DOCSLIB.ORG

James Higginbotham

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
James Higginbotham JAMES HIGGINBOTHAM ON LINGUISTICS IN PHILOSOPHY, AND PHILOSOPHY IN LINGUISTICS ABSTRACT. After reviewing some major features of the interactions between Linguistics and Philosophy in recent years, I suggest that the depth and breadth of current inquiry into semantics has brought this subject into contact both with questions of the nature of linguistic competence and with modern and traditional philosophical study of the nature of our thoughts, and the problems of metaphysics. I see this development as promising for the future of both subjects. First, a clarification. Philosophy is a large, many-limbed creature, whose variety of interests and methods, even if loosely gathered under the name of inquiry through reason (rather than through faith or revelation), may touch upon any special subject in a number of ways. Likewise Linguistics, comprising as it does the study of human language and languages across a manifold of social and historical concerns, only some of which are rel- evant to my discussion here. By speaking of Linguistics in Philosophy, or of Philosophy in Linguistics, I refer only to the typical subjects of this Journal from its inception, subjects that grew from the interaction between elements of the philosophy of language and the study of generative or formal linguistics, and chiefly of semantics. My question, with reference to the work carried out during this distinguished history, is what these interactions have led to, and where we might see things developing. Writing, now, as a member of a generation of academic philosophers for whom the material of linguistics was an exciting new arena of inquiry, it may be appropriate first to explain why, at least in my own and I hope not unrepresentative respect, this arena was one that had promise for philo- sophical inquiry, conceived in a certain purity, and was also continuous with the development of philosophy. Subsequently, I shall turn to what I see coming about in these latter days. Philosophy asks big questions. Among them: what is thought? what is the place of mind and rationality in a natural world? what is truth? what is there in the world? As Michael Dummett has remarked, philosophy aims at these questions even in its apparently removed, local, and most arcane discussions; must so aim, to be in keeping with the traditions of the subject. Linguistics and Philosophy 25: 573–584, 2002. © 2002 Kluwer Academic Publishers. Printed in the Netherlands. 574 JAMES HIGGINBOTHAM Philosophy has its methods, different ones at different times. How- ever, the methods of philosophy (themselves supported or questioned upon philosophical grounds) are typically not just methods, but also formats, within which the whole of philosophy, or at least the whole of what in- terests their proponents, may be transacted. It is in this sense, as the format within which exposition, discussion, and argument took place, that the philosophy of language of the first period of this Journal may be under- stood (and it is in this sense also that Zeno Vendler published Linguistics in Philosophy, from which I have borrowed part of my title). This format is not, now, as favored as it was. But it continues to hold a place in the subject, one that stems from the oldest traditions. If there is any single topic that can be said not only to deploy methods and to aim at results of inquiry typical of linguistics on the one hand and philosophy on the other, but even to constitute a domain that is, at the same time, a part of linguistics and a part of philosophy, it is the details of meaning and the conveyance of meaning in language. It is a measure of the continuity of this subject that the great work of the past, from Plato and Aristotle through medieval figures such as William of Sherwood and Jean Buridan, and down to Antoine Arnauld and Otto Jespersen, is readable today, and that they are concerned with what is recognizably the same subject. David Lewis wrote in 1980 (reprinted in Lewis 1998): We have made it part of the business of philosophy to set down, in an explicit and systematic fashion, the broad outlines of our common knowledge about the practice of language.1 Our making it so was not a novelty. But our making so much of it was a novelty, made possible by achievements especially in logic and the theory of formal languages, by the concentrated effort of part of the represent- atives of “the linguistic turn” in philosophy, and by the work of Rudolf Carnap, W.V. Quine, and others. It was exciting. There were things to be discovered. Only in the late 1970s, for example, did a coherent even if still partial theory of the conditions on taking anaphoric pronouns as bound variables begin to emerge, along with full accounts of restricted quantification, steps toward a