Bob Hale

A companion to the philosophy of language

Preface.Notes on Contributors.Part I: Meaning and Theories of Meaning:1. Meaning and Truth Conditions: From Freges Grand Design to Davidsons: David Wiggins (University of Oxford).2. Meaning, Use, Verification: John Skorupski (University of St Andrews).3. Intention and Convention: Anita Avramides (St Hildas College, University of Oxford).4. Pragmatics: Charles Travis (University of Stirling).5. A Guide to Naturalising Semantics: Charles Travis (University of Stirling).6. Meaning and Privacy: Edward Craig (University of Cambridge).7. Tacit Knowledge: Alexander Miller (University of Michigan).8. Radical Interpretation: Jane Heal (University of Cambridge).9. Propositional Attitudes: Mark Richard (Tufts University).10. Holism: Christopher Peacocke (University of Oxford).11. Metaphor: Richard Moran (Harvard University).Part II: Language, Truth and Reality:12. Realism and its Oppositions: Bob Hale (University of Glasgow).13. Theories of Truth: Ralph C. S. Walker (Magdalen College, University of Oxford).14. Analyticity: Paul Artin Boghossian (New York University).15. Rule-following, Objectivity and Meaning: Bob Hale (University of Oxford).16. The Interdeterminacy of Translation: Crispin Wright (University of St. Andrews).17. Putnams Model-theoretical Argument against Metaphysical Realism: Bob Hale and Crispin Wright (University of St. Andrews).18. Sorites: R. M. Sainsbury and Timothy Williamson (University of Edinburgh).Part III: Reference, Identity and Necessity:19. Modality: Bob Hale (University of Oxford).20. Essentialism: Graeme Forbes (Tulane University).21. Reference and Necessity: Robert Stalnaker (MIT).22. Names and Rigid Designation: Jason Stanley (Cornell University).23. Indexicals and Demonstratives: John Perry (Stanford University).24. Objects and Criteria of Identity: E. J. Lowe (University of Durham).25. Relative Identity: Harold Noonan (University of Birmingham).Glossary.Index.

Necessary beings : an essay on ontology, modality, and the relations between them

In Necessary Beings, Bob Hale brings together his views on the source and explanation of necessity. It is a very thorough book and Hale covers a lot of ground. It contains not only new research but also useful summaries of Hale’s views and overviews of the various positions he opposes or develops. Thus it is not only of interest to experts in the field, but it can also serve as an introduction to the topic to readers with a general knowledge of logic and metaphysics. It can be read with little background in the specific topic of the metaphysics of necessity, as a reader unacquainted with the particulars can rely on Hale’s clear and accessible exposition and many pointers to further literature. The core thesis of the book is that ontology and modality are interdependent and equally fundamental and irreducible. Hale explains modality in terms of the natures or identities of things, ‘what it is to be that thing—what makes it the thing it is, and distinguishes it from every other thing.’ (132) Each thing α has a nature Φ peculiar to it, and ‘truths about it are necessary [...] Φα tells us what it is for α to be the thing it is’ (133). A thing could not have lacked its nature, but could have had different properties that are not part of its nature. This leaves space for possibilities. Hale presents an essentialist theory of modality, set out in chapter 6: propositions are metaphysically necessary in virtue of the natures of things, and propositions are metaphysically possible in virtue of not being ruled out by those natures. Metaphysics and ontology are further intertwined due to Hale’s Fregean approach to the questions of what kinds of things there are, presented in the ‘Ontological Preliminaries’. There are objects, properties, relations and functions, where the distinction is made linguistically in terms of the differences in expressions of a language that can be used to refer to things of different kinds. Hale follows Frege in drawing ontological distinctions on the basis of syntactic ones within the expressions of a language. Roughly, an object is the kind of thing that is typically referred to by a proper name, a property the kind of thing that is typically referred to by a predicate, a relation typically by a relational expression, a function typically by a functional expression. To avoid relativising ontology to the expressive power of actual languages, Hale appeals to the irreducible and fundamental nature of modality. It is not the existence of expressions in actual

Logic, Thought and Language

1. What logic should we think with? R. M. Sainsbury 2. Mental representation and mental presentation Gregory McCulloch 3. Self-knowledge, normativity and construction Julia Tanney 4. The normativity of meaning Alan Millar 5. Two theories of names Gabriel M. A. Segal 6. Relativism and classical logic Crispin Wright 7. Principles for possibilia Christopher Peacocke 8. What are these familiar words doing here? A. W. Moore 9. Particular thoughts and singular thought M. G. F. Martin 10. Conditional belief and the Ramsey Test Scott Sturgeon 11. Necessary existents Timothy Williamson 12. Ambiguity and belief S. G. Williams 13. Basic logical knowledge Bob Hale 14. Freges target Charles Travis.

Abstraction and Set Theory

ION AND SET THEORY

Focus restored: Comments on John MacFarlane

In “Double Vision Two Questions about the Neo-Fregean Programme”, John MacFarlane’s raises two main questions: (1) Why is it so important to neo-Fregeans to treat expressions of the form ‘the number of Fs’ as a species of singular term? What would be lost, if anything, if they were analysed instead as a type of quantifier-phrase, as on Russell’s Theory of Definite Descriptions? and (2) Granting—at least for the sake of argument—that Hume’s Principle may be used as a means of implicitly defining the number operator, what advantage, if any, does adopting this course possess over a direct stipulation of the Dedekind-Peano axioms? This paper attempts to answer them. In response to the first, we spell out the links between the recognition of numerical terms as vehicles of singular reference and the conception of numbers as possible objects of singular, or object-directed, thought, and the role of the acknowledgement of numbers as objects in the neo-Fregean attempt to justify the basic laws of arithmetic. In response to the second, we argue that the crucial issue concerns the capacity of either stipulation—of Hume’s Principle, or of the Dedekind-Peano axioms—to found knowledge of the principles involved, and that in this regard there are crucial differences which explain why the former stipulation can, but the latter cannot, play the required foundational role.

