Paul Benacerraf's argument from multiple reductions consists of a general argument against realism about the natural numbers (the view that numbers are objects), and a limited argument against reductionism about them (the view that numbers are identical with prima facie distinct entities). There is a widely recognized and severe difficulty with the former argument, but no comparably recognized such difficulty with the latter. Even so, reductionism in mathematics continues to thrive. In this paper I develop a difficulty for Benacerraf's argument (...) against reductionism that is of comparable severity to the now widely recognized difficulty with his general argument against realism. Thanks to Kit Fine, Hartry Field, Jeff Sebo, Ted Sider, Stephen Schiffer, and anonymous referees at Philosophia Mathematica for helpful comments on earlier versions of this paper. Thanks to Aron Edidin for many helpful discussions of the problems that inspired it. CiteULike Connotea Del.icio.us What's this? (shrink)

It is widely agreed that the intelligibility of modal metaphysics has been vindicated. Quine's arguments to the contrary supposedly confused analyticity with metaphysical necessity, and rigid with non-rigid designators.2 But even if modal metaphysics is intelligible, it could be misconceived. It could be that metaphysical necessity is not absolute necessity – the strictest real notion of necessity – and that no proposition of traditional metaphysical interest is necessary in every real sense. If there were nothing otherwise “uniquely metaphysically significant” about (...) metaphysical necessity, then paradigmatic metaphysical necessities would be necessary in one sense of “necessary”, not necessary in another, and that would be it. The question of whether they were necessary simpliciter would be like the question of whether the Parallel Postulate is true simpliciter – understood as a pure mathematical conjecture, rather than as a hypothesis about physical spacetime. In a sense, the latter question has no objective answer. In this article, I argue that paradigmatic questions of modal metaphysics are like the Parallel Postulate question. I then discuss the deflationary ramifications of this argument. I conclude with an alternative conception of the space of possibility. According to this conception, there is no objective boundary between possibility and impossibility. Along the way, I sketch an analogy between modal metaphysics and set theory. (shrink)

_Justin Clarke-Doane* * Morality and Mathematics. _ Oxford University Press, 2020. Pp. xx + 208. ISBN: 978-0-19-882366-7 ; 978-0-19-2556806.† †.

Is the Axiom of Foundation a truth or a falsehood about the universe of sets? Such questions have always struck this reviewer as unmathematical and a bit silly. Of course, that appraisal is more like a grunt of disapproval than an argument. We would welcome arguments. Justin Clarke-Doane offers a pretty good one that goes roughly as follows.Mathematicians making reasoned judgments about set-theoretic principles sometimes take positions that appear incompatible: one mathematician making a claim that would contradict the (...) claim of another if both claims were treated as assertions about a single universe of sets. If the claims are sincerely made and contradict each another, one party to the dispute must be expressing a false belief. It is characteristic of reliable methods that they significantly impede the formation of false beliefs. Reliable methods for fixing set-theoretic beliefs significantly impede the formation of false beliefs about sets. So, if we knew which party in a set-theoretic dispute has got it wrong, we would have evidence that that party’s methods are unreliable. But it is frequently unclear why the reasons offered by one side should prevail over those offered by the other. Unable to pinpoint the error, we could find ourselves less confident about the methods of each party. We might even wonder if there is much hope of establishing the reliability of set-theoretic methods in general. (shrink)

ObjectiveTo compare techniques for computing clustering and switching scores in terms of agreement, correlation, and empirical value as predictors of incident cognitive impairment.MethodsWe transcribed animal and letter F fluency recordings on 640 cases of ICI and matched controls from a national epidemiological study, amending each transcription with word timings. We then calculated clustering and switching scores, as well as scores indexing speed of responses, using techniques described in the literature. We evaluated agreement among the techniques with Cohen’s κ and calculated (...) correlations among the scores. After fitting a base model with raw scores, repetitions, and intrusions, we fit a series of Bayesian logistic regression models adding either clustering and switching scores or speed scores, comparing the models in terms of several metrics. We partitioned the ICI cases into acute and progressive cases and repeated the regression analysis for each group.ResultsFor animal fluency, we found that models with speed scores derived using the slope difference algorithm achieved the best values of the Watanabe–Akaike Information Criterion, but with good net reclassification improvement only for the progressive group. For letter fluency, different models excelled for prediction of acute and progressive cases. For acute cases, NRI was best for speed scores derived from a network model, while for progressive cases, the best model used clustering and switching scores derived from the same network model. Combining variables from the best animal and letter F models led to marginal improvements in model fit and NRI only for the all-cases and acute-cases analyses.ConclusionSpeed scores improve a base model for predicting progressive cognitive impairment from animal fluency. Letter fluency scores may provide complementary information. (shrink)

To have free will is to have what it takes to act freely. When an agent acts freely—when she exercises her free will—what she does is up to her. A plurality of alternatives is open to her, and she determines which she pursues. When she does, she is an ultimate source or origin of her action. So runs a familiar conception of free will.

