Science Without Numbers caused a stir in 1980, with its bold nominalist approach to the philosophy of mathematics and science. It has been unavailable for twenty years and is now reissued in a revised edition with a substantial new preface presenting the author's current views and responses to the issues raised in subsequent debate.

A selective background -- Broadly classical approaches -- Paracompleteness -- More on paracomplete solutions -- Paraconsistent dialetheism.

Presenting a selection of thirteen essays on various topics at the foundations of philosophy--one previously unpublished and eight accompanied by substantial new postscripts--this book offers outstanding insight on truth, meaning, and propositional attitudes; semantic indeterminacy and other kinds of "factual defectiveness;" and issues concerning objectivity, especially in mathematics and in epistemology. It will reward the attention of any philosopher interested in language, epistemology, or mathematics.

We argue that some recent theories of attentional normativity license predictable misevaluations of neurodivergent cognizers. We suggest that this is because norms of attention have mostly been theorized without neuroatypical cognizers in mind. We argue that because these norms tend to focus on features that only correlate with positively evaluable cognition in neurotypical agents, they are very often false when applied to neurodivergent cognition. Additionally, we suggest that these norms license unjust evaluations of neurodivergent cognizers, because they predictably evaluate neurodivergent (...) cognition negatively, in many cases erroneously. After exploring some ways that existing views of attentional normativity might try to accommodate neurodivergent cognition, we propose a new constitutivist framework for evaluating cognition that does better. (shrink)

The paper tries to spell out a connection between deductive logic and rationality, against Harman's arguments that there is no such connection, and also against the thought that any such connection would preclude rational change in logic. One might not need to connect logic to rationality if one could view logic as the science of what preserves truth by a certain kind of necessity (or by necessity plus logical form); but the paper points out a serious obstacle to any such (...) view. (shrink)

What are people who disagree about logic disagreeing about? The paper argues that (in a wide range of cases) they are primarily disagreeing about how to regulate their degrees of belief. An analogy is drawn between beliefs about validity and beliefs about chance: both sorts of belief serve primarily to regulate degrees of belief about other matters, but in both cases the concepts have a kind of objectivity nonetheless.

The paper outlines a view of normativity that combines elements of relativism and expressivism, and applies it to normative concepts in epistemology. The result is a kind of epistemological anti-realism, which denies that epistemic norms can be (in any straightforward sense) correct or incorrect; it does allow some to be better than others, but takes this to be goal-relative and is skeptical of the existence of best norms. It discusses the circularity that arises from the fact that we need to (...) use epistemic norms to gather the facts with which to evaluate epistemic norms; relatedly, it discusses how epistemic norms can rationally evolve. It concludes with some discussion of the impact of this view on "ground level" epistemology. (shrink)

Common-sense reasoning with truth involves both (i) the use of classical logic and (ii) the assumption of the transparency of truth (the equivalence between a sentence and the attribution of truth to it). The semantic paradoxes show that at least one of these must go, and different theorists make different choices. But whatever one’s choice, it’s valuable to carve out one or more domains where common sense reasoning ((i) and (ii) together) can be safely used; domains where everything is well-behaved. (...) The paper explores adding a predicate of well-behavedness to various truth theories, both classical and nonclassical (including non-classical theories with special conditionals). With such a predicate, one can reason more easily, and formulate important generalizations that are unavailable without such a predicate. The paper explores general model-theoretic techniques that can be applied to both classical and non-classical theories of truth to get corresponding accounts of well-behaved truth, and some of the important generalizations that such model theories validate. It has incidental remarks about axiomatic theories that might be associated with the model theories, and their proof-theoretic strength. (shrink)

