Mark Balaguer’s project in this book is extremely ambitious; he sets out to defend both platonism and fictionalism about mathematical entities. Moreover, Balaguer argues that at the end of the day, platonism and fictionalism are on an equal footing. Not content to leave the matter there, however, he advances the anti-metaphysical conclusion that there is no fact of the matter about the existence of mathematical objects.1 Despite the ambitious nature of this project, for the most part Balaguer does (...) not shortchange the reader on rigor; all the main theses advanced are argued for at length and with remarkable clarity and cogency. There are, of course, gaps in the account but these should not be allowed to overshadow the sig-. (shrink)

This study addresses a central theme in current philosophy: Platonism vs Naturalism and provides accounts of both approaches to mathematics, crucially discussing Quine, Maddy, Kitcher, Lakoff, Colyvan, and many others. Beginning with accounts of both approaches, Brown defends Platonism by arguing that only a Platonistic approach can account for concept acquisition in a number of special cases in the sciences. He also argues for a particular view of applied mathematics, a view that supports Platonism against Naturalist alternatives. (...) Not only does this engaging book present the Platonist-Naturalist debate over mathematics in a comprehensive fashion, but it also sheds considerable light on non-mathematical aspects of a dispute that is central to contemporary philosophy. (shrink)

Contrary to popular opinion, non-natural realism can explain both why normative properties supervene on descriptive properties, and why this pattern is analytic. The explanation proceeds by positing a subtle polysemy in normative predicates like “good”. Such predicates express slightly different senses when they are applied to particulars (like Florence Nightingale) and to kinds (like altruism). The former sense, “goodPAR”, can be defined in terms of the latter, “goodKIN”, as follows: x is goodPAR iff there is a kind K such that (...) x is a token of K, and K is goodKIN. Now if x and y are descriptively exactly similar, then they are tokens of exactly the same kinds, so x is a token of a goodKIN kind if and only if y is. Therefore, by the definition, x is goodPAR if and only if y is. Supervenience just falls out of the definition of “goodPAR”. (shrink)

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.

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.

'Middle' Platonism has some claim to be the single most influential philosophical movement of the last two thousand years, as the common background to 'Neoplatonism' and the early development of Christian theology. This book breaks with the tradition of considering it primarily in terms of its sources, instead putting its contemporary philosophical engagements front and centre to reconstruct its philosophical motivations and activity across the full range of its interests. The volume explores the ideas at the heart of Platonist (...) philosophy in this period and includes a comprehensive selection of primary sources, a significant number of which appear in English translation for the first time, along with dedicated guides to the questions that have been, and might be, asked about the movement. The result is a tool intended to help bring the study of Middle Platonism into mainstream discussions of ancient philosophy. (shrink)

No detailed description available for "Concord in Discourse".

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)

Review of Brian Dobell, Augustine's Intellectual Conversion.

I argue that peter wenz's claim, That berkeley's view is that abstract ideas are impossible for us but not for god, Is untenable. But the impossibility of God having abstract ideas does not, Contrary to wenz, Entail that there is no room for the divine archetypes in berkeley's system.

In his third and concluding volume, Lloyd P. Gerson presents an innovative account of Platonism, the central tradition in the history of philosophy, in conjunction with Naturalism, the "anti-Platonism" in antiquity and contemporary philosophy. In this broad and sweeping argument, Gerson contends that Platonism identifies philosophy with a distinct subject matter, namely, the intelligible world and seeks to show that the Naturalist rejection of Platonism entails the elimination of a distinct subject matter for philosophy. Thus, the (...) possibility of philosophy depends on the truth of Platonism. From Aristotle to Plotinus to Proclus, Gerson clearly links the construction of the Platonic system well beyond simply Plato's dialogues, providing strong evidence of the vast impact of Platonism on philosophy throughout history. Platonism and Naturalism concludes that attempts to seek rapprochement between Platonism and Naturalism are unstable and likely indefensible. (shrink)

_Brill's Companion to Medieval and Early Platonism_ explores the impact exercised by Platonism on philosophy and many other fields of European culture, and the links it established with Christian, Jewish, Byzantine and Arabic traditions of thought during the Middle Ages and the early modern period.

The paper surveys the problem of language and translation in Antoine Berman’s pioneering achievements. This French philosopher of translation was deeply influenced not only by Schleiermacher, who affirmed the unity of thought and expression, but also by Benjamin, who drew attention to the formalism of language. In Berman’s view the essence of language lies in signifiers and letters. He criticized the Platonic view of language and translation which endows non-sensual, mental, and universal elements, with a higher ontological status. Thus Berman (...) proposed a modern theory of translation without Platonism. Meanings can be realized through and within letters not only in the source language, but also in the target language. In this sense, Berman’s philosophy of translation clearly reflects “the achievements of modern semiotics” . The paper criticizes the conception of translation as trapped within the logic of identity, which ignores the differences between, and the multiplicity of, languages as a result of a deep-rooted drive to obtain a universal meaning. The paper shows that Berman’s philosophy reflects and accepts this multiplicity allowing thereby the logic of difference/otherness to flourish in translation. (shrink)

Modal Platonism utilizes "weak" logical possibility, such that it is logically possible there are abstract entities, and logically possible there are none. Modal Platonism also utilizes a non-indexical actuality operator. Modal Platonism is the EASY WAY, neither reductionist nor eliminativist, but embracing the Platonistic language of abstract entities while eliminating ontological commitment to them. Statement of Modal Platonism. Any consistent statement B ontologically committed to abstract entities may be replaced by an empirically equivalent modalization, MOD(B), not (...) so ontologically committed. This equivalence is provable using Modal/Actuality Logic S5@. Let MAX be a strong set theory with individuals. Then the following Schematic Bombshell Result (SBR) can be shown: MAX logically yields [T is true if and only if MOD(T) is true], for scientific theories T. The proof utilizes Stephen Neale's clever model-theoretic interpretation of Quantified Lewis S5, which I extend to S5@. (shrink)

Discuter de leurs propres doctrines selon une méthode “scolaire”, qui consiste à retrouver les doctrines de Platon afin de construire par ce moyen leur propre pensée, est une caractéristique commune aux médio-platoniciens. Un tel procédé est donc conditionné par l’exégèse de Platon ; d’ailleurs, l’exégèse elle-même devient un objet de discussion durant le moyen-platonisme, où surgit le problème très controversé de la meilleure interprétation de Platon. Une enquête sur la présence du Phèdre – qui était l’un des dialogues les plus (...) lus de Platon – chez ces philosophes doit prendre en compte diverses méthodes d’interprétation mise en place, notamment l’interprétation grammaticale, l’interprétation physique et l’interprétation épistémologique, que cet article s’efforce de mettre en lumière. (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)

Thrasyllus, best known as the Roman emperor Tiberius' astrologist, figured prominently in the development of ancient Platonism. How prominently and to what effect are questions that have puzzled philosophers down to our day; Harold Tarrant's important new book attempts to answer them.

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)

Platonism about mathematics (or mathematical platonism) isthe metaphysical view that there are abstract mathematical objectswhose existence is independent of us and our language, thought, andpractices. Just as electrons and planets exist independently of us, sodo numbers and sets. And just as statements about electrons and planetsare made true or false by the objects with which they are concerned andthese objects' perfectly objective properties, so are statements aboutnumbers and sets. Mathematical truths are therefore discovered, notinvented., Existence. There are mathematical (...) objects. (shrink)