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Profile: Edward Zalta (Stanford University)
  1. Ed Zalta, The 5 Questions.
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  2. Edward N. Zalta, Basic Concepts in Modal Logic.
    These 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 me the most, though the order of (...)
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  3. Edward N. Zalta, The Theory of Relations, Complex Terms, and a Connection Between Λ and Ε Calculi.
    This paper introduces a new method of interpreting complex relation terms in a second-order quantified modal language. We develop a completely general second-order modal language with two kinds of complex terms: one kind for denoting individuals and one kind for denoting n-place relations. Several issues arise in connection with previous, algebraic methods for interpreting the relation terms. The new method of interpreting these terms described here addresses those issues while establishing an interesting connection between λ and ε calculi. The resulting (...)
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  4. Alexander J. McKenzie & Edward N. Zalta (forthcoming). Evolutionary Game Theory. Stanford Encyclopedia of Philosophy.
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  5. Uri Nodelman & Edward N. Zalta (2014). Foundations for Mathematical Structuralism. Mind 123 (489):39-78.
    We investigate the form of mathematical structuralism that acknowledges the existence of structures and their distinctive structural elements. This form of structuralism has been subject to criticisms recently, and our view is that the problems raised are resolved by proper, mathematics-free theoretical foundations. Starting with an axiomatic theory of abstract objects, we identify a mathematical structure as an abstract object encoding the truths of a mathematical theory. From such foundations, we derive consequences that address the main questions and issues that (...)
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  6. Otávio Bueno, Christopher Menzel & Edward N. Zalta (2013). Worlds and Propositions Set Free. Erkenntnis (4):1-24.
    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 worlds. Next the authors show that an (...)
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  7. Christopher Menzel & Edward N. Zalta (2013). The Fundamental Theorem of World Theory. Journal of Philosophical Logic (2-3):1-31.
    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 (...)
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  8. Edward N. Zalta (2013). The Tarski T-Schema is a Tautology (Literally). Analysis (1):ant099.
    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 (...)
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  9. Michael Nelson & Edward N. Zalta (2012). A Defense of Contingent Logical Truths. Philosophical Studies 157 (1):153-162.
    A formula is a contingent logical truth when it is true in every model M but, for some model M , false at some world of M . We argue that there are such truths, given the logic of actuality. Our argument turns on defending Tarski’s definition of truth and logical truth, extended so as to apply to modal languages with an actuality operator. We argue that this extension is the philosophically proper account of validity. We counter recent arguments to (...)
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  10. Paul Oppenheimer & Edward N. Zalta (2011). A Computationally-Discovered Simplification of the Ontological Argument. Australasian Journal of Philosophy 89 (2):333 - 349.
    The authors investigated the ontological argument computationally. The premises and conclusion of the argument are represented in the syntax understood by the automated reasoning engine PROVER9. Using the logic of definite descriptions, the authors developed a valid representation of the argument that required three non-logical premises. PROVER9, however, discovered a simpler valid argument for God's existence from a single non-logical premise. Reducing the argument to one non-logical premise brings the investigation of the soundness of the argument into better focus. Also, (...)
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  11. Paul Oppenheimer & Edward N. Zalta (2011). Relations Vs Functions at the Foundations of Logic: Type-Theoretic Considerations. Journal of Logic and Computation 21:351-374.
    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 functions. There is an interesting (...)
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  12. Edward N. Zalta (2010). Logic and Metaphysics. Journal of Indian Council of Philosophical Research 27 (2):155-184.
    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 (...)
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  13. Michael Nelson & Edward N. Zalta (2009). Bennett and “Proxy Actualism”. Philosophical Studies 142 (2):277-292.
    Karen Bennett has recently argued that the views articulated by Linsky and Zalta (Philos Perspect 8:431–458, 1994) and (Philos Stud 84:283–294, 1996) and Plantinga (The nature of necessity, 1974) are not consistent with the thesis of actualism, according to which everything is actual. We present and critique her arguments. We first investigate the conceptual framework she develops to interpret the target theories. As part of this effort, we question her definition of ‘proxy actualism’. We then discuss her main arguments that (...)
