Reality Conditions

Monday, February 26, 2007

A Riff from Ross to Rorty

The topic of Marcus Ross, as Scott Aaronson has noticed, seems ideally suited for being picked up and discussed in blogs; and indeed few among those I read have said nothing about it in the last couple of weeks. (Besides Scott’s own most excellent post, see Janet (also here), PZ, Brandon, Rob Knop and Steve Gimbel for a variety of opinions). In case you have somehow missed all this discussion, Marcus Ross has received recently a PhD in geophysical science at the University of Rhode Island, after presenting a perfectly normal thesis which does research assuming the normally accepted facts about the age of the Earth. However, Ross is at the same time a Young Earth Creationist, who believes that the world was created by God a few thousands years ago, and so –one would presume- does not believe any of the things he wrote in the thesis.

Most of the discussion has centered in whether this is or should have been be grounds for denying him the degree, and whether Ross did anything contrary to the scientific ethos. While acknowledging that in the real world it is a possibility that Ross will attempt to use his scientific credentials to lend credibility to anti-scientific creationist propaganda, and this would certainly be dishonest, I side with those who see nothing wrong in doing research and completing a thesis based on assumptions one does not belief. As many have pointed out, to a lesser degree this is done all the time; it is commonplace for scientists to explore the consequences of a model they do not believe to be true. There is no rule that a scientist must believe what he publishes; only that what he publishes is research done according to the scientific method. Even more, for granting a PhD to someone it is required just that he must display understanding of the topics researched in and of the proper methods to research into them. Understanding, not belief.

Perhaps some think that Ross really believing that the Earth was created as in Genesis is a sign that he does not “really understand” the facts of geophysics he was taught or the scientific method he used in his thesis. But if the examining comitee was satisfied from the thesis that he did really understand all this, then isn’t this a much more reliable criterion? (It is not so easy to write a thesis about something one does not understand; more than “parrotting” is involved!) Others might be concerned that Ross was being untruthful, and violating scientific ethos; to this, I like Greg Kuperberg’s response to Larry Moran at Scott’s comment thread: “He is truthful in his thesis. His thesis has a series of true statements about paleontology. They aren’t statements about his own beliefs, they are statements about the history of the planet. The real issue is that he’s untruthful at other times, when he promotes creationism.”

As these arguments, and counterarguments to them, can be found already all over the place, I will try to riff from the topic of Ross’ thesis to a diferent, philosophical one. Let us ask, what does Ross really believe about the age of the Earth? Of course, I have no way to know the answer. Perhaps he believes there is a fundamental flaw in the methods used by conventional science to date the Earth. Or perhaps he is okey with those methods as far as science goes, but interprets the results in an instrumentalistic way, not as representing reality. Perhaps he is a Gossean, who believes the Earth was created by God with exact signs of old age, so the recent creation is not empirically detectable. But there is another possibility I want to explore. Could he possibly believe both that the Earth is old, and that it is young?

To be clear, I am not considering the interesting and realistic possibility that Ross does not perceive that his set of beliefs is inconsistent; that some of his scientific beliefs have logical consequences incompatible with his creationist ones. I am considering the unrealistic, purely academic and philosophical thought-experiment possibility of a Ross who avowed, loudly, clearly and self-consciously, both the old and the young age of the earth. (From now on, “Ross” will refer to this fictional Ross, not the real one.) Perhaps he avows both propositions at different times, and when pointed out the contradiction he says “I believe one thing in scientific contexts, and another I religious ones”. Moreover, suppose lying detection techinques show that in neither of both occasions Ross is counsciously lying. What would we say then?

Probably, that he is schizophrenical or has some other kind of deep cognitive malfunction. But why? Why would we not be okey with simply accepting his self-description?

The problem cuts deeper than it seems, because on some popular philosophical positions, there would be nothing wrong with the Ross I have described! I will focus on Richard Rorty as a representative of these positions, because he is the only one I have read more or less extensively. Very roughly, Rorty says that beliefs do not aim at representing the world, but are just tools we use to cope with it. Accepting or rejecting a belief is akin to using or discarding a particular tool for dealing with some problem. “Truth” is just a label we use for those beliefs we endorse. It would seem to be a consequence from this account that there is no problem in holding contradictory beliefs, as long as one uses them in strictly separate spheres. The Ross of my thought experiment could believe that the earth is old to “cope” successfully with dating fossils and rocks and publishing scientific papers, and that the Earth is young to cope successfully with reading, interpreting, and teaching the Bible, praying, etc.; and the extent to which this activities did not raise in him any doubts of consistency would not be a mark of schizophrenia but of rational sanity: the enviable ability to cope with full success in two different areas of life using two different tools.

