In a world plagued by disagreement and conflict one might expect that the exact sciences of logic and mathematics would provide a safe harbor. In fact these disciplines are rife with internal divisions between different, often incompatible, systems. Do these disagreements admit of resolution? Can such resolution be achieved without disturbing assumptions that the theorems of logic and mathematics state objective truths about the real world? In this original and historically rich book John Woods explores apparently intractable disagreements in logic (...) and the foundations of mathematics and sets out conflict resolution strategies that evade or disarm these stalemates. An important sub-theme of the book is the extent to which pluralism in logic and the philosophy of mathematics undermines realist assumptions. This book makes an important contribution to such areas of philosophy as logic, philosophy of language and argumentation theory. It will also be of interest to mathematicians and computer scientists. (shrink)

The Liar paradox raises foundational questions about logic, language, and truth (and semantic notions in general). A simple Liar sentence like 'This sentence is false' appears to be both true and false if it is either true or false. For if the sentence is true, then what it says is the case; but what it says is that it is false, hence it must be false. On the other hand, if the statement is false, then it is true, since (...) it says (only) that it is false. -/- How, then, should we classify Liar sentences? Are they true or false? A natural suggestion would be that Liars are neither true nor false; that is, they fall into a category beyond truth and falsity. This solution might resolve the initial problem, but it beckons the Liar's revenge. A sentence that says of itself only that it is false or beyond truth and falsity will, in effect, bring back the initial problem. The Liar's revenge is a witness to the hydra-like nature of Liars: in dealing with one Liar you often bring about another. -/- JC Beall presents fourteen new essays and an extensive introduction, which examine the nature of the Liar paradox and its resistance to any attempt to solve it. Written by some of the world's leading experts in the field, the papers in this volume will be an important resource for those working in truth studies, philosophical logic, and philosophy of language, as well as those with an interest in formal semantics and metaphysics. (shrink)

Newtonian cosmology is logically inconsistent. I show its inconsistency in a rigorous but simple and qualitative demonstration. "Logic driven" and "content driven" methods of controlling logical anarchy are distinguished.

This book intervenes in contemporary debates about the threat posed to democratic life by political emergencies. Must emergency necessarily enhance and centralize top-down forms of sovereignty? Those who oppose executive branch enhancement often turn instead to law, insisting on the sovereignty of the rule of law or demanding that law rather than force be used to resolve conflicts with enemies. But are these the only options? Or are there more democratic ways to respond to invocations of emergency politics? Looking at (...) how emergencies in the past and present have shaped the development of democracy, Bonnie Honig argues that democracies must resist emergency's pull to focus on life's necessities because these tend to privatize and isolate citizens rather than bring us together on behalf of hopeful futures. Emphasizing the connections between mere life and more life, emergence and emergency, Honig argues that emergencies call us to attend anew to a neglected paradox of democratic politics: that we need good citizens with aspirational ideals to make good politics while we need good politics to infuse citizens with idealism.Honig takes a broad approach to emergency, considering immigration politics, new rights claims, contemporary food politics and the infrastructure of consumption, and the limits of law during the Red Scare of the early twentieth century. Taking its bearings from Moses Mendelssohn, Franz Rosenzweig, and other Jewish thinkers, this is a major contribution to modern thought about the challenges and risks of democratic orientation and action in response to emergency. (shrink)

Social interaction is both ubiquitous and central to understanding human behavior. Such interactions depend, we argue, on shared intentionality: the parties must form a common understanding of an ambiguous interaction (e.g., one person giving a present to another requires that both parties appreciate that a voluntary transfer of ownership is intended). Yet how can shared intentionality arise? Many well-known accounts of social cognition, including those involving “mind-reading,” typically fall into circularity and/or regress. For example, A’s beliefs and behavior may depend (...) on her prediction of B’s beliefs and behavior, but B’s beliefs and behavior depend in turn on her prediction of A’s beliefs and behavior. One possibility is to embrace circularity and take shared intentionality as imposing consistency conditions on beliefs and behavior, but typically there are many possible solutions and no clear criteria for choosing between them. We argue that addressing these challenges requires some form of we-reasoning, but that this raises the puzzle of how the collective agent (the “we”) arises from the individual agents. This puzzle can be solved by proposing that the will of the collective agent arises from a simulated process of bargaining: agents must infer what they would agree, were they able to communicate. This model explains how, and which, shared intentions are formed. We also propose that such “virtual bargaining” may be fundamental to understanding social interactions. (shrink)

