The aim of the paper is to argue that all—or almost all—logical rules have exceptions. In particular, it is argued that this is a moral that we should draw from the semantic paradoxes. The idea that we should respond to the paradoxes by revising logic in some way is familiar. But previous proposals advocate the replacement of classical logic with some alternative logic. That is, some alternative system of rules, where it is taken for granted that these hold without exception. (...) The present proposal is quite different. According to this, there is no such alternative logic. Rather, classical logic retains the status of the ‘one true logic’, but this status must be reconceived so as to be compatible with (almost) all of its rules admitting of exceptions. This would seem to have significant repercussions for a range of widely held views about logic: e.g. that it is a priori, or that it is necessary. Indeed, if the arguments of the paper succeed, then such views must be given up. (shrink)

This paper argues that we should solve paradoxes for propositions (such as the Russell–Myhill paradox) in essentially the same way that we solve Russellian paradoxes for sets. That is, the standard, iterative approach to sets is extended to include properties, and then the resulting hierarchy of sets and properties is used to construct propositions. Propositions on this account are structured in the sense of mirroring the sentences that express them, and they would seem to serve the needs of philosophers of (...) language and metaphysicians who rely on such propositions. The resulting account has limitations, comparable to those faced by the iterative approach to sets, but it is argued to be in important ways preferable to others that have been proposed. (shrink)

Are there ‘self-referential’ propositions? That is, propositions that say of themselves that they have a certain property, such as that of being false. There can seem reason to doubt that there are. At the same time, there are a number of reasons why it matters. For suppose that there are indeed no such propositions. One might then hope that while paradoxes such as the Liar show that many plausible principles about sentences must be given up, no such fate will befall (...) principles about propositions. But the existence of self-referential propositions would dash such hopes. Further, the existence of such propositions would also seem to challenge the widespread claim that Liar sentences fail to express propositions. The aim of this paper is thus to settle the question–at least given an assumption. In particular, I argue that if propositions are structured, then self-referential propositions exist. (shrink)

Ontological pluralism is the view that there are different ways to exist. It is a position with deep roots in the history of philosophy, and in which there has been a recent resurgence of interest. In contemporary presentations, it is stated in terms of fundamental languages: as the view that such languages contain more than one quantifier. For example, one ranging over abstract objects, and another over concrete ones. A natural worry, however, is that the languages proposed by the pluralist (...) are mere notational variants of those proposed by the monist, in which case the debate between the two positions would not seem to be substantive. Jason Turner has given an ingenious response to this worry, in terms of a principle that he calls ‘logical realism’. This paper offers a counter-response on behalf of the ‘notationalist’. I argue that, properly applied, the principle of logical realism is no threat to the claim that the languages in question are notational variants. Indeed, there seems to be every reason to think that they are. (shrink)

Are there different sizes of infinity? That is, are there infinite sets of different sizes? This is one of the most natural questions that one can ask about the infinite. But it is of course generally taken to be settled by mathematical results, such as Cantor’s theorem, to the effect that there are infinite sets without bijections between them. These results settle the question, given an almost universally accepted principle relating size to the existence of functions. The principle is: for (...) any sets A and B, if A is the same size as B, then there is a bijection from A to B. The aim of the paper, however, is to argue that this question is in fact wide open: to argue that we are not in a position to know the answer, because we are not in one to know the principle. The aim, that is, is to argue that for all we know there is only one size of infinity. (shrink)

I argue that dialetheists have a problem with the concept of logical consequence. The upshot of this problem is that dialetheists must appeal to a hierarchy of concepts of logical consequence. Since this hierarchy is akin to those invoked by more orthodox resolutions of the semantic paradoxes, its emergence would appear to seriously undermine the dialetheic treatments of these paradoxes. And since these are central to the case for dialetheism, this would represent a significant blow to the position itself.

