Is consistency the sort of thing that could provide a guide to mathematical ontology? If so, which notion of consistency suits this purpose? Mark Balaguer holds such a view in the context of platonism, the view that mathematical objects are non-causal, non-spatiotemporal, and non-mental. For the purposes of this paper, we will examine several notions of consistency with respect to how they can provide a platon-ist epistemology of mathematics. Only a Gödelian notion, we suggest, can provide a satisfactory guide (...) to a platonist ontology. Is consistency the sort of thing that could provide a guide to mathematical ontology? If so, which notion of consistency suits this purpose? Mark Bala-guer holds such a view in the context of platonism, the view that mathematical objects are non-causal, non-spatiotemporal, and non-mental. Balaguer's version of Platonism, Full-Blooded Platonism (FBP), is the view that "there are as many abstract mathematical objects as there could be-i.e., there actually exist abstract mathematical objects of all possible kinds" (Balaguer, 2017, p. 381). He continues: Since FBP says that there are abstract mathematical objects of all possible kinds, it follows that if FBP is true, then every purely mathematical theory that could be true-i.e., that is internally consistent-accurately describes some collection of actually existing abstract objects. Thus it follows from FBP that in order to acquire knowledge of abstract objects, all we have to do is come up with an internally consistent purely mathematical theory (and know that it is internally consistent). (Balaguer, 2017, p. 381) * To be published in 43rd International Wittgenstein Symposium proceedings. (shrink)

In On the Plurality of Worlds (Lewis 1986), David Lewis imposes a condition on realist theories of modality which he calls ‘plenitude’. Lewis apparently assigns this condition considerable importance, and uses it to motivate his Humean principle of recombination, but he never says exactly what plenitude amounts to. This chapter first sets aside some obvious ways of reconstructing the plenitude criterion which do not fit with the textual evidence. An objection to modal realism due to John Divers (...) and Joseph Melia (Divers and Melia 2002) is diagnosed as equivocating between an overly-demanding plenitude constraint and a weaker constraint which fails to establish their conclusion. An alternative deflationary interpretation of the plenitude condition has it following from an application of standard theoretical virtues to a modal realist’s total theory; Lewis’ correspondence provides new evidence in support of this interpretation. The deflationary plenitude criterion also has broader application, beyond Lewisian modal realism. (shrink)

Dispositionalism about modality is the view that metaphysical modality is a matter of the dispositions possessed by actual objects. In a recent paper, David Yates has raised an important worry about the formal adequacy of dispositionalism. This paper responds to Yates’s worry by developing a reply that Yates discusses briefly but dismisses as ad hoc: an appeal to a ’plenitude of powers’ including such powers as the necessarily always manifested power for 2+2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} (...) \setlength{\oddsidemargin}{-69pt} \begin{document}$$2+2$$\end{document} to be 4. I argue that the reply is not ad hoc at all, by defending the metaphysics of dispositions that should underly it. I then argue, first, that a proper understanding of dispositions’ degrees provides us with an argument for such necessarily always manifested dispositions; second, that all the natural attempts to block that argument can be resisted without being ad hoc; and third, that pragmatic considerations explain our intuitive resistance to the ascription of necessarily always manifested dispositions. Dispositionalism can be formally adequate after all. (shrink)

Plenitude, roughly, the thesis that for any non-empty region of spacetime there is a material object that is exactly located at that region, is often thought to be part and parcel of the standard Lewisian package in the metaphysics of persistence. While the wedding of plentitude and Lewisian four-dimensionalism is a natural one indeed, there are a hand-full of dissenters who argue against the notion that Lewisian four-dimensionalism has exclusive rights to plentitude. These ‘promiscuous’ three-dimensionalists argue that a temporalized (...) version of plenitude is entirely compatible with a three-dimensional ontology of enduring entities. While few would deny the coherence of such a position, and much work has been done by its proponents to appease critics, there has been surprisingly little by way of exploring the various forms such an ontology might take as well as the potential advantages of one plenitudinous three-dimensional ontology over another. Here I develop a novel form of plenitudinous three-dimensionalism, what John Hawthorne (Metaphysical essays, 2006a, b) has called “Neo-Aristotelian Plenitude,” and argue that if one is inclined to endorse an abundant three-dimensional ontology, one is wise to opt for a plenitude of accidental unities. (shrink)

