This is an excerpt from a report on the workshop on multisensory integration at the University of Toronto, on May 9th and 10th, 2014, written by Kevin Connolly, Aaron Henry, Zoe Jenkin, and Andrew MacGregor, and available at: http://networksensoryresearch.utoronto.ca/Events_%26_Discussion.html This excerpt explores the question: What can multisensory processing tell us about multisensory awareness?

Kevin McCain’s Evidentialism and Epistemic Justification is the most thorough defense of evidentialism to date. In this work, McCain proposes insightful new theses to fill in underdeveloped parts of evidentialism. One of these new theses is an explanationist account of evidential fit that appeals to dispositional properties. We argue that this explanationist account faces counterexamples, and that, more generally, explanationists should not understand evidential fit in terms of dispositional properties.

In my paper ‘Three Forms of Internalism and the New Evil Demon Problem,’ I argued that the new evil demon problem, long considered to be one of the biggest obstacles for externalism, is also a problem for virtually all internalists. In (McCain 2014a) and in his recent book (McCain 2014b), Kevin McCain provides a challenging and thought provoking reasons for thinking that many internalists do not have any such problem. In this paper, I’ll provide some replies to McCain. Of (...) note, I’ll show that a Frankfurt-style counterfactual intervener, who commonly appears in the free will literature, can also serve as a new evil demon in the epistemology literature. (shrink)

This collection of original essays--by philosophers of biology, biologists, and cognitive scientists--provides a wide range of perspectives on species. Including contributions from David Hull, John Dupre, David Nanney, Kevin de Queiroz, and Kim Sterelny, amongst others, this book has become especially well-known for the three essays it contains on the homeostatic property cluster view of natural kinds, papers by Richard Boyd, Paul Griffiths, and Robert A. Wilson.

This article constructively retrieves St. Anselm of Canterbury’s theory of retributive justice and provides a defense of what can be called the retributive model of hell. In the first part of this article, we develop the place of retributive punishment in Anselm’s thinking and discuss how and when retributive punishment is a good thing. In the second part, we apply Anselm’s thinking on retributive justice to the problem of hell and provide a defense of how hell, defined as a state (...) of receiving retributive, damnatory, and irreversible punishment, is good. We then address a series of objections. Despite some criticism that both Anselm and the retributive model of hell receive in the contemporary literature, Anselm’s account of retributive justice can make unique and constructive contributions to the contemporary discussion of hell; by retrieving and applying Anselm’s thought to the problem of hell, we intend to kill two birds with one stone. (shrink)

Environmental historian Kevin Armitage’s new book offers welcome relief to readers grown weary of anthropocentrism versus nonanthropecentrism debates and Muir-Pinchot-Leopold “third way” arguments. It will also find a receptive audience among those who have maintained all along that education is the key to addressing our environmental woes. In the United States, environmental education has a vibrant history. During the late nineteenth and early twentieth century, a critical mass of policy makers, educators, scientists, and philosophers shared the belief that a (...) curriculum based on the careful observation and study of nature should be taught in primary and secondary school classrooms. The “nature study movement,” as it was called, advanced an ambitious agenda for education reform based on a simple theory: children who develop a deep and abiding interest in the natural world mature into environmentally conscious adults and good citizens. Organized thematically, Armitage’s book lays out the meaning of nature study as well as its scientific and sentimental interpretations (introduction and chap. 1), the influence of progressive education on nature study (chap. 2), the connection between recapitulation theory and nature study (chap. 3), nature study and bird conservation (chap. 4), school gardening as an extension of nature study (chap. 5), the growth of nature photography in tandem with nature study (chap. 6), and finally nature study’s role in promoting agricultural reform (chap. 7). In case the significance of this progressive-era movement is still in doubt, the movement’s legacy can still be felt, Armitage contends, in the ideas of perhaps two of the most influential environmental thinkers of the past century: Aldo Leopold and Rachel Carson (conclusion). (shrink)

This three-part chapter explores a higher-order logic we call ‘Classicism’, which extends a minimal classical higher-order logic with further axioms which guarantee that provable coextensiveness is sufficient for identity. The first part presents several different ways of axiomatizing this theory and makes the case for its naturalness. The second part discusses two kinds of extensions of Classicism: some which take the view in the direction of coarseness of grain (whose endpoint is the maximally coarse-grained view that coextensiveness is sufficient for (...) identity), and some which take the view in the direction of fineness of grain (whose endpoint is the maximally fine-grained theory containing all distinctness claims compatible with Classicism). The third part introduces some techniques for constructing models of Classicism, and uses them to prove the consistency of many of the extensions of Classicism introduced in the second part. (shrink)

