Probabilistic Arguments in Philosophy

So here's a sort of trivial, but I think interesting, observation about probabilistic arguments in philosophy:

There are two criterion for the soundness of a deductive argument: That its conclusion follow from its premises, and that its premises be true. The former is self-explanatory, but the latter is interesting. Typically, what a philosopher means by the truth of the premises of an argument is really just that the premise(s) be more likely than their negation. In essence, then, the soundness of a deductive argument is partially judged by a sort of loose probability, e.g. the probability of the given premises being true relative to their negations. But then, is there really a significant difference between, say, the following two arguments:

A1.

(1) If the sun has risen every day until now, it will rise tomorrow.
(2) The sun has risen every day until now.
(3) Therefore, the sun will rise tomorrow.

A2.

(1) If the sun has risen ever day until now, it will probably rise tomorrow.
(2) The sun has risen every day until now.
(3) Therefore, the sun will probably rise tomorrow.

The only difference between (A1) and (A2), it seems to me, is the following: In (A1) the question of the probability of the given premises being true is a meta-argumentative issue (you judge whether or not the premises are true apart from the argument itself). In (A2), the question of the probability of the premises is built into the argument itself. When you ask of premise 1 of (A1), "does the consequent in the conditional follow from its antecedent?" you're asking for a judgment that can only be assessed a posteriori, probabilistically. Premise 1 of (A2) just assumes the a posteriori work has already been done. So really, the difference between the two is more in form than in kind.

Of course, this isn't true of all deductive/inductive arguments. In some arguments with conditionals and/or biconditionals, the consequent of the conditional necessarily follows from its antecedent in an analytic way, as in "If one is a bachelor, then one is unmarried". But the point is this: Philosophers tend to use arguments they would think of as deductive just because of their structure, but which would need a posteriori evidence to confirm or disconfirm the truth of their premises. But the fact is that many of these arguments are easily transformed into inductive arguments.