In this paper, we develop an alternative strategy, Platonized Naturalism, for reconciling naturalism and Platonism and to account for our knowledge of mathematical objects and properties. A systematic (Principled) Platonism based on a comprehension principle that asserts the existence of a plenitude of abstract objects is not just consistent with, but required (on transcendental grounds) for naturalism. Such a comprehension principle is synthetic, and it is known a priori. Its synthetic a priori character is grounded in the (...) fact that it is an essential part of the logic in which any scientific theory will be formulated and so underlies (our understanding of) the meaningfulness of any such theory (this is why it is required for naturalism). Moreover, the comprehension principle satisfies naturalist standards of reference, knowledge, and ontological parsimony! As part of our argument, we identify mathematical objects as abstract individuals in the domain governed by the comprehension principle, and we show that our knowledge of mathematical truths is linked to our knowledge of that principle. (shrink)

Atheistic Platonism is an alternative to both theism and nihilistic atheism. It shows how any jobs allegedly done by God are better done by impersonal Platonic objects. Without Platonic objects, atheism degenerates into an illogical nihilism. Atheistic Platonism instead provides reality with foundations that are eternal, necessary, rational, beautiful, and utterly mindless. It argues for a plenitude of mathematical objects, and an infinite plurality of possible universes. It provides mindless rational grounds for objective values, and for objective (...) moral laws for the persons who evolve in universes. It defines a meaningful way of life, which facilitates self-improvement. Atheistic Platonists argue for computational theories of life after death. Atheistic Platonism includes a rich system of spiritual symbols. It values transformational practices and ecstatic experiences. Where atheisms based on materialism fail, atheisms based on Platonism succeed. (shrink)

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)

According to standard mathematical platonism, mathematical entities (numbers, sets, etc.) are abstract entities. As such, they lack causal powers and spatio-temporal location. Platonists owe us an account of how we acquire knowledge of this inaccessible mathematical realm. Some recent versions of mathematical platonism postulate a plenitude of mathematical entities, and Mark Balaguer has argued that, given the existence of such a plenitude, the attainment of mathematical knowledge is rendered non-problematic. I assess his epistemology for such a (...) profligate platonism and find it unsatisfactory because it lacks an adequate semantics, in particular, an adequate account of reference. (shrink)

The great chain of being is an ontological conception in which all beings, from inanimate things to God, are ranked on a scale according to their perfectness. This hierarchical scheme, though widely known in the history of ideas, was systematically addressed by Arthur Lovejoy in 1936. The great chain of being as formulated by Lovejoy is composed of three main principles, whose roots can be found in Plato and Aristotle’s philosophies. These principles are “the principle of plenitude”, “the principle (...) of gradation” and “the principle of continuity.” The first principle, the principle of plenitude, was pointed out in Plato’s philosophy and the latter two, the principle of gradation and the principle of continuity, were addressed in Aristotle’s philosophy. According to Lovejoy, these three principles were systematically addressed in Plotinus’s philosophy and became an essential part of Neo-Platonic cosmology. Platon explains the abundance of beings with reference to the absolute goodness of the God in his famous book Timaios. Accordingly, God has absolute goodness and this attribution has given rise to an abundance of beings as goodness requires the existence of things. The other two principles, the principle of gradation and the principle of continuity, were forwarded by Aristotle and through his works affected Western thought. While the principle of gradation refers to the ranking of beings in a chain based on the criteria of their perfection, the principle of continuity is the natural consequence of that ranking in that all beings share at least a minimum level of similarity. Plotinus synthesized and systematized those three principles as an expression of ranked beings specific to emanation theory and added three hypostasis -One, Nous, and Soul- in addition to the natural world addressed in Aristotle’s works. Therefore, we see that beings were ranked from inanimate things to God in Plotinus’s works. This concept of hierarchical order of beings, the great chain of being, affected many cultures and philosophical ideas from Classical Islamic philosophy to the Western tradition. In this article, we confine our subject to only Western thought, including Medieval Christian theology and philosophy, the Renaissance period, and the Age of Enlightenment as well as a peculiar implication and interpretation of the great chain of being specific to modern times. In every period we will deal with just one thinker and their ideas to demonstrate the effect of the great chain of being on those thinkers’ philosophies and systems. In this context, we examined how Thomas Aquinas used the great chain of being to justify some theological and philosophical matters and tried to show how he utilized the principle of continuity effectively to explain the relationship between matter and soul. Marcilio Ficino, a Neo-Platonist philosopher of the Renaissance period, also used the great chain of being to explain the hierarchical order of beings and their ontological relationship to the perfect being, which is God, placing them in a rising line according to their closeness to God. On the other hand, when we come to the Age of Enlightenment we see that the great chain of being continues to be apparent in some philosophical works. One example is John Locke’s famous book An Essay Concerning Human Understanding. Here Locke tries to make sense of the existence of many species of spirits with reference to the great chain of being, especially by using the principle of continuity. This attempt of justification shows us that the great chain of being, as an old philosophical and ontological concept, was still used even in the Enlightenment. Finally, it would be beneficial to address how the chain of being in question was presented and understood in modern times. Unlike the justification of some philosophical or theological subjects, in modern times the hierarchical structure of the great chain of being has been anachronistically read into the theory of evolution with reference to some medieval Muslim philosophers’ works. This approach, however, springs from the figural similarities between the great chain of being and the theory of evolution, although the contents of both theories are completely different. It would be accepted easily that similarities in figure do not necessitate similarities in content. In short, the great chain of being has been very effectively used in the history of philosophy to justify different subjects in different areas such as philosophy and theology. In this article, we address the usages of the chain in question and trace its effects specific to the Western tradition from the ancient period to modern times. (shrink)

