It is said that logic is "the science of what follows from what." This is exactly right. Indeed, you may well consider this a first attempt to nail down our subject matter. Obviously the characterization is imprecise, but imprecision in this matter will be unavoidable at the outset of a course in logic -- but only at the outset. Logic is indeed a science: it is rigorous; it is symstematizable; and (above all else) it is objective. In saying that it is objective, one is saying (at a minimum) that there is a solid core of logic with which all rational individuals ought to agree, and that this solid core is immune to our subjective impressions, our intuitions, our gut instincts about what exactly follows from what.
Taken from Chapter One: Propositional Logic: A Formal Language, Part One from "Classical Logic and its Rabbit Holes, A First Course" by Nelson P. Lande.