Results for 'Zalta Edward'

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  1. Abstract Objects: An Introduction to Axiomatic Metaphysics.Edward N. Zalta - 1983 - Dordrecht, Netherland: D. Reidel.
    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. The main reason (...)
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  2. Intensional Logic and the Metaphysics of Intentionality.Edward N. Zalta - 1988 - Cambridge, MA, USA: MIT Press.
    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 but also unifies the study of intensional contexts (...)
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  3. Abstract Objects.Edward N. Zalta - 1983 - Revue de Métaphysique et de Morale 90 (1):135-137.
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  4. The modal object calculus and its interpretation.Edward N. Zalta - 1997 - In Maarten de Rijke, Advances in Intensional Logic. Dordrecht, Netherland: Kluwer Academic Publishers. pp. 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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  5. (1 other version)Fregean senses, modes of presentation, and concepts.Edward N. Zalta - 2001 - Philosophical Perspectives 15:335-359.
    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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  6. Natural Numbers and Natural Cardinals as Abstract Objects: A Partial Reconstruction of Frege"s Grundgesetze in Object Theory.Edward N. Zalta - 1999 - 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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  7. (2 other versions)Stanford Encyclopedia of Philosophy.Edward N. Zalta (ed.) - 1995 - Stanford University.
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  8. A (leibnizian) theory of concepts.Edward N. Zalta - 2000 - History of Philosophy & Logical Analysis 3 (1):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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  9.  84
    Mathematical Pluralism.Edward N. Zalta - 2024 - Noûs 58 (2):306-332.
    Mathematical pluralism can take one of three forms: (1) every consistent mathematical theory consists of truths about its own domain of individuals and relations; (2) every mathematical theory, consistent or inconsistent, consists of truths about its own (possibly uninteresting) domain of individuals and relations; and (3) the principal philosophies of mathematics are each based upon an insight or truth about the nature of mathematics that can be validated. (1) includes the multiverse approach to set theory. (2) helps us to understand (...)
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  10. Bayes' Theorem.Edward N. Zalta - 2012 - In Ed Zalta, Stanford Encyclopedia of Philosophy. Stanford, CA: Stanford Encyclopedia of Philosophy.
     
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  11.  78
    Singular Propositions, Abstract Constituents, and Propositional Attitudes.Edward N. Zalta - 1989 - In Joseph Almog, John Perry & Howard Wettstein, Themes From Kaplan. New York: Oxford University Press. pp. 455--78.
    The author resolves a conflict between Frege's view that the cognitive significance of coreferential names may be distinct and Kaplan's view that since coreferential names have the same "character", they have the same cognitive significance. A distinction is drawn between an expression's "character" and its "cognitive character". The former yields the denotation of an expression relative to a context (and individual); the latter yields the abstract sense of an expression relative to a context (and individual). Though coreferential names have the (...)
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  12. Reflections on the Logic of the Ontological Argument.Edward N. Zalta - 2007 - Studia Neoaristotelica 4 (1):28-35.
    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 (...)
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  13.  18
    (1 other version)Scientific representation.Edward N. Zalta - 2012 - In Ed Zalta, Stanford Encyclopedia of Philosophy. Stanford, CA: Stanford Encyclopedia of Philosophy.
    Science provides us with representations of atoms, elementary particles, polymers, populations, genetic trees, economies, rational decisions, aeroplanes, earthquakes, forest fires, irrigation systems, and the world’s climate. It's through these representations that we learn about the world. This entry explores various different accounts of scientific representation, with a particular focus on how scientific models represent their target systems. As philosophers of science are increasingly acknowledging the importance, if not the primacy, of scientific models as representational units of science, it's important to (...)
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  14. Essence and modality.Edward N. Zalta - 2006 - 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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  15. In Defence of the Law of Non-Contradiction.Edward N. Zalta - 2004 - In Graham Priest, Jc Beall & Bradley P. Armour-Garb, The law of non-contradiction : new philosophical essays. New York: Oxford University Press.
  16. Basic Concepts in Modal Logic.Edward N. Zalta - manuscript
    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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  17.  10
    The Power of Predication and Quantification.Edward N. Zalta - 2025 - Open Philosophy 8 (1):1-16.
    In this article, I show how two modes of predication and quantification in a modal context allow one to (a) define what it is for an individual or relation to exist, (b) define identity conditions for properties and relations conceived hyperintensionally, (c) define identity conditions for individuals and prove the necessity of identity for both individuals and relations, (d) derive the central definition of free logic as a theorem, (e) define the essential properties of abstract objects and provide a framework (...)
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  18. The Stanford Encyclopedia of Philosophy.Edward N. Zalta (ed.) - 2016
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  19.  85
    A Common Ground and Some Surprising Connections.Edward N. Zalta - 2002 - Southern Journal of Philosophy 40 (S1):1-25.
