Prior Probabilities Have No Probative Force

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Rob
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Prior Probabilities Have No Probative Force

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Fitelson wrote:In Chapter 12 of Warrant and Proper Function, Alvin Plantinga constructs two arguments against evolutionary naturalism, which he construes as a conjunction of E&N. The hypothesis E says that "human cognitive faculties arose by way of the mechanisms to which contemporary evolutionary thought directs our attention" (p. 220). With respect to proposition N, Plantinga (p. 270) says "it isn't easy to say precisely what naturalism is," but then adds that "crucial to metaphysical naturalism, of course, is the view that there is no such person as the God of traditional theism."

[Of course, Plantinga is overlooking the fact that their is a difference between methodological naturalism and philosophical naturalism, and that science is based upon methodological naturalism, and it is mistaken to conflate the two. (See Pennock, p. 57) Platinga goes on to assign subjective propabilities to his propostions, upon which there is no "objective basis for such probability assignments." (Pennock, p. 412)]

Plantinga says (p. 220, footnote 7) that his probabilities can be interpreted either "epistemically" or "objectively," but that he prefers the objective interpretation. However, Bayesians have never been able to make sense of the idea that prior probabilities have an objective basis. The siren song of the Principle of Indifference has tempted many to think that hypotheses can be assigned probabilities without the need of empirical evidence, but no consistent version of this principle has ever been articulated. The alternative to which Bayesians typically retreat is to construe probabilities as indicating an agent's subjective degree of belief. The problem with this approach is that it deprives prior probabilities (and the posterior probabilities that depend on them) of probative force. If one agent assigns similar prior probabilities to evolutionary naturalism and to traditional theism, this is entirely consistent with another agent's assigning very unequal probabilities to them, if probabilities merely reflect intensities of belief. (Fitelson et al. 2002: 411; cited in Pennock)

Although Plantinga's arguments don't work, he has raised a question that needs to be answered by people who believe evolutionary theory and who also believe that this theory says that our cognitive abilities are in various ways imperfect. Evolutionary theory does say that a device that is reliable in the environment in which it evolved may be highly unreliable when used in a novel environment. [Evo-devo is revealing new levels of plasticity in the development and adaptation of the organism.] It is perfectly possible that our mental machinery should work well on simple perceptual tasks, but be much less reliable when applied to theoretical matters. We hasten to add that this is possible, not inevitable. It may be that the cognitive procedures that work well in one domain also work well in another; Modus Ponens may be useful for avoiding tigers and for doing quantum physics. (Fitelson et al. 2002: 424-425; cited in Pennock)

Anyhow, if evolutionary theory does say that our ability to theorize about the world is apt to be rather unreliable, how are evolutionists to apply this point to their own theoretical beliefs, including their belief in evolution? One lesson that should be extracted is a certain humility--an admission of fallibility. This will not be news to evolutionists who have absorbed the fact that science in general is a fallible enterprise. Evolutionary theory just provides an important part of the explanation of why our reasoning about theoretical matters is fallible. (Fitelson et al. 2002: 425; cited in Pennock)

Far from showing that evolutionary theory is self-defeating, this consideration should lead who believe the theory to admit that the best they can do in theorizing is to do the best they can. We are stuck with the cognitive equipment that we have. We should try to be as scrupulous and circumspect about how we use this equipment as we can. When we claim that evolutionary theory is a very well confirmed theory, we are judging this theory by using the fallible cognitive resources we have at our disposal. We can do no other. (Fitelson et al. 2002: 425; cited in Pennock)

