Though William Lane Craig believes his anti-Platonism is compatible with objective, Christian morality, I argue that it is not. First, I survey the main contours of his nominalism. Second, I discuss how he sees those points in relation to objective, Christian morality. Then, I argue that his view cannot sustain the qualitative aspects of moral virtues or principles, or even human beings. Moreover, Craig’s view loses any connection between those morals and humans, thereby doing great violence to objective, (...) Christian morals. Finally, I sketch two advantages of a Platonic realism in regards to Christian morals. (shrink)

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)

This book does three main things. First, it defends mathematical platonism against the main objections to that view (most notably, the epistemological objection and the multiple-reductions objection). Second, it defends anti-platonism (in particular, fictionalism) against the main objections to that view (most notably, the Quine-Putnam indispensability objection and the objection from objectivity). Third, it argues that there is no fact of the matter whether abstract mathematical objects exist and, hence, no fact of the matter whether platonism (...) or anti-platonism is true. (shrink)

Famously, Plato argues that the soul pre-exists the body, continues to exist after the body dies, and can come to exist afterwards in another body. Aristotle argues against the transmigration of souls in On Generation and Corruption and for the most part appears not to endorse these Platonic doctrines. But in De Anima III.5 Aristotle also seems to argue that a part of the soul, usually dubbed the nous poiētikos, is separable from the body and eternal. This has presented interpreters (...) of Aristotle with a problem: how can we reconcile Aristotle the naturalist philosopher with the apparently Platonist philosopher of De Anima III.5? Can we understand Aristotle’s position in De Anima III.5 in a way that does not conflict with the anti-Platonism he expresses in texts like On Generation and Corruption? I will argue that we can and offer an interpretation of De Anima III.5 that does not commit Aristotle to the position that the human soul is eternal. Even if Plato is right about the concept of the human soul, about what the human soul is in its own nature, he is wrong on ontological grounds. There are no eternal human souls. (shrink)

This paper considers two strategies for undermining indispensability arguments for mathematical Platonism. We defend one strategy (the Trivial Strategy) against a criticism by Joseph Melia. In particular, we argue that the key example Melia uses against the Trivial Strategy fails. We then criticize Melia’s chosen strategy (the Weaseling Strategy.) The Weaseling Strategy attempts to show that it is not always inconsistent or irrational knowingly to assert p and deny an implication of p . We argue that Melia’s case for (...) this strategy fails. (shrink)

Mark Balaguer has written a provocative and original book. The book is as ambitious as a work of philosophy of mathematics could be. It defends both of the dominant views concerning the ontology of mathematics, Platonism and Anti-Platonism, and then closes with an argument that there is no fact of the matter which is right.

This paper argues that it is scientific realists who should be most concerned about the issue of Platonism and anti-Platonism in mathematics. If one is merely interested in accounting for the practice of pure mathematics, it is unlikely that a story about the ontology of mathematical theories will be essential to such an account. The question of mathematical ontology comes to the fore, however, once one considers our scientific theories. Given that those theories include amongst their laws (...) assertions that imply the existence of mathematical objects, scientific realism, when construed as a claim about the truth or approximate truth of our scientific theories, implies mathematical Platonism. However, a standard argument for scientific realism, the 'no miracles' argument, falls short of establishing mathematical Platonism. As a result, this argument cannot establish scientific realism as it is usually defined, but only some weaker position. Scientific 'realists' should therefore either redefine their position as a claim about the existence of unobservable physical objects, or alternatively look for an argument for their position that does establish mathematical Platonism. (shrink)

The author reviews and summarizes, in as jargon-free way as he is capable of, the form of anti-platonist anti-nominalism he has previously developed in works since the 1980s, and considers what additions and amendments are called for in the light of such recently much-discussed views on the existence and nature of mathematical objects as those known as hyperintensional metaphysics, natural language ontology, and mathematical structuralism.

