TimS comments on Making Beliefs Pay Rent (in Anticipated Experiences) - Less Wrong
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That's much clearer. I didn't intend to assert that falsifiability was a sufficient condition for a theory being scientific, only that it is a necessary condition. That's what I mean by saying it was a partial definition.
Thus, I don't intend to assert the first sentence of your syllogism. Instead, I would say, "If a hypothesis is not falsifiable, then it is not scientific." Adding the second statement yields: "If a hypothesis is know to be false, then it might be scientific." That's a true statement, but I don't claim it is very insightful.