I suggest that in Kant’s conception of autonomy, we have a faithful variant of a perennial philosophical conception of divinity, distinctively re-configured by Kant’s own preoccupations and system, but still recognisably oriented around some philosophical conceptions of the divine, which have their origins in deep classical wells, with dreams and memories of thought-thinking-itself, and joyously diffusing itself, generating plenitude and harmony. If this is correct, then we might find that the most interesting dialogue in the realm of ‘public theology’ (...) is not necessarily between Christianity and secularism, but between Christianity and a latent pagan religious philosophy, that draws upon a perennial strand of Platonism in Western philosophy. (shrink)

A discussion of views first presented by this author and Edward Zalta in 1995 in the paper “Naturalized Platonism vs. Platonized Naturalism”. That paper presents an application of Zalta’s “object theory” to the ontology of mathematics, and claims that there is a plenitude of abstract objects, all the creatures of distinct mathematical theories. After a summary of the position, two questions concerning the view are singled out for discussion: just how many mathematical objects there are by our account, (...) and the nature of the properties we use to characterize abstract objects. The difference between the authors in more recent developments of the view are also discussed. (shrink)

Edited book containing the following essays: 1 Getting over Gettier, Alan Musgrave.- 2 Justified Believing: Avoiding the Paradox Gregory W. Dawes.- 3 Literature and Truthfulness,Gregory Currie.- 4 Where the Buck-passing Stops, Andrew Moore.- 5 Universal Darwinism: Its Scope and Limits, James Maclaurin, - 6 The Future of Utilitarianism,Tim Mulgan. 7 Kant on Experiment, Alberto Vanzo.- 8 Did Newton ʻFeignʼ the Corpuscular Hypothesis? Kirsten Walsh.- 9 The Progress of Scotland: The Edinburgh Philosophical Societies and the Experimental Method, Juan Gomez.- 10 Propositions: (...) Truth vs. Existence, Heather Dyke.- 11 Against Advanced Modalizing, Josh Parsons.- 12 Spread Worlds, Plenitude and Modal Realism: A Problem for DavidLewis, Charles R. Pigden and Rebecca E. B. Entwisle.- 13 Defending Quine on Ontological Commitment. 14. The Scandal of Platonism, Vladimír Svoboda.- 15 A Neglected Reply to Prior's Dilemma J. C. Beall. 16 Mathematical and Empirical Concepts, Pavel Materna.- 17 Post-Fregean Thoughts on Propositional Unity, Bjørn Jespersen.- 18 Best-path Theorem Proving: Compiling Derivations, Martin Frické.- 19 Is Imperative Inference Impossible?, Hannah Clark-Younger. ​. (shrink)

