In a unique collection of essays and poems written in English, French, German and Russian (with a seasoning of Greek and Japanese), Constantine Shapiro explores fascinating universal questions and connections. Why, he asks, do so many people feel unhappy? Why do so many go to the doctor? Why is there so much criminality? Why is there international unrest? What is a healthy soul? In his investigation of these and other "Big Questions," the author examines such disparate areas as (...) Japanese kanji ideograms and personal character, spiritual ontology and science, Zeus and Christianity, objectivity and subjectivity in time and space, the nature of experience, and the flow of consciousness. The modern reader will find much to ponder in this second, expanded edition of Selected Writings. Also included are facsimiles of the typescript of Two Mathematical Problems and the Japanese translation of Transzendentale Musiklehre. (shrink)

The central contention of this book is that second-order logic has a central role to play in laying the foundations of mathematics. In order to develop the argument fully, the author presents a detailed description of higher-order logic, including a comprehensive discussion of its semantics. He goes on to demonstrate the prevalence of second-order concepts in mathematics and the extent to which mathematical ideas can be formulated in higher-order logic. He also shows how first-order languages are often insufficient to codify (...) many concepts in contemporary mathematics, and thus that both first- and higher-order logics are needed to fully reflect current work. Throughout, the emphasis is on discussing the associated philosophical and historical issues and the implications they have for foundational studies. For the most part, the author assumes little more than a familiarity with logic comparable to that provided in a beginning graduate course which includes the incompleteness of arithmetic and the Lowenheim-Skolem theorems. All those concerned with the foundations of mathematics will find this a thought-provoking discussion of some of the central issues in the field today. (shrink)

What is law (and why should we care)? -- Crazy little thing called "law" -- Austin's sanction theory -- Hart and the rule of recognition -- How to do things with plans -- The making of a legal system -- What law is -- Legal reasoning and judicial decision making -- Hard cases -- Theoretical disagreements -- Dworkin and distrust -- The economy of trust -- The interpretation of plans -- The value of legality.

A line of research within embodied cognition seeks to show that an organism’s body is a determinant of its conceptual capacities. Comparison of this claim of body determinism to linguistic determinism bears interesting results. Just as Slobin’s (1996) idea of thinking for speaking challenges the main thesis of linguistic determinism, so too the possibility of thinking for acting raises difficulties for the proponent of body determinism. However, recent studies suggest that the body may, after all, have a determining role in (...) cognitive processes of sentence comprehension. (shrink)

Equivalences and translations between consequence relations abound in logic. The notion of equivalence can be defined syntactically, in terms of translations of formulas, and order-theoretically, in terms of the associated lattices of theories. W. Blok and D. Pigozzi proved in [4] that the two definitions coincide in the case of an algebraizable sentential deductive system. A refined treatment of this equivalence was provided by W. Blok and B. Jónsson in [3]. Other authors have extended this result to the cases of (...) k-deductive systems and of consequence relations on associative, commutative, multiple conclusion sequents. Our main result subsumes all existing results in the literature and reveals their common character. The proofs are of order-theoretic and categorical nature. (shrink)

Jaegwon Kim’s causal exclusion argument has rarely been evaluated from an empirical perspective. This is puzzling because its conclusion seems to be making a testable claim about the world: supervenient properties are causally inefficacious. An empirical perspective, however, reveals Kim’s argument to rest on a mistaken conception about how to test whether a property is causally efficacious. Moreover, the empirical perspective makes visible a metaphysical bias that Kim brings to his argument that involves a principle of non-inclusion.

Democracy and justice are often mutually antagonistic ideas, but in this innovative book Ian Shapiro shows how and why they should be pursued together. Justice must be sought democratically if it is to garner legitimacy in the modern world, he claims, and democracy must be justice-promoting if it is to sustain allegiance over time. _Democratic Justice_ meets these criteria, offering an attractive vision of a practical path to a better future. Wherever power is exercised in human affairs, Shapiro (...) argues, the lack of democracy will be experienced as injustice. The challenge is to democratize social relations so as to diminish injustice, but to do this in ways that are compatible with people’s values and goals. Shapiro shows how this can be done in different phases of the human life cycle, from childhood through the adult worlds of work and domestic life, retirement, old age, and approaching death. He spells out the implications for pressing debates about authority over children, the law of marriage and divorce, population control, governing the firm, basic income guarantees, health insurance, retirement policies, and decisions made by and for the infirm elderly. This refreshing encounter between political philosophy and practical politics will interest all those who aspire to bequeath a more just world to our children than the one we have inherited. (shrink)