reasonable story about the logic of conditionals, and much else. Latterly, the philosophy of mind (an appropriate label for a rather loosely connected family of inquiries, more or less involved with the cognitive sciences, or their interpretation) has become the center of specu- lative philosophy, and the philosophy of language is no longer the general, preferred format for philosophical exposition. I do not rehearse here the 1 Reprinted in Lewis 1998, 22. ON LINGUISTICS IN PHILOSOPHY, AND PHILOSOPHY IN LINGUISTICS 575 steps taken in this direction. Instead, or so I shall argue, we can see the beginnings of new problems and questions, within the philosophy of lan- guage conceived as a specialty, not just within philosophy, but also within linguistics. Linguistics and philosophy, like steak and barbecue sauce, have much to give each other. Philosophy has acted for many years as a kind of logic delivery system to linguistics, a role that will doubtless continue; and formal linguistics, by opening up investigations in philosophical logic to the question of the details of particular sentences, their precise syntax and combinatorics of meaning, has enriched and deepened these investig- ations. What I wish to dwell upon, however, is the prospect of a common enterprise, wherein elements typical of philosophy and those typical of linguistics interact. This common enterprise, I suggest, is the clarification of the nature of our thoughts, what we actually express when we understand one another. Assume, what is common enough although open to question, that this clarification calls first of all for the exposition of the truth conditions of sentences, as they occur as parts of total languages, and within the con- texts of their potential utterance; and assume also that any correct account of what we are inclined to assert must, over a wide domain, make us pretty much right about the way things are.2 Then the truth conditions of much of what we believe must be such as to be actually met; and this implies that what turns up in the metaphysics of semantic investigation cannot be passed off as a mere manner of speaking, but constitutes our best conception of the way the world is. Examples of metaphysical features that have been deployed in contem- porary investigation are many: Davidson 1967 and subsequent work on individual events; Montague 1960 on what he called “philosophical entit- ies”; and elements such as propositions and individual concepts, advanced in Carnap 1947, but now understood in terms of possible-worlds semantics or counterpart theory, and others. If the proffered semantics employing these elements is correct, then they must form, not merely part of our conception of the world, but part of the world itself. To say this much is not to commit semantics to an all-out realism with respect to the elements invoked. It does, however, imply that the question of realism must be taken seriously, including familiar questions of pos- sible reduction or relativization of the objects involved, as for instance whether individual events can be reduced to regions of space and time, or whether possible worlds can be modeled as maximally consistent sets of propositions. 2 This view is identified especially with Davidson 1984. 576 JAMES HIGGINBOTHAM Alternatives are perhaps possible, and have certainly been advanced; but it is not, in my view, easy to see that they are alternatives. Thus Jackendoff 1998 writes in this Journal in defense of the view that, at least for that conception of linguistics that takes a “mentalist stance”, and is interested in language as a chapter of the study of the “properties of the mind”, there is to be a contrast between the view that there is reference in language to “entities in the world”, and the view that there is reference to “entities in the world as conceptualized by the language user”.3 First of all, it is hard to see how the “mentalist stance” is at odds with any conception of reference to ordinary things; reference to the salt cellar on the table, for example, which will come across the table to me if I say to my neighbor, “Please pass the salt”. Presumably, ‘x sees the salt on the table’, with its unabashed reference to salt and to tables, expresses a “property of the mind” of x if anything does. Furthermore, what is to drive a wedge between “entities in the world as conceptualized”, and “entities in the world”? Jackendoff mentions examples of fictions (broadly speaking, thus including Santa Claus): this gives him a semantics (Jackendoff 1998, 215) where Santa Claus is imaginary is, if true, true of a “conceptualized entity” that is not “real”. Many alternatives have been explored, in criticism of the thesis, which appears to be Jackendoff’s, that not only the evident grammatical form, but even the logical form, of Santa Claus is imaginary is the same as that of My shirt is red.
