venus as probable, or thinks that it is the reason why Venus sometimes precedes and sometimes follows the sun by forty degrees and even more. Is there anyone who is not aware that from this assumption it necessarily follows that the diameter of the planet at perigee should appear more than four times, and the body of the planet more than sixteen times, as great as at apogee? Yet this variation is refuted by the experience of every age. In this science there are some other no less important absurdities, which need not be set forth at the moment. For this art, it is quite clear, is completely and absolutely ignorant of the causes of the apparent nonuniform motions. And if any causes are devised by the imagination, as indeed very many are, they are not put forward to convince anyone that are true, but merely to provide a reliable basis for computation. However, since different hypotheses are sometimes offered for one and the same motion (for example, eccentricity and an epicycle for the sun’s motion), the astronomer will take as his first choice that hypothesis which is the easiest to grasp. The philosopher will perhaps rather seek the semblance of the truth. But neither of them will understand or state anything certain, unless it has been divinely revealed to him.”

Nicholas Copernicus, On the Revolutions, Translation and Commentary by Edward Rosen, THE JOHNS HOPKINS UNIVERSITY PRESS, Baltimore and London

If we eliminate the final qualification, “unless it has been divinely revealed to him,” Osiander’s preface is a straight-forward argument for instrumentalism. Osiander recommends Copernicus’ work because it gives the right results; we can stop there, and need not make any metaphysical claims on behalf of the theory. This ought to sound very familiar to the modern reader, because this kind of instrumentalism has been common in positivist thought, and especially so since the advent of quantum theory. Quantum theory is the most thoroughly confirmed theory in the history of science, confirmed to a degree of precision almost beyond comprehension. And yet quantum theory still lacks an intuitive correlate. Thus we use quantum theory because it gives us the right results, but many scientists hesitate to give any metaphysical interpretation to the theory.

Copernicus, and those most convinced of his theory, like Rheticus, was a staunch scientific realist. He did not propose his cosmology as a mere system of calculation, but insisted that his theory was the true theory describing the motions of the planets around the sun. It follows from this uncompromising scientific realism that other theories are not merely less precise in calculating the movements of the planets, but false. Scientific realism accords with common sense realism when it comes to the idea that there is a correct account of the world, and other accounts that deviate from the correct account are false. But we all know that scientific theories are underdetermined by the evidence. To formulate a law is to go beyond the finite evidence and to be able to predict an infinitude of possible future states of the phenomenon predicted.

Scientific realism, then, is an ontologically robust position, and this ontological robustness is a function of the underdetermination of the theory by the evidence. Osiander argues of Copernicus’ theory that, “if they provide a calculus consistent with the observations, that alone is enough.” So Osiander is not willing to go beyond the evidence and posit the truth of an underdetermined theory. Moreover, Osiander was willing to maintain empirically equivalent theories, “since different hypotheses are sometimes offered for one and the same motion.” Given empirically equivalent theories that can both “provide a calculus consistent with the observations,” why would one theory be favored over another? Osiander states that the astronomer will prefer the simplest explanation (hence explaining Copernicus’ position) while the philosopher will seek a semblance of truth. Neither, however, can know what this truth is without divine revelation.

Osiander’s Ockham is the convenience of the astronomer to seek the simplest explanation for his calculations; the astronomer is justified in employing the simplest explanation of the most precise method available to calculate and predict the course of the heavens, but he cannot know the truth of his theory unless that truth is guaranteed by some outside and transcendent evidence not available through science — a deus ex machina for the mind.

Copernicus stands at the beginning of the scientific revolution, and he stands virtually alone.

Copernicus stands at the beginning of the scientific revolution, and he stands virtually alone.

The origins of the scientific revolution in Copernicus

Copernicus’ Ockham was ontological parsimony; Osiander’s Ockham was methodological parsimony. Are we forced to choose between the two, or are we forced to find a balance between ontological and methodological parsimony? These are still living questions in the philosophy of science today, and there is a sense in which it is astonishing that they appeared so early in the scientific revolution.

As noted above, the world of Copernicus was essentially a medieval world. Toruń and Frombork were far from the medieval centers of learning in Paris and Oxford, and about as far from the renaissance centers of learning in Florence and Nuremberg. Nevertheless, the new cosmology that emerged from the scientific revolution, and which is still our cosmology today, continuously revised and improved, can be traced to the Baltic coast of Poland in the late fifteenth and early sixteenth century. The controversy over how to interpret the findings of science can be traced to the same root.

