This is about Gassendi's 5th Objections to the Meditations and Descartes' Reply. The main issue is what clear and distinct perception consists in and whether we need a criterion in order to know if we perceive something clearly and distinctly.

In lieu of an abstract, here is a brief excerpt of the content:102. ONE CONSEQUENCE OF HUME'S NOMINALISM It is commonly assumed, and sometimes argued, that Hume held the Uniformity Thesis regarding causation : something, a, is the cause of something else, b, if and only if when a occurs, b occurs contiguous with and successive to a and whenever anything relevantly similar to a, "no matter where or when, observed or unobserved," something relevantly similar to b occurs. Everyone knows (...) that Hume denies there is any necessary connection between a cause and its effect. Since the invariability of conjunctions of causes and effects follows from their necessary connection and its possibility is not affected by the denial of that conjunction, the Uniformity Thesis seems a plausible retrenchment. Besides, we should deny that a causes b were any similar a to occur without the occurrence of a similar b. So the assumption of the Uniformity Thesis seems natural. When the issue is argued on textual grounds, the appeal is to Hume's first definition of cause at the end of his long analysis of causation. A cause is An object precedent and contiguous to another, and where all the objects resembling the former are plac'd in like relations of precedency and contiguity to those objects, that resemble the latter (T 170). This is construed as Hume's real definition of the causal relation and taken to state the Uniformity Thesis. Both the argument and the assumption presuppose that Hume was concerned with the conditions for something 's being a cause. But, I wish to argue, in the Treatise at any rate Kume was concerned not with causal relations, but with causal judgments. He was 103. concerned with what must be true for us to call or judge a a cause and, only as a consequence of that concern, with what is true of a for a to be a cause. We must take seriously his asking us to cast our eye on any two objects, which we call cause and effect (T 75, my emphasis), and his saying, after introducing constant conjunction, that contiguity and succession are not sufficient to make us pronounce any two objects to be cause and effect, unless we perceive, that these two relations are preserv'd in several instances (T 87, my emphasis). To determine the conditions for causal judgments, one must determine what we observe of a cause, but in making that determination, I am claiming, Hume is not addressing the question he is commonly assumed to have answered. Making that claim plausible requires a detailed analysis of what Hume is about when he gives two 4 definitions of the causal relation and an explication of how what he does in regard to causal judgments fits the paradigm of analysis for judgments in the 17th and 18th centuries, viz. that given by Boyle, Locke, and --- 5 others of such judgments as "That ball is red^" I shall do neither here. I wish to concern myself with another point which is not necessary to make my claim plausible, but would help were it true. I shall develop this point informally, for it is prima facie implausible and I would like to see how it fares unadorned. If it fares well, there will be time enough to deck it out in symbols. The point is that for Hume one literally cannot think the Uniformity Thesis. If this is true, it would certainly help my claim, for it would not help Hume to claim of him that he answers a question with what for him cannot even be thought. But it is certainly an implausible point prima facie. We can think it. Why can't Hume? The answer lies with his 104. nominalism. Hume holds that everything that exists in nature is individual (T 19) and that this is true of- ideas as well as of anything else that exists (T 19-20). Thus, when someone says, "Smoking causes cancer," then, if we understand what is being said and if anything comes to mind, what must come to mind according to those who hold the Uniformity Thesis is a particular instance of smoking, a, and a particular instance of cancer, b, and particular instances of the relations of... (shrink)

Leibniz considered the Cartesian version of the ontological argument not as an inconsistent proof but only as an incomplete one: it requires a preliminary proof of possibility to show that the concept of ‘the most perfect being’ involves no contradiction. Leibniz raised this objection to Descartes’s proof already in 1676, then repeated it throughout his entire life. Before 1676, however, he suggested a more substantial objection to the Cartesian argument. I take into account a text written around 1671-72, (...) in which Leibniz considers the Cartesian proof as a paralogism and a petition of principle. I argue that this criticism is modelled on Gassendi’s objections to the Cartesian proof, and that Leibniz’s early rejection of the ontological argument has to be understood in the general context of his early philosophy, which was inspired by nominalist authors, such as Hobbes and Gassendi. Then, I take into account the reconsideration of the ontological argument in a series of texts of 1678, showing how Leibniz implicitly replies to the kind of criticism to the argument he himself shared in his earlier works. (shrink)

William Lane Craig has claimed that Platonism is incompatible theologically with Christian theism in that it undermines God’s aseity. He develops three main objections to Platonism, as well as his own nominalist theory of reference, for which he draws from philosophy of language. However, I rebut his arguments. I argue that, unlike on Platonism, his view will not preserve a real essence of intentionality. Without that, his view undermines our abilities to know reality. As an implication, I also will (...) highlight the importance methodologically of approaching this issue from the primacy of the ontology of knowledge, not philosophy of language. (shrink)

In this paper, we outline and critically evaluate Thomas Hofweber’s solution to a semantic puzzle he calls Frege’s Other Puzzle. After sketching the Puzzle and two traditional responses to it—the Substantival Strategy and the Adjectival Strategy—we outline Hofweber’s proposed version of Adjectivalism. We argue that two key components—the syntactic and semantic components—of Hofweber’s analysis both suffer from serious empirical difficulties. Ultimately, this suggests that an altogether different solution to Frege’s Other Puzzle is required.