    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, and I try to show (...)
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  20. The Tarski T-Schema is a tautology (literally).Edward N. Zalta - 2013 - 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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  21.  42
    On Mally's Alleged Paradox: A Reply'.Edward Zalta - 1992 - History and Philosophy of Logic 13:55-86.
    In this paper, the author responds to D. Jacquette's paper, "Mally's Heresy and the Logic of Meinong's Object Theory'' (History and Philosophy of Logic, 10, 1989, 1-14), in which it is claimed that Ernst Mally's distinction between two modes of predication, as it is employed in the theory of abstract objects, is reducible to, and analyzable in terms of, a single mode of predication plus the distinction between nuclear and extranuclear properties. The argument against Jacquette's claims consists of counterexamples to (...)
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  22. Twenty-five basic theorems in situation and world theory.Edward N. Zalta - 1993 - Journal of Philosophical Logic 22 (4):385-428.
    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 are derived (see Notes (...)
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  23.  2
    Models in science.Edward N. Zalta - 2012 - In Ed Zalta, Stanford Encyclopedia of Philosophy. Stanford, CA: Stanford Encyclopedia of Philosophy.
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  24. Logical and analytic truths that are not necessary.Edward N. Zalta - 1988 - Journal of Philosophy 85 (2):57-74.
    The author describes an interpreted modal language and produces 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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  25. A classically-based theory of impossible worlds.Edward N. Zalta - 1997 - 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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  26. Computer Science and Metaphysics: A Cross-Fertilization.Edward N. Zalta, Christoph Benzmüller & Daniel Kirchner - 2019 - Open Philosophy 2 (1):230-251.
    Computational philosophy is the use of mechanized computational techniques to unearth philosophical insights that are either difficult or impossible to find using traditional philosophical methods. Computational metaphysics is computational philosophy with a focus on metaphysics. In this paper, we (a) develop results in modal metaphysics whose discovery was computer assisted, and (b) conclude that these results work not only to the obvious benefit of philosophy but also, less obviously, to the benefit of computer science, since the new computational techniques that (...)
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  27.  6
    (1 other version)Models in science.Edward N. Zalta - 2012 - In Ed Zalta, Stanford Encyclopedia of Philosophy. Stanford, CA: Stanford Encyclopedia of Philosophy.
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  28.  42
    Mally's Determinates and Husserl's Noemata.Edward N. Zalta - 1998 - In Alexander Hieke, 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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  29.  22
    Lambert, Mally, and the Principle of Independence.Edward N. Zalta - 1985 - Grazer Philosophische Studien 25-26 (1):447-495.
    In a recent book, K. Lambert argues that philosophers should adopt Mally's Principle of Independence (the principle that an object can have properties even though it lacks being of any kind) by abandoning a constraint on true predications, namely, that all of the singular terms in a true predication denote objects which have being. The constraint may be abandoned either by supposing there is a true predication in which one of the terms denotes a beingless object (Meinong) or by supposing (...)
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  30.  30
    Lambert, Mally and the Principle of Independence.Edward N. Zalta - 1985 - Grazer Philosophische Studien 25 (1):447-459.
    In a recent book, K. Lambert argues that philosophers should adopt Mally's Principle of Independence (the principle that an object can have properties even though it lacks being of any kind) by abandoning a constraint on true predications, namely, that all of the singular terms in a true predication denote objects which have being. The constraint may be abandoned either by supposing there is a true predication in which one of the terms denotes a beingless object (Meinong) or by supposing (...)
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  31. Reflections on mathematics.Edward N. Zalta - 2007 - In V. F. Hendricks & Hannes Leitgeb, 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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  32.  74
    The Theory of Relations, Complex Terms, and a Connection Between λ and ε Calculi.Edward N. Zalta - manuscript
    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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  33.  1
    In Defence of the Law of Non-Contradiction.Edward N. Zalta - 2004 - In Graham Priest, Jc Beall & Bradley P. Armour-Garb, The law of non-contradiction : new philosophical essays. New York: 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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  34. The road between pretense theory and abstract object theory.Edward N. Zalta - 2000 - In T. Hofweber & A. Everett, 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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  35. On the structural similarities between worlds and times.Edward N. Zalta - 1987 - Philosophical Studies 51 (2):213-239.
    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 (...)
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  36. Referring to fictional characters.Edward N. Zalta - 2003 - 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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  37. Neo-logicism? An ontological reduction of mathematics to metaphysics.Edward N. Zalta - 2000 - 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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  38.  13
    Metaphysics of Routley Star.Edward Zalta - 2024 - Australasian Journal of Logic 21 (4):141-176.