A number of prominent metaphysicians have recently defended the idea of material plenitude: wherever there is one material object, there is in fact a great multitude of them, all coincident and sharing many properties, but differing in which of these properties they have essentially and which accidentally. The main goal of this paper is to put on the agenda an important theoretical decision that plenitudinists face, regarding whether their plenitude is egalitarian or elitist, depending on whether or not (...) they take all objects that coincide at a certain location to be in some sense ontologically on a par. Many current proponents of plenitude tend toward egalitarianism. But current proponents often also point to an Aristotelian tradition they claim to carry on; indeed, the view is sometimes referred to as “neo-Aristotelian plenitude.” By examining some of the historical protagonists of Aristotelian plenitude, however, I show that they defended rather an elitist form of plenitude, wherein a single coincident is ontologically privileged in every occupied region. In the final section of the paper, I also try to articulate the basic motivation for each outlook, by way of initiating discussion of which view plenitudinists should believe. (shrink)

Fairchild (2019) advertised the humility of material plenitude, arguing that despite the profligate ontology of coincident objects it entails, the best version of plenitude is one that takes no stand on a range of nearby questions about modality and coincidence. Roughly, the thought is that plenitude says only that there are coincident objects corresponding to every consistent pattern of essential and accidental properties. Plenitude says (or should say) nothing about which patterns those might be, and so (...) should be compatible with any reasonable hypothesis about which combinations of properties it is possible for something to have. I argued in the earlier paper that a particular formulation of the target view (Global Plenitude) has exactly that virtue. But, unfortunately, Global Plenitude turns out not to be very humble at all. Global Plenitude is incompatible with an exceptionally compelling hypothesis about coincidence: that there are some things which coincide, but might not have. Scandal ensues. (shrink)

One of the salient developments in recent metaphysics is the increasing popularity of _material plenitude_: roughly, the thesis that wherever there is one material object there is in fact a great multitude of co-located but numerically distinct objects that differ principally in which of their properties they have essentially and which accidentally. Here I argue that we have at least as much reason to look favorably on _event plenitude_: wherever one event occurs there occur a great multitude of co-located but (...) numerically distinct events that differ principally in which of their properties they have essentially and which accidentally. I argue, first, that the standard reasons to adopt material plenitude extend fairly straightforwardly to events, and secondly, that only event plenitude can protect the plausible idea that causality is an extensional relation. (shrink)

An analysis of the counter-intuitive properties of infinity as understood differently in mathematics, classical physics and quantum physics allows the consideration of various paradoxes under a new light (e.g. Zeno’s dichotomy, Torricelli’s trumpet, and the weirdness of quantum physics). It provides strong support for the reality of abstractness and mathematical Platonism, and a plausible reason why there is something rather than nothing in the concrete universe. The conclusions are far reaching for science and philosophy.

I introduce an argument for Platonism based on intra-mathematical explanation: the explanation of one mathematical fact by another. The argument is important for two reasons. First, if the argument succeeds then it provides a basis for Platonism that does not proceed via standard indispensability considerations. Second, if the argument fails it can only do so for one of three reasons: either because there are no intra-mathematical explanations, or because not all explanations are backed by dependence relations, or because (...) some form of noneism-the view according to which non-existent entities possess properties and stand in relations-is true. The argument thus forces a choice between nominalism without noneism, intra-mathematical explanation and a backing conception of explanation. You can have any two, but not all three. (shrink)

The idea of “material plenitude” has been gaining traction in recent discussions of the metaphysics of material objects. My main goal here is to show that this idea may have important dialectical implications for the metaphysics of properties – more specifically, that it provides nominalists with new resources in their attempt to reject an ontology of universals. I will recapitulate one of the main arguments against nominalism – due to David Armstrong – and show how plenitude helps the (...) nominalist overcome the argument. (shrink)

In the opening chapter of the Monologion, Anselm offers an intriguing proof for the existence of a Platonic form of goodness. This proof is extremely interesting, both in itself and for its place in the broader argument for God’s existence that Anselm develops in the Monologion as a whole. Even so, it has yet to receive the scholarly attention that it deserves. My aim in this article is to begin correcting this state of affairs by examining Anslem’s proof in some (...) detail. In particular, I aim to clarify the proof’s structure, motivate and explain its central premises, and begin the larger project of evaluating its overall success as an argument for Platonism about goodness. (shrink)

