“Free Will” is a philosophical term of art for a particular sort of capacity of rational agents to choose a course of action from among various alternatives. Which sort is the free will sort is what all the fuss is about. (And what a fuss it has been: philosophers have debated this question for over two millennia, and just about every major philosopher has had something to say about it.) Most philosophers suppose that the concept of free will is very closely connected to the concept of moral responsibility. Acting with free will, on such views, is just to satisfy the metaphysical requirement on being responsible for one's action. (Clearly, there will also be epistemic conditions on responsibility as well, such as being aware—or failing that, being culpably unaware—of relevant alternatives to one's action and of the alternatives' moral significance.) But the significance of free will is not exhausted by its connection to moral responsibility. Free will also appears to be a condition on desert for one's accomplishments (why sustained effort and creative work are praiseworthy); on the autonomy and dignity of persons; and on the value we accord to love and friendship. (See Kane 1996, 81ff. and Clarke 2003, Ch.1; but see also Pereboom 2001, Ch.7.)
The principle of set theory known as the Axiom of Choice has been hailed as “probably the most interesting and, in spite of its late appearance, the most discussed axiom of mathematics, second only to Euclid’s axiom of parallels which was introduced more than two thousand years ago” (Fraenkel, Bar-Hillel & Levy 1973, §II.4). The fulsomeness of this description might lead those unfamiliar with the axiom to expect it to be as startling as, say, the Principle of the Constancy of the Velocity of Light or the Heisenberg Uncertainty Principle. But in fact the Axiom of Choice as it is usually stated appears humdrum, even self-evident. For it amounts to nothing more than the claim that, given any collection of mutually disjoint nonempty sets, it is possible to assemble a new set—a transversal or choice set—containing exactly one element from each member of the given collection. Nevertheless, this seemingly innocuous principle has far-reaching mathematical consequences—many indispensable, some startling—and has come to figure prominently in discussions on the foundations of mathematics. It (or its equivalents) have been employed in countless mathematical papers, and a number of monographs have been exclusively devoted to it.
Most of us are certain that we have free will, though what exactly this amounts to is much less certain. According to David Hume, the question of the nature of free will is “the most contentious question of metaphysics.” If this is correct, then figuring out what free will is will be no small task indeed. Minimally, to say that an agent has free will is to say that the agent has the capacity to choose his or her course of action. But animals seem to satisfy this criterion, and we typically think that only persons, and not animals, have free will. Let us then understand free will as the capacity unique to persons that allows them to control their actions. It is controversial whether this minimal understanding of what it means to have a free will actually requires an agent to have a specific faculty of will, whether the term "free will" is simply shorthand for other features of persons, and whether there really is such a thing as free will at all.
“Philosophy of Economics” consists of inquiries concerning (a) rational choice, (b) the appraisal of economic outcomes, institutions and processes, and (c) the ontology of economic phenomena and the possibilities of acquiring knowledge of them. Although these inquiries overlap in many ways, it is useful to divide philosophy of economics in this way into three subject matters which can be regarded respectively as branches of action theory, ethics (or normative social and political philosophy), and philosophy of science. Economic theories of rationality, welfare, and social choice defend substantive philosophical theses often informed by relevant philosophical literature and of evident interest to those interested in action theory, philosophical psychology, and social and political philosophy. Economics is of particular interest to those interested in epistemology and philosophy of science both because of its detailed peculiarities and because it possesses many of the overt features of the natural sciences, while its object consists of social phenomena.
Science is an enormously successful human enterprise. The study of scientific method is the attempt to discern the activities by which that success is achieved. Among the activities often identified as characteristic of science are systematic observation and experimentation, inductive and deductive reasoning, and the formation and testing of hypotheses and theories. How these are carried out in detail can vary greatly, but characteristics like these have been looked to as a way of demarcating scientific activity from non-science, where only enterprises which employ some canonical form of scientific method or methods should be considered science (see also the entry on science and pseudo-science). On the other hand, more recent debate has questioned whether there is anything like a fixed toolkit of methods which is common across science and only science.