From the perspective of a certain kind of physicalist naturalism, both mathematical and moral discourse look problematic. Our knowledge of the world is via caus.

In response to comments on my book, Being Realistic about Reasons, by Justin Clarke-Doane, David Enoch and Tristram McPherson, and Gideon Rosen, I try to clarify my domain-based view of ontology, my understanding of the epistemology of normative judgments, and my interpretation of the phenomenon of supervenience.

For Socrates, the virtues are a kind of knowledge, and the virtues form a unity. Sometimes, Socrates suggests that the virtues are all ‘one and the same’ thing. Other times, he suggests they are ‘parts of a single whole.’ I argue that the ‘what is x?’ question is sophisticated, it gives rise to two distinct kinds of investigations into virtue, a conceptual investigation into the ousia and a psychological investigation into the dunamis, Plato recognized the difference between definitional accounts of (...) the ousia and a psychological accounts of the dunamis, and the distinction between these two investigations can effectively resolve various interpretive puzzles regarding the unity of the virtues. It is argued that the virtues are ‘one and the same’ psychologically, while they are ‘parts of a single whole’ conceptually. (shrink)

This paper argues that the provision of effective informed consent by surgical patients requires the disclosure of material information about the comparative clinical performance of available surgeons. We develop a new ethical argument for the conclusion that comparative information about surgeons' performance - surgeons' report cards - should be provided to patients, a conclusion that has already been supported by legal and economic arguments. We consider some recent institutional and legal developments in this area, and we respond to some common (...) objections to the use of report cards on the clinical performance of surgeons. (shrink)

In raising the “What-is-F?” question, commentators disagree about whether Socrates is asking a conceptual question or a causal question. I argue that the contexts surrounding Socrates' two most prominent examples of adequate answers confirm that the “What-is-F?” question is a conceptual question in both the Meno and Euthyphro, but a causal question in the Laches and Protagoras. The “What-is-F?” question is multifunctional. Plato's Socrates consistently employs two separate vocabularies in connection with these two types of questions. By outlining their vocabularies, (...) and by examining other important contextual signals, I pave the way for readers to distinguish between conceptual and causal investigation in the “dialogues of definition.”. (shrink)

In the so-called ‘dialogues of definition,’ Socrates appears to endorse the ‘priority of definition.’ This principle states that an agent cannot know anything about F-ness (its instances, examples, properties, etc.) without knowing what F-ness is (the definition of F-ness). Not only is this principle implausible, it is also difficult to square with Socrates’ method. In employing his method, Socrates appeals to truths about the instances and properties of F-ness, even while pursuing definitional knowledge; meanwhile, he holds that one cannot know (...) those truths without already knowing the definition. Thus, there is a tension between Socrates’ principle and his method. Commentators have tried to resolve this problem in various ways, though typically without a careful examination of his ‘What is F-ness?’ question. I argue that Socrates employs the ‘What is F-ness?’ question as a way of introducing two distinct types of investigation into F-ness (conceptual and causal). With this established, the relationship between Socrates’ principle and his method comes to light, and the tension is resolved. (shrink)

I want to motivate an account of what it is for an object to have a property, which may as well be called a deflationary view about properties. Such a view follows from a conception of predication I ground in the work of Donald Davidson, some of which remains unpublished. I claim that if we take seriously Davidson’s account of predication, by maintaining that sentences are the primary linguistic unit, we can define properties in terms of predicates. The aim of (...) this paper is twofold. First, I argue that this account is present in Davidson’s systematic treatment of the problem of predication. Second, I claim that this account is serviceable and economical, as it can accommodate a wide scope of properties and abstract objects without appealing to entities such as truthmakers or joints in nature. (shrink)

In this dissertation I defend the claim, long held by Donald Davidson, that truth is a primitive concept that cannot be correctly or informatively defined in terms of more basic concepts. To this end I articulate the history of the primitive thesis in the 20th century, working through early Moore, Russell, and Frege, and provide improved interpretations of their reasons for advancing and eventually abandoning the primitive thesis. I show the importance of slingshot-style arguments in the work of Frege, Church, (...) Davidson, and Gödel for resisting certain versions of the correspondence theory of truth. I argue that most slingshots fail to convincingly establish a collapsing conclusion, but that a Gödelian version of the slingshot is terminal to certain varieties of the correspondence theory of truth. I then provide a Davidsonian theory of truth and interpretation that is consistent with and makes use of the primitive thesis. Finally, I provide an account of predication, properties, and universals that I argue is both serviceable and consistent with Davidson’s overall program. (shrink)

