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.
Many philosophers believe that when a theory is committed to an apparently unexplainable massive correlation, that fact counts significantly against the theory. Philosophical theories that imply that we have knowledge of non-causal mind-independent facts are especially prone to this objection. Prominent examples of such theories are mathematical Platonism, robust normative realism and modal realism. It is sometimes thought that theists can easily respond to this sort of challenge and that theism therefore has an epistemic advantage over atheism. In this (...) paper, I will argue that, contrary to widespread thought, some versions of theism only push the challenge one step further and thus are in no better position than atheism. (shrink)
Heavy duty platonism is of great dialectical importance in the philosophy of mathematics. It is the view that physical magnitudes, such as mass and temperature, are cases of physical objects being related to numbers. Many theorists have assumed HDP’s falsity in order to reach their own conclusions, but they are only justified in doing so if there are good arguments against HDP. In this paper, I present all five arguments against HDP alluded to in the literature and show that (...) they all fail. In doing so, I establish two related truths: HDP has been unfairly ignored, and the arguments which take its falsity as a key premise should be re-assessed. (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.
Modal Platonism utilizes "weak" logical possibility, such that it is logically possible there are abstract entities, and logically possible there are none. Modal Platonism also utilizes a non-indexical actuality operator. Modal Platonism is the EASY WAY, neither reductionist nor eliminativist, but embracing the Platonistic language of abstract entities while eliminating ontological commitment to them. Statement of Modal Platonism. Any consistent statement B ontologically committed to abstract entities may be replaced by an empirically equivalent modalization, MOD(B), not (...) so ontologically committed. This equivalence is provable using Modal/Actuality Logic S5@. Let MAX be a strong set theory with individuals. Then the following Schematic Bombshell Result (SBR) can be shown: MAX logically yields [T is true if and only if MOD(T) is true], for scientific theories T. The proof utilizes Stephen Neale's clever model-theoretic interpretation of Quantified Lewis S5, which I extend to S5@. (shrink)
Draft. Berkeley denied the existence of abstract ideas and any faculty of abstraction. At the same time, however, he embraced innate ideas and a faculty of pure intellect. This paper attempts to reconcile the tension between these commitments by offering an interpretation of Berkeley's Platonism.
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)
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)
This paper considers two strategies for undermining indispensability arguments for mathematical Platonism. We defend one strategy (the Trivial Strategy) against a criticism by Joseph Melia. In particular, we argue that the key example Melia uses against the Trivial Strategy fails. We then criticize Melia’s chosen strategy (the Weaseling Strategy.) The Weaseling Strategy attempts to show that it is not always inconsistent or irrational knowingly to assert p and deny an implication of p . We argue that Melia’s case for (...) this strategy fails. (shrink)
This paper is divided into two main sections. In the first, I attempt to show that the characterization of Frege as a redundancy theorist is not accurate. Using one of Wolfgang Carl's recent works as a foil, I argue that Frege countenances a realm of abstract objects including truth, and that Frege's Platonist commitments inform his epistemology and embolden his antipsychologistic project. In the second section, contrasting Frege's Platonism with pragmatism, I show that even though Frege's metaphysical position concerning (...) truth has been criticized as reproachable, I argue that it may be useful for people to think like Platonists while conducting their scientific and philosophical inquiries. (shrink)
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)
This article examines Heidegger’s interpretation of Plato’s Sophist, focusing on his attempts to grasp Plato’s original thinking of being and non-being. Some contemporary thinkers and commentators argue that Heidegger’s view of Plato is simply based on his criticism against the traditional metaphysics of Platonism and its language. But a close reading of his lecture on the Sophist reveals that his view of Plato is grounded in Plato’s questioning struggle with the ambiguous nature of human speech or language. For Heidegger, (...) Plato’s way of philosophizing is deeper than the metaphysical understanding of Platonism which sees only fixed ideas of being. In the Sophist, dialectical thinking of Plato constantly confronts the questionable force of the logos which betrays the natural possibility of non-being based on the tension between movement and rest. Thus, from Plato’s original insight Heidegger uncovers the dynamic association of being and non-being as a natural ground of everyday living with others. However, although Heidegger’s understanding of the Sophist powerfully demonstrates the lively possibility of being beyond the customary perspective of Platonic metaphysics, his interpretation fails to further disclose Plato’s political question of being emerging in the Sophist, which seeks the true associative ground of human beings. (shrink)
