In their (2008) article Liar-Like Paradox and Object Language Features C.S. Jenkins and Daniel Nolan (henceforth, JN) argue that it is possible to construct Liar-like paradox in a metalanguage even though its object language is not semantically closed. I do not take issue with this claim. I find fault though with the following points contained in JN’s article: First, that it is possible to construct Liar-like paradox in a metalanguage, even though this metalanguage is not (...) semantically closed. Second, that the presented examples of Liar-like paradox are supposed to be counterexamples to Tarski’s diagnosis of the classic Liar paradox. Third, that JN fail to notice Tarski’s postulate. And finally, that JN fail to recognize that the world they are pondering is not among the possible worlds. (shrink)

The subject of my article is the principle of characterization – the most controversial principle of Meinong’s Theory of Objects. The aim of this text is twofold. First of all, I would like to show that Russell’s well-known objection to Meinong’s Theory of Objects can be reformulated against a new modal interpretation of Meinongianism that is presented mostly by Graham Priest. Secondly, I would like to propose a strategy which gives uncontroversial restriction to the principle of characterization and which allows (...) to avoid Russell’s argument. The strategy is based on the distinction between object- and metalanguage, and it applies to modal Meinongianism as well as to other so-called Meinongian theories. (shrink)

In the period after the First World War when the various national-ideological “truths” that led to it were not well resolved which resulted in the Second World War, one of the greatest world crises occurs. In those turbulent times, one philosopher renounces his national identity (changes his religion and name), wanting not to save himself from an evil world that is emerging but to join the creation of a completely new world – the world of modern logic. This man is (...) Alfred Tarski, whom many recognize as “the man who defined truth”, linking him to the formulation of the distinction between object and metalanguage. In the paper, I argue with historians of philosophy who claim that this distinction was first set by the logician and philosopher of the Lvov-Warsaw school Stanislaw Leśniewski (whose Tarski was the only doctoral student) accusing Tarski of violating professional laws without attributing the authorship of this distinction to Leśniewski. I show that this is not true and I cite the places where Tarski clearly emphasizes Leśniewski ‘s contribution. (shrink)

Talking about objects requires talking with objects, presenting objects in speech to identify a term's referent. I say This figure is a circle while handing you a ring. The ring is a prop, a perceptual object referenced by an extra-sentential event to identify the extension of a term, its director ('This figure'). Props operate in speech acts and their products, not in sentences. Intra-sentential objects we talk with are displays. Displayed objects needn't be words but must be like words, (...) perceptually, reproductively, and syntactically. Displays are presented by their syntactical position, as terms, with a term-like function. Semantically they are props. The O in FOD (This figure O is a circle) is a prop-like referent, not a term. The O in OD (O is a circle) may be that of FOD, but that display may have semantically and syntactically diverse directors, and without a specific one OD has no determinate sense Describing the display of quotations demands distinguishing displays from quotations. Quotations are repetitions of something said. Displays are perceptual objects, linguistic and non-linguistic, reproductions and originals, presented in sentences to identify a referent. Display markers are disambiguators that say: Read this as a prop. They may mark direct speech from indirect speech. Markers of quotation say: Someone said this. That historical claim is outside a sentence's propositional content. Those marks don't say: This is a display. They do make it true. Calling displays quotations muddies the study of speaking with speech. Calling both displays and intranyms quotations muddies the study of meaning and truth. Intranyms are terms, consisting of an expression flanked by lines, that denote that interior expression. Intranyms are created by stipulation to formalize a metalanguage. Formalization of a metalanguage replaces displays with intranyms. Formalized metalanguages lack the logical form and subject matter of our natural metalanguage. (shrink)

Along with offering an historically-oriented interpretive reconstruction of the syntax of PM ( rst ed.), I argue for a certain understanding of its use of propositional function abstracts formed by placing a circum ex on a variable. I argue that this notation is used in PM only when de nitions are stated schematically in the metalanguage, and in argument-position when higher-type variables are involved. My aim throughout is to explain how the usage of function abstracts as “terms” (loosely speaking) (...) is not inconsistent with a philosophy of types that does not think of propositional functions as mind- and language-independent objects, and adopts a nominalist/substitutional semantics instead. I contrast PM’s approach here both to function abstraction found in the typed λ-calculus, and also to Frege’s notation for functions of various levels that forgoes abstracts altogether, between which it is a kind of intermediary. (shrink)