Plantinga suggests that evolutionary naturalism is self-defeating, but that traditional theism is not. However, what is true is that neither position has an answer to hyperbolic doubt. Evolutionists have no way to justify the theory they believe other than by critically assessing the evidence that has been amassed and employing rules of inference that seem on reflection to be sound. If someone challenges all the observations and rules of inference that are used in science and in everyday life, demanding that they be justified from the ground up, the challenge cannot be met. A similar problem arises for theists who think that their confidence in the reliability of their own reasoning powers is shored up by the fact that the human mind was designed by a God who is no deceiver. The theist, like the evolutionary naturalist, is unable to construct a non-question-begging argument that refutes global skepticism. (Fitelson et al. 2002: 425; cited in Pennock)

-- Fitelson, Branden and Sober Elliott. Plantinga's Probability Arguments against Evolutionary Naturalism. In Intelligent Design Creationism and Its Critics: Philosophical, Theological, and Scientific Perspectives (Robert T. Pennock, ed.). Cambridge: MIT Press; 2002; p. 411; 424-425.
Kitcher wrote:Throughout his book, Behe repeats the same story. He describes, often charmingly, the complexities of molecular structures and processes. There would be nothing to complain of if he stopped here and said: "Here are some interesting problems for molecularly minded evolutionists to work on, and, in a few decades time, perhaps, in light of increased knowledge of how development works at the molecular level, we may be able to see what the precursors were like.” But he doesn’t. He tries to argue that the precursors and intermediaries required by Darwinian evolutionary theory couldn’t have existed. This strategy has to fail because Behe himself is just as ignorant about the molecular basis of development as his Darwinian opponents. Hence he hasn’t a clue what kinds of precursors and intermediaries the Darwinian account is actually committed to--so it’s impossible to demonstrate that the commitment can’t be honored. However, again and again, Behe disguises his ignorance by suggesting to the reader that the Darwinian story must take a very particular form--that it has to consist in something like the simple addition of components, for example--and on that basis he can manufacture the illusion of giving an impossibility of proof. (Kitcher 2002: 265)

Although this is the main rhetorical trick of the book, there are some important subsidiary bits of legerdemain. Like pre-Reformation creationists, Behe loves to flash probability calculations, offering spurious precision to his criticisms. Here’s his attack on a scenario for the evolution of a blood-clotting mechanism, tentatively proposed by Russell Doolittle:

“… let’s do our own quick calculation. Consider that animals with blood-clotting cascades have roughly 10,000 genes, each of which is divided into an average of three pieces. This gives a total of about 30,000 gene pieces. TPA [Tissue Plasminogen Activator] has four different types of domains. By “variously shuffling,” the odds of getting those four domains together is 30,000 to the fourth power, which is approximately one-tenth to the eighteenth power, and if a million people played the lottery each year, it would take an average of about a thousand billion years before anyone (not just a particular person) won the lottery…. Doolittle apparently needs to shuffle and deal himself a number of perfect bridge hands to win the game.” (DBB 94) (Kitcher 2002: 265-266)

This sounds quite powerful, and Behe drives home the point by noting that Doolittle provides no quantitative estimates, adding that “without numbers, there is no science” (DBB 95)--presumably to emphasize that born-again creationists are better scientists than the distinguished figures they attack. But consider a humdrum phenomenon suggested by Behe’s analogy to bridge. Imagine that you take a standard deck of cards and deal yourself thirteen. What’s the probability that you got exactly those cards in exactly that order? The answer is 1 in 4 x 10. Suppose you repeat this process ten times. You’ll now have received ten standard bridge hands, ten sets of thirteen cards, each one delivered in a particular order. The chance of getting those cards in just that order is 1 in 410 x 10. This is approximately 1 in 10. Notice that the denominator is far larger than that of Behe’s trifling 1018. So it must be really improbable that you (or anyone else) would ever receive just those cards in just that order in the entire history of the universe. But, whatever the cards were, you did. (Kitcher 2002: 266)

What my analogy shows is that, if you describe events that actually occur from a particular perspective, you can make them look improbable. Thus, given a description of the steps in Doolittle’s scenario for the evolution of TPA, the fact that you can make the probability look small doesn’t mean that that isn’t (or couldn’t) have been the way things happened. One possibility is the evolution of blood-clotting was genuinely improbable. But there are others. (Kitcher 2002: 266)

