Olszewski claims that the Church-Turing thesis can be used in an argument against platonism in philosophy of mathematics. The key step of his argument employs an example of a supposedly effectively computable but not Turing-computable function. I argue that the process he describes is not an effective computation, and that the argument relies on the illegitimate conflation of effective computability with there being a way to find out . ‘Ah, but,’ you say, ‘what’s the use of its being right twice (...) a day, if I can’t tell when the time comes?’ Why, suppose the clock points to eight o’clock, don’t you see that the clock is right at eight o’clock? Consequently, when eight o’clock comes round your clock is right. Lewis Carroll. (shrink)

When we talk about the coherence of a story, we seem to think of how well its individual pieces fit together—how to explicate this notion formally, though? We develop a Bayesian network based coherence measure with implementation in _R_, which performs better than its purely probabilistic predecessors. The novelty is that by paying attention to the network structure, we avoid simply taking mean confirmation scores between all possible pairs of subsets of a narration. Moreover, we assign special importance to the (...) weakest links in a narration, to improve on the other measures’ results for logically inconsistent scenarios. We illustrate and investigate the performance of the measures in relation to a few philosophically motivated examples, and (more extensively) using the real-life example of the Sally Clark case. (shrink)

Reason and Value collects 15 new papers by leading contemporary philosophers on themes from the work of Joseph Raz. Raz has made major contributions in a wide range of areas, including jurisprudence, political philosophy, and the theory of practical reason; but all of his work displays a deep engagement with central themes in moral philosophy. The subtlety and power of Raz's reflections on ethical topics make his writings a fertile source for anyone working in this area. Especially significant are his (...) explorations of the connections between practical reason and the theory of value, which constitute a sustained and penetrating treatment of a set of issues at the very center of moral philosophy as it is practiced today. The contributors to the volume acknowledge the importance of Raz's contributions by engaging critically with his positions and offering independent perspectives on the topics that he has addressed. The volume aims both to honour Raz's accomplishments in the area of ethical theorizing, and to contribute to an enhanced appreciation of the significance of his work for the subject. (shrink)

The Nature of God explores a perennial problem in the philosophy of religion.

We investigate what happens when ‘truth’ is replaced with ‘provability’ in Yablo’s paradox. By diagonalization, appropriate sequences of sentences can be constructed. Such sequences contain no sentence decided by the background consistent and sufficiently strong arithmetical theory. If the provability predicate satisfies the derivability conditions, each such sentence is provably equivalent to the consistency statement and to the Gödel sentence. Thus each two such sentences are provably equivalent to each other. The same holds for the arithmetization of the existential Yablo (...) paradox. We also look at a formulation which employs Rosser’s provability predicate. (shrink)

While there is a general consensus around the role of religion in the abolition of the Slave Trade, historians continue to give little to no detail on exactly how Christian theology influenced the abolitionist movement. This article seeks to interrogate one major theological factor inherent in the spirituality that underpinned the activism of the British abolitionists, namely their notion of Divine Providence, and particularly its moral-emotive correlate: the fear of God’s wrath. These theological notions are discussed based mainly on the (...) analysis of the primary sources and within the theoretical framework of judicial providentialism, aptly captured by John Coffey among others. (shrink)

While there is a general consensus around the role of religion in the abolition of the Slave Trade, historians continue to give little to no detail on exactly how Christian theology influenced the abolitionist movement. This article seeks to interrogate one major theological factor inherent in the spirituality that underpinned the activism of the British abolitionists, namely their notion of Divine Providence, and particularly its moral-emotive correlate: the fear of God’s wrath. These theological notions are discussed based mainly on the (...) analysis of the primary sources and within the theoretical framework of judicial providentialism, aptly captured by John Coffey among others. (shrink)

Despite All Critique (2014) -- World Politics and Western Reason (1980) -- The Doubled Outsides of the Modern International (2005) -- The Subject of Security (1995) -- The Protection of Nature and the Nature of Protection (2005) -- Social Movements/World Politics (1994) -- Europe is Not Where It is Supposed to Be (2000) -- They Seek it Here, They Seek it There : Looking for Politics in Clayoquot Sound (2003) -- Violence, Modernity, Silence : From Weber to International Relations (1993) (...) -- Hobbes, Origins, Limits (2011) -- War, Terror, Judgement (2002) -- International, Imperial, Exceptional (2005) -- Which Democracy for Which Demos? (2013) -- The Political Theory of Boundaries and the Boundaries of Political Theory : Interview With Raia Prokhovnik (2012). (shrink)