Resumo Neste artigo o autor apresenta cinco abordagens diferentes ao debate entre o platonismo e o nominalismo: a quantificacional, a reducionista, a dependência da mente / linguagem, a extensional versus intensional, a hierárquica. Cada uma apresenta suas vantagens e desvantagens que devem ser discutidas em detalhe. Palavras-chave : existência, meta-metafísica, nominalismo, platonismoIn this paper I present five different approaches to the debate between Platonism and Nominalism: the quantifier approach, the reductionist approach, the mind / language dependence approach, the extension (...) versus intension approach and the hierarchichal approach. Each one has its advantages and disadvantages that have to be discussed in detail. Keywords : existence, metametaphysics, nominalism, platonism. (shrink)
The sum of all objects of a science, the objects’ features and their mutual relations compose the reality described by that sense. The reality described by mathematics consists of objects such as sets, functions, algebraic structures, etc. Generally speaking, the use of terms reality and existence, in relation to describing various objects’ characteristics, usually implies an employment of physical and perceptible attributes. This is not the case in mathematics. Its reality and the existence of its objects, leaving aside its application, (...) are completely virtual and yet clearly organized. This organization can be recognized in the creation of axioms or in the arrival at new theorems and definitions. It results either from a formalization of an intuitive idea or from a combinatorics that has not been guided by intuition. In all four possible cases—therefore, also in the two in which there is no intuitive “lead”, we can plausibly talk about a discovery of mathematical facts and thus support the Platonist view. (shrink)
In this paper I argue against Divers and Miller's 'Lightness of Being' objection to Hale and Wright's neo-Fregean Platonism. According to the 'Lightness of Being' objection, the neo-Fregean Platonist makes existence too cheap: the same principles which allow her to argue that numbers exist also allow her to claim that fictional objects exist. I claim that this is no objection at all" the neo-Fregean Platonist should think that fictional characters exist. However, the pluralist approach to truth developed by WQright (...) in 'Truth and Objectivity' allows us to salvage our intuitions about the metaphysicial lightweightness of fictional characters: truth for discourse about fictional characters fails to exert 'Cognityive Command', whereas truth about arithmetic does. (shrink)
This essay explores the use of platonist and nominalist concepts, derived from the philosophy of mathematics and metaphysics, as a means of elucidating the debate on spacetime ontology and the spatial structures endorsed by scientific realists. Although the disputes associated with platonism and nominalism often mirror the complexities involved with substantivalism and relationism, it will be argued that a more refined three-part distinction among platonist/nominalist categories can nonetheless provide unique insights into the core assumptions that underlie spatial ontologies, but (...) it also assists in critiquing alternative uses of nominalism, platonism, and both ontic and epistemic structural realism. (shrink)
Quine rejects intensional Platonism and, with it, also rejects attributes (properties) as designations of predicates. He pragmatically accepts extensional Platonism, but conceives of classes as merely auxiliary entities needed to express some laws of set theory. At the elementary logical level, Quine develops an “ontologically innocent” logic of predicates. What in standard quantification theory is the work of variables is in the logic of predicates the work of a few functors that operate on predicates themselves: variables are eliminated. (...) This “predicate functor logic” may be conceived as a peculiar sort of Platonism - ontologically neutral, reduced to schematized linguistic forms. (shrink)
Departing from modal logic, Jean-Yves Girard, as a logician interested in philosophy, presented a distinction between essentialism and existentialism in logic. Carlos Lobo reflected about the Girard’s concept to reinterpret the Husserlian Platonism in regard of the status of logical modalities. We start rescuing the notion of modal logic in the Edmund Husserl’s works, especially Formal and Transcendental Logic and First Philosophy. Developing this reflexion, we propose a new contribution to this discussion, reinterpreting the platonic influence in the Husserlian (...) notions of eidos and science, light of some readings of Lee Hardy and Johanna M. Tito. As a conclusion of this dialogue between Husserl and Girard, the method of eidetic variation is presented as a tool to review the idea of science, in a manner consistent with the phenomenological approach. (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)
