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18Logical and Analytic Truths that are not NecessaryJournal of Philosophy 85 (2): 57-74. 1988.After defining a standard modal language and semantics, we offer some clear examples of logical and analytic truths that are not necessary. These examples: (a) are far simpler than the ones cited in the literature, (b) show that a popular conception of logical truth in modal languages is incorrect, and (c) show that there are contingent truths knowable ``a priori'' that do not depend on fixing the reference of a term.
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147Frege's logic, theorem, and foundations for arithmeticStanford Encyclopedia of Philosophy. 2008.In this entry, Frege's logic is introduced and described in some detail. It is shown how the Dedekind-Peano axioms for number theory can be derived from a consistent fragment of Frege's logic, with Hume's Principle replacing Basic Law V.
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168Twenty-five basic theorems in situation and world theoryJournal of Philosophical Logic 22 (4): 385-428. 1993.The foregoing set of theorems forms an effective foundation for the theory of situations and worlds. All twenty-five theorems seem to be basic, reasonable principles that structure the domains of properties, relations, states of affairs, situations, and worlds in true and philosophically interesting ways. They resolve 15 of the 19 choice points defined in Barwise (1989) (see Notes 22, 27, 31, 32, 35, 36, 39, 43, and 45). Moreover, important axioms and principles stipulated by situation theorists…Read more
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348Abstract Objects: An Introduction to Axiomatic MetaphysicsD. Reidel. 1983.In this book, Zalta attempts to lay the axiomatic foundations of metaphysics by developing and applying a (formal) theory of abstract objects. The cornerstones include a principle which presents precise conditions under which there are abstract objects and a principle which says when apparently distinct such objects are in fact identical. The principles are constructed out of a basic set of primitive notions, which are identified at the end of the Introduction, just before the theorizing begins.…Read more
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138On the structural similarities between worlds and timesPhilosophical Studies 51 (2): 213-239. 1987.In the debate about the nature and identity of possible worlds, philosophers have neglected the parallel questions about the nature and identity of moments of time. These are not questions about the structure of time in general, but rather about the internal structure of each individual time. Times and worlds share the following structural similarities: both are maximal with respect to propositions (at every world and time, either p or p is true, for every p); both are consistent; both are close…Read more
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225How to say goodbye to the third manNoûs 34 (2). 2000.In (1991), Meinwald initiated a major change of direction in the study of Plato’s Parmenides and the Third Man Argument. On her conception of the Parmenides , Plato’s language systematically distinguishes two types or kinds of predication, namely, predications of the kind ‘x is F pros ta alla’ and ‘x is F pros heauto’. Intuitively speaking, the former is the common, everyday variety of predication, which holds when x is any object (perceptible object or Form) and F is a property which x exemplifi…Read more
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144The Tarski T-Schema is a tautology (literally)Analysis (1). 2013.The Tarski T-Schema has a propositional version. If we use ϕ as a metavariable for formulas and use terms of the form that-ϕ to denote propositions, then the propositional version of the T-Schema is: that-ϕ is true if and only if ϕ. For example, that Cameron is Prime Minister is true if and only if Cameron is Prime Minister. If that-ϕ is represented formally as [λ ϕ], then the T-Schema can be represented as the 0-place case of λ-Conversion. If we interpret [λ…] as a truth-functional context, the…Read more
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35Mally's Determinates and Husserl's NoemataIn A. Hieke (ed.), Ernst Mally - Versuch einer Neubewertung, Academia Verlag. 1998.In this paper, the author compares passages from two philosophically important texts and concludes that they have fundamental ideas in common. What makes this comparison and conclusion interesting is that the texts come from two different traditions in philosophy, the analytic and the phenomenological. In 1912, Ernst Mally published *Gegenstandstheoretische Grundlagen der Logik und Logistik*, an analytic work containing a combination of formal logic and metaphysics. In 1913, Edmund Husserl pu…Read more
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227Worlds and Propositions Set FreeErkenntnis 79 (4). 2014.The authors provide an object-theoretic analysis of two paradoxes in the theory of possible worlds and propositions stemming from Russell and Kaplan. After laying out the paradoxes, the authors provide a brief overview of object theory and point out how syntactic restrictions that prevent object-theoretic versions of the classical paradoxes are justified philosophically. The authors then trace the origins of the Russell paradox to a problematic application of set theory in the definition of worl…Read more
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86Gottlob FregeStanford Encyclopedia of Philosophy. 2008.This entry introduces the reader to the main ideas in Frege's philosophy of logic, mathematics, and language.
