Philosophy in a nutshell

How should we live? What really exists? And how do we know for sure? 

These three questions are at the heart of philosophy as an academic discipline.  This raises the question as to what the "philosophy of physics" is and what it should be? Philosophy of Physics: A Very Short Introduction by David Wallace explores this. He begins by stating that "Daniel Dennett defines philosophy as what we do when we don't know what questions to ask." I found that somewhat unsatisfying and went to The Oxford Companion to Philosophy. 

Most definitions of philosophy are fairly controversial, particularly if they aim to be at all interesting or profound. That is partly because what has been called philosophy has changed radically in scope in the course of history, with many inquiries that were originally part of it having detached themselves from it. The shortest definition, and it is quite a good one, is that philosophy is thinking about thinking. That brings out the generally second-order character of the subject, as reflective thought about particular kinds of thinking—formation of beliefs, claims to knowledge—about the world or large parts of it.

A more detailed, but still uncontroversially comprehensive, definition is that philosophy is rationally critical thinking, of a more or less systematic kind about the general nature of the world (metaphysics or theory of existence), the justification of belief (epistemology or theory of knowledge), and the conduct of life (ethics or theory of value). 

Each of the three elements in this list has a non-philosophical counterpart, from which it is distinguished by its explicitly rational and critical way of proceeding and by its systematic nature. 

Everyone has some general conception of the nature of the world in which they live and of their place in it. Metaphysics replaces the unargued assumptions embodied in such a conception with a rational and organized body of beliefs about the world as a whole. 

Everyone has occasion to doubt and question beliefs, their own or those of others, with more or less success and without any theory of what they are doing. Epistemology seeks by argument to make explicit the rules of correct belief-formation. 

Everyone governs their conduct by directing it to desired or valued ends. Ethics, or moral philosophy, in its most inclusive sense, seeks to articulate, in rationally systematic form, the rules or principles involved. 

The three main parts of philosophy are related in various ways. For us to guide our conduct rationally we need a general conception of the world in which it is carried out and of ourselves as acting in it. Metaphysics presupposes epistemology, both to authenticate the special forms of reasoning on which it relies and to assure the correctness of the large assumptions which, in some of its varieties, it makes about the nature of things, such as that nothing comes out of nothing, that there are recurrences in the world and our experience of it, that the mental is not in space.

On the lighter side here is Philomena Cunk's brief engagement with philosophy.