In his book 'Wittgenstein on the foundations of Mathematics', Crispin Wright notes that remarkably little has been done to provide an unpictorial, substantial account of what mathematical platoninism comes to. Wright proposes to investigate whether there is not some more substantial doctrine than the familiar images underpinning the platonist view. He begins with the suggestion that the essential element in the platonist claim is that mathematical truth is objective. Although he does not demarcate them as such, Wright proposes several different (...) tests for objectivity. The paper finds problems with each of these tests. (shrink)
The following paper argues that Blaise Pascal, in spite of his famous opposition between the God of the Philosophers and the God of “Abraham, Isaac and Jacob” has significant affinities with the tradition of Renaissance Platonism and is in fact a Platonist in his overall outlook. This is shown in three ways. Firstly, it is argued that Pascal’s skeptical fideism has roots in the notion of faith developed in post-Plotinian neo-Platonism. Secondly, it is argued that Pascal makes considerable (...) use of the Platonic notion of an indefinite dyadic principle. Thirdly, it is argued that Pascal’s religious psychology gives a centrality to the body that brings it close to the theurgical standpoint of figures like Iamblichus. Pascal is then contrasted to figures like Cusanus and Pico in that a dyadic principle of opposition is more prominent in his work than a triadic logic of mediation. (shrink)
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)
Contrary to popular opinion, non-natural realism can explain both why normative properties supervene on descriptive properties, and why this pattern is analytic. The explanation proceeds by positing a subtle polysemy in normative predicates like “good”. Such predicates express slightly different senses when they are applied to particulars (like Florence Nightingale) and to kinds (like altruism). The former sense, “goodPAR”, can be defined in terms of the latter, “goodKIN”, as follows: x is goodPAR iff there is a kind K such that (...) x is a token of K, and K is goodKIN. Now if x and y are descriptively exactly similar, then they are tokens of exactly the same kinds, so x is a token of a goodKIN kind if and only if y is. Therefore, by the definition, x is goodPAR if and only if y is. Supervenience just falls out of the definition of “goodPAR”. (shrink)
Psychology is dead. The self is a fiction invented by the brain. Brain plasticity isn?t all it?s cracked up to be. Our conscious learning is an observation post factum, a recollection of something already accomplished by the brain. We don?t learn to speak; speech is generated when the brain is ready to say something. False memories are more prevalent than one might think, and they aren?t all that bad. We think we?re in charge of our lives, but actually we are (...) not. On top of all this, the common belief that reading to a young child will make her brain more attuned to reading is simply untrue. (shrink)
According to Quine’s indispensability argument, we ought to believe in just those mathematical entities that we quantify over in our best scientific theories. Quine’s criterion of ontological commitment is part of the standard indispensability argument. However, we suggest that a new indispensability argument can be run using Armstrong’s criterion of ontological commitment rather than Quine’s. According to Armstrong’s criterion, ‘to be is to be a truthmaker (or part of one)’. We supplement this criterion with our own brand of metaphysics, 'Aristotelian (...) (...) realism', in order to identify the truthmakers of mathematics. We consider in particular as a case study the indispensability to physics of real analysis (the theory of the real numbers). We conclude that it is possible to run an indispensability argument without Quinean baggage. (shrink)
Mathematical apriorism holds that mathematical truths must be established using a priori processes. Against this, it has been argued that apparently a priori mathematical processes can, under certain circumstances, fail to warrant the beliefs they produce; this shows that these warrants depend on contingent features of the contexts in which they are used. They thus cannot be a priori. -/- In this paper I develop a position that combines a reliabilist version of mathematical apriorism with a platonistic view of mathematical (...) ontology. I argue that this view both withstands the above objection and explains the reliability of a priori mathematical warrant. (shrink)
In this paper, I defend traditional Platonic mathematical realism from its contemporary detractors, arguing that numbers, understood as abstract, non-physical objects of rational intuition, are indispensable for the act of counting.
