Sets are multitudes which are also unities. It is surprising that the fact that multitudes are also unities leads to no contradictions: this is the main fact of mathematics.Kurt Gödel (Hao Wang,A Logical Journey: From Gödel to Philosophy)In what sense can something be at the same time one and many? The problem is familiar since Plato (for example,Republic524e). In recent times, Whitehead and Russell, inPrincipia Mathematica,have been struck by the difficulty of the problem: ‘If there is such an object as (...) a class, it must be in some senseoneobject, yet it is only of classes that many can be predicated. Hence, if we admit classes as objects, we must suppose that the same object can be both one and many, which seems impossible.' It is, however, in Frege's great work,The Foundations of Arithmetic(henceforth,Grundlagen),that many see the final resolution of the old question: how can something be at the same time one and many? (shrink)

One of the most pressing challenges facing virtue theorists is the conflation problem. This problem concerns the difficulty of explaining the distinction between different types of virtue, such as the distinction between moral virtues and intellectual virtues. Julia Driver has argued that only an outcomes-based understanding of virtue can provide an adequate solution to the conflation problem. In this paper, I argue against Driver’s outcomes-based account, and propose an alternative motivations-based solution. According to this proposal, intellectual virtues can be identified (...) by the shared motivation for cognitive contact with reality, while moral virtues are identified by appeal to the characteristic motivations of kindness and justice. I defend the proposal by demonstrating that it produces plausible verdicts concerning the virtue status of candidate moral and intellectual virtues. (shrink)

The current emphasis that organisations are placing upon knowledge and the corresponding attention that workplace epistemological values are receiving within the educational community has resulted in an interesting convergence of discourses—school-based and work-based. Even as workplaces are tending toward abstraction over practice—based knowing, schools are being nudged into doing the reverse. The result of this ferment is that traditional barriers between these kinds of knowledge are being removed. As can be seen from workplace examples, it is possible for liberal learning (...) to be in the service of instrumental ends. So too schools may come to see more clearly the value of situatedness and team-work in the transaction of liberal learning. More generally, we see also new possibilities for retreat from received views about the worth of practical knowledge. (shrink)

Several contemporary virtue scholars trace the origin of the concept of intellectual virtues back to Aristotle. In contrast, my aim in this paper is to highlight the strong indications showing that Plato had already conceived of and had begun developing the concept of intellectual virtues in his discussion of the ideal city-state in the Republic. I argue that the Platonic conception of rational desires satisfies the motivational component of intellectual virtues while his dialectical method satisfies the success component. In addition, (...) I show that Plato considers episteme as the primary intellectual virtue. Episteme, which is quite similar to Pritchard’s The nature and value of knowledge: three investigations, Oxford University Press, Oxford, 2010) conception of understanding, is a cognitive achievement that cannot be attained by luck or testimony. The realization that Plato was the first to conceive of and develop the concept of intellectual excellences is not merely of historic significance. I illustrate, through the example of Zagzebski’s virtue theory, how the Platonic conception of intellectual virtues could prove promising in contemporary debates on virtue epistemology theories. (shrink)

I propose to refer to Plato's view on the development and life of the philosophical knowledge which is can be taught.