If certain versions of the correspondence theory of truth are correct, then truth can be informatively defined as correspondence to facts; facts would be truth-makers, and we could explain truth in terms of truth-bearers, correspondence, and truth-makers. I explain how slingshot arguments work generally, as collapsing arguments (regardless of their targets). Working through the slingshots of Davidson, and Gödel, I claim that Davidson’s slingshot involves dubitable premises, but that Gödel’s slingshot is terminal to certain versions of the correspondence theory, as (...) it poses a fatal dilemma between what I call fact fission and fact fusion. My claim is that it is impossible to informatively define truth in terms of correspondence to facts. (shrink)

Moral rationalism, the belief that acting contra a moral requirement is always irrational, is a strong claim; if true, seems to greatly reduce in scope the number of plausible moral theories due to what has been called the demandingness objection. One response to this consequence of moral rationalism has been to adopt moral anti-rationalism. Dale Dorsey thinks one can escape the demandingess objection with a weak form of anti-rationalism that still grants morality pride of place among normative systems. In this (...) paper I’ll argue that the demandingness objection is a formidable challenge to moral rationalism, and that Dorsey is correct in arguing that his weak anti-rationalism neatly offers a way to evade the objection. I’ll maintain, however, that weak anti-rationalism opens theories up to another powerful objection, the permissiveness objection, which ought to lead someone comfortable abandoning moral rationalism to abandon weak anti-rationalism as well, accepting moral anti-rationalism. (shrink)

Toward the end of the Charmides, Socrates declares the search for temperance a ‘complete failure’ (175b2‐3). Despite this, commentators have suspected that the dialogue might contain an implicit answer about temperance. I propose a new interpretation: the dialogue implies that temperance is the knowledge of good and bad, when this knowledge is applied specifically to certain operations of the soul. This amounts to a kind of self‐knowledge; it also involves a kind of reflexivity, for it involves knowing about the value (...) of one's knowledge. This positive reading, more than any other, makes sense of the dialogue's dramatic and dialectic features. (shrink)

BackgroundWe conducted a survey to identify what types of health/medical research could be exempt from research ethics reviews in Australia.MethodsWe surveyed Australian health/medical researchers and Human Research Ethics Committee members. The survey asked whether respondents had previously changed or abandoned a project anticipating difficulties obtaining ethics approval, and presented eight research scenarios, asking whether these scenarios should or should not be exempt from ethics review, and to provide comments. Qualitative data were analysed thematically; quantitative data in R.ResultsWe received 514 responses. (...) Forty-three per cent of respondents to whom the question applied, reported changing projects in anticipation of obstacles from the ethics review process; 25% reported abandoning projects for this reason. Research scenarios asking professional staff to provide views in their area of expertise were most commonly exempted from ethics review ; scenarios involving surplus samples and N-of-1 studies were most commonly required to undergo ethics review. HREC members were 26% more likely than researchers to require ethics review. Need for independent oversight, and low risk, were most frequently cited in support of decisions to require or exempt from ethics review, respectively.ConclusionsConsiderable differences exist between researchers and HREC members, about when to exempt from review the research that ultimately serves the interests of patients and the public. It is widely accepted that evaluative research should be used to reduce clinical uncertainties—the same principle should apply to ethics reviews. (shrink)

Alterations to cognitive function are often reported with depression and anxiety symptoms, yet few studies have examined the same associations with mental well-being. This study examined the association between mental well-being, depression and anxiety symptoms and cognitive function in 1502 healthy adult monozygotic and dizygotic twins, and the shared/unique contribution of genetic and environmental variance. Using linear mixed models, mental well-being was positively associated with sustained attention, inhibition, cognitive flexibility, motor coordination and working memory, whereas depression and anxiety symptoms were (...) associated with poorer sustained attention, inhibition, cognitive flexibility and executive function. Bivariate twin modelling showed well-being shared a small environmental correlation with motor coordination and a small genetic correlation with working memory. Trivariate twin modelling showed well-being shared a small genetic correlation with inhibition, whereas depression and anxiety symptoms shared a small environmental correlation with inhibition. The remaining variance was mostly driven by unique G and/or E variance. Overall, well-being and depression and anxiety symptoms show both independent and shared relationships with cognitive functions but this is largely attributable to unique G or E variance and small shared G/E variance between pairs of variables. (shrink)

Family Matters in Indian Buddhist Monasticism. By Shayne Clarke. Honolulu: University of Hawai’i Press, 2014. Pp. xvi + 275. $52; Family in Buddhism. Edited by LIz WILsON. Albany: State University of New York Press, 2013. Pp. 298. $85.

