d

Posts Tagged ‘philosophy of science’

Incommensurability

In holism, irrationalism, kuhn on 17/10/2011 at 4:26 am

When Kuhn says that the “most fundamental aspect of … incommensurability” is “the proponents of competing paradigms practice their trades in different worlds” (Structure, 150) or that a scientific revolution is “a displacement of the conceptual network through which scientists view the world (ibid., 102), it is difficult to understand Kuhn as saying anything other than that incommensurability implies incomparability. With the incomparability of two theories, then theory choice is necessarily irrational, commitment to a paradigm or lexicon follows, and so on.

The assumption that theories are incommensurable can lead to, in this most radical version, parroted by post-modernist college kids all across the globe, ‘conversation-stoppers’, modes of speech that deny the very possibility of an assumption’s falsity, and are self-reinforcing enough that the most committed individual can defend the assumption come what may. In short, it’s far too convenient for anyone to claim that they do not understand the meaning of a sentence.

Read the rest of this entry »

Popper on Uncertain Truth

In popper on 13/10/2011 at 4:17 am

//

It’s Worse Being Green

In empiricism, induction, justificationism, underdetermination on 12/10/2011 at 5:19 am

In It’s Not Easy Being Grue, I argued for skepticism — or at least incredulity — towards any inductive inference made solely by appealing to a posteriori evidence. Two hypotheses, as long as they have a logical content greater than the evidence and are not yet refuted are, as a matter of following the rules of logic, necessarily equally favored by the evidence. Even if one should appeal to one of the two hypotheses having a natural property, this problem still stands, since it cannot be uncovered through a posteriori investigation. Of course, more than two hypotheses fit this criteria — any number of empirically adequate hypotheses with greater logical content than the evidence may be constructed. In sum, favoring one hypothesis over another, even with an a prior warrant, cannot be determined from a posteriori evidence at all.

Read the rest of this entry »

It’s Not Easy Being Grue

In empiricism, experiments, induction, quine, skepticism, underdetermination on 10/10/2011 at 1:52 am

One solution to Goodman’s new riddle of induction, as proposed by David Lewis and WVO Quine, is that certain languages describe natural properties, which have a special metaphysical status. All things being equal, the evidence will favor the hypothesis that uses languages that have natural properties over any other language in all cases. The problem of choosing between hypotheses that will be favored by the evidence and hypotheses that will not is solved by choosing a hypothesis expressed in a language that uses natural properties. There is, however, a problem with this solution: how can a scientist decide whether a language is using a natural property?

Read the rest of this entry »

Discovery

In critical rationalism, empiricism, the ancient greeks, xenophanes on 05/10/2011 at 4:27 am

The imagination has made more discoveries than the eye. (Joseph Joubert)

We make a conjecture, a guess. We make tentative proposals, and then see how they work. If they don’t withstand criticism, we try again, either making an iteration on the initial theory, or making a drastic revision that explains why the initial theory was mistaken. If they withstand criticism, this says nothing about their truth or falsity. What happens, though, before the criticism?

Anaximander, the first scientist, said the Earth was unsupported in space. From the modern point of view, we do not understand that at the time this was a highly controversial supposition, one that went against the firm foundation of the senses. It is obvious (and I rarely use the word, for very few things are truly obvious) that this was something Anaximander could not possibly have observed. Here we have one of the most revolutionary conjectures, for while it happened to be true (or at least approximately true), it is the first known case of an individual going against the assumption that the senses were the final arbiters of the truth.

Anaximander deduced that if the Earth was supported on pillars, or the back of a turtle, or four elephants, or water, that the pillars, turtle, elephants, or water would themselves require some support. And this new support would require a support as well, and so on, in an infinite regress of supports. So Anaximander did away with the whole notion of support entirely and said that the Earth did not rest on anything.

The eye and the ear are notoriously unreliable, but more importantly, they do not give us any interesting theories. Cosmology does not come from the senses; cosmology is created from the mind. Here we have the first scientist acting — unwittingly, and centuries before the 18th century — as a Kantian, not an empiricist. Science began without empiricism, for empiricism in science is unnecessary and possibly unproductive.

