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.
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)
A debated issue in the mathematical foundations in at least the last two decades is whether one can plausibly argue for the merits of treating undecidable questions of mathematics, e.g., the Continuum Hypothesis, by relying on the existence of a plurality of set-theoretical universes except for a single one, i.e., the well-known set-theoretical universe V associated with the cumulative hierarchy of sets. The multiverse approach has some varying versions of the general concept of multiverse yet my intention is to primarily (...) address ontological multiversism as advocated, for instance, by Hamkins or Väätänen, precisely for the reason that they proclaim, to the one or the other extent, ontological preoccupations for the introduction of respective multiverse theories. Taking also into account Woodin’s and Steel’s multiverse versions, I take up an argumentation against multiversism, and in a certain sense against platonism in mathematical foundations, mainly on subjectively founded grounds, while keeping an eye on Clarke-Doane’s concern with Benacerraf’s challenge. I note that even though the paper is rather technically constructed in arguing against multiversism, the non-negligible philosophical part is influenced to a certain extent by a phenomenologically motivated view of the matter. (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)
Introduction -- What is platonism? -- Schleiermacher's pedagogical interpretation of Plato -- What's wrong with the current debate -- The romantic rediscovery of Plato's ineffable ontology -- Conclusions: Ineffability and dialogue form -- Untying Schleiermacher's gordian knot -- Metaphysical ineffability : the argument from language and human finitude -- Spiritual ineffability: the argument from self-transformation -- Existential ineffability : the argument from life choice -- Platonism reconsidered -- The context of Heidegger's interpretation of Plato -- What it all means and (...) why it matters -- Stage one: the realm of shadows -- Stage two: the fire -- Stage three: the realm of light -- The good : Heidegger's Plato is the later Heidegger -- Stage four: the return to the shadows -- The virtues of heidegger's plato -- Heidegger's crisis and opportunity -- Setting the stage -- Heidegger's crisis -- Understanding Heidegger's crisis : Nietzsche -- Heidegger as reformed madman -- Revolutionary thinker or utopian social engineer -- The Greeks and university reform -- Theoria and fundamental ontology -- A community of similarly striving researchers -- University reform and nihilism -- Back from Syracuse : four reasons to rethink Heidegger's politics -- The ontological problem -- The epistemological problem -- The moral problem -- The political problem -- What was plato doing in Syracuse -- Back from Syracuse or Eros Tyrannos -- How Heidegger should have read Plato -- Plato anticipate Heidegger's critique of technology -- Plato's problems with periclean Athens -- Alcibiades as embodiment of periclean Athens -- Alcibiades as inverted image of Socrates -- Conclusions: What Heidegger missed. (shrink)
Enhanced indispensability arguments claim that Scientific Realists are committed to the existence of mathematical entities due to their reliance on Inference to the best explanation. Our central question concerns this purported parity of reasoning: do people who defend the EIA make an appropriate use of the resources of Scientific Realism to achieve platonism? We argue that just because a variety of different inferential strategies can be employed by Scientific Realists does not mean that ontological conclusions concerning which things we should (...) be Scientific Realists about are arrived at by any inferential route which eschews causes, and nor is there any direct pressure for Scientific Realists to change their inferential methods. We suggest that in order to maintain inferential parity with Scientific Realism, proponents of EIA need to give details about how and in what way the presence of mathematical entities directly contribute to explanations. (shrink)
Jody Azzouni has offered the following argument against the existence of mathematical entities: if, as it seems, mathematical entities play no role in mathematical practice, we therefore have no reason to believe in them. I consider this argument as it applies to mathematical platonism, and argue that it does not present a legitimate novel challenge to platonism. I also assess Azzouni's use of the ‘epistemic role puzzle’ (ERP) to undermine the platonist's alleged parallel between skepticism about mathematical entities (...) and external-world skepticism. I conclude that ERP fails to undermine this parallel. (shrink)