I propose this as a reductio ad absurdum of Rorty’s philosophy. Perhaps he would say that beliefs are tools which only can function when constrained by consistency criteria, but this is a weak reply; it is true in most occasions, but if someone could manage to “compartimentalize” the scientific and the religious aspects of life in such a way that the inconsistent beliefs did not bring about any practical problems, then consistency seems not only unnecessary but positively harmful. I think that ultimately, Rorty should embrace the idea that incompatible beliefs are possible and can even be a feature more than a bug.

The problem with Rorty, of course, is that belief is not just any tool for coping, but one that has as primary purpose the grasping of true facts about the world. Coping successfully is a secondary consequence, achieved via the possesion of true beliefs. Belief, we could say, is intrinsically “truth-aimed”; and thus saying “I believe in X and also in not-X because each of them enables me to cope successfully with some things” is absurd; because one must know that the facts about X cannot agree with both beliefs. However, I don’t think this kind of argument is very good against Rorty, who has a stock-reply for it: “Perhaps with our present concepts of belief, truth, etc. what you say is true and what I want to say is inconsistent; but if we find that these concepts bring upon us too much philosophical trouble to understand what “truth” and “facts” really mean, then we may better switch to a purely pragmatic concept of belief which does not has these problems. Concepts, after all, are just tools as well. So in the future in which we all use the new concepts I propose, there will be no inconsistency.” This reply tends to irritate professional philosophers, who see it as an evasion. (John Holbo whimsically summarises it as “all your bases will have been belong to us”.) But I confess to like it to a certain extent; I do agree that some philosophical matters (unlike “factual” ones like the age of the earth –but don’t ask me to explain the difference!) can be decided pragmatically, and in particular I think this kind of move can be used (with due care) against mind-body dualism or free-will incompatibilism. So I don’t think one can refute Rorty simply by saying that the possibility of incompatible beliefs is "conceptually absurd".

What is possible, however, is to defeat Rorty in his own playing ground, and say that we do not have strong pragmatic reasons to change our concepts of belief; that we want to go on saying that my ultra-compartimentalizer Ross would be crazy instead of rational; because we find the basic concept of beliefs as tools which (unlike others) are intrinsically truth-aiming, a very useful and good one to have. For me at least, the philosophical perplexities which the notions of truth and representation may cause are a small price to pay for using these concepts.

Friday, February 16, 2007

My Erdös Number is 5

There are two chains:

1) Alejandro Satz - Jorma Louko - Raymond Laflamme - Peter W. Shor - Nathan Linial - Paul Erdös.

2) Alejandro Satz - Francisco Diego Mazzitelli - Bei Lok Hu - Stephen A. Fulling - Itshak Borosh - Paul Erdös.

You can find your own Erdös number at the AMS Search Page.

Sunday, February 11, 2007

Lagrangians, Hamiltonians, and Scientific Realism

Up at Mormon Philosophy, Clark has a couple of posts concerning the interpretation of physical theories, with the concrete example of Newtonian mechanics. Probably most of my readers are aware that there are different versions of the theory which are mathematically equivalent, but very different in intuitive terms. Thus the traditional formulation in terms of Newton’s Laws describes the world as elemnts of matter, with the intrinsic property of mass, acting on each other by forces and responding to forces by accelerating; the more “global” Lagrangian formulation says that a system will behave in such as way as to minimize the difference between the potential energy and the kinetic energy across different possible behaviours, and the Hamiltonian formulation gives equations for how position and momentum treated as independent quantities will vary depending on the total energy of the system. In his posts Clark states his belief in scientific realism, defined as the assumption that “the entities we discuss in science correspond in some way to entities in the real world”. Then he ponders:

Now when we consider this statement of realism with the three formulations of mechanics we quickly see the problem. There are three different, yet ultimately incompatible, sets of entities mechanics is framed in terms of. Now I'm sure some will jump up and contest this, arguing for momentum, potential and kinetic energy, mass and so forth. But if we take Sellars to be saying that is the ultimate entities the theory is framed in terms of that we have epistemic justification to believe exist, then we see the problem. We can have multiple mathematically equivalent theories in this sense of theory. This is often called having the theory underdetermined.

An other way of looking at the issue is to talk about empirical adequacy. In this view the acceptance of a theory isn't to necessarily accept the entities postulated by the theory. It is just to accept that the theory accounts for the kinds of phenomena we encounter or would potentially encounter. So, for instance, we might be unable to say if mechanics really is about minimize the difference in kinds of energy or is due to forces between masses. We can just say that whatever's going on underneath, the theory explains the kinds of phenomena we encounter.