//

Van Fraassen on Technology

In van fraassen on 07/09/2011 at 6:10 am

Note to self…

There’s one huge problem I have with Bas Van Fraassen’s argument against realism of scientific entities: I have myopia, and have to wear glasses all the time. What clear distinction can I make between using glasses to fix my myopia and using a magnifying glass to see cells? In both cases, I would use a piece of theory-laden technology to improve upon my evolved senses. It might be said that my myopia is, at least in this case, an outlier, as would someone that is born deaf requiring a cochlear implant. The general senses of a community is what matters, not any particular individual. This looks like, at least to me, to be an ad hoc solution: we’re dealing with things in middle-world that are, I should hope, deserving of a stronger epistemological status than atoms. The use of glasses is a technological fix, rather than a widening of my epistemological horizons. But then we return to the problem: where is the hard distinction between a pair of glasses and a magnifying glass?

Imagine that the human race had instead evolved a set of eyes that were far more exact than an eagle’s. The veil surrounding the atom would be pierced. But would it? Our senses are designed only for adequacy, and frequently do not track the truth. The difference between the eagle-eyed race of humans and our own would be what, exactly? Their ‘technology’ has undergone a process of conjecture and refutation on the species-level, refining particular tools over billions of years. Our technology has undergone the same process, but on a different level, the theoretical level. While the differences are superficial, since one is to a large extent innate and the other manufactured, this difference does not extend to the level of epistemological warrant. Why should innate senses be elevated over acquired senses?

Here is the rub: I think Van Fraassen’s argument doesn’t just apply only to the very small, but to any and all possible objects. All sensory experience is theory-laden, not just technological ‘experience’. While there is an extra step between seeing a read-out on a Geiger counter and seeing an apple, none of the two are on surer epistemological footing (think of Plantinga). Van Fraassen’s argument then, if we wish to be conservative in the properties, relations between properties, and objects in our epistemological bag, applies not just to theoretical scientific entities, but to theoretical everyday entities. We ought to be as strongly against realism of the everyday.

//

Understanding Reality

In critical rationalism on 29/08/2011 at 6:39 am

Physical concepts are free creations of the human mind, and are not, however it may seem, uniquely determined by the external world. In our endeavour to understand reality, we are somewhat like a man trying to understand the mechanism of a closed watch … He will never be able to compare his picture with the real mechanism, and he cannot even imagine the possibility or the meaning of such a comparison. But he certainly believes that, as his knowledge increases, his picture of reality will become simpler and … explain a … wider range of his sensuous expressions. He may also believe in the existence of the ideal limit of knowledge and that it is approached by the human mind. He may call this limit the objective truth. (Albert Einstein, The Evolution of Physics Simon and Schuster, New York, 1938, 33)

//

Trust

In critical rationalism, irrationalism, skepticism on 26/08/2011 at 2:39 pm

People accept without reflection the ideas, fads, styles, and tastes of their times. Everyone is subject to this problem, even those that harp on this problem.

Why do we dismiss the stories printed in the National Enquirer and accept the articles printed in Scientific American? Is the difference in the presentation? Are we clued in to the problems in trusting the National Enquirer after seeing the sensationalistic headlines and poor typesetting?

We’re just going about begging the question, since we are using the guilty verdict as part of the prosecution. It sounds like a matter of taste to prefer Scientific American for its excellent formatting. What are we to make of the discovery by the National Inquirer of the John Edwards scandal?

Read the rest of this entry »

Induction Machines

In critical rationalism, induction on 23/08/2011 at 12:26 pm

Imagine that a computer is built to make empirical generalizations with inductive logic (whatever that may be) and that this computer is in a simple universe with a limited number of individuals,number of properties, and relationships between these properties the individuals can have. Furthermore, the universe operates with a limited number of ‘natural laws’. In this universe a computer can be created such that in some reasonable period of time it will discover the ‘natural laws’. If the laws were modified, then the computer would find a new set of laws. If this universe were further complicated, then this computer could be enhanced to be able to formulate hypotheses, to test these hypotheses, and to eliminate those that do not survive testing.

This induction machine is limited insofar as it is limited by its programmer’s intellectual horizon: the programmer decides what is or is not a property or relation; the programmer decides what the induction machine can recognize as repetitions; it is the programmer that decides what kinds of questions the machine should address. All the most important and difficult problems are already solved by the programmer, and this induction machine is little more than a speeding-up process of a room full of bean-counters or punch-card holders.