Enrico Berti and others hold that Aquinas’s notion of God as ipsum esse subsistens conflicts with Aristotle’s view that positing an Idea of being treats being as a genus and nullifies all differences. The paper first shows how one of Aquinas’s ways of distinguishing esse from essence supposes an intimate tie between a thing’s esse and its differentia. Then it argues that for Aquinas the (one) divine essence differs from the (manifold) “essence of esse.” God is his very esse. This (...) somehow “contains” all esse, but it also transcends it, because although simple, it also “contains” all forms and differentiae. (shrink)
In this book, Balaguer demonstrates that there are no good arguments for or against mathematical platonism. He does this by establishing that both platonism and anti-platonism are defensible views. Introducing a form of platonism ("full-blooded platonism") that solves all problems traditionally associated with the view, he proceeds to defend anti-platonism (in particular, mathematical fictionalism) against various attacks, most notably the Quine-Putnam indispensability attack. He concludes by arguing that it is not simply that we do (...) not currently have any good argument for or against platonism, but that we could never have such an argument and, indeed, that there is no fact of the matter as to whether platonism is correct. (shrink)
Since Benacerraf’s “Mathematical Truth” a number of epistemological challenges have been launched against mathematical platonism. I first argue that these challenges fail because they unduely assimilate mathematics to empirical science. Then I develop an improved challenge which is immune to this criticism. Very roughly, what I demand is an account of how people’s mathematical beliefs are responsive to the truth of these beliefs. Finally I argue that if we employ a semantic truth-predicate rather than just a deflationary one, there (...) surprisingly turns out to be logical space for a response to the improved challenge where no such space appeared to exist. (shrink)
Mark Balaguer’s project in this book is extremely ambitious; he sets out to defend both platonism and ﬁctionalism about mathematical entities. Moreover, Balaguer argues that at the end of the day, platonism and ﬁctionalism are on an equal footing. Not content to leave the matter there, however, he advances the anti-metaphysical conclusion that there is no fact of the matter about the existence of mathematical objects.1 Despite the ambitious nature of this project, for the most part Balaguer does (...) not shortchange the reader on rigor; all the main theses advanced are argued for at length and with remarkable clarity and cogency. There are, of course, gaps in the account but these should not be allowed to overshadow the sig-. (shrink)
In the introduction to his Realism, mathematics and modality, and in earlier papers included in that collection, Hartry Field offered an epistemological challenge to platonism in the philosophy of mathematics. Justin Clarke-Doane Truth, objects, infinity: New perspectives on the philosophy of Paul Benacerraf, 2016) argues that Field’s challenge is an illusion: it does not pose a genuine problem for platonism. My aim is to show that Clarke-Doane’s argument relies on a misunderstanding of Field’s challenge.
Central to the philosophical understanding of music is the status of musical works. According to the Platonist, musical works are abstract objects; that is, they are not located in space or time, and we have no causal access to them. Moreover, only a particular physical occurrence of these musical works is instantiated when a performance ofthe latter takes place. But even if no performance ever took place, the Platonist insists, the musical work would still exist, since its existence is not (...) tied to spatiotemporal constraints (Kivy , and Dodd ). In this paper, I offer a critical assessment of the Platonist view. I argue that, despite some benefits, Platonism faces significant difficulties in the interpretation of music. In spite ofthe Platonist’s attempt to overcome the problem, the view ultimately doesn’t mesh well with the way we actively respond to performances and fail to respond, in any way similar, to abstract patterns. Platonism also makes knowledge of music something extremely mysterious, given that we have no access to the abstract objects that, according to the Platonist, characterize the musical works. The ability to understand how we respond to musical works is, of course, central to any interpretation of music. This ability is also crucial in explaining the role music plays in various aspects of our culture, Rom bounding with others to music therapy. Given the problems faced by Platonism, it makes more sense to adopt an altemative, non-Platonist view. I conclude the paper by sketching such a non-Platonist proposal. (shrink)
Platonism in the philosophy of mathematics is the doctrine that there are mathematical objects such as numbers. John Burgess and Gideon Rosen have argued that that there is no good epistemological argument against platonism. They propose a dilemma, claiming that epistemological arguments against platonism either rely on a dubious epistemology, or resemble a dubious sceptical argument concerning perceptual knowledge. Against Burgess and Rosen, I show that an epistemological anti- platonist argument proposed by Hartry Field avoids both horns (...) of their dilemma. (shrink)
This paper aims to provide modal foundations for mathematical platonism. I examine Hale and Wright’s (2009) objections to the merits and need, in the defense of mathematical platonism and its epistemology, of the thesis of Necessitism. In response to Hale and Wright’s objections to the role of epistemic and metaphysical modalities in providing justification for both the truth of abstraction principles and the success of mathematical predicate reference, I examine the Necessitist commitments of the abundant conception of properties (...) endorsed by Hale and Wright and examined in Hale (2013a); examine cardinality issues which arise depending on whether Necessitism is accepted at first- and higher-order; and demonstrate how a multi-dimensional intensional approach to the episte- mology of mathematics, augmented with Necessitism, is consistent with Hale and Wright’s notion of there being epistemic entitlement rationally to trust that abstraction principles are true. Epistemic and metaphysical modality may thus be shown to play a constitutive role in vindicating the reality of mathematical objects and truth, and in explaining our possible knowledge thereof. (shrink)