The conventions of the scientific method were established in the work of Copernicus, Galileo, and Newton, which means that it was the work of these seminal thinkers who established these conventions. Like the cosmologies of Copernicus, Galileo, and Newton, the scientific method has also been continuously revised and improved. That Copernicus grasped in essence as much of the scientific method as he did, working in near isolation far from intellectual centers of western civilization, demonstrates both the power of Copernicus’ mind and the power of the scientific method itself. As implied above, once grasped, the scientific method has an internal logic of its own that directs the development of scientific thought.

The scientific method — methodological naturalism — exists in an uneasy partnership with scientific realism — ontological naturalism. We can see that this tension was present right from the very beginning of the scientific revolution, before the scientific method was ever formulated, and the tension continues down to the present day. Contemporary analytical philosophers discuss the questions of scientific realism in highly technical terms, but it is still the same debate that began with Copernicus, Rheticus, and Osiander. Perhaps we can count the tension between methodological naturalism and ontological naturalism as one of the fundamental tensions of scientific civilization.

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Updates and Addenda

This post began as a single sentence in one of my note books, and continued to grow as I worked on it. As soon as I posted it I realized that the discussions of scientific realism, instrumentalism, and methodological naturalism in relation to parsimony could be much better. With additional historical and philosophical discussion, this post might well be transformed into an entire book. So for the questioning reader, yes, I understand the inadequacy of what I have written above, and that I have not done justice to my topic.

Shortly after posting the above Paul Carr pointed out to me that the joint ESA-NASA Ulysses deep-space mission sent a spacecraft to study the poles of the sun, so we have sent a spacecraft out of the plane of the solar system, which could “look down” on our star and its planetary system, although the mission was not designed for this and had no cameras on board. If we did position a camera “above” our solar system, it would be able to take pictures of our heliocentric solar system. This, however, would be more indirect evidence — more direct than deductions from observations, but not as direct as seeing this with one’s own eyes — like the famous picture of the “blue marble” Earth, which is an overview experience for those of us who have not been into orbit to the moon, but which is not quite the same as going into orbit or to the moon.

Paul Carr also drew my attention to Astronomy Cast Episode 390: Occam’s Razor and the Problem with Probabilities, with Fraser Cain and Pamela Gay, which discusses Ockham’s razor in relation to positing aliens as a scientific explanation.

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Sunday


In several earlier posts I have made a trial of distinct definitions of naturalism. These posts include:

A Formulation of Naturalism
Two Thoughts on Naturalism
Naturalism: Yet Another Formulation, and
Naturalism and Object Oriented Ontology

I regard all of these formulations of tentative, but there may be something to learn from these tentative formulations if we employ them as a kind of experiment for understanding methodological naturalism. That is to say, each of these attempts to formulate naturalism implies a formulation of methodological naturalism. Furthermore, in so far as methodological naturalism is definitive of contemporary science, each formulation of methodological naturalism implies a distinct conception of science.

In A Formulation of Naturalism I suggested that, “Naturalism is on a par with materialism, and philosophically is to be treated as far as possible like materialism.”

In Two Thoughts on Naturalism I suggested that “Naturalism is on a par with mechanism, and philosophically is to be treated as far as possible like mechanism.” I also suggested that, “Naturalism entails that all ideas will first be manifest in embodied form… there are no abstract ideas that are given to us as abstract ideas; all ideas are ultimately derived from experience.”

In Naturalism: Yet Another Formulation I noted that these earlier efforts at formulations of naturalism are implicitly parsimonious, tending toward conceptual minimalism, and further suggested that, “we can characterize naturalism in terms of a quantitative parsimony, following quantitative formulations as far as they will go, and only appealing to qualitative formulations when quantitative formulations break down.” There is a sense, then, in which we can speak of deflationary naturalism. In so far as these formulations of naturalism embody the principle of parsimony, we need not separately formulate the principle of parsimony as a regulative norm of science.

In Naturalism and Object Oriented Ontology I suggested that an approach to naturalism might be made by way of object oriented ontology, which I there compared to Colin McGinn’s transcendental naturalism thesis, i.e., that the world is “flatly natural” though we are unable to see this for what it is because of our perceptual and cognitive limitations.