William Lane Craig rejects Platonism (the view that uncreated abstract objects (AOs) exist) in favor of nominalism because he believes Platonism fatally compromises God’s aseity. For Craig, concrete particulars (including essences) exist, but properties do not. Yet, we use property-talk, following Carnap’s “linguistic frameworks.” There is, however, a high cost to Craig’s view. I survey his views and then explore the importance of essences. But, next, I show that his nominalism undermines them. Thus, we have just interpretations of reality. Worse, (...) nominalism undermines creation’s determinacy. Last, I suggest AOs are created, but in a more fundamental sense than Craig considers. (shrink)

It is generally recognized that the content of a philosophy cannot be adequately understood apart from the form in which it is couched and the style of reasoning with which it is supported. Matter and form go together in a philosophy, as they do in all human creations and everywhere in nature. Thus, Werner Jaeger has shown the importance of form in the development of Aristotle’s Metaphysics and Julius Stenzel has stressed the interrelation of dialectical method and content in the (...) philosophy of Plato. In the study of the philosophies of the Middle Ages the common scholastic method has long been the object of attention; but, with the exception of Thomism, their individual and special modes of procedure and styles of reasoning have largely been neglected. All too often they have been studied with an eye simply to their content, as “static systems of conceptions”, with little if any regard for their living form and method. (shrink)

In this paper, I introduce an intrinsic account of the quantum state. This account contains three desirable features that the standard platonistic account lacks: (1) it does not refer to any abstract mathematical objects such as complex numbers, (2) it is independent of the usual arbitrary conventions in the wave function representation, and (3) it explains why the quantum state has its amplitude and phase degrees of freedom. -/- Consequently, this account extends Hartry Field’s program outlined in Science Without Numbers (...) (1980), responds to David Malament’s long-standing impossibility conjecture (1982), and establishes an important first step towards a genuinely intrinsic and nominalistic account of quantum mechanics. I will also compare the present account to Mark Balaguer’s (1996) nominalization of quantum mechanics and discuss how it might bear on the debate about “wave function realism.” In closing, I will suggest some possible ways to extend this account to accommodate spinorial degrees of freedom and a variable number of particles (e.g. for particle creation and annihilation). -/- Along the way, I axiomatize the quantum phase structure as what I shall call a “periodic difference structure” and prove a representation theorem as well as a uniqueness theorem. These formal results could prove fruitful for further investigation into the metaphysics of phase and theoretical structure. -/- (For a more recent version of this paper, please see "The Intrinsic Structure of Quantum Mechanics" available on PhilPapers.). (shrink)

Yet, he also says that it is philosophically indeterminate which criterion for what exists is correct. Nominalism is the view that certain objects ( i.e ., abstract objects) do not exist, and not the view that it is philosophically indeterminate whether or not they do. I resolve the dilemma that Azzouni's claims pose: Azzouni is a non-factualist about what exists, but he is a factualist about which criterion for what exists our community of speakers has adopted. It is in the (...) latter sense only that Azzouni can call himself a nominalist. My thanks to Jody Azzouni and to an anonymous referee for helpful suggestions. CiteULike Connotea Del.icio.us What's this? (shrink)

This excellent book consists of a translation of Plato's Euthyphro, plus "interspersed comment" intended "partly as a help to the Greekless reader in finding his way, and partly as a means of embedding the discussion of the earlier theory of Forms which follows it." That subsequent discussion is a series of sections aimed at establishing "that there is an earlier theory of Forms, found in the Euthyphro and other early dialogues as an essential adjunct of Socratic dialect" and that it (...) is not the same as the theory of Forms found in the Phaedo, Republic and other middle dialogues. In the Euthyphro Socrates' question of what holiness is assumes that there is a Form of holiness, "that this Form is a universal, the same in all holy things;... that that Form may be used as a standard, by which to judge what things are holy and what are not...; that it is an essence, by which or in virtue of which holy things are holy." As essences Forms are causes--formal, not efficient. They are "causes in the sense that they are that by which things are what they are. They therefore affect the career of the world, in that if they did not exist, the world would not be what it is." They "are not identical with their instances and [are] prior to their instances" and, hence, they are not in their instances. In fact, "Forms are as 'separate' from their instances in the early dialogues as they are" in the later ones. Do they not differ, then, from these latter Forms? Yes, because "of the way in which separation is conceived." In the Phaedo and other middle dialogues separation "involves something more than... nonidentity, independence, or priority. It involves the claim that instances of Forms are deficient imitations or resemblances of Forms.... To that theory was later conjoined, as a natural corollary, the theory that sensibles and Forms differ in their degree of reality, that Forms are more real than their instances." There are, in fact, "Two Worlds, Visible and Invisible.... The objects of the Visible World... are in a perpetually changing mortal realm, never the same with respect to each other or themselves. By contrast, Forms, the reality of whose existence we render an account in questioning and answering, exist always in the same way with respect to the same things, single in nature, alone by themselves, never in any way under any circumstances admitting alteration." This contrast between the Two Worlds is not drawn in the Euthyphro and earlier writings. Hence, between them and the middle dialogues there is a development in the theory of Forms. Of course, there also is "a unity to Plato's thought; but it is not the unity of a monument. It is the unity of growth and development, the unity of life." In these splendid pages one point remains unclear: how can a Form be universal and thus distinct from its instances and yet be their formal cause? Allen leaves no doubt that this is his position: "In Plato's early dialogues Forms are not the being of that of which they are Forms. A universal, being one, cannot constitute the being of a plurality--precisely why Aristotle was led to distinguish substantial form from universal. The Euthyphro does not imply that holiness is the being of any given holy thing or action as holy; it implies only that holiness is that by which holy things are holy. It implies, to borrow another bit of Aristotelian vocabulary, that holiness is a cause." But precisely in what way is a Form "that by which" something is what it is? Plato subsequently answers by distinguishing the Form itself, its character as participated by a particular thing, and the participant : the Form is that by which some thing is what it is through the participated character which the thing has. Is this answer implied in the Euthyphro? Or in what sense is a Form distinct from particular things? In what sense a formal cause? That puzzlement, though, is minor in the context of the entire book, which is valuable not only for the interpretation Allen gives of the early and middle dialogues but also for all sorts of unexpected bonuses. These are points either newly made or brilliantly reiterated--for example, the influence of Anaxagoras on Plato re the notion of essence and in philosophical vocabulary; Aristotle's abandonment of the contrast made in the Categories between primary and secondary substance; the crucial difference between genus/species in Aristotle and in Plato (enriched/impoverished; the analogy of a Platonic definition to mapping a field; the evaluation of Aristotle's interpretation of Plato's Forms, of his report on the "unwritten doctrines," of esoteric and exoteric teachings. This last culminates in a paragraph which all students of Plato should reflect upon constantly: "It is possible to treat Plato's text, not as evidence for something else, but as itself the primary object of historical understanding. The aim of the inquiry is then to interpret a set of literary documents, not to fathom the entertained beliefs of their author. It is reasonable, of course, to assume that the documents are a reliable index to the beliefs; but the connection, after all, is contingent, and as far as interpretation is concerned, unimportant. If Plato, in his heart of hearts, had been a nominalist, an atheist, a sceptic about immortality, and a hedonist, and had yet gone on to write the dialogues which he wrote for some obscure motive now unknown, this would not change the proper interpretation of what he wrote and privately disbelieved by one iota: when a man says what he does not believe, we may still perfectly well understand what it is he has said. The question, then, of whether Plato had beliefs he did not express, or beliefs contrary to what he did express, may be left to those with skill in the arts of divination; the historian may more reasonably limit himself to the study of texts and their meaning. If inquiry is construed in this way, it is self-referentially inconsistent to prefer the testimony of Aristotle to the evidence of Plato's text in the interpretation of Plato."--L. S. (shrink)