This book offers a detailed study of the political philosophies of Thomas Hobbes and Benedict de Spinoza, focussing on their concept of power as potentia, concrete power, rather than power as potestas, authorised power. The focus on power as potentia generates a new conception of popular power. Radical democrats–whether drawing on Hobbes's 'sleeping sovereign' or on Spinoza's 'multitude'–understand popular power as something that transcends ordinary institutional politics, as for instance popular plebsites or mass movements. However, the book argues that these (...) understandings reflect a residual scholasticism which Hobbes and Spinoza ultimately repudiate. Instead, on the book's revisionist conception, a political phenomenon should be said to express popular power when it is both popular (it eliminates oligarchy and encompasses the whole polity), and also powerful (it robustly determines political and social outcomes). Two possible institutional forms that this popular power might take are distinguished: Hobbesian repressive egalitarianism, or Spinozist civic strengthening. But despite divergent institutional proposals, the book argues that both Hobbes and Spinoza share the conviction that there is nothing spontaneously egalitarian or good about human collective existence. From this point of view, the book accuses radical democrats of pernicious romanticism; the slow, meticulous work of organizational design and maintenance is the true centre of popular power. Three minute video summary available via HPBin3. Extended discussion on The Political Theory Review podcast. First chapter open access available via Oxford Scholarship Online. Videos of book talks at National University of Singapore (Centre for Legal Theory) and Universidad de Buenos Aires (Instituto de Investigaciones Gino Germani) available via YouTube. (See links below.). (shrink)

There are quite a few theses about logic that are in one way or another pluralist: they hold (i) that there is no uniquely correct logic, and (ii) that because of this, some or all debates about logic are illusory, or need to be somehow reconceived as not straightforwardly factual. Pluralist theses differ markedly over the reasons offered for there being no uniquely correct logic. Some such theses are more interesting than others, because they more radically affect how we are (...) initially inclined to understand debates about logic. Can one find a pluralist thesis that is high on the interest scale, and also true? (shrink)

Nonclassical theories of truth that take truth to be transparent have some obvious advantages over any classical theory of truth. But several authors have recently argued that there’s also a big disadvantage of nonclassical theories as compared to their “external” classical counterparts: proof-theoretic strength. While conceding the relevance of this, the paper argues that there is a natural way to beef up extant internal theories so as to remove their proof-theoretic disadvantage. It is suggested that the resulting internal theories are (...) preferable to their external counterparts. (shrink)

Bayesian decision theory can be viewed as the core of psychological theory for idealized agents. To get a complete psychological theory for such agents, you have to supplement it with input and output laws. On a Bayesian theory that employs strict conditionalization, the input laws are easy to give. On a Bayesian theory that employs Jeffrey conditionalization, there appears to be a considerable problem with giving the input laws. However, Jeffrey conditionalization can be reformulated so that the problem disappears, and (...) in fact the reformulated version is more natural and easier to work with on independent grounds. (shrink)

Can we make mistakes about what rationality requires? A natural answer is that we can, since it is a platitude that rational belief does not require truth; it is possible for a belief to be rational and mistaken, and this holds for any subject matter at all. However, the platitude causes trouble when applied to rationality itself. The possibility of rational mistakes about what rationality requires generates a puzzle. When combined with two further plausible claims – the enkratic principle, and (...) the claim that rational requirements apply universally – we get the result that rationality generates inconsistent requirements. One popular and attractive solution to the puzzle denies that it is possible to make rational mistakes about what rationality requires. I show why (contra Titelbaum (2015b), and Littlejohn (2015)) this solution is doomed to fail. (shrink)

1. Of what use is the concept of causation? Bertrand Russell [1912-13] argued that it is not useful: it is “a relic of a bygone age, surviving, like the monarchy, only because it is erroneously supposed to do no harm.” His argument for this was that the kind of physical theories that we have come to regard as fundamental leave no place for the notion of causation: not only does the word ‘cause’ not appear in the advanced sciences, but the (...) laws that these sciences state are incompatible with causation as we normally understand it. But Nancy Cartwright has argued [1979] that abandoning the concept of causation would cripple science; her conclusion was based not on fundamental physics, but on more ordinary science such as the search for the causes of cancer. She argues that Russell was right that the fundamental theories of modern physics say nothing, even implicitly, about causation, and concludes on this basis that such theories are incomplete. It is with this cluster of issues that I will begin my discussion. (shrink)

Neurodiversity is the idea that many psychological traits commonly conceived of as deficiencies are better described merely as differences. Epistemic appraisal sorts good cognition from bad, so epistemologists should be particularly aware of when cognition that departs from the norm is different, rather than deficient. This entry gives an overview of the relevance of neurodiversity to epistemic appraisal.

