The idea that sentences can be closer or further apart in meaning is highly intuitive. Not only that, it is also a pillar of logic, semantic theory and the philosophy of science, and follows from other commitments about similarity. The present paper proposes a novel way of comparing the ‘distance’ between two pairs of propositions. We define ‘\ is closer in meaning to \ than \ is to \’ and thereby give a precise account of comparative propositional similarity facts. Notably, (...) our definition eschews metric assumptions, which are unrealistic in most applications of interest. (shrink)

The revival of the philosophy of mathematics in the 60s following its post-1931 slump left us with two conflicting positions on arithmetic’s ontological relationship to set theory. W.V. Quine’s view, presented in 'Word and Object' (1960), was that numbers are sets. The opposing view was advanced in another milestone of twentieth-century philosophy of mathematics, Paul Benacerraf’s 'What Numbers Could Not Be' (1965): one of the things numbers could not be, it explained, was sets; the other thing numbers could not be, (...) even more dramatically, was objects. Curiously, although Benacerraf’s article appeared in the heyday of Quine’s influence, it declined to engage the Quinean position squarely, even seemed to think it was not its business to do so. Despite that, in my experience, most philosophers believe that Benacerraf’s article put paid to the reductionist view that numbers are sets (though perhaps not the view that numbers are objects). My chapter will attempt to overturn this orthodoxy. (shrink)

The idea of finding Foucault first looks at the many influences on Foucault, including his Nietzschean acclamations. It examines Foucault’s critical history of thought, his work on the orders of discourse with his emphasis on being a pluralist: the problem he says that he has set himself is that of the individualization of discourses. Finally, it addresses his work on the culture of the self which became a philosophical and historical question for Foucault later in his life as he investigated (...) the historical form of relations between subjectivity and truth in Western philosophy since Antiquity and how philosophy as an activity taught about the care of the self. The conclusion suggests some ways that students might approach his work as they proceed in finding Foucault and their own selves. (shrink)

Since the publication of Miranda Fricker’s seminal book Epistemic Injustice, philosophy of education scholarship has been mostly limited to analyses of culprit-based epistemic injustice in education. This has left structural manifestations relatively underexplored with great detriment to those who are most vulnerable to experience such injustice. This paper aims to address this oversight and open avenues for further research by exploring approaches to theorizing structural epistemic injustice in education and envisioning efficacious remedies. The author identifies three approaches: one that focusses (...) on educational institutions; one that focusses on institutional processes that impact educational outcomes; and one that focusses on epistemological processes that are internal to education. Whilst the approaches differ as to their explanatory power and ease of implementation, it is argued that all three demonstrate that epistemic injustice in education is often the result of structural factors which cannot be attributed to individual epistemic agents. The author concludes by suggesting that educational philosophers must examine each of these approaches in greater depth to make significant progress in disrupting the impact of epistemic injustice in education. (shrink)

Examines the arguments for and against religion and advocates for humanism as a logical alternative.

The overgeneration argument attempts to show that accepting second-order validity as a sound formal counterpart of logical truth has the unacceptable consequence that the Continuum Hypothesis is either a logical truth or a logical falsehood. The argument was presented and vigorously defended in John Etchemendy’s The Concept of Logical Consequence and it has many proponents to this day. Yet it is nothing but a seductive fallacy. I demonstrate this by considering five versions of the argument; as I show, each is (...) either unsound or lacks a troubling conclusion. (shrink)

The overgeneration argument attempts to show that accepting second-order validity as a sound formal counterpart of logical truth has the unacceptable consequence that the Continuum Hypothesis is either a logical truth or a logical falsehood. The argument was presented and vigorously defended in John Etchemendy’s The Concept of Logical Consequence and it has many proponents to this day. Yet it is nothing but a seductive fallacy. I demonstrate this by considering five versions of the argument; as I show, each is (...) either unsound or lacks a troubling conclusion. (shrink)

This is the best general book on philosophy for university students: not just an introduction, but a guide which will serve them throughout their studies. It comprises specially commissioned explanatory surveys of the main areas of philosophy, written by thirteen leading philosophers.

The Compactness Theorem The compactness theorem is a fundamental theorem for the model theory of classical propositional and first-order logic. As well as having importance in several areas of mathematics, such as algebra and combinatorics, it also helps to pinpoint the strength of these logics, which are the standard ones used in mathematics and arguably … Continue reading Compactness →.

In this new collection A.C. Grayling adds to the variety of discussion and insight in his previous three essay collections. He returns to questions of personal ethics and the problems of the contemporary world, but also looks at the lives and ideas of great thinkers, the role of the arts in civilisation, and the need for reason everywhere Anthony Grayling illustrates in his celebrated accessible prose what each area offers to thought. In a wide-ranging array of illuminating topics, THE HEART (...) OF THINGS shows how far-reaching Grayling's masterly, and timely, commentary on the humanities is to general readers. (shrink)