The philosophy of mathematics of the later Wittgenstein is normally not taken very seriously. According to a popular objection, it cannot account for mathematical necessity. Other critics have dismissed Wittgenstein's approach on the grounds that his anti-platonism is unable to explain mathematical objectivity. This latter objection would be endorsed by somebody who agreed with Paul Benacerraf that any anti-platonistic view fails to describe mathematical truth. This paper focuses on the problem proposed by Benacerraf of reconciling the semantics (...) with the epistemology for mathematics. It is claimed that there is a way of solving Benacerrafs problem along the lines suggested by Wittgenstein's later remarks on mathematics. This will require demonstrating that a satisfactory conception of mathematical objectivity can be extracted from his mature philosophy. (shrink)

The philosophy of mathematics of the later Wittgenstein is normally not taken very seriously. According to a popular objection, it cannot account for mathematical necessity. Other critics have dismissed Wittgenstein's approach on the grounds that his anti-platonism is unable to explain mathematical objectivity. This latter objection would be endorsed by somebody who agreed with Paul Benacerraf that any anti-platonistic view fails to describe mathematical truth. This paper focuses on the problem proposed by Benacerraf of reconciling the semantics (...) with the epistemology for mathematics. It is claimed that there is a way of solving Benacerrafs problem along the lines suggested by Wittgenstein's later remarks on mathematics. This will require demonstrating that a satisfactory conception of mathematical objectivity can be extracted from his mature philosophy. (shrink)

Does Wittgenstein have a coherent philosophy of mathematics? Here, I will be concerned with showing that the answer is positive. However, given that his life-long philosophical perspective on mathematics tends to be misleading, I focus on the specific problem posed by Paul Benacerraf in ‘Mathematical Truth’, that is: the puzzle about how to reconcile the metaphysics with the epistemology for mathematics. My aim is to show that there is an adequate anti-platonistic solution to that puzzle in the mature writings (...) of the Austrian philosopher. (shrink)

Mathematics tells us there exist infinitely many prime numbers. Nominalist philosophy, introduced by Goodman and Quine, tells us there exist no numbers at all, and so no prime numbers. Nominalists are aware that the assertion of the existence of prime numbers is warranted by the standards of mathematical science; they simply reject scientific standards of warrant.

This article offers a reading of Colin Gunton’s trinitarian theology in light of recent theological attempts to develop accounts of ‘new trinitarian ontologies’ in a strongly Christian Neo-Platonic vein. In particular, this article seeks to situate Gunton’s work within the broader context of late twentieth-century European thought by comparing his ‘trinitarian ontology’ to the anti-Platonic ontologies of Martin Heidegger and Gilles Deleuze. By way of considering the ‘anti-Platonic’ aspects of Gunton’s trinitarian theology, this article presents his theological project (...) as a testcase which highlights the stakes in constructing ‘new’ trinitarian ontologies as well as possible objections to the affirmative attitude towards Christian Neo-Platonism in contemporary theological metaphysics. (shrink)

Many interpreters have noted that §§138–242 of Wittgenstein's Philosophical Investigations is dominated by an attack on a platonist or classical realist conception of rules and meaning. In this paper, I address the lack of clarity that still exists concerning the nature and strength of the arguments in those sections. I argue that Wittgenstein's attack is genuinely compelling if viewed as an intricate reductio ad absurdum argument that runs all the way through §§138–201. On my reading, the well-known regress-of-interpretations argument is (...) merely one stage in the overall reductio and is not sufficient on its own to generate the rule-following paradox. (shrink)

Many interpreters have noted that §§138–242 of Wittgenstein's Philosophical Investigations is dominated by an attack on a platonist or classical realist conception of rules and meaning. In this paper, I address the lack of clarity that still exists concerning the nature and strength of the arguments in those sections. I argue that Wittgenstein's attack is genuinely compelling if viewed as an intricate reductio ad absurdum argument that runs all the way through §§138–201. On my reading, the well-known regress-of-interpretations argument is (...) merely one stage in the overall reductio and is not sufficient on its own to generate the rule-following paradox. (shrink)

Mathematics tells us there exist infinitely many prime numbers. Nominalist philosophy, introduced by Goodman and Quine, tells us there exist no numbers at all, and so no prime numbers. Nominalists are aware that the assertion of the existence of prime numbers is warranted by the standards of mathematical science; they simply reject scientific standards of warrant.