This article examines Gilles Deleuze’s concept of the simulacrum, which Deleuze formulated in the context of his reading of Nietzsche’s project of “overturning Platonism.” The essential Platonic distinction, Deleuze argues, is more profound than the speculative distinction between model and copy, original and image. The deeper, practical distinction moves between two kinds of images or eidolon, for which the Platonic Idea is meant to provide a concrete criterion of selection “Copies” or icons (eikones) are well-grounded claimants to the transcendent (...) Idea, authenticated by their internal resemblance to the Idea, whereas “simulacra” (phantasmata) are like false claimants, built on a dissimilarity and implying an essential perversion or deviation from the Idea. If the goal of Platonism is the triumph of icons over simulacra, the inversion of Platonism would entail an affirmation of the simulacrum as such, which must thus be given its own concept. Deleuze consequently defines the simulacrum in terms of an internal dissimilitude or “disparateness,” which in turn implies a new conception of Ideas, no longer as self-identical qualities (the auto kath’hauto), but rather as constituting a pure concept of difference. An inverted Platonism would necessarily be based on a purely immanent and differential conception of Ideas. Starting from this new conception of the Idea, Deleuze proposes to take up the Platonic project anew, rethinking the fundamental figures of Platonism (selection, repetition, ungrounding, the question-problem complex) on a purely differential basis. In this sense, Deleuze’s inverted Platonism can at the same time be seen as a rejuvenated Platonism and even a completed Platonism. (shrink)
Predication is an indisputable part of our linguistic behavior. By contrast, the metaphysics of predication has been a matter of dispute ever since antiquity. According to Plato—or at least Platonism, the view that goes by Plato’s name in contemporary philosophy—the truths expressed by predications such as “Socrates is wise” are true because there is a subject of predication (e.g., Socrates), there is an abstract property or universal (e.g., wisdom), and the subject exemplifies the property.1 This view is supposed to (...) be general, applying to all predications, whether the subject of predication is a person, a planet, or a property.2 Despite the controversy surrounding the metaphysics of predication, many theistic philosophers—including the majority of contemporary analytic theists—regard Platonism as extremely attractive. At the same time, however, such philosophers are also commonly attracted to a form of traditional theism that has at its core the thesis that God is an absolutely independent.. (shrink)
Platonism is the view that there exist such things as abstract objects — where an abstract object is an object that does not exist in space or time and which is therefore entirely non-physical and nonmental. Platonism in this sense is a contemporary view. It is obviously related to the views of Plato in important ways, but it is not entirely clear that Plato endorsed this view, as it is defined here. In order to remain neutral on this (...) question, the term ‘platonism’ is spelled with a lower-case ‘p’. (See entry on Plato.) The most important figure in the development of modern platonism is Gottlob Frege (1884, 1892, 1893-1903, 1919). The view has also been endorsed by many others, including Kurt Gödel (1964), Bertrand Russell (1912), and W.V.O. Quine (1948, 1951). (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)
It is argued here that mathematical objects cannot be simultaneously abstract and perceptible. Thus, naturalized versions of mathematical platonism, such as the one advocated by Penelope Maddy, are unintelligble. Thus, platonists cannot respond to Benacerrafian epistemological arguments against their view vias Maddy-style naturalization. Finally, it is also argued that naturalized platonists cannot respond to this situation by abandoning abstractness (that is, platonism); they must abandon perceptibility (that is, naturalism).
The aim of this paper is to present a perspective on Iris Murdoch conception of metaphysics, starting from her puzzling contention that she could describe herself as a ?Wittgensteinian Neo-Platonist?. I argue that this statement is a central clue to the nature both of her philosophical method which is strongly reminiscent of Wittgenstein's, and of her Platonism, which in its emphasis on the everyday and metaphorical aspects of his work differs starkly from received modern interpretations. Placing Murdoch between Plato (...) and Wittgenstein can help us to understand the nature of her metaphysics as a complex, continuous, pictorial activity, which shows a deep awareness of and is compatible with the late twentieth century and contemporary distrust of large metaphysical systems or explanations. (shrink)
Once the reality of properties is admitted, there are two fundamentally different realist theories of properties. Platonist or transcendent realism holds that properties are abstract objects in the classical sense, of being nonmental, nonspatial, and causally inefficacious. By contrast, Aristotelian or moderate realism takes properties to be literally instantiated in things. An apple’s color and shape are as real and physical as the apple itself. The most direct reason for taking an Aristotelian realist view of properties is that we perceive (...) them. We perceive an individual apple, but only as a certain shape, color, and weight, because it is those properties that confer on it the power to affect our senses. It is in virtue of being blue that a body reflects certain light and looks blue. Since “causality is the mark of being,” the properties that confer causal power are real. And that means a reality, not in a Platonic and acausal world of “abstract objects,” but in the ordinary concrete world in which we live. On an Aristotelian view, it is the business of science to determine which properties there are and to classify and understand the properties we perceive, and to find the laws connecting them. (shrink)