Here we have today’s work in artificial intelligence, which is precisely limited by this constraint. The theories that these computer programs develop are conditional on the initial conditions that are needed for in an induction machine. Inductive inferences does not then occur within the context of discovery; the programmer provides these. Inductive inferences occur within the context of justification, and even then it still does not satisfactorily solve the problem of induction, for the problem cannot logically be solved. These computers have become problem-solving machines that operate on conjecturing the most parsimonious theory and attempted refutation of that theory.

//

Local and Global Anomalies

In critical rationalism on 20/08/2011 at 9:38 am

An anomaly, a recalcitrant fact, may bode trouble for either a local part of a theoretical system, easily detached and replaced without significant revision to other parts of the system, or the theoretical system as a whole. If religious practices developed long before settled communities, then the findings at Gobekli Tepe would overturn a local part, and such a correction would be (comparatively) made without much fuss in the sociology of religion. However, if a fossilized rabbit was uncovered in Precambrian strata, this is not merely a problem for the theory of evolution. If it is in fact a fossilized rabbit in Precambrian strata, it knocks over central assumptions in radiometric dating, physics, and geology.

In the sea of anomalies, it is rational not to engage in a scientific revolution when anomalies are seemingly local rather than global; conversely, it is irrational to refuse a scientific revolution when anomalies are seemingly global rather than local. There remains a problem: the seriousness of anomalies is not currently subject to calculation, and may not in principle be calculated. Without a mathematical underpinning, a sociological, political, or methodological underpinning may be of service.

//

Fideism

In bartley, critical rationalism, empiricism, fideism, quine, van fraassen on 12/08/2011 at 11:18 am
Empiricism in the philosophy of science, even in its modern variants, takes observation reports of phenomenal states as a reliable route to knowledge. The problem for empiricists is as follows: Why adopt the theory (T1) that observation reports are a reliable way to sort out true from false theories and not adopt the theory (T2) that theories are a reliable way to sort out true from false observation reports? If the empiricist rejects T1 and adopts T2, the empiricist rejects empiricism and becomes a Kantian; however, this does not address the problem, for why should the Kantian adopt T2 and reject T1? The epistemological pendulum swings back.

If a basic statement and theory are incoherent, then observation reports cannot inform us that theories are wrong and theories cannot inform us that observation reports are wrong. Either the theories or observation reports are wrong — or both. Neither T1 nor T2 should be adopted a priori, for they effectively annihilate one another: all we can see is an incoherence between T1 and T2.

Furthermore, even after we recognize an incoherence between an observation report and a theory, this ‘recognizing’ is relative to a given system of logic, background assumptions, language, and cognitive framework: we are even fallible in recognizing incoherence. Whatever method or route we follow that leads to preferring one over the other will either not rest on an Archimedean point, or will not be known to rest on an Archimedean point. All is theory-laden and subject to error. We must admit that it is possible to change the logic we employ, statements we adopt, theories we accept, methods we follow, language we use, or the cognitive frameworks we inhabit, for none of them are privileged.

//

The Sun Also Rises

In induction on 08/08/2011 at 5:57 am

As simply as possible …

Do we know that the Sun will rise tomorrow because it has risen in the past? No. Hume’s psychological account of inductive inferences is mistaken, for it misstated the problem. Somehow empiricists have taken Hume as the final word that the justification for the belief that the Sun will rise tomorrow is that the Sun has risen in the past.  It is easy to undermine that argument, for there is no logical inference made. We know the Sun will rise tomorrow because we know why it rises. We have an explanation: the Earth rotates on its axis roughly every 24 hours, and we have an explanation for why that happens, and so on. The rising Sun has led us to seek an explanation, and that explanation is our ‘justification,’ for if the Earth rotates on its axis roughly every 24 hours, then the Sun will rise tomorrow.

The logical content is transmitted from the conditional “if” to the “then,” for while the phrase ‘the Sun will rise tomorrow’ is clearly not true when understood in its broadest sense (the Sun does not ‘rise’, solar eclipses are infrequent events, and people in the far North experience no sunlight for months at a time), when understood colloquially, it is but an observation report of the Sun rising in the East when viewed from a particular vantage point at a particular time. In other words, it would be like saying “If all dogs are brown, then all other things being equal, an individual will, upon seeing a dog, report that it is brown.”