This volume contains the selected discourses of four seventeenth-century philosophers, carefully chosen to illustrate the tenets characteristic of the influential movement known as Cambridge Platonism. Fundamental to their beliefs is the statement most clearly voiced by Benjamin Whichcote, their leader by common consent, that the spiritual is not opposed to the rational, nor Grace to nature. Religion is based on reason, even in the presence of 'mystery'. Free will and Grace are not mutually exclusive. The editor's comprehensive introduction delineates (...) the main principles of the Cambridge Platonists, in the light of their heritage. It compares their attitude to contemporary thought, stressing their mistrust both of institutionalised religion and of the rising tide of materialism. The sermons are reprinted from the original texts and fully annotated with comparisons and references to a wide range of works. The editor also includes a useful list for further reading, biographical notes and a comprehensive index. (shrink)
The Sovereignty of Reason is a survey of the rule of faith controversy in seventeenth-century England. It examines the arguments by which reason eventually became the sovereign standard of truth in religion and politics, and how it triumphed over its rivals: Scripture, inspiration, and apostolic tradition. Frederick Beiser argues that the main threat to the authority of reason in seventeenth-century England came not only from dissident groups but chiefly from the Protestant theology of the Church of England. (...) The triumph of reason was the result of a new theology rather than the development of natural philosophy, which upheld the orthodox Protestant dualism between the heavenly and earthly. Rationalism arose from a break with the traditional Protestant answers to problems of salvation, ecclesiastical polity, and the true faith. Although the early English rationalists were not able to defend all their claims on behalf of reason, they developed a moral and pragmatic defense of reason that is still of interest today. Beiser's book is a detailed examination of some neglected figures of early modern philosophy, who were crucial in the development of modern rationalism. There are chapters devoted to Richard Hooker, the Great Tew Circle, the Cambridge Platonists, the early ethical rationalists, and the free-thinkers John Toland and Anthony Collins. (shrink)
Recently Colin Cheyne and Charles Pigden have challenged supporters of mathematical indispensability arguments to give an account of how causally inert mathematical entities could be indispensable to science. Failing to meet this challenge, claim Cheyne and Pigden, would place Platonism in a no win situation: either there is no good reason to believe in mathematical entities or mathematical entities are not causally inert. The present paper argues that Platonism is well equipped to meet this challenge.
In this dissertation, I defend a view that combines an analytic conception of a priori knowledge with a version of reliabilist platonism. Roughly put, the analytic theory is the view that our a priori knowledge can be explained by our grasp of analytic truths. Platonism is the view that there are abstract objects and those objects are partly responsible for some of our knowledge. My primary goal is to show that the hybrid account I develop solves central problems that arise (...) for the analytic view and platonism on their own. One well-known difficulty facing platonism is the following epistemological concern: given that abstracta are causally inefficacious, it is unclear how we can ever come to know anything about them. I argue that platonism on its own cannot adequately address this problem. Likewise, there is the following serious difficulty for the analytic theory: given the central role of implicit definitions for the analytic theory, if there are good reasons to doubt the unqualified success of such stipulations, it seems that the analytic theory fails to explain our a priori knowledge. I also show that this is a serious problem for the analytic theory. However, I show how a combination of the analytic theory and platonism can address both sets of difficulties: one view makes up for the shortcomings of the other. On the one hand, reliabilist platonism helps explain the success of the relevant stipulations; on the other hand, the analytic theory helps show why the causal inefficacy of abstracta is not a problem for our a priori knowledge. (shrink)
INTRODUCTION TO THE ARGUMENT AND ITS HISTORY PRIOR TO THE AND CENTURIES In the history of ideas, there is an argument that has been used repeatedly, ...
I present a new argument to the effect that platonism about abstract entities undermines metaphysical naturalism and provides some support to theism. I further suggest that there are ways of extending this line of reasoning to point toward one or another more specific varieties of Christian theism.
Mark Balaguer argues for full blooded platonism (FBP), and argues that FBP alone can solve Benacerraf's familiar epistemic challenge. I note that if FBP really can solve Benacerraf's epistemic challenge, then FBP is not alone in its capacity so to solve; RFBP—really full blooded platonism—can do the trick just as well, where RFBP differs from FBP by allowing entities from inconsistent mathematics. I also argue briefly that there is positive reason for endorsing RFBP.