Current versions of nominalism in the philosophy of mathematics have the benefit of avoiding commitment to the existence of mathematical objects. But this comes with the cost of not taking mathematical theories literally. Jody Azzouni's _Deflating Existential Consequence_ has recently challenged this conclusion by formulating a nominalist view that lacks this cost. In this paper, we argue that, as it stands, Azzouni's proposal does not yet succeed. It faces a dilemma to the effect that either the view is not (...) nominalist or it fails to take mathematics literally. After presenting the dilemma, we suggest a possible solution for the nominalist. (shrink)

Charles Chihara's new book develops and defends a structural view of the nature of mathematics, and uses it to explain a number of striking features of mathematics that have puzzled philosophers for centuries. The view is used to show that, in order to understand how mathematical systems are applied in science and everyday life, it is not necessary to assume that its theorems either presuppose mathematical objects or are even true. Chihara builds upon his previous work, in which he presented (...) a new system of mathematics, the constructibility theory, which did not make reference to, or presuppose, mathematical objects. Now he develops the project further by analysing mathematical systems currently used by scientists to show how such systems are compatible with this nominalistic outlook. He advances several new ways of undermining the heavily discussed indispensability argument for the existence of mathematical objects made famous by Willard Quine and Hilary Putnam. And Chihara presents a rationale for the nominalistic outlook that is quite different from those generally put forward, which he maintains have led to serious misunderstandings.A Structural Account of Mathematics will be required reading for anyone working in this field. (shrink)

We observe that Putnam’s model-theoretic argument against determinacy of the concept of second-order quantification or that of the set is harmless to the nominalist. It serves as a good motivation for the nominalist philosophy of mathematics. But in the end it can lead to a serious challenge to the nominalist account of mathematical objectivity if some minimal assumptions about the relation between mathematical objectivity and logical objectivity are made. We consider three strategies the nominalist might take (...) to meet this challenge, and we argue that all these strategies are untenable. (shrink)

The standard argument for the existence of distinctively mathematical objects like numbers has two main premises: some mathematical claims are true, and the truth of those claims requires the existence of distinctively mathematical objects. Most nominalists deny. Those who deny typically reject Quine’s criterion of ontological commitment. I target a different assumption in a standard type of semantic argument for. Benacerraf’s semantic argument, for example, relies on the claim that two sentences, one about numbers and the other about cities, have (...) the same grammatical form. He makes this claim on the grounds that the two sentences are superficially similar. I argue that these grounds are not sufficient. Other sentences with the same superficial form appear to have different grammatical forms. I offer two plausible interpretations of Benacerraf’s number sentence that make use of plural quantification. These interpretations appear not to incur ontological commitments to distinctively mathematical objects, even assuming Quine’s criterion. Such interpretations open a new, plural strategy for the mathematical nominalist. (shrink)

The present paper will argue that, for too long, many nominalists have concentrated their researches on the question of whether one could make sense of applications of mathematics (especially in science) without presupposing the existence of mathematical objects. This was, no doubt, due to the enormous influence of Quine's "Indispensability Argument", which challenged the nominalist to come up with an explanation of how science could be done without referring to, or quantifying over, mathematical objects. I shall admonish nominalists to (...) enlarge the target of their investigations to include the many uses mathematicians make of concepts such as structures and models to advance pure mathematics. I shall illustrate my reasons for admonishing nominalists to strike out in these new directions by using Hartry Field's nominalistic view of mathematics as a model of a philosophy of mathematics that was developed in just the sort of way I argue one should guard against. I shall support my reasons by providing grounds for rejecting both Field's fictionalism and also his deflationist account of mathematical knowledge—doctrines that were formed largely in response to the Indispensability Argument. I shall then give a refutation of Mark Balaguer's argument for his thesis that fictionalism is "the best version of anti-realistic anti-platonism". (shrink)

Introduction: I lay out the broad contours of my thesis: a defence of mathematical nominalism, and nominalism more generally. I discuss the possibility of metaphysics, and the relationship of nominalism to naturalism and pragmatism. Chapter 2: I delineate an account of abstractness. I then provide counter-arguments to claims that mathematical objects make a di erence to the concrete world, and claim that mathematical objects are abstract in the sense delineated. Chapter 3: I argue that the epistemological problem with abstract objects (...) is not best understood as an incompatibility with a causal theory of knowledge, or as an inability to explain the reliability of our mathematical beliefs, but resides in the epistemic luck that would infect any belief about abstract objects. To this end, I develop an account of epistemic luck that can account for cases of belief in necessary truths and apply it to the mathematical case. Chapter 4: I consider objections, based on metaphysical considerations and linguistic data, to the view that the existential quantifier expresses existence. I argue that these considerations can be accommodated by an existentially committing quantifier when the pragmatics of quantified sentences are properly understood. I develop a semi-formal framework within which we can define a notion of nominalistic adequacy. I show how our notion of nominalistic adequacy can show why it is legitimate for the nominalist to make use of platonistic “assumptions” in inference-making. Chapter 5: I turn to the application of mathematics in science, including explanatory applications, and its relation to a number of indispensability arguments. I consider also issues of realism and anti-realism, and their relation to these arguments. I argue that abstraction away from pragmatic considerations has acted to skew the debate, and has obscured possibilities for a nominalistic understanding of mathematical practices. I end by explaining the notion of a pragmatic meta-vocabulary, and argue that this notion can be used to carve out a new way of locating our ontological commitments. Chapter 6: I show how the apparatus developed in earlier chapters can be utilised to roll out the nominalist project to other domains of discourse. In particular, I consider propositions and types. I claim that a unified account of nominalism across these domains is available. Conclusion: I recapitulate the claims of my thesis. I suggest that the goal of mathematical enquiry is not descriptive knowledge, but understanding. (shrink)