I argue that dialetheists have a problem with the concept of logical consequence. The upshot of this problem is that dialetheists must appeal to a hierarchy of concepts of logical consequence. Since this hierarchy is akin to those invoked by more orthodox resolutions of the semantic paradoxes, its emergence would appear to seriously undermine the dialetheic treatments of these paradoxes. And since these are central to the case for dialetheism, this would represent a significant blow to the position itself.

This chapter challenges Cantor’s notion of the ‘power’, or ‘cardinality’, of an infinite set. According to Cantor, two infinite sets have the same cardinality if and only if there is a one-to-one correspondence between them. Cantor showed that there are infinite sets that do not have the same cardinality in this sense. Further, he took this result to show that there are infinite sets of different sizes. This has become the standard understanding of the result. The chapter challenges this, arguing (...) that we have no reason to think there are infinite sets of different sizes. It begins with an initial argument against Cantor’s claim that there are infinite sets of different sizes and then proceeds, by way of an analogy between Cantor’s mathematical result and Russell’s paradox, to a more direct argument. (shrink)

Metaphysically possible worlds have many uses. Epistemically possible worlds promise to be similarly useful, especially in connection with propositions and propositional attitudes. However, I argue that there is a serious threat to the natural accounts of epistemically possible worlds, from a version of Russell’s paradox. I contrast this threat with David Kaplan’s problem for metaphysical possible world semantics: Kaplan’s problem can be straightforwardly rebutted, the problems I raise cannot. I argue that although there may be coherent accounts of epistemically possible (...) worlds with fruitful applications, any such an account must fundamentally compromise the basic idea behind epistemic possibility. (shrink)

The notion of a proposition is central to philosophy. But it is subject to paradoxes. A natural response is a hierarchical account and, ever since Russell proposed his theory of types in 1908, this has been the strategy of choice. But in this paper I raise a problem for such accounts. While this does not seem to have been recognized before, it would seem to render existing such accounts inadequate. The main purpose of the paper, however, is to provide a (...) new hierarchical account that solves the problem. (shrink)

A necessarily true sentence is 'brute' if it does not rigidly refer to anything and if it cannot be reduced to a logical truth. The question of whether there are brute necessities is an extremely natural one. Cian Dorr has recently argued for far-reaching metaphysical claims on the basis of the principle that there are no brute necessities: he initially argued that there are no non-symmetric relations, and later that there are no abstract objects at all. I argue that there (...) are nominalistically acceptable brute necessities, and that Dorr's arguments thus fail. My argument is an application of Gödel's first incompleteness theorem. (shrink)

Kripke [1975] gives a formal theory of truth based on Kleene's strong evaluation scheme. It is probably the most important and influential that has yet been given—at least since Tarski. However, it has been argued that this theory has a problem with generalized quantifiers such as All—that is, All ϕs are ψ—or Most. Specifically, it has been argued that such quantifiers preclude the existence of just the sort of language that Kripke aims to deliver—one that contains its own truth predicate. (...) In this paper I solve the problem by showing how Kleene's strong scheme, and Kripke's theory based on it, can in a natural way be extended to accommodate the full range of generalized quantifiers. (shrink)

This is a reply to Vann McGee’s response to my paper, ‘On Infinite Size’.

Plausibly, mathematical claims are true, but the fundamental furniture of the world does not include mathematical objects. This can be made sense of by providing mathematical claims with paraphrases, which make clear how the truth of such claims does not require the fundamental existence of mathematical objects. This paper explores the consequences of this type of position for explanatory structure. There is an apparently straightforward relationship between this sort of structure, and the logical sort: i.e. logically complex claims are explained (...) by logically simpler ones. For example, disjunctions are explained by their (true) disjuncts, while generalizations are explained by their (true) instances. This would seem as plausible in the case of mathematics as elsewhere. Also, it would seem to be something that the anti-realist approaches at issue would want to preserve. It will be argued, however, that these approaches cannot do this: they lead not merely to violations of the familiar principles relating logical and explanatory structure, but even to reversals of these. That is, there are cases where generalizations explain their instances, or disjunctions their disjuncts. (shrink)

