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  1. S. Awodey & C. Butz (2000). Topological Completeness for Higher-Order Logic. 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. Irving M. Copi (1973/1968). Symbolic Logic. New York,Macmillan.
  3. Matti Eklund (1996). On How Logic Became First-Order. 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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  4. Salvatore Florio (2014). Semantics and the Plural Conception of Reality. 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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  5. Gottlob Frege, P. T. Geach & Max Black (1951). On Concept and Object. Mind 60 (238):168-180.
  6. Joseph S. Fulda (2008). Pragmatics, Montague, and “Abstracts From Logical Form”. 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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  7. Joseph S. Fulda (2006). Abstracts From Logic Form: An Experimental Study of the Nexus Between Language and Logic I. Journal of Pragmatics 38 (5):778-807.
    See the abstract for the "Abstracts from Logical Form II".
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  8. Joseph S. Fulda (2006). Abstracts From Logical Form: An Experimental Study of the Nexus Between Language and Logic II. 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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  9. B. Hale (2013). Properties and the Interpretation of Second-Order Logic. 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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  10. A. P. Hazen (1997). Relations in Monadic Third-Order Logic. 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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  11. Simon Hewitt (2012). The Logic of Finite Order. 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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  12. Michael Kohlhase, Higher-Order Automated Theorem Proving.
    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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  13. Franck Lihoreau & Manuel Rebuschi (eds.) (2014). Epistemology, Context, and Formalism. Springer Science & Business Media.
    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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  14. Øystein Linnebo (2006). Sets, Properties, and Unrestricted Quantification. 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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  15. Øystein Linnebo & David Nicolas (2008). Superplurals in English. Analysis 68 (299):186–197.
    where ‘aa’ is a plural term, and ‘F’ a plural predicate. Following George Boolos (1984) and others, many philosophers and logicians also think that plural expressions should be analysed as not introducing any new ontological commitments to some sort of ‘plural entities’, but rather as involving a new form of reference to objects to which we are already committed (for an overview and further details, see Linnebo 2004). For instance, the plural term ‘aa’ refers to Alice, Bob and Charlie simultaneously, (...)
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  16. Eugene C. Luschei (1962). The Logical Systems of Lesniewski. Amsterdam, North-Holland Pub. Co..
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  17. Bert Mosselmans (2008). Aristotle's Logic and the Quest for the Quantification of the Predicate. 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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  18. Lucas Rosenblatt (2012). On the Possibility of a General Purge of Self-Reference. 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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  19. Stewart Shapiro (2001). Classical Logic II: Higher-Order Logic. In Lou Goble (ed.), The Blackwell Guide to Philosophical Logic. Blackwell. 33--54.
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  20. Peter Simons (1993). Who's Afraid of Higher-Order Logic? 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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  21. Rafal Urbaniak (2013). Lesniewski's Systems of Logic and Foundations of Mathematics. 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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  22. Gabriel Uzquiano & Agustin Rayo (eds.) (2006). Absolute Generality. 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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  23. Jan Woleński (1998). The Limits of Higher-Order Logic and the Löwenheim-Skolem Theorem. Erkenntnis 49 (3).
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  24. Crispin Wright (2007). On Quantifying Into Predicate Position: Steps Towards a New (Tralist) Perspective. In Mary Leng, Alexander Paseau & Michael D. Potter (eds.), Mathematical Knowledge. Oxford University Press. 150--74.