This paper argues that the theory of structured propositions is not undermined by the Russell-Myhill paradox. I develop a theory of structured propositions in which the Russell-Myhill paradox doesn't arise: the theory does not involve ramification or compromises to the underlying logic, but rather rejects common assumptions, encoded in the notation of the $\lambda$-calculus, about what properties and relations can be built. I argue that the structuralist had independent reasons to reject these underlying assumptions. The theory is given both a (...) diagrammatic representation, and a logical representation in a novel language. In the latter half of the paper I turn to some technical questions concerning the treatment of quantification, and demonstrate various equivalences between the diagrammatic and logical representations, and a fragment of the $\lambda$-calculus. (shrink)

In this paper the logic of broad necessity is explored. Definitions of what it means for one modality to be broader than another are formulated, and it is proven, in the context of higher-order logic, that there is a broadest necessity, settling one of the central questions of this investigation. It is shown, moreover, that it is possible to give a reductive analysis of this necessity in extensional language. This relates more generally to a conjecture that it is not possible (...) to define intensional connectives from extensional notions. This conjecture is formulated precisely in higher-order logic, and concrete cases in which it fails are examined. The paper ends with a discussion of the logic of broad necessity. It is shown that the logic of broad necessity is a normal modal logic between S4 and Triv, and that it is consistent with a natural axiomatic system of higher-order logic that it is exactly S4. Some philosophical reasons to think that the logic of broad necessity does not include the S5 principle are given. (shrink)

Philosophers commonly say that beliefs come in degrees. Drawing from the literature, I make precise three arguments for this claim: an argument from degrees of confidence, an argument from degrees of firmness, and an argument from natural language. I show that they all fail. I also advance three arguments that beliefs do not come in degrees: an argument from natural language, an argument from intuition, and an argument from the metaphysics of degrees. On the basis of these arguments, I conclude (...) that beliefs do not come in degrees. (shrink)

In this paper, I present and defend a novel account of doubt. In Part 1, I make some preliminary observations about the nature of doubt. In Part 2, I introduce a new puzzle about the relationship between three psychological states: doubt, belief, and confidence. I present this puzzle because my account of doubt emerges as a possible solution to it. Lastly, in Part 3, I elaborate on and defend my account of doubt. Roughly, one has doubt if and only if (...) one believes one might be wrong; I argue that this is superior to the account that says that one has doubt if and only if one has less than the highest degree of confidence. (shrink)

In explaining the notion of a fundamental property or relation, metaphysicians will often draw an analogy with languages. The fundamental properties and relations stand to reality as the primitive predicates and relations stand to a language: the smallest set of vocabulary God would need in order to write the “book of the world.” This paper attempts to make good on this metaphor. To that end, a modality is introduced that, put informally, stands to propositions as logical truth stands to sentences. (...) The resulting theory, formulated in higher-order logic, also vindicates the Humean idea that fundamental properties and relations are freely recombinable and a variant of the structural idea that propositions can be decomposed into their fundamental constituents via logical operations. Indeed, it is seen that, although these ideas are seemingly distinct, they are not independent, and fall out of a natural and general theory about the granularity of reality. (shrink)

Prior to Kripke’s seminal work on the semantics of modal logic, McKinsey offered an alternative interpretation of the necessity operator, inspired by the Bolzano–Tarski notion of logical truth. According to this interpretation, ‘it is necessary that A’ is true just in case every sentence with the same logical form as A is true. In our paper, we investigate this interpretation of the modal operator, resolving some technical questions, and relating it to the logical interpretation of modality and some views in (...) modal metaphysics. In particular, we present an hitherto unpublished solution to problems 41 and 42 from Friedman’s 102 problems, which uses a different method of proof from the solution presented in the paper of Tadeusz Prucnal. (shrink)

In this paper I present a precise version of Stalnaker's thesis and show that it is both consistent and predicts our intuitive judgments about the probabilities of conditionals. The thesis states that someone whose total evidence is E should have the same credence in the proposition expressed by 'if A then B' in a context where E is salient as they have conditional credence in the proposition B expresses given the proposition A expresses in that context. The thesis is formalised (...) rigorously and two models are provided that demonstrate that the new thesis is indeed tenable within a standard possible world semantics based on selection functions. Unlike the Stalnaker-Lewis semantics the selection functions cannot be understood in terms of similarity. A probabilistic account of selection is defended in its place. -/- I end the paper by suggesting that this approach overcomes some of the objections often leveled at accounts of indicatives based on the notion of similarity. (shrink)