Social interaction is both ubiquitous and central to understanding human behavior. Such interactions depend, we argue, on shared intentionality: the parties must form a common understanding of an ambiguous interaction. Yet how can shared intentionality arise? Many well-known accounts of social cognition, including those involving “mind-reading,” typically fall into circularity and/or regress. For example, A’s beliefs and behavior may depend on her prediction of B’s beliefs and behavior, but B’s beliefs and behavior depend in turn on her prediction of A’s (...) beliefs and behavior. One possibility is to embrace circularity and take shared intentionality as imposing consistency conditions on beliefs and behavior, but typically there are many possible solutions and no clear criteria for choosing between them. We argue that addressing these challenges requires some form of we-reasoning, but that this raises the puzzle of how the collective agent arises from the individual agents. This puzzle can be solved by proposing that the will of the collective agent arises from a simulated process of bargaining: agents must infer what they would agree, were they able to communicate. This model explains how, and which, shared intentions are formed. We also propose that such “virtual bargaining” may be fundamental to understanding social interactions. (shrink)

After preliminarily pointing to the undeniable differences between Jonas’ philosophical biology and Schelling’s philosophy of nature, I contend that, besides their divergencies, the two philosophers agree on several important points. I then show to what extent, based on these elements of convergence, their two approaches could even be taken as complementary. In the core of my paper I lay emphasis on what I believe to be the main ground for the complementarity of the two philosophical inquiries, that is to say, (...) their common radicalization and superseding of Kant’s principle of self-organization. In this respect – all differences considered – they both can be said to delineate a philosophy of the organic that can fruitfully contribute, even better than Kant’s input, to the currently widely discussed topic of biological autonomy. (shrink)

This study investigated faculty attitudes towards student violations of academic integrity in Canada using a qualitative review of 17 universities’ academic integrity/dishonesty policies combined with a quantitative survey of faculty members’ (N = 412) attitudes and behaviours around academic integrity and dishonesty. Results showed that 53.1% of survey respondents see academic dishonesty as a worsening problem at their institutions. Generally, they believe their respective institutional policies are sound in principle but fail in application. Two of the major factors identified by (...) faculty as contributing to academic dishonesty are administrative. Many faculty members feel unsupported by their administration and are reluctant to formally report academic dishonesty due to the excessive burdens of dealing with paperwork and providing proof. Faculty members also cite unprepared students and international students who struggle with language issues and the Canadian academic context as major contributors to academic dishonesty. This study concludes with recommendations for educators and recommendations for future research. (shrink)

We explore the developmental paradox of false belief understanding. This paradox follows from the claim that young infants already have an understanding of false belief, despite the fact that they consistently fail the elicited-response false belief task. First, we argue that recent proposals to solve this paradox are unsatisfactory because they (i) try to give a full explanation of false belief understanding in terms of a single system, (ii) fail to provide psychological concepts that are sufficiently fine-grained (...) to capture the cognitive requirements for the various manifestations of false belief understanding, and (iii) ignore questions about system interaction. Second, we present a dual-system solution to the developmental paradox of false belief understanding that combines a layered model of perspective taking with an inhibition-selection-representation mechanism that operates on different levels. We discuss recent experimental findings that shed light on the interaction between these two systems, and suggest a number of directions for future research. (shrink)