In this paper, I defend Rudolf Carnap's Principle of Tolerance from an accusation, due to Michael Friedman, that it is self-defeating by prejudicing any debate towards the logically stronger theory. In particular, Friedman attempts to show that Carnap's reconstruction of the debate between classicists and intuitionists over the foundations of mathematics in his book The Logical Syntax of Language, is biased towards the classical standpoint since the metalanguage he constructs to adjudicate between the rival positions is fully classical. I (...) argue that this criticism is mistaken on two counts: (1) it fails to fully appreciate the freedom with regard to the construction of linguistic frameworks that Carnap intended his Principle to embody, and (2) Friedman's objection underestimates the extent to which the evaluation of a framework is task-relative. I conclude that Tolerance is not self-undermining in the way that Friedman claims it is. While this is a restricted conclusion -- and is not a vindication of Carnap's views on logic and mathematics tout court -- it nonetheless suggests that his tolerant perspective has been dismissed too quickly, even by his supporters. (shrink)

In “Psychopower and Ordinary Madness” my ambition, as it relates to Bernard Stiegler’s recent literature, was twofold: 1) critiquing Stiegler’s work on exosomatization and artefactual posthumanism—or, more specifically, nonhumanism—to problematize approaches to media archaeology that rely upon technical exteriorization; 2) challenging how Stiegler engages with Giuseppe Longo and Francis Bailly’s conception of negative entropy. These efforts were directed by a prevalent techno-cultural qualifier: the rise of Synthetic Intelligence (including neural nets, deep learning, predictive processing and Bayesian models of cognition). This (...) paper continues this project but first directs a critical analytic lens at the Derridean practice of the ontologization of grammatization from which Stiegler emerges while also distinguishing how metalanguages operate in relation to object-oriented environmental interaction by way of inferentialism. Stalking continental (Kapp, Simondon, Leroi-Gourhan, etc.) and analytic traditions (e.g., Carnap, Chalmers, Clark, Sutton, Novaes, etc.), we move from artefacts to AI and Predictive Processing so as to link theories related to technicity with philosophy of mind. Simultaneously drawing forth Robert Brandom’s conceptualization of the roles that commitments play in retrospectively reconstructing the social experiences that lead to our endorsement(s) of norms, we compliment this account with Reza Negarestani’s deprivatized account of intelligence while analyzing the equipollent role between language and media (both digital and analog). (shrink)

The present discussion takes up an issue raised in Section 5 of Ross Brady and Penelope Rush’s paper ‘Four Basic Logical Issues’ concerning the (claimed) triviality – in the sense of automatic availability – of soundness and completeness results for a logic in a metalanguage employing at least as much logical vocabulary as the object logic, where the metalogical behaviour of the common logical vocabulary is as in the object logic. We shall see – in Propositions 4.5–4.7 (...) – that this triviality claim faces difficulties in the face of Halldén incompleteness, for essentially the same reasons that Halldén thought this phenomenon raised seman- tic difficulties for the modal logics of C. I. Lewis exhibiting it. To counter any inclination to dismiss the phenomenon as providing at best a marginal range of counterexamples to the triviality claim, a Postscript assembles some reminders of the extent of – and the varied considerations favouring – Halldén incompleteness. (shrink)

What's wrong with modalities in (Wittgenstein 1922)? In (Suszko 1968), the writer argued that "Wittgenstein was somewhat confused and wrong in certain points. For example, he did not see the clear-cut distinction between language (theory) and metalanguage (metatheory): a confusion between use and mention of expressions". Furthermore, a modal logic was proposed in (von Wright 1986) as depicting Wittgenstein's bipolarity thesis in a S5 frame. -/- The aim of the present paper is to deal with the specific case of (...) epistemic modal logic: such a logic of propositional attitudes assumes a philosophy of language that would violate Wittgenstein's two main assumptions. (shrink)

An evaluation of David Burrell's theory of the nature of analogy in Thomas Aquinas.

