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  1. Topological Completeness for Higher-Order Logic.S. Awodey & C. Butz - 2000 - Journal of Symbolic Logic 65 (3):1168-1182.
    Using recent results in topos theory, two systems of higher-order logic are shown to be complete with respect to sheaf models over topological spaces- so -called "topological semantics." The first is classical higher-order logic, with relational quantification of finitely high type; the second system is a predicative fragment thereof with quantification over functions between types, but not over arbitrary relations. The second theorem applies to intuitionistic as well as classical logic.
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  2. Higher-Order Free Logic and the Prior-Kaplan Paradox.Andrew Bacon, John Hawthorne & Gabriel Uzquiano - 2016 - Canadian Journal of Philosophy 46 (4-5):493-541.
    The principle of universal instantiation plays a pivotal role both in the derivation of intensional paradoxes such as Prior’s paradox and Kaplan’s paradox and the debate between necessitism and contingentism. We outline a distinctively free logical approach to the intensional paradoxes and note how the free logical outlook allows one to distinguish two different, though allied themes in higher-order necessitism. We examine the costs of this solution and compare it with the more familiar ramificationist approaches to higher-order logic. Our assessment (...)
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  3. On the Ordered Dedekind Real Numbers in Toposes.Marcelo E. Coniglio & Luís A. Sbardellini - 2015 - In Edward H. Haeusler, Wagner Sanz & Bruno Lopes (eds.), Why is this a Proof? Festschrift for Luiz Carlos Pereira. College Publications. pp. 87-105.
    In 1996, W. Veldman and F. Waaldijk present a constructive (intuitionistic) proof for the homogeneity of the ordered structure of the Cauchy real numbers, and so this result holds in any topos with natural number object. However, it is well known that the real numbers objects obtained by the traditional constructions of Cauchy sequences and Dedekind cuts are not necessarily isomorphic in an arbitrary topos with natural numbers object. Consequently, Veldman and Waaldijk's result does not apply to the ordered structure (...)
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  4. Symbolic Logic.Irving M. Copi - 1954 - New York: Macmillan.
  5. Grounding, Essence, and Identity.Fabrice Correia & Alexander Skiles - forthcoming - Philosophy and Phenomenological Research.
    Recent metaphysics has turned its focus to two notions that are—as well as having a common Aristotelian pedigree—widely thought to be intimately related: grounding and essence. Yet how, exactly, the two are related remains opaque. We develop a unified and uniform account of grounding and essence, one which understands them both in terms of a generalized notion of identity examined in recent work by Fabrice Correia, Cian Dorr, Agustín Rayo, and others. We argue that the account comports with antecedently plausible (...)
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  6. On How Logic Became First-Order.Matti Eklund - 1996 - Nordic Journal of Philosophical Logic 1 (2):147-67.
    Added by a category editor--not an official abstract. -/- Discusses the history (and reasons for the history) implicit in the title, as well as the author's view on same.
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  7. Untyped Pluralism.Salvatore Florio - 2014 - Mind 123 (490):317-337.
    In the semantic debate about plurals, pluralism is the view that a plural term denotes some things in the domain of quantification and a plural predicate denotes a plural property, i.e. a property that can be instantiated by many things jointly. According to a particular version of this view, untyped pluralism, there is no type distinction between objects and properties. In this article, I argue against untyped pluralism by showing that it is subject to a variant of a Russell-style argument (...)
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  8. Semantics and the Plural Conception of Reality.Salvatore Florio - 2014 - Philosophers' Imprint 14 (22):1-20.
    According to the singular conception of reality, there are objects and there are singular properties, i.e. properties that are instantiated by objects separately. It has been argued that semantic considerations about plurals give us reasons to embrace a plural conception of reality. This is the view that, in addition to singular properties, there are plural properties, i.e. properties that are instantiated jointly by many objects. In this article, I propose and defend a novel semantic account of plurals which dispenses with (...)
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  9. On the Innocence and Determinacy of Plural Quantification.Salvatore Florio & Øystein Linnebo - 2016 - Noûs 50 (3):565–583.
    Plural logic is widely assumed to have two important virtues: ontological innocence and determinacy. It is claimed to be innocent in the sense that it incurs no ontological commitments beyond those already incurred by the first-order quantifiers. It is claimed to be determinate in the sense that it is immune to the threat of non-standard interpretations that confronts higher-order logics on their more traditional, set-based semantics. We challenge both claims. Our challenge is based on a Henkin-style semantics for plural logic (...)
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  10. On Concept and Object.Gottlob Frege, P. T. Geach & Max Black - 1951 - Mind 60 (238):168-180.