Platonism and Christian Thought in Late Antiquity examines the various ways in which Christian intellectuals engaged with Platonism both as a pagan competitor and as a source of philosophical material useful to the Christian faith. The chapters are united in their goal to explore transformations that took place in the reception and interaction process between Platonism and Christianity in this period. -/- The contributions in this volume explore the reception of Platonic material in Christian thought, showing that (...) the transmission of cultural content is always mediated, and ought to be studied as a transformative process by way of selection and interpretation. Some chapters also deal with various aspects of the wider discussion on how Platonic, and Hellenic, philosophy and early Christian thought related to each other, examining the differences and common ground between these traditions. -/- Platonism and Christian Thought in Late Antiquity offers an insightful and broad ranging study on the subject, which will be of interest to students of both philosophy and theology in the Late Antique period, as well as anyone working on the reception and history of Platonic thought, and the development of Christian thought. (shrink)

Neo‐Aristotelian Plenitude is the thesis that, necessarily, any property that could be had essentially by something or other is had essentially by something or other if and only if and because it is instantiated; any essentializable property is essentialized iff and because it is instantiated. In this paper, I develop a partial nonmodal characterization of ‘essentializable' and show it cannot be transformed into a full characterization. There are several seemingly insurmountable obstacles that any full characterization of essentializability must overcome. (...) Moreover, these obstacles threaten other views in the conceptual neighborhood such as Counterpart Theoretic Plenitude and Conceptualist Plenitude. (shrink)

The paper discusses the arguments for and against animalism and concludes that a pluralist position which rejects animalism and embraces a multiplicity of thinkers is the best option.

In the section “Validity and Existence in Logik, Book III,” I explain Lotze’s famous distinction between existence and validity in Book III of Logik. In the following section, “Lotze’s Platonism,” I put this famous distinction in the context of Lotze’s attempt to distinguish his own position from hypostatic Platonism and consider one way of drawing the distinction: the hypostatic Platonist accepts that there are propositions, whereas Lotze rejects this. In the section “Two Perspectives on Frege’s Platonism,” I (...) argue that this is an unsatisfactory way of reading Lotze’s Platonism and that the Ricketts-Reck reading of Frege is in fact the correct way of thinking about Lotze’s Platonism. (shrink)

In this dissertation I examine the NeoFregean metaontology of mathematics. I try to clarify the relationship between what is sometimes called Priority Thesis and Platonism about mathematical entities. I then present three coherent ways in which one might endorse both these stances, also answering some possible objections. Finally I try to show which of these three ways is the most promising.

This chapter contains section titled: Historical Background Early Modern Eclecticism and Philosophical Humanism Early Modern Platonism Conclusion.

I examine what the mathematical theory of random structures can teach us about the probability of Plenitude, a thesis closely related to David Lewis's modal realism. Given some natural assumptions, Plenitude is reasonably probable a priori, but in principle it can be (and plausibly it has been) empirically disconfirmed—not by any general qualitative evidence, but rather by our de re evidence.

According to the traditional bundle theory, particulars are bundles of compresent universals. I think we should reject the bundle theory for a variety of reasons. But I will argue for the thesis at the core of the bundle theory: that all the facts about particulars are grounded in facts about universals. I begin by showing how to meet the main objection to this thesis (which is also the main objection to the bundle theory): that it is inconsistent with the possibility (...) of distinct qualitative indiscernibles. Here, the key idea appeals to a non-standard theory of haecceities as non-well-founded properties of a certain sort. I will then defend this theory from a number of objections, and finally argue that we should accept it on the basis of considerations of parsimony about the fundamental. (shrink)

The clean separation between manifold phenomena and a systematic order that prevails in them is a basic feature of the rational-scientific orientation system. The first authoritative formulation of this premise is found in Plato. His discussion of constitutive forms of world events has initiated a broad development in the history of philosophy, which is also effective today in the preference for reason-guided analyses of often confusing circumstances. The authors of this volume address the lasting relevance of this idea within two (...) interrelated areas of research, namely Plato scholarship and contemporary Platonism. Of particular interest is the relationship between Plato and Wittgenstein. Following this overall idea, this volume is divided into three sections: Plato scholarship, Platonism, and Plato and Wittgenstein. As the contributions show, Platonism proves to be not only a purely historical-exegetical field of research but rather a fruitful stimulus for contemporary discussions on logical, linguistic, and social topics. (shrink)

Draft version of essay. ABSTRACT: Benjamin Whichcote developed a distinctive account of human nature centered on our moral psychology. He believed that this view of human nature, which forms the foundation of “Cambridge Platonism,” showed that the demands of reason and faith are not merely compatible but dynamically supportive of one another. I develop an interpretation of this oft-neglected and widely misunderstood account of human nature and defend its viability against a key objection.