Return to your experiment with the deck of cards. Let’s suppose that all the hands you were dealt were pretty mundane--fairly evenly distributed among the suits, with a scattering of high cards in each. If you calculated the probability of receiving ten mundane hands in succession, it would of course be much higher than then priority of being dealt those very particular mundane hands with the cards arriving in just that sequence (although it wouldn’t be as large as you might expect). There might be an analogue for blood-clotting, depending on how many candidates there are among the 3,000 “gene pieces” to which Behe alludes that would yield a protein able to play the necessary role. Suppose that there are a hundred acceptable candidates for each position. That means that the chance of success on any particular draw is (1/30), which is about 1 in 2.5 million. Now, if there were 10,000 tries per year, it would take, on average, two or three centuries to arrive at the right combination, a flicker of an instant in evolutionary time. (Kitcher 2002: 266-267)

Of course, neither Behe nor I know how tolerant the blood-clotting system is, how many different molecular ways it allows to get the job done. Thus we can’t say if the right way to look at the problem is to think of the situation as an analogue to being dealt a very particular sequence of cards in a very particular order, or whether the right comparison is with cases in which a more general type of sequence occurs. But these two suggestions don’t exhaust the relevant cases. (Kitcher 2002: 267)

Suppose you know the exact order of cards in the deck prior to each deal. The probability that the particular sequence would occur would be extremely high (barring fumbling or sleight of hand, the probability would be 1). The sequence only looks improbable because we don’t know the order. Perhaps that’s true for the Doolittle shuffling process as well. Given the initial distribution of pieces of DNA, plus the details of the biochemical milieu, principles of chemical recombination might actually make it very probable that the cascade Doolittle hypothesizes would ensue. Once again, nobody knows whether this is so. Behe simply assumes that it isn’t. (Kitcher 2002: 267)

Let me sum up. There are two questions to pose: What is the probability that the Doolittle sequence would occur? What is the significance of a low value for that probability? The answer to the first question is that we haven’t a clue: it might be close to 1, it might be small but significant enough to make it likely that the sequence would occur in a flicker of evolutionary time, or it might be truly tiny (as Behe suggests). The answer to the second question is that genuinely improbable things sometimes happen, and one shouldn’t confuse improbability with impossibility. [Nor should one confuse so-called probability with certainty.] Once these points are recognized, it’s clear that, for all its rhetorical force, Behe’s appeal to numbers [prior probabilities which are really indicators of intensity of belief; subjective probabilities] smacks more of numerology than of science. As with his main line of argument, it turns out to be an attempt to parlay ignorance of molecular details into an impossibility proof. (Kitcher 2002: 267)

-- Kitcher, Philip. Born-Again Creationism. In Intelligent Design Creationism and Its Critics: Philosophical, Theological, and Scientific Perspectives (Robert T. Pennock, ed.). Cambridge: MIT Press; 2002; pp. 265-267.
Fox wrote:The steps that have been identified by experiment are:

1. Formation of amino acids from primordial reactants.
2. Formation of proteinoids by polymerization of sets of amino acid.
3. Formation of microstructures by contact of polymers with water.
4. Origin of the genetic apparatus within such microstructures.

The experimental results show that the probability of each step is close to unity .... For purposes of argument let us assume 90%, although the experiments indicate > 90%. The probability of reproductive, infrastructured cell-like entities arising in steps from inorganic matter containing atoms of carbon, hydrogen, oxygen, and nitrogen is then at least (9/10) = 65%. (All such "numerology," however, on either side may be considered a quantitative euphemism for ignorance.)

-- Fox, Sidney W. Creationism and Evolutionary Protobiogenesis. In Science and Creationism (Ashley Montagu ed.). Oxford: Oxford University Press; 1984; p. 212.

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