The view that perceptual experience has representational content, or the content view, has recently been criticized by the defenders of the so-called object view. Part of the dispute, I claim here, is based on a lack of grasp of the notion of content. There is, however, a core of substantial disagreement. Once the substantial core is revealed, I aim to: (1) reject the arguments raised against the content view by Campbell (2002), Travis (2004), and Brewer (2006); (2) criticize Brewer’s (...) (2006, 2007, 2008, 2011) attempts to defend the object view; (3) refine Pautz’ (2007, 2008, 2009, 2010, 2011) arguments against the object view, which mainly resort to the fact that it cannot account for the grounding role of hallucinatory experiences; (4) and finally adjudicate in favor of the content view and against the overestimation of the naïve intuition. (shrink)

This book pursues the question of how and whether natural language allows for reference to abstract objects in a fully systematic way. By making full use of contemporary linguistic semantics, it presents a much greater range of linguistic generalizations than has previously been taken into consideration in philosophical discussions, and it argues for an ontological picture is very different from that generally taken for granted by philosophers and semanticists alike. Reference to abstract objects such as properties, numbers, propositions, and degrees (...) is considerably more marginal than generally held. (shrink)

If an ordinary object causes an event, and if its atoms acting in concert cause the same event, then the event in question is overdetermined by two independent causes. The overdetermination argument aims to show that effects are never overdetermined in this way, and that we should only admit that the atoms acting in concert are the cause of the event in question. This means that the object constituted by those atoms does not cause anything, and if this (...) is so, then the object does not exist. I submit that it is possible to resist the overdetermination argument by claiming that causation is strictly an event-event relation. However, the argument can be reformulated in a way that blocks this objection. I explain how the reformulated version of the argument can be resisted by claiming that there is only one causal event that is undergone by both the object and its atoms acting in concert. Additionally, I show how the epistemic argument that can be formulated in support of the overdetermination argument can be resisted as well. (shrink)

Perceptual experience has the phenomenal character of encountering a mind-independent objective world. What we encounter in perceptual experience is not presented to us as a state of our own mind. Rather, we seem to encounter facts, objects, and properties that are independent from our mind. In short, perceptual experience has phenomenal objectivity. This paper proposes and defends a Kantian account of phenomenal objectivity that grounds it in experiences of lawlike regularities. The paper offers a novel account of the connection between (...) phenomenology and intentionality. It also sheds some light on one of the central themes in Kant’s Critique of Pure Reason. (shrink)

Climate change assessments rely upon scenarios of socioeconomic developments to conceptualize alternative outcomes for global greenhouse gas emissions. These are used in conjunction with climate models to make projections of future climate. Specifically, the estimations of greenhouse gas emissions based on socioeconomic scenarios constrain climate models in their outcomes of temperatures, precipitation, etc. Traditionally, the fundamental logic of the socioeconomic scenarios—that is, the logic that makes them plausible—is developed and prioritized using methods that are very subjective. This introduces a fundamental (...) challenge for climate change assessment: The veracity of projections of future climate currently rests on subjective ground. We elaborate on these subjective aspects of scenarios in climate change research. We then consider an alternative method for developing scenarios, a systems dynamics approach called ‘Cross-Impact Balance’ (CIB) analysis. We discuss notions of ‘objective’ and ‘objectivity’ as criteria for distinguishing appropriate scenario methods for climate change research. We distinguish seven distinct meanings of ‘objective,’ and demonstrate that CIB analysis is more objective than traditional subjective approaches. However, we also consider criticisms concerning which of the seven meanings of ‘objective’ are appropriate for scenario work. Finally, we arrive at conclusions regarding which meanings of ‘objective’ and ‘objectivity’ are relevant for climate change research. Because scientific assessments uncover knowledge relevant to the responses of a real, independently existing climate system, this requires scenario methodologies employed in such studies to also uphold the seven meanings of ‘objective’ and ‘objectivity.’. (shrink)

There is widespread excitement in the literature about the method of arbitrary functions: many take it to show that it is from the dynamics of systems that the objectivity of probabilities emerge. In this paper, I differentiate three ways in which a probability function might be objective, and I argue that the method of arbitrary functions cannot help us show that dynamics objectivise probabilities in any of these senses.

In this paper we present a new metaphysical theory of material objects. On our theory, objects are bundles of property instances, where those properties give the nature or essence of that object. We call the theory essential bundle theory. Property possession is not analysed as bundle-membership, as in traditional bundle theories, since accidental properties are not included in the object’s bundle. We have a different story to tell about accidental property possession. This move reaps many benefits. Essential bundle (...) theory delivers a simple theory of the essential properties of material objects; an explanation of how object coincidence can arise; an actual-world ground for modal differences between coincident objects; a simple story about intrinsic properties; and a plausible account of certain ubiquitous cases of causal overdetermination. (shrink)

Olfaction represents odors, if it represents anything at all. Does olfaction also represent ordinary objects like cheese, fish and coffee-beans? Many think so. This paper argues that it does not. Instead, we should affirm an austere account of the intentional objects of olfaction: olfactory experience is about odors, not objects. Visuocentric thinking about olfaction has tempted some philosophers to say otherwise.