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  14. Edward N. Zalta (2009). Reply to P. Ebert and M. Rossberg's Friendly Letter of Complaint. In. In Hieke Alexander & Leitgeb Hannes (eds.), Reduction, Abstraction, Analysis. Ontos Verlag. 11--311.
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  15. Edward Zalta (ed.) (2008). Stanford Encyclopedia of Philosophy.
     
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  16. Edward N. Zalta (2008). Bayes' Theorem. In Edward Zalta (ed.), Stanford Encyclopedia of Philosophy.
     
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  17. Edward N. Zalta, Frege's Logic, Theorem, and Foundations for Arithmetic. Stanford Encyclopedia of Philosophy.
    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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  18. Edward N. Zalta, Gottlob Frege. Stanford Encyclopedia of Philosophy.
    This entry introduces the reader to the main ideas in Frege's philosophy of logic, mathematics, and language.
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  19. Branden Fitelson & Edward N. Zalta (2007). Steps Toward a Computational Metaphysics. Journal of Philosophical Logic 36 (2):227-247.
    In this paper, the authors describe their initial investigations in computational metaphysics. Our method is to implement axiomatic metaphysics in an automated reasoning system. In this paper, we describe what we have discovered when the theory of abstract objects is implemented in PROVER9 (a first-order automated reasoning system which is the successor to OTTER). After reviewing the second-order, axiomatic theory of abstract objects, we show (1) how to represent a fragment of that theory in PROVER9's first-order syntax, and (2) how (...)
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  20. Paul E. Oppenheimer & Edward N. Zalta (2007). O logice ontologického důkazu. Studia Neoaristotelica 4 (1):5-27.
    In this paper, the authors show that there is a reading of St. Anselm’s ontological argument in Proslogium II that is logically valid (the premises entail the conclusion). This reading takes Anselm’s use of the definite description “that than which nothing greater can be conceived” seriously. Consider a first-order language and logic in which definite descriptions are genuine terms, and in which the quantified sentence “there is an x such that…” does not imply “x exists”. Then, using an ordinary logic (...)
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  21. Paul E. Oppenheimer & Edward N. Zalta (2007). Reflections on the Logic of the Ontological Argument. Studia Neoaristotelica 4 (1):28-35.
    In this paper, the authors evaluate the ontological argument they developed in their 1991 paper as to soundness. They focus on Anselm's first premise, which asserts: there is a conceivable thing than which nothing greater is conceivable. After suggesting reasons why this premise is false, the authors show that there is a reading of this premise on which it is true. Such a premise can be used in a valid and sound reconstruction of the ontological argument. This argument is developed (...)
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  22. Ed Zalta (2007). Frege's Theorem'. In Thaddeus Metz (ed.), Stanford Encyclopedia of Philosophy.
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  23. Edward N. Zalta (2007). O logice ontologického důkazu. Studia Neoaristotelica 4 (1):5-27.
    De argumenti ontologici forma logicaTractatione proposita auctores manifestant, „Argumentum Ontologicum“ St. Anselmi in 2° capitulo eius Proslogii inscriptum ut validum exponi posse (i. e. consequentiam bonam servando). Hac in interpretatione vis et notio descriptionis illae „id quo maius cogitari nequit“, qua Anselmus usus est, rite agnoscitur. Datis enim lingua formali „primi ordinis“, ut aiunt, et systemati deductivo logicae huiusmodi, in quo descriptiones definitae genuini sunt termini et ubi a sententia „datur x quod…“ signo quantitatis praefixa ad sententiam „x exsistit“ consequentia (...)
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  24. Edward N. Zalta (2007). Reflections on Mathematics. In V. F. Hendricks & Hannes Leitgeb (eds.), Philosophy of Mathematics: Five Questions. Automatic Press/VIP.
    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 the most (...)
