Research suggests that the mind contains a set of adaptations for detecting alliances: an alliance detection system, which monitors for, encodes, and stores alliance information and then modifies the activation of stored alliance categories according to how likely they will predict behavior within a particular social interaction. Previous studies have established the activation of this system when exposed to explicit competition or cooperation between individuals. In the current studies we examine if shared political opinions produce these same effects. In particular, (...) if participants will spontaneously categorize individuals according to the parties they support, even when explicit cooperation and antagonism are absent, and if party support is sufficiently powerful to decrease participants’ categorization by an orthogonal but typically-diagnostic alliance cue . Evidence was found for both: Participants spontaneously and implicitly kept track of who supported which party, and when party cross-cut race—such that the race of targets was not predictive of party support—categorization by race was dramatically reduced. To verify that these results reflected the operation of a cognitive system for modifying the activation of alliance categories, and not just socially-relevant categories in general, an identical set of studies was also conducted with in which party was either crossed with sex or age . As predicted, categorization by party occurred to the same degree, and there was no reduction in either categorization by sex or by age. All effects were replicated across two sets of between-subjects conditions. These studies provide the first direct empirical evidence that party politics engages the mind’s systems for detecting alliances and establish two important social categorization phenomena: that categorization by age is, like sex, not affected by alliance information and that political contexts can reduce the degree to which individuals are represented in terms of their race. (shrink)
What is morality? How many moral values are there? And what are they? According to the theory of morality-as-cooperation, morality is a collection of biological and cultural solutions to the problems of cooperation recurrent in human social life. This theory predicts that there will be as many different types of morality as there are different types of cooperation. Previous research, drawing on evolutionary game theory, has identified at least seven different types of cooperation, and used them to explain seven different (...) types of morality: family values, group loyalty, reciprocity, heroism, deference, fairness and property rights. Here we explore the conjecture that these simple moral ‘elements’ combine to form a much larger number of more complex moral ‘molecules’, and that as such morality is a combinatorial system. For each combination of two elements, we hypothesise a candidate moral molecule, and successfully locate an example of it in the professional and popular literature. These molecules include: fraternity, blood revenge, family pride, filial piety, gavelkind, primogeniture, friendship, patriotism, tribute, diplomacy, common ownership, honour, confession, turn taking, restitution, modesty, mercy, munificence, arbitration, mendicancy, and queuing. These findings indicate that morality – like many other physical, biological, psychological and cultural systems – is indeed a combinatorial system. Thus morality-as-cooperation provides a principled and powerful theory, that explains why there are many moral values, and successfully predicts what they will be; and it generates a systematic framework that has the potential to explain all moral ideas, possible and actual. Pursuing the many implications of this theory will help to place the study of morality on a more secure scientific footing. (shrink)
For more than 10 years, Ulrich Beck has dominated discussion of risk issues in the social sciences. We argue that Beck's criticisms of the theory and practise of risk analysis are groundless. His understanding of what risk is is badly flawed. His attempt to identify risk and risk perception fails. He misunderstands and distorts the use of probability in risk analysis. His comments about the insurance industry show that he does not understand some of the basics of that industry. And (...) his assertions about the wrongness of allowing acceptable levels of exposure to toxic chemicals do not stand up to scrutiny. Key Words: Beck risk analysis risk perception probability insurance. (shrink)