A metaphysically robust, as opposed to lightweight, Platonism with respect to uncreatable abstract objects is theologically unacceptable because it fatally compromises creatio ex nihilo and divine aseity. The principal argument for Platonism is the so-called Indispensability Argument based on the ontological commitments required by singular terms and existential quantifiers in true sentences. Different varieties of Nominalism challenge each of the argument’s premises. Fictionalism accepts the assumed criterion of ontological commitment but rejects the truth of the relevant sentences. Neutralism accepts the (...) truth of the relevant sentences but denies the assumed criterion of ontological commitment. Both of these perspectives, but especially the last, are plausible routes available for the Christian theist. (shrink)

Probably there is no position in Goodman’s corpus that has generated greater perplexity and criticism than Goodman’s “nominalism”. As is abundantly clear from Goodman’s writings, it is not “abstract entities” generally that he questions—indeed, he takes sensory qualia as “basic” in his Carnap-inspired constructional system in Structure—but rather just those abstracta that are so crystal clear in their identity conditions, so fundamental to our thought, so prevalent and seemingly unavoidable in our discourse and theorizing that they have come to form (...) the generally accepted framework for the most time-honored, exact, sophisticated, refined, central, and secure branch of human knowledge yet devised, mathematics itself! Of all the abstracta to question, why sets? Of course, Goodman gave his “reasons”, the unintelligibility of “generating” an infinitude of “constructed objects” automatically from any given object or objects. But critics have been quick to point out that set theory is intended not as a theory of what can be “generated” or “constructed” from given objects in any literal sense but rather as a theory of a certain realm of objects independently existing in their own right. “Construction” is a metaphor. (shrink)

Scholars in the early seventeenth century who studied ancient Greek scientific theories often drew upon philology and history to reconstruct a more general picture of the Greek past. Gassendi's training as a humanist historiographer enabled him to formulate a conception of the history of philosophy in which the rationality of scientific and philosophical inquiry depended on the historical justifications which he developed for his beliefs. Professor Joy examines this conception and analyzes the nature of Gassendi's historical training, especially its relationship (...) to his career as a physicist and astronomer. She shows how he rehabilitated Epicurean atomism by bringing together the arguments of the Greek atomists and those of his contemporaries. In doing so, he produced an account of the natural world which made it an object of empirical study and mechanical explanation. (shrink)

Theoria, EarlyView. -/- In his recent book Thin Objects, Øystein Linnebo (2018) argues for the existence of a hierarchy of abstract objects, sufficient to model ZFC, via a novel and highly interesting argument that relies on a process called dynamic abstraction. This paper presents a way for a nominalist, someone opposed to the existence of abstract objects, to avoid Linnebo's conclusion by rejecting his claim that certain abstraction principles are sufficient for reference (RBA). Section 1 of the paper explains (...) Linnebo's argument for RBA. It offers a reading of Linnebo's work upon which he has two arguments for RBA: one deductive and one abductive, and argues that whilst the deductive argument is unsound the abductive one is prima facie plausible. The nominalist must therefore find a way to respond to the abductive argument. Section 2 outlines just such a response, by offering an alternative explanation of the cases Linnebo wishes to argue from. Most interestingly, it shows that abstraction in Linnebo's most difficult case (the “reference to ordinary bodies” case) can be achieved using mereological means, rather than relying on RBA. (shrink)

Gassendi holds both that we only have ideas of material things and that we know – by faith and, at least in later works, by reason as well – that the mind is immaterial. I examine the account of the mind provided in Gassendi’s Objections to the Meditations and show how Gassendi’s two theses can be rendered compatible. Indeed, the two theses, taken together, exemplify Gassendi’s account of the scope and limits of human understanding.

Resumen En general la disputa entre Gassendi y Descartes ha sido tratada desde el punto de vista cartesiano y, en ese contexto, nuestro artículo se centra en la filosofía de Gassendi. Buscamos un modo para entender la lógica o la estrategia de las objeciones gassendianas, tratando de mostrar los supuestos filosóficos que operan bajo las críticas a Descartes. Junto con ello, mostraremos parte de la recepción contemporánea de la polémica y explicaremos los tópicos más problemáticos adoptados por Gassendi relativos al (...) método y las asunciones relativas a la sustancia. Para cumplir estos objetivos, estudiaremos las objeciones de Gassendi a Descartes en las Quintas Objeciones a las Meditaciones Metafísicas y, también, en la Disquisitio metaphysica seu dubitationes et instantiae adversus Renati Cartesii metaphysicam et responsa, obra publicada por Gassendi en 1644.The quarrel between Pierre Gassendi and René Descartes has been treated generally from the Cartesian perspective, but our work focuses on Gassendi’s philosophy instead. In this sense, we want to find a more comprehensive way to integrate the internal logic that articulated Gassendi’s objections. We will try to show the contemporary reception and the logic of his philosophical assumptions or the strategy that operates under these objections. Besides, we will explain the contemporary reception of this polemic and the main critical issues adopted by Gassendi about “method” and “substance”. To accomplish these tasks, we will study Gassendi’s objections to the Meditations on first philosophy, as well as the Disquisitio metaphysica seu dubitationes et instantiae adversus Renati Cartesii metaphysicam et responsa, a work published by Gassendi in 1644. (shrink)

Byrne & Hilbert are right that it might be an objective fact that a particular tomato is unique red, but wrong that it cannot simultaneously be yellowish-red (not only objectively, but from somebody else's point of view). Sensory categorization varies among organisms, slightly among conspecifics, and sharply across taxa. There is no question of truth or falsity concerning choice of categories, only of utility and disutility. The appropriate framework for color categories is Nominalism and Pluralistic Realism.