Here are two plausible ideas about belief. First: beliefs are our means of storing information. Second: if we believe something, then we are willing to use it in reasoning. But in this paper I introduce a puzzle that seems to show that these cannot both be right. The solution, I argue, is a new picture, on which there is a kind of belief for each idea. An account of these two kinds of belief is offered in terms of two components: (...) a relatively stable one, which represents our information; and a more variable one, which represents what we are taking seriously. I also consider the possibility of solving the puzzle by less radical means; and an alternative argument for the proposed account of belief in terms of considerations from desire. (shrink)

Unfortunately, there is a mistake in line 10 of Section 1.2. The correct reference should read: As Kripke pointed out, we can produce one simply by baptizing the string ‘Jack is short’: Jack.

This paper addresses the question: given some theory T that we accept, is there some natural, generally applicable way of extending T to a theory S that can prove a range of things about what it itself (i.e. S) can prove, including a range of things about what it cannot prove, such as claims to the effect that it cannot prove certain particular sentences (e.g. 0 = 1), or the claim that it is consistent? Typical characterizations of Gödel’s second incompleteness (...) theorem, and its significance, would lead us to believe that the answer is ‘no’. But the present paper explores a positive answer. The general approach is to follow the lead of recent (and not so recent) approaches to truth and the Liar paradox. (shrink)

Approaches to truth and the Liar paradox seem invariably to face a dilemma: either appeal to some sort of hierarchy, or declare apparently perfectly coherent concepts incoherent. But since both options lead to severe expressive restrictions, neither seems satisfactory. The aim of this paper is a new approach, which avoids the dilemma and the resulting expressive restrictions. Previous approaches tend to appeal to some new sort of semantic value for the truth predicate to take. I argue that such approaches inevitably (...) lead to the dilemma in question. In contrast, the present proposal sticks with classical semantic values, but allows the compositional rules associated with these to admit of exceptions. I show how such an approach can be developed systematically. (shrink)

I distinguish between two opposing intuitions about the nature of the singular causal relation. The first stresses the nomological character of causation, while the second emphasises is seemingly local character. My question is this: is it possible to formulate an account of causation which incorporates both intuitions? Anscombe gives us reason to think that these intuitions could not be jointly met in an account of causation. Foster and Tooley's acount seems to provide a counter-instance to her claim, but this proves (...) to be a false start. I put forward an alternative suggestion which, by utilising tropes, manages to reconcile both the local and nomological character of causation. (shrink)

From the book: What is to be done with political ecology? Nothing. What is to be done? Political ecology!

This book presents a posthumous collection of previously uncollected works of political theory written by Whittle Johnston. Johnston believed that both the liberal tradition of political thought and the realist tradition of international thought had contributed much to humanity's store of political wisdom, but that each had limitations that could most easily be recognized by its encounter with the other. His method of accomplishing this task was to examine the liberal conception of political life in general and international political (...) life in particular and then to explore the realist critique of the liberal view, particularly as it was expressed by three great twentieth-century realist thinkers, all of whom were, in their various ways, skeptical of liberal assumptions: Reinhold Niebuhr, Hans Morgenthau, and E. H. Carr. In doing so, Johnston reveals the power of the realist outlook, but also the areas in which it remains insufficient, and insufficient particularly where it underestimates the complexity and prudence that liberalism is capable of displaying. There have been studies of both liberalism and realism, but no other work has put them into conversation with each other in the way that this book does. (shrink)

In an outline of a paper found amongst his philosophical papers and correspondence after his untimely death in 2001—“Nihil Obstat: An Analysis of Ability,” reproduced in this volume—David Lewis sketched a new compatibilist account of abilities, according to which someone is able to A if and only if there is no obstacle to their A-ing, where an obstacle is a ‘robust preventer’ of their A-ing. In this paper, we provide some background context for Lewis’s outline, a section-by-section commentary, and a (...) general discussion of the account’s main features. (shrink)