The principle of universal instantiation plays a pivotal role both in the derivation of intensional paradoxes such as Prior’s paradox and Kaplan’s paradox and the debate between necessitism and contingentism. We outline a distinctively free logical approach to the intensional paradoxes and note how the free logical outlook allows one to distinguish two different, though allied themes in higher-order necessitism. We examine the costs of this solution and compare it with the more familiar ramificationist approaches to higher-order logic. Our assessment (...) of both approaches is largely pessimistic, and we remain reluctantly inclined to take Prior’s and Kaplan’s derivations at face value. (shrink)

We explore the view that Frege's puzzle is a source of straightforward counterexamples to Leibniz's law. Taking this seriously requires us to revise the classical logic of quantifiers and identity; we work out the options, in the context of higher-order logic. The logics we arrive at provide the resources for a straightforward semantics of attitude reports that is consistent with the Millian thesis that the meaning of a name is just the thing it stands for. We provide models to show (...) that some of these logics are non-degenerate. (shrink)

An increasing amount of twenty-first century metaphysics is couched in explicitly hyperintensional terms. A prerequisite of hyperintensional metaphysics is that reality itself be hyperintensional: at the metaphysical level, propositions, properties, operators, and other elements of the type hierarchy, must be more fine-grained than functions from possible worlds to extensions. In this paper I develop, in the setting of type theory, a general framework for reasoning about the granularity of propositions and properties. The theory takes as primitive the notion of a (...) substitution on a proposition (property, etc.) and, among other things, uses this idea to elucidate a number of theoretically important distinctions. A class of structures are identified which can be used to model a wide range of positions about the granularity of reality; certain of these structures are seen to receive a natural treatment in the category of M-sets. (shrink)

Most work on the semantic paradoxes within classical logic has centered around what this essay calls “linguistic” accounts of the paradoxes: they attribute to sentences or utterances of sentences some property that is supposed to explain their paradoxical or nonparadoxical status. “No proposition” views are paradigm examples of linguistic theories, although practically all accounts of the paradoxes subscribe to some kind of linguistic theory. This essay shows that linguistic accounts of the paradoxes endorsing classical logic are subject to a particularly (...) acute form of the revenge paradox: that there is no exhaustive classification of sentences into “good” and “bad” such that the T-schema holds when restricted to the “good” sentences unless it is also possible to prove some “bad” sentences. The foundations for an alternative classical nonlinguistic approach is outlined that is not subject to the same kinds of problems. Although revenge paradoxes of different strengths can be formulated, they are found to be indeterminate at higher orders and not inconsistent. (shrink)

Traditional geometry concerns itself with planimetric and stereometric considerations, which are at the root of the division between plane and solid geometry. To raise the issue of the relation between these two areas brings with it a host of different problems that pertain to mathematical practice, epistemology, semantics, ontology, methodology, and logic. In addition, issues of psychology and pedagogy are also important here. To our knowledge there is no single contribution that studies in detail even one of the aforementioned areas.

Many say that ontological disputes are defective because they are unimportant or without substance. In this paper, we defend ontological disputes from the charge, with a special focus on disputes over the existence of composite objects. Disputes over the existence of composite objects, we argue, have a number of substantive implications across a variety of topics in metaphysics, science, philosophical theology, philosophy of mind, and ethics. Since the disputes over the existence of composite objects have these substantive implications, they are (...) themselves substantive. (shrink)

One thousand fair causally isolated coins will be independently flipped tomorrow morning and you know this fact. I argue that the probability, conditional on your knowledge, that any coin will land tails is almost 1 if that coin in fact lands tails, and almost 0 if it in fact lands heads. I also show that the coin flips are not probabilistically independent given your knowledge. These results are uncomfortable for those, like Timothy Williamson, who take these probabilities to play a (...) central role in their theorizing. (shrink)

A number of authors have objected to the application of non-classical logic to problems in philosophy on the basis that these non-classical logics are usually characterised by a classical metatheory. In many cases the problem amounts to more than just a discrepancy; the very phenomena responsible for non-classicality occur in the field of semantics as much as they do elsewhere. The phenomena of higher order vagueness and the revenge liar are just two such examples. The aim of this paper is (...) to show that a large class of non-classical logics are strong enough to formulate their own model theory in a corresponding non-classical set theory. Specifically I show that adequate definitions of validity can be given for the propositional calculus in such a way that the metatheory proves, in the specified logic, that every theorem of the propositional fragment of that logic is validated. It is shown that in some cases it may fail to be a classical matter whether a given sentence is valid or not. One surprising conclusion for non-classical accounts of vagueness is drawn: there can be no axiomatic, and therefore precise, system which is determinately sound and complete. (shrink)