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)

In Science without numbers Hartry Field attempted to formulate a nominalist version of Newtonian physics?one free of ontic commitment to numbers, functions or sets?sufficiently strong to have the standard platonist version as a conservative extension. However, when uses for abstract entities kept popping up like hydra heads, Field enriched his logic to avoid them. This paper reviews some of Field's attempts to deflate his ontology by inflating his logic.

SummaryThe platonist, in affirming the principle of bivalence for sentences for which there is no decision procedure, disconnects their truth‐conditions from conditions that would enable us to prove them ‐ as if Goldbach's conjecture, say, might just happen to be true. According to Dummett, what has gone wrong here is that the meaning of the relevant sentences has been conceived so as to go beyond what could be learned in learning to use them, or displayed in using them competently. Dummett (...) draws the general conclusion that accounts of meaning must traffic only in decidable circumstances. I suggest that Dummett can be right about platonism but wrong in this general conclusion: the centrality of decidable circumstances in competent use of language is a special feature of mathematical language. This means that someone who recoils from the anti‐realism constituted by Dummett's generalized anti‐platonism, in the case of, say, statements about other minds, need not be recoiling into a close analogue of platonism, as Dummett suggests. We can reinstate the intuitive idea that platonism goes wrong by inappropriately modelling the epistemology and metaphysics of mathematics on the epistemology and metaphysics of the natural world. And we make room for the suggestion that anti‐realism makes a converse mistake; in this vein, I propose a picture of Dummettian anti‐realism as a novel expression of familiar and suspect epistemological and metaphysical thoughts. (shrink)

Abstract An anonymous manuscript from the fourteenth or early fifteenth century, recently discovered, apparently transmitted Thierry of Chartres's philosophical theology to Nicholas of Cusa around 1440. Yet the author of the treatise is not endorsing Thierry's views, as both Cusanus and modern readers have assumed, but in fact is writing in order to refute them. Curiously the author never mentions Thierry's best known triad of unitas, aequalitas and conexio . But a careful comparison of the structure of the author's argument (...) to Thierry's extant works shows that the author was nevertheless quite familiar with the Breton master's writings. The reatise's author offers an incisive critique of Thierry's theory of “four modes of being“ and rejects two of the modes in particular. From this new perspective, the manuscript can be valued as the first known evidence of Thierry of Chartres's late medieval reception. (shrink)

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)

"An account of the central tradition in the history of philosophy, Platonism, along with the class of philosophical positions collectively known as Naturalism and the 'anti-Platonism' of Naturalism both in antiquity and in contemporary philosophy"--.

"Aristotle versus Plato. For a long time that is the angle from which the tale has been told, in textbooks on the history of philosophy and to university students. Aristotle's philosophy, so the story goes, was au fond in opposition to Plato's. But it was not always thus."--from the Introduction In a wide-ranging book likely to cause controversy, Lloyd P. Gerson sets out the case for the "harmony" of Platonism and Aristotelianism, the standard view in late antiquity. He aims (...) to show that the twentieth-century view that Aristotle started out as a Platonist and ended up as an anti-Platonist is seriously flawed. Gerson examines the Neoplatonic commentators on Aristotle based on their principle of harmony. In considering ancient studies of Aristotle's Categories, Physics, De Anima, Metaphysics, and Nicomachean Ethics, the author shows how the principle of harmony allows us to understand numerous texts that otherwise appear intractable. Gerson also explains how these "esoteric" treatises can be seen not to conflict with the early "exoteric" and admittedly Platonic dialogues of Aristotle. Aristotle and Other Platonists concludes with an assessment of some of the philosophical results of acknowledging harmony. (shrink)