This, roughly is the distinction in science between realism and anti-realism.

He thinks that the existence of alternative formulations for mechanics, or other physical theories, is an argument against realism and for anti-realistic instrumentalism; and though he reiterates that he is still a realist, he does not provide any solution for the problem. I will try to suggest one for him.

In a nutshell, I see the problem as a manufactured one due to trying to translate mathematical language into ordinary language. The three formulations of mechanics, being mathematically equivalent, must be saying the same thing “about reality” (if we choose to interpret them realistically). The appearance that they say reality is made of “three different, yet ultimately incompatible, sets of entities” cannot be correct, because equivalent statements cannot be incompatible, and this logical fact is independent of whether we interpret the statements in a realistic or instrumentalistc way. The problem arises only because we are not satisfied with a mathematical equation as a description of reality, but we want an explanation of “what it means”, which amounts to a translation of the statement from mathematical language into non-mathematical language. The translation of Newton’s laws seems to be “objects exert forces and accelerate in response to them” and the translation of a Lagrangian action principle seems to be “systems try to minimize action”, and at first view these descriptions seem hardly compatible, especially if the second is interpreted teleologically. But insofar as there is a problem with the compatibility of the translations, this is only a reason to suppose that the translation has been done carelessly and must be corrected. It is as if we started from two Spanish sentences with equivalent meaning, tried to translate each literally into English and got two English sentences differing in meaning because two Spanish words have a shared possible meaning which is not shared by the most literal English equivalent of each of them.

The three formulations of mechanics, then, say the same thing about reality: that there exist certain quantities (given the names of mass, energy, momentum, etc.) which are related mathematically in ways given by the equations of the theory. It makes little or no sense to ask which of these quantities or equations are “fundamental” and which are merely “derived”. I am skeptical even of the possibility of distinguishing “definitions” from “empirical laws” among these mathematical equations; p = mv (momentum = mass x velocity) is a “definition” in the Newtonian formulation and a “dynamical equation” at equal level with F = ma (force = mass x acceleration) in the Hamiltonian one. The ordinary language translations (“objects exert forces”; “systems try to minimize action”) are just pedagogical or heuristic devices, useful and perhaps indispensable for actual scientific practice but not related to the austere philosophical question “What does the theory say about the world?”

There are theories for which “interpretation” is a serious question: quantum mechanics is the primary example. But the “interpretations” of quantum mechanics are a very different thing from the “interpretations” of classical mechanics we have been discussing, and raise very different issues. The equivalent kind of question would be a contrast between, for example, the Heisenberg and the Schroedinger pictures, asking whether reality consists in “states evolving in time and timeless operators” or “timeless states and operators evolving in time” (both descriptions are related by a simple mathematical equivalence). And these alternative formulations, just like those of classical mechanics, raise no philosophical problems at all.

Tuesday, February 06, 2007

Fun fact of the day

Question: To what food item did Johannes Kepler compare the shape of planetary orbits in the geocentric system?


Answer: To pretzels.

Saturday, February 03, 2007

Who can name the largest number?

On Friday, Jan. 26, two philosophers, MIT Associate Professor Agustin Rayo (The Mexican Multiplier) and Princeton Associate Professor Adam N. Elga (Dr. Evil) engaged in the Large Number Duel, in which they attempted to one-up each other by inscribing the largest finite number ever to be written on an ordinary-sized chalkboard. The feat, if successfully accomplished, would be worthy of a note in the Guinness Book of World Records. (...)

The rules of the duel gave free rein to the contestants’ creativity and humor, maintaining only a ban on the use of infinity, and restricting statements about the number proposed to a primitive semantic vocabulary. The battle itself was intense and the room in the Dreyfoos wing of the Stata Center was packed, with people standing on chairs and at least 20 students craning their necks from the doorway.

The contest opened in the style of a boxing match, with competitors presented “in the red corner” and “in the blue corner.” Elga went first, writing the number one. “Ha!” announced Rayo, as he countered with a string of ones across the board. Elga retaliated with a clever trick, erasing a line through the base of half of the ones to turn them into factorials. (...)

Near the end of the duel, Rayo furiously scribbled on the whiteboard: “The smallest number bigger than any number that can be named by an expression in the language of first order set-theory with less than a googol (10100) symbols.”

Although this definition took a bit of tweaking, including what Rayo described as his “second order logic trick,” it soon won him the duel.

As Elga collapsed, slain, the referee closed the ceremony.

Friday, February 02, 2007

Philosophia Naturalis is up

... at Science and Reason. Lots of interesting physics blogging collected there. I am usually very bad at keeping up with carnivals and posting links to them, but I will try to keep posting links to further editions.