Plato can claim a preeminent place in the philosophy of education, for two reasons at least. The first is that he started the subject; the second is that he expressed with a force which has not since been surpassed a particular, seemingly authoritarian, view about it. Any liberal has to come to grips with this view, for which ‘Platonism’ is still the most appropriate name; and the first step is to determine more exactly what, in essence, the view is. This (...) paper will not be concerned with the close examination of Plato’s text; that must be left for a book about his moral philosophy that I am working on. I shall say nothing about the quaint details of the educational curriculum in the Republic or the Laws, which have distracted the attention of some commentators from more fundamental problems. What I aim to discuss is the question ‘Can virtue be taught?’, with which Plato introduces the subject in the Meno—the question which more than any other provides the incentive for his entire philosophical enterprise. (shrink)
Though many working mathematicians embrace a rough and ready form of Platonism, that venerable position has suffered a checkered philosophical career. Indeed the three schools of thought with which most of us began our official philosophizing about mathematics—Intuitionism, Formalism, and Logicism—all stand in fundamental disagreement with Platonism. Nevertheless, various versions of Platonistic thinking survive in contemporary philosophical circles. The aim of this paper is to describe these views, and, as my title suggests, to trace their roots.I'll begin with some preliminary (...) remarks about the big three schools. This seems a reasonable approach to the issues both because most observers are familiar, at least in a general way, with the tenets of Intuitionism, Formalism, and Logicism, and because it is in reaction to these that contemporary Platonism has taken shape. (shrink)
The present dissertation includes three chapters: chapter one 'Challenges to platonism'; chapter two 'counterparts of non-mathematical statements'; chapter three 'Nominalizing platonistic accounts of the predictive success of mathematics'. The purpose of the dissertation is to articulate a fundamental problem in the philosophy of mathematics and explore certain solutions to this problem. The central problematic is that platonistic mathematics is involved in the explanation and prediction of physical phenomena and hence its role in such explanations gives us good reason to (...) believe that platonism is true. On the other hand, we have grounds, essentially epistemological, for avoiding the use of platonistic mathematics. ;This philosophical tension can be relieved only by showing that good non-platonistic explanations of physical phenomena are available or by showing that the epistemological objections to platonism may be overcome. While both options are discussed in some detail, a certain emphasis is placed on the task of fashioning non-platonistic accounts of physical phenomena to replace the usual platonistic accounts. As is suggested in chapter one, the reason for this emphasis is that the referential and more broadly epistemological objections to platonism seem quite convincing. Of paramount interest in regards to an inquiry into the utility of mathematics is the status of biconditional statements connecting non-mathematical statements with their mathematical counterparts. ;In chapters two and three of the dissertation I address certain key philosophical issues surrounding the status of these biconditionals. The upshot of these chapters is that these biconditionals can be used to illuminate the utility of mathematics; and there is good reason to think an account of the utility of mathematics can be given without acknowledging the truth of mathematics. (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)
John Smith (1618-1652), long known for the elegance of his prose and the breadth of his erudition, has been underappreciated as a philosophical theologian. This book redresses this by showing how the spiritual senses became an essential tool for responding to early modern developments in philosophy, science, and religion for Smith. Through a close reading of the Select Discourses (1660) it is shown how Smith’s theories of theological knowledge, method, and prophecy as well as his prescriptive account of Christian piety (...) rely on his spiritual aesthetics. Smith offers a coherent system with intellectual intuition informing natural theology and revelation supplemented by spiritual perception via the imagination too. The central uniting feature of Smith’s philosophical theology is thus ‘spiritual sensation’ broadly construed. The book closes with proposals for research on Smith’s influence on the accounts of the spiritual senses developed by significant later figures including Jonathan Edwards (1703-1758) and John Wesley (1703-1791). (shrink)
Books M and N of Aristotle's Metaphysics receive relatively little careful attention. Even scholars who give detailed analyses of the arguments in M-N dismiss many of them as hopelessly flawed and biased, and find Aristotle's critique to be riddled with mistakes and question-begging. This assessment of the quality of Aristotle's critique of his predecessors (and of the Platonists in particular), is widespread. The series of arguments in M 2 (1077a14-b11) that targets separate mathematical objects is the subject of particularly strong (...) criticism by Annas and Ross. Two related arguments in this series (1077a14-20 and 1077a24-31) will serve as cases in point. The principal charges made against these arguments (that Aristotle misunderstands or misrepresents his opponents' views, and that he engages in question-begging because he presupposes his own metaphysical views) are frequently made against Aristotle's critique of Platonist positions more generally. If, as I argue, these charges are false for our two test case arguments, then there is good reason to think that they might also be false when they are leveled against the other arguments in this M 2 series. And, although presenting an argument for this is beyond the scope of this paper, this suggests that these two charges are more often than not false when applied to Aristotle's critique of Platonist mathematical views in M-N and beyond. (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)
