What is mathematics about? And if it is about some sort of mathematical reality, how can we have access to it? This is the problem raised by Plato, which still today is the subject of lively philosophical disputes. This book traces the history of the problem, from its origins to its contemporary treatment. It discusses the answers given by Aristotle, Proclus and Kant, through Frege's and Russell's versions of logicism, Hilbert's formalism, Gödel's platonism, up to the the current debate (...) on Benacerraf's dilemma and the indispensability argument. Through the considerations of themes in the philosophy of language, ontology, and the philosophy of science, the book aims at offering an historically-informed introduction to the philosophy of mathematics, approached through the lenses of its most fundamental problem. (shrink)

Timothy Chappell develops a picture of what philosophical ethics can be like, once set aside from conventional moral theory. His question is 'How are we to know what to do?', and the answer he defends is 'By developing our moral imaginations'--a key part of human excellence, which plays many roles in our practical and evaluative lives.

In this book, Balaguer demonstrates that there are no good arguments for or against mathematical platonism. He does this by establishing that both platonism and anti-platonism are defensible views. Introducing a form of platonism ("full-blooded platonism") that solves all problems traditionally associated with the view, he proceeds to defend anti-platonism (in particular, mathematical fictionalism) against various attacks, most notably the Quine-Putnam indispensability attack. He concludes by arguing that it is not simply that we do (...) not currently have any good argument for or against platonism, but that we could never have such an argument and, indeed, that there is no fact of the matter as to whether platonism is correct. (shrink)

Taking Plato’s allegory of the cave as its starting-point, this book demonstrates how later European thinkers can be read as a reaction and a response to key aspects of this allegory and its discourse of enchainment and liberation. Focusing on key thinkers in the tradition of European political thought including Kant, Marx, Hegel, Nietzsche, Heidegger, and the Frankfurt School, it relates them back to such foundational figures as Rousseau, Aristotle, and in particular Plato. All these thinkers are considered in relation (...) to key passages from their major works, accompanied by an explanatory commentary which seeks to follow a conceptual and imagistic thread through the labyrinth of these complex, yet fascinating, texts. This book will appeal in particular to scholars of political theory, philosophy, and German language and culture. (shrink)

A study of the effect of mysticism & theology on the philosophy & the works of three noteworthy 17th century poets: Donne, Browne & Vaughan.

Traversing the genres of philosophy and literature, this book elaborates Deleuze's notion of difference, conceives certain individuals as embodying difference, and applies these conceptions to their writings.

In this essay I first outline contemporary Platonism about musical works – the theory that musical works are abstract objects. I then consider reasons to be suspicious of such a view, motivating a consideration of nominalist theories of musical works. I argue for two conclusions: first, that there are no compelling reasons to be a nominalist about musical works in particular, i.e. that nominalism about musical works rests on arguments for thoroughgoing nominalism, and, second, that if Platonism fails, (...) fictionalism about musical works is to be preferred to other nominalist ontologies of musical works. (shrink)

Rationalism, Platonism and God comprises three main papers on Descartes, Spinoza and Leibniz, with extensive responses. It provides a significant contribution to the exploration of the common ground of the great early-modern Rationalist theories, and an examination of the ways in which the mainstream Platonic tradition permeates these theories. -/- John Cottingham identifies characteristically Platonic themes in Descartes's cosmology and metaphysics, finding them associated with two distinct, even opposed attitudes to nature and the human condition, one ancient and 'contemplative', (...) the other modern and 'controlling'. He finds the same tension in Descartes's moral theory, and believes that it remains unresolved in present-day ethics. -/- Was Spinoza a Neoplatonist theist, critical Cartesian, or naturalistic materialist? Michael Ayers argues that he was all of these. Analysis of his system reveals how Spinoza employed Neoplatonist monism against Descartes's Platonist pluralism. Yet the terminology - like the physics - is Cartesian. And within this Platonic-Cartesian shell Spinoza developed a rigorously naturalistic metaphysics and even, Ayers claims, an effectually empiricist epistemology. -/- Robert Merrihew Adams focuses on the Rationalists' arguments for the Platonist, anti-Empiricist principle of 'the priority of the perfect', i.e. the principle that finite attributes are to be understood through corresponding perfections of God, rather than the reverse. He finds the given arguments unsatisfactory but stimulating, and offers a development of one of Leibniz's for consideration. -/- These papers receive informed and constructive criticism and development at the hands of, respectively, Douglas Hedley, Sarah Hutton and Maria Rosa Antognazza. (shrink)

