Finishing Cooper
Well, I think I should put this to bed now.
Cooper has a schematic for "life strategies". They look like this:
The way to think of this is to regard it as a branching diagram of the probabilities of outcomes in a population. An organism - say, a vole - that faces predation has, say, two alternative strategies - to dig and hide or to flee its predators. If it flees, it has a .1 likelihood of getting away, and if it survives it has 1.4 progeny per survivor, the average for this vole. So the fitness of the FLEE branch is 1.4 times .1 = .14. Of course, those that are eaten have a fitness of 0 in this artificial example.
But the other strategy is DIG, and here .36 are consumed anyway, while .64 escape. The fitness that results from DIG is therefore .64 times 1.4 progeny, or .9. So, the DIG strategy is the one that will take over the vole population, because eventually all the FLEEing voles will be eaten. [Note that this population is doomed anyway, because the replacement of voles once all the FLEEers have been eliminated is 9/10 per generation. Selection can drive populations to extinction.]
Now Cooper want to use these diagrams as a basis for deriving, first decision theory, then inductive logic, then deductive logic, mathematics, and so on. Why this? Well, he believes as others have before him that logic evolved (Wigner and Hamming's point) and that therefore the logic must be somehow a subset of evolution.
I disagree with the motivation. Logic evolved - so too did over-optimism (those who are unduly optimistic about their abilities achieve beyond their skills more than those who have a realistic self-assessment). That doesn't mean that evolution is over-optimistic. Moreover, the "logic" of evolution is the mathematics of populations genetics - so are we just describing a circular relation here?
And that logic includes stochastic processes as well - drift in particular, but also peripheral population founder-effect sampling (atypical distributions of alleles in populations at the edge of a range of a species) - are all these to be characterised in terms of the selective fitness of strategies? Perhaps we should recall Ghiselin's comment and move on.
The diagrams are, however, rather an elegant way of representing selectively biased processes. While it is hardly a major revelation that a population's allele frequencies are iteratively added, as a flow diagram it is a useful way to make the implications of larger and more complex situations easy to follow.
A logic of evolution is yet to be worked through. I think that it will be many-valued (continuously as Cooper has shown it - the "truth-value" of an evolutionary trait ranges from 0 (false, or totally unfit) through to 1 (true, or totally fit). However, this sort of truth is merely an indexical way to keep track of the eventual outcomes of the things symbolised. As Wimsatt once said, genes are a way of "bookkeeping" in evolution. Truth is a way of doing the same thing in reasoning.
Read the book if you have an interest in logic and evolution. Let me know if I have been unfair to Cooper. I very much wanted him to succeed, but I very much doubt that he has, at least in doing what I wanted him to do. We have to naturalise logic and reason, for they must be natural. But this is not the way to do it, I think.
Cooper has a schematic for "life strategies". They look like this:
The way to think of this is to regard it as a branching diagram of the probabilities of outcomes in a population. An organism - say, a vole - that faces predation has, say, two alternative strategies - to dig and hide or to flee its predators. If it flees, it has a .1 likelihood of getting away, and if it survives it has 1.4 progeny per survivor, the average for this vole. So the fitness of the FLEE branch is 1.4 times .1 = .14. Of course, those that are eaten have a fitness of 0 in this artificial example.
But the other strategy is DIG, and here .36 are consumed anyway, while .64 escape. The fitness that results from DIG is therefore .64 times 1.4 progeny, or .9. So, the DIG strategy is the one that will take over the vole population, because eventually all the FLEEing voles will be eaten. [Note that this population is doomed anyway, because the replacement of voles once all the FLEEers have been eliminated is 9/10 per generation. Selection can drive populations to extinction.]
Now Cooper want to use these diagrams as a basis for deriving, first decision theory, then inductive logic, then deductive logic, mathematics, and so on. Why this? Well, he believes as others have before him that logic evolved (Wigner and Hamming's point) and that therefore the logic must be somehow a subset of evolution.
I disagree with the motivation. Logic evolved - so too did over-optimism (those who are unduly optimistic about their abilities achieve beyond their skills more than those who have a realistic self-assessment). That doesn't mean that evolution is over-optimistic. Moreover, the "logic" of evolution is the mathematics of populations genetics - so are we just describing a circular relation here?
And that logic includes stochastic processes as well - drift in particular, but also peripheral population founder-effect sampling (atypical distributions of alleles in populations at the edge of a range of a species) - are all these to be characterised in terms of the selective fitness of strategies? Perhaps we should recall Ghiselin's comment and move on.
The diagrams are, however, rather an elegant way of representing selectively biased processes. While it is hardly a major revelation that a population's allele frequencies are iteratively added, as a flow diagram it is a useful way to make the implications of larger and more complex situations easy to follow.
A logic of evolution is yet to be worked through. I think that it will be many-valued (continuously as Cooper has shown it - the "truth-value" of an evolutionary trait ranges from 0 (false, or totally unfit) through to 1 (true, or totally fit). However, this sort of truth is merely an indexical way to keep track of the eventual outcomes of the things symbolised. As Wimsatt once said, genes are a way of "bookkeeping" in evolution. Truth is a way of doing the same thing in reasoning.
Read the book if you have an interest in logic and evolution. Let me know if I have been unfair to Cooper. I very much wanted him to succeed, but I very much doubt that he has, at least in doing what I wanted him to do. We have to naturalise logic and reason, for they must be natural. But this is not the way to do it, I think.
posted by John S. Wilkins @ 4:09 pm
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