Aristotle is essentially human; that is, for all possible worlds metaphysically consistent with our own, if Aristotle exists, then he is human. This is a claim about the essential property of an object. The claim that objects have essential properties has been hotly disputed, but for present purposes, we can bracket that issue. In this essay, we are interested, rather, in the question of whether properties themselves have essential properties (or features) for their existence. We call those who suppose they (...) do “property essentialists”; those who do not, “property anti-essentialists,” or “quidditists.” We offer two complementary arguments. Our total argument is under-girded by two assumptions: transworld identity theory and “received view” counterfactual semantics, a la David Lewis. We then argue that, if one presumes that these are true, then one risks running headlong into paradox if one also accepts property anti-essentialism. That's the first argument. By contrast, if one accepts these same assumptions in conjunction with property essentialism, then the paradox is avoided. This is the second argument. We take it that our arguments work to show that, between property essentialism and quidditism, the property essentialist is on better footing. Plausibly, properties themselves do have essential properties for their existence. (shrink)

We develop a theory of necessity operators within a version of higher-order logic that is neutral about how fine-grained reality is. The theory is axiomatized in terms of the primitive of *being a necessity*, and we show how the central notions in the philosophy of modality can be recovered from it. Various questions are formulated and settled within the framework, including questions about the ordering of necessities under strength, the existence of broadest necessities satisfying various logical conditions, and questions about (...) their logical behaviour. We also wield the framework to probe the conditions under which a logicist account of necessities is possible, in which the theory is completely reducible to logic. (shrink)

Deep disagreements are characteristically resistant to rational resolution. This paper explores the contribution a virtue theoretic approach to argumentation can make towards settling the practical matter of what to do when confronted with apparent deep disagreement, with particular attention to the virtue of courage.

Aesthetic reasons are reasons to do and think various things. For example, it makes sense to wonder if a tree stump on the lawn was left there for environmental rather than aesthetic reasons, or for no reason at all. Aesthetic considerations of this kind are often contrasted with non-aesthetic reasons—such as moral or epistemic reasons. For example, they seem connected to pleasure-in-experience in a distinctive way that differs from paradigmatic moral reasons. Relatedly, the authority of aesthetic reasons has often been (...) thought to involve less of an “external demand” upon us than in the other cases. In this chapter, I suggest that such distinctiveness and modesty coheres well with an anti-realist treatment that views them as non-objective in nature. I then go on to consider an alternative, more robustly realist conception of aesthetic reasons. (shrink)

The traditional view of evidence in mathematics is that evidence is just proof and proof is just derivation. There are good reasons for thinking that this view should be rejected: it misrepresents both historical and current mathematical practice. Nonetheless, evidence, proof, and derivation are closely intertwined. This paper seeks to tease these concepts apart. It emphasizes the role of argumentation as a context shared by evidence, proofs, and derivations. The utility of argumentation theory, in general, and argumentation schemes, in particular, (...) as a methodology for the study of mathematical practice is thereby demonstrated. Argumentation schemes represent an almost untapped resource for mathematics education. Notably, they provide a consistent treatment of rigorous and non-rigorous argumentation, thereby working to exhibit the continuity of reasoning in mathematics with reasoning in other areas. Moreover, since argumentation schemes are a comparatively mature methodology, there is a substantial body of existing work to draw upon, including some increasingly sophisticated software tools. Such tools have significant potential for the analysis and evaluation of mathematical argumentation. The first four sections of the paper address the relationships of evidence to proof, proof to derivation, argument to proof, and argument to evidence, respectively. The final section directly addresses some of the educational implications of an argumentation scheme account of mathematical reasoning. (shrink)

Terence Horgan, George Graham and John Tienson argue that some intentional content is constitutively determined by phenomenology alone. We argue that this would require a certain kind of covariation of phenomenal states and intentional states that is not established by Horgan, Tienson and Graham’s arguments. We make the case that there is inadequate reason to think phenomenology determines perceptual belief, and that there is reason to doubt that phenomenology determines any species of non-perceptual intentionality. We also raise worries about the (...) capacity of phenomenology to map onto intentionality in a way that would be appropriate for any determiner of content/fixer of truth conditions. (shrink)

In recent years there has been a revitalised interest in non-classical solutions to the semantic paradoxes. In this paper I show that a number of logics are susceptible to a strengthened version of Curry's paradox. This can be adapted to provide a proof theoretic analysis of the omega-inconsistency in Lukasiewicz's continuum valued logic, allowing us to better evaluate which logics are suitable for a naïve truth theory. On this basis I identify two natural subsystems of Lukasiewicz logic which individually, but (...) not jointly, lack the problematic feature. (shrink)