Since the publication of his first book in 1953, Yves Bonnefoy has become one of the most important French poets of the postwar years. At last, we have the long-awaited English translation of Yves Bonnefoy’s celebrated work, _L’Arrière-pays_, which takes us to the heart of his creative process and to the very core of his poetic spirit. In his poem, “The Convex Mirror,” Bonnefoy writes: “Look at them down there, at that crossroads, / They seem to hesitate, then go on.” (...) The idea of the crossroads haunts Bonnefoy’s work, as he is troubled by the idea that the path not taken may lead to the _arrière-pays_, a place of greater plenitude, and of more authentic being—an “elsewhere in the absolute.” Seized by this fear that what he terms “presence” exists always somewhere else, a little further on, Bonnefoy here sets out on a labyrinthine quest to find traces of this “original place,” which he locates not only in objects of knowledge and experience as diverse as the deserts of Asia, a hill fort in India, a church in Armenia, the painting of Piero della Francesca but also, crucially, in the undivided intensity of his experiences as a child. Written with a visionary grace, _The Arrière-pays_ is a spiritual testament to art, philosophy, and poetry. Enriched by a new preface by the poet, this volume also includes three recent essays in which he returns to his original account of an ethical and aesthetic haunting, one that recounts the struggle between our instinct to idealize—what he deems our eternal Platonism—and the equally strong need to combat this and to be reconciled with our nature as finite beings, made of flesh and blood, in the world of the here and now. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:BOOK REVIEWS 89 To fill the gap between the two worlds seems to have been one of the most important of their problems. Philo filled it with angels and powers, the Gnostics, whatever their individual differences, filled it with other supernatural creatures begotten by their chief god. Origen filled it with Intelligences, created and corporeal spirits who rose or fell according to their sinfulness (p. 437). The discrepancy between (...) the two worlds remains to be bridged by the later Greek philosophers not by reason but by the appeal to myth, imagination and authority. Only in Plotinus, among the late Greek philosophers, does Boas find a significant remainder of rationalism. Plotinus's problem is similar, to be sure, to that of the other late thinkers: to bridge the metaphysical gap. Appeals to myth and to the authority of earlier Greek thinkers are quite as irrational here as in the earlier thinkers. And the resort to powerful metaphors is as pronounced in Plotinus as in any other philosopher one can name. All this is brought out very well. Yet Boas finds it important to try to expound Plotinus's philosophy as "... a sample of rationalism with axioms and inferences, with dialectical distinctions, with the Law of Contradiction utilized to produce consistency" (p. 455). He doesn't claim to have succeeded in doing this; on the contrary, his account gives little ground on which to justify the attempt, and one wonders why it was undertaken. This is not to deny that Plotinus uses rational arguments and logical inferences, but rather to say that the semblance of a "rational structure" depends instead on poetical and metaphorical elements. Nevertheless, the discussion of Plotinus's thought as a "sample of rationalism" is of interest because it serve to bring out an element in the conception of rationalism which emerges only too rarely in the book? Boas pays special attention to Plotinus's "full fledged hierarchy of being," and his attempt to derive (or "deduce"?) the degrees of being from the One. This rests on the "principle of plenitude," or on the notion that all possible being must be exemplified in existence. This in turn is suggested by one or more powerful metaphors. Plotinus's speculative imagination, in other words, was still unfettered to a considerable degree by authority, revelation, or other restrictions. Kegardless of how adequate one might judge Plotinus's system to be in terms of axioms, definitions and consistency (and surely it is very inadequate), Boas's interest in him as a "sample of rationalism" derives from this freedom in speculation and in choice of "assumptions." This does not mean that logical criteria are not the proper tools of the critic nor that they can be disregarded by the speculative philosopher. It means only that Greek rationalism rested on considerably more; a magnificently free and speculative strain of mind. This is one matter that Boas's discussion makes amply clear. JOHN D. GOHEEN Stanford University Origbne et la Philosophie. By Henri Crouzel. (l~tudes Publi6es sous la Direction de la Facult6 de Th6ologie SJ de Lyon-Fourvi~re; Aubier, 1962. Pp. 238.) This is a painstaking and important essay set between fairly narrow limits. It deliberately stays short of becoming a study of Origenism rather than Origen, and thus avoids the mistake made by so many books about Origen. The field is quite difficult of course. We are still a long way from proper evaluation of the Christian-Hellenist synthesis in 4 However, explicitly stated on pp. 355-356. 90 HISTORY OF PHILOSOPHY the thinking of many Christian figures from the second century to the fourth. Could not the same be said perhaps, rnutatis mutandis, of some Hellenist writers, Celsus, Porphyry, Plotinus? Origen, as well as being more important, is considerably more complicated than most. Is he the first great Christian sumrnator, ~ la Aquinas? Is he a Platonist masquerading as a Christian? Or a Christian masquerading as a Hellenist? In the rough phrase that used to be applied in the schools of theology, auctores scinduntur, sometimes with extreme acrimony. He has been receiving a good deal of attention over the past fifty years, from Bohringer, De Faye, Koch--the list is awfully long-right... (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)