Porphyry, the Phoenician polymath, having studied with Plotinus when he was thirty years old, was a well-known Hellenic philosopher, an opponent of Christianity, and was born in Tyre, in the Roman Empire. We know of his anti-Christian ideology and of his defence of traditional Roman religions, by means of a fragment of his Adversus Christianos. This work incurred controversy among early Christians. His Adversus Christianos has been served as a critique of Christianity and a defence of the worship of (...) the traditional gods, so it is inevitable that his texts involved Biblical culture and religious Hellenism. Augustine, in his De Civitate Dei 10. 28, reproves Porphyry for wasting so much time in learning the theurgic arts and rites. This paper does not inquire into whether Porphyry’s philosophical monistic theology is shown in Plotinus’ Enneads, but focuses on his anti-Christian thought through the fragments that we have, particularly Augustine’s De Civitate Dei. (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)

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)

PurposeThis paper aims to establish that a certain sort of mathematical pluralism is true. MethodsThe paper proceeds by arguing that that the best versions of mathematical Platonism and anti-Platonism both entail the relevant sort of mathematical pluralism. Result and ConclusionThis argument gives us the result that mathematical pluralism is true, and it also gives us the perhaps surprising result that mathematical Platonism and mathematical pluralism are perfectly compatible with one another.

Mathematical concepts play at least three roles in the application of mathematics: an inferential role, a representational role, and an expressive role. In this paper, I argue that, despite what has often been alleged, platonists do not fully accommodate these features of the application of mathematics. At best, platonism provides partial ways of handling the issues. I then sketch an alternative, anti-realist account of the application of mathematics, and argue that this account manages to accommodate these features of (...) the application process. In this way, a better account of mathematical applications is, in principle, available. (shrink)

The basic question of ontology is “What exists?”. The basic question of metaontology is: are there objective answers to the basic question of ontology? Here ontological realists say yes, and ontological anti-realists say no. (Compare: The basic question of ethics is “What is right?”. The basic question of metaethics is: are there objective answers to the basic question of ethics? Here moral realists say yes, and moral anti-realists say no.) For example, the ontologist may ask: Do numbers exist? (...) The Platonist says yes, and the nominalist says no. The metaontologist may ask: is there an objective fact of the matter about whether numbers exist? The ontological realist says yes, and the ontological anti-realist says no. Likewise, the ontologist may ask: Given two distinct entities, when does a mereological sum of those entities exist? The universalist says always, while the nihilist says never. The metaontologist may ask: is there an objective fact of the matter about whether the mereological sum of two distinct entities exists? The ontological realist says yes, and the ontological anti-realist says no. Ontological realism is often traced to Quine (1948), who held that we can determine what exists by seeing which entities are endorsed by our best scientific theory of the world. In recent years, the practice of ontology has often presupposed an ever-stronger ontological realism, and strong versions of ontological realism have received explicit statements by Fine (this volume), Sider (2001; this volume), van Inwagen (1998; this volume), and others. (shrink)

This paper responds to Colin Cheyne's new anti-platonist argument according to which knowledge of existential claims—claims of the form such-tmd-so exist—requires a caused connection with the given such-and-so. If his arguments succeed then nobody can know, or even justifiably believe, that acausal entities exist, in which case (standard) platonism is untenable. I argue that Cheyne's anti-platonist argument fails.