How do we access the authentic self in order to live fulfilling, meaningful lives? In straightforward terms, The Heart of the Matter: Gifts in Strange Wrapping Paper explains a simple but extraordinarily powerful technique called the See, Feel, Hear Challenge that enables people to easily gain entry into the storehouse of their subconscious core beliefs. In the process, it cracks the coded messages that those beliefs release in the form of disease, suffering, addictions, unhappy relationships, and victimized circumstances. Based in (...) the latest findings in neuroscience and neurocardiology, this book guides readers to an uncomplicated understanding of the astounding power of our emotions and how life automatically delivers experiences that trigger negative reactions that subconsciously impact us. These emotions form the foundation of core beliefs that create unhealthy attitudes and dis-ease patterns that keep us from experiencing the authentic, satisfying lives we desire. Using clear examples and true stories from clients, Dr. Weissman’s latest work demonstrates how we can release these stored emotions and their wisdom via the See, Feel, Hear Challenge. It then explains how to use this simple method to evoke feelings that positively impact the quantum field, remolding our bodies, minds, and everyday lives into purposeful expressions of inner joy and radiant well-being. Whether you’re dealing with addictions, dysfunctional relationships, or illness, or are focused on becoming an Olympic champion, The Heart of the Matter gives you a potent tool for positive change and transformation that you can use for the rest of your life. (shrink)

Elliot R. Wolfson intervenes in the debate over Martin Heidegger and Nazism from a unique perspective, as a scholar of Jewish mysticism and philosophy who has been profoundly influenced by Heidegger's work. He reveals crucial aspects of Heidegger's thinking that betray an affinity with dimensions of Jewish thought.

Legal probabilism is the view that juridical fact-finding should be modeled using Bayesian methods. One of the alternatives to it is the narration view, according to which instead we should conceptualize the process in terms of competing narrations of what happened. The goal of this paper is to develop a reconciliatory account, on which the narration view is construed from the Bayesian perspective within the framework of formal Bayesian epistemology.

With material on his early philosophical views, his contributions to set theory and his work on nominalism and higher-order quantification, this book offers a uniquely expansive critical commentary on one of analytical philosophy’s great ...

This book focuses upon the perennial question of the existence and nature of an obligation to obey the law. Leading writers have, at one time or another, emphasized considerations such as gratitude, 'divine ordering, ' prudence, contract, autonomy, and utility in seeking to justify, or to deny any justification for, some sort of obligation to obey the positive law. The book provides relevant selections from a sampling of the historical approaches to legal obligation taken by writers such as Plato, Augustine, (...) Aquinas, Hobbes, Locke, Hume, Rousseau, Thoreau, Bentham, Marx and Engels, and Martin Luther King, Jr. These classical discussions are augmented by critical questions and commentary, by independent discussions of the question of legal obligation by a wide range of contemporary writers, and by relevant judicial cases discussing matters such as conscientious objection and civil disobedience. (shrink)

One of the standard views on plural quantification is that its use commits one to the existence of abstract objects–sets. On this view claims like ‘some logicians admire only each other’ involve ineliminable quantification over subsets of a salient domain. The main motivation for this view is that plural quantification has to be given some sort of semantics, and among the two main candidates—substitutional and set-theoretic—only the latter can provide the language of plurals with the desired expressive power (given that (...) the nominalist seems committed to the assumption that there can be at most countably many names). To counter this approach I develop a modal-substitutional semantics of plural quantification (on which plural variables, roughly speaking, range over ways names could be) and argue for its nominalistic acceptability. (shrink)

The goal is to sketch a nominalist approach to mathematics which just like neologicism employs abstraction principles, but unlike neologicism is not committed to the idea that mathematical objects exist and does not insist that abstraction principles establish the reference of abstract terms. It is well-known that neologicism runs into certain philosophical problems and faces the technical difficulty of finding appropriate acceptability criteria for abstraction principles. I will argue that a modal and iterative nominalist approach to abstraction principles circumvents those (...) difficulties while still being able to put abstraction principles to a foundational use. (shrink)

This paper evaluates Richard Swinburne’s modal argument for the existence of souls. After a brief presentation of the argument, wedescribe the main known objection to it, which is called the substitution objection (SO for short), and explain Swinburne’s response to that objection. With this as background, we formalize Swinburne’s argument in a quantified propositional modal language, modifying it so that it is logically valid and contains no tacit assumptions, and we explain why we find Swinburne’s response to SO unsatisfactory. Next, (...) we indicate that, even though SO is quite compelling, a weakening of one of the premises yields a valid argument for the same conclusion which is immune to SO. This version of the argument, however, is epistemically circular. (shrink)