This paper elaborates distinctions between a core and a periphery in the ontological and the conceptual domain associated with natural language. The ontological core-periphery distinction is essential for natural language ontology and is the basis for the central thesis of my 2013 book Abstract Objects and the Semantics of Natural Language, namely that natural language permits reference to abstract objects in its periphery, but not its core.

Though many linguists have shown a strong concern for social issues, there is an apparent contradiction between the principles of objectivity needed for scientific work and commitment to social action. The Black English trial in Ann Arbor showed one way in which this contradiction could be resolved. The first decade of research on Black English was marked by violent differences between creolists and dialectologists on the structure and origin of the dialect. The possibility of a joint point of view first (...) appeared in the general reaction of linguists against the view that blacks were linguistically and genetically inferior. The entrance of black linguists into the field was a critical factor in the further development of the creole hypothesis and the recognition of the distinctive features of the tense and aspect system. At the trial, linguists were able to present effective testimony in the form of a unified view on the origins and structural characteristics of the Black English Vernacular and argue for its validity as an alternate to standard English. (shrink)

In the section ‘Unity and Objectivity’ of The Bounds of Sense, P. F. Strawson argues for the thesis that unity of consciousness requires experience of an objective world. My aim in this essay is to evaluate this claim. In the first and second parts of the essay, I explicate Strawson's thesis, reconstruct his argument, and identify the point at which the argument fails. Strawson's discussion nevertheless raises an important question: are there ways in which we must think of our experiences (...) if we are to self-ascribe them? In the third part of the essay, I use Kant's remarks concerning the passivity of experience to suggest one answer to this question: in self-ascribing experiences, we must be capable of thinking of them as passive to their objects. This can be used to provide an alternative route from unity to objectivity. (shrink)

I this article, I introduce the notion of pluralism about an area, and use it to argue that the questions at the center of our normative lives are not settled by the facts -- even the normative facts. One upshot of the discussion is that the concepts of realism and objectivity, which are widely identified, are actually in tension. Another is that the concept of objectivity, not realism, should take center stage.

What follows is a contribution to the theory of space and of spatial objects. It takes as its starting point the philosophical subfield of ontology, which can be defined as the science of what is: of the various types and categories of objects and relations in all realms of being. More specifically, it begins with ideas set forth by Aristotle in his Categories and Metaphysics, two works which constitute the first great contributions to ontological science. Because Aristotle’s ontological ideas were (...) developed prior to the scientific discoveries of the modern era, he approached the objects and relations of everyday reality with the same ontological seriousness with which scientists today approach the objects of physics. We shall seek to show that what Aristotle has to say about these commonsensical objects and relations can, when translated into more formal terms, be of use also to contemporary ontologists. More precisely, we shall argue that his ideas can contribute to the development of a rigorous theory of those social and institutional components of everyday reality – the settings of human behavior – which are the subject of this volume. When modern-day philosophers turn their attentions to ontology they begin not with Aristotle but rather, in almost every case, with a set-theoretic ontology of the sort which is employed in standard model-theoretic semantics. Set-theoretic ontology sees the world in atomistic terms: it postulates a lowest level of atoms or urelements, from out of which successively higher levels of set-theoretic objects are then constructed. The approach to ontology to be defended here, in contrast, starts not with atoms but with the mesoscopic objects by which we are surrounded in our normal day-to-day.. (shrink)

The emphasis on the limitations of objectivity, in specific guises and networks, has been a continuing theme of contemporary analytic philosophy for the past few decades. The popular sport of baiting feminist philosophers — into pointing to what's left out of objective knowledge, or into describing what methods, exactly, they would offer to replace the powerful objective methods grounding scientific knowledge — embodies a blatant double standard which has the effect of constantly putting feminist epistemologists on the defensive, on the (...) fringes, on the run.This strategy can only work if objectivity is transparent, simple, stable, and clear in its meaning. It most certainly is not. In fact, taking objectivity as a sort of beautiful primitive, self-evident in its value, and all-powerful in its revelatory power, requires careless philosophy, and the best workers in metaphysics, epistemology, and philosophy of science have made reworked definitions of objectivity absolutely central to their own projects. In fact, classic feminist concerns with exploring the impact of sex and gender on knowledge, understanding, and other relations between human beings and the rest of the world fall squarely within the sort of human and social settings thatare already considered central in most current analytic metaphysics, epistemology, and philosophy of science. I argue that the burden of proof is clearly on those who wish toreject the centrality and relevance of sex and gender to our most fundamental philosophical work on knowledge and reality. (shrink)

A detailed examination of the philosophy of science of Evelyn Fox Keller, with special emphasis on her account of "objectivity" and her understanding of the methodology of Barbara McClintock.