Why and under what conditions are individuals altruistic to family and friends in their social networks? Evolutionary psychology suggests that such behaviour is primarily the product of adaptations for kin- and reciprocal altruism, dependent on the degree of genetic relatedness and exchange of benefits, respectively. For this reason, individuals are expected to be more altruistic to family members than to friends: whereas family members can be the recipients of kin and reciprocal altruism, friends can be the recipients of reciprocal altruism (...) only. However, there is a question about how the effect of kinship is implemented at the proximate psychological level. One possibility is that kinship contributes to some general measure of relationship quality (such as ‘emotional closeness’), which in turn explains altruism. Another possibility is that the effect of kinship is independent of relationship quality. The present study tests between these two possibilities. Participants (N= 111) completed a self-report questionnaire about their willingness to be altruistic, and their emotional closeness, to 12 family members and friends at different positions in their extended social networks. As expected, altruism was greater for family than friends, and greater for more central layers of the network. Crucially, the results showed that kinship made a significant unique contribution to altruism, even when controlling for the effects of emotional closeness. Thus, participants were more altruistic towards kin than would be expected if altruism was dependent on emotional closeness alone – a phenomenon we label a ‘kinship premium’. These results have implications for the ongoing debate about the extent to which kin relations and friendships are distinct kinds of social relationships, and how to measure the ‘strength of ties’ in social networks. (shrink)
Cooperation requires that individuals are able to identify, and preferentially associate with, others who have compatible preferences and the shared background knowledge needed to solve interpersonal coordination problems. The present study investigates the nature of such similarity within social networks, asking: What do friends have in common? And what is the relationship between similarity and altruism? The results show that similarity declines with frequency of contact; similarity in general is a significant predictor of altruism and emotional closeness; and, specifically, sharing (...) a sense of humor, hobbies and interests, moral beliefs, and being from the same area are the best predictors. These results shed light on the structure of relationships within networks and provide a possible checklist for predicting attitudes toward strangers, and in-group identification. (shrink)
Reciprocal altruism involves foregoing an immediate benefit for the sake of a greater long-term reward. It follows that individuals who exhibit a stronger preference for future over immediate rewards should be more disposed to engage in reciprocal altruism – in other words, ‘patient’ people should be more cooperative. The present study tested this prediction by investigating whether participants’ contributions in a public-good game correlated with their ‘discount rate’. The hypothesis was supported: patient people are indeed more cooperative. The paper discusses (...) alternative interpretations of this result, and makes some suggestions for future research. (shrink)
The critical examination of current hypotheses is one of the key ways in which scientific fields develop and grow. Therefore, any critique, including Haidle and Schlaudt’s article, “Where Does Cumulative Culture Begin? A Plea for a Sociologically Informed Perspective,” represents a welcome addition to the literature. However, critiques must also be evaluated. In their article, Haidle and Schlaudt review some approaches to culture and cumulative culture in both human and nonhuman primates. H&S discuss the “zone of latent solutions” hypothesis as (...) applied to nonhuman primates and stone-toolmaking premodern hominins. Here, we will evaluate whether H&S’s critique addresses its target. (shrink)
This collection of essays explore the long-standing,intricate relationship between law and faith. Faith in this context is to be read in the broadest sense, as extending beyond religion to embrace the knowledge, beliefs, understandings and practices which are at work alongside the familiar and seemingly more reliable, trusted and relatively certain content and conventionally accepted methods of law and legal reasoning. The essays deal with three broad themes. The first concerns the extent to which faith should be involved in legal (...) decision making. Ought decisions to aspire simply to right reason or ought faith-based models of decision-making to be incorporated into the legal system? If the latter, how is this best done? Ought faith to operate simply as a reason itself or ought it to help to structure the method by which legal decisions are reached? The second, and perhaps most familiar theme, stemming in part from rights discourse, is the extent to which law does, and ought to, respect the rights of those whose religious beliefs conflict with the dominant social norms and practices. Liberal