Are there questions for which 'there is no determinate fact of the matter' as to which answer is correct? Most of us think so, but there are serious difficulties in maintaining the view, and in explaining the idea of determinateness in a satisfactory manner. The paper argues that to overcome the difficulties, we need to reject the law of excluded middle; and it investigates the sense of 'rejection' that is involved. The paper also explores the logic that is required if (...) we reject excluded middle, with special emphasis on the conditional. There is also discussion of higher order indeterminacy (in several different senses) and of penumbral connections; and there is a suggested definition of determinateness in terms of the conditional and a discussion of the extent to which the notion of determinateness is objective. And there are suggestions about a unified treatment of vagueness and the semantic paradoxes. (shrink)

Any theory of truth must find a way around Curry’s paradox, and there are well-known ways to do so. This paper concerns an apparently analogous paradox, about validity rather than truth, which JC Beall and Julien Murzi call the v-Curry. They argue that there are reasons to want a common solution to it and the standard Curry paradox, and that this rules out the solutions to the latter offered by most “naive truth theorists.” To this end they recommend a radical (...) solution to both paradoxes, involving a substructural logic, in particular, one without structural contraction. In this paper I argue that substructuralism is unnecessary. Diagnosing the “v-Curry” is complicated because of a multiplicity of readings of the principles it relies on. But these principles are not analogous to the principles of naive truth, and taken together, there is no reading of them that should have much appeal to anyone who has absorbed the morals of both the ordinary Curry paradox and the second incompleteness theorem. (shrink)

This paper extends Kripke’s theory of truth to a language with a variably strict conditional operator, of the kind that Stalnaker and others have used to represent ordinary indicative conditionals of English. It then shows how to combine this with a different and independently motivated conditional operator, to get a substantial logic of restricted quantification within naive truth theory.

Since the 1970’s there has been a major increase in adventure sports participation but it seems that engagement in such sports comes with a stigma: adventure sports participants are often regarded as reckless ‘daredevils’. We approach the questions about people’s perception of risk and recklessness in adventure sports by combining empirical research with philosophical analysis. First, we provide empirical evidence that suggests that laypeople tend to assess the danger of adventure sports as greater than more mundane sports and judge adventure (...) sports participants as more reckless than participants in non-adventure sports. We contextualise these findings within existing psychological risk perception paradigms and outline new philosophical explanations of the identified pattern in laypeople’s risk perception. (shrink)

I argue that there are some situations in which it is praiseworthy to be motivated only by moral rightness de dicto, even if this results in wrongdoing. I consider a set of cases that are challenging for views that dispute this, prioritising concern for what is morally important in moral evaluation. In these cases, the agent is not concerned about what is morally important, does the wrong thing, but nevertheless seems praiseworthy rather than blameworthy. I argue that the views under (...) discussion cannot accommodate this, and should be amended to recognise that it is often praiseworthy to be motivated to do what is right. (shrink)

A correspondence theory of truth explains truth in terms of various correspondence relations (e.G., Reference) between words and the extralinguistic world. What are the consequences of quine's doctrine of indeterminacy for correspondence theories? in "ontological relativity" quine implicitly claims that correspondence theories are impossible; that is what the doctrine of 'relative reference' amounts to. But quine's doctrine of relative reference is incoherent. Those who think the indeterminacy thesis valid should not try to relativize reference, They should abandon the relation and (...) replace it by certain more general correspondence relations between words and extralinguistic objects. Doing so will not interfere with the task of defining truth in terms of correspondence relations. (shrink)