In lieu of an abstract, here is a brief excerpt of the content:Readymades, Monochromes, Etc.:Nominalism and the Paradox of ModernismJ. M. Bernstein (bio)If Schopenhauer's thesis of art as an image of the world once over bears a kernel of truth, then it does so only insofar as this second world is composed out of elements that have been transposed out of the empirical world in accord with Jewish descriptions of the messianic order as an order just like the habitual order (...) but changed in the slightest degree.—T. W. Adorno, Aesthetic TheoryAdorno's philosophy as a whole, and his aesthetic theory in particular, is irrevocably bound to the tradition and achievements of high modernism. Although Adorno himself did not recognize American Abstract Expression as the apotheosis of high modernism in painting, that judgment now hardly seems contentious.1 And that raises a problem: it is the problem of R. Mutt, again, the problem of the porcelain urinal called Fountain, which was refused admittance to the Society of Independent Artists' Exhibition in April 1917 in spite of the Society's proclaimed democratic slogan "No jury, no prizes"—the work whose life or after-life begins with the beautiful photograph of it by Stieglitz set against the background of Marsden Hartley's The Warriors and that appeared shortly thereafter in the new avant-garde journal The Blind Man. Whatever the immediate repercussions of Fountain, there can be little doubt that much of what is most vital in art in the second half of this century is unthinkable without it; Duchamp's readymade offers an exemplary alternative to the tradition of high modernist painting that has continued to be generative. For a modernist like Adorno, for whom authentic art is that which best rises to the demands and necessities of artistic materials, for whom internal consistency and rigor would appear to be everything, for whom, finally, aesthetic form is the "objective organization within each artwork of what appears as bindingly eloquent" [AT 143; emphasis mine], Duchamp's gesture of simply naming or claiming artistic status for an ordinary bathroom fixture must be anathema. In this respect, Adorno's aesthetic theory would seem to be in the same predicament as Clement Greenberg's modernism: inextricably bound to a tradition that history has left behind. And while the option of refuting the claim of Fountain is certainly possible, and should not be too quickly suppressed (there is something in the claim that will forever be skeptically self-defeating), nonetheless there does appear to be an exemplariness to Fountain that exceeds the narrow provocation of Duchamp's nominalist gesture; something in the readymade, in fact, seems (art historically? aesthetically? conceptually?) irresistible. If so, then modernist [End Page 83] formalism must either find a way of accommodating the readymade without departing from its internal logic or find its claim to our attention forfeited.After laying out the bold outlines of Adorno's formalism, the remainder of this essay will seek to uncover an account of the readymade in the context of what I will eventually call "the paradox of modernism" in order to locate in what way the readymade can be accommodated to a defense of Adorno's late modernism. For the purposes of this argument, I am going to assume that the best overall defense of Duchamp's gesture, which makes it foundational for the understanding of modern art, is that offered by Thierry de Duve in his Kant after Duchamp. My elaboration of Adorno's late modernism will hence proceed, in part, through a charting of some of the fault lines in de Duve's Duchamp. My contention shall be that the generativity of Fountain as readymade not only belongs within modernism, but is only intelligible within a wholly modernist and formalist frame of reference.Adorno's Formalism and the Material MotiveAdorno opens the section of Aesthetic Theory entitled "Coherence and Meaning" with the drastic sounding thesis that "Although artworks are neither conceptual nor judgmental, they are logical" [AT 136]. He continues:In them nothing would be enigmatic if their immanent logicality did not accommodate discursive thought, which criteria they nevertheless regularly disappoint. They most resemble the form of a syllogism and its prototype in empirical thought. That in the temporal... (shrink)

Charles Chihara argues that many scholars in the philosophy of mathematics have adopted a false assumption, the Fregean Assumption, that mathematical theorems are propositions about the actual world. Chihara, who does not believe in the existence of abstract objects but does believe in abstract notions such as satisfiability in a structure, contends that mathematical theorems are rather only true in the sense that they are satisfied by appropriate kinds of structures. Chihara's thesis is presented and analyzed particularly in the context (...) of Set Theory. (shrink)

This edition features reliable, accessible translations; useful editorial materials; and a straightforward presentation of the Objections and Replies, including the objections from Caterus, Arnauld, and Hobbes, accompanied by Descartes' replies, in their entirety. The letter serving as a reply to Gassendi--in which several of Descartes' associates present Gassendi's best arguments and Descartes' replies--conveys the highlights and important issues of their notoriously extended exchange. Roger Ariew's illuminating Introduction discusses the Meditations and the intellectual environment surrounding its reception.

Nominalism is the view that mathematical objects do not exist. This chapter delimits several types of nominalistic projects: revolutionary programs that attempt to change mathematics and hermeneutic programs that attempt to interpret mathematics. Some programs accord with naturalism, and some oppose naturalism. Steven Yablo’s fictionalism is brought into the fold and discussed at some length.

The object of this paper is to provide a solution to Nelson Goodman’s Imperfect Community difficulty as it arises for Resemblance Nominalism, the view that properties are classes of resembling particulars. The Imperfect Community difficulty consists in that every two members of a class resembling each other is not sufficient for it to be a class such that there is some property common to all their members, even if ‘x resembles y’ is understood as ‘x and y share some property’. (...) In the paper I explain and criticise several solutions to the difficulty. Then I develop my own solution, which is not subject to the objections I make to the other solutions, and which accords completely with the basic tenets of Resemblance Nominalism. (shrink)

In my book *Resemblance Nominalism* I argued that the truthmakers of ´a and b resemble each other´ are just a and b. In his "Resemblance Nominalism and counterparts" Alexander Bird objects to my claim that the truthmakers of ´a and b resemble each other´ are just a and b. In this paper I respond to Bird´s objections.