democratic constitutions typically provide protection for religion and religious beliefs. Are these justified, and if so how? Can such protection as exists suffice from the perspective of the faithful, or does law's otherwise pervasive agnosticism make this impossible or illusory? Thirdly, questions of identity and difference arise. Assuming that most societies remain a mix of many faiths and no faith, how should law and legal theory understand the varying and, it must be said, conflicting claims for recognition. Should we encourage conformity in the hope of reducing friction, or should we preserve and promote difference, seeking to understand others, whether groups or individuals, without removing that which makes them distinct? More radically and controversially, should we be more sceptical of individual and group claims to authenticity and see them rather as strategies in an ongoing power game? Faith after all, like reason and law, has never been far from politics and intrigue, especially in its institutional representation. Contributors: Zenon Bankowski, Anthony Bradney, Claire Davis, John Gardner, Adam Gearey, Tim Macklem, Maleiha Malik, Victor Tadros. (shrink)
In this chapter, we investigate the idea of trade marks as property. Three questions need to be answered. The first is a conceptual matter: are trade marks capable of being property or are they ruled out as a matter of conceptual necessity? The second is conceptual-cum-descriptive: is the current law's treatment of trade marks treatment of them as property? The third is normative: if the current law does in fact treat them as property, is it right to do so? The (...) questions need to be tackled in turn. (shrink)
Creativity pervades human life. It is the mark of individuality, the vehicle of self-expression, and the engine of progress in every human endeavor. It also raises a wealth of neglected and yet evocative philosophical questions: What is the role of consciousness in the creative process? How does the audience for a work for art influence its creation? How can creativity emerge through childhood pretending? Do great works of literature give us insight into human nature? Can a computer program really be (...) creative? How do we define creativity in the first place? Is it a virtue? What is the difference between creativity in science and art? Can creativity be taught? -/- The new essays that comprise The Philosophy of Creativity take up these and other key questions and, in doing so, illustrate the value of interdisciplinary exchange. Written by leading philosophers and psychologists involved in studying creativity, the essays integrate philosophical insights with empirical research. -/- CONTENTS -/- I. Introduction Introducing The Philosophy of Creativity Elliot Samuel Paul and Scott Barry Kaufman -/- II. The Concept of Creativity 1. An Experiential Account of Creativity Bence Nanay -/- III. Aesthetics & Philosophy of Art 2. Creativity and Insight Gregory Currie 3. The Creative Audience: Some Ways in which Readers, Viewers and/or Listeners Use their Imaginations to Engage Fictional Artworks Noël Carroll 4. The Products of Musical Creativity Christopher Peacocke -/- IV. Ethics & Value Theory 5. Performing Oneself Owen Flanagan 6. Creativity as a Virtue of Character Matthew Kieran -/- V. Philosophy of Mind & Cognitive Science 7. Creativity and Not So Dumb Luck Simon Blackburn 8. The Role of Imagination in Creativity Dustin Stokes 9. Creativity, Consciousness, and Free Will: Evidence from Psychology Experiments Roy F. Baumeister, Brandon J. Schmeichel, and C. Nathan DeWall 10. The Origins of Creativity Elizabeth Picciuto and Peter Carruthers 11. Creativity and Artificial Intelligence: a Contradiction in Terms? Margaret Boden -/- VI. Philosophy of Science 12. Hierarchies of Creative Domains: Disciplinary Constraints on Blind-Variation and Selective-Retention Dean Keith Simonton -/- VII. Philosophy of Education (& Education of Philosophy) 13. Educating for Creativity Berys Gaut 14. Philosophical Heuristics Alan Hájek. (shrink)
The adaptationist framework is necessary and sufficient for unifying the social and natural sciences. Gintis's “beliefs, preferences, and constraints” (BPC) model compares unfavorably to this framework because it lacks criteria for determining special design, incorrectly assumes that standard evolutionary theory predicts individual rationality maximisation, does not adequately recognize the impact of psychological mechanisms on culture, and is mute on the behavioural implications of intragenomic conflict. (Published Online April 27 2007).
D. Scott in his paper  on the mathematical models for the Church-Curry -calculus proved the following theorem.A topological space X. is an absolute extensor for the category of all topological spaces iff a contraction of X. is a topological space of Scott's open sets in a continuous lattice.