    This paper investigates two forms of the Routley star operation, one in Routley & Routley 1972 and the other in Leitgeb 2019. We use the background of object theory to define both forms of the Routley star operation and show how the basic principles governing both forms become derivable and need not be stipulated. Since no mathematics is assumed by our background formalism, the existence of the Routley star image s* of a situation s is therefore guaranteed not by set (...)
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  39.  98
    Gottlob Frege.Edward N. Zalta - 2008 - 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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  40.  6
    (1 other version)The ergodic hierarchy.Edward N. Zalta - 2012 - In Ed Zalta, Stanford Encyclopedia of Philosophy. Stanford, CA: Stanford Encyclopedia of Philosophy.
    The so-called ergodic hierarchy (EH) is a central part of ergodic theory. It is a hierarchy of properties that dynamical systems can possess. Its five levels are egrodicity, weak mixing, strong mixing, Kolomogorov, and Bernoulli. Although EH is a mathematical theory, its concepts have been widely used in the foundations of statistical physics, accounts of randomness, and discussions about the nature of chaos. We introduce EH and discuss its applications in these fields.
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  41. Logic and Metaphysics.Edward N. Zalta - 2010 - Journal of the 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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  42.  28
    (1 other version)Reply to P. Ebert and M. Rossberg's friendly letter of complaint.Edward N. Zalta - 2009 - In Alexander Hieke & Hannes Leitgeb, Reduction: Between the Mind and the Brain. Frankfurt: Ontos Verlag. pp. 11--311.
    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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  43.  1
    The ergodic hierarchy.Edward N. Zalta - 2012 - In Ed Zalta, Stanford Encyclopedia of Philosophy. Stanford, CA: Stanford Encyclopedia of Philosophy.
    The so-called ergodic hierarchy (EH) is a central part of ergodic theory. It is a hierarchy of properties that dynamical systems can possess. Its five levels are egrodicity, weak mixing, strong mixing, Kolomogorov, and Bernoulli. Although EH is a mathematical theory, its concepts have been widely used in the foundations of statistical physics, accounts of randomness, and discussions about the nature of chaos. We introduce EH and discuss its applications in these fields.
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  44. (2 other versions)Frege's logic, theorem, and foundations for arithmetic.Edward N. Zalta - 2008 - 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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  45. Worlds and Propositions Set Free.Otávio Bueno, Christopher Menzel & Edward N. Zalta - 2014 - Erkenntnis 79 (4):797–820.
    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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  46.  47
    Number Theory and Infinity Without Mathematics.Uri Nodelman & Edward N. Zalta - 2024 - Journal of Philosophical Logic 53 (5):1161-1197.
    We address the following questions in this paper: (1) Which set or number existence axioms are needed to prove the theorems of ‘ordinary’ mathematics? (2) How should Frege’s theory of numbers be adapted so that it works in a modal setting, so that the fact that equivalence classes of equinumerous properties vary from world to world won’t give rise to different numbers at different worlds? (3) Can one reconstruct Frege’s theory of numbers in a non-modal setting without mathematical primitives such (...)
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  47.  89
    On mally's alleged heresy:A reply.Edward N. Zalta - 1992 - History and Philosophy of Logic 13 (1):59-68.
    In this paper, I respond to D. Jacquette's paper, "Mally's Heresy and the Logic of Meinong's Object Theory" (History and Philosophy of Logic, 10 (1989): 1-14), in which it is claimed that Ernst Mally's distinction between two modes of predication, as it is employed in the theory of abstract objects, is reducible to, and analyzable in terms of, a single mode of predication plus the distinction between nuclear and extranuclear properties. The argument against Jacquette's claims consists of counterexamples to his (...)
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  48. A comparison of two intensional logics.Edward N. Zalta - 1988 - Linguistics and Philosophy 11 (1):59-89.
    The author examines the differences between the general intensional logic defined in his recent book and Montague's intensional logic. Whereas Montague assigned extensions and intensions to expressions (and employed set theory to construct these values as certain sets), the author assigns denotations to terms and relies upon an axiomatic theory of intensional entities that covers properties, relations, propositions, worlds, and other abstract objects. It is then shown that the puzzles for Montague's analyses of modality and descriptions, propositional attitudes, and directedness (...)
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  49. Two (related) world views.Edward N. Zalta - 1995 - Noûs 29 (2):189-211.
    A. Plantinga develops a challenging critique of Castañeda's guise theory, by identifying fundamental intuitions that guise theory gives up and by developing several objections to the guise-theoretic world view as a whole. In this paper, I examine whether Plantinga's criticisms apply to the theory of abstract objects. The theory of abstract objects and guise theory can be fruitfully compared because they share a common intellectual heritage---both follow Ernst Mally [1912] in postulating a special realm of objects distinguished by their "internal" (...)
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  50. Deriving and validating Kripkean claims using the theory of abstract objects.Edward N. Zalta - 2006 - 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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