Jaegwon Kim’s causal inheritance principle says that the causal powers of a mental property instance are identical with the causal powers of its particular physical realizer. Sydney Shoemaker’s subset account of realization is at odds with Kim’s principle: it says that a mental property instance has fewer causal powers than Kim’s principle entails. In this paper, I argue that the subset account should be rejected because it has intolerable consequences for mental causation, consequences that are avoided by accepting causal inheritance. (...) I develop my argument in part by drawing on one of the central debates that has arisen regarding the extended mind hypothesis defended by Andy Clark and David Chalmers. (shrink)

Justin Clarke-Doane offers what purports to be a stand-alone argument, relying on Gödel’s second incompleteness theorem, that if we hold that PA + Con(PA) and PA + ~ Con(PA) are equally true of their intended subjects, then there is no objective fact as to whether PA is consistent. It is shown that the argument is fallacious, although illuminating: The fallaciousness of the argument arises from a 20th-century shift in our understanding of interpreted languages from the view—derived from our (...) experience of language—of sentences as intrinsically interpreted to one which sharply distinguishes syntax and semantics, and treats uninterpreted syntactic forms as endowed with interpretations by models. It is shown that this syntax/semantic distinction, because it is “unintuitive” induces fallacies such as the one that Clarke-Doane’s argument exemplifies. (shrink)

In Morality & Mathematics, Justin Clarke-Doane argues that it is hard to imagine being "a realist about, for example, the standard model of particle physics, but not about mathematics." I try to explain how that seems very possible from the perspective of a physicist. What is real is the physical world; mathematics starts from descriptions of the natural world and extrapolates from there, but that extrapolation does not imply any independent reality. -/- Submitted to an Analysis Reviews symposium (...) on Clarke-Doane's Morality & Mathematics. (shrink)

There are many domains about which we think we are reliable. When there is prima facie reason to believe that there is no satisfying explanation of our reliability about a domain given our background views about the world, this generates a challenge to our reliability about the domain or to our background views. This is what is often called the reliability challenge for the domain. In previous work, I discussed the reliability challenges for logic and for deductive inference. I argued (...) for four main claims: First, there are reliability challenges for logic and for deduction. Second, these reliability challenges cannot be answered merely by providing an explanation of how it is that we have the logical beliefs and employ the deductive rules that we do. Third, we can explain our reliability about logic by appealing to our reliability about deduction. Fourth, there is a good prospect for providing an evolutionary explanation of the reliability of our deductive reasoning. In recent years, a number of arguments have appeared in the literature that can be applied against one or more of these four theses. In this paper, I respond to some of these arguments. In particular, I discuss arguments by Paul Horwich, Jack Woods, Dan Baras, Justin Clarke-Doane, and Hartry Field. (shrink)

The fourteen papers in this collection offer a variety of original contributions to the epistemology of modality. In seeking to explain how we might account for our knowledge of possibility and necessity, they raise some novel questions, develop some unfamiliar theoretical perspectives, and make some intriguing proposals. Collectively, they advance our understanding of the field. In Part I of this Introduction, I give some general background about the contemporary literature in the area, by sketching a timeline of the main tendencies (...) of the past twenty-five years or so, up to the present debates. Next, I focus on four features that largely characterize the latest literature, and the papers in the present collection in particular: (i) an endorsement of the importance of essentialism; (ii) a shift to a “metaphysics-first” approach to modal epistemology; (iii) a focus on metaphysical modality as opposed to other kinds of modality; and (iv) a preference for non-uniform modal epistemology. In Part II, I present the individual papers in the volume. These are organized around the following four chapters, based on their topic: (A) Skepticism & Deflationism; (B) Essentialism; (C) Non-Essentialist Accounts; (D) Applications. -/- LIST OF CONTRIBUTORS: Francesco Berto; Stephen Biggs & Jessica Wilson; Justin Clark-Doane; Philip Goff; Bob Hale; Frank Jackson; Mark Jago; Boris Kment; Antonella Mallozzi; Graham Priest; Gabriel Rabin; Amie Thomasson; Anand Vaidya & Michael Wallner; Jennifer Wang. -/- The volume is dedicated to the memory of Bob Hale. -/- . (shrink)