The special composition question asks, roughly, under what conditions composition occurs. The common sense view is that composition only occurs among some things and that all and only ‘ordinary objects’ exist. Peter van Inwagen has marshaled a devastating argument against this view. The common sense view appears to commit one to giving what van Inwagen calls a ‘series-style answer’ to the special composition question, but van Inwagen argues that series-style answers are impossible because they are inconsistent with the transitivity of (...) parthood. In what follows I answer this objection in addition to other, less troubling objections raised by van Inwagen. (shrink)

The twin goals of this essay are: to investigate a family of cases in which the goal of guaranteed convergence to the truth is beyond our reach; and to argue that each of three strands prominent in contemporary epistemological thought has undesirable consequences when confronted with the existence of such problems. Approaches that follow Reichenbach in taking guaranteed convergence to the truth to be the characteristic virtue of good methods face a vicious closure problem. Approaches on which there is a (...) unique rational doxastic response to any given body of evidence can avoid incoherence only by rendering epistemology a curiously limited enterprise. Bayesian approaches rule out humility about one’s prospects of success in certain situations in which failure is typical. (shrink)

This is a prepublication version of my book Objects and Attitudes. The book develops a novel semantics of attitude reports, modal sentences, and quotation based on the view that sentences semantically act as predicates of various attitudinal and modal objects, entities like claims, requests, promises, obligations, and permissions, rather than standing for abstract propositions playing the role of objects. The approach develops truthmaker semantics for attitudinal and modal objects and has a wide range of applications to issues in philosophy of (...) language, semantics, and philosophy of mind. (shrink)

Religion is often singled out for special legal treatment in Western societies - which raises an important question: what, if anything, is special about religious conscience beliefs that warrants such special legal treatment? In this paper, I will offer an answer to this specialness question by investigating the relationship between religious conscientious objections and their insulation from relevant evidence. I will begin my analysis by looking at Brian Leiter’s arguments that religious beliefs are insulated from evidence and not worthy of (...) special legal treatment as a result. I will argue that he fails to show that religious conscience beliefs are both in principle responsive to empirical evidence and in practice typically more insulated from this evidence than secular conscience beliefs. If I am right about this, then Leiter fails to answer the “central puzzle” of his recent book and fails to sufficiently distinguish the religious conscience from the secular conscience. Second, I will look at whether or not it is plausible to understand the religious conscience as insulated from other forms of evidence. Following the research of social-psychologist Jonathan Haidt, I will argue that, typically, both forms of conscience seem to be similarly insulated from moral argumentation. I will also show that, while it seems as though the religious conscience usually draws from a larger set of moral values when compared to the secular conscience, this should make no legal difference overall. To conclude, I will explain that the arguments in this paper can be understood as evidence in support of an egalitarian response to religion’s specialness. (shrink)

This paper will focus on a philosophically significant construction whose semantics brings together two important notions in Kit Fine’s philosophy, the notion of truthmaking and the notion of a variable embodiment, or its extension, namely what I call a ‘variable object’. This is the construction of definite NPs like 'the number of people that can fit into the bus', 'the book John needs to write', and 'the gifted mathematician John claims to be'. Such NPs are analysed as standing for (...) variable objects, which are part of the 'shallow', construction-driven ontology of natural language, yet are real. (shrink)

The aim of this paper is to bring the resources of virtue epistemology to bear on the issue of the epistemic objectivity of science. A distinction is made between theoretical virtues that may be possessed by scientific theories and epistemic virtues that may be exercised by individual scientists. A distinction is then made between ontological objectivity, objectivity of truth and epistemic objectivity, the latter being the principal focus of the paper. It is then noted that a role must be played (...) by deliberative judgement in determining how to apply the theoretical virtues. It is suggested that such judgement may be virtuous in light of the exercise of the epistemic virtues. It is argued that the primary location of epistemic objectivity is the theoretical virtues, whereas the epistemic virtues of scientists play a subordinate role. (shrink)