The principle of plenitude says that every material object coincides with abundantly many further objects that differ in their modal profiles. A necessarily unmanifested disposition is a disposition that necessarily does not manifest. This paper argues that if the principle of plenitude holds, then there are some necessarily unmanifested dispositions. These necessarily unmanifested dispositions will be argued to evade some objections against the cases of necessarily unmanifested dispositions put forward by Carrie Jenkins and Daniel Nolan.

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)

Which mathematical structures are possible, that is, instantiated by the concrete inhabitants of some possible world? Are there worlds with four-dimensional space? With infinite-dimensional space? Whence comes our knowledge of the possibility of structures? In this paper, I develop and defend a principle of plenitude according to which any mathematically natural generalization of possible structure is itself possible. I motivate the principle pragmatically by way of the role that logical possibility plays in our inquiry into the world.

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)

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 a set of ideas which I will call ‘essentialist plenitude.’ Very roughly, and to a first approximation, essentialist plenitude says that wherever there is an object with properties P1, …, Pn there is in fact a plenitude of coincident objects that differ only in the distribution of essentiality and accidentality across P1, …, Pn (§1). The main purpose of this paper is to arouse the suspicion that essentialist plenitude (...) may have far-reaching consequences for the semantics of proper names. More specifically, I will argue that neither descriptivist nor causal theories of proper names work in a plenitude setting (§2). I will close by suggesting that our use of proper names may be thoroughly infected by semantic indecision about which among many coincident objects is referred to (§3). (shrink)

Platonism about mathematics (or mathematical platonism) is the metaphysical view that there are abstract mathematical objects whose existence is independent of us and our language, thought, and practices. In this survey article, the view is clarified and distinguished from some related views, and arguments for and against the view are discussed.

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)

El autor aborda el tema de la plenitud y la escasez conectándolos al conflicto entre la orientación hacia el bien común y hacia el cálculo individual de la utilidad, como realidad que debe ser reconocida y que solo puede ser solucionada por medio de mediaciones. En el desarrollo del artículo el autor nos presenta los elementos de dicho conflicto, y desarrolla su propuesta que se fundamenta en que existe para el hombre la cualidad de realizar el cielo en la tierra, (...) pues existiría un núcleo celeste de lo terrenal, que la modernidad occidental requiere redescubrir para liberarse del mundo del cálculo de utilidad. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Ideas 61.4 (2000) 539-560 [Access article in PDF] Plenitude, Possibility, and the Limits of Reason: A Medieval Arabic Debate on the Metaphysics of Nature Taneli Kukkonen In a recent article Simo Knuuttila has examined the argumentative patterns of modern cosmology, especially the search in fundamental physics for an "ultimate explanation," a unified "Theory of Everything" that would subsume all more local theories under (...) its aegis. Knuuttila goes on to compare contemporary modes of explanation with previous ways of conceiving of the metaphysics of understanding. As it turns out, on the cosmological borderline where physics shades into metaphysics desires similar at heart have fueled the efforts of thinkers throughout the history of western thought. When what is at stake is the final intelligibility of the world, shared ideals of necessity, transparency, and simplicity come to the fore. More often than not, theological concerns and preconceptions accompany these notions. 1One can react to this finding in one of two ways, either by retorting that the moderns have not gotten very far or by pointing out that earlier discussions on the topic were often quite philosophically sophisticated. In this article I propose to investigate how some of the issues raised by Knuuttila figure in a specific historical context. This is the debate on the pre-eternity of the world initiated by the celebrated Muslim theologian Abû Hâmid al-Ghazâlî (1058-1111) in his polemic arguing for The Incoherence of the Philosophers (Tahâfut al-falâsifa, 1095) and later picked up by the Andalusian philosopher Averroës (1126-98) in [End Page 539] his reply, The Incoherence of the Incoherence (Tahâfut al-tahâfut, 1180). 2 The exceptionally rich cosmological materials could be taken in any number of directions, but I will focus on three main issues: the discussants' construction of the domain of possibilities (i.e. the relation of the possible to the actual), their understanding of the reasonability of creation, and the question of its finitude and infinity. The study is undertaken partly to illustrate the sophistication with which the topics were handled in medieval Islamic philosophy, but in each case I will also draw parallels with certain modern conceptions, and I submit that in each case al-Ghazâlî's and Averroës's debate throws light on the contemporary discussion. In the final section I will develop this contention further by pointing to a connection between finitude and possibilities which I believe has both heuristic and existential value. Plenitude and Possibility Among historians of philosophy it is now acknowledged that in late medieval discussions certain modal theoretical innovations were instrumental in bringing about profound change in the western worldview. A conceptual shift occurred where, roughly speaking, a single intelligible universe was exchanged for several possible worlds. In Knuuttila's estimation this change in worldviews was in some ways more fundamental than anything modern science has produced since. 3 This claim deserves consideration but I would like first to outline what the change was about, for in al-Ghazâlî's and Averroës's debate this shift in modal paradigms is clearly discernible.Representative of the philosophers' point of view, Averroës holds onto the received Arabic Aristotelian interpretation of setting possibilities in a statistical temporal-frequency framework. According to this account, what is truly possible must at some time be realized--this is a technical interpretation of what has after Lovejoy commonly become known as the principle of plenitude. 4 As a [End Page 540] corollary, what always is is necessarily. The cosmological consequences of these assumptions can be outlined as follows. First, lest God's creative possibilities be limited, it must be admitted that the world could have been created however long ago in the past. By extension God must have been able to create the world an infinite time ago. But if it is a genuine possibility that the world is eternally old, then according to the principle of plenitude, this possibility is an actual fact. Once it is... (shrink)

