“But scientific induction can lead to conclusions that have been validated to such a degree that we can comfortably act as if they are true.” This assumes induction, such as the swan hypothesis being near-certain. I tend to accept induction in terms of probability/confidence, but I don’t know how Popper would view that kind of reasoning…

“If the speed of light were not constant and changed over time we could detect it. Therefore the constancy of the speed of light is falsifiable, but so far has been verified.” This begs the question that the speed tests are correct, which goes back to assuming induction (that the test is valid) and the issue of which theory to reject. This tends to be an issue with Popper’s Critical Rationalism.

1) Technically, our current measurement standards already assume that the velocity of light is constant, so they cannot be used to validate that assumption. However, people just use different standards when testing for its constancy.

2) The principle of uniformity is a priori true because it is informatively empty. All it says, essentially, is that physics is looking for those aspects of nature which are universally regular. Since it doesn’t stipulate what these are, or even if there are any, the principle is trivially true. All that our experience can do is push such patterns to new heights of abstraction. For example, when we found out that spacetime is expanding we didn’t say the laws of nature change so that space expands – instead, we formulated new eternal laws that included the expansion. The question is therefore not whether the principle is justified, but whether it is practical – whether it is useful to describe nature via universal patterns. As Steven brilliantly showed, it is.

“Inference is any act of deliberate assent, in any degree, however slight, which a man accords to a proposition because he thinks that assent warranted by his already accorded assent to another proposition or propositions, called the premises. It is one act of inference to adopt a hypothesis on probation. Such an act may be called an abduction. It is an act of the same kind, when a hypothesis is merely suggested as possible worth consideration. For even then some degree of favor is extended to it.” (‘Hume’s Argument against Miracles, and the Idea of Natural Law (Hume)’, MS 873: (Variant) 3, n.d.)

Hume felt that at best we could create were “constant conjunctions” between an object and our experiences with that object. At least he was being honest enough so that we as a scientific community could understand how to rightfully approach our empirical knowledge when considered under the light of possible logical systems.

Kant took it a step further and stated that we will never know objects in and of themselves, only the way that they appear to us under our personal sensibility. He even went as far as to create a logical system that accounts for logical truths that could be arrived at by any sensibility, logical truths that arise from human sensibility alone, and logical truths that transcend our sensibilities but are still dependent on the initial thought that they create.

And even more disconcerting for mathematicians and scientists is that any time they try to show a model is internally consistent, some jerk comes along and shows it leads to a contradiction unless some other mathematical or logical system can intervene to account for the contradiction (or they just define the terms in such a way that the contradiction is side-stepped).

With this in mind, science is still the strongest epistemological argument, because our minds are already ill-equipped to handle objective metaphysical truths (as shown by our models and limitation of sensibility), but with science, we at least keep gathering new data to allow possibility of building upon our sensibilities and refining our models. Without science, we would most likely would give up once our knowledge hit a contradiction (unless we were content with living based on contradictory knowledge).

Yes, this is the classic Hume dilemma – which I guess I should have mentioned. Massimo goes more into the philosophy and spends less time on the solution, which I think I summarized adequately above. But I think his take is in basic agreement with mine.

By DeMorgan’s Tautology, (P ^ ~Q)

Therefore, by conjunction,

“God exists” (P)

and

“Flies are not insects” (~Q)