Many philosophers accept a ‘layered’ world‐view according to which the facts about the higher ontological levels supervene on the facts about the lower levels. Advocates of such views often have in mind a version of atomism, according to which there is a fundamental level of indivisible objects known as simples or atoms upon whose spatiotemporal locations and intrinsic properties everything at the higher levels supervenes.1 Some, however, accept the possibility of ‘gunk’ worlds in which there are parts ‘all the way (...) down’ such that there are no simples and insofar as composite objects exist these are composed of smaller objects which in turn are composed of smaller objects, and so on. It may nonetheless still be claimed that the facts about each ontological level supervene on the facts about the lower levels. (shrink)

Though feminists are correct to note that conventional standards of sexiness are oppressive, we argue that feminism should reclaim sexiness rather than reject it. We argue for an aesthetic and ethical practice of working to shift from conventional attributions of sexiness to respectful attributions, in which embodied sexual subjects are appreciated in their full individual magnificence. We argue that undertaking this practice is an ethical obligation, since it contributes to the full recognition of others’ humanity. We discuss the relationship of (...) ethical to aesthetic considerations and argue that the respectful notion of sexiness is a genuinely aesthetic one, even though it does not involve assessment in relation to standards. (shrink)

talk Oslo-Kant congress. In this paper, I explain why for Kant self-consciousness is intimately related to objectivity, how this intimacy translates to real objects, what it means to make judgements about objects, and what idealism has got to do with all of this.

This paper defends the view that attitudinal objects such as claims, beliefs, judgments, and requests form an ontological category of its own sharply distinguished from that of events and states and that of propositions. Attitudinal objects play a central role in attitude reports and avoid the conceptual and empirical problems for propositions. Unlike the latter, attitudinal objects bear a particular connection to normativity. The paper will also discuss the syntactic basis of a semantics of attitude reports based on attitudinal objects.

This paper argues for a distinction between fictional characters, as parts of intentionally created abstract artifacts, and intentional objects, as nonexistent objects generated by referential acts that fail to refer. It argues that intentional objects as the nonexistent objects of imagination and other objectual attitudes are well-reflected in natural language, though in a highly restricted way, reflecting their ontological dependence on referential acts. The paper elaborates how that ontological dependence can be understood.

Adam Smith sought to explain the persistence of slavery as an institution in Wealth of Nations and Lectures on Jurispridence. In order to accomplish this he also drew on arguments he had developed in the Theory of Moral Sentiments. The result was a sophisticated explanation which bridged economic, psychological, and moral considerations. After presenting Smith’s explanation I will consider a discussion of the moral wrong of slavery in Ottobah Cugoano, the author of the incisive criticism of the slave trade Thoughts (...) and Sentiments on the Evil of Slavery (1787). I will suggest that Cugoano’s account of what is morally wrong in slavery shows an important lacuna in Smith‘s views. (shrink)

We examine some of Connes’ criticisms of Robinson’s infinitesimals starting in 1995. Connes sought to exploit the Solovay model S as ammunition against non-standard analysis, but the model tends to boomerang, undercutting Connes’ own earlier work in functional analysis. Connes described the hyperreals as both a “virtual theory” and a “chimera”, yet acknowledged that his argument relies on the transfer principle. We analyze Connes’ “dart-throwing” thought experiment, but reach an opposite conclusion. In S , all definable sets of reals are (...) Lebesgue measurable, suggesting that Connes views a theory as being “virtual” if it is not definable in a suitable model of ZFC. If so, Connes’ claim that a theory of the hyperreals is “virtual” is refuted by the existence of a definable model of the hyperreal field due to Kanovei and Shelah. Free ultrafilters aren’t definable, yet Connes exploited such ultrafilters both in his own earlier work on the classification of factors in the 1970s and 80s, and in Noncommutative Geometry, raising the question whether the latter may not be vulnerable to Connes’ criticism of virtuality. We analyze the philosophical underpinnings of Connes’ argument based on Gödel’s incompleteness theorem, and detect an apparent circularity in Connes’ logic. We document the reliance on non-constructive foundational material, and specifically on the Dixmier trace −∫ (featured on the front cover of Connes’ magnum opus) and the Hahn–Banach theorem, in Connes’ own framework. We also note an inaccuracy in Machover’s critique of infinitesimal-based pedagogy. (shrink)

