What is philosophy?

The aim of philosophy, abstractly formulated, is to understand how things in the broadest possible sense of the term hang together in the broadest possible sense of the term. Under 'things in the broadest possible sense' I include such radically different items as not only 'cabbages and kings', but numbers and duties, possibilities and finger snaps, aesthetic experience and death. To achieve success in philosophy would be, to use a contemporary turn of phrase, to 'know one's way around' with respect to all these things, not in that unreflective way in which the centipede of the story knew its way around before it faced the question, 'how do I walk?', but in that reflective way which means that no intellectual holds are barred.
Wilfrid Sellars

The word philosophy means the love of wisdom, but what philosophers really love is reasoning. They formulate theories and marshal reasons to support them, they consider objections and try to meet these, they construct arguments against other views. Even philosophers who proclaim the limitations of reason—the Greek skeptics, David Hume, doubters of the objectivity of science—all adduce reasons for their views and present difficulties for opposing ones. Proclamations or aphorisms are not considered philosophy unless they also enshrine and delineate reasoning.
Robert Nozick

The point of philosophy is to start with something so simple as not to seem worth stating and to end with something so paradoxical that no one will believe it.
Bertrand Russell

Philosophy is an activity that uses reasoning and rigorous argument to promote human flourishing.