Brown (The laboratory of the mind. Thought experiments in the natural science, 1991a , 1991b ; Contemporary debates in philosophy of science, 2004 ; Thought experiments, 2008 ) argues that thought experiments (TE) in science cannot be arguments and cannot even be represented by arguments. He rest his case on examples of TEs which proceed through a contradiction to reach a positive resolution (Brown calls such TEs “platonic”). This, supposedly, makes it impossible to represent them as arguments for logical reasons: (...) there is no logic that can adequately model such phenomena. (Brown further argues that this being the case, “platonic” TEs provide us with irreducible insight into the abstract realm of laws of nature). I argue against this approach by describing how “platonic” TEs can be modeled within the logical framework of adaptive proofs for prioritized consequence operations. To show how this mundane apparatus works, I use it to reconstruct one of the key examples used by Brown, Galileo’s TE involving falling bodies. (shrink)

A theory of definitions which places the eliminability and conservativeness requirements on definitions is usually called the standard theory. We examine a persistent myth which credits this theory to Leśniewski, a Polish logician. After a brief survey of its origins, we show that the myth is highly dubious. First, no place in Leśniewski's published or unpublished work is known where the standard conditions are discussed. Second, Leśniewski's own logical theories allow for creative definitions. Third, Leśniewski's celebrated ‘rules of definition’ lay (...) merely syntactical restrictions on the form of definitions: they do not provide definitions with such meta-theoretical requirements as eliminability or conservativeness. On the positive side, we point out that among the Polish logicians, in the 1920s and 1930s, a study of these meta-theoretical conditions is more readily found in the works of Łukasiewicz and Ajdukiewicz. (shrink)

David Lewis has formulated a well-known challenge to his Best System account of lawhood: the content of any system whatever can be formulated very simply if one allows for perverse choices of primitive vocabulary. We show that the challenge is not that dangerous, and that to account for it one need not invoke natural properties or relativized versions of the Best System account. This way, we help to move towards an even better Best System account. We discuss extensions of our (...) strategy to the discussions about the indexicality of the notion of laws of nature, and to another trivialization argument. (shrink)

The concept of yinyang lies at the heart of Chinese thought and culture. The relationship between these two opposing, yet mutually dependent, forces is symbolized in the familiar black and white symbol that has become an icon in popular culture across the world. The real significance of yinyang is, however, more complex and subtle. This brilliant and comprehensive analysis by one of the leading authorities in the field captures the richness and multiplicity of the meanings and applications of yinyang, including (...) its visual presentations. Through a vast range of historical and textual sources, the book examines the scope and role of yinyang, the philosophical significance of its various layers of meanings and its relation to numerous schools and traditions within Chinese philosophy. By putting yinyang on a secure and clear philosophical footing, the book roots the concept in the original Chinese idiom, distancing it from Western assumptions, frameworks and terms, yet also seeking to connect its analysis to shared cross-cultural philosophical concerns. (shrink)

It is a commonplace remark that the identity relation, even though not expressible in a first-order language without identity with classical set-theoretic semantics, can be defined in a language without identity, as soon as we admit second-order, set-theoretically interpreted quantifiers binding predicate variables that range over all subsets of the domain. However, there are fairly simple and intuitive higher-order languages with set-theoretic semantics in which the identity relation is not definable. The point is that the definability of identity in higher-order (...) languages not only depends on what variables range over, but also is sensitive to how predication is construed. This paper is a follow-up to , where it has been proven that no actual axiomatization of Leśniewski’s Ontology determines the standard semantics for the epsilon connective. (shrink)

Sobocinski in his paper on Leśniewski's solution to Russell's paradox (1949b) argued that Leśniewski has succeeded in explaining it away. The general strategy of this alleged explanation is presented. The key element of this attempt is the distinction between the collective (mereological) and the distributive (set-theoretic) understanding of the set. The mereological part of the solution, although correct, is likely to fall short of providing foundations of mathematics. I argue that the remaining part of the solution which suggests a specific (...) reading of the distributive interpretation is unacceptable. It follows from it that every individual is an element of every individual. Finally, another Leśniewskian-style approach which uses so-called higher-order epsilon connectives is used and its weakness is indicated. (shrink)

A defence of the idea that there are sui generis duties of love: duties, that is, that we owe to people in virtue of standing in loving relationships with them. I contrast this non-reductionist position with the widespread reductionist view that our duties to those we love all derive from more generic moral principles. The paper mounts a cumulative argument in favour of the non-reductionist position, adducing a variety of considerations that together speak strongly in favour of adopting it. The (...) concluding section connects this debate with larger issues in moral theory concerning the general idea of obligation. (shrink)

