Epistemology studies questions about knowledge and rational belief.  Traditional questions include the following: How can we know that the ordinary physical objects around us are real (as opposed to dreamed, or hallucinated, as in the Matrix)?  What are the factors that determine whether a belief is rational or irrational?  What is the difference between knowing something and just believing it?  (Part of the answer is that you can have false beliefs, but you can only know things that are true.  But that’s not the whole answer—after all, you might believe something true on the basis of a lucky guess, and that wouldn’t be knowledge!)   Some other questions that have recently been the subject of lively debate in epistemology include: Can two people with exactly the same evidence be completely rational in holding opposite beliefs?  Does whether I know something depend on how much practical risk I would face if I believed falsely?  Can I rationally maintain confident beliefs about matters on which I know that others, who are seemingly every bit as intelligent, well-informed, unbiased and diligent as I am, have come to opposite conclusions?

Metaphysics is the study of what the world is like—or (some would say) what reality consists in. Metaphysical questions can take several forms. They can be questions about what exists (questions of ontology); they can be questions what is fundamental (as opposed to derivative); and they can be questions about what is an objective feature of the world (as opposed to a mere consequence the way in which creatures like us happen to interact with that world). Questions that are central to the study of metaphysics include questions about the nature of objects, persons, time, space, causation, laws of nature, and modality. The rigorous study of these questions has often led metaphysicians to make surprising claims. Plato thought that alongside the observable, concrete world there was a realm of eternal, unchanging abstract entities like Goodness, Beauty, and Justice. Gottfried Wilhelm Leibniz claimed that the world was composed of tiny indivisible souls, called monads. Even today contemporary metaphysicians have been known to doubt the existence of ordinary objects, to deny the possibility of free will, and to argue that our world is just one of a plurality of worlds.

Logic is the study of the validity of patterns of inference. Logic is not a branch of psychology: It does not concern how people actually reason or which kinds of reasoning they find intuitively compelling. Rather, logic concerns the question of when a claim is conclusively supported by other claims. For instance, the inference from the claims “it is raining” and “if it is raining then the streets are wet” to the claim “the streets are wet” is logically valid – the premises conclusively support the conclusion. The validity of this specific inference, and of other inferences of the same form, is tied to the nature of the concept “if … then”. More generally, the notion of logical validity is closely connected to the nature of concepts such as “and”, “or”, “not”, “if … then”, “all”, and “some”. In studying the notion of logical validity, logicians have developed symbolic languages. These enable us to state claims clearly and precisely, and to investigate the exact structure of an argument. These languages have turned out to be useful within philosophy and other disciplines, including mathematics and computer science. Some of the questions about logic studied by members of the philosophy department include: Given that logic is not an empirical science, how can we have knowledge of basic logical truths? What is the connection between logic and rationality? Can mathematics be reduced to logic? Should we revise logic to accommodate vague or imprecise language? Should we revise logic to answer the liar paradox and other paradoxes concerning truth? 

Political philosophy is the philosophical study of concepts and values associated with political matters. For one example, is there any moral obligation to do what the law says just because the law says so, and if so on what grounds? Many have said we consent to obey. Did you consent to obey the laws? Can one consent without realizing it? Are there other grounds for an obligation to obey the law? Another central question is what would count as a just distribution of all the wealth and opportunity that is made possible by living in a political community? Is inequality in wealth or income unjust? Much existing economic inequality is a result of different talents, different childhood opportunities, different gender, or just different geographical location. What might justify inequalities that are owed simply to bad luck? Some say that inequality can provide incentives to produce or innovate more, which might benefit everyone. Others say that many goods belong to individuals before the law enters in, and that people may exchange them as they please even if this results in some having more than others. So (a third question), what does it mean for something to be yours, and what makes it yours?

The Philosophy of Language is devoted to the study of questions concerned with meaning and communication. Such questions range from ones that interact closely with linguistic theory to questions that are more akin to those raised in the study of literature. Very large questions include: What is linguistic meaning? How is the meaning of linguistic performances similar to and different from the meanings of, say, gestures or signals? What is the relationship between language and thought? Is thought more fundamental than language? Or is there some sense in which only creatures that can speak can think? To what extent does the social environment affect the meaning and use of language? Other questions focus on the communicative aspect of language, such as: What is it to understand what someone else has said? What is it to assert something? How is assertion related to knowledge and belief? And how is it that we can gain knowledge from others through language? Yet other questions focus on specific features of the languages we speak, for example: What is it a name to be a name of a particular thing? What's the relationship between the meanings of words and the meanings of sentences? Is there an important difference between literal and figurative uses of language? What is metaphor? And how does it work?

Ethics is the study of what we ought to do and what sorts of people we ought to be. Ethicists theorize about what makes acts right and wrong and what makes outcomes good and bad, and also about which motivations and traits of character we should admire and cultivate. Some other questions that ethicists try to answer are closely related to the central ones. They include: What does it mean to act freely? Under what conditions are we responsible for our good and bad acts? Are moral claims true and false, like ordinary descriptive claims about our world, and if they are what makes them so?

The History of Philosophy plays a special role in the study of philosophy. Like every other intellectual discipline, philosophy has of course a history.  However, in the case of philosophy an understanding of its history - from its ancient and medieval beginnings through the early modern period (the 17th and 18th centuries) and into more recent times - forms a vital part of the very enterprise of philosophy, whether in metaphysics and epistemology or in ethics, aesthetics, and political philosophy.  To study the great philosophical works of the past is to learn about the origins and presuppositions of many of the problems that occupy philosophy today.  It is also to discover and to come to appreciate different ways of dealing with these problems, different conceptions of what the fundamental problems of philosophy are, and indeed different ways of doing philosophy altogether.  And it is also the study of works—from Plato and Aristotle, through Kant and Mill and more recent writers—that have shaped much of Western culture far beyond academic philosophy. Many of the most creative philosophers working today have also written on various topics in the history of philosophy and have found their inspiration in great figures of the past.