I consider three candidates for ultimate understanding: (1) ultimate agency, the familiar idea of understanding the existence and nature of the universe as created by God for good reasons; (2) axiarchism, the initially counter-intuitive idea that goodness is the first cause of contingent reality; and (3) plenitude, the thesis that all possible types of situation are real. After some initial clarification, I note the problems with axiarchism, and offer solutions. These solutions require the unification of space and time as (...) space-time, and the consequent introduction of what might be called hypertime, but which I take to be true time—Time with an upper case “T”. I note how axiarchism and plenitude may be combined into the Plenum Bonum thesis that all and only good universes are real. Next, I note some problems with agency as an ultimate way of understanding. Finally, I solve these by means of a theory of agency as completing axiarchism, the Good versus Good theory. (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)

A response is given here to Benacerraf's 1973 argument that mathematical platonism is incompatible with a naturalistic epistemology. Unlike almost all previous platonist responses to Benacerraf, the response given here is positive rather than negative; that is, rather than trying to find a problem with Benacerraf's argument, I accept his challenge and meet it head on by constructing an epistemology of abstract (i.e., aspatial and atemporal) mathematical objects. Thus, I show that spatio-temporal creatures like ourselves can attain knowledge about (...) mathematical objects by simply explaininghow they can do this. My argument is based upon the adoption of a particular version of platonism — full-blooded platonism — which asserts that any mathematical object which possiblycould exist actuallydoes exist. (shrink)

'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)

Leibniz entertained the idea that, as a set of “striving possibles” competes for existence, the largest and most perfect world comes into being. The paper proposes 8 criteria for a Leibniz-world. It argues that a) there is no algorithm e.g., one involving pairwise compossibility-testing that can produce even possible Leibniz-worlds; b) individual substances presuppose completed worlds; c) the uniqueness of the actual world is a matter of theological preference, not an outcome of the assembly-process; and d) Goedel’s theorem implies that (...) there can be no algorithm for producing optimal worlds, assuming an optimal world contains truth-discerning creatures, though this is not to say that such worlds cannot arise naturally. (shrink)