Load more

Recommended publications
  • The Anaphoric Theory of Tense
    The Anaphoric Theory of Tense James Higginbotham University of Southern California In this article I extend the discussion of Sequence of Tense phenomena in English that I have presented in earlier work (particularly Higginbotham 2002a and 1995) so as to include some properties of the English Perfect, and so as to clarify some pieces of the construction that I left open or unarticulated there. I also call attention to some features of what I call here indexical mismatch as between adverbials and tenses, a phenomenon that may well extend in a number of directions, both within individual languages and cross-linguistically. In large part, however, my purpose here is critical: I aim to show, despite arguments to the contrary, that anaphoric theories of tense do exactly what needs to be done to explain the dependencies of c-commanded tenses upon c-commanding ones, and that alternatives, notably those of the sort proposed in Ogihara (1995), von Stechow (1995) and Abusch (1994) and (1997), must build back into their respective accounts the anaphoric properties of Sequence of Tense if those accounts are to be part of an empirically adequate system. The semantics that I deploy here will require abandonment, or at least radical modification, of any framework that takes sentential complements in a “notation-free” manner, as in possible-worlds semantics; but that framework wants modification anyway, or so (for familiar reasons) I will assume. 1. Introduction Anaphoric theories of tense may be elaborated in several ways. As I am using the term, an anaphoric theory will account for the familiar properties of a sentence such as English (1.1) by establishing some basis for coreference between the Tense-bearing element of the main clause (in this case futurate will), and that of the complement clause (here the Present, or –Past, inflection on the copula): (1.1) John will say that Mary is happy.
    [Show full text]
  • Curriculum Vitae
    CURRICULUM VITAE Robert C. May Department of Philosophy (530) 554-9554 (office) University of California [email protected] Davis, CA 95616 Degrees Swarthmore College; B.A. with High Honors, 1973. • Massachusetts Institute of Technology, Department of Linguistics and Philosophy; Ph.D., 1977. • Faculty Positions Assistant Professor of Linguistics. Barnard College and The Graduate School of Arts and Sciences, • Columbia University. 1981 - 1986. Associate Professor of Linguistics and Cognitive Sciences. University of California, Irvine. 1986 - 1989. • Professor of Linguistics. University of California, Irvine. 1989 - 1997 • Professor of Linguistics and Philosophy, University of California, Irvine. 1997 - 2001. • Professor of Logic and Philosophy of Science, Linguistics and Philosophy, University of California, • Irvine, 2001 - 2006. Professor of Philosophy and Linguistics, University of California, Davis, 2006 - 2012 • Distinguished Professor of Philosophy and Linguistics, University of California, Davis. 2012 - present. • Other Academic Positions Post-doctoral research fellow. Laboratory of Experimental Psychology. The Rockefeller University.1977 • -1979. Research Stipendiate. Max-Planck-Institut für Psycholinguistik. Nijmegen, The Netherlands. 1979, • 1980. Post-doctoral research fellow. Center for Cognitive Science, Massachusetts Institute of Technology, • 1980 -1981. Visiting Lecturer. Graduate School of Languages and Linguistics. Sophia University, Tokyo, Japan. • 1983. Visiting Research Scholar. The Graduate Center, City University of New York. 1985 - 1986. • Fulbright Distinguished Professor. University of Venice. 1994. • Visiting Scholar. Department of Philosophy. Columbia University. 2013, 2014 - 15. • Visiting Professor, Ecole Normale Superieure and Ecole des Hautes Etudes en Sciences Sociales. 2014. • 1 Professional Positions and Activities Director. Syntax and Semantics Workshop: Logical Form and Its Semantic Interpretation. 1985 - • 1987. Editor. The Linguistic Review Dissertation Abstracts. 1984 - 1988. • Associate Editorial Board.