The Quine/Putnam indispensability argument is regarded by many as the chief argument for the existence of platonic objects. We argue that this argument cannot establish what its proponents intend. The form of our argument is simple. Suppose indispensability to science is the only good reason for believing in the existence of platonic objects. Either the dispensability of mathematical objects to science can be demonstrated and, hence, there is no good reason for believing in the existence of platonic objects, (...) or their dispensability cannot be demonstrated and, hence, there is no good reason for believing in the existence of mathematical objects which are genuinely platonic. Therefore, indispensability, whether true or false, does not support platonism. (shrink)
Vetter (2015) develops a localised theory of modality, based on potentialities of actual objects. Two factors play a key role in its appeal: its commitment to Hardcore Actualism, and to Naturalism. Vetter’s commitment to Naturalism is in part manifested in her adoption of Aristotelian universals. In this paper, we argue that a puzzle concerning the identity of unmanifested potentialities cannot be solved with an Aristotelian conception of properties. After introducing the puzzle, we examine Vetter’s attempt at amending the Aristotelian conception (...) in a way that avoids the puzzle, and conclude that this amended version is no longer to be considered naturalistic. Potentiality theory cannot be both actualist and naturalist. We then argue that, if naturalism is to be abandoned by the actualist, there are good reasons to adopt a Platonist conception of universals, for they offer a number of theoretical advantages and allow us to avoid some of the problems facing Vetter’s theory. (shrink)
I first ask what it is to make up a story. In order to answer that question, I give existence and identity conditions for stories. I argue that a story exists whenever there is some narrative content that has intentionally been made accessible. I argue that stories are abstract types, individuated by the conditions that must be met by something in order to be a properly formed token of the type. However, I also argue that the truth of our story (...) identity attributions---sentences like, "Peter Jackson's Lord of the Rings is the same story as JRR Tolkien's Lord of the Rings''---are relative to their context of use, so that the same attribution of identity might be true in one context or false in another because of a change in what's being said about the works in the differing contexts. From those existence and identity conditions, I draw the conclusions that story is best understood to be a phase sortal of some abstract types, and that what it is to make up a story is to identify a type of narrative representation and its content, such that the content is neither based on actual events nor on the content of other stories to an objectionable degree. In chapter 2, I ask what it is for a story to be complete. I argue for the general meta-thesis I call "Completion Pluralism", viz. that there are many kinds of artwork completeness, many corresponding senses of 'complete', and no kind of artwork completeness is objectively more important than any other. I give a pair of arguments against those who would deny Completion Pluralism, endorsing Completion Monism instead. First, I show how Monistic analyses of the one kind of artwork completeness fail. I also show that each Monistic theory's failure is contingent on the assumption of Completion Monism: the denial of Completion Monism dissolves each argument against the extensional adequacy of extant theories of artwork completeness. I argue that this is all best explained by the idea that Completion Pluralism is true. Second, I argue that Completion Pluralism fits best with the variety of interests that we bring to questions about artwork completeness: there is no single or overriding concern we have when we want to know whether an artwork is complete. We shouldn't expect completeness to be a single sort of thing, then. I show how to put Completion Pluralism to work by identifying different kinds of artwork completeness in artworks. Finally, I introduce a new kind of completeness particular to stories, what I call "narrative completion", and show how it's distinct from other kinds of completeness discussed. In chapter 3, I argue that the distinction between fictional and non-fictional stories is the degree to which stories are made-up. In short, a fictional story is a made-up story. I first provide a couple desiderata for thinking about theories of fiction, then show how the two most popular extant theories of fiction---the prop theory and the genre theory---fall short in meeting one or more of those desiderata to some extent. I then show how the theory that fictions are made-up stories better meets the desiderata, using my account of what it is to make up a story from chapter 1. I turn to explicitly ontological matters in chapter 4. Addressing