Both in church and culture, discussion of sexual orientation has far outpaced discussion of gender identity, leaving the churches with limited resources to respond to “bathroom bills” or to walk faithfully with transgender persons in their midst. This paper draws on the work of Rowan Williams and Sarah Coakley to argue for understanding gender transition as an eschatological formation ordered to the body’s grace. In critical conversation with Oliver O’Donovan, John Milbank, and David Cloutier, the paper offers a constructive, (...) non-voluntarist theological proposal for transgender affirmation in the service of participation in the triune life that exceeds gender. (shrink)
Motivated by a conviction that mass incarceration and state execution are among the most important ethical and political problems of our time, the contributors to this volume come together from a diverse range of backgrounds to analyze, critique, and envision alternatives to the injustices of the U.S. prison system, with recourse to deconstruction, phenomenology, critical race theory, feminism, queer theory, and disability studies. They engage with the hyper-incarceration of people of color, the incomplete abolition of slavery, the exploitation of prisoners (...) as workers and as "raw material" for the prison industrial complex, the intensive confinement of prisoners in supermax units, and the complexities of capital punishment in an age of abolition. -/- Contents -/- Introduction: Death and Other Penalties Geoffrey Adelsberg, Lisa Guenther, and Scott Zeman -/- Part I. Legacies of Slavery -/- Excavating the Sedimentations of Slavery: The Unfinished Project of American Abolition Brady Heiner -/- From Commodity Fetishism to Prison Fetishism: Slavery, Convict-leasing, and the Ideological Productions of Incarceration James Manos -/- Maroon Philosophy: An Interview with Russell Maroon Shoatz Russell Maroon Shoatz -/- Part II. Death Penalties -/- In Reality-from the Row Derrick Quintero -/- Inheritances of the Death Penalty: American Racism and Derrida's Theologico-Political Sovereignty Geoffrey Adelsberg -/- Making Death a Penalty: Or, Making "Good" Death a "Good" Penalty Kelly Oliver -/- Death Penalty Abolition in Neoliberal Times: The SAFE California Act and the Nexus of Savings and Security Andrew Dilts -/- On the Inviolability of Human Life Julia Kristeva (translated by Lisa Walsh) -/- Part III. Rethinking Power and Responsibility -/- Punishment, Desert, and Equality: A Levinasian Analysis Benjamin S. Yost -/- Prisons and Palliative Politics Ami Harbin -/- Sovereignty, Community, and the Incarceration of Immigrants Matt S. Whitt -/- Without the Right to Exist: Mass Incarceration and National Security Andrea Smith -/- Prison Abolition and a Culture of Sexual Difference Sarah Tyson -/- Part IV. Isolation and Resistance -/- Statement on Solitary Confinement Abu Ali Abdur'Rahman -/- The Violence of the Supermax: Toward a Phenomenological Aesthetics of Prison Space Adrian Switzer -/- Prison and the Subject of Resistance: A Levinasian Inquiry Shokoufeh Sakhi -/- Critical Theory, Queer Resistance, and the Ends of Capture Liat Ben-Moshe, Che Gossett, Nick Mitchell, and Eric A. Stanley. (shrink)