Those inclined to positions in the philosophy of time that take tense seriously have typically assumed that not all regions of space-time are equal: one special region of space-time corresponds to what is presently happening. When combined with assumptions from modern physics this has the unsettling consequence that the shape of this favored region distinguishes people in certain places or people traveling at certain velocities. In this paper I shall attempt to avoid this result by developing a tensed picture of (...) reality that is nonetheless consistent with ‘hypersurface egalitarianism’—the view that all hypersurfaces are equal. (shrink)

Virtue theories have lately enjoyed a modest vogue in the study of argumentation, echoing the success of more far-reaching programmes in ethics and epistemology. Virtue theories of argumentation (VTA) comprise several conceptually distinct projects, including the provision of normative foundations for argument evaluation and a renewed focus on the character of good arguers. Perhaps the boldest of these is the pursuit of the fully satisfying argument, the argument that contributes to human flourishing. This project has an independently developed epistemic analogue: (...) eudaimonistic virtue epistemology. Both projects stress the importance of widening the range of cognitive goals beyond, respectively, cogency and knowledge; both projects emphasize social factors, the right sort of community being indispensable for the cultivation of the intellectual virtues necessary to each project. This paper proposes a unification of the two projects by arguing that the intellectual good life sought by eudaimonistic virtue epistemologists is best realized through the articulation of an account of argumentation that contributes to human flourishing. (shrink)

Can new technology enhance purpose-driven, democratic dialogue in groups, governments, and societies? Online Deliberation: Design, Research, and Practice is the first book that attempts to sample the full range of work on online deliberation, forging new connections between academic research, technology designers, and practitioners. Since some of the most exciting innovations have occurred outside of traditional institutions, and those involved have often worked in relative isolation from each other, work in this growing field has often failed to reflect the full (...) set of perspectives on online deliberation. This volume is aimed at those working at the crossroads of information/communication technology and social science, and documents early findings in, and perspectives on, this new field by many of its pioneers. -/- CONTENTS: -/- Introduction: The Blossoming Field of Online Deliberation (Todd Davies, pp. 1-19) -/- Part I - Prospects for Online Civic Engagement -/- Chapter 1: Virtual Public Consultation: Prospects for Internet Deliberative Democracy (James S. Fishkin, pp. 23-35) -/- Chapter 2: Citizens Deliberating Online: Theory and Some Evidence (Vincent Price, pp. 37-58) -/- Chapter 3: Can Online Deliberation Improve Politics? Scientific Foundations for Success (Arthur Lupia, pp. 59-69) -/- Chapter 4: Deliberative Democracy, Online Discussion, and Project PICOLA (Public Informed Citizen Online Assembly) (Robert Cavalier with Miso Kim and Zachary Sam Zaiss, pp. 71-79) -/- Part II - Online Dialogue in the Wild -/- Chapter 5: Friends, Foes, and Fringe: Norms and Structure in Political Discussion Networks (John Kelly, Danyel Fisher, and Marc Smith, pp. 83-93) -/- Chapter 6: Searching the Net for Differences of Opinion (Warren Sack, John Kelly, and Michael Dale, pp. 95-104) -/- Chapter 7: Happy Accidents: Deliberation and Online Exposure to Opposing Views (Azi Lev-On and Bernard Manin, pp. 105-122) -/- Chapter 8: Rethinking Local Conversations on the Web (Sameer Ahuja, Manuel Pérez-Quiñones, and Andrea Kavanaugh, pp. 123-129) -/- Part III - Online Public Consultation -/- Chapter 9: Deliberation in E-Rulemaking? The Problem of Mass Participation (David Schlosberg, Steve Zavestoski, and Stuart Shulman, pp. 133-148) -/- Chapter 10: Turning GOLD into EPG: Lessons from Low-Tech Democratic Experimentalism for Electronic Rulemaking and Other Ventures in Cyberdemocracy (Peter M. Shane, pp. 149-162) -/- Chapter 11: Baudrillard and the Virtual Cow: Simulation Games and Citizen Participation (Hélène Michel and Dominique Kreziak, pp. 163-166) -/- Chapter 12: Using Web-Based Group Support Systems to Enhance Procedural Fairness in Administrative Decision Making in South Africa (Hossana Twinomurinzi and Jackie Phahlamohlaka, pp. 167-169) -/- Chapter 13: Citizen Participation Is Critical: An Example from Sweden (Tomas Ohlin, pp. 171-173) -/- Part IV - Online Deliberation in Organizations -/- Chapter 14: Online Deliberation in the Government of Canada: Organizing the Back Office (Elisabeth Richard, pp. 177-191) -/- Chapter 15: Political Action and Organization Building: An Internet-Based Engagement Model (Mark Cooper, pp. 193-202) -/- Chapter 16: Wiki Collaboration Within Political Parties: Benefits and Challenges (Kate Raynes-Goldie and David Fono, pp. 203-205) -/- Chapter 17: Debian’s Democracy (Gunnar Ristroph, pp. 207-211) -/- Chapter 18: Software Support for Face-to-Face Parliamentary Procedure (Dana Dahlstrom and Bayle Shanks, pp. 213-220) -/- Part V - Online Facilitation -/- Chapter 19: Deliberation on the Net: Lessons from a Field Experiment (June Woong Rhee and Eun-mee Kim, pp. 223-232) -/- Chapter 20: The Role of the Moderator: Problems and Possibilities for Government-Run Online Discussion Forums (Scott Wright, pp. 233-242) -/- Chapter 21: Silencing the Clatter: Removing Anonymity from a Corporate Online Community (Gilly Leshed, pp. 243-251) -/- Chapter 22: Facilitation and Inclusive Deliberation (Matthias Trénel, pp. 253-257) -/- Chapter 23: Rethinking the ‘Informed’ Participant: Precautions and Recommendations for the Design of Online Deliberation (Kevin S. Ramsey and Matthew W. Wilson, pp. 259-267) -/- Chapter 24: PerlNomic: Rule Making and Enforcement in Digital Shared Spaces (Mark E. Phair and Adam Bliss, pp. 269-271) -/- Part VI - Design of Deliberation Tools -/- Chapter 25: An Online Environment for Democratic Deliberation: Motivations, Principles, and Design (Todd Davies, Brendan O’Connor, Alex Cochran, Jonathan J. Effrat, Andrew Parker, Benjamin Newman, and Aaron Tam, pp. 275-292) -/- Chapter 26: Online Civic Deliberation with E-Liberate (Douglas Schuler, pp. 293-302) -/- Chapter 27: Parliament: A Module for Parliamentary Procedure Software (Bayle Shanks and Dana Dahlstrom, pp. 303-307) -/- Chapter 28: Decision Structure: A New Approach to Three Problems in Deliberation (Raymond J. Pingree, pp. 309-316) -/- Chapter 29: Design Requirements of Argument Mapping Software for Teaching Deliberation (Matthew W. Easterday, Jordan S. Kanarek, and Maralee Harrell, pp. 317-323) -/- Chapter 30: Email-Embedded Voting with eVote/Clerk (Marilyn Davis, pp. 325-327) -/- Epilogue: Understanding Diversity in the Field of Online Deliberation (Seeta Peña Gangadharan, pp. 329-358). -/- For individual chapter downloads, go to odbook.stanford.edu. (shrink)