The Enkratic Principle enjoys something of a protected status as a requirement of rationality. I argue that this status is undeserved, at least in the epistemic domain. Compliance with the principle should not be thought of as a requirement of epistemic rationality, but rather as defeasible indication of epistemic blamelessness. To show this, I present the Puzzle of Inconsistent Requirements, and argue that the best way to solve it is to distinguish two kinds of epistemic evaluation – requirement evaluations and (...) appraisal evaluations. This allows us to solve the puzzle while accommodating traditional motivations for thinking of the Enkratic Principle as a requirement of rationality. (shrink)

This paper is concerned with the debate between substantival and relational theories of space-time, and discusses two difficulties that beset the relationalist: a difficulty posed by field theories, and another difficulty called the problem of quantities. A main purpose of the paper is to argue that possibility can not always be used as a surrogate of ontology, and that in particular that there is no hope of using possibility to solve the problem of quantities.

This paper offers a substantial improvement in the revision-theoretic approach to conditionals in theories of transparent truth. The main modifications are (i) a new limit rule; (ii) a modification of the extension to the continuum-valued case; and (iii) the suggestion of a variation on how universal quantification is handled, leading to more satisfactory laws of restricted quantification.

The paper offers a solution to the semantic paradoxes, one in which (1) we keep the unrestricted truth schema “True(A)↔A”, and (2) the object language can include its own metalanguage. Because of the first feature, classical logic must be restricted, but full classical reasoning applies in “ordinary” contexts, including standard set theory. The more general logic that replaces classical logic includes a principle of substitutivity of equivalents, which with the truth schema leads to the general intersubstitutivity of True(A) with A (...) within the language.The logic is also shown to have the resources required to represent the way in which sentences (like the Liar sentence and the Curry sentence) that lead to paradox in classical logic are “defective”. We can in fact define a hierarchy of “defectiveness” predicates within the language. Contrary to claims that any solution to the paradoxes just breeds further paradoxes (“revenge problems”) involving defectiveness predicates, there is a general consistency/conservativeness proof that shows that talk of truth and the various “levels of defectiveness” can all be made coherent together within a single object language. (shrink)

The naive theory of properties states that for every condition there is a property instantiated by exactly the things which satisfy that condition. The naive theory of properties is inconsistent in classical logic, but there are many ways to obtain consistent naive theories of properties in nonclassical logics. The naive theory of classes adds to the naive theory of properties an extensionality rule or axiom, which states roughly that if two classes have exactly the same members, they are identical. In (...) this paper we examine the prospects for obtaining a satisfactory naive theory of classes. We start from a result by Ross Brady, which demonstrates the consistency of something resembling a naive theory of classes. We generalize Brady’s result somewhat and extend it to a recent system developed by Andrew Bacon. All of the theories we prove consistent contain an extensionality rule or axiom. But we argue that given the background logics, the relevant extensionality principles are too weak. For example, in some of these theories, there are universal classes which are not declared coextensive. We elucidate some very modest demands on extensionality, designed to rule out this kind of pathology. But we close by proving that even these modest demands cannot be jointly satisfied. In light of this new impossibility result, the prospects for a naive theory of classes are bleak. (shrink)

The term ‘social capital’ is a way of defining the intangible resources of community, shared values and trust upon which we draw in daily life. It has achieved considerable international currency across the social sciences through the very different work of Pierre Bourdieu in France and James Coleman and Robert Putnam in the United States, and has been widely taken up within politics and sociology as an explanation for the decline in social cohesion and community values in western societies. It (...) has also been adopted by policy makers, particularly in international governmental bodies such as the World Bank. (shrink)

Ethics and the Community of Inquiry gets to the heart of democratic education and how best to achieve it. The book radically reshapes our understanding of education by offering a framework from which to integrate curriculum, teaching and learning and to place deliberative democracy at the centre of education reform. It makes a significant contribution to current debates on educational theory and practice, in particular to pedagogical and professional practice, and ethics education.