    [Show full text]
  • GEOFFREY B. GEORGI USC School of Philosophy 430 N
    GEOFFREY B. GEORGI USC School of Philosophy 430 N. Holliston Ave. #202 Mudd Hall of Philosophy Pasadena, CA 91106 3709 Trousdale Parkway m: 626-354-2742 Los Angeles, CA 90089 [email protected] f: 213-740-5174 www-scf.usc.edu/~ggeorgi EDUCATION Ph.D., Philosophy, University of Southern California (USC) School of Philosophy, August 2011 Dissertation Title: Demonstratives in Logic and Natural Language Dissertation Advisor: Scott Soames Ph.D. Candidate, Philosophy, University of California (UC), Davis, 2001 – 2004 M.A., Philosophy, Tufts University, June 2001 Honors B.A., Celtic Studies & Literary Studies, University of Toronto, June 1997 AREAS OF RESEARCH SPECIALIZATION AND TEACHING COMPETENCE Areas of Specialization: Philosophy of Language, Philosophical Logic Areas of Competence: Logic, Metaphysics and Epistemology, History of Analytic Philosophy, Philosophy of Mind, Ancient Philosophy FELLOWSHIPS AND AWARDS USC Summer Dissertation Award, Summer 2008, Summer 2009 USC School of Philosophy Flewelling Summer Research Award, Summer 2006 UC Davis Summer Research Award, Summer 2002 University of California Eugene Cota-Robles Fellow, 2001 – 2003 PUBLICATIONS “Reference and Ambiguity in Complex Demonstratives,” to appear in Reference and Referring: Topics in Contemporary Philosophy, v. 10, ed. Campbell, J. K., Kabasenche, W., and O'Rourke, M. (Cambridge, MA: MIT Press) CONFERENCE PRESENTATIONS “Logical Truth and Consequence in the Logic of Demonstratives,” Arché Conference on Foundations of Logical Consequence, June 2010 “Demonstratives and Pragmatic
    [Show full text]
  • Collections and Paradox
    Collections and Paradox Remko Scha Institute for Logic, Language and Computation [email protected] 1 Preface This essay is dedicated to Jeroen Groenendijk, Martin Stokhof, and Frank Veltman — but not to each of them separately, but to all of them jointly, as a group, or a set, or a mereological sum. This group was an important part of a community of logicians and philosophers at the University of Amsterdam, that had a stimulating influence on my first ventures into formal semantics in the course of the 1970’s. The discussion below ties in directly with that work. My topic will be the conceptual viability of the very idea of ”collective entities” such as “Frank, Martin and Jeroen” and “the Amsterdam Montagovians.” Most theories of formal semantics assume that such plural noun phrases denote higher-level entities of some sort, that have individuals (such as Frank, Jeroen and Martin) as their members or parts. But this assumption has been challenged. A sweeping argument against ”collections” of any kind was raised in the eighties and nineties by George Boolos, James Higginbotham and Barry Schein [4, 5, 8, 27]: collections engender paradox. The chapters on plurals in some fairly recent handbooks in the Philosophy of Language [28, 15] still discuss this argument at great length, treating it as one of the most important issues in the field. Nonetheless, most researchers in this area seemed not at all disturbed by this challenge, and did not feel the need to deal with it. Fred Landman [11] for instance, in the context of an otherwise detailed discussion of Schein’s proposals about plurals, shrugs it o↵with a deadpan witticism: “Schein 1993 invokes an argument for his approach involving Russell’s paradox.
    [Show full text]
  • Three Grades of Instrumentalism Russell Marcus, Ph.D. Chauncey
    Three Grades of Instrumentalism Russell Marcus, Ph.D. Chauncey Truax Post-Doctoral Fellow Department of Philosophy, Hamilton College 198 College Hill Road Clinton NY 13323 [email protected] (315) 859-4056 (office) (315) 381-3125 (home) (917) 903-7483 (mobile) January 2008 5602 words Abstract: I defend a view, mathematical instrumentalism, on which quantification over mathematical objects in scientific theory does not entail commitment to their existence. I present a puzzle about the status of our beliefs in mathematical objects, and show how instrumentalism resolves it. MI undermines both the indispensability argument and the primary response to it which demands reformulations of scientific theory to avoid mathematical commitments. Three Grades of Instrumentalism, 1 §1. Posits and Homogeny You look skyward on a clear night and say, “There are stars.” We conclude that you believe that there are stars. You study atomic theory and say, “There are atoms.” We conclude that you believe that atoms exist. You study quantum physics and say, “There are Hilbert spaces.” We conclude that you believe that there are abstract structures called Hilbert spaces.1 These three inferences are supported by Quine’s dictum that to be is to be the value of a variable, which connects ontic commitment with quantification. In contrast, I wish to urge that the third inference, unlike the first two, is invalid. I do not deny that there are Hilbert spaces. Nor do I deny that quantum mechanics refers to Hilbert spaces. My claim, in this paper, is merely that the inference from the sentences of quantum mechanics to the existence of mathematical objects is unjustified.
