A long-standing tenet of virtue theory is that moral virtue and knowledge are connected in some important way. Julia Driver attacks the traditional assumption that virtue requires knowledge. I argue that the examples of virtues of ignorance Driver offers are not compelling and that the idea that knowledge is required for virtue has been taken to be foundational for virtue theory for good reason. I propose that we understand modesty as involving three conditions: 1) having genuine accomplishments, 2) being aware (...) of the value of these accomplishments, and 3) having a disposition to refrain from putting forward one's accomplishments. When we understand modesty this way, we can properly identify genuine cases of modesty and see how modesty requires knowledge. Something similar can be said about other alleged virtues of ignorance. With the proposal in place, we have no serious reason to think that moral virtue requires ignorance. Additionally, we have good reasons for thinking that acting virtuously requires having good intentions and that a necessary condition of having a virtue is having knowledge. Although some might take these results to be trivial or obviously true, I think the Julia Driver's challenge should not be dismissed out of hand. Even though there are some reasons for thinking that some situations suggest that knowledge and virtue can be separated from one another, close analysis reveals this impression is only surface deep. (shrink)

The standard model for mereotopological structures are Boolean subalgebras of the complete Boolean algebra of regular closed subsets of a nonempty connected regular T 0 topological space with an additional "contact relation" C defined by xCy x ØA (possibly) more general class of models is provided by the Region Connection Calculus (RCC) of Randell et al. We show that the basic operations of the relational calculus on a "contact relation" generate at least 25 relations in any model of the RCC, (...) and hence, in any standard model of mereotopology. It follows that the expressiveness of the RCC in relational logic is much greater than the original 8 RCC base relations might suggest. We also interpret these 25 relations in the the standard model of the collection of regular open sets in the two-dimensional Euclidean plane. (shrink)

The standard model for mereotopological structures are Boolean subalgebras of the complete Boolean algebra of regular closed subsets of a nonempty connected regular T0 topological space with an additional "contact relation" C defined by xCy ? x n ? Ø.

More attention has been paid in recent years to the relationship between Aristotle’s science and his ethics, but little effort has been directed toward constructing a concrete model of a science of Aristotle’s ethics. I offer a proposal about how we might go about constructing a science of Aristotle’s ethics. I argue that constructing an axiomatic model for a portion of Aristotle’s ethics is not only possible, but helpful in making explicit relationships among concepts at the core of Aristotle’s theory. (...) The model of an axiomatic approach to Aristotle’s ethics, which I propose in this paper, is only a small first step in constructing a full-blown science of Aristotle’s ethics, but taking this first step goes a long way toward showing that this project is promising. (shrink)

More attention has been paid in recent years to the relationship between Aristotle’s science and his ethics, but little effort has been directed toward constructing a concrete model of a science of Aristotle’s ethics. I offer a proposal about how we might go about constructing a science of Aristotle’s ethics. I argue that constructing an axiomatic model for a portion of Aristotle’s ethics is not only possible, but helpful in making explicit relationships among concepts at the core of Aristotle’s theory. (...) The model of an axiomatic approach to Aristotle’s ethics, which I propose in this paper, is only a small first step in constructing a full-blown science of Aristotle’s ethics, but taking this first step goes a long way toward showing that this project is promising. (shrink)

This article presents a case for thinking that moral principles within Aristotle's ethical theory can be both codifiable and action-guiding without minimizing the role of practical reason in determining what should be done. I argue that McDowell dismisses this possibility too hastily. Much of the force of this case rests on my interpretation of "for the most part" relationships in Aristotle.

Goguen categories extend the relational calculus and its categorical formalization to the fuzzy world. Starting from the fundamental concepts of sets, binary relations and lattices, this book introduces several categorical formulations of an abstract theory of relations such as allegories, Dedekind categories and related structures. It is shown that neither theory is sufficiently rich to describe basic operations on fuzzy relations.