A number of `no-proposition' approaches to the liar paradox find themselves implicitly committed to a moderate disquotational principle: the principle that if an utterance of the sentence `$P$' says anything at all, it says that $P$ (with suitable restrictions). I show that this principle alone is responsible for the revenge paradoxes that plague this view. I instead propose a view in which there are several closely related language-world relations playing the `semantic expressing' role, none of which is more central to (...) semantic theorizing than any other. I use this thesis about language and the negative result about disquotation to motivate the view that people do say things with utterances of paradoxical sentences, although they do not say the proposition you'd always expect, as articulated with a disquotational principle. (shrink)

I intend to bring recent work applying virtue theory to the study of argument to bear on a much older problem, that of disagreements that resist rational resolution, sometimes termed "deep disagreements". Just as some virtue epistemologists have lately shifted focus onto epistemic vices, I shall argue that a renewed focus on the vices of argument can help to illuminate deep disagreements. In particular, I address the role of arrogance, both as a factor in the diagnosis of deep disagreements and (...) as an obstacle to their mutually acceptable resolution. Arrogant arguers are likely to make any disagreements to which they are party seem deeper than they really are and arrogance impedes the strategies that we might adopt to resolve deep disagreements. As a case in point, since arrogant or otherwise vicious arguers cannot be trusted not to exploit such strategies for untoward ends, any policy for deep disagreement amelioration must require particularly close attention to the vices of argument, lest they be exploited by the unscrupulous. (shrink)

In this article, we identify three key design dimensions along which cryptocurrencies differ -- privacy, censorship-resistance, and consensus procedure. Each raises important normative issues. Our discussion uncovers new ways to approach the question of whether Bitcoin or other cryptocurrencies should be used as money, and new avenues for developing a positive answer to that question. A guiding theme is that progress here requires a mixed approach that integrates philosophical tools with the purely technical results of disciplines like computer science and (...) economics. Note: this article is the second entry within a two-part sequence on the Philosophy, Politics, and Economics of Cryptocurrency. (shrink)