For much of the twentieth century, philosophy and science went their separate ways. In moral philosophy, fear of the so-called naturalistic fallacy kept moral philosophers from incorporating developments in biology and psychology. Since the 1990s, however, many philosophers have drawn on recent advances in cognitive psychology, brain science, and evolutionary psychology to inform their work. This collaborative trend is especially strong in moral philosophy, and these volumes bring together some of the most innovative work by both philosophers and psychologists in (...) this emerging interdisciplinary field. The contributors to volume 1 discuss recent work on the evolution of moral beliefs, attitudes, and emotions. Each chapter includes an essay, comments on the essay by other scholars, and a reply by the author of the original essay. Topics include a version of naturalism that avoids supposed fallacies, distinct neurocomputational systems for deontic reasoning, the evolutionary psychology of moral sentiments regarding incest, the sexual selection of moral virtues, the evolution of symbolic thought, and arguments both for and against innate morality. Taken together, the chapters demonstrate the value for both philosophy and psychology of collaborative efforts to understand the many complex aspects of morality. Contributors: William Casebeer, Leda Cosmides, OliverCurry, Michael Dietrich, Catherine Driscoll, Susan Dwyer, Owen Flanagan, Jerry Fodor, Gilbert Harman, Richard Joyce, Debra Lieberman, Ron Mallon, John Mikhail, Geoffrey Miller, Jesse Prinz, Peter Railton, Michael Ruse, Hagop Sarkissian, Walter Sinnott-Armstrong, Chandra Sekhar Sripada, Valerie Tiberius, John Tooby, Peter Tse, Kathleen Wallace, Arthur Wolf, David Wong Walter Sinnott-Armstrong is Professor of Philosophy and Hardy Professor of Legal Studies at Dartmouth College. (shrink)
We present a Kripke model for Girard's Linear Logic (without exponentials) in a conservative fashion where the logical functors beyond the basic lattice operations may be added one by one without recourse to such things as negation. You can either have some logical functors or not as you choose. Commutatively and associatively are isolated in such a way that the base Kripke model is a model for noncommutative, nonassociative Linear Logic. We also extend the logic by adding a coimplication operator, (...) similar to Curry's subtraction operator, which is resituated with Linear Logic's contensor product. And we can add contraction to get nondistributive Relevance Logic. The model rests heavily on Urquhart's representation of nondistributive lattices and also on Dunn's Gaggle Theory. Indeed, the paper may be viewed as an investigation into nondistributive Gaggle Theory restricted to binary operations. The valuations on the Kripke model are three valued: true, false, and indifferent. The lattice representation theorem of Urquhart has the nice feature of yielding Priestley's representation theorem for distributive lattices if the original lattice happens to be distributive. Hence the representation is consistent with Stone's representation of distributive and Boolean lattices, and our semantics is consistent with the Lemmon-Scott representation of modal algebras and the Routley-Meyer semantics for Relevance Logic. (shrink)
: According to Kelly Oliver and Elizabeth Grosz, while Friedrich Nietzsche begins to open Western philosophy to the other, the body, he cuts off feminine body. Here I create a framework through which the possibility and questionability of a symbolically feminine body begins to emerge. I do this by using the metaphor of Indian curry. The metaphor works on two levels: 1) as a symbolically feminine body; 2) as Nietzsche's conception of subject-formation as a dynamic monism.
According to Kelly Oliver and Elizabeth Grosz, while Friedrich Nietzsche begins to open Western philosophy to the other, the body, he cuts off feminine body. Here I create a framework through which the possibility and questionability of a symbolically feminine body begins to emerge. I do this by using the metaphor of Indian curry. The metaphor works on two levels: 1) as a symbolically feminine body; 2) as Nietzsche's conception of subject-formation as a dynamic monism.