Byzantium has recently attracted much attention, principally among cultural, social and economic historians. This book shifts the focus to philosophy and intellectual history, exploring the thought-world of visionary reformer Gemistos Plethon. It argues that Plethon brought to their fulfilment latent tendencies among Byzantine humanists towards a distinctive anti-Christian and pagan outlook. His magnum opus, the pagan Nomoi, was meant to provide an alternative to, and escape-route from, the disputes over the Orthodoxy of Gregory Palamas and Thomism. It was also (...) a groundbreaking reaction to the bankruptcy of a pre-existing humanist agenda and to aborted attempts at the secularisation of the State, whose cause Plethon had himself championed in his two utopian Memoranda. Inspired by Plato, Plethon's secular utopianism and paganism emerge as the two sides of a single coin. On another level, the book challenges anti-essentialist scholarship that views paganism and Christianity as social and cultural constructions. (shrink)

Platonism in the philosophy of mathematics is the doctrine that there are mathematical objects such as numbers. John Burgess and Gideon Rosen have argued that that there is no good epistemological argument against platonism. They propose a dilemma, claiming that epistemological arguments against platonism either rely on a dubious epistemology, or resemble a dubious sceptical argument concerning perceptual knowledge. Against Burgess and Rosen, I show that an epistemological anti- platonist argument proposed by Hartry Field avoids both (...) horns of their dilemma. (shrink)

Mark Balaguer's Platonism and Anti-Platonism in Mathematics presents an intriguing new brand of platonism, which he calls plenitudinous platonism, or more colourfully, full-blooded platonism. In this paper, I argue that Balaguer's attempts to characterise full-blooded platonism fail. They are either too strong, with untoward consequences we all reject, or too weak, not providing a distinctive brand of platonism strong enough to do the work Balaguer requires of it.

This paper is divided into two main sections. In the first, I attempt to show that the characterization of Frege as a redundancy theorist is not accurate. Using one of Wolfgang Carl's recent works as a foil, I argue that Frege countenances a realm of abstract objects including truth, and that Frege's Platonist commitments inform his epistemology and embolden his antipsychologistic project. In the second section, contrasting Frege's Platonism with pragmatism, I show that even though Frege's metaphysical position concerning (...) truth has been criticized as reproachable, I argue that it may be useful for people to think like Platonists while conducting their scientific and philosophical inquiries. (shrink)

State of the art paper on the topic realism/anti-realism. The first part of the paper elucidates the notions of existence and independence of the metaphysical characterization of the realism/anti-realism dispute. The second part of the paper presents a critical taxonomy of the most important positions and doctrines in the contemporary literature on the domains of science and mathematics: scientific realism, scientific anti-realism, constructive empiricism, structural realism, mathematical Platonism, mathematical indispensability, mathematical empiricism, intuitionism, mathematical fictionalism and second (...) philosophy. (shrink)

Wittgenstein is generally supposed to have abandoned in the 1930's a realistic conception of the meaning of mathematical propositions, founded on the idea of tmth-conditions which could in certain cases transcend any possibility of verification, for a realistic one, where the idea of truth-conditions is replaced by that of conditions of justification of assertability. It is argued that for Wittgenstein mathematical propositions, which are, as he says, "grammatical" propositions, have a meaning and a role which differ to a much greater (...) degree from those of ordinary propositions than either platonistic realism or intuitionistic anti-realism would admit, and that is the tendency to assimilate the mathematical proposition to an ordinary descriptive proposition which confers on it an appearance of meaning independent of the possibility of proving it, and not, as Dummett would say, that it is a decision concerning the kind of meaning it has which gives it the status of a proposition describing a determinate objective reality. (shrink)