Roughly, a proof of a theorem, is “pure” if it draws only on what is “close” or “intrinsic” to that theorem. Mathematicians employ a variety of terms to identify pure proofs, saying that a pure proof is one that avoids what is “extrinsic,” “extraneous,” “distant,” “remote,” “alien,” or “foreign” to the problem or theorem under investigation. In the background of these attributions is the view that there is a distance measure (or a variety of such measures) between mathematical statements and (...) proofs. Mathematicians have paid little attention to specifying such distance measures precisely because in practice certain methods of proof have seemed self- evidently impure by design: think for instance of analytic geometry and analytic number theory. By contrast, mathematicians have paid considerable attention to whether such impurities are a good thing or to be avoided, and some have claimed that they are valuable because generally impure proofs are simpler than pure proofs. This article is an investigation of this claim, formulated more precisely by proof- theoretic means. After assembling evidence from proof theory that may be thought to support this claim, we will argue that on the contrary this evidence does not support the claim. (shrink)

An increasing amount of contemporary philosophy of mathematics posits, and theorizes in terms of special kinds of mathematical modality. The goal of this paper is to bring recent work on higher-order metaphysics to bear on the investigation of these modalities. The main focus of the paper will be views that posit mathematical contingency or indeterminacy about statements that concern the `width' of the set theoretic universe, such as Cantor's continuum hypothesis. Within a higher-order framework I show that contingency about the (...) width of the set-theoretic universe refutes two orthodoxies concerning the structure of modal reality: the view that the broadest necessity has a logic of S5, and the "Leibniz biconditionals" stating that what is possible, in the broadest sense of possible, is what is true in some possible world. Nonetheless, I suggest that the underlying picture of modal set-theory is coherent and has attractions. (shrink)

Douglas Walton’s multitudinous contributions to the study of argumentation seldom, if ever, directly engage with argumentation in mathematics. Nonetheless, several of the innovations with which he is most closely associated lend themselves to improving our understanding of mathematical arguments. I concentrate on two such innovations: dialogue types (§1) and argumentation schemes (§2). I argue that both devices are much more applicable to mathematical reasoning than may be commonly supposed.

The subject of this essay is the classical problem of induction, which is sometimes attributed to David Hume and called “the Humean Problem of Induction.” Here, I examine a certain sort of Neo-Aristotelian solution to the problem, which appeals to the concept of natural kinds in its response to the inductive skeptic. This position is most notably represented by Howard Sankey and Marc Lange. The purpose of this paper is partly destructive and partly constructive. I raise two questions. The first (...) is: Are the natural kind solutions to the problem successful? The first thesis of this paper is that they are not, and I will show how and why they fail. And the second question I raise here is: Is there nonetheless some alternative Neo-Aristotelian solution to the problem which is successful and can overcome the shortcomings endemic to the Sankey-Lange account? The second thesis is that there is, and I’ll attempt to sketch one. My stance here may be summarized by saying that, while I agree with Sankey and Lange that the problem of induction can be adequately resolved, and while I am on the whole sympathetic with the Aristotelian spirit of their account, I am, for all that, dissatisfied with the letter of them. Nothing short of a more thoroughgoing Aristotelianism about the epistemology of induction will do. (shrink)

It has been argued recently that classical theism and Lewisian modal realism are incompatible theses. The most substantial argument to this effect takes the form of a trilemma. It argues that no sense can be made of God’s being a necessary being in the modal realistic picture, on pain of, among other things, modal collapse. The question of this essay is: Is that so? My goal here is to detail the reasons that have been offered in support of this contention (...) and then defend the coherence of theistic modal realism from the trilemma. I call my reply to the argument an “Anselmian-Thomistic” defense, since it appeals to resources from classical medieval philosophy, especially from Anselm and Aquinas. (shrink)

Many mathematicians have cited depth as an important value in their research. However, there is no single widely accepted account of mathematical depth. This article is an attempt to bridge this gap. The strategy is to begin with a discussion of Szemerédi's theorem, which says that each subset of the natural numbers that is sufficiently dense contains an arithmetical progression of arbitrary length. This theorem has been judged deep by many mathematicians, and so makes for a good case on which (...) to focus in analyzing mathematical depth. After introducing the theorem, four accounts of mathematical depth will be considered. (shrink)