According to Hartry Field, the mathematical Platonist is hostage of a dilemma. Faced with the request of explaining the mathematicians’ reliability, one option could be to maintain that the mathematicians are reliably responsive to a realm populated with mathematical entities; alternatively, one might try to contend that the mathematical realm conceptually depends on, and for this reason is reliably reflected by, the mathematicians’ (best) opinions; however, both alternatives are actually unavailable to the Platonist: the first one because it is in (...) tension with the idea that mathematical entities are causally ineffective, the second one because it is in tension with the suggestion that mathematical entities are mind-independent. John Divers and Alexander Miller have tried to reject the conclusion of this argument—according to which Platonism is inconsistent with a satisfactory epistemology for arithmetic—by redescribing the second horn of the dilemma in light of Crispin Wright’s notion of judgment-dependent truth; in particular they have contended that once arithmetical truth is conceived in this way the Platonist can have a substantial epistemology which does not conflict with the idea that the mathematical entities exist mind-independently. In this paper I analyze Wright’s notion of judgment-dependent truth, and reject Divers and Miller’s argument for the conclusion that arithmetical truth can be so characterized. In the final part, I address the worry that my argument generalizes very quickly to the conclusion that no area of discourse could be characterized as judgment-dependent. As against this conclusion, I indicate under what conditions—notably not satisfied in Divers and Miller’s case, but possibly satisfied in others—a discourse’s judgment-dependency can be successfully vindicated. (shrink)

This paper revisits Derrida’s and Deleuze’s early discussions of “Platonism” in order to challenge the common claim that there is a fundamental divergence in their thought and to challenge one standard narrative about the history of deconstruction. According to that narrative, deconstruction should be understood as the successor to phenomenology. To complicate this story, I read Derrida’s “Plato’s Pharmacy” alongside Deleuze’s discussion of Platonism and simulacra at the end of Logic of Sense. Both discussions present Platonism as (...) the effort to establish a representative order (of original ideas and authorized reproductions of them) with no excess or outside (simulacra, or ideas that cannot be tied to an eidos). Since such pure representation is impossible, Platonism functions by means of the violent suppression of the simulacra and pharamakoi that exceed its eidetic structures. To overcome Platonism is thus not to reverse it, but to establish something like a practice of counter-memorials: detecting, exhuming, and writing back textual traces of what Platonism excludes. I then briefly apply this practice to narratives about the history of deconstruction, and suggest that they tend to occlude precisely the materialist elements of that history, as (for example) the importance of Spinoza as an interlocutor. In other words, the emerging canonical narrative about deconstruction runs the risk of repeating the Platonic gesture that Derrida spent his career writing against. (shrink)

According to Leininger, presentists and growing blockers cannot explain why past and present regularities persist in the future. In order to do so, they would have to appeal to enforcers, such as causation, laws or dispositions. But in a world with no future, these enforcers are powerless and cannot guarantee future regularity. I disagree and argue that Leininger’s coordination problem can be met by distinguishing type- from token-level necessitation. Whereas token-level necessitation is cross-temporal and subject to Leininger’s coordination problem, type-level (...) necessitation is atemporal and immune to the coordination problem. For this solution to work, though, type-level necessitation must be ontologically prior to token-level necessitation. This forces us to adopt a Platonist position according to which universals are transcendent, and not immanent. (shrink)

Does natural science give us reason to believe that mathematical statements are true? And does natural science give us reason to believe in some particular metaphysics of mathematics? These two questions should be firmly distinguished. My argument in this chapter is that a negative answer to the second question is compatible with an affirmative answer to the first. Loosely put, even if science settles the truth of mathematics, it does not settle its metaphysics.

Are numbers and other mathematical objects "out there" in some philosophically meaningful sense?

In this paper, I defend traditional Platonic mathematical realism from its contemporary detractors, arguing that numbers, understood as abstract, non-physical objects of rational intuition, are indispensable for the act of counting.