In his Telluris Theoria Sacra and its English translation The Theory of the Earth (1681–90), the English clergyman and schoolmaster Thomas Burnet (c.1635–1715) constructed a geological history from the Creation to the Final Consummation, positing predominantly natural causes to explain biblical events and their effects on the Earth and life on it. Burnet's insistence on appealing primarily to natural rather than miraculous causes has been interpreted both by his contemporaries and by some historians as an essentially Cartesian principle. On this (...) reading, Burnet adhered to a Cartesian style of explanation in which there was no place for miracles. In this paper, I propose a different interpretation. Burnet's commitment to natural over miraculous causes, I argue, was grounded in an anti-voluntarist theology which he inherited from the Cambridge Platonists and Latitudinarians. This anti-voluntarism, moreover, also dictated the kind of miracles to which he did appeal. This reading of Burnet contrasts with the view that he was simply following Cartesian principles. First, Descartes had espoused a radical form of theological voluntarism. Second, Burnet's and Descartes's views of providence were based on distinct attributes of God, and these attributes had quite different implications regarding the place of miracles in the providential order. (shrink)

Wittgenstein is generally supposed to have abandoned in the 1930's a realistic conception of the meaning of mathematical propositions, founded on the idea of tmth-conditions which could in certain cases transcend any possibility of verification, for a realistic one, where the idea of truth-conditions is replaced by that of conditions of justification of assertability. It is argued that for Wittgenstein mathematical propositions, which are, as he says, "grammatical" propositions, have a meaning and a role which differ to a much greater (...) degree from those of ordinary propositions than either platonistic realism or intuitionistic anti-realism would admit, and that is the tendency to assimilate the mathematical proposition to an ordinary descriptive proposition which confers on it an appearance of meaning independent of the possibility of proving it, and not, as Dummett would say, that it is a decision concerning the kind of meaning it has which gives it the status of a proposition describing a determinate objective reality. (shrink)

G. E. Moore’s early essay, “The Nature of Judgment,” makes common cause with F. H. Bradley’s Principles of Logic against British empiricism’s characteristic view of judgment. But primarily it attacks positions Bradley and the empiricists share. I develop a fuller analysis of both aspects of “The Nature of Judgment” than has appeared. Bradley’s rejection of empiricist nominalism, I argue, enables him to develop what Moore considers a superior account of judgment to empiricism’s. But positions carried over from empiricism require Bradley (...) to seek all judgments’ truth conditions in existing circumstances, a result intolerable to Moore, who views mathematical and ethical judgments as being true independently of the world. Moore abandons Bradley’s vestigal empiricism, arguing that it leads invariably to self-contradiction. I reconstruct this argument, and draw out of it an unrecognized tension between the anti-empiricist and the anti-idealist themes of Moore’s early writings. (shrink)

In chapters twenty and twenty-one of his Life of Plotinus Porphyry identifies Thrasyllus as the first of four Neopythagorean forerunners of Plotinus, the others being Moderatus, Cronius, and Numenius. That means that Thrasyllus was recognized by Porphyry as the earliest representative of one of the strands of the Plotinian philosophical synthesis. More widely--and Tarrant is concerned with the wider theme throughout his book--we must learn to recognize Thrasyllus as one of those to whom we must look if we are to (...) understand more of the shift in the last century B.C. and the first century of the Christian era from the empiricism and anti-transcendentalism of Hellenistic philosophy, with its predominantly epistemological emphases, to the restored theories of transcendentalist Platonism which dominated the final centuries of ancient thought. (shrink)

Introduction 1. Alexander in Modern Scholarship; The Present Translation The anti-Manichaean treatise of Alexander of Lycopolis has for a long time been...

God Over All: Divine Aseity and the Challenge of Platonism is a defense of God's aseity and unique status as the Creator of all things apart from Himself in the face of the challenge posed by mathematical Platonism. After providing the biblical, theological, and philosophical basis for the traditional doctrine of divine aseity, William Lane Craig explains the challenge presented to that doctrine by the Indispensability Argument for Platonism, which postulates the existence of uncreated abstract objects. Craig (...) provides detailed examination of a wide range of responses to that argument, both realist and anti-realist, with a view toward assessing the most promising options for the theist. A synoptic work in analytic philosophy of religion, this groundbreaking volume engages discussions in philosophy of mathematics, philosophy of language, metaphysics, and metaontology. (shrink)