    [Show full text]
  • Truth and Meaning—In Perspective
    March 2008 March 2008 Truth and Meaning – In Perspective by Scott Soames School of Philosophy University of Southern California To Appear In Truth and Its Deformities Edited by Peter French Midwest Studies in Philosophy Volume XXXII 2008 Truth and Meaning – In Perspective Scott Soames My topic is the attempt by Donald Davidson, and those inspired by him, to explain knowledge of meaning in terms of knowledge of truth conditions. For Davidsonians, these attempts take the form of rationales for treating theories of truth, constructed along Tarskian lines, as empirical theories of meaning. In earlier work1, I argued that Davidson’s two main rationales – one presented in “Truth and Meaning”2 and “Radical Interpretation,”3 and the other in his “Reply to Foster”4 – were unsuccessful. Here, I extend my critique to cover an ingenious recent attempt by James Higginbotham to establish Davidson’s desired result. I will argue that it, too, fails, and that the trajectory of Davidsonian failures indicates that linguistic understanding, and knowledge of meaning, require more than knowledge of that which a Davidsonian truth theory provides. I begin with a look at the historical record. The Evolution of an Idea: A Historical Summary When Davidson enunciated his idea, in the 1960s, that theories of meaning can be taken to be nothing more than theories of truth, it met with a warm reception. For devotees of Ordinary Language, its attraction lay in its promise of providing a theoretically respectable way of grounding claims about meaning, and distinguishing them from claims about use, that those who still placed meaning at the center of philosophy had come to recognize the need for.5 For 1 Scott Soames, “Truth, Meaning, and Understanding,” Philosophical Studies, 65, 1992; 17-35, and chapter 12 of Philosophical Analysis in the Twentieth Century, Volume 2 (Princeton and Oxford: Princeton University Press), 2003.
    [Show full text]
  • Oxford University Working Papers, in Linguistics, Philology & Phonetics
    Oxford University Working Papers, in Linguistics, Philology & Phonetics VOLUME 6 May 2001 Edited by Maria Liakata Britta Jensen Didier Maillat Editorial assistant Joanna Levene Contents Page Editorial Note iii Complex Aspectual Structure in Hindi/Urdu 1 MIRIAM BUTT & GILLIAN RAMCHAND Grammar learning using Inductive Logic Programming 31 JAMES CUSSENS & STEPHEN PULMAN Two strategies to construct Telicity: A comparative analysis of 47 English and Italian RAFFAELLA FOLLI Why is Sequence of Tense obligatory? 67 JAMES HIGGINBOTHAM On the Information-Structural effects of Scrambling in German 91 CAROLIN HOYER On sentential negation in the Mainland Scandinavian languages 115 BRITTA JENSEN How to resolve Pronouns combining syntactic information and 137 an induced domain theory MARIA LIAKATA Which template for behind? Empirical considerations 151 of the meaning of Directional PPs DIDIER MAILLAT A Minimalist Approach to Quantifiers 167 HISASHI MORITA Syntactic Ergativity in Tongan 189 YUKO OTSUKA iii Editorial note Oxford Working Papers in Linguistics, Philology and Phonetics presents research being undertaken by past and present staff and graduate students from the University of Oxford. The current volume concentrates on topics in Syntax and Semantics, with two papers from the field of Computational Linguistics. Comments on the work included here are welcome: the authors’ addresses are provided at the end of each paper. To get in touch with the editors or for further information you can write to: The Centre for Linguistics & Philology Clarendon
    [Show full text]
  • Issues in the Philosophical Foundations of Lexical Semantics
