Open-mindedness enjoys widespread recognition as an intellectual virtue. This is evident, among other ways, in its appearance on nearly every list of intellectual virtues in the virtue epistemology literature. Despite its popularity, however, it is far from clear what exactly openmindedness amounts to: that is, what sort of intellectual orientation or activity is essential to it. In fact, there are ways of thinking about open-mindedness that cast serious doubt on its status as an intellectual virtue.

Consider the following description, from Robert Roberts and Jay Wood (2007), of a ‘bright college freshman, taking an introductory course in philosophy.’

Questions about sincerity play a central role in our lives. But what makes an assertion insincere? In this paper we argue that the answer to this question is not as straightforward as it has sometimes been taken to be. Until recently the dominant answer has been that a speaker makes an insincere assertion if and only if he does not believe the proposition asserted. There are, however, persuasive counterexamples to this simple account. It has been proposed instead that an insincere assertion that p is one made by a speaker who (a) does not express his belief that p; or (b) does not believe that he believes that p; (c) does not assent to p; or (d) does not express any of these cognitive states. We show that these alternative accounts also face counterexamples.

Two conditions guiding permissible use of force in self-defence are proportionality and success. According to the proportionality condition the means used to prevent an attack can be permissible only if they are proportional to the interest at stake. According to the success condition, otherwise impermissible acts can be justified under the right to self-defence only if they are likely to succeed in preventing the perceived threat. These requirements should not always be interpreted narrowly. Sometimes people are permitted to kill culpable aggressors in order to avoid a non-lethal harm. Sometimes people are permitted to take up arms to defend themselves against culpable aggressors they have little or no hope of defeating.

Much of what Hume calls probable reasoning is deliberate and reflective. Since there are aspects to Hume's psychology that tempt some commentators to think, on the contrary, that for Hume all such reasoning is simple and immediate, I will be concerned to emphasize Hume's recognition of the sophisticated sort of probable reasoning (section I). Though some of the details of my case may be new, the overall point of this section should not be news to recent scholarship. But once we recognize that this reflective and deliberate reasoning constitutes a significant portion of all probable reasoning, it becomes legitimate to ask how Hume accommodates this reasoning in his psychology, his ‘science of man.’ I believe that Hume has an answer to this question. I will explain in what way Hume could have thought that probable reasoning can be sophisticated: in short, sophisticated probable reasoning involves the use of the concept of evidence or epistemic support (section II). Hume's psychology, constrained by his empiricism, must therefore explain how we come to have this idea.

In the Categories Aristotle defined substance as that which is neither predicable of nor in another. In saying that a substance is not predicable of another, Aristotle meant to exclude genera and species from the category substance. Aman is a substance but not man. In saying that a substance is not in another, Aristotle meant to exclude property particulars from the category. A man is a substance, not his color.

The Categories treats substances as simples. Though a particular substance, Bucephalus the horse, has parts, it is nevertheless a single entity in the category substance and, hence, incomplex in the way a black thing or a running man are not. Black things and runners are complex because they are aggregates of substances and property particulars. Even if a horse is one substance and, thus, an entity (unlike a substance cum some of its attributes or a group of related substances), a horse is made of parts and one may wonder how it is related to its parts, as well as how its being made of parts coheres with the definition of substance given in the Categories.

According to a prominent line of thought, we can be physicalists, but not reductive physicalists, by holding that mental and other ‘higher-level’ or ‘nonbasic’ properties — properties that are not obviously physical properties — are all physically realized. Spelling this out requires an account of realization, an account of what it is for one property to realize another. And while several accounts of realization have been advanced in recent years, my interest here is in the ‘subset view,’ which has often been invoked explicitly in defense of nonreductive physicalist positions.