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  25. Edward N. Zalta (2007). Reflections on the Logic of the Ontological Argument. Studia Neoaristotelica 4 (1):28-35.
    Forma logica argumenti ontologici reconsiderataHac in tractatione auctores veritatem praemissarum argumenti ontologici, quod in dissertatione sua anno 1991 publicata proposuerunt, examinant. Auctores praesertim de prima Anselmi praemissa, qua asseritur, dari cogitabile quid, quo maius cogitari nequit, dubitant. Primo scilicet argumentum, quod Anselmus pro hac assertione astruit, reiciunt; deinde ostendunt, aliam interpretationem formalem huius praemissae dari posse, secundum quam vera evenit. Haec interpretatione adhibita, argumentum Anselmi non solum validum, sed etiam efficax esse constat. Reconstructio praecisa argumenti in hoc sensu intellectinihilominus revelat, (...)
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  26. Bernard Linsky & Edward N. Zalta (2006). What is Neologicism? Bulletin of Symbolic Logic 12 (1):60-99.
    In this paper, we investigate (1) what can be salvaged from the original project of "logicism" and (2) what is the best that can be done if we lower our sights a bit. Logicism is the view that "mathematics is reducible to logic alone", and there are a variety of reasons why it was a non-starter. We consider the various ways of weakening this claim so as to produce a "neologicism". Three ways are discussed: (1) expand the conception of logic (...)
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  27. Edward N. Zalta (2006). Deriving and Validating Kripkean Claims Using the Theory of Abstract Objects. Noûs 40 (4):591–622.
    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 Kripkean semantic claims about natural language.
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  28. Edward N. Zalta (2006). Essence and Modality. Mind 115 (459):659-693.
    Some recently-proposed counterexamples to the traditional definition of essential property do not require a separate logic of essence. Instead, the examples can be analysed in terms of the logic and theory of abstract objects. This theory distinguishes between abstract and ordinary objects, and provides a general analysis of the essential properties of both kinds of object. The claim ‘x has F necessarily’ becomes ambiguous in the case of abstract objects, and in the case of ordinary objects there are various ways (...)
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  29. Otávio Bueno & Edward N. Zalta (2005). A Nominalist's Dilemma and its Solution. Philosophia Mathematica 13 (3):297-307.
    Current versions of nominalism in the philosophy of mathematics have the benefit of avoiding commitment to the existence of mathematical objects. But this comes with the cost of not taking mathematical theories literally. Jody Azzouni's Deflating Existential Consequence has recently challenged this conclusion by formulating a nominalist view that lacks this cost. In this paper, we argue that, as it stands, Azzouni's proposal does not yet succeed. It faces a dilemma to the effect that either the view is not nominalist (...)
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  30. David J. Anderson & Edward N. Zalta (2004). Frege, Boolos, and Logical Objects. Journal of Philosophical Logic 33 (1):1-26.
    In this paper, the authors discuss Frege's theory of "logical objects" (extensions, numbers, truth-values) and the recent attempts to rehabilitate it. We show that the 'eta' relation George Boolos deployed on Frege's behalf is similar, if not identical, to the encoding mode of predication that underlies the theory of abstract objects. Whereas Boolos accepted unrestricted Comprehension for Properties and used the 'eta' relation to assert the existence of logical objects under certain highly restricted conditions, the theory of abstract objects uses (...)
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  31. Edward N. Zalta (2004). In Defense of the Law of Noncontradiction. In J. C. Beall, B. Armour-Garb & G. Priest (eds.), The Law of Noncontradiction: New Philosophical Essays. Oxford University Press.
    The arguments of the dialetheists for the rejection of the traditional law of noncontradiction are not yet conclusive. The reason is that the arguments that they have developed against this law uniformly fail to consider the logic of encoding as an analytic method that can resolve apparent contradictions. In this paper, we use Priest [1995] and [1987] as sample texts to illustrate this claim. In [1995], Priest examines certain crucial problems in the history of philosophy from the point of view (...)
