14 Nov '09 17:24>
Originally posted by PalynkaOn likelihood, I think it is important to think about what considerations of probability might legitimately allow us to do, and what they can't.
As to likelihood, there are two issues.
First, it's clear that to claim that evolution says anything about likelihood of survival we would required to take the first interpretation. Because if the mapping is from G' to G, then there is no stochasticity involved anymore and so no possible claim on likelihood. It's simply a question of labelling the mapping. ...[text shortened]... instead. Making the first claim (about likelihood), is then comparing these two populations.[/b]
So first let's distinguish between the countless events of reproduction and death and all the causal factors involved therein over time on the one hand. On the other hand we have our theoretical explanatory framework called the modern evolutionary synthesis.
When we consider probabilities, we are thinking and using the latter to explain some features of the former. In your criticism of my position you have called into question whether an a posteriori appraisal of a situation by extrapolation back in time from G' to G allows us to talk about probability.
I think your objection, that there is no stochasticity involved anymore and so no possible claim on likelihood, is flawed. To see why, let's turn to a national lottery game in order to ask which questions might make sense and which would fall foul of your objection.
Imagine that the game is run by having a set of balls numbered 1 to 49 released into a machine like a transparent rotating sphere. (We assume the balls are the same size and made out of the same material.) A mechanism, when triggered, allows six balls out.
A question that would fall to your objection would be something like this:
i) Oh look, the result this week was 2, 7, 8, 9, 28, 31. What are the chances of that?
The question isn't sensible in that the answer is 1 if we treat the question literally. But the philosophical fun begins if we interpret i) to mean:
ii) What were the chances of that at time t-100?
Now it is not clear that ii) can be ruled out, since if we allow the concept of stochasticity at all, we can see that at time t-100 it still applies.
Now let us suppose that a group of statisticians had no access to the actual draws and didn't know the details of the ball or machines, but they did have all the data for the results of the draws carried out to date. With suitable analysis, and providing the weekly draw had been going for a good few years, they would rationally be able to deduce that the system involved the random selection of six numbers from 49. At that point they would rationally be able to conclude something like:
iii) 'at time t=0, the probability that, for the subsequent ten years the same result would recur for every draw was less than the probability that different sets of numbers would occur.'
They might even indulge in some shorthand by saying
iv)'the machine is more likely to select different numbers each week than the same ones over and over again'.
It is my contention that your objections, and Bosse's are analogous to somebody criticising iv) above by saying that the machine has already done it, so there's no stochasticity so we can't talk of likelihood, and (in Bosse's case) saying that the machine has no mind so it can't select anything.
So I don't think your objection works.