Conditional knowledge, however, is in no way justified by appealing to the explanation. Another explanation about laws of gravitation is necessary. This new explanation requires another explanation, and so on, creating an infinite regress of explanations. This conditional knowledge is in no way justified, for our explanations have in the past been false, and there is no way to know if our explanations are true, for explanations always have a logical content that extends far into the future and past, discussing events that we will never have a chance to observe.

//

The Spirit of Truth

In kolakowski on 05/08/2011 at 9:04 am

Philosophy can never discover any universally admissible truths … The cultural role of philosophy is not to deliver the truth but to build the spirit of truth, and this means never to let the inquisitive energy of mind go to sleep, never to stop questioning what appears to be obvious or definitive, always to defy the seemingly intact resources of common sense, always to suspect that there might be “another side” in what we take for granted, and never to allow us to forget that there are questions that lie beyond the legitimate horizon of science and are nonetheless crucially important to the survival of humanity as we know it. (Leszek Kolakowski, Modernity on Endless Trial, p. 135)

//

Strevens on Induction

In induction on 04/08/2011 at 4:38 pm

When two theories are empirically equivalent, their likelihoods relative to any given body of evidence are equal. Thus the difference in anyone’s subjective probabilities for the theories must be due entirely to the difference in the prior probabilities that were assigned to the theories before any evidence came in. Bayesian confirmation theory preserves a prior bias towards simplicity, but it implements no additional bias of its own. …

Bayesian confirmation theory does impose an objective constraint on inductive inference, in the form of the likelihood lover’s principle, but this is not sufficient to commit the Bayesian to assuming the uniformity of nature, or the superiority of “non-grueish” vocabulary or simple theories. The first of these failures, in particular, implies that [Bayesian confirmation theory] does not solve the problem of induction in its old-fashioned sense.

If the old-fashioned problem of induction cannot be solved, what can we nevertheless say about [Bayesian confirmation theory]’s contribution to the justification of induction? There are two kinds of comments that can be made. First, we can identify unconditional, though relatively weak, constraints that [Bayesian confirmation theory] puts on induction, most notably the likelihood lover’s principle. Second, we can identify conditional constraints on induction, that is, constraints that hold given other, reasonable, or at least psychologically compelling, assumptions. We can say, for example, that if we assign low priors to grueish hypotheses, [Bayesian confirmation theory] directs us to expect a future that resembles the past. This is, remember, considerably more than we had before we began. (Michael Strevens, Notes on Bayesian Confirmation Theory [.pdf], 66)

Strevens is admirable, for he is upfront about the inadequacies of Bayesianism. That said, Strevens at times overstates his case. For instance, tet me simplify the bolded passages: “The evidence for any particular theory is underdetermined … however, if we reject theories that are incompatible with our assumption that the future will resemble the past, we will expect a future that resembles the past.” At least two problems for Strevens:

(1) The future does not resemble the past in all domains: black swans, white ravens — in fact, all falsified scientific theories — should give us pause before assuming something that is demonstrably false when applied to all domains. Therefore, if the future resembles the past in only some domains, why we should assume that the future will resemble the past in any particular domain?

(2) Even if the future should resemble the past in this particular domain, it does not follow that any theory that assumes a future that resembles the past is true, for while ‘grueish hypotheses’ are ruled out, there may still be an alternative theory that follows from that same assumption that the future will resemble the past that is in fact true. After all, it’s happened in the past (Einstein replacing Newton).

//

The ‘Grounds Clause’

In gettier, justificationism on 03/08/2011 at 9:36 am

I begin with the ‘grounds clause’ and then expand on whether the two clauses satisfy a proper definition of knowledge in light of the justificationist program.

Read the rest of this entry »

Practical Prediction

In experiments, induction, justificationism, popper, salmon on 01/08/2011 at 5:24 am

Wesley Salmon objects to Popper’s theory of knowledge on the grounds that, contrary to its stated rejection of a principle of induction, in order to explain how one can rationally decide between competing unfalsified theories, it requires the adoption of a principle of induction. The advice to an applied scientist or engineer to act as if the best-tested theories are probably true and the untested theories are probably false, though no doubt excellent advice, does not have any claim to be dubbed ‘rational’ unless a pragmatic principle of induction is adopted.

If the applied scientist’s choice is guided by the best-tested scientific theories available to him, then it appears that he is assuming that what was successful in the past will remain successful in the future. This would be an  assumption rejected by Popper, for it employs the principle of induction. However, if a scientist, following Popper’s theory of knowledge, renounces a principle of induction, then he is not allowed to say that ‘future unobserved events will resemble past observed events.’