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722The Stanford Encyclopedia of Philosophy (edited book)The Metaphysics Research Lab. 2014.The Stanford Encyclopedia of Philosophy is an open access, dynamic reference work designed to organize professional philosophers so that they can write, edit, and maintain a reference work in philosophy that is responsive to new research. From its inception, the SEP was designed so that each entry is maintained and kept up to date by an expert or group of experts in the field. All entries and substantive updates are refereed by the members of a distinguished Editorial Board before they are made…Read more
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221These lecture notes were composed while teaching a class at Stanford and studying the work of Brian Chellas (Modal Logic: An Introduction, Cambridge: Cambridge University Press, 1980), Robert Goldblatt (Logics of Time and Computation, Stanford: CSLI, 1987), George Hughes and Max Cresswell (An Introduction to Modal Logic, London: Methuen, 1968; A Companion to Modal Logic, London: Methuen, 1984), and E. J. Lemmon (An Introduction to Modal Logic, Oxford: Blackwell, 1977). The Chellas text influenced…Read more
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22Reply to P. Ebert and M. Rossberg's friendly letter of complaintIn Hieke Alexander & Leitgeb Hannes (eds.), Reduction, Abstraction, Analysis, Ontos Verlag. pp. 11--311. 2009.This is a letter written in reply to some criticisms of object theory's analysis of mathematics. The criticisms were offered by Philip Ebert and Marcus Rossberg, in connection with my talk at the 31st International Wittgenstein Symposium, in Kirchberg, 2008. The exchange was published in the volume of proceedings.
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381A classically-based theory of impossible worldsNotre Dame Journal of Formal Logic 38 (4): 640-660. 1997.The appeal to possible worlds in the semantics of modal logic and the philosophical defense of possible worlds as an essential element of ontology have led philosophers and logicians to introduce other kinds of `worlds' in order to study various philosophical and logical phenomena. The literature contains discussions of `non-normal worlds', `non-classical worlds', `non-standard worlds', and `impossible worlds'. These atypical worlds have been used in the following ways: (1) to interpret unusual …Read more
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22Reflections on the Logic of the Ontological ArgumentStudia Neoaristotelica 4 (1): 28-35. 2007.The authors evaluate the soundness of the ontological argument they developed in their 1991 paper. They focus on Anselm’s first premise, which asserts that there is a conceivable thing than which nothing greater can be conceived. After casting doubt on the argument Anselm uses in support of this premise, the authors show that there is a formal reading on which it is true. Such a reading can be used in a sound reconstruction of the argument. After this reconstruction is developed in precise detai…Read more
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54Reflections on the Logic of the Ontological ArgumentStudia Neoaristotelica 4 (1): 28-35. 2007.The authors evaluate the soundness of the ontological argument they developed in their 1991 paper. They focus on Anselm’s first premise, which asserts that there is a conceivable thing than which nothing greater can be conceived. After casting doubt on the argument Anselm uses in support of this premise, the authors show that there is a formal reading on which it is true. Such a reading can be used in a sound reconstruction of the argument. After this reconstruction is developed in precise detai…Read more
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226Reflections on mathematicsIn V. F. Hendricks & Hannes Leitgeb (eds.), Philosophy of Mathematics: Five Questions, Automatic Press/vip. 2007.This paper contains answers to the following Five questions, posed by the editors are answered: (1) Why were you initially drawn to the foundations of mathematics and/or the philosophy of mathematics? (2) What example(s) from your work (or the work of others) illustrates the use of mathematics for philosophy? (3) What is the proper role of philosophy of mathematics in relation to logic, foundations of mathematics, the traditional core areas of mathematics, and science? (4) What do you consider t…Read more
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100Logic and MetaphysicsJournal of the Indian Council of Philosophical Research 27 (2): 155-184. 2010.In this article, we canvass a few of the interesting topics that philosophers can pursue as part of the simultaneous study of logic and metaphysics. To keep the discussion to a manageable length, we limit our survey to deductive, as opposed to inductive, logic. Though most of this article will focus on the ways in which logic can be deployed in the study of metaphysics, we begin with a few remarks about how metaphysics might be needed to understand what logic is. When we ask the question, “What …Read more
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271Fregean senses, modes of presentation, and conceptsPhilosophical Perspectives 15 335-359. 2001.of my axiomatic theory of abstract objects.<sup>1</sup> The theory asserts the ex- istence not only of ordinary properties, relations, and propositions, but also of abstract individuals and abstract properties and relations. The
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27The Intentional Stance (review)Review of Metaphysics 43 (2): 397-400. 1989.In this book, Dennett determines just how far we can push the idea that mental states are distinguished by intentionality, that is, by the fact that they have content in virtue of being about, or directed towards, the world at large. Intentionality is characteristic of such states as belief and desire, since all belief is belief of something or that something be the case. In contrast to the physical stance and the design stance, the intentional stance is the predictive attitude or strategy philo…Read more
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122A philosophical conception of propositional modal logicPhilosophical Topics 21 (2): 263-281. 1993.The author revises the formulation of propositional modal logic by interposing a domain of structured propositions between the modal language and the models. Interpretations of the language (i.e., ways of mapping the language into the domain of propositions) are distinguished from models of the domain of propositions (i.e., ways of assigning truth values to propositions at each world), and this contrasts with the traditional formulation. Truth and logical consequence are defined, in the first in…Read more
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21Philosophy and the world wide webAmerican Philosophical Association Newsletter on Computer Use in Philosophy 94 (2): 29-33. 1995.In this note, I plan to describe some of the procedures I followed in creating the World Wide Web site for the Metaphysics Research Lab at CSLI. Its URL (Uniform Resource Locator) is.
