"Some ungentle reader will check us here by informing us that philosophy is as useless as chess, as obscure as ignorance, and as stagnant as content. “There is nothing so absurd,” said Cicero, “but that it may be found in the books of the philosophers.” Doubtless some philosophers have had all sorts of wisdom except common sense; and many a philosophic flight has been due to the elevating power of thin air. Let us resolve, on this voyage of ours, to put in only at the ports of light, to keep out of the muddy streams of metaphysics and the “many-sounding seas” of theological dispute. But is philosophy stagnant? Science seems always to advance, while philosophy seems always to lose ground. Yet this is only because philosophy accepts the hard and hazardous task of dealing with problems not yet open to the methods of science—problems like good and evil, beauty and ugliness, order and freedom, life and death; so soon as a field of inquiry yields knowledge susceptible of exact formulation it is called science. Every science begins as philosophy and ends as art; it arises in hypothesis and flows into achievement. Philosophy is a hypothetical interpretation of the unknown (as in metaphysics), or of the inexactly known (as in ethics or political philosophy); it is the front trench in the siege of truth. Science is the captured territory; and behind it are those secure regions in which knowledge and art build our imperfect and marvelous world. Philosophy seems to stand still, perplexed; but only because she leaves the fruits of victory to her daughters the sciences, and herself passes on, divinely discontent, to the uncertain and unexplored."

Even the Juris Doctor is a branch of philosophy. After all, what is justice?

Not a crazy idea – that is called logic. Which is a field of philosophy. Philosophy and math intersect more than many people think.