W.V. Quine is a well-known proponent of naturalism, the view on which reality is described only in science. He is also well-known for arguing that our current scientific theories commit us to the existence of abstract objects. It is tempting to believe that the naturalistic philosopher should think scientists outside of philosophy are in the best position to assess the merits of revising our current commitment to abstract objects. But Quine rejects this deferential view. On the reading of Quine’s philosophical (...) methodology that I defend in this paper, the naturalistic philosopher not only may assess the merits of revising the commitments of our scientific theories, but also will recommend we make such revisions if doing so simplifies and clarifies our science. To develop my reading, I will examine John Burgess and Gideon Rosen’s naturalism in ontology that includes the deferential view Quine rejects. By explaining how Quine’s naturalism differs from the anti-revisionist, deferential naturalism in philosophy of mathematics that Burgess and Rosen advance, I seek to clarify and advance contemporary debates on naturalism. (shrink)

Nominalism faces the task of explaining away the ontological commitments of applied mathematical statements. This paper reviews an argument from the philosophy of logic that focuses on this task and which has been used as an objection to certain specific formulations of nominalism. The argument as it is developed in this paper aims to show that nominalism in general does not have the epistemological advantages its defendants claim it has. I distinguish between two strategies that are available to the (...) nominalist: The Evaluation Programme, which tries to preserve the common truth‐values of mathematical statements even if there are no mathematical objects, and Fictionalism, which denies that mathematical sentences have significant truth‐values. It is argued that the tenability of both strategies depends on the nominalist’s ability to account for the notion of consequence. This is a problem because the usual meta‐logical explications of consequence do themselves quantify over mathematical entities. While nominalists of both varieties may try to appeal to a primitive notion of consequence, or, alternatively, to primitive notions of logical or structural possibilities, such measures are objectionable. Even if we are equipped with a notion of either consequence or possibility that is primitive in the relevant sense, it will not be strong enough to account for the consequence relation required in classical mathematics. These examinations are also useful in assessing the possible counter‐intuitive appeal of the argument from the philosophy of logic. (shrink)

Arda Denkel, in "Real Resemblances," argues for a moderate Nominalism where substances objectively have properties and relations, the latter being particulars, but dependent particulars, grouped into classes by objective relations of resemblance. This view is contrasted unfavorably with the view that properties and relations are universals instantiated by particulars. It is conceded that Denkel's scheme has much to commend it. But it is argued that the universals view has much more to be said for it than Denkel allows, and that (...) it is indeed, on balance, the superior view. (shrink)

Nelson Goodman’s paper ‘About’ (1961) was a milestone in aboutness theory. Although it has been much discussed, an interesting fact about it has so far been completely ignored: the important debt it owes to two papers it cites by Gilbert Ryle. With Ryle’s ‘About’ (1933) it shares much more than the title – it, too, offers a three-fold account of different ways a sentence can relate to a subject matter and a separate account for fictitious objects. More importantly, although Goodman’s (...) approach is quite different, the inspiration for the crucial element in his account, ‘differential consequence’, may well have come from a parenthetical suggestion of entailment in Ryle’s ‘About’. The second essential tool Goodman uses, viz. compound predicates which incorporate the (fictitious) object, is also the crucial element in Ryle’s ‘Imaginary Objects’ (also 1933). Goodman turns them into a predicate schema for fictitious subject matters as well as for a nominalist version of his account. (shrink)

Nominalists need some account of correctness for sentences committed to the existence of abstract objects. This paper proposes a new statement of such conditions specifically for properties. The account builds on an earlier proposal of mine, but avoids the counter-examples against the latter pointed out by Thomas Schindler, particularly, the sentence ‘There are inexpressible properties’. I argue that the new proposal is independently motivated and more faithful to the spirit of the kind of error-theoretic nominalism that the original proposal was (...) part of. Along the way, I also propose novel treatments of Arthur Pap’s and W.V.O. Quine’s notoriously hard-to-paraphrase sentences about abstracta. (shrink)

One major motivation for nominalism, at least according to Hartry Field, is the desirability of intrinsic explanations: explanations that don’t invoke objects that are causally irrelevant to the phenomena being explained. There is something right about the search for such explanations. But that search must be carefully implemented. Nothing is gained if, to avoid a certain class of objects, one only introduces other objects and relations that are just as nominalistically questionable. We will argue that this is the case for (...) two alleged nominalist views: Field’s fictionalism, and Frank Arntzenius and Cian Dorr’s geometricalism. Central to our competing approach to nominalism is a distinction between terms that refer to objects and ones that instead code empirical phenomena while being referentially empty. We next contrast our approach to nominalism, which uses this term-grained distinction between coding and referring, with approaches that instead attempt to make a sentence-grained distinction between mathematical and non-mathematical content. We show the latter approach fails to be responsive to objections raised by van Fraassen. In the end, only one last approach to nominalism is left standing. 1 Introduction2 Troubles for Mathematical Fictionalism2.1 A distinction2.2 Field’s programme2.3 Parts of nominalistically acceptable entities are nominalistically acceptable2.4 Structural assumptions: How far can these be pushed?2.5 Cases of indispensable theories where the mathematical posits are known not to be real2.6 How does science distinguish between the indispensable structural presuppositions taken to be real and those that aren’t?2.7 Do physicists distinguish between mathematical posits and non-mathematical posits?2.8 Mathematical coding versus genuine metaphysics. Case study: Fields2.9 The upshot3 Troubles for Topologism4 Contrasts: Kitcher, Maddy, Sober, and van Fraassen4.1 Sober’s approach4.2 Maddy’s approach4.3 Kitcher’s approach4.4 Where do we go from here?4.5 Van Fraassen’s objection to Maddy’s approach to ontological commitment5 Conclusion. (shrink)

