Probabilistic palaeo
Guessing biological events in the past is often highly probabilistic; physical laws usually aren't. As many, e.g. John Damuth, have pointed out, there is a certain difference in character here. The basic Popperian refutation process requires certainty since it involves standard deduction. If nothing is certain, then the apparent absence of B tells you nothing for certain about A.
But that doesn't mean all is lost and we have to give up. There are fairly well understood formal ways of dealing with uncertainty, and in any case, the world is assumed by people in everyday life to be uncertain however sound our techniques may be for dealing with it, so we shouldn't be too shocked.
Change from a basis of certainty to one of probability, and suddenly positive and negative evidence acquire a much more equal status. Popper knew this of course, and suggested in 1959 that hypotheses should be rejected when they say that what we observe is very improbable. I would say identification of refutation scenarios is now more complex - and of course it's hard to say something is untestable.
We can though cope with uncertain evidence. However, not everything in palaeontology is irredeemably fuzzy. A theory claiming powered feathered flight originated in the Late Jurassic would be 100% refuted by a perfect fully articulated Early J typical enant bird.
It's a good job we can work with probability, because if we throw out Popper's definition of science, what is the alternative? Even if we understood induction, a consensus on it's use in the scientific process is a long way off. We're just going to have to rely on refutation in a somewhat probabilistic context.
That's what I say. Some say: "Popperianism isn't really suitable for phylogenetic investigation, and although we don't actually have any remotely consistent code to replace it with (unless you count our dependence on parsimony), we'll retain the bit of pure Popper by which we brand theories we don't like (almost always wrongly) as untestable, and various other snippets we find it contingent to trot out from time to time."
I'll leave you to decide which makes less sense.
So we needn't worry about these three problems for Popperianism:
the comparison of incompatible paradigms doesn't apply to us,
the probabilistic requirement can be adapted to,
and the return to the golden calf of inductionism as a criterion for science is premature and unnecessary.
So why not just keep an open mind?
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