Relative Necessity Reformulated

This paper discusses some serious difficulties for what we shall call the standard account of various kinds of relative necessity, according to which any given kind of relative necessity may be defined by a strict conditional - necessarily, if C then p - where C is a suitable constant proposition, such as a conjunction of physical laws. We argue, with the help of Humberstone (Reports on Mathematical Logic, 31, 33–421, 1981), that the standard account has several unpalatable consequences. We argue that Humberstone’s alternative account has certain disadvantages, and offer another - considerably simpler - solution.

II–Bob Hale: Arithmetic Reflection without Intuition

Michael Potter considers several versions of the view that the truths of arithmetic are analytic and finds difficulties with all of them. There is, I think, no gainsaying his claim that arithmetic cannot be analytic in Kant’s sense. However, his pessimistic assessment of the view that what is now widely called Hume’s principle can serve as an analytic foundation for arithmetic seems to me unjustified. I consider and offer some answers to the objections he brings against it.

Essence and definition by abstraction

We may define words or concepts, and we may also, as Aristotle and others have thought, define the things for which words stand and of which concepts are concepts. Definitions of words or concepts may be explicit or implicit, and may seek to report preexisting synonymies, as Quine put it, but they may instead be wholly or partly stipulative. Definition by abstraction, of which Hume’s principle is a much discussed example, seek to define a term-forming operator, such as the number operator, by fixing the truth-conditions of identity-statements featuring terms formed by means of that operator. Such definitions are a species of implicit definition. They are typically at least partly stipulative. Definitions of things, or real definitions, are, by contrast, typically conceived as true or false statements about the nature or essence of their definienda, and so not stipulative. There thus appears to be an obvious and head-on clash between taking Hume’s principle as an implicit and at least partly stipultative definition of the number operator and taking it as a real definition, stating the nature or essence of cardinal numbers. This paper argues that this apparent tension can be resolved, and that resolving it sheds light on part of the epistemology or essence and necessity, showing how some of our knowledge of essence and necessity can be a priori.

Second-order logic: properties, semantics, and existential commitments

Quine’s most important charge against second-, and more generally, higher-order logic is that it carries massive existential commitments. The force of this charge does not depend upon Quine’s questionable assimilation of second-order logic to set theory. Even if we take second-order variables to range over properties, rather than sets, the charge remains in force, as long as properties are individuated purely extensionally. I argue that if we interpret them as ranging over properties more reasonably construed, in accordance with an abundant or deflationary conception, Quine’s charge can be resisted. This interpretation need not be seen as precluding the use of model-theoretic semantics for second-order languages; but it will preclude the use of the standard semantics, along with the more general Henkin semantics, of which it is a special case. To that extent, the approach I recommend has revisionary implications which some may find unpalatable; it is, however, compatible with the quite different special case in which the second-order variables are taken to range over definable subsets of the first-order domain, and with respect to such a semantics, some important metalogical results obtainable under the standard semantics may still be obtained. In my final section, I discuss the relations between second-order logic, interpreted as I recommend, and a strong version of schematic ancestral logic promoted in recent work by Richard Heck. I argue that while there is an interpretation on which Heck’s logic can be contrasted with second-order logic as standardly interpreted, when it is so interpreted, its differences from the more modest form of second-order logic I advocate are much less substantial, and may be largely presentational.

Bolzano's Definition of Analytic Propositions

We begin by drawing attention to some drawbacks of what we shall call the Frege-Quine definition of analytic truth. With this we contrast the definition of analytic propositions given by Bolzano in his Wissenschaftslehre. If Bolzano’s definition is viewed, as Bolzano himself almost certainly did not view it, as attempting to capture the notion of analyticity as truthin-virtue-of-meaning which occupied centre stage during the first half of the last century and which, Quine’s influential assault on it notwithstanding, continues to attract philosophical attention, it runs into some very serious problems. We argue that Bolzano’s central idea can, nevertheless, be used as the basis of a new definition which avoids these problems and possesses definite advantages over the Frege-Quine approach. Our title notwithstanding, we make no claim to contribute to the exegesis of Bolzano’s thought and works, which we must leave to those more expert in these matters than we are. Naturally, we have done our best not to misrepresent Bolzano’s views, and believe we have avoided doing so. But it bears emphasis that it is no part of our intention to suggest that the modifications to his definition which we propose would have had any appeal for him, or that he had, or would have had, any sympathy with the project which motivates them. 1 Frege’s definition A noteworthy feature of Frege’s explanation of the distinction between analytic and synthetic judgements is that he views the distinction as an epistemological one, in parallel with the obviously epistemological distinction between a priori and a posteriori judgements: Now these distinctions between a priori and a posteriori, synthetic and analytic, concern . . . not the content of the judgement ∗We are both pleased to be able to contribute to this special issue for Peter, and grateful to Sandra Lapointe for inviting us to do so. In addition to his worthy contributions to the philosophy of mathematics and metaphysics, Peter has made a huge contribution to our appreciation and understanding of Central European philosophy and logic. It is, accordingly, an added pleasure to contribute a paper on a topic close to his intellectual heart.