Many of the central theses of Hume's philosophy – his rejection of real relations, universals, abstract objects and necessary causal relations – had precedents in the later medieval nominalist tradition. Hume and his medieval predecessors developed complex semantic theories to show both how ontologies are apt to become inflated and how, if we understand carefully the processes by which meaning is generated, we can achieve greater ontological parsimony. Tracing a trajectory from those medieval traditions to Hume reveals Hume to (...) be more radical, particularly in his rejection of abstraction and abstract ideas. Hume's denial of general, abstract ideas is consistent with his philosophical principles but fails to appreciate the more sophisticated nominalist approaches to abstraction, the result of which is a theoretically impoverished account of our capacity for generalization. (shrink)

When we understand that something is a pot, is it because of one property that all pots share? This seems unlikely, but without this common essence, it is difficult to see how we could teach someone to use the word "pot" or to see something as _a_ pot. The Buddhist apoha theory tries to resolve this dilemma, first, by rejecting properties such as "potness" and, then, by claiming that the element uniting all pots is their very difference from all non-pots. (...) In other words, when we seek out a pot, we select an object that is not a non-pot, and we repeat this practice with all other items and expressions. Writing from the vantage points of history, philosophy, and cognitive science, the contributors to this volume clarify the nominalist apoha theory and explore the relationship between apoha and the scientific study of human cognition. They engage throughout in a lively debate over the theory's legitimacy. Classical Indian philosophers challenged the apoha theory's legitimacy, believing instead in the existence of enduring essences. Seeking to settle this controversy, essays explore whether apoha offers new and workable solutions to problems in the scientific study of human cognition. They show that the work of generations of Indian philosophers can add much toward the resolution of persistent conundrums in analytic philosophy and cognitive science. (shrink)

In this dissertation I consider the merits of certain nominalist accounts of phenomena related to the character of ordinary objects. What these accounts have in common is the fact that none of them is an error theory about standard cases of predication and none of them deploys God or uniquely theistic resources in its explanatory framework. -/- The aim of the dissertation is to answer the following questions: -/- • What is the best nominalist account on offer? • (...) How might it be improved? • Does it ultimately succeed? -/- I will argue that while so-called trope theory is the best account on offer, it can be significantly improved—or replaced—by a novel version of nominalism that is modeled after trope theory. Ultimately, however, I will argue that even the novel version fails. -/- The dissertation unfolds as follows. In Chapter 1, I introduce Austere Nominalism (AN), which is perhaps the most extreme version of nominalism that falls within the scope of the dissertation. AN is often described as the view that there exist only concrete particulars. According to AN, it is unnecessary to posit any entities other than ordinary objects—turkeys, tables, and the like—in order to account for explananda related to the character of those objects. (Such explananda include the phenomenon of attribute agreement, of attribute possession, of true subject-predicate sentences, etc.) In this chapter I argue that AN fails to provide an adequate account of these explananda. In addition, introducing and criticizing AN serves an important heuristic role for the rest of the dissertation. To understand this role, we must distinguish between the basic explanatory strategy deployed by the austere nominalist and the type of explananda for which she deploys that strategy. The austere nominalist deploys the strategy to account for the character of ordinary objects. As I argue in Chapter 1, this deployment is a failure. As I go on to show in Chapter 2, the widespread rejection AN has led to a variety of rival accounts of the character of ordinary objects. In rejecting AN, however, these accounts also tacitly reject its basic explanatory strategy. Thus goes the baby with the bathwater, since, arguably, there are some attractive features of AN’s basic explanatory strategy. Indeed, those who defend the most prominent version of nominalism—trope theory—seem to overlook the advantages of AN’s basic strategy, and by so doing, make an unnecessary concession to the realist. Or so I argue in Chapter 3. And, as I will argue in Chapter 4, the strongest version of nominalism is a novel account, modeled after trope theory, that deploys AN’s basic strategy at a more fundamental level than that of ordinary objects. This novel account—troper theory—is closer in spirit to AN than is traditional trope theory. (Thus, AN serves as a foil for the discussion of other nominalist views.) Finally, in the Afterword I indicate how troper theory is equally vulnerable to some of the traditional objections that plague trope theory. Thus, if you are not convinced that traditional objections to trope theory are conclusive and you want to be a nominalist, then you should abandon trope theory and adopt troper theory. If you take traditional objections against trope theory to have significant force, then you should reject both theories. (shrink)

Leibniz can be counted among the remote, but still significant, sources of Sellars's philosophy. Such thesis, however, is meaningless unless its conceptual relevance is displayed. Therefore, it will be immediately added that Sellars's relation with Leibniz is focused on three main fundamental issues, which respectively concern (1) the concept of nature, (2) the concept of truth and (3) the concept itself of nominalism. Besides, there are other seemingly minor topics, which actually refers to the definition of abstract entities, of predicates, (...) of proper names and to the datum/factum distinction. Another challenge the paper is faced with, regards the fact that Sellars does not consider Leibniz only in himself, given that he very often positions him in a close relation to Kant: it is as though there were multifaceted issues brought forward by Leibniz and Kant together forming a complex theoretical unity (over and above their differences). According to Sellars, in fact, they both undermine some of the most solid epistemological principles of the early modern times (mainly founded upon the subject- object lexicon and the idea of veritas as adaequatio rei et intellectus) and they both reshape the meaning of expressions such as “being actual” or “being true”. (shrink)

A painstakingly-argued, well-documented, scholarly work arguing for a sophisticated representative realism. Heuristically the analysis centers principally around Brentano, Meinong, Frege, and Bergmann. Some distinctive theses are mind is not substantial but a pluralism of momentary mental acts in which a subsequent act may have a predecessor for its object; things are really states of affairs; bare particulars are individuating principles; every mental act is propositional—its content does not intend a particular; possible states of affairs, which are nothing but could be, (...) can be intended ; thought-world, language-world correspondences do not coincide ; and a behavioristic reduction of intentional contexts would not account for "how certain mental phenomena give rise to the occurrence of intentional contexts". The organizational theme is the idealist-realist controversy in perception, with the nominalist-realist controversy covered by excellent discussions of universals and relations.—P. S. (shrink)