the question of what stories are, I show that both the theses that they are eternal and immutable and that they are created and historical seem plausible for independent reasons. I discuss a schema of an argument some philosophers who hold to the latter view attempt to give for their view. However, I show how those who hold to the view that stories are eternal and immutable can account for all the same appearances as the Creationists, usually at least as well and sometimes with a better accounting. Similar, deductive arguments for Platonism will give rise to similar responses from the Creationist, however. In the end, then, the style of argument in particular is unlikely to advance the discussion much. Finally, I attempt to advance the discussion by building an abductive case for Platonism. First, I vindicate a particular metaontological methodology for the debate at hand, a methodology that allows for "revisionary" outcomes in our ontologies of art objects. Second, I build a case for Platonism by arguing that it best explains a number of features of stories discussed in the previous chapters. Moreover, I argue that Creationism is committed to an implausible account of how some abstract objects come into existence. Given the combination of those facts, I argue that we should prefer Platonism to Creationism. (shrink)
The problem of Divine Ideas is one of the most consequential in the entire history of Western Thought, and effects of the Medieval debate on exempla-rism can still be found in Early Modern and Modern metaphysics. Speaking of the Middle Ages, such a topic provides a vivid example of the prominent role played by Platonism in the tradition of the Schools in the 13th and the 14th century, often associated with the sole authority of Aristotle. Among the different traditions animating (...) the Schools at this stage, the Franciscan is surely one of the most sensitive to this topic, both because of the relevance attributed to Augustine as a fundamental authority of the Order, and of the turning point brought about by Bonaventure. These are just a few of the reasons why the collective volume Divine Ideas in Franciscan Thought (XIIIth-XIVth Century), edited by Jacopo Francesco Falà and Irene Zavattero, should be welcomed. The book is published within the series of medieval studies Flumen Sapientiae, directed by Irene Zavattero. It collects chapters in English and Italian, all dealing with Medieval Franciscan thought in the 13th to the 14th centuries, authored by a team made up of experienced and younger scholars. Five precious textual appendixes in Latin (Olivi, Trabibus, Novocastro, Caracciolus, Mayronis) accompany the essays, providing very useful study materials. (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)
Matthew arnold maintains in the nineteenth century the renaissance school of the cambridge platonists. for them, reason and religion are by no means at odds: reason is in fact "the candle of the lord." for matthew arnold in "literature and dogma", christianity will prevail only by being shorn of its supernaturalist elements and set on its true rational ground. ernst cassirer has shown how the cambridge platonists bridge the gap between the italian renaissance and the german humanists of (...) the "goethezeit", chiefly through shaftesbury. arnold accordingly finds in herder and goethe the corroboration of his revered countrymen glanvill, whichcote, more and smith. (shrink)
ABSTRACT‘expressionist’ accounts of applied mathematics seek to avoid the apparent Platonistic commitments of our scientific theories by holding that we ought only to believe their mathematics-free nominalistic content. The notion of ‘nominalistic content’ is, however, notoriously slippery. Yablo's account of non-catastrophic presupposition failure offers a way of pinning down this notion. However, I argue, its reliance on possible worlds machinery begs key questions against Platonism. I propose instead that abstract expressionists follow Geoffrey Hellman's lead in taking the assertoric content of (...) empirical science to be irreducibly modal, using the ‘non-interference’ of mathematical objects as justification for detaching nominalistic consequences. (shrink)
This paper is a critical examination the claim that Galileo was a Platonist. It contends that neither his use of mathematics (as Koyre asserts), nor his hypothetic-deductive method of testing (as Cassirer maintains), nor a realistic interpretation of this abstract theories (as Crombie argues) offers reasonable and consistent evidence that Galileo shared or advocated the metaphysics or methods of Plato.
Pascal is well known to be an early modern disciple of Augustine, but it has not always been sufficiently emphasized that Pascal’s Augustinianism differs profoundly from its source in many ways. The following essay examines his re-ordering of Augustine’s psychology and its implications for philosophy and religion in the modern period. For Augustine, intellect and will are equal moments in the activity of mens, but Pascal is radically voluntarist. For him, the will’s relation to the good radically transcends intellect’s relation (...) to being. This moves Pascal to a position closer in some respects to neo-Platonism. It also prevents him from appropriating Augustine’s claim that the triadic human mens is a created analogue of the Trinity. Pascal drops Augustine’s teaching on this point, with profound consequences for his conception of humanity’s relation to God. (shrink)