Giordano Bruno's notorious public death in 1600, at the hands of the Inquisition in Rome, marked the transition from Renaissance philosophy to the Scientific Revolution of the seventeenth century. In his philosophical works he addressed such delicate issues as the role of Christ as mediator and the distinction, in human beings, between soul and matter. This volume presents new translations of Cause, Principle and Unity, in which he challenges Aristotelian accounts of causality and spells out the implications of Copernicanism (...) for a new theory of an infinite universe, and of two essays on magic, On Magic and A General Account of Bonding, in which he interprets earlier theories about magical events in the light of the unusual powers of natural phenomena. (shrink)

L'origine dell'anima umana secondo Dante.--La dottrina d'Alberto Magno sull'Inchoatio formae.--Alberto Magno e san Tommaso.--La posizione di Alberto Magno di fronte all'averroismo.--L'anima umana secondo Sigieri.--Anima e corpo nel pensiero di san Tommaso.--L'aristotelismo della scolastica e i francescani.--Individualità e immortalità nell'averroismo e nel tomismo.

Whilst the academic literature on leadership has identified authenticity as an important leadership attribute, few studies have examined how authentic leadership is evaluated in naturally occurring discourse. This article explores how authentic leadership was characterised and evaluated in the discourse of the British press during the 2015 Labour Party leadership election—won, against the odds, by veteran left-winger Jeremy Corbyn. Using membership categorisation analysis, we show that the media discourse about authentic leadership was both ambiguous and ambivalent. In their representation of (...) authentic leadership, we found that a discourse of ‘ethical’ leadership was played out in tension with a discourse of ‘effective’ leadership. We propose that this complex and contradictory discursive landscape is also relevant in business contexts where ‘ethical’ leaders are subjected to praise for their virtues but also criticism for their ineffectiveness. Future research could usefully study how ‘ethical’ leaders in different settings can be subject to competing evaluations when their ethical values are discursively contrasted to expectations concerning what it takes to be an ‘effective’ leader. (shrink)

Ann Whittle offers a fresh approach to questions about whether our actions are free and whether we are morally responsible for them. She argues that the answers to these questions depend on the contexts in which we make claims about our abilities and our control over our actions.

Dispositional compatibilists argue that a proper understanding of our abilities vindicates both compatibilism and the principle of Alternate Possibilities (the claim that the ability to do otherwise is required for freedom and moral responsibility). In this paper, I argue that this is mistaken. Both analyses of dispositions and abilities should distinguish between local and global dispositions or abilities. Once this distinction is in place, we see that neither thesis is established by an analysis of abilities.

Fichte assigns ‘intellectual intuition’ a new meaning after Kant. But in 1799, his doctrine of intellectual intuition is publicly deemed indefensible by Kant and nihilistic by Jacobi. I propose to defend Fichte’s doctrine against these charges, leaving aside whether it captures what he calls the ‘spirit’ of transcendental idealism. I do so by articulating three problems that motivate Fichte’s redirection of intellectual intuition from being to acting: (1) the regress problem, which states that reflecting on empirical facts of consciousness leads (...) only to further facts and so cannot yield a first principle; (2) the rhapsody problem, which states that the categories form a haphazard set and so lack necessity unless they derive from a first principle; and (3) the nihilism problem, which states that a first principle cannot lie outside our cognition of it, lest it be the cause of our cognition and, being first, the cause of all our actions, reducing us to machines. Crucially, Fichte’s three motivating problems are in fact aspects of a single problem. Leaving any aspect unsolved spoils putative solutions to the other two. Consequently, Fichte requires a single unified solution to all three, which his doctrine of intellectual intuition provides. (shrink)