Contemporary platonism has been conditioned in large part by two dogmas. One is the belief in a fundamental cleavage between intelligible but invisible Platonic forms that are real and eternal, and perceptible objects whose confinement to spacetime constitutes an inferior existence and about which knowledge is impossible. The other dogma involves a kind of reductionism: the belief that Plato’s unhypothetical first principle of the all is identical to the form of the good. Both dogmas, I argue, are ill-founded.

Discussion of atomistic and monistic theses about abstract reality.

This rich book differs from much contemporary philosophy of mathematics in the author’s witty, down to earth style, and his extensive experience as a working mathematician. It accords with the field in focusing on whether mathematical entities are real. Franklin holds that recent discussion of this has oscillated between various forms of Platonism, and various forms of nominalism. He denies nominalism by holding that universals exist and denies Platonism by holding that they are concrete, not abstract - looking (...) to Aristotle for inspiration. (shrink)

Non-well-founded set theories allow set-theoretic exotica that standard ZFC will not allow, such as a set that has itself as its sole member. We can distinguish plenitudinous non-well-founded set theories, such as Boffa set theory, that allow infinitely many such sets, from restrictive theories, such as Finsler-Aczel or AFA, that allow exactly one. Plenitudinous non-well-founded set theories face a puzzle: nothing seems to explain the identity or distinctness of various of the sets they countenance. In this paper I aim to (...) sharpen this puzzle, make clear who it does and does not apply to and, ultimately, to argue in favor of a plenitudinous theory like Boffa. (shrink)

Augustine′s conversion to Christianity in A.D. 386 is a pivotal moment not only in his own life, but in Christian and world history, for the theology of Augustine set the course of theological and cultural development in the western Christian church. But to what exactly was Augustine converted? Scholars have long debated whether he really converted to Christianity in 386, whether he was a Platonist, and, if he adhered to both Platonism and Christianity, which dominated his thought. The debate (...) of the last thirteen decades spans an immense body of literature in multiple languages. In this literature, four major views on Augustine′s conversion may be discerned. The first view is associated with Gaston Boissier and Adolph von Harnack, and was famously championed by Prosper Alfaric: that Augustine in 386 converted to neo-Platonism but not to Christianity. Second, there is the view recently promoted by Catherine Conybeare: that Augustine in 386 converted to Christianity and rejected neo-Platonism. Third, there is the view that he converted to Christianity and was also a neo-Platonist; the most famous adherents of this view are Robert J. O′Connell and Pierre Courcelle. Finally, there is the view recently promoted by Carol Harrison: that Augustine committed to Christianity in 386, yet did not utterly reject neo-Platonism; rather, he aimed to develop a Christian faith that was informed by neo-Platonic insight. In this article, I first explain and distinguish these four general views, and then I explain why I prefer the fourth view. -/- More Info: This is the pre-peer reviewed version of Boone, Mark, "The Role of Platonism in Augustine's 386 Conversion to Christianity," Religion Compass 9.5 (May 2015), 151-61. This article has been published in final form at http://onlinelibrary.wiley.com/doi/10.1111/rec3.12149/abstract. (shrink)

A problem for Aristotelian realist accounts of universals (neither Platonist nor nominalist) is the status of those universals that happen not to be realised in the physical (or any other) world. They perhaps include uninstantiated shades of blue and huge infinite cardinals. Should they be altogether excluded (as in D.M. Armstrong's theory of universals) or accorded some sort of reality? Surely truths about ratios are true even of ratios that are too big to be instantiated - what is the truthmaker (...) of such truths? It is argued that Aristotelianism can answer the question, but only a semi-Platonist form of it. (shrink)

Predication is an indisputable part of our linguistic behavior. By contrast, the metaphysics of predication has been a matter of dispute ever since antiquity. According to Plato—or at least Platonism, the view that goes by Plato’s name in contemporary philosophy—the truths expressed by predications such as “Socrates is wise” are true because there is a subject of predication (e.g., Socrates), there is an abstract property or universal (e.g., wisdom), and the subject exemplifies the property.1 This view is supposed to (...) be general, applying to all predications, whether the subject of predication is a person, a planet, or a property.2 Despite the controversy surrounding the metaphysics of predication, many theistic philosophers—including the majority of contemporary analytic theists—regard Platonism as extremely attractive. At the same time, however, such philosophers are also commonly attracted to a form of traditional theism that has at its core the thesis that God is an absolutely independent.. (shrink)