Bibliography of A. A. Fraenkel (p. ix-x)--Axiomatic set theory. Zur Frage der Unendlichkeitsschemata in der axiomatischen Mengenlehre, von P. Bernays.--On some problems involving inaccessible cardinals, by P. Erdös and A. Tarski.--Comparing the axioms of local and universal choice, by A. Lévy.--Frankel's addition to the axioms of Zermelo, by R. Mantague.--More on the axiom of extensionality, by D. Scott.--The problem of predicativity, by J. R. Shoenfield.--Mathematical logic. Grundgedanken einer typenfreien Logik, von W. Ackermann.--On the use of Hilbert's [epsilon]-operator in scientific (...) theories, by R. Carnap.--Basic verifiability in the combinatory theory of restricted generality, by H. B. Curry.--Uniqueness ordinals in constructive number classes, by H. Putnam.--On the construction of models, by A. Robinson.--Interpretation of mathematical theories in the first order predicate calculus, by T. Skolem.--The elementary character of two notions from general algebra, by R. Vaught.--Foundations of arithmetic and analysis. Axiomatic method and intuitionism, by A. Heyting.--On rank-decreasing functions, by G. Kurepa.--On non-standard models for number theory, by E. Mendelson.--Concerning the problem of axiomatizability of the field of real numbers in the weak second order logic, by A. Mostowski.--Non-standard models and independence of the induction axiom, by M. O. Rabin.--Sur les ensembles raréfiés de nombres naturels, par W. Sierpinski.--Philosophy of logic and mathematics. Remarks on the paradoxes of logic and set theory, by E. W. Beth.--Logique formalisée et raisonnement juridique, par R. Feys.--Im Umkreis der sogenannten Raumprobleme, von H. Freudenthal.--Process and existence in mathematics, by H. Wang. (shrink)
We are happy to present the Winter 2017 Edition of Constellations that is comprised of six outstanding undergraduate works. The edition is loosely tied together by a theme of material history and showcases the diverse, but consistently excellent work of our undergraduate students here at the University of Alberta. The Winter 2017 Edition includes:Curries, Chutneys and Imperial Britain investigates the intriguing correlation between British imperialism in India and Indian food in British society. Incredibly relevant to the world today “Your Tired, (...) Your Poor, Your Huddled Masses” American Responses to the Indochinese and Syrian Refugee Crises explores the the contributing factors to American’s feelings to refugees.Revolutionary Gender Equality: The Dimensions and Limits of Female Emancipation in the Sandinista Revolution provides an intriguing analysis of the changes to women’s expected roles during revolution. Neither Full Nor Flat: Women, Representation and Politics in Walter Scott's Rob Roy an analysis of women’s role in the novel as indication of the contemporary politics. ‘Daring to Ride Skirtless’: Anti-Fashion and Emancipation for the New British Woman, 1880-1910 provides an interesting look into the role of fashion in women’s emancipation. Custodians of Morality, Motherhood, and Whiteness: Sex Education for Girls in American Schools During the 1920s explores the emergence of sex education programs in the United States the implications on the social roles of young girls and women. Thank you for your interest in Constellations. We are indebted to our volunteers for all of their hard work that went into this edition. We would like to thank the Department of History and Classics for their support of Constellations.Co-Editors: Emily Kaliel and Jean MiddletonAssistant Editors:Lee Klippenstein and Sean OliverSenior Reviewers:Connor ThompsonEmily TranBronte Wells. (shrink)
Curry’s paradox is well known. The original version employed a conditional connective, and is not forthcoming if the conditional does not satisfy contraction. A newer version uses a validity predicate, instead of a conditional, and is not forthcoming if validity does not satisfy structural contraction. But there is a variation of the paradox which uses “external validity”. And since external validity contracts, one might expect the appropriate version of the Curry paradox to be inescapable. In this paper we (...) show that this is not the case. We consider two ways of formalising the notion of external validity, and show that in both of these the paradox is not forthcoming without the appropriate forms of contraction. (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)