Read the rest of this entry »

What’s Day is Night

In experiments, induction on 23/07/2011 at 3:23 am

Over at the impressive community blog of Less Wrong, Eliezer Yudkowsky published an interesting article titled “Einstein’s Arrogance.” Check it out. It’s worth a read. One point stands out:

To assign more than 50% probability to the correct candidate from a pool of 100,000,000 possible hypotheses, you need at least 27 bits of evidence (or thereabouts).  You cannot expect to find the correct candidate without tests that are this strong, because lesser tests will yield more than one candidate that passes all the tests.  If you try to apply a test that only has a million-to-one chance of a false positive (~20 bits), you’ll end up with a hundred candidates.  Just finding the right answer, within a large space of possibilities, requires a large amount of evidence. (bolding mine)

The argumentation is impressive, but Yudkowsky should note that the pool of possible hypotheses is far greater than 100,000,000 — it is infinite. Just as an infinite number of curves can fit two, three, four … up to n points on a graph, and there is a one-to-one match between equations that express these curves and the curves, so can the logical consequences of an infinite number of hypotheses ‘predict’ the results of any finite number of experiments. Therefore, no number of bits of evidence can ever permit assigning a probability more than 50% to any candidate from the pool, much less assigning a probability to the correct candidate.

Ah, but there is a way to limit the number of theories in the pool of possible hypotheses to a finite number. The only way the pool is limited is, so I conjecture, by the elimination of theories that are incompatible with our background assumptions. And yet, any of our background assumptions could be false. Yudkowsky advances the thought-experiment of black boxes that always beep when the properly-ordered six numbers are entered, but have a 25% chance of beeping when the combination is wrong. But how does one know that these black boxes always beep when the properly-ordered six numbers are entered? Yes, this is a thought-experiment, but it is an assumption that is more often than not false in science: our background assumptions, even about the accuracy of black boxes, are unjustified, constantly open to revision, and have historically been revised.

Up until the Michelson-Morley experiment (and for some time after), one of our background assumptions was that light traveled through a medium called ‘luminiferous aether.’ Before the background assumptions deductively entailed by luminiferious aether were rejected, Einstein’s hypothesis was ruled out from swimming in the pool of possible hypotheses, for the two contradict one another about the speed of light: Einstein assumed that the speed of light in a vacuum was constant regardless of reference frame. Everything else follows from this assumption (and some mathematical equations formulated by Lorentz). Therefore, the pool of possible hypotheses in light of our background assumptions is never fixed at an arbitrary number, and this pool may not even contain at any one time a correct candidate.

In fact, if we are to work with probabilities, I pull out the pessimistic meta-induction argument and see how it flies: every previous theory we have rejected rested on false background assumptions. It is highly probable that our current background assumptions are false, therefore it is highly probable that we exclude from the pool of possible hypotheses a true hypothesis.

If that argument does not sit well, then we can appeal to a more robust interpretation of probability: we have an infinite number of hypotheses at our disposal that equally fit the available results of a finite number of tests. How could we ever claim that a finite number of hypotheses (only one hundred million?) should include the true hypothesis?

And so on.

//

Of What is Rationally Permitted

In critical rationalism, empiricism, van fraassen on 21/07/2011 at 2:52 am

Bas van Fraassen’s work is, to use the words of another philosopher said to me during a brief Skype conversation, “one of the best philosophers of science alive.” But why? The concluding pages of his article The False Hopes of Traditional Epistemology (2000) stand out as bucking the trend in philosophy of science and epistemology in much the same way Bartley and Popper did–he considers the historical problem-situation, finds faults with all the available options, and then reconfigures the problem in such a way as to dig out an underlying assumption.

In this case, his language is still laden with certain terms that make him far more understandable to others that still cling to these assumptions, but his conclusions are, when understood, close enough to critical rationalism as to deserve either catcalls and gnashing of teeth from the traditionalist monkeys that cling to the rafters, or a long time spent reflecting by critical rationalists. I’ve already taken on board several of his positions, and may take on more in time, but even if I should reject them in due course, he has provided, even implicitly, a powerful alternative to critical rationalism.