The aim of this paper is to deeply rethink the traditional notion of “ideological emendation”. By taking Taurus T27 as a test-case, I shall emphasise that Taurus’ intervention on Timaeus 27c5 is the result of a conjecture, and that such an emendation meets the requirements for a philological conjecture on Plato’s text. Indeed, Taurus’ fragment, which is usually taken as a typical example of “ideological emendation”, only reflects an effort to recover what Plato actually wrote, and is nothing but a (...) textual emendation. Accordingly, the ideological core of such an emendation is what must lie at the basis of any conjecture, that is an attempt to re-establish (what is assumed to be) Plato’s text in accordance with his consistent doctrine. (shrink)

This is the first study to deal with Greek mathematics from the viewpoint of cultural history. Mathematics, and especially the teaching of mathematics, did not proceed in isolation, but developed along lines parallel to the development of general literate culture.

The first comprehensive account of Platonism in Antiquity, from the foundation of Plato's Academy in the fourth century BC to Late Antiquity. Written in a clear language, the book shows that Platonism is philosophically engaging and very influential in the history of philosophy. Useful for both students and scholars.

Heavy duty platonism is of great dialectical importance in the philosophy of mathematics. It is the view that physical magnitudes, such as mass and temperature, are cases of physical objects being related to numbers. Many theorists have assumed HDP’s falsity in order to reach their own conclusions, but they are only justified in doing so if there are good arguments against HDP. In this paper, I present all five arguments against HDP alluded to in the literature and show that (...) they all fail. In doing so, I establish two related truths: HDP has been unfairly ignored, and the arguments which take its falsity as a key premise should be re-assessed. (shrink)

Was Plato a Platonist? While ancient disciples of Plato would have answered this question in the affirmative, modern scholars have generally denied that Plato's own philosophy was in substantial agreement with that of the Platonists of succeeding centuries. In From Plato to Platonism, Lloyd P. Gerson argues that the ancients are correct in their assessment. He arrives at this conclusion in an especially ingenious manner, challenging fundamental assumptions about how Plato's teachings have come to be understood. Through deft readings (...) of the philosophical principles found in Plato's dialogues and in the Platonic tradition beginning with Aristotle, he shows that Platonism, broadly conceived, is the polar opposite of naturalism and that the history of philosophy from Plato until the seventeenth century was the history of various efforts to find the most consistent and complete version of "anti-naturalism." Gerson contends that the philosophical position of Plato--Plato's own Platonism, so to speak--was produced out of a matrix he calls "Ur-Platonism." According to Gerson, Ur-Platonism is the conjunction of five "antis" that in total arrive at anti-naturalism: anti-nominalism, anti-mechanism, anti-materialism, anti-relativism, and anti-skepticism. Plato's Platonism is an attempt to construct the most consistent and defensible positive system uniting the five "antis." It is also the system that all later Platonists throughout Antiquity attributed to Plato when countering attacks from critics including Peripatetics, Stoics, and Sceptics. In conclusion, Gerson shows that Late Antique philosophers such as Proclus were right in regarding Plotinus as "the great exegete of the Platonic revelation.". (shrink)

Journal Name: Apeiron Issue: Ahead of print.

For decades now, the end of metaphysics has been heralded. Engaging with the issue at stake, first, I will present and critically discuss Jan Patočka’s prophetic reflection on the fate of metaphysics after metaphysical philosophy. This will show that the problem is far more complicated and that attempts devoted to overcoming metaphysics often unjustly reduce it. To be able properly address the complexities of the crisis of metaphysics, I will move beyond Patočka and will introduce the agent, which played a (...) decisive role in the history of metaphysics and its development, that is, theology. I will point out that Patočka’s reconsideration of metaphysical thinking via the reinterpretation of the Platonic Idea correlates with the category of faith. Thus, I will argue that ‘a providential marriage’ between Athens and Jerusalem should not be divorced and that, despite numerous attempts to prove the contrary, the alliance of theology metaphysical thinking is unavoidable and even beneficial for both parts. (shrink)