What sorts of things are there in the world? Clearly enough, there are concrete, material things; but are there other things too, perhaps nonconcrete or non-material things? Some people believe that there are such things, which are often called abstract ; purported examples of such objects include numbers, properties, possible but non-actual states of affairs, propositions, and sets. Following a long-standing tradition, I shall describe persons who believe that there are abstract objects as ‘platonists’. In this paper, I shall not (...) directly address the plausibility of platonism, as compared with its rivals; instead, I shall confine my attention to one way in which some people have tried to combine platonism and theism. More specifically, I shall concentrate upon the claim that abstract objects depend upon God ontologically ; I shall argue that platonistic theists should reject DEP in favour of the claim that abstract objects exist independently of God . In order to evaluate the relative merits of DEP versus IND, it will be helpful to examine in some detail a particular articulation of DEP. When it comes to recent work on DEP, we can do no better in this regard than to examine the recent work of Thomas V. Morris and Christopher H. Menzel. According Morris and Menzel, there is a sense in which God literally creates such abstracta through engaging in intellective activities. (shrink)
Rights of Women attracted much UK media attention in late 2014 by bringing a judicial review that challenged the reduced provisions for family law legal aid available for victims of domestic violence: R v The Lord Chancellor and Secretary of State for Justice  EWHC 35. In June 2015, within Rights of Women’s 40th anniversary year, Hannah Camplin interviewed the organisation’s Director Emma Scott about the decision to bring the judicial review, the advantages and challenges of the judicial review (...) process, and the experience of strategic litigation within the context of Rights of Women’s long history of campaigning for women’s rights. What emerged is a portrait of a feminist organisation in 2015, and, in a fast changing political and financial landscape, the dual importance of collaborative working and the need for flexibility in service provision and campaigning tools. (shrink)
In this paper, we distinguish two versions of Curry's paradox: c-Curry, the standard conditional-Curry paradox, and v-Curry, a validity-involving version of Curry's paradox that isn’t automatically solved by solving c-curry. A uniﬁed treatment of curry paradox thus calls for a uniﬁed treatment of both c-Curry and v-Curry. If, as is often thought, c-Curry paradox is to be solved via non-classical logic, then v-Curry may require a lesson about the structure—indeed, (...) the substructure—of the validity relation itself. (shrink)
Several authors have argued that a version of Curry's paradox involving validity motivates rejecting the structural rule of contraction. This paper criticizes two recently suggested alternative responses to “validity Curry.” There are three salient stages in a validity Curry derivation. Rejecting contraction blocks the first, while the alternative responses focus on the second and third. I show that a distinguishing feature of validity Curry, as contrasted with more familiar forms of Curry's paradox, is that paradox (...) arises already at the first stage. Accordingly, blocking the second or third stages won't suffice for resolving the paradox. (shrink)
Scott Sturgeon presents an original account of mental states and their dynamics. He develops a detailed story of coarse- and fine-grained mental states, a novel perspective on how they fit together, an engaging theory of the rational transitions between them, and a fresh view of how formal methods can advance our understanding in this area. In doing so, he addresses a deep four-way divide in literature on epistemic rationality. Formal epistemology is done in specialized languages--often seeming a lot more (...) like mathematics than Plato--and so can alienate philosophers who are drawn to more traditional work on thought experiments in epistemic rationality. Conversely, informal epistemology appears to be a lot more like Plato than mathematics and, as such, it tends to deter philosophers drawn to formal models of the phenomena. Similarly, the epistemology of coarse-grained states boils down everything to a discussion of rational belief--making the area appear a lot more like foundations of knowledge than anything useful for the theory rational decision, such as decision-making under uncertainty. The Rational Mind unifies work in all of these areas for the first time. (shrink)
The Curry-Howard isomorphism states an amazing correspondence between systems of formal logic as encountered in proof theory and computational calculi as found in type theory. For instance, minimal propositional logic corresponds to simply typed lambda-calculus, first-order logic corresponds to dependent types, second-order logic corresponds to polymorphic types, sequent calculus is related to explicit substitution, etc. The isomorphism has many aspects, even at the syntactic level: formulas correspond to types, proofs correspond to terms, provability corresponds to inhabitation, proof normalization corresponds (...) to term reduction, etc. But there is more to the isomorphism than this. For instance, it is an old idea---due to Brouwer, Kolmogorov, and Heyting---that a constructive proof of an implication is a procedure that transforms proofs of the antecedent into proofs of the succedent; the Curry-Howard isomorphism gives syntactic representations of such procedures. The Curry-Howard isomorphism also provides theoretical foundations for many modern proof-assistant systems (e.g. Coq). This book give an