Newcomb's paradox was first presented by Robert Nozick and has been discussed by a considerable number of writers. You are playing a game with a Being who seems to have extraordinary predictive powers. Before you are two boxes, in one of which you can see $1,000. The other is closed and you cannot see what it contains, but you know that the Being has put a million dollars into it if he has predicted that you will take it only, (...) but nothing if he has predicted that you will take both boxes; you may take either both boxes or the closed one only. The Being has correctly predicted the choices of all who have so far played with him. What should you do?Let us call the Being the seer, and his opponent the player. I should also like to reduce the amount that may, or may not, be in the closed box to $10,000. Nearly everyone could make good use of $1,000 and better use of $10,000 or $11,000, but it is hard to say whether a million dollars would be a blessing or a curse. (shrink)

In this paper I argue that there is a preface paradox for intention. The preface paradox for intention shows that intentions do not obey an agglomeration norm, requiring one to intend conjunctions of whatever else one intends. But what norms do intentions obey? I will argue that intentions come in degrees. These partial intentions are governed by the norms of the probability calculus. First, I will give a dispositional theory of partial intention, on which degrees of intention are (...) the degrees to which one possesses the dispositions characteristic of full intention. I will use this dispositional theory to defend probabilism about intention. Next, I will offer a more general argument for probabilism about intention. To do so, I will generalize recent decision theoretic arguments for probabilism from the case of belief to the case of intention. (shrink)

We begin with a prepositional languageLpcontaining conjunction (Λ), a class of sentence names {Sα}αϵA, and a falsity predicateF. We (only) allow unrestricted infinite conjunctions, i.e., given any non-empty class of sentence names {Sβ}βϵB,is a well-formed formula (we will useWFFto denote the set of well-formed formulae).The language, as it stands, is unproblematic. Whether various paradoxes are produced depends on which names are assigned to which sentences. What is needed is a denotation function:For example, theLPsentence “F(S1)” (i.e.,Λ{F(S1)}), combined with a denotation functionδsuch (...) thatδ(S1)“F(S1)”, provides the (or, in this context, a)Liar Paradox.To give a more interesting example,Yablo's Paradox[4] can be reconstructed within this framework.Yablo's Paradoxconsists of an ω-sequence of sentences {Sk}kϵωwhere, for eachnϵω:WithinLPan equivalent construction can be obtained using infinite conjunction in place of universal quantification - the sentence names are {Si}iϵωand the denotation function is given by:We can express this in more familiar terms as:etc. (shrink)

The ?no???no? paradox (so-called by Sorensen) consists of a pair of propositions each of which says of the other that it is false. It is not immediately paradoxical, since it has a solution in which one proposition is true, the other false. However, that is itself paradoxical, since there is no clear ground for determining which is which. The two propositions should have the same truth-value. The paper shows how a proposal by the medieval thinker Thomas Bradwardine solves not (...) only the Liar paradox, but also symmetric paradoxes like the ?no???no?, the descending ?no???no?, and the Truth-teller paradoxes. (shrink)

This paper sets out a predicative response to the Russell-Myhill paradox of propositions within the framework of Church’s intensional logic. A predicative response places restrictions on the full comprehension schema, which asserts that every formula determines a higher-order entity. In addition to motivating the restriction on the comprehension schema from intuitions about the stability of reference, this paper contains a consistency proof for the predicative response to the Russell-Myhill paradox. The models used to establish this consistency also model (...) other axioms of Church’s intensional logic that have been criticized by Parsons and Klement: this, it turns out, is due to resources which also permit an interpretation of a fragment of Gallin’s intensional logic. Finally, the relation between the predicative response to the Russell-Myhill paradox of propositions and the Russell paradox of sets is discussed, and it is shown that the predicative conception of set induced by this predicative intensional logic allows one to respond to the Wehmeier problem of many non-extensions. (shrink)