This Oxford Handbook covers the current state of the art in the philosophy of maths and logic in a comprehensive and accessible manner, giving the reader an overview of the major problems, positions, and battle lines. The 26 newly-commissioned chapters are by established experts in the field and contain both exposition and criticism as well as substantial development of their own positions. Select major positions are represented by two chapters - one supportive and one critical. The book includes a comprehensive (...) bibliography. (shrink)

_The Philosophy of Action: An Anthology_ is an authoritative collection of key work by top scholars, arranged thematically and accompanied by expert introductions written by the editors. This unique collection brings together a selection of the most influential essays from the 1960s to the present day. An invaluable collection that brings together a selection of the most important classic and contemporary articles in philosophy of action, from the 1960’s to the present day No other broad-ranging and detailed coverage of this (...) kind currently exists in the field Each themed section opens with a synoptic introduction and includes a comprehensive further reading list to guide students Includes sections on action and agency, willing and trying, intention and intentional action, acting for a reason, the explanation of action, and free agency and responsibility Written and organised in a style that allows it to be used as a primary teaching resource in its own right. (shrink)

Some authors have claimed that ante rem structuralism has problems with structures that have indiscernible places. In response, I argue that there is no requirement that mathematical objects be individuated in a non-trivial way. Metaphysical principles and intuitions to the contrary do not stand up to ordinary mathematical practice, which presupposes an identity relation that, in a sense, cannot be defined. In complex analysis, the two square roots of –1 are indiscernible: anything true of one of them is true of (...) the other. I suggest that ‘i’ functions like a parameter in natural deduction systems. I gave an early version of this paper at a workshop on structuralism in mathematics and science, held in the Autumn of 2006, at Bristol University. Thanks to the organizers, particularly Hannes Leitgeb, James Ladyman, and Øystein Linnebo, to my commentator Richard Pettigrew, and to the audience there. The paper also benefited considerably from a preliminary session at the Arché Research Centre at the University of St Andrews. I am indebted to my colleagues Craige Roberts, for help with the linguistics literature, and Ben Caplan and Gabriel Uzquiano, for help with the metaphysics. Thanks also to Hannes Leitgeb and Jeffrey Ketland for reading an earlier version of the manuscript and making helpful suggestions. I also benefited from conversations with Richard Heck, John Mayberry, Kevin Scharp, and Jason Stanley. CiteULike Connotea Del.icio.us What's this? (shrink)

This chapter provides broad coverage of the notion of logical consequence, exploring its modal, semantic, and epistemic aspects. It develops the contrast between proof-theoretic notion of consequence, in terms of deduction, and a model-theoretic approach, in terms of truth-conditions. The main purpose is to relate the formal, technical work in logic to the philosophical concepts that underlie reasoning.

The subject of this paper is the philosophical problem of accounting for the relationship between mathematics and non-mathematical reality. The first section, devoted to the importance of the problem, suggests that many of the reasons for engaging in philosophy at all make an account of the relationship between mathematics and reality a priority, not only in philosophy of mathematics and philosophy of science, but also in general epistemology/metaphysics. This is followed by a (rather brief) survey of the major, traditional philosophies (...) of mathematics indicating how each is prepared to deal with the present problem. It is shown that (the standard formulations of) some views seem to deny outright that there is a relationship between mathematics and any non-mathematical reality; such philosophies are clearly unacceptable. Other views leave the relationship rather mysterious and, thus, are incomplete at best. The final, more speculative section provides the direction of a positive account. A structuralist philosophy of mathematics is outlined and it is proposed that mathematics applies to reality though the discovery of mathematical structures underlying the non-mathematical universe. (shrink)

Jaegwon Kim’s causal exclusion argument has rarely been evaluated from an empirical perspective. This is puzzling because its conclusion seems to be making a testable claim about the world: supervenient properties are causally inefficacious. An empirical perspective, however, reveals Kim’s argument to rest on a mistaken conception about how to test whether a property is causally efficacious. Moreover, the empirical perspective makes visible a metaphysical bias that Kim brings to his argument that involves a principle of non‐inclusion.

He concludes with an assessment of democracy's strengths and limitations as the font of political legitimacy. The book offers a lucid and accessible introduction to urgent ongoing conversations about the sources of political allegiance.