The classification of algebraic surfaces by the Italian School of algebraic geometry is universally recognized as a breakthrough in 20th-century mathematics. The methods by which it was achieved do not, however, meet the modern standard of rigor and therefore appear dubious from a contemporary viewpoint. In this article, we offer a glimpse into the mathematical practice of the three leading exponents of the Italian School of algebraic geometry: Castelnuovo, Enriques, and Severi. We then bring into focus their distinctive conception of (...) rigor and intuition. Unlike what is often assumed today, from their perspective, rigor is neither opposed to intuition nor understood as a unitary phenomenon – Enriques distinguishes between small-scale rigor and large-scale rigor and Severi between formal rigor and substantial rigor. Finally, we turn to the notion of mathematical objectivity. We draw from our case study in order to advance a multi-dimensional analysis of objectivity. Specifically, we suggest that various types of rigor may be associated with different conceptions of objectivity: namely, objectivity as faithfulness to facts and objectivity as intersubjectivity. (shrink)

Interest in the concept of objectivity is part of the legacy of Modern Philosophy, tracing back to a new way of understanding the starting point of philosophical reflection. It traces back to an “epistemological turn” that attended the development of New Science of the 16th and 17th Century. These origins are an indication that what a thinker takes as the starting point of philosophical reflection deeply affects how they approach key philosophical concepts, including truth, knowledge, and objectivity. Chapter 1 Introduces (...) this key concept in philosophy, and some of the history of its use. (shrink)

I discuss Benacerraf's epistemological challenge for realism about areas like mathematics, metalogic, and modality, and describe the pluralist response to it. I explain why normative pluralism is peculiarly unsatisfactory, and use this explanation to formulate a radicalization of Moore's Open Question Argument. According to the argument, the facts -- even the normative facts -- fail to settle the practical questions at the center of our normative lives. One lesson is that the concepts of realism and objectivity, which are widely identified, (...) are actually in tension. (shrink)

While there is a prolific debate surrounding the issue of conscientious objection of individuals towards performing certain clinical acts, this debate ignores the fact that there are other reasons why clinicians might wish to object providing specific services. This paper briefly discusses the idea that healthcare workers might object to providing specific services because they are against their professional judgement, they want to maintain a specific reputation, or they have pragmatic reasons. Reputation here is not simply understood as (...) being in good standing with a professional body. Rather, reputation is treated in the sense that a craftsman might wish to be known for providing a specific type, quality, and style of service. Professionalism is understood as acting according to the philosophical and scientific principles that are the basis of healthcare (such as acting for the benefit of the patient’s health and following well- evidenced treatment pathways). (shrink)

Conscientious objection in health care is a form of compromise whereby health care practitioners can refuse to take part in safe, legal, and beneficial medical procedures to which they have a moral opposition (for instance abortion). Arguments in defense of conscientious objection in medicine are usually based on the value of respect for the moral integrity of practitioners. I will show that philosophical arguments in defense of conscientious objection based on respect for such moral integrity are extremely weak and, if (...) taken seriously, lead to consequences that we would not (and should not) accept. I then propose that the best philosophical argument that defenders of conscientious objection in medicine can consistently deploy is one that appeals to (some form of) either moral relativism or subjectivism. I suggest that, unless either moral relativism or subjectivism is a valid theory—which is exactly what many defenders of conscientious objection (as well as many others) do not think—the role of moral integrity and conscientious objection in health care should be significantly downplayed and left out of the range of ethically relevant considerations. (shrink)

I defend the thesis that Kantian analytic judgments are about objects (as opposed to concepts) against two challenges raised by recent scholars. First, can it accommodate cases like “A two-sided polygon is two-sided”, where no object really falls under the subject-concept as Kant sees it? Second, is it compatible with Kant’s view that analytic judgments make no claims about objects in the world and that we can know them to be true without going beyond the given concepts? I address (...) these challenges in two steps. First, given Kant’s distinction between an object in general = x from an object of sensible intuition, I argue that analytic judgments are about objects in the former sense, no matter whether the purported objects can be given in our intuition. Second, using Kant’s method of representing certain logical relations of concepts with such figures as circles, I construct a model to show that analytic truths are truths about objects in general = x and yet can be determined solely by the intensional relation between the given concepts plus certain Kantian-logical laws. Analytic truths are thus shown as formal in the Kantian sense that they do not presuppose the purported objects as givable in our intuition. This account of the formality of analytic truths captures Kant’s diagnosis of the Leibnizian illusion that we can make material claims about the world by analytically true judgments. (shrink)