ABSTRACT Pierre Gassendi (1592–1655) has not been perceived as one of the early modern philosophers who had something interesting to say about the role of the desire for esteem in social life and the moral duties connected with this desire. Nevertheless, in his Animadversiones in decimum librum Diogenis Laertii (1649) there are some scattered, but interrelated remarks about how the desire for esteem could be supportive of civic virtue. These remarks were written during the years when Jansenism became a considerable (...) intellectual force in France, and the specific strengths of Gassendi's approach to the desire for esteem can be seen when it is read against this background. In the second volume of Augustinus (1640), Cornelius Jansen comments upon Augustine's objections to the moral value of striving for esteem. Contextualizing Gassendi's remarks against the Augustinian challenge is made plausible by two circumstances: The Augustinian challenge with respect to the desire for esteem contains explicit criticism of Epicurean ethics; and Gassendi responded to Augustine's central charge that, in desiring temporal goods such as esteem, one confuses things that are useful with things that should be enjoyed. (shrink)

Hofweber (Ontology and the ambitions of metaphysics, Oxford University Press, 2016) argues for a thesis he calls “internalism” with respect to natural number discourse: no expressions purporting to refer to natural numbers in fact refer, and no apparent quantification over natural numbers actually involves quantification over natural numbers as objects. He argues that while internalism leaves open the question of whether other kinds of abstracta exist, it precludes the existence of natural numbers, thus establishing what he calls “restricted nominalism” about (...) natural numbers. We argue that Hofweber’s internalism fails to establish restricted nominalism. Not only is his primary argument for restricted nominalism invalid, the analysis of quantification proposed threatens to collapse internalism into either a traditional form of error theory or realism. (shrink)

Aldo Antonelli offers a novel view on abstraction principles in order to solve a traditional tension between different requirements: that the claims of science be taken at face value, even when involving putative reference to mathematical entities; and that referents of mathematical terms are identified and their possible relations to other objects specified. In his view, abstraction principles provide representatives for equivalence classes of second-order entities that are available provided the first- and second-order domains are in the equilibrium dictated by (...) the abstraction principles, and whose choice is otherwise unconstrained.entities are the referents of abstraction terms: such referents are to an extent indeterminate, but we can still quantify over them, predicate identity or non-identity, etc. Our knowledge of them is limited, but still substantial: we know whatever has to be true no matter how the representatives are chosen, i.e., what is true in all models of the corresponding abstraction principles. This view is backed up by an “austere” conception of universals, according to which these are first-order objects, i.e., ways of collecting first-order objects. Antonelli thus claims that second-order logic does not import any novel ontological commitment beyond ontology of first-order, naturalistically acceptable, objects. Moreover, in the case of arithmetic, even if Hume’s Principle is construed as described above, Frege’s Theorem goes through unaffected, since there is nothing in its proof that depends on an account of the “true nature” of numbers. A viable construal of logicism is then given by the combination of semantic nominalism and a naturalistic conception of abstraction. [Editors note]. (shrink)

Mathematicalnominalists have argued that we can reformulate scientific theories without quantifying over mathematical objects.However, worries about the nature and meaningfulness of these nominalistic reformulations have been raised, like Burgess and Rosen’s dilemma. In this paper, I’ll review (what I take to be) a kind of emerging consensus response to this dilemma: appeal to the idea of different levels of analysis and explanation, with philosophy providing an extra layer of analysis “below” physics, much as physics does below chemistry. I’ll argue that (...) one can address certain lingering worries for this approach by appeal to the apparent usefulness of a distinction between foundational and non-foundational contexts within mathematics and certain (admittedly controversial) arguments for Potentialism about set theory. (shrink)

The 17th century's new science and new philosophy was roughly equally divided between Cartesians and Gassendists. Scholars agree that understanding Gassendi's metaphysics, epistemology and scientific method is crucial for understanding the development of modern philosophy, as Gassendis version of Epicureanism provides a third strand of influence on modern philosophy paralleling Cartesianism and scholasticism. Despite this, Gassendi is rather little understood today. I look at Gassendi in the context of his Objections and Counter-Objections to the Meditations, along with Descartes' Replies. This (...) context provides an explicit display of the opposition between two main strands of the new philosophy. I argue---contra a popular characterization of Gassendi's thought as primarily skeptical or even wholly unsystematic---that Gassendi's objections derive from a systematic psychology and cannot be well understood without a grasp of this psychology. ;I begin with a central methodological question in the dispute, the status of clear and distinct perception and what this tells us about proper procedure. This disagreement has it source in competing accounts of the cognitive faculties. Hence I go on to develop an account of Gassendi's theory of the cognitive faculties, and in particular perception, the acquisition of ideas, and reasoning. I then examine Gassendi's initially rather puzzling objections to the cogito, which act as a test-case for my interpretation of Gassendi's theory of cognition. I end with the dispute over the mind-body relationship. Gassendi objects that Descartes has failed to give any more than a nominal definition of the mind, having failed to make intelligible the modes of the mind in terms of its essence. Gassendi, in contrast, seeks an account of the operations of the mind in terms of the micro-level structure of the parts of the brain, and understands this micro-level structure as the genuine essence of the mind. This objection provides an excellent case for examining how Descartes and Gassendi's rival psychologies influenced two very different notions of scientific method. (shrink)

In a series of works, Jody Azzouni has defended deflationary nominalism, the view that certain sentences quantifying over mathematical objects are literally true, although such objects do not exist. One alleged attraction of this view is that it avoids various philosophical puzzles about mathematical objects. I argue that this thought is misguided. I first develop an ontologically neutral counterpart of Field’s reliability challenge and argue that deflationary nominalism offers no distinctive answer to it. I then show how this reasoning generalizes (...) to other philosophically problematic entities. The moral is that puzzle avoidance fails to motivate deflationary nominalism. (shrink)