Modalists think that knowledge requires forming your belief in a “modally stable” way: using a method that wouldn't easily go wrong, or using a method that wouldn't have given you this belief had it been false. Recent Modalist projects from Justin Clarke-Doane and Dan Baras defend a principle they call “Modal Security,” roughly: if evidence undermines your belief, then it must give you a reason to doubt the safety or sensitivity of your belief. Another recent Modalist project from (...) Carlotta Pavese and Bob Beddor defends “Modal Virtue Epistemology”: knowledge is a belief that is maximally modally robust across “normal” worlds. We'll offer new objections to these recent Modalist projects. We will then argue for a rival view, Explanationism: knowing something is believing it because it's true. We will show how Explanationism offers a better account of undermining defeaters than Modalism, and a better account of knowledge. (shrink)

According to principles of modal security, evidence undermines a belief only when it calls into question certain purportedly important modal connections between one’s beliefs and the truth (e.g., safety or sensitivity). Justin Clarke-Doane and Dan Baras have advanced such principles with the aim of blocking evolutionary moral debunking arguments. We examine a variety of different principles of modal security, showing that some of these are too strong, failing to accommodate clear cases of undermining, while others are too weak, (...) failing to do their advertised work of blocking evolutionary moral debunking arguments. If there is a security principle that slips between the horns of this dilemma—one that is both viable and debunker-blocking—it remains to be formulated. (shrink)

According to a certain pluralist view in philosophy of mathematics, there are as many mathematical objects as there can coherently be. Recently, Justin Clarke-Doane has explored what consequences the analogous view on normative properties would have. What if there is a normative pluriverse? Here I address this same question. The challenge is best seen as a challenge to an important form of normative realism. I criticize the way Clarke-Doane presents the challenge. An improved challenge is presented, and (...) the role of pluralism in this challenge is assessed. (shrink)

In the introduction to his Realism, mathematics and modality, and in earlier papers included in that collection, Hartry Field offered an epistemological challenge to platonism in the philosophy of mathematics. Justin Clarke-Doane Truth, objects, infinity: New perspectives on the philosophy of Paul Benacerraf, 2016) argues that Field’s challenge is an illusion: it does not pose a genuine problem for platonism. My aim is to show that Clarke-Doane’s argument relies on a misunderstanding of Field’s challenge.

This volume features essays about and by Paul Benacerraf, whose ideas have circulated in the philosophical community since the early nineteen sixties, shaping key areas in the philosophy of mathematics, the philosophy of language, the philosophy of logic, and epistemology. The book started as a worskhop held in Paris at the Collège de France in May 2012 with the participation of Paul Benacerraf. The introduction addresses the methodological point of the legitimate use of so-called “Princess Margaret Premises” in drawing philosophical (...) conclusions from Gödel’s first incompleteness theorem. The book is then divided into three sections. The first is devoted to an assessment of the improved version of the original dilemma of “Mathematical Truth” due to Hartry Field: the challenge to the platonist is now to explain the reliability of our mathematical beliefs given the very subject matter of mathematics, either pure or applied. The second addresses the issue of the ontological status of numbers: Frege’s logicism, fictionalism, structuralism, and Bourbaki’s theory of structures are called up for an appraisal of Benacerraf’s negative conclusions of “What Numbers Could Not Be.” The third is devoted to supertasks and bears witness to the unique standing of Benacerraf’s first publication: “Tasks, Super-Tasks, and Modern Eleatics” in debates on Zeno’s paradox and associated paradoxes, infinitary mathematics, and constructivism and finitism in the philosophy of mathematics. Two yet unpublished essays by Benacerraf have been included in the volume: an early version of “Mathematical Truth” from 1968 and an essay on “What Numbers Could Not Be” from the mid 1970’s. A complete chronological bibliography of Benacerraf’s work to 2016 is provided.Essays by Jody Azzouni, Paul Benacerraf, Justin Clarke-Doane, Sébastien Gandon, Brice Halimi, Jon Pérez Laraudogoitia, Mary Leng, Antonio Leòn-Sànchez and Ana Leòn-Mejía, Marco Panza, Fabrice Pataut, Philippe de Rouilhan, Andrea Sereni, and Stewart Shapiro. (shrink)

In this article, I discuss a trivialization worry for Hartry Field’s official formulation of the access problem for mathematical realists, which was pointed out by Øystein Linnebo (and has recently been made much of by Justin Clarke-Doane). I argue that various attempted reformulations of the Benacerraf problem fail to block trivialization, but that access worriers can better defend themselves by sticking closer to Hartry Field’s initial informal characterization of the access problem in terms of (something like) general epistemic (...) norms of coincidence avoidance. (shrink)