John Smith (1618-1652), the 17th century Cambridge Platonist, employed the traditional language of the spiritual senses of the soul to develop an early modern theological aesthetic central to his religious epistemology and thus to his philosophy of religion and systematic theology. As a Christian Platonist, Smith advocated intellectual intuition of Divine Goodness as the key to theological knowledge and spiritual practice. Additionally, Smith’s theory of prophecy rests on the reception of sensible images in the imagination. Chapter one lays (...) out how Smith’s place in this tradition has been under-appreciated by scholars working on the Cambridge Platonists and the spiritual senses. Chapter two presents an interpretive summary of the spiritual senses tradition and proposes a functional typology that registers three uses of non-corporeal perception throughout the history of Christian theology: (1) accounts of the origin and methods of theological knowledge, (2) descriptions of spirituality, and (3) attempts to systematically present or defend Christian theology. Chapter three places Smith in his historical and intellectual context in early seventeenth century England noting especially how his education prepared him to contribute to the mystical tradition of the spiritual senses of the soul. Chapter four argues that Smith’s theories of theological knowledge, method, and prophecy rest on his development of the spiritual senses tradition, combining intellectual intuition and imaginative perception. Chapter five addresses the role of spiritual aesthetics in Smith’s prescriptive account of Christian piety. Here the spiritual senses are both means and reward in the spiritual life in the process of deification (theosis). Chapter six demonstrates how Smith’s theology forms a coherent system with intellectual intuition informing natural theology and revelation being supplemented by spiritual perception via the imagination. The central uniting feature therefore is the spiritual perception of theological truth. Chapter seven closes with a summary of Smith’s various uses of the spiritual senses and proposes future research on his influence upon later figures including Jonathan Edwards, John Wesley, and prospective constructive work inspired by Smith’s combination of reason and experience in religion. (shrink)
Penelope Maddy has defended a modified version of mathematical platonism that involves the perception of some sets. Frederick Suppe has developed a conclusive reasons account of empirical knowledge that, when applied to the sets of interest to Maddy, yields that we have knowledge of these sets. Thus, Benacerraf's challenge to the platonist to account for mathematical knowledge has been met, at least in part. Moreover, it is argued that the modalities involved in Suppe's conclusive reasons account of knowledge can (...) be handled without recourse to either laws of nature or possible worlds, and that this approach is preferable. (shrink)
Resumo O autor defenderá, por um lado, a existência dos objectos abstractos e, por outro, o seu papel causal, numa ontologia platónica, tal como enquadrada por Roderick Chisholm. Se plausível, a natureza e o papel dos abstracta sob a forma de estados de coisas, oferecem-nos razões para acreditar em uma descrição bem-sucedida e explicativa da intencionalidade humana e animal que não está encerrada no mundo físico. Palavras-chave : causalidade, encerramento causal, fisicalismo, objectos abstractos, platonismo, Roderick ChisholmA defense of the existence (...) and causal role of abstract objects in a Platonic ontology as influenced by the work of Roderick Chisholm. If plausible, the nature and role of abstracta in the form of states of affairs gives us some reason to believe that a successful description and explanation of human and animal intentionality that is not closed to the physical world. Keywords : abstract objects, causal closure, causation, physicalism, platonism, Roderick Chisholm. (shrink)
Platonists in mathematics endeavour to prove the truthfulness of the proposal about the existence of mathematical objects. However, there have not been many explicit proofs of this proposal. One of the explicit ones is doubtlessly Baker’s Enhanced Indispensability Argument, formulated as a sort of modal syllogism. We aim at showing that the purpose of its creation – the defence of Platonist viewpoint – was not accomplished. Namely, the second premise of the Argument was imprecisely formulated, which gave space for (...) various interpretations of the EIA. Moreover, it is not easy to perceive which of the more precise formulations of the above-mentioned premise would be acceptable. For all these reasons, it is disputable whether the EIA can be used to defend Platonist outlook. At the beginning of this century, Baker has shown that the so-called Quine-Putnam Indispensability Argument can not provide “full” platonism - a guarantee of the existence of all mathematical objects. It turns out, however, that the EIA has a similar disadvantage. (shrink)
