Reading through the philosophy threads I see a lot of people talking about Popper/falsificationism and philosophy of science in general. So I thought I'd start a thread that was more specific.
Do you work with stats in your field? Do you favour a bayesian or frequentist approach? If not, what do you think of stats/probability in general?
I keep meaning to read ET Jaynes' Probability Theory The Logic Of Science [1] but haven't got around to it yet. Overall it seems to me that the bayesian/information theoretical approach solves most of the unresolved philosophy of science questions. For example, people often say that 'it only takes one contradictory experiment to falsify a theory' but this assumes perfect evidence (i.e. no experimental error) which clearly isn't right. The solution is to look at the prior probability of the truth of a proposition, and compare that with what the evidence is telling you. The only way to do this rigorously is to use Bayes' Theorem.
Or maybe you disagree?
I think statistics are important in all fields of science, because they are a tool to deal with incompleteness of information. But sometimes you don't need completeness of information to falsify a theory, and hence you don't need statistics or probabilities for that job.
Let's say you design a theory that predicts that insects cannot structurally be bigger than 50 cm. Then it only takes you 1 bigger sized insect (or fossil of it) to disprove the theory. You don't need statistics for that. On the same vein, if you have a theory that predicts that birds descend from mammals and not dinosaurs, it only takes one fossil of a feathered dinosaur to disprove your theory, no need for statistics or probabilities. Of course, IRL things are not so neat. Predictions are usually tested at the detection limit of the current technologies (otherwise they would have been tested before), there is lots of information incompleteness, and you need statistics and probabilities to qualify the results. Let's assume you had a theory that the Earth is flat. Nowadays, it would take a single satellite snapshot of the Earth to disprove your theory. But at the time at which this was still a scientific issue, technologies were much worse, and the measurements required to disprove earth flatness would probably have required some statistics and probabilities to compensate for information incompleteness.
So I disagree with your assertion that "the bayesian/information theoretical approach solves most of the unresolved philosophy of science questions". Mathematics are used in all sciences, but for sure do not solve scientific or philosophical issues.
BTW: your link is not working anymore, I could only access it through googlecache.