Plato’s depiction of the first city in the Republic (Book II), the so-called ‘city of pigs’, is often read as expressing nostalgia for an earlier, simpler era in which moral norms were secure. This goes naturally with readings of other Platonic texts (including Republic I and the Gorgias) as expressing a sense of moral decline or crisis in Plato’s own time. This image of Plato as a spokesman for ‘moral nostalgia’ is here traced in various nineteenth- and twentieth-century interpretations, and (...) rejected. Plato’s pessimism about human nature in fact precludes any easy assumption that things, or people, were better in the old days. (shrink)

Even though Frege is a major figure in the history of analytic philosophy, it is not surprising that there are still issues surrounding his views, interpreting them, and labeling them. Frege’s view on numbers is typically termed as ‘Platonistic’ or at least a type of Platonism (Reck 2005). Still, the term ‘Platonism’ has views and assumptions ascribed to it that may be misleading and leads to mischaracterizations of Frege’s outlook on numbers and ideas. So, clarification of the term (...) ‘Platonism’ is required to portray Frege’s views more accurately (Reck 2005). This clarification gives us a better picture of what Frege is interested in and what he does not emphasize. Moreover, in such a clarifying process, we find that Frege draws significant influence from Rudolf Hermann Lotze, who is frequently called a Neo-Kantian (Vagnetti 2018). In Lotze’s major work, Logik, Lotze has a central focus on validity, in its most general form as he used it, that investigates various related topics, i.e., concepts, language, etc. (Vagnetti 2018; Lotze 1888). Furthermore, we observe that Frege’s work is so similar to Lotze, that it seems questionable to call his outlook ‘Platonism’. Therefore, attributing ‘Platonism’ to Frege may be a slight misnomer. This paper’s entirety is mostly a synthesis of a variety of articles related to Frege, Lotze, and their respective outlooks and the original works of Frege and Lotze that I use to support the view that the term ‘Platonism’ is a slight issue when predicated to Frege. As such, I include an overview of Frege’s treatment in other work that highlights the usage of the term ‘Platonism’ and how broad its uses tend to be utilized (Balaguer 2006; Burge 1992). In sum, it is observed that the general label ‘Platonism’ becomes less appropriate when we consider Lotze in the picture and contrast Lotze alongside Mr. Frege. Overall, this paper is just an explanatory one of Mr. Frege, the Platonist, and the issues of applying the term ‘Platonism’ onto him as his views are seemingly more of a segue from Lotze. Keywords: Frege, Lotze, number, objectification, Platonism, validity. (shrink)

The present article is the third part of a trilogy of papers, devoted to analysing the influence of semantic Platonism on contemporary philosophy of language. In Part I (Picazo 2021), the discussion was set out by examining a number of typical traces of Platonism in semantic theory since Frege. In Part II (Picazo 2021a), additional illustrations of such traces were provided, taken from a collection of recent commissioned essays on the philosophy of language (Schantz 2012). The present part (...) is devoted to providing yet additional illustrations of such traces, taken from a collection of classic essays on the subject: the book Modern Philosophy of Language, edited by Maria Baghramian in 1998. We shall, thus, describe a number of examples in which the influence of semantic Platonism on these essays can be felt. Prominent among these examples are the confusion between sentences and propositions (and related confusions), the avoidant attitude with respect to basic aspects of linguistic meaning, the overuse of analytic methodology for semantic research, the adoption of a background Platonic metaphysics of meanings and the overreaction against semantic Platonism and germane views, witnessing an inverse influence (‘by opposition’) from these views. (shrink)

This paper concerns an epistemological objection against mathematical platonism, due to Hartry Field.The argument poses an explanatory challenge – the challenge to explain the reliability of our mathematical beliefs – which the platonist, it’s argued, cannot meet. Is the objection compelling? Philosophers disagree, but they also disagree on (and are sometimes very unclear about) how the objection should be understood. Here I distinguish some options, and highlight some gaps that need to be filled in on the potentially most compelling (...) version of the argument. (shrink)

In this paper I argue that from the point of view of a theist, inclusivism with respect to the issue whether adherents of different religious traditions can have veridical experience of God (or Ultimate Reality) now, is more plausible than the Alstonian exclusivism. I suggest that mystical inclusivism of the kind I imply in this paper may contribute to the development of cross-cultural philosophy of religion, as well as to the theoretical framework for inter-religious dialogue, because (1) it allows for (...) the possibility of veridical experience of God in a variety of religious traditions, but (2) it avoids the radical revisionist postulates of Hickian pluralism and (3) it leaves open the question whether the creed of any specific tradition is a better approximation to the truth about God than the creeds of other traditions. (edited). (shrink)