While when I first formulated naturalism such that, “Naturalism is on a par with materialism, and philosophically is to be treated as far as possible like materialism,” I intended naturalism as consisting of a more comprehensive scope than materialism, though when applied to the scientific method I see that it can be taken as a doctrine of limiting one’s scope to the problem at hand. This approach to science is as familiar as Newton’s aphorism, Hypotheses non fingo. Science often proceeds by providing a very limited explanation for a very limited range of phenomena. This leaves many explanatory gaps, but the iteration of the scientific method means that subsequent scientists return to the gaps time and again, and when they do so they do so from the perspective of the success of the earlier explanation of surrounding phenomena. Once a species of explanation becomes generally received as valid, the perception of the later extension of this species of explanation (perhaps already considered radical in its initial formulation) becomes more acceptable, and more explanatory power can be derived from the explanation.

Similar considerations to those above hold for the same formulation in terms of mechanism rather than materialism, or in terms of quantification rather than materialism. Initial formulations of mechanism (or quantification) can be crude and seem only to apply to macroscopic features, and is possibly seen as impossibly awkward to explain the fine-grained features of the world. As the mechanistic explanation becomes more refined and flexible, the idea of its application to more delicate matters appears less problematic.

An object-oriented ontological account of naturalism would be the most difficult to formulate and would take us the farthest from methodological concerns and the deepest into ontological concerns, so I will not pursue this at present (as I write this I can feel that my mind is not up to the task at the moment), but I will only mention it here as a viable possibility.

In any case, our formulations of methodological naturalism based on these formulations of naturalism would run something like this:

Methodological materialism pursued as far as possible, leaving any non-material account aside

Methodological mechanism pursued as far as possible, leaving any non-mechanistic account aside

Methodological quantification pursued as far as possible, leaving any qualitative account aside

Methodological flat naturalism, or transcendental naturalism, pursued as fas a possible, leaving any non-flat or non-transcendental account aside

I think that all of these approaches do, in fact, closely describe the methodology of the scientific method, especially as I mentioned above considered from the perspective of the growth of knowledge through the iteration of the scientific method.

The growth of knowledge through the iteration of the scientific method is a formulation of the historicity of scientific knowledge in terms of the future of that knowledge. The formulation of the historicity of scientific knowledge in terms of the past is nothing other than that embodied in the Foucault quote that, “A real science recognizes and accepts its own history without feeling attacked.” (from “Truth, Power, Self: An Interview with Michel Foucault”)

All present scientific knowledge will eventually become past scientific knowledge, and it will become past knowledge through the continued pursuit of the scientific method, which is to say, methodological naturalism in some form or another.

The distant future of scientific knowledge, if only we had access to it, would seem as unlikely and as improbable as the distant past of scientific knowledge, but the past, present, and future of scientific knowledge are all connected in a continuum of iterated method.

It is ultimately the task of philosophy of see scientific knowledge whole, and to this end we must see the whole temporal continuum as the expression of science, and not any one, single point on the continuum as definitive of science. The unity of science, then, is the unity of the scientific method that is the connective tissue between these diverse epochs of science, part, present, and future.

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Parsimonious Formulations

30 December 2009

Wednesday


William of Ockham was one of the greatest philosophers of the Western tradition, who more-or-less single-handedly inaugurated the tradition of philosophical parsimony that still reigns today.

The principle of parsimony — also called Ockham’s Razor, after William of Ockham who gave the principle some of its most compelling formulations — is among the most venerable of principles in human thought. This must be one of the few medieval philosophical principles that remains a staple of thought even today. Few but Thomists would be able to make it through the bulk of the Summa Theologiae, and far fewer still would find much in it with which they could agree, but there are parts of Ockham that can be read like a contemporary. Ockham is among the very few medieval writers of whom we can say this, and he shares this status with the canonical texts of classical antiquity.

I can't think of much of anything in Saint Thomas Aquinas that we can read while nodding with approval.