Information can be public among a group. Whether or not information is public matters, for example, for accounts of interdependent rational choice, of communication, and of joint intention. A standard analysis of public information identifies it with (some variant of) common belief. The latter notion is stipulatively defined as an infinite conjunction: for p to be commonly believed is for it to believed by all members of a group, for all members to believe that all members believe it, and so (...) forth. This analysis is often presupposed without much argument in philosophy. Theoretical entrenchment or intuitions about cases might give some traction on the question, but give little insight about why the identification holds, if it does. The strategy of this paper is to characterize a practical-normative role for information being public, and show that the only things that play that role are (variants of) common belief as stipulatively characterized. In more detail: a functional role for “taking a proposition for granted” in non-isolated decision making is characterized. I then present some minimal conditions under which such an attitude is correctly held. The key assumption links this attitude to beliefs about what is public. From minimal a priori principles, we can argue that a proposition being public among a group entails common commitment to believe among that group. Later sections explore partial converses to this result, the factivity of publicity and publicity from the perspective of outsiders to the group, and objections to the aprioricity of the result deriving from a posteriori existential presuppositions. (shrink)

This article builds on my recent engagement with James Cone’s binary view of Africanness and Christianity which focused on his Western locus of enunciation and the criticism he received from his African American colleagues. I believe that analogical questions regarding Christian theology’s attitude towards Africanness in general and African religiosity in particular present themselves to us who live in and try to make sense of South African reality today, including white people like myself. I start by introducing a decolonial perspective (...) as it manifests itself through the recent #MustFall student movements. In this context, I offer three theses regarding the decolonial perspective on African religiosity, each of which constitutes a more or less direct critique of Cone’s ambivalent attitude towards Africanness, and African Traditional Religions in particular. The first thesis concerns the distinction between postcoloniality and decoloniality; the second thesis concerns engaging African religiosity as a requirement for decolonising Christian theology; and the third thesis concerns problematising the relationship between the categories of blackness and Africanness. (shrink)

According to the dialetheist argument from the inconsistency of informal mathematics, the informal version of the Gödelian argument leads us to a true contradiction. On one hand, the dialetheist argues, we can prove that there is a mathematical claim that is neither provable nor refutable in informal mathematics. On the other, the proof of its unprovability is given in informal mathematics and proves that very sentence. We argue that the argument fails, because it relies on the unjustified and unlikely assumption (...) that the informal Gödel sentence is informally provable. (shrink)

Classical logic of formal provability includes Löb’s theorem, but not reflection. In contrast, intuitions about the inferential behavior of informal provability (in informal mathematics) seem to invalidate Löb’s theorem and validate reflection (after all, the intuition is, whatever mathematicians prove holds!). We employ a non-deterministic many-valued semantics and develop a modal logic T-BAT of an informal provability operator, which indeed does validate reflection and invalidates Löb’s theorem. We study its properties and its relation to known provability-related paradoxical arguments. We also (...) argue that T-BAT is a fairly sensible candidate for a formal logic of informal provability. (shrink)

BAT is a logic built to capture the inferential behavior of informal provability. Ultimately, the logic is meant to be used in an arithmetical setting. To reach this stage it has to be extended to a first-order version. In this paper we provide such an extension. We do so by constructing non-deterministic three-valued models that interpret quantifiers as some sorts of infinite disjunctions and conjunctions. We also elaborate on the semantical properties of the first-order system and consider a couple of (...) its strengthenings. It turns out that obtaining a sensible strengthening is not straightforward. We prove that most strategies commonly used for strengthening non-deterministic logics fail in our case. Nevertheless, we identify one method of extending the system which does not. (shrink)

This book features mathematical and formal philosophers’ efforts to understand philosophical questions using mathematical techniques. It offers a collection of works from leading researchers in the area, who discuss some of the most fascinating ways formal methods are now being applied. It covers topics such as: the uses of probable and statistical reasoning, rational choice theory, reasoning in the environmental sciences, reasoning about laws and changes of rules, and reasoning about collective decision procedures as well as about action. Utilizing mathematical (...) techniques has been very fruitful in the traditional domains of formal philosophy – logic, philosophy of mathematics and metaphysics – while formal philosophy is simultaneously branching out into other areas in philosophy and the social sciences. These areas particularly include ethics, political science, and the methodology of the natural and social sciences. Reasoning about legal rules, collective decision-making procedures, and rational choices are of interest to all those engaged in legal theory, political science and economics. Statistical reasoning is also of interest to political scientists and economists. (shrink)