ABSTRACT:I reflect critically on the early modern philosophical canon in light of the entrenchment and homogeneity of the lineup of seven core figures: Descartes, Spinoza, Leibniz, Locke, Berkeley, Hume, and Kant. After distinguishing three elements of a philosophical canon—a causal story, a set of core philosophical questions, and a set of distinctively philosophical works—I argue that recent efforts contextualizing the history of philosophy within the history of science subtly shift the central philosophical questions and allow for a greater range of (...) figures to be philosophically central. However, the history of science is but one context in which to situate philosophical works. Looking at the historical context of seventeenth-century philosophy of mind, one that weaves together questions of consciousness, rationality, and education, does more than shift the central questions—it brings new ones to light. It also shows that a range of genres can be properly philosophical and seamlessly diversifies the central philosophers of the period. (shrink)

There is an interesting logical/semantic issue with some mathematical languages and theories. In the language of (pure) complex analysis, the two square roots of i’ manage to pick out a unique object? This is perhaps the most prominent example of the phenomenon, but there are some others. The issue is related to matters concerning the use of definite descriptions and singular pronouns, such as donkey anaphora and the problem of indistinguishable participants. Taking a cue from some work in linguistics and (...) the philosophy of language, I suggest that i functions like a parameter in natural deduction systems. This may require some rethinking of the role of singular terms, at least in mathematical languages. (shrink)

The neo-logicist argues tliat standard mathematics can be derived by purely logical means from abstraction principles—such as Hume's Principle— which are held to lie 'epistcmically innocent'. We show that the second-order axiom of comprehension applied to non-instantiated properties and the standard first-order existential instantiation and universal elimination principles are essential for the derivation of key results, specifically a theorem of infinity, but have not been shown to be epistemically innocent. We conclude that the epistemic innocence of mathematics has not been (...) established by the neo-logicist. (shrink)

We are logical pluralists who hold that the right logic is dependent on the domain of investigation; different logics for different mathematical theories. The purpose of this article is to explore the ramifications for our pluralism concerning normativity. Is there any normative role for logic, once we give up its universality? We discuss Florian Steingerger’s “Frege and Carnap on the Normativity of Logic” as a source for possible types of normativity, and then turn to our own proposal, which postulates that (...) various logics are constitutive for thought within particular practices, but none are constitutive for thought as such. (shrink)

According to ante rem structuralism a branch of mathematics, such as arithmetic, is about a structure, or structures, that exist independent of the mathematician, and independent of any systems that exemplify the structure. A structure is a universal of sorts: structure is to exemplified system as property is to object. So ante rem structuralist is a form of ante rem realism concerning universals. Since the appearance of my Philosophy of mathematics: Structure and ontology, a number of criticisms of the idea (...) of ante rem structures have appeared. Some argue that it is impossible to give identity conditions for places in homogeneous ante rem structures, invoking a version of the identity of indiscernibles. Others raise issues concerning the identity and distinctness of places in different structures, such as the the natural number 2 and the real number 2. The purpose of this paper is to take the measure of these objections, and to further articulate ante rem structuralism to take them into account. (shrink)

The articles in this volume represent a part of the philosophical literature on higher-order logic and the Skolem paradox. They ask the question what is second-order logic? and examine various interpretations of the Lowenheim-Skolem theorem.

My talk today will be about Newton’s avowed methodology, and specifically the place of experiment in his conception of science, and how his ideas changed significantly over the course of his career. I also want to look at his actual scientific practice and see how this influenced his views on the nature of the experimental sciences.

Hofweber (Ontology and the ambitions of metaphysics, Oxford University Press, 2016) argues for a thesis he calls “internalism” with respect to natural number discourse: no expressions purporting to refer to natural numbers in fact refer, and no apparent quantification over natural numbers actually involves quantification over natural numbers as objects. He argues that while internalism leaves open the question of whether other kinds of abstracta exist, it precludes the existence of natural numbers, thus establishing what he calls “restricted nominalism” about (...) natural numbers. We argue that Hofweber’s internalism fails to establish restricted nominalism. Not only is his primary argument for restricted nominalism invalid, the analysis of quantification proposed threatens to collapse internalism into either a traditional form of error theory or realism. (shrink)

Though the “internal point of view” is perhaps H.L.A. Hart’s greatestcontribution to legal theory, this concept is also often and easily misunderstood. This is unfortunate, not only because these misreadings distort Hart’s theory, but, more importantly, because they prevent us from appreciating the infirmities of sanction-centered theories of law and the compelling reasons why they ought to be rejected. In this paper, I try to address some of these confusions. What, exactly, is the internal point of view? What role (or (...) roles) does it play in Hart’s theory? And how does an adequate appreciation for the centrality of the internal point of view lead to the rejection of sanction-centered theories? (shrink)

Christian List and Peter Menzies 2009 have looked to interventionist theories of causation for an answer to Jaegwon Kim's causal exclusion problem. Important to their response is the idea of realization-insensitivity. However, this idea becomes mired in issues concerning multiple realization, leaving it unable to fulfil its promise to block exclusion. After explaining why realization-insensitivity fails as a solution to Kim's problem, I look to interventionism to describe a different kind of solution.

We dispute Henrich et al.'s analysis of cultural differences at the level of a narrow behavioral-expression for assessing a universalist argument. When Researchers Overlook uNderlying Genotypes (WRONG), they fail to detect universal processes that generate observed differences in expression. We reify this position with our own cross-cultural research on self-enhancement and self-esteem.