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  32. Edward N. Zalta (ed.) (2004). The Stanford Encyclopedia of Philosophy. The Metaphysics Research Lab.
    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 (...)
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  33. Edward N. Zalta (2003). Referring to Fictional Characters. Dialectica 57 (2):243–254.
    The author engages a question raised about theories of nonexistent objects. The question concerns the way names of fictional characters, when analyzed as names which denote nonexistent objects, acquire their denotations. Since nonexistent objects cannot causally interact with existent objects, it is thought that we cannot appeal to a `dubbing' or a `baptism'. The question is, therefore, what is the starting point of the chain? The answer is that storytellings are to be thought of as extended baptisms, and the details (...)
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  34. Colin Allen, Uri Nodelman & Edward N. Zalta (2002). The Stanford Encyclopedia of Philosophy: A Developed Dynamic Reference Work. In James Moor & Terrell Ward Bynum (eds.), Cyberphilosophy: The Intersection of Philosophy and Computing. Blackwell Pub.. 210-228.
    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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  35. Edward N. Zalta (2002). A Common Ground and Some Surprising Connections. Southern Journal of Philosophy (Supplement) 40 (S1):1-25.
    This paper serves as a kind of field guide to certain passages in the literature which bear upon the theory of abstract objects. This theory assimilates ideas from key philosophers in both the analytical and phenomenological traditions. The paper explains how the theory of abstract objects serves as a common ground where analytic and phenomenological concerns meet.
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  36. David Braun, Jeffrey C. King & Edward N. Zalta (2001). The Metaphysics of Reference. Philosophical Perspectives 15:253-359.
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  37. Edward N. Zalta (2001). Fregean Senses, Modes of Presentation, and Concepts. Philosophical Perspectives 15 (s15):335-359.
    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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  38. Francis Jeffry Pelletier & Edward N. Zalta (2000). How to Say Goodbye to the Third Man. Noûs 34 (2):165–202.
    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 (...)
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  39. Edward N. Zalta (2000). A (Leibnizian) Theory of Concepts. Logical Analysis and History of Philosophy 3:137-183.
    In this paper, the author develops a theory of concepts and shows that it captures many of the ideas about concepts that Leibniz expressed in his work. Concepts are first analyzed in terms of a precise background theory of abstract objects, and once concept summation and concept containment are defined, the axioms and theorems of Leibniz's calculus of concepts (in his logical papers) are derived. This analysis of concepts is then seamlessly connected with Leibniz's modal metaphysics of complete individual concepts. (...)
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  40. Edward N. Zalta (2000). Neo-Logicism? An Ontological Reduction of Mathematics to Metaphysics. Erkenntnis 53 (1-2):219-265.
    In this paper, we describe "metaphysical reductions", in which the well-defined terms and predicates of arbitrary mathematical theories are uniquely interpreted within an axiomatic, metaphysical theory of abstract objects. Once certain (constitutive) facts about a mathematical theory T have been added to the metaphysical theory of objects, theorems of the metaphysical theory yield both an analysis of the reference of the terms and predicates of T and an analysis of the truth of the sentences of T. The well-defined terms and (...)
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  41. Edward N. Zalta (2000). The Road Between Pretense Theory and Abstract Object Theory. In T. Hofweber & A. Everett (eds.), Empty Names, Fiction, and the Puzzles of Non-Existence. CSLI Publications.
    In its approach to fiction and fictional discourse, pretense theory focuses on the behaviors that we engage in once we pretend that something is true. These may include pretending to name, pretending to refer, pretending to admire, and various other kinds of make-believe. Ordinary discourse about fictions is analyzed as a kind of institutionalized manner of speaking. Pretense, make-believe, and manners of speaking are all accepted as complex patterns of behavior that prove to be systematic in various ways. In this (...)
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  42. Mark Colyvan & Edward N. Zalta (1999). Mathematics: Truth and Fiction? Review of Mark Balaguer's. Philosophia Mathematica 7 (3):336-349.