    Issues in the Philosophical Foundations of Lexical Semantics by Brian Edward Ulicny B.A. Philosophy, B.S. Electrical Engineering, University of Notre Dame (1986) Submitted to the Department of Linguistics and Philosophy in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Philosophy at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY May 1993 © Massachusetts Institute of Technology 1993. All rights reserved. Author ................ ......... ................................. Department of Linguistics and Philosophy April 20, 1993 Certified by... ........ .... ........... ................. .......... James Higginbotham Professor, Linguistics and Philosophy Thesis Supervisor A ccepted by ................................. George Boolos Chairman, Departmental Committee on Graduate Studies ARCHIVES MASSACHUSETTS INSTITUTE OF TFCHNOLOGY ¶JUN 03 1993 Issues in the Philosophical Foundations of Lexical Semantics by Brian Edward Ulicny Submitted to the Department of Linguistics and Philosophy on April 20, 1993, in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Philosophy Abstract My dissertation defends and explores the thesis that in order for a speaker to un- derstand a natural language it is not only sufficient but necessary that the speaker tacitly know or "cognize" the truth-conditional contribution of the words and other sentential elements to the truth-conditions of the whole expression. A speaker's se- mantic competence is to be explained as the employment of an internally-represented axiomatized truth theory for that speaker's first language. By providing a theory of truth for a language, the truth of certain sentences follows on the basis of that theory alone. In the first chapter, I develop and defend a notion of analyticity suggested by Noam Chomsky in his Language and Problems of Knowledge (1986) against skeptical worries due to Quine and Burge.
    [Show full text]
  • DAVIDSON's PROGRAM and INTERPRETED LOGICAL FORMS the “Interpreted Logical Form” (ILF) Analysis of Attitude Ascriptions
    LENNY CLAPP DAVIDSON’S PROGRAM AND INTERPRETED LOGICAL FORMS 1. INTRODUCTION The “Interpreted Logical Form” (ILF) analysis of attitude ascriptions has been proffered, most notably by Higginbotham (1986) and Larson and Ludlow (1993), as a means of resolving within the framework of Davidson’s semantic program the familiar problems posed by attitude ascriptions.1 In this paper I argue that only an analysis of attitude ascrip- tions along the lines of Davidson’s (1968) “paratactic” analysis can resolve the problem posed by attitude ascriptions within the constraints of Dav- idson’s semantic program. The ILF analyses, though following Davidson in providing recursive formal theories that entail statements of the truth conditions of sentences, violate theoretical constraints that Davidson takes pains to satisfy. That the ILF analyses violate these constraints raises two theoretical questions: First, do the ILF analyses nonetheless adequately perform what Davidson calls the “central task of a theory of meaning”, viz. explain- ing how “speakers of a language can effectively determine the meaning or meanings of an arbitrary expression” (Davidson, 1967)? Or does this violation serve to undermine their plausibility as explanations of our se- mantic competence? I will argue that because the ILF analyses violate the theoretical constraints of Davidson’s semantic program their plausibility as explanations of our semantic competence is significantly undermined. I am grateful to Mark Richard, Robert Stainton, Irene Heim, Brian Ulicny, Paul Piet- roski, Andrew Botterell, James Higginbotham, Jason Stanley, Zoltan Szabo, Peter Ludlow, and several anonymous referees for helpful discussion and comments. 1 Versions of Higginbotham’s proposal are endorsed by Segal (1989) and Pietrosky (1994).