I argue against the interpretation of propositions as intentions and proof-objects as fulfillments proposed by Heyting and defended by Tieszen and van Atten. The idea is already a frequent target of criticisms regarding the incompatibility of Brouwer’s and Husserl’s positions, mainly by Rosado Haddock and Hill. I raise a stronger objection in this paper. My claim is that even if we grant that the incompatibility can be properly dealt with, as van Atten believes it can, two fundamental issues indicate that (...) the interpretation is unsustainable regardless: (1) it is hard to determine, without appealing to propositional intentions on pain of circularity, what intention a proof-object should be understood as a fulfillment of; (2) due to a difficult fulfillment dilemma, it is unclear, at best, what the object of an intention corresponding to a proposition is. (shrink)

One of the most debated questions in psychology and cognitive science is the nature and the functioning of the mental processes involved in deductive reasoning. However, all existing theories refer to a specific deductive domain, like syllogistic, propositional or relational reasoning.Our goal is to unify the main types of deductive reasoning into a single set of basic procedures. In particular, we bring together the microtheories developed from a mental models perspective in a single theory, for which we provide a formal (...) foundation. We validate the theory through a computational model (UNICORE) which allows fine‐grained predictions of subjects' performance in different reasoning domains.The performance of the model is tested against the performance of experimental subjects—as reported in the relevant literature—in the three areas of syllogistic, relational and propositional reasoning. The computational model proves to be a satisfactory artificial subject, reproducing both correct and erroneous performance of the human subjects. Moreover, we introduce a developmental trend in the program, in order to simulate the performance of subjects of different ages, ranging from children (3–6) to adolescents (8–12) to adults (>21). The simulation model performs similarly to the subjects of different ages.Our conclusion is that the validity of the mental model approach is confirmed for the deductive reasoning domain, and that it is possible to devise a unique mechanism able to deal with the specific subareas. The proposed computational model (UNICORE) represents such a unifying structure. (shrink)

General-elimination harmony articulates Gentzen’s idea that the elimination-rules are justified if they infer from an assertion no more than can already be inferred from the grounds for making it. Dummett described the rules as not only harmonious but stable if the E-rules allow one to infer no more and no less than the I-rules justify. Pfenning and Davies call the rules locally complete if the E-rules are strong enough to allow one to infer the original judgement. A method is given (...) of generating harmonious general-elimination rules from a collection of I-rules. We show that the general-elimination rules satisfy Pfenning and Davies’ test for local completeness, but question whether that is enough to show that they are stable. Alternative conditions for stability are considered, including equivalence between the introduction- and elimination-meanings of a connective, and recovery of the grounds for assertion, finally generalizing the notion of local completeness to capture Dummett’s notion of stability satisfactorily. We show that the general-elimination rules meet the last of these conditions, and so are indeed not only harmonious but also stable. (shrink)

_Badiou and Politics_ offers a much-anticipated interpretation of the work of the influential French philosopher Alain Badiou. Countering ideas of the philosopher as a dogmatic, absolutist, or even mystical thinker enthralled by the force of the event as a radical break, Bruno Bosteels reveals Badiou’s deep and ongoing investment in the dialectic. Bosteels draws on all of Badiou’s writings, from the philosopher’s student days in the 1960s to the present, as well as on Badiou’s exchanges with other thinkers, from (...) his avowed “masters” Louis Althusser and Jacques Lacan, to interlocutors including Gilles Deleuze, Slavoj Žižek, Daniel Bensaïd, Jacques Derrida, Ernesto Laclau, and Judith Butler. Bosteels tracks the philosopher’s political activities from the events of May 1968 through his embrace of Maoism and the work he has done since the 1980s, helping to mobilize France’s illegal immigrants or _sans-papiers_. Ultimately, Bosteels argues for understanding Badiou’s thought as a revival of dialectical materialism, and he illuminates the philosopher’s understanding of the task of theory: to define a conceptual space for thinking emancipatory politics in the present. (shrink)