    <span class='Hi'>Mark</span> Balaguer’s project in this book is extremely ambitious; he sets out to defend both platonism and fictionalism about mathematical entities. Moreover, Balaguer argues that at the end of the day, platonism and fictionalism are on an equal footing. Not content to leave the matter there, however, he advances the anti-metaphysical conclusion that there is no fact of the matter about the existence of mathematical objects.1 Despite the ambitious nature of this project, for the most part Balaguer does not (...)
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  43. Mark Colyvan & Edward N. Zalta (1999). Mathematics: Truth and Fiction? Review of Mark Balaguer's Platonism and Anti-Platonism in Mathematics. Philosophia Mathematica 7 (3):336-349.
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  44. Edward N. Zalta (1999). Natural Numbers and Natural Cardinals as Abstract Objects: A Partial Reconstruction of Frege"s Grundgesetze in Object Theory. [REVIEW] Journal of Philosophical Logic 28 (6):619-660.
    In this paper, the author derives the Dedekind-Peano axioms for number theory from a consistent and general metaphysical theory of abstract objects. The derivation makes no appeal to primitive mathematical notions, implicit definitions, or a principle of infinity. The theorems proved constitute an important subset of the numbered propositions found in Frege's Grundgesetze. The proofs of the theorems reconstruct Frege's derivations, with the exception of the claim that every number has a successor, which is derived from a modal axiom that (...)
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  45. Edward N. Zalta (1998). Mally's Determinates and Husserl's Noemata. In A. Hieke (ed.), Ernst Mally - Versuch einer Neubewertung. Academia Verlag.
    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 published *Ideen zu einer reinen Phänomenologie und phänomenologischen Philosophie*, a seminal (...)
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  46. Eric Hammer & Edward N. Zalta (1997). A Solution to the Problem of Updating Encyclopedias. Computers and the Humanities 31 (1):47-60.
    This paper describes a way of creating and maintaining a `dynamic encyclopedia', i.e., an encyclopedia whose entries can be improved and updated on a continual basis without requiring the production of an entire new edition. Such an encyclopedia is therefore responsive to new developments and new research. We discuss our implementation of a dynamic encyclopedia and the problems that we had to solve along the way. We also discuss ways of automating the administration of the encyclopedia.
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  47. Edward N. Zalta (1997). A Classically-Based Theory of Impossible Worlds. Notre Dame Journal of Formal Logic 38 (4):640-660.
    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 modal logics, (2) to distinguish logically equivalent propositions, (3) (...)
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  48. Edward N. Zalta (1997). The Modal Object Calculus and its Interpretation. In M. de Rijke (ed.), Advances in Intensional Logic. Kluwer. 249--279.
    The modal object calculus is the system of logic which houses the (proper) axiomatic theory of abstract objects. The calculus has some rather interesting features in and of itself, independent of the proper theory. The most sophisticated, type-theoretic incarnation of the calculus can be used to analyze the intensional contexts of natural language and so constitutes an intensional logic. However, the simpler second-order version of the calculus couches a theory of fine-grained properties, relations and propositions and serves as a framework (...)
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  49. Bernard Linsky & Edward N. Zalta (1996). In Defense of the Contingently Nonconcrete. Philosophical Studies 84 (2-3):283-294.
    In "Actualism or Possibilism?" (Philosophical Studies, 84 (2-3), December 1996), James Tomberlin develops two challenges for actualism. The challenges are to account for the truth of certain sentences without appealing to merely possible objects. After canvassing the main actualist attempts to account for these phenomena, he then criticizes the new conception of actualism that we described in our paper "In Defense of the Simplest Quantified Modal Logic" (Philosophical Perspectives 8: Philosophy of Logic and Language, Atascadero, CA: Ridgeview, 1994). We respond (...)
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  50. Bernard Linsky & Edward N. Zalta (1995). Current Periodical Articles 705. ARGUMENT 92 (11).
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