This article moves from the observation that one of the key characteristics of contemporary Italian fiction is a preoccupation with ethics and more specifically with the issues raised by the “ethical turn” in contemporary philosophy and theory. Current literary criticism, it is argued, has been slow to respond to the ethical dimension of these narratives whose innovative and important cultural contribution has yet to be fully appreciated. It is therefore necessary to develop a keener sensitivity to the ethical discourses developed (...) in these literary texts, but this can only be achieved by first confronting some fundamental questions about the relationship between ethics and literature today. The answers to these questions make it possible to elaborate an initial conceptual framework that can re-orient reading and enable the critic to respond adequately to the ethical issues raised in and by the narrative. Accordingly, in this article the author proposes to explore from a theoretical perspective the relationship between ethics and literature in the context of the historical and philosophical predicaments of contemporary society. The discussion is divided into two parts: the first is devoted to an exploration of contemporary ethical thinking, and the second on the contribution that literature can make to that thinking. In the first part, the author proposes an approach to ethics based on the virtue tradition which, since Aristotle, has defined ethics as the search for "the good life." This tradition, however, is transformed through an engagement with the work of Gilles Deleuze and Immanuel Levinas. From Deleuze the author draws the idea that the good life is one devoted to pursuing human plenitude through the multiplication of connections and intensities. From Levinas, on the other hand, emerges a powerfully haunting description of an ethical life marked by absolute responsibility for and obligation to the other. These two seemingly opposed views are not construed as irreconcilable and contradictory but rather as vectors which keep opposing tensions in check and ultimately define a necessary negotiation between the desire for human plenitude and the acknowledgement of responsibility for other human and non human life. Ultimately my argument is that such tensions establish the ethical terrain in which contemporary narratives seek to intervene. In the second part of the article, the nature and possibilities of such an intervention are explored through six theses which provocatively articulate the relationship between literature and ethics. The cornerstone thesis is that literature is an encounter. Each subsequent thesis endeavours to develop this initial assertion and explore its consequences. The theses are accompanied by a gloss which unfolds its meaning and significance: the answers that the given thesis provides but also the questions that it raises. Together, the theses provide a heuristic framework for a literary criticism sensitive to ethical issues and therefore capable of grappling with the important cultural work carried out in fictions that have struggled to receive the recognition they deserve. (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)

Leibniz entertained the idea that, as a set of “striving possibles” competes for existence, the largest and most perfect world comes into being. The paper proposes 8 criteria for a Leibniz-world. It argues that a) there is no algorithm e.g., one involving pairwise compossibility-testing that can produce even possible Leibniz-worlds; b) individual substances presuppose completed worlds; c) the uniqueness of the actual world is a matter of theological preference, not an outcome of the assembly-process; and d) Goedel’s theorem implies that (...) there can be no algorithm for producing optimal worlds, assuming an optimal world contains truth-discerning creatures, though this is not to say that such worlds cannot arise naturally. (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)

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)

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.

A fierce critique of productivity and sovereignty in the world of labor and everyday life, Bruno Gullì’s Earthly Plenitudes asks, can labor exist without sovereignty and without capitalism? He introduces the concept of dignity of individuation to prompt a rethinking of categories of political ontology. Dignity of individuation stresses the notion that the dignity of each and any individual being lies in its being individuated as such; dignity is the irreducible and most essential character of any being. Singularity is a (...) more universal quality. Gullì first reviews approaches to sovereignty by philosophers as varied as Gottfried Leibniz and Georges Bataille, and then looks at concrete examples where the alliance of sovereignty and capital cracks under the potency of living labor. He examines contingent academic labor as an example of the super-exploitation of labor, which has become a global phenomenon, and as such, a clear threat to the sovereign logic of capital. Gullì also looks at disability to assert that a new measure of humanity can only be found outside the schemes of sovereignty, productivity, efficiency, and independence, through care and caring for others, in solidarity and interdependence. (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"--.

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.

Material Plenitude is the view that there is an abundance of coincident objects wherever there is any material object. Although plenitude has garnered increased attention from metaphysicians in recent years, it has yet to be well‐understood beyond its slogan from. The goal of this article is to explore a few places for puzzlement about plenitude; in particular, how we ought to motivate and formulate the target view. I'll suggest along the way that an investigation of plenitude (...) is not merely of interest in its own right, but can provide valuable insights into abundant ontologies more generally. (shrink)

Platonism has played a central role in Christianity and is essential to a deep understanding of the Christian theological tradition. At times, Platonism has constituted an essential philosophical and theological resource, furnishing Christianity with an intellectual framework that has played a key role in its early development, and in subsequent periods of renewal. Alternatively, it has been considered a compromising influence, conflicting with the faith's revelatory foundations and distorting its inherent message. In both cases the fundamental importance of (...) Platonism, as a force which Christianity defined itself by and against, is clear. Written by an international team of scholars, this landmark volume examines the history of Christian Platonism from antiquity to the present day, covers key concepts, and engages issues such as the environment, natural science and materialism. (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.

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)

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)

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)