introduction to parts of proof theory and related aspects of type theory relevant for the Curry-Howard isomorphism. It can serve as an introduction to any or both of typed lambda-calculus and intuitionistic logic. Key features - The Curry-Howard Isomorphism treated as common theme - Reader-friendly introduction to two complementary subjects: Lambda-calculus and constructive logics - Thorough study of the connection between calculi and logics - Elaborate study of classical logics and control operators - Account of dialogue games for classical and intuitionistic logic - Theoretical foundations of computer-assisted reasoning · The Curry-Howard Isomorphism treated as the common theme. · Reader-friendly introduction to two complementary subjects: lambda-calculus and constructive logics · Thorough study of the connection between calculi and logics. · Elaborate study of classical logics and control operators. · Account of dialogue games for classical and intuitionistic logic. · Theoretical foundations of computer-assisted reasoning. (shrink)
Beall and Cotnoir (2017) argue that theists may accept the claim that God's omnipotence is fully unrestricted if they also adopt a suitable nonclassical logic. Their primary focus is on the infamous Stone problem (i.e., whether God can create a stone too heavy for God to lift). We show how unrestricted omnipotence generates Curry‐like paradoxes. The upshot is that Beall and Cotnoir only provide a solution to one version of the Stone problem, but that unrestricted omnipotence generates other problems (...) which they do not adequately address. (shrink)
Curry's paradox, so named for its discoverer, namely Haskell B. Curry, is a paradox within the family of so-called paradoxes of self-reference (or paradoxes of circularity). Like the liar paradox (e.g., ‘this sentence is false’) and Russell's paradox , Curry's paradox challenges familiar naive theories, including naive truth theory (unrestricted T-schema) and naive set theory (unrestricted axiom of abstraction), respectively. If one accepts naive truth theory (or naive set theory), then Curry's paradox becomes a direct challenge (...) to one's theory of logical implication or entailment. Unlike the liar and Russell paradoxes Curry's paradox is negation-free; it may be generated irrespective of one's theory of negation. An intuitive version of the paradox runs as follows. (shrink)
Curry's paradox for "if.. then.." concerns the paradoxical features of sentences of the form "If this very sentence is true, then 2+2=5". Standard inference principles lead us to the conclusion that such conditionals have true consequents: so, for example, 2+2=5 after all. There has been a lot of technical work done on formal options for blocking Curry paradoxes while only compromising a little on the various central principles of logic and meaning that are under threat. -/- Once we (...) have a sense of the technical options, though, a philosophical choice remains. When dealing with puzzles in the logic of conditionals, a natural place to turn is independently motivated semantic theories of the behaviour of "if... then...". This paper argues that the closest-worlds approach outlined in Nolan 1997 offers a philosophically satisfying reason to deny conditional proof and so block the paradoxical Curry reasoning, and can give the verdict that standard Curry conditionals are false, along with related "contraction conditionals". (shrink)
Substantivalists believe that spacetime and its parts are fundamental constituents of reality. Relationalists deny this, claiming that spacetime enjoys only a derivative existence. I begin by describing how the Galilean symmetries of Newtonian physics tell against both Newton's brand of substantivalism and the most obvious relationalist alternative. I then review the obvious substantivalist response to the problem, which is to ditch substantival space for substantival spacetime. The resulting position has many affinities with what are arguably the most natural interpretations of (...) special and general relativity. I move on to consider and reject two recent antisubstantivalist lines of thought. The interim conclusion is that the best argument for relationalism is an appeal to Ockham's razor. However, for this to be successful there must be genuine relationalist theories that share the theoretical virtues of their substantivalist rivals but without the additional ontological commitment. The bulk of the paper is therefore an investigation of various concrete relationalist proposals. I distinguish three options for the relationalist in the face of the success of Galilean invariant physics and trace how these generalise to relativistic physics. One of the options is particularly promising but, since its basic objects end up being spacetime points, this does not help the prospects of relationalism as traditionally conceived. I end with some reflections on the fate of substantivalism in the aftermath of the Hole Argument, concluding that we have as yet to be given good reasons to abandon the natural, substantivalist interpretation of current physics. (shrink)