There are two primary methods of argumentation; one is to make use of the observable and empirical facts, which is called empiricism, the other is to solely rely on ontological reasoning and a priori logic, which is what I will call Medieval logic, because that was the method that the philosophers and theologians of the Medieval ages used. To give an example of each of these methods being utilized, I will present a hypothesis and will support it with just empiricism and then with just ontological reasoning.
My Hypothesis is this: Creating the Federal Reserve, contrary to its initial purposes, has created more monetary instability and inflation than would otherwise be the case if it were never established. Now then, if I were to take an empirical approach in demonstrating my case, I would make use of the facts and inflation statistics since its establishment in 1913, which show tremendous inflation and several boom-bust cycles, then I would juxtapose that data with what happened at a time where there was no central bank. If the observable facts show that there was more inflation with a central bank than there was with a gold standard, for example, then my argument is sound from an empirical approach.
But if I were to try to prove my hypothesis through logical means, then I would say that that is exactly what a central bank does, it prints money, and that if money is not connected to gold or silver or whatever, then inflation is bound to happen.
As it happens, both approaches lead to the same conclusion. But sometimes it is not always that simple. To give a recent example, conservatives rightly concluded the Obama stimulus package failed because it didn't bring unemployment down to its intended levels. Paul Krugman, however, has not let the observable facts get in the way with his philosophical pre-conceptions, as he has invariably stated that the stimulus package was "too small" and wasn't "applied properly," which is why it didn't work. This is why Murray Rothbard has argued that only logic can reliably test an economic theory, which explains the Austrian distaste for empiricism and emphasis on arguing by first principles and fundamental axioms (more on that later).
But sometimes just relying on philosophical reasoning can also lead to wrong conclusions. This is especially true with regards to human behavior. Because human action is seldom rational, and thus not easily predictable, taking a logical approach is bound to produce wildly inaccurate results.
For these reasons, it is shaky to solely base an argument on one or the other. And that the most effective argument is the one that utilizes both methods.
A perfect example is the case against Socialism. In 1922, Ludwig von Mises published a paper in which he argued that Socialism precluded rational economic calculation. Capitalism solves this through a price point, which is determined by supply and demand. But where the government owns the means of production, there can be no price point, and thus no room for economic calculation. This was a sound philosophical thesis, but it was only when the mass of observable failures in the countries where Socialism was enacted was the theory largely abandoned.
So while it is true that the proper balance between philosophical reasoning and empiricism differs from field to field, it is almost surely wise to be makes of both methods; to cite the relevant facts and then explain logically why this should be the case.