. The concept of bodily health is problematic for mechanists like Descartes, as it seems that they need to appeal to something extrinsic to a machine, i.e., its purpose, to determine whether the machine is working well or badly, and so healthy or unhealthy. I take issue with this claim. By drawing on the history of medicine, I suggest that in the seventeenth century there was space for a non-teleological account of health. I further argue that mechanists can and did (...) appeal to structural integrity, as a non-teleological notion of form, to ground the norms required for ascriptions of health. (shrink)

Understanding the Infinite is a loosely connected series of essays on the nature of the infinite in mathematics. The chapters contain much detail, most of which is interesting, but the reader is not given many clues concerning what concepts and ideas are relevant for later developments in the book. There are, however, many technical cross-references, so the reader can expect to spend much time flipping backward and forward.

The partisan and ideological polarization of American politics since the 1970s appears to have affected pubic opinion in striking ways. The American public has become increasingly partisan and ideological along liberal-conservative lines on a wide range of issues, including even foreign policy. This has raised questions about how rational the public is, in the broad sense of the public's responsiveness to objective conditions. Widespread partisan disagreements over what those conditions arei.e., disagreements about the factssuggest that large proportions of the public (...) may be perceiving the facts incorrectly. The facts in question are important enough that these partisan disagreements may translate into sub-optimal policy preferences and electoral decisions. (shrink)

The purpose of this paper is to assess the prospects for a neo‐logicist development of set theory based on a restriction of Frege's Basic Law V, which we call (RV): ∀P∀Q[Ext(P) = Ext(Q) ≡ [(BAD(P) & BAD(Q)) ∨ ∀x(Px ≡ Qx)]] BAD is taken as a primitive property of properties. We explore the features it must have for (RV) to sanction the various strong axioms of Zermelo–Fraenkel set theory. The primary interpretation is where ‘BAD’ is Dummett's ‘indefinitely extensible’.1 Background: what (...) and why?2 Framework3 GOOD candidates, indefinite extensibility4 The framework of (RV) alone, or almost alone5 The axioms6 Brief closing. (shrink)

Huw Price holds that a recognizable version of expressivism about normative and modal language can be “globalized” so as to apply to all areas of discourse. He focuses on globalizing the anti-representationalism of expressivist theories. By contrast, this paper’s topic is the seldom-discussed way Price seeks to globalize the expressivist view that “non-descriptive” discourse exhibits subjectivity. I argue that Price’s own argument against the possibility of a purely objective domain conflicts with his anti-representationalism and is self-undermining. I then defend a (...) different strategy for arguing that a kind of subjectivity can emerge even in domains traditional expressivists have regarded as purely objective. I do so by using an account of assertoric practice to offer a new solution to a puzzle concerning how to describe contingent histories in the use of natural kind terms. (shrink)

There are multiple formal characterizations of the natural numbers available. Despite being inter-derivable, they plausibly codify different possible applications of the naturals – doing basic arithmetic, counting, and ordering – as well as different philosophical conceptions of those numbers: structuralist, cardinal, and ordinal. Nevertheless, some influential philosophers of mathematics have argued for a non-egalitarian attitude according to which one of those characterizations is more “legitmate” in virtue of being “more basic” or “more fundamental”. This paper addresses two related issues. First, (...) we review some of these non-egalitarian arguments, lay out a laundry list of different, legitimate, notions of relative priority, and suggest that these arguments plausibly employ different such notions. Secondly, we argue that given a metaphysical-cum-epistemological gloss suggested by Frege’s foundationalist epistomology, the ordinals are plausibly more basic than the cardinals. This is just one orientation to relative priority one could take, however. Ultimately, we subscribe to an egalitarian attitude towards these formal characterizations: they are, in some sense, equally “legitimate”. (shrink)

There are multiple formal characterizations of the natural numbers available. Despite being inter-derivable, they plausibly codify different possible applications of the naturals – doing basic arithmetic, counting, and ordering – as well as different philosophical conceptions of those numbers: structuralist, cardinal, and ordinal. Some influential philosophers of mathematics have argued for a non-egalitarian attitude according to which one of those characterizations is ‘more basic’ or ‘more fundamental’ than the others. This paper addresses two related issues. First, we review some of (...) these non-egalitarian arguments, lay out a laundry list of different, legitimate, notions of relative priority, and suggest that these arguments plausibly employ different such notions. Secondly, we argue that given a metaphysical-cum-epistemological gloss suggested by Frege's foundationalist epistemology, the ordinals are plausibly more basic than the cardinals. This is just one orientation to relative priority one could take, however. Ultimately, we subscribe to an egalitarian attitude towards these formal characterizations: they are, in some sense, equally ‘legitimate’. (shrink)