  11. Higher-Order Contingentism, Part 1: Closure and Generation.Peter Fritz & Jeremy Goodman - 2016 - Journal of Philosophical Logic 45 (6):645-695.
    This paper is a study of higher-order contingentism – the view, roughly, that it is contingent what properties and propositions there are. We explore the motivations for this view and various ways in which it might be developed, synthesizing and expanding on work by Kit Fine, Robert Stalnaker, and Timothy Williamson. Special attention is paid to the question of whether the view makes sense by its own lights, or whether articulating the view requires drawing distinctions among possibilities that, according to (...)
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  12. Pragmatics, Montague, and “Abstracts From Logical Form”.Joseph S. Fulda - 2008 - Journal of Pragmatics 40 (6):1146-1147.
    In "Abstracts from Logical Form I/II," it was stated in the abstract that it remained necessary to put the pilot experiments into a "comprehensive theory." It is suggested here that the comprehensive theory is nothing other than classical logic modestly extended to include higher-order predicates, functions, and epistemic predicates, as well as a quantitative quantifier to deal with cases other than "all" (taken literally) or "some" in the sense of at least one. It is further suggested that up to a (...)
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  13. Abstracts From Logic Form: An Experimental Study of the Nexus Between Language and Logic I.Joseph S. Fulda - 2006 - Journal of Pragmatics 38 (5):778-807.
    See the abstract for the "Abstracts from Logical Form II".
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  14. Abstracts From Logical Form: An Experimental Study of the Nexus Between Language and Logic II.Joseph S. Fulda - 2006 - Journal of Pragmatics 38 (6):925-943.
    This experimental study provides further support for a theory of meaning first put forward by Bar-Hillel and Carnap in 1953 and foreshadowed by Asimov in 1951. The theory is the Popperian notion that the meaningfulness of a proposition is its a priori falsity. We tested this theory in the first part of this paper by translating to logical form a long, tightly written, published text and computed the meaningfulness of each proposition using the a priori falsity measure. We then selected (...)
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  15. Properties and the Interpretation of Second-Order Logic.B. Hale - 2013 - Philosophia Mathematica 21 (2):133-156.
    This paper defends a deflationary conception of properties, according to which a property exists if and only if there could be a predicate with appropriate satisfaction conditions. I argue that purely general properties and relations necessarily exist and discuss the bearing of this conception of properties on the interpretation of higher-order logic and on Quine's charge that higher-order logic is ‘set theory in sheep's clothing’. On my approach, the usual semantics involves a false assimilation of the logic to set theory. (...)
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  16. Relations in Monadic Third-Order Logic.A. P. Hazen - 1997 - Journal of Philosophical Logic 26 (6):619-628.
    The representation of quantification over relations in monadic third-order logic is discussed; it is shown to be possible in numerous special cases of foundational interest, but not in general unless something akin to the Axiom of Choice is assumed.
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  17. The Logic of Finite Order.Simon Hewitt - 2012 - Notre Dame Journal of Formal Logic 53 (3):297-318.
    This paper develops a formal system, consisting of a language and semantics, called serial logic ( SL ). In rough outline, SL permits quantification over, and reference to, some finite number of things in an order , in an ordinary everyday sense of the word “order,” and superplural quantification over things thus ordered. Before we discuss SL itself, some mention should be made of an issue in philosophical logic which provides the background to the development of SL , and with (...)
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  18. Higher-Order Automated Theorem Proving.Michael Kohlhase - unknown
    The history of building automated theorem provers for higher-order logic is almost as old as the field of deduction systems itself. The first successful attempts to mechanize and implement higher-order logic were those of Huet [13] and Jensen and Pietrzykowski [17]. They combine the resolution principle for higher-order logic (first studied in [1]) with higher-order unification. The unification problem in typed λ-calculi is much more complex than that for first-order terms, since it has to take the theory of αβη-equality into (...)
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  19. Stanisław Leśniewski's Collected Works.Stanisław Leśniewski, Surma, Srzednicki, Barnett & Rickey (eds.) - 1991 - Kluwer Academic Publishers.
  20. Epistemology, Context, and Formalism.Franck Lihoreau & Manuel Rebuschi (eds.) - 2014 - Springer Verlag.
    Acknowledgements Five out of the 13 contributions to this volume originate from papers which were presented at the international workshop on “Epistemology, Context, Formalism” held at the MSH-Lorraine in Nancy, France, on November the ...
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  21. Sets, Properties, and Unrestricted Quantification.Øystein Linnebo - 2006 - In Gabriel Uzquiano & Agustin Rayo (eds.), Absolute Generality. Oxford University Press.