ABSTRACT Section 1 discusses properties and propositions, and some of the motivation for an account in which property instantiation and propositional truth behave ‘naively’. Section 2 generalizes a standard Kripke construction for naive properties and propositions, in a language with modal operators but no conditionals. Whereas Kripke uses a 3-valued value space, the generalized account allows for a broad array of value spaces, including the unit interval [0,1]. This is put to use in Section 3, where I add to the (...) language a conditional suitable for restricting quantification. The shift from a value space based on the ‘mini-space’ {0,, 1} to one based on the ‘mini-space’ [0,1] leads to more satisfactory results than I was able to achieve in previous work: a vast variety of paradoxical sentences can now be treated very simply. In Section 4 I make a further addition to the language, a conditional modeled on the ordinary English conditional, paying particular attention to how it interacts with the restricted quantifier conditional. This is all done in the [0,1] framework, and two alternatives are considered for how the ordinary conditional is to be handled; one of them results from adding a tweak to a construction by Ross Brady. Section 5 discusses a further alternative, a standard relevance conditional (for the ordinary conditional, perhaps for use with a different quantifier-restricting conditional), but argues that it is not promising. Section 6 discusses the identity conditions of properties and propositions (again in the setting of a value space based on [0,1]); the issue of achieving naivety for coarse-grained properties is seen to be more complicated than some brief remarks in Field [2010] suggested, but a way to get a fair degree of coarse-grainedness is shown. (shrink)

The paper presents a kind of normative anti-realist view of epistemology, in the same ballpark as recent versions of expressivism. But the primary focus of the paper is less on this meta-epistemological view itself than on how it should affect ground-level issues in epistemology: for instance, how it should deal with certain forms of skepticism, and how it allows for fundamental revision in epistemic practices. It is hoped that these methodological consequences will seem attractive independent of the normative anti-realism. Indeed, (...) some normative realists seem to embrace the view on skepticism, but it is argued that their position is unstable: the realism undermines the methodology. The general theme of the paper is that the issue of normative realism is deeply entwined with issues of methodology, in strong contrast to the common claim that meta-epistemological views in the tradition of expressivism have no first order impact. (shrink)

Conventionalism about mathematics has much in common with two other views: fictionalism and the multiverse view (aka plenitudinous platonism). The three views may differ over the existence of mathematical objects, but they agree in rejecting a certain kind of objectivity claim about mathematics, advocating instead an extreme pluralism. The early parts of the paper will try to elucidate this anti‐objectivist position, and question whether conventionalism really offers a third form of it distinct from fictionalism and the multiverse view. The paper (...) then turns to anti‐objectivism about logic, and suggests that here too conventionalism offers no distinct alternative, and that there are limits on the extent of pluralism/anti‐objectivism. It also argues that these limits can't be used to argue for more extensive objectivity within mathematics, and also that they do allow for more limited pluralism within logic, e.g. as regards resolution of semantic and property‐theoretic paradoxes. (shrink)

Both in dealing with the semantic paradoxes and in dealing with vagueness and indeterminacy, there is some temptation to weaken classical logic: in particular, to restrict the law of excluded middle. The reasons for doing this are somewhat different in the two cases. In the case of the semantic paradoxes, a weakening of classical logic (presumably involving a restriction of excluded middle) is required if we are to preserve the naive theory of truth without inconsistency. In the case of vagueness (...) and indeterminacy, there is no worry about inconsistency; but a central intuition is that we must reject the factual status of certain sentences, and it hard to see how we can do that while claiming that the law of excluded middle applies to those sentences. So despite the different routes, we have a similar conclusion in the two cases. (shrink)