Not long ago in A Formulation of Naturalism I cited Hallett’s book Cantorian Set Theory and Limitation of Size for its treatment of what Hallett called Cantor’s finitism, i.e., Cantor’s treatment of transfinite numbers as being like finite numbers as far as this methodological analogy could be made to hold. I suggested that a similar approach could be used to characterize naturalism in terms of materialism: we can treat naturalism like materialism by way of a methodological analogy that is employed as long as it can be made to work. Later, in Two Thoughts on Naturalism, I suggested that naturalism could be given a similar treatment vis-à-vis mechanism.

Such formulations — the transfinite in terms of the finite, and naturalism in terms of materialism or mechanism — are minimalist formulations. Conceptual minimalism makes the most it can from the fewest resources. This is an application of the principle of parsimony. It has always been felt most strongly in the formal sciences. Axiomatization is an expression of this spirit of minimalism. Łukasiewicz’s reduction of the propositional calculus to a single axiom is another expression of the spirit of parsimony, as is the Polish notation for symbolic logic that he first formulated. The later Russell’s formulations in terms of “minimum vocabularies” must be counted a part of the same tradition, though Russell’s parsimonious roots go much deeper and are perhaps expressed most profoundly in his theory of descriptions.

Russell's theory of descriptions, called a 'paradigm of philosophy' by Frank Ramsey, is a classically parsimonious theory.

The language of parsimony is pervasive throughout contemporary logic and mathematics, such as when one says that, for example, Von Neumann–Bernays–Gödel set theory is a conservative extension of Zermelo–Fraenkel set theory (ZF). There is even a conservativity theorem of mathematical logic that formalizes this approach to parsimony. Perhaps counter-intuitively, a conservative extension of a theory extends the language of a theory without extending the theorems that can be derived from the original (unextended) theory. Michael Dummett is sometimes credited with originating the idea of a conservative extension (by Neil Tennant, for example), and he wrote in his Frege: Philosophy of Mathematics that:

“The notion of a conservative extension makes sense only if the theory to be extended is formulated in a language more restricted than that of the extended theory.” (p. 297)

It sounds puzzling at first, but it shouldn’t surprise us. Quine noted that the more we conserve on the elements of our theory, the larger the apparatus of derivation must become, and vice versa: there is an inverse relationship between the two.

dummett michael

The short Wikipedia article on conservative extensions observes as follows:

“a conservative extension of a consistent theory is consistent. Hence, conservative extensions do not bear the risk of introducing new inconsistencies. This can also be seen as a methodology for writing and structuring large theories: start with a theory, T0, that is known (or assumed) to be consistent, and successively build conservative extensions T1, T2, … of it.”

Thus the methodologically parsimonious tool of conservative extensions has implications for theoretical work over all. One can imagine an entire theoretical discipline given over to gradual and incremental extensions of an originally modest theory, which implies a model of theoretical thought innocent of Kuhnian paradigm shifts and revolutions in knowledge.

Sufficiently gradual (and sufficiently conservative) extensions of an existing theory may obviate the need for a Kuhnian paradigm shift.

Sufficiently gradual (and sufficiently conservative) extensions of an existing theory may obviate the need for a Kuhnian paradigm shift.

Of course, all parsimonious theories must rely upon some original bold insight upon which later conservative extensions can build. Cantor’s informal insights into set theory and transfinite numbers begat such an embarrassment of riches that almost all subsequent mathematical thought has consisted of various restrictions and codifications of Cantor’s intuitive and informal ideas. There is scarcely anything in the history of science to compare with it, except for Darwin’s conceptual breakthrough to natural selection. But mathematical theory and biological theory are developed so differently that the resemblance of these two insights followed by decades (and, I would guess, coming centuries) and elaboration and qualification is easier to miss than to see.

There is an implicit recognition in the conceptualization of parsimonious formulations of the power of more sweeping formulations, the proactive character of conceptual innovation that goes beyond accepted formulations, even while there is at the same time an implicit recognition of the danger and perhaps also irresponsibility of such theorizing.

Some time ago I noted in Exaptation of the Law that the law has an intrinsic bias in favor of the past that makes it a conservative force in society. With the law, this influence is concrete and immediate, often deciding the fates of individuals. It strikes me now that the minimalism and parsimony of much (if not most) formal thought is intrinsically conservative in an intellectual sense, and constitutes the ontological equivalent of bias in favor of the past. This intrinsic bias of formal thought is likely to be less concrete and immediate than that of the law, but no less pervasive.

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