I take it that what is rational is precisely what is rationally permitted. Thus we are rational in believing something exactly when we are not rationally compelled to believe the opposite. This implies, tautologically, that nothing more than staying within the bounds of reason is needed for this status of rationality–not good reasons, not a rationale, not support of any special sort, not a pedigree of inductive reasoning or confirmation, nothing is needed above and beyond coherence. Thus any truly coherent position is rational.

Now this may strike you as absurd, because it seems to imply that ‘anything goes’, the ugly brought of skepticism’s ‘nothing goes’. But that is simply not so. If it were so, I would have come to an impasse and would have to admit that the constrains of rationality are more than coherence. But it is not so, and we have not in fact come to an impasse.

… Logically speaking there may be infinitely many coherent alternatives to our posterior opinion, but almost none of these will be live options for us. This is not an accidental feature of our situation, but integral to it, exactly because we have prior opinion and prior understanding, which is not laid out for us on the side, like a textbook, but which is already our own. Any small part of it we can think of changing as part of our response, and any large part of it we can think as possibly changed, to any imaginable alterative, over the long run, in the course of time. But we do not have the wherewithal to respond in more than a limited variety of ways at any given time. Many of the imaginable alteratives to what seems plausible to us cannot be incorporated by us.

… It does not mean that there are constraints on rationality beyond coherence, and it does not mean that we are following apliative rules after all. It means simply that the Neurath ‘mariners repairing their boat at sea’ for m of relativism does not lead us into a damagingly enfeebled epistemic enterprise. The ‘already on a boat’ part defeats the skeptical argument based on the ‘at sea’ part.

So here is my conclusion. We supply our own opinion, with nothing to ground it, and no method to give us an extra source of knowledge. Only the ’empty’ techniques of logic and pure math are available either to refine and improve or expose the defects of this option. That is the human condition. But it is enough. (Bas van Fraassen, The False Hopes of Traditional Epistemology, Philosophy and Phenomenological Research, Vol. LX, No. 2, March 2000, 277-279)

//

Adherence

In fideism, kuhn, lakatos on 18/07/2011 at 12:14 pm

Because they can ordinarily take current theories for granted, exploiting rather than criticizing it, the practitioners of mature sciences are freed to explore nature to an esotoric depth and detail otherwise unimaginable. (Thomas Kuhn, Reflections on my critics. In: I. Lakatos and A. Musgrave (eds.) Criticism and the Growth of Knowledge, p. 247. Cambridge, UK: Cambridge University Press.)

[T]rial attempts [to solve puzzles], whether by the chess player or by the scientist, are trials only of themselves, not of the rules of the game. They are possible only so long as the paradigm itself is taken for granted. (Kuhn, 1993, The Structure of Scientific Revolutions, 3rd edition. Chicago, IL: University of Chicago Press, pp.144-5.)

Kuhn implies that if a scientist is super-critical, they can never begin to practice science. They’ll spend their time tackling foundations of disciplines, rather than addressing the logical consequences of all manner of scientific theories. While puzzle solving is a critical activity, according to Kuhn, it is a very limited kind of criticism, for it leaves certain questions as verboten. Is Kuhn right that most scientists practicing normal science need to uncritically accept theories?

A scientist can accept a theory for any purposes they so choose — practical, theoretical, or critical purposes are all acceptable. Kuhn thinks that ‘normal science’ can be conducted “only so long as the paradigm itself is taken for granted,” yet all that is needed is to consider what would be the case if the paradigm were valid.

Many scientists are more than willing to look at cases of dowsing even when they find the very idea absurd. Rather than uncritically accepting dowsing, scientists provisionally adopt the theory in order to parse out its logical consequences, one of them being the ability to determine the location of water with sticks. In fact, this is a commonplace tactic in science and philosophy: in order to undermine a rival theory, one must address it on its own terms and simultaneously attempt to catch it in a contradiction.

//

Simplicity

In critical rationalism, popper on 15/07/2011 at 9:32 am

Why should scientists prefer theories that are simple and not complex? There is a very simple answer to this complex problem: Leibniz points out in section VI of his Discourse on Metaphysics that a theory ought to be simpler than the data it sets out to explain, otherwise it does not explain anything. A theory becomes vacuous if an arbitrarily complex mathematical statement is permitted to count as a theory, for one can always construct a theory to fit the data, even if the data is random.

Read the rest of this entry »