    Call a quantifier unrestricted if it ranges over absolutely all things: not just over all physical things or all things relevant to some particular utterance or discourse but over absolutely everything there is. Prima facie, unrestricted quantification seems to be perfectly coherent. For such quantification appears to be involved in a variety of claims that all normal human beings are capable of understanding. For instance, some basic logical and mathematical truths appear to involve unrestricted quantification, such as the truth that (...)
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  22. Hierarchies Ontological and Ideological.Øystein Linnebo & Agustín Rayo - 2012 - Mind 121 (482):269 - 308.
    Gödel claimed that Zermelo-Fraenkel set theory is 'what becomes of the theory of types if certain superfluous restrictions are removed'. The aim of this paper is to develop a clearer understanding of Gödel's remark, and of the surrounding philosophical terrain. In connection with this, we discuss some technical issues concerning infinitary type theories and the programme of developing the semantics for higher-order languages in other higher-order languages.
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  23. The Logical Systems of Lesniewski.Eugene C. Luschei - 1962 - Amsterdam: North-Holland Pub. Co..
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  24. Aristotle's Logic and the Quest for the Quantification of the Predicate.Bert Mosselmans - 2008 - Foundations of Science 13 (3-4):195-198.
    This paper examines the quest for the quantification of the predicate, as discussed by W.S. Jevons, and relates it to the discussion about universals and particulars between Plato and Aristotle. We conclude that the quest for the quantification of the predicate can only be achieved by stripping the syllogism from its metaphysical heritage.
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  25. Absolute Generality.Agustín Rayo & Gabriel Uzquiano (eds.) - 2006 - Oxford University Press.
    The problem of absolute generality has attracted much attention in recent philosophy. Agustin Rayo and Gabriel Uzquiano have assembled a distinguished team of contributors to write new essays on the topic. They investigate the question of whether it is possible to attain absolute generality in thought and language and the ramifications of this question in the philosophy of logic and mathematics.
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  26. On the Possibility of a General Purge of Self-Reference.Lucas Rosenblatt - 2012 - Análisis Filosófico 32 (1):53-59.
    My aim in this paper is to gather some evident in favor of the view that a general purge of self-reference is possible. I do this by considering a modal-epistemic version of the Liar Paradox introduced by Roy Cook. Using yabloesque techniques, I show that it is possible to transform this circular paradoxical construction (and other constructions as well) into an infinitary construction lacking any sort of circularity. Moreover, contrary to Cook’s approach, I think that this can be done without (...)
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  27. Some Results on Ordered Structures in Toposes.Luís Sbardellini & Marcelo Coniglio - 2006 - Reports on Mathematical Logic:181-198.
    A topos version of Cantor’s back and forth theorem is established and used to prove that the ordered structure of the rational numbers (Q, <) is homogeneous in any topos with natural numbers object. The notion of effective homogeneity is introduced, and it is shown that (Q, <) is a minimal effectively homogeneous structure, that is, it can be embedded in every other effectively homogeneous ordered structure.
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  28. Classical Logic II: Higher-Order Logic.Stewart Shapiro - 2001 - In Lou Goble (ed.), The Blackwell Guide to Philosophical Logic. Blackwell. pp. 33--54.
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  29. Who's Afraid of Higher-Order Logic?Peter Simons - 1993 - Grazer Philosophische Studien 44:253-264.
    Suppose you hold the following opinions in the philosophy of logic. First-order predicate logic is expressively inadequate to regiment concepts of mathematic and natural language; logicism is plausible and attractive; set theory as an adjunct to logic is unnatural and ontologically extravagant; humanly usable languages are finite in lexicon and syntax; it is worth striving for a Tarskian semantics for mathematics; there are no Platonic abstract objects. Then you are probably already in cognitive distress. One way to decease your unhappiness, (...)
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  30. Lesniewski's Systems of Logic and Foundations of Mathematics.Rafal Urbaniak - 2013 - Springer.
    With material on his early philosophical views, his contributions to set theory and his work on nominalism and higher-order quantification, this book offers a uniquely expansive critical commentary on one of analytical philosophy’s great ...
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  31. Reply to Goodman.Timothy Williamson - 2016 - Canadian Journal of Philosophy 46 (4-5):640-653.
  32. Reply to Linnebo.Timothy Williamson - 2016 - Canadian Journal of Philosophy 46 (4-5):677-682.
  33. The Limits of Higher-Order Logic and the Löwenheim-Skolem Theorem.Jan Woleński - 1998 - Erkenntnis 49 (3).
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  34. On Quantifying Into Predicate Position: Steps Towards a New (Tralist) Perspective.Crispin Wright - 2007 - In Mary Leng, Alexander Paseau & Michael D. Potter (eds.), Mathematical Knowledge. Oxford University Press. pp. 150--74.