Much of the time philosophers study what other people take for granted. They ask "Why?" and "How?" when others are content to accept what seems obvious and in need of no justification. Philosophy thus involves explanations, arguments, and their critical evaluation. Here argument is meant not in the sense of dispute or controversy but in the sense of "arguing (for or against)", or "making a case (for or against)".
In evaluating arguments and explanations two features are significant: whether the premises, the "starting points", are jointly plausible; and whether what is said to follow from them does so. When we reflect on these features we arrive at logic: the systematic study of what follows from, and of the relations that hold within and between, bodies of belief, loosely speaking. (Loosely speaking, for in logic we are not so much concerned with what we do accept or believe rationally and what inferences we in fact make but with rather what one could so accept or believe and what inferences one would be warranted in making whether or not one actually does so.)
As an attempt at a systematic theory logic has to start somewhere. Its "raw data" are our intuitions, our inferential practice, and our reflective judgments. Now, we have no guarantee that these cohere well: in fact there are tensions. At the very least, we may find it difficult to construct a systematic account that accommodates all, or even most, of the raw data. A systematic theory may therefore lead us to refine (i.e. revise) our intuitions and change our practice. Logic is a much less cut-and-dried affair than many text-books suggest.
Formal logic constitutes a "body of knowledge", not in the sense that all its findings are incontrovertible facts but somewhat in the same way as moral philosophy does: in each case there is a standard set of concepts, theories involving those concepts, forms of argument and a ragbag of tricky cases that is played off against intuitions, and perhaps used to subject those intuitions to critical scrutiny and to refinement. Formal logic is also more like the sciences than is any other part of philosophy: it aims at a systematic account of a body of "phenomena" on which there is fairly widespread agreement and in order to do so it uses formal methods of representation (a feature of logic that goes back to the ancient Greeks) and formal techniques. Formal logic is formal in that it seeks to give a systematic account of the validity of individual arguments only insofar as they exemplify certain "patterns of argument". Patterns, or forms, of argument are the main object of study. It is this feature of logic that allows us to establish some results in and about logic with the same exactness as one encounters in mathematics (but at least when logic is studied as part of philosophy one should not lose sight of the wider goal).
Two further considerations are often given as reasons for studying logic:
Logic is "therapeutic": one learns logic in order to become better able to recognize and to construct good arguments (in philosophy or any other discipline).
Formal logic is an indispensable item in the contemporary philosopher's toolkit.
Learning about any systematic discipline improves one's own abilities in thinking systematically. And certainly, the methods and techniques of formal logic are used by some philosophers, mostly those working in philosophy of language and philosophy of science. Two text-books that integrate formal logic into a range of topics in philosophy are Brenner's Logic and Philosophy and Bradley and Swartz'sPossible Worlds.
Further reading:
The two "Introductions", by Quine and Strawson, reprinted as Chapters 1 and 2 of R. I. G. Hughes, ed., A Philosophical Companion to First-Order Logic, Indianapolis: Hackett, 1993.
Mark Sainsbury, Logical Forms, Oxford: Blackwell, 1991, Chapter 1, Section 1.
William Brenner, Logic and Philosophy: An Integrated Introduction, Notre Dame: University of Notre Dame Press, 1993.
Raymond Bradley and Norman Swartz, Possible Worlds: An Introduction to Logic and Its Philosophy, Oxford: Blackwell, 1978.
Ethics takes up the meanings of our moral concepts—such as right action, obligation and justice—and formulates principles to guide moral decisions, whether in private or public life. What are our moral obligations to others? How can moral disagreements be rationally settled? What rights must a just society accord its citizens? What constitutes a valid excuse for wrong-doing?
Metaphysics seeks basic criteria for determining what sorts of things are real. Are there mental, physical, and abstract things (such as numbers), for instance, or is there just the physical and the spiritual, or merely matter and energy? Are persons highly complex physical systems, or do they have properties not reducible to anything physical?
Epistemology concerns the nature and scope of knowledge. What does it mean to know (the truth), and what is the nature of truth? What sorts of things can be known, and can we be justified in our beliefs about what goes beyond the evidence of our senses, such as the inner lives of others or events of the distant past? Is there knowledge beyond the reach of science? What are the limits of self-knowledge?
The History of Philosophy studies both major philosophers and entire periods in the development of philosophy such as the Ancient, Medieval, Modern, Nineteenth Century, and Twentieth Century periods. It seeks to understand great figures, their influence on others, and their importance for contemporary issues. The history of philosophy in a single nation is often separately studied, as in the case of American Philosophy. So are major movements within a nation, such as British Empiricism and German Idealism, as well as international movements with a substantial history, such as existentialism and phenomenology. The history of philosophy not only provides insight into the other subfields of philosophy; it also reveals many of the foundations of Western Civilization.