ABSTRACT:The oft-cited privacy paradox is the perceived disconnect between individuals’ stated privacy expectations, as captured in surveys, and consumer market behavior in going online: individuals purport to value privacy yet still disclose information to firms. The goal of this paper is to empirically examine the conceptualization of privacy postdisclosure assumed in the privacy paradox. Contrary to the privacy paradox, the results here suggest consumers retain strong privacy expectations even after disclosing information. Privacy violations are valued akin to (...) security violations in creating distrust in firms and in consumer willingness to engage with firms. This paper broadens the scope of corporate responsibility to suggest firms have a positive obligation to identify reasonable expectations of privacy of consumers. In addition, research perpetuating the privacy paradox, through the mistaken framing of disclosure as proof of anti-privacy behavior, gives license to firms to act contrary to the interests of consumers. (shrink)

Fitch’s Paradox shows that if every truth is knowable, then every truth is known. Standard diagnoses identify the factivity/negative infallibility of the knowledge operator and Moorean contradictions as the root source of the result. This paper generalises Fitch’s result to show that such diagnoses are mistaken. In place of factivity/negative infallibility, the weaker assumption of any ‘level-bridging principle’ suffices. A consequence is that the result holds for some logics in which the “Moorean contradiction” commonly thought to underlie the result (...) is in fact consistent. This generalised result improves on the current understanding of Fitch’s result and widens the range of modalities of philosophical interest to which the result might be fruitfully applied. Along the way, we also consider a semantic explanation for Fitch’s result which answers a challenge raised by Kvanvig. (shrink)

There is significant interest in type-free systems that allow flexible self-application. Such systems are of interest in property theory, natural language semantics, the theory of truth, theoretical computer science, the theory of classes, and category theory. While there are a variety of proposed type-free systems, there is a particularly natural type-free system that we believe is prototypical: the logic of recursive algorithms. Algorithmic logic is the study of basic statements concerning algorithms and the algorithmic rules of inference between such statements. (...) As shown in [1], the threat of paradoxes, such as the Curry paradox, requires care in implementing rules of inference in this context. As in any type-free logic, some traditional rules will fail. The first part of the paper develops a rich collection of inference rules that do not lead to paradox. The second part identifies traditional rules of logic that are paradoxical in algorithmic logic, and so should be viewed with suspicion in type-free logic generally. (shrink)

The Preface Paradox apparently shows that it is sometimes rational to believe logically incompatible propositions. In this paper, I propose a way out of the paradox based on the ideas of fallibilism and verisimilitude. More precisely, I defend the view that a rational inquirer can fallibly believe or accept a proposition which is false, or likely false, but verisimilar; and I argue that this view makes the Preface Paradox disappear. Some possible objections to my proposal, and an (...) alternative view of fallible belief, are briefly discussed in the final part of the paper. (shrink)

Charlie Pelling has recently argued that two leading accounts of the norm of assertion, the truth account and a version of the knowledge account, invite paradoxand so must be false. Pelling’s arguments assume that an isolated utterance of the sentence “This assertion is improper” counts as making an assertion. I argue that this assumption is questionable.

The premises that a four foot man is short and that a man one tenth of an inch taller than a short man is also short entail by universal instantiation and "modus ponens" that a seven foot man is short. The negation of the second premise seems to entail there are virtually no borderline cases of short men, While to deny the second premise and its negation conflicts with the principle of bivalence, If not excluded middle. But the paradox (...) can be dissolved without resort to degrees of truth or any non-Classical system of logic. If some true predications can be semantically uncertain in a sense suitable for defining borderline cases, The second premise can be denied without denying the vagueness of "short" or reintroducing a sorites paradox along with higher order borderline cases. (shrink)

The Gibbs Paradox is essentially a set of open questions as to how sameness of gases or fluids are to be treated in thermodynamics and statistical mechanics. They have a variety of answers, some restricted to quantum theory, some to classical theory. The solution offered here applies to both in equal measure, and is based on the concept of particle indistinguishability. Correctly understood, it is the elimination of sequence position as a labelling device, where sequences enter at the level (...) of the tensor product of one-particle state spaces. In both cases it amounts to passing to the quotient space under permutations. ‘Distinguishability’, in the sense in which it is usually used in classical statistical mechanics, is a mathematically convenient, but physically muddled, fiction. (shrink)