What can science prove?

[Tiberius]

In the first instance I simply asserted that it cannot be said science is incapable of conclusively proving anything. Nonetheless, I'll give your challenge a try. Not only are a priori facts defacto conclusive, but so are posteriori facts. Therefore, we can trust that (for example) tunafish exist.

Your use of words I believe reveal the flaw behind your position. You say we can "trust" that tunafish exist, yet trust is not proof, and proof is what we are arguing about here. I do not dispute that science is a measure of probability of something being true, and the highly the probability, the more trust we put into the result, but to say that something is knowledge (i.e. 100% certain) is ridiculous given the nature of science.

Assuming the fundamental laws of the natural world remain unaltered:

1) All fish now living on earth eventually die
2) Tuna is a type of fish now living on earth
3) Therefore, all tunafish now living on earth will eventually die

You are assuming what you set out to prove, that science can prove certain things. The natural laws are descriptions of reality that come from scientific observation; they are not laws in the sense that they can never be refuted or changed.

I'd also like to see the proof that all fish on Earth eventually die, also the proof that tuna is a type of fish (and whilst you are at it, that fish exist). There is an interesting thread here called "Prove China exists" or something; I suggest you take a look as in it we discussed the nature of science, and how it cannot prove anything.

It is true that scientists haven't observed every single tuna fish in our oceans. However, the volumes of data they've collected over the centuries with regard to aquatic life makes statements one and two posteriori knowledge. Therefore, through simple deductive reasoning we arrive at the conclusion that all tunafish now living on earth will die (with no exceptions).

Deductive reasoning isn't proof, and bringing up the volumes of data is an argumentum ad populum of sorts. No amount of data can prove something, as a single piece of data can destroy a theory. If, for instance, we find fossil rabbits in the pre-cambrian, Evolution by Natural Selection as we know it will be disproved. I should also point out that "with no exceptions" relies on data collected up to this point; you cannot tell the future, so you cannot know whether there will be exceptions in the future.

This argument is affirmative, however, it also applies in the negative. Here, we can say science has conclusively ruled out the possibility that any tunafish now living on earth can be immortal (and we can say this conclusively). I'm just playing around with the logic here. In truth the fact that all tunafish on earth will eventually die is itself posteriori knowledge (and doesn't require a deductive argument to prove it). By caveat of the same sort of data science can use to prove all fish now living on earth will die, they can prove all tunafish on earth die. Therefore, the same applies in the negative (e.g. they can rule out the possibility of an immortal tunafish; and that conclusion is posteriori knowledge based on scientific data).

You haven't demonstrated how it is knowledge at all. All you have demonstrated is that you think knowledge depends on the largest amount of data available...it doesn't. You have provided no proof, only reasoning based on an assumption of materialism and data collection. If materialism isn't true, your "proof" evaporates. If the data collection changes to support another theory, your "proof" evaporates.

The idea of a proof is that it cannot possibly evaporate under any circumstances. Otherwise it wouldn't be a proof...