To supplement @JosephO'Rourke's good answer, I would note that the "logicist" philosophy of mathematics is by no means inclusive of mathematical practice... by a long shot... despite various enthusiasts' tendency to implicitly or explicitly claim that first-order logic is the underpinning for mathematics, that formal set theory (axiomatized in first-order logic) is the next layer, ... and, supposedly, everything else is superstructure. An afterthought.
But, srsly, apart from the haute-bourgeois pretenses (however clever) of the (slave-holding, not-working...) classical Greeks, it is easily arguable that the true appeal of mathematics for human civilization is its explanatory power about actual phenomena in the world... even phenomena human-abstracted from chaotic physical events.
I would claim that "mathematical logic", and, to a much lesser degree, "logic" in a more general sense, is a program of backfilling upon realization of weaknesses in prior understanding. Not with the expectation that very much is truly in error, but that the same truths need deeper foundations from some viewpoint...
Thus, in particular, to only look at "(mathematical) logic" is to look at a sort of symptom rather than cause or most substantial effect. Thus, analysis of this symptom, no matter how energetic, can scarcely manage to divine the real events, causes, and causalities.