This examination makes the case that the tradition of Christian Platonism can constitute a valuable resource for addressing the long-running and increasingly-acute environmental crisis that threatens the global ecosystem and all who inhabit it. More than a scientific, technological or political challenge, the crisis requires a fundamental shift in the way humans understand nature and their place within it. Key to implementing this shift is the need to address the problematic anthropocentric conceptualisation of nature characteristic of the contemporary social (...) imaginary that determines a wide range of present day economic, religious and scientific perspectives. The case made here is that Christian Platonism, and in particular its participatory ontology, can offer a radically non-anthropocentric alternative to the present-day understanding of nature, reconceptualising the way we understand the meaning, value, and way we know nature. (shrink)

Field’s challenge to platonists is the challenge to explain the reliable match between mathematical truth and belief. The challenge grounds an objection claiming that platonists cannot provide such an explanation. This objection is often taken to be both neutral with respect to controversial epistemological assumptions, and a comparatively forceful objection against platonists. I argue that these two characteristics are in tension: no construal of the objection in the current literature realises both, and there are strong reasons to think that no (...) version of Field’s epistemological objection which has both Neutrality and Force can be construed. (shrink)

This article examines Gilles Deleuze’s concept of the simulacrum, which Deleuze formulated in the context of his reading of Nietzsche’s project of “overturning Platonism.” The essential Platonic distinction, Deleuze argues, is more profound than the speculative distinction between model and copy, original and image. The deeper, practical distinction moves between two kinds of images or eidolon, for which the Platonic Idea is meant to provide a concrete criterion of selection “Copies” or icons (eikones) are well-grounded claimants to the transcendent (...) Idea, authenticated by their internal resemblance to the Idea, whereas “simulacra” (phantasmata) are like false claimants, built on a dissimilarity and implying an essential perversion or deviation from the Idea. If the goal of Platonism is the triumph of icons over simulacra, the inversion of Platonism would entail an affirmation of the simulacrum as such, which must thus be given its own concept. Deleuze consequently defines the simulacrum in terms of an internal dissimilitude or “disparateness,” which in turn implies a new conception of Ideas, no longer as self-identical qualities (the auto kath’hauto), but rather as constituting a pure concept of difference. An inverted Platonism would necessarily be based on a purely immanent and differential conception of Ideas. Starting from this new conception of the Idea, Deleuze proposes to take up the Platonic project anew, rethinking the fundamental figures of Platonism (selection, repetition, ungrounding, the question-problem complex) on a purely differential basis. In this sense, Deleuze’s inverted Platonism can at the same time be seen as a rejuvenated Platonism and even a completed Platonism. (shrink)

Plato’s philosophy is important to Badiou for a number of reasons, chief among which is that Badiou considered Plato to have recognised that mathematics provides the only sound or adequate basis for ontology. The mathematical basis of ontology is central to Badiou’s philosophy, and his engagement with Plato is instrumental in determining how he positions his philosophy in relation to those approaches to the philosophy of mathematics that endorse an orthodox Platonic realism, i.e. the independent existence of a realm of (...) mathematical objects. The Platonism that Badiou makes claim to bears little resemblance to this orthodoxy. Like Plato, Badiou insists on the primacy of the eternal and immu- table abstraction of the mathematico-ontological Idea; however, Badiou’s reconstructed Platonism champions the mathematics of post-Cantorian set theory, which itself af rms the irreducible multiplicity of being. Badiou in this way recon gures the Platonic notion of the relation between the one and the multiple in terms of the multiple-without-one as represented in the axiom of the void or empty set. Rather than engage with the Plato that is gured in the ontological realism of the orthodox Platonic approach to the philosophy of mathematics, Badiou is intent on characterising the Plato that responds to the demands of a post-Cantorian set theory, and he considers Plato’s philosophy to provide a response to such a challenge. In effect, Badiou reorients mathematical Platonism from an epistemological to an ontological problematic, a move that relies on the plausibility of rejecting the empiricist ontology underlying orthodox mathematical Platonism. To draw a connec- tion between these two approaches to Platonism and to determine what sets them radically apart, this paper focuses on the use that they each make of model theory to further their respective arguments. (shrink)