I want to say something about the sort of arguments that it is possible to lose, and whether losing arguments can be done well. I shall focus on losing philosophical arguments, and I will be talking about arguments in the sense of acts of arguing. This is the sort of act that one can perform on one’s own or with one other person in private. But in either of these cases it is difficult to win—or to lose. So I shall (...) concentrate on arguments with audiences. We may think of winning or losing such arguments in terms of whether the audience is convinced. Of course, this doesn’t necessarily have anything to do with who is in the right. That means that there are two sorts of loser: real losers, who lose the argument deservedly, because they are in the wrong, and mere losers, who lose the argument undeservedly, because they are in the right. Hence there must also be two sorts of winner: real winners, who win the argument deservedly, because they are in the right, and mere winners, who win the argument undeservedly, because they are in the wrong. An optimal outcome for arguments with losers would be if all the losers are real losers. (shrink)

Essentialists suppose that for every individual, if that individual exists at any possible world, then necessarily that individual exemplifies some non-trivial qualitative property essential to it, as such. Anti-essentialists deny this. One important argument leveled by some anti-essentialists against essentialism takes the form of a thought experiment, one originally introduced by Roderick Chisholm, sometimes referred to as Chisholm's Paradox (CP). In this essay, I defend essentialism against CP. I begin by presenting the argument and showing how it leads to a (...) contradiction of the essentialist thesis. I then consider one of the most popular solutions to CP to date, that given by Nathan Salmon. Next, I critique Salmon's proposal and show that it is an insufficient response on behalf of the essentialist. And finally, I propose a novel solution to the paradox and discuss why it is that many metaphysician in the past have found CP plausible, despite being fallacious. (shrink)

This article will consider imagination in mathematics from a historical point of view, noting the key moments in its conception during the ancient, modern and contemporary eras.

The fact that physical laws often admit certain kinds of space-time symmetries is often thought to be problematic for substantivalism --- the view that space-time is as real as the objects it contains. The most prominent alternative, relationism, avoids these problems but at the cost of giving abstract objects (rather than space-time points) a pivotal role in the fundamental metaphysics. This incurs related problems concerning the relation of the physical to the mathematical. In this paper I will present a version (...) of substantivalism that respects Leibnizian theses about space-time symmetries, and argue that it is superior to both relationism and the more orthodox form of substantivalism. (shrink)

The moral principle that Ought Implies Can (“OIC”) is often assumed without argument in normative discourse. Is this assumption defensible? Some would argue that it is not, as there are many purported counterexamples against it in the literature. However, OIC is not so much a single principle as rather a family of them. In this paper, I will argue that, while not every OIC-type principle is defensible, at least one of them may be. I defend the cognate moral principle that (...) Ought Implies Can or Could Have (“OICCH”). I first show that it is able to circumvent the traditional counterexamples to OIC. And then I show that OICCH is even more plausible than some of the best alternative OIC-type principles to date. The upshot of this paper is that those who find OIC compelling should consider accepting OICCH instead. (shrink)

Bullshit is not the only sort of deceptive talk. Spurious definitions are another important variety of bad reasoning. This paper will describe some of these problematic tactics, and show how Harry Frankfurt’s treatment of bullshit may be extended to analyze their underlying causes. Finally, I will deploy this new account of definition to assess whether Frankfurt’s definition of bullshit is itself legitimate.

Over the years many mathematicians have voiced a preference for proofs that stay “close” to the statements being proved, avoiding “foreign”, “extraneous”, or “remote” considerations. Such proofs have come to be known as “pure”. Purity issues have arisen repeatedly in the practice of arithmetic; a famous instance is the question of complex-analytic considerations in the proof of the prime number theorem. This article surveys several such issues, and discusses ways in which logical considerations shed light on these issues.

In this article we examine Kant’s understanding of toleration by including a study of all instances in which he directly uses the language of toleration and related concepts. We use this study to resolve several key areas of interpretative dispute concerning Kant’s views on toleration. We argue that Kant offers a nuanced and largely unappreciated approach to thinking about toleration, and related concepts, across three normative spheres: the political, the interpersonal and the personal. We examine shortcomings in earlier interpretations and (...) conclude by arguing that the theme of toleration in Kant’s work, while coherent and important, is neither as central nor as peripheral as suggested by previous interpretations. Further, while Kant is critical of the arrogance of toleration in the political sphere, he is more positive toward the role of toleration in the interpersonal and personal spheres since it promotes virtue. (shrink)

Recommender Systems (RS) on digital platforms increasingly influence user behavior, raising ethical concerns, privacy risks, harmful content promotion, and diminished user autonomy. This article examines RS within the framework of regulations and lawsuits in the United States and advocates for legislation that can withstand constitutional scrutiny under First Amendment protections. We propose (re)framing RS-curated content as commercial speech, which is subject to lessened free speech protections. This approach provides a practical path for future legislation that would allow for effective oversight (...) of RS, particularly in areas of substantial public interest like child safety, national security, and misinformation. (shrink)