Differentiate philosophy from other branches of thought. -Why is philosophy not science? Why is philosophy not religion? Why is philosophy not myth? — David Mo
...no definition of philosophy would be complete without demarcating it from those other fields, showing where the line lies between philosophy and something else.
Philosophy is not Religion
The first line of demarcation is between philosophy and religion, which also claims to hold answers to all of those big questions. I would draw the demarcation between them along the line dividing faith and reason, with religions appealing to faith for their answers to these questions, and philosophies attempting to argue for them with reasons. While it is a contentious position within the field of philosophy to conclude that it is never warranted to appeal to faith, it is nevertheless generally accepted that philosophy as an activity characteristically differs from religion as an activity by not appealing to faith to support philosophical positions themselves, even if one of those positions should turn out to be that appeals to faith are sometimes acceptable. The very first philosopher recognized in western history, Thales, is noted for breaking from the use of mythology to explain the world, instead practicing a primitive precursor to what would eventually become science, appealing to observable phenomena as evidence for his attempted explanations.
Philosophy is not Sophistry
Despite turning to argumentation to establish its answers, philosophy is not some relativistic endeavor wherein there are held to be no actually correct answers, only winning and losing arguments. While there are those within philosophy who contentiously advocate for relativism about various topics, philosophy as an activity is characteristically conducted in a manner seeking out answers that are genuinely correct, not merely seeking to win an argument. Though the historical accuracy is disputed, a founding story of the classical era of philosophy ushered in by Socrates, at least as recounted by his student Plato, is that philosophers like them were to be distinguished from the prevailing practitioners of reasoned argumentation of their time, the Sophists, who on Plato's account were precisely such relativists uninterested in genuine truth, only in winning. It is from that account that the contemporary use of the word "sophistry" derives, meaning wise-sounding but secretly manipulative or deceptive argumentation, aimed more at winning than at finding the truth. And whether or not the historical Sophists actually practiced such argumentation, philosophy since the time of Socrates has defined itself in opposition to that.
Philosophy is not Science
What we today call "science" was once considered a sub-field of philosophy, "natural philosophy". This had been the case for thousands of years since at least the time of Aristotle, such that even Issac Newton's seminal work on physics, often considered the capstone of the Scientific Revolution, was titled "Mathematical Principles of Natural Philosophy". But increasingly since then, what was once considered a sub-field of philosophy is now considered separate from it. What remains still as philosophy is demarcated from science in that while philosophy relies only upon reason or evidence to reach its conclusions, rather than appeals to faith, as an activity it does not appeal to empirical observation either, even though within philosophy one may conclude that empirical observation is the correct way to reach conclusions about reality. It is precisely when one transitions from using empirical observation to support some conclusion, to reasoning about why or whether something like empirical observation (or faith, or so on) is the correct thing to appeal to at all, that one transitions from doing science to doing philosophy.
Philosophy is not Ethics
One may be tempted to conclude that this means philosophy is entirely about prescriptive matters, rather than descriptive ones; that philosophy is all about using reason alone, without appeals to faith, to reach conclusions not about what is or isn't real, but about what one ought or ought not do, or broadly speaking, about morality. In other words, that philosophy is equivalent to the field of ethics. But as described just previously, philosophy does treat other topics concerning not just morality but also reality, at least the topics of how to go about an investigation of what is real. And while ethics is currently considered soundly within the field of philosophy, I contend that it properly should not be, for I hold that there are analogues to the physical sciences, what we might call the ethical sciences, that I consider to be outside the domain of philosophy, in that they appeal to specific, contingent hedonic experiences in the same way the physical sciences appeal to specific, contingent empirical experiences. I hold that philosophy bears the same kind of relation to both the physical and the ethical sciences, providing the justification for each to appeal to their respective kinds of a posteriori experiences, while never itself appealing to either of them, instead dealing entirely with a priori reasoning.
Philosophy is not Math
That in turn may raise the question of how philosophy is to be demarcated from mathematics, which also deals entirely with a priori logical reasoning without any appeal to a posteriori experience. Indeed in some ancient philosophy, such as that of Pythagoras, mathematics and philosophy bleed together in much the same way that what we now consider the separate field of science once did with philosophy as well. But today there is a clear distinction between them, in that while philosophy and mathematics share much in common in their application of logic, they differ in that mathematical proofs merely show that if certain axioms or definitions are taken as true, then certain conclusions follow, while philosophy both does that and asserts the truth of some axioms or definitions. So while mathematics says things of the form "if [premise] then [conclusion]", philosophy says things of the form "[premise], therefore [conclusion]". Mathematics explores the abstract relations of ideas to each other without concern for the applicability of any of those ideas to any more practical matters (although applications for them are nevertheless frequently found), but philosophy is directly concerned with the practical application of the abstractions it deals with. It is not enough to merely define axiomatically some concept of "existence", "knowledge", "mind", etc, and validly expound upon the implications of that concept; it also matters if that is the correct, practically applicable concept of "existence", "knowledge", "mind", etc, that is useful for the purposes to which we want to employ that concept.
Philosophy is not Art
Similarly, philosophy has many similarities to the arts, broadly construed as communicative works presented so as to evoke some reaction in some audience. Philosophy is likewise an evocative, more specifically persuasive, discipline, employing not just logic, as with mathematics above, but also rhetoric, to convince its audience to accept some ideas. But philosophy is not simply a genre of literature. Whereas works of literature, like all works of art, are not the kinds of things that are capable of being correct or incorrect, in the way that scientific theories are, but rather they are only effective or ineffective at evoking their intended reactions, with works of philosophy correctness matters. It is not enough that a philosophical theory be beautiful or intriguing; a philosopher aims for their theories to be right.