According to the New Angle, any explanation of the Knobe effect must be gradable and asymmetric. It has been argued that only Hindriks’ approach meets both criteria. First, we argue that Holton’s hypothesis also meets the criteria. Second, we show that the authors are not justified in taking the criteria to be empirically justified. We have failed to replicate the asymmetry result in two experiments. Moreover, gradability can be objective or epistemic. We show that the New Angle presupposes objective gradability. (...) In our experiments, the patterns of responses to questions about epistemic and objective gradability are the same, irrespective of whether the feature is objectively gradable (e.g., blameworthiness) or not (e.g., intentionality). Our results thus question the extent to which the New Angle is empirically grounded. Moreover, they raise doubt whether the answers to questions about epistemic and objective gradability can be taken at face value at all. (shrink)

Closed time-like curves (CTCs) naturally appear in a variety of chronology-violating space{times. In these space{times, the principle of self-consistency demands a harmony between local and global a airs that excludes grandfather-like paradoxes. However, selfexisting objects trapped in CTCs are not seemingly avoided by the standard interpretation of this principle, usually constrained to a dynamical framework. In this letter we discuss whether we are committed to accept an ontology with self-existing objects if CTCs actually occur in the universe. In addition, the (...) epistemological status of the principle of self-consistency is analyzed and a discussion on the information flux through CTCs is presented. (shrink)

We show how some model-theoretical devices (local reasoning, modes of presentation, an additional accessibility relation) can be combined in first-order modal logic to formalize the consequence relation that includes de dicto and de re contradictory beliefs. Instead of special ``sense objects'', appearances of objects in an agent's belief are introduced and presented as ordered pairs consisting of an object and an individual constant. A non-classical identity relation is applied. A relation S on the set of possible worlds is introduced, (...) which models possible distortions in an agent's picture of a (real) world. The application of such models in deontic logic is illustrated by a characteristic example. (shrink)

Pluralists believe in the occurrence of numerically distinct spatiotemporal coincident objects. They argue that there are coincident objects that share all physical and spatiotemporal properties and relations; nevertheless, they differ in terms of modal and some other profiles. Appealing to the grounding problem according to which nothing can ground the modal differences between coincident objects, monists reject the occurrence of coincident objects. In the first part of this paper, I attempt to show that the dispute between monists and pluralists cannot (...) be settled based upon the grounding problem tout court. I argue that the grounding problem or a very similar problem is a challenge for all monists and pluralists alike if they are ontologically committed to the existence of composite objects as independent entities. In the final part, adopting the Aristotelian account of essence, I propose a solution that enables pluralists to plausibly ground modal differences between coincident objects. (shrink)

The purpose of this work is to address what notion of geometrical object and geometrical figure we have in different kinds of geometry: practical, pure, and applied. Also, we address the relation between geometrical objects and figures when this is possible, which is the case of pure and applied geometry. In practical geometry it turns out that there is no conception of geometrical object.

We sley Salmon, in his influential and detailed book, Four Decades of Scientific Explanation, argues that the pragmatic approach to scientific explanation, “construed as the claim that scientific explanation can be explicated entirely in pragmatic terms” (1989, 185) is inadequate. The specific inadequacy ascribed to a pragmatic account is that objective relevance relations cannot be incorporated into such an account. Salmon relies on the arguments given in Kitcher and Salmon (1987) to ground this objection. He also suggests that Peter Railton’s (...) concepts of the ideal explanatory text and explanatory information (Railton 1981) can provide what the pragmatic approach lacks. This suggestion is not a conclusion of course; we read it as the promotion of part of a research program aimed at forging a greater consensus on scientific explanation-an admirable goal. However, we do not see the pragmatic approach as inadequate. We will show that a synthetic account inspired by Salmon’s adaptation of Railton would be equivalent to van Fraassen’s pragmatic account in three respects: accepting or rejecting requests for explanation; the practice of giving scientific explanations; and the evaluation of the goodness of explanations. We include all three under the general rubric of explanatory “practice.” Admittedly these are not the only three features by which an account of explanation might be evaluated. Roughly, we mean to show that a synthetic account cannot do a better job of accounting for the scientific practices which are of importance to the constructive empiricist, and therefore no argument can be presented to the constructive empiricist to convince her that by her own standards the synthetic account is superior. (shrink)