    [Show full text]
  • 1 Curriculum Vitae Jeffrey C. King Department of Philosophy
    Curriculum Vitae Jeffrey C. King Department of Philosophy Rutgers, the State University of New Jersey 106 Somerset St. 5th floor New Brunswick, NJ 08901-1107 Phone: (732) 932-9861 - Fax: (732) 932-8617 e-mail: [email protected] AREAS OF SPECIALIZATION Philosophy of Language, Formal Semantics, Philosophical Logic, Metaphysics AREAS OF COMPETENCE: Logic, History of Analytic Philosophy, Philosophy of Mind EDUCATION: B.A. 1979 University of California, San Diego (Major: Philosophy; Minor: Mathematics) Ph.D. 1985 University of California, San Diego (Dissertation Advisors: Zeno Vendler and Mark Wilson) EMPLOYMENT: Distinguished Professor, Rutgers University 2011-present Professor I, Rutgers University 2007-2011 Professor, University of Southern California 2004-2007 Professor, University of California, Davis 1999-2004 Associate Professor, University of California, Davis 1993-1999 Assistant Professor, University of California, Davis 1991-1993 Associate Professor, California State University, San Bernardino 1988-1990 Assistant Professor, California State University, San Bernardino 1985-1988 VISITING APPOINTMENTS 1 Visiting Fellow, Australian National University, Summer 2003 Visiting Professor, Harvard University, Fall 2002 Visiting Professor, University of California, Berkeley, Fall 2001 WORKS IN PROGRESS ‘Acquaintance, Singular Thought and Singular Propositions’, under submission ‘Singular Thought, Russellianism and Mental Files’ forthcoming. ‘ “Descriptive Readings” of Indexicals and Demonstratives’, unpublished ms. ‘Semantic values
    [Show full text]
  • Parsons Ch-Math.Pdf
    This page intentionally left blank P1: JZP CUNY1138-FM CUNY1138/Parsons 978 0 521 45279 3 November 8, 2007 21:58 MATHEMATICAL THOUGHT AND ITS OBJECTS In Mathematical Thought and Its Objects,Charles Parsons examines the notion of object, with the aim of navigating between nominalism, which denies that distinctively mathematical objects exist, and forms of Platonism that postulate a transcendent realm of such objects. He introduces the central mathematical notion of structure and defends a version of the structuralist view of mathematical objects, according to which their existence is relative to a structure and they have no more of a “nature” than that confers on them. Parsons also analyzes the concept of intuition and presents a conception of it distantly inspired by that of Kant, which describes a basic kind of access to abstract objects and an element of a first conception of the infinite. An intuitive model witnesses the possibility of the structure of natural numbers. However, the full concept of number and knowledge of numbers involve more that is conceptual and rational. Parsons considers how one can talk about numbers, even though they are not objects of intuition. He explores the conceptual role of the principle of mathematical induction and the sense in which it determines the natural numbers uniquely. Parsons ends with a discussion of reason and its role in mathematical knowledge, attempting to do justice to the complementary roles in mathe- matical knowledge of rational insight, intuition, and the integration of our theory as a whole. Charles Parsons is Edgar Pierce Professor of Philosophy, Emeritus, at Harvard University.
    [Show full text]
  • James Higginbotham Tense, Aspect, and Indexicality
    Philosophy in Review XXXI (2011), no. 2 James Higginbotham Tense, Aspect, and Indexicality. Oxford: Oxford University Press 2009. 288 pages US$125.00 (cloth ISBN 978-0-19-923931-3); US$49.95 (paper ISBN 978-0-19-923932-0) James Higginbotham, Distinguished Professor of Philosophy and Linguistics at the University of Southern California (and formerly Professor of General Linguistics at the University of Oxford), has always been concerned with philosophical problems in linguistics, especially semantics. He justifies his largely English-centered approach in the following way: ‘despite its hybrid Germanic-Romance status, and its limited morphology, English is after all well constructed, in the sense that its Tenses and Indexicals, and the Progressive and Perfect aspectual heads, contribute definite context-independent conditions on interpretation, to be clarified through the application of modern logic’ (x-xi). This book brings together revised versions of twelve articles published between 1995 and 2008, devoted to tense, aspect, events and indexical expressions in natural language. The articles are followed by cumulative references and an index. The first nine chapters focus predominantly on tense, from a very broad—linguistic, logical and philosophical—perspective. Higginbotham assumes, following an early proposal by Bar- Hillel, that the tenses of human languages are indexical expressions ‘in that repetitions of the same sentence may differ in truth value simply because of tense’ (83); however, in contrast to context-dependent temporal adverbials, they are not fixed in interpretation. Chapter 1 relates the issue of tense and temporal cross-reference to indexicality, and the extension of the notions of logic to indexical languages.
    [Show full text]