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71A Common Ground and Some Surprising ConnectionsSouthern Journal of Philosophy 40 (S1): 1-25. 2002.This paper serves as a kind of field guide to certain passages in the literature which bear upon the foundational theory of abstract objects. The foundational theory assimilates ideas from key philosophers in both the analytical and phenomenological traditions. I explain how my foundational theory of objects serves as a common ground where analytic and phenomenological concerns meet. I try to establish how the theory offers a logic that systematizes a well-known phenomenological kind of entity…Read more
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178The Stanford encyclopedia of philosophy: A developed dynamic reference workIn James Moor & Terrell Ward Bynum (eds.), Cyberphilosophy: the intersection of philosophy and computing, Blackwell. pp. 210-228. 2002.In this entry, the authors outline the goals of a "dynamic reference work", and explain how the Stanford Encyclopedia of Philosophy has been designed to achieve those goals.
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43Meinongian type theory and its applicationsStudia Logica 41 (2-3): 297-307. 1982.In this paper I propose a fundamental modification of standard type theory, produce a new kind of type theoretic language, and couch in this language a comprehensive theory of abstract individuals and abstract properties and relations of every type. I then suggest how to employ the theory to solve the four following philosophical problems: the identification and ontological status of Frege's Senses; the deviant behavior of terms in propositional attitude contexts; the non-identity of necessarily…Read more
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272The Fundamental Theorem of World TheoryJournal of Philosophical Logic 43 333-363. 2014.The fundamental principle of the theory of possible worlds is that a proposition p is possible if and only if there is a possible world at which p is true. In this paper we present a valid derivation of this principle from a more general theory in which possible worlds are defined rather than taken as primitive. The general theory uses a primitive modality and axiomatizes abstract objects, properties, and propositions. We then show that this general theory has very small models and hence that it…Read more
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168Intensional Logic and the Metaphysics of IntentionalityMIT Press. 1988.This book tackles the issues that arise in connection with intensional logic -- a formal system for representing and explaining the apparent failures of certain important principles of inference such as the substitution of identicals and existential generalization -- and intentional states --mental states such as beliefs, hopes, and desires that are directed towards the world. The theory offers a unified explanation of the various kinds of inferential failures associated with intensional logic b…Read more
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101Deriving and validating Kripkean claims using the theory of abstract objectsNoûs 40 (4). 2006.In this paper, the author shows how one can independently prove, within the theory of abstract objects, some of the most significant claims, hypotheses, and background assumptions found in Kripke's logical and philosophical work. Moreover, many of the semantic features of theory of abstract objects are consistent with Kripke's views — the successful representation, in the system, of the truth conditions and entailments of philosophically puzzling sentences of natural language validates certain K…Read more
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161Replies to the criticsPhilosophical Studies 69 (2-3): 231-242. 1993.In an author-meets-critics session at the March 1992 Pacific APA meetings, the critics (Christopher Menzel, Harry Deutsch, and C. Anthony Anderson) commented on the author's book *Intensional Logic and the Metaphysics of Intentionality* (Cambridge, MA: MIT/Bradford, 1988). The critical commentaries are published in this issue together with these replies by the author. The author responds to questions concerning the system he proposes, and in particular, to questions concerning the treatment of …Read more
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121Relations vs functions at the foundations of logic: type-theoretic considerationsJournal of Logic and Computation 21 351-374. 2011.Though Frege was interested primarily in reducing mathematics to logic, he succeeded in reducing an important part of logic to mathematics by defining relations in terms of functions. By contrast, Whitehead & Russell reduced an important part of mathematics to logic by defining functions in terms of relations (using the definite description operator). We argue that there is a reason to prefer Whitehead & Russell's reduction of functions to relations over Frege's reduction of relations to funct…Read more
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