The paper argues that ancient dogmatic Platonists, beginning with Antiochus, reconstructed Plato’s ethics in different ways, as a result of their different emphasis on parts of Plato’s work and often argued with each other about what Plato’s ethics actually was. This situation, it is argued, is due to the existence of different strands of ethical views found in Plato’s work itself, such as, for instance, the Protagoras and the Gorgias versus the central books of the Republic and the Philebus on (...) the question of what eudaimonia consists in. The paper argues against the thesis of Julia Annas, outlined in her Platonic Ethics Old and New, that ancient dogmatic Platonists considered the argument of the Republic as being essentially the same with that of all Platonic dialogues and that they unanimously represented Plato’s ethical position as the view that virtue is sufficient for happiness. The testimonies regarding the ethics of Platonists like Antiochus, Plutarch, Numenius, Taurus, or Atticus rather suggest a picture of variance and tension about the reconstruction of Plato’s ethics. Antiochus, Plutarch, and Taurus, for instance, are guided by the theory of the partite soul and maintain that for Plato emotions should be balanced by reason, a view they also find in Aristotle, whereas Eudorus and Atticus appear to favor the elimination of all emotions. Alcinous and, more systematically, Plotinus tend to reconcile and synthesize into a system the different views found in Plato’s dialogues, which brings them to attribute to Plato a complex ethical doctrine. This synthesis corroborates the evidence examined in the paper in support of the view that ancient Platonists recognized diverse strands of ethics in Plato and, far from being unanimous about what Plato’s ethics was, varied significantly in their reconstruction of it. (shrink)
In his Realism, Mathematics, and Modality, Hartry Field attempted to revitalize the epistemological case against mathematical platontism by challenging mathematical platonists to explain how we could be epistemically reliable with regard to the abstract objects of mathematics. Field suggested that the seeming impossibility of providing such an explanation tends to undermine belief in the existence of abstract mathematical objects regardless of whatever reason we have for believing in their existence. After more than two decades, Field’s explanatory challenge remains among (...) the best available motivations for mathematical nominalism. This paper argues that Field’s explanatory challenge misidentifies the central epistemological problem facing mathematical platonism. Contrary to Field’s suggestion, inexplicability of epistemic reliability does not act as an epistemic defeater. The failure to explain our epistemic reliability with respect to the existence and properties of abstract mathematical objects is simply one aspect of a broader failure to establish that we are epistemically reliable with respect to abstract mathematical objects in the first place. Ultimately, it is this broader failure that is the source of mathematical platonism’s real epistemological problems. (shrink)
The expression 'platonism in mathematics' or 'mathematical platonism' is familiar in the philosophy of mathematics at least since the use Paul Bernays made of it in his paper of 1934, 'Sur le Platonisme dans les Mathématiques'. But he was not the first to point out the similarities between the conception of the defenders of mathematical realism and the ideas of Plato. Poincaré had already stressed the 'platonistic' orientation of the mathematicians he called'Cantorian', as opposed to those who (like himself) were (...) 'pragmatist' ones. I examine in this paper some very perplexing aspects of the use which is made at that time of a number of concepts, particularly 'idealism' (which generally designates what we would call 'mathematical realism') and 'empiricism' (which can designate almost any form of antirealism, even if, like for example intuitionism, it is not empiricist at all). There are, of course, historical reasons that may explain why it was for a time so easy and natural to use the words and the concepts in a way that may seem now very strange and to treat as if they were equivalent the two oppositions: realism/antirealism and idealism/empiricism. (shrink)
The expression 'platonism in mathematics' or 'mathematical platonism' is familiar in the philosophy of mathematics at least since the use Paul Bernays made of it in his paper of 1934, 'Sur le Platonisme dans les Math?matiques'. But he was not the first to point out the similarities between the conception of the defenders of mathematical realism and the ideas of Plato. Poincar? had already stressed the 'platonistic' orientation of the mathematicians he called 'Cantorian', as opposed to those who (like himself) (...) were 'pragmatist' ones. I examine in this paper some very perplexing aspects of the use which is made at that time of a number of concepts, particularly 'idealism' (which generally designates what we would call 'mathematical realism') and 'empiricism' (which can designate almost any form of antirealism, even if, like for example intuitionism, it is not empiricist at all). There are, of course, historical reasons that may explain why it was for a time so easy and natural to use the words and the concepts in a way that may seem now very strange and to treat as if they were equivalent the two oppositions: realism/antirealism and idealism/empiricism. (shrink)
In his account of Plato’s ideas in the first book of the “Transcendental Dialectic”, “On the concepts of pure reason”, Kant, in describing how for Plato ideas were “archetypes of things themselves”, adds that these ideas “flowed from the highest reason, through which human reason partakes in them”.1 Later, in the section of the Transcendental Dialectic treating the “ideals of pure reason”, he again attributes to Plato the notion of a “divine mind” within which the “ideas” (...) exist. An “ideal”, Kant says, “was to Plato, an idea in the divine understanding”.2 But as the editors of the Cambridge University Press translation of the Critique of Pure Reason point out, the idea of a divine mind as container of the ideas was not Plato’s and did not originate until the “syncretistic Platonism from the period of the Middle Academy”. From there it “was later adopted by Platonists as diverse as Philo of Alexandria, Plotinus and St Augustine, and became fundamental to later Christian interpretations of Platonism”. (shrink)
