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  1. Logical Combinatorialism.Andrew Bacon - forthcoming - Philosophical Review.
    In explaining the notion of a fundamental property or relation, metaphysicians will often draw an analogy with languages. The fundamental properties and relations stand to reality as the primitive predicates and relations stand to a language: the smallest set of vocabulary God would need in order to write the `book of the world'. In this paper I attempt to make good on this metaphor. In order to do this I introduce a modality that, put informally, stands to propositions as logical (...)
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  2. The Broadest Necessity.Andrew Bacon - 2018 - Journal of Philosophical Logic 47 (5):733-783.
    In this paper the logic of broad necessity is explored. Definitions of what it means for one modality to be broader than another are formulated, and it is proven, in the context of higher-order logic, that there is a broadest necessity, settling one of the central questions of this investigation. It is shown, moreover, that it is possible to give a reductive analysis of this necessity in extensional language. This relates more generally to a conjecture that it is not possible (...)
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  3. The Logic of Opacity.Andrew Bacon & Jeffrey Sanford Russell - 2019 - Philosophical and Phenomenological Research 99 (1):81-114.
    We explore the view that Frege's puzzle is a source of straightforward counterexamples to Leibniz's law. Taking this seriously requires us to revise the classical logic of quantifiers and identity; we work out the options, in the context of higher-order logic. The logics we arrive at provide the resources for a straightforward semantics of attitude reports that is consistent with the Millian thesis that the meaning of a name is just the thing it stands for. We provide models to show (...)
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  4. Information Recovery Problems.John Corcoran - 1995 - Theoria 10 (3):55-78.
    An information recovery problem is the problem of constructing a proposition containing the information dropped in going from a given premise to a given conclusion that folIows. The proposition(s) to beconstructed can be required to satisfy other conditions as well, e.g. being independent of the conclusion, or being “informationally unconnected” with the conclusion, or some other condition dictated by the context. This paper discusses various types of such problems, it presents techniques and principles useful in solving them, and it develops (...)
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  5. Categorial Grammar and Discourse Representation Theory.Reinhard Muskens - 1994 - In Proceedings of COLING 94. Kyoto: pp. 508-514.
    In this paper it is shown how simple texts that can be parsed in a Lambek Categorial Grammar can also automatically be provided with a semantics in the form of a Discourse Representation Structure in the sense of Kamp [1981]. The assignment of meanings to texts uses the Curry-Howard-Van Benthem correspondence.
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  6. Intensional Models for the Theory of Types.Reinhard Muskens - 2007 - Journal of Symbolic Logic 72 (1):98-118.
    In this paper we define intensional models for the classical theory of types, thus arriving at an intensional type logic ITL. Intensional models generalize Henkin's general models and have a natural definition. As a class they do not validate the axiom of Extensionality. We give a cut-free sequent calculus for type theory and show completeness of this calculus with respect to the class of intensional models via a model existence theorem. After this we turn our attention to applications. Firstly, it (...)
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  7. First- and Second-Order Logic of Mass Terms.Peter Roeper - 2004 - Journal of Philosophical Logic 33 (3):261-297.
    Provided here is an account, both syntactic and semantic, of first-order and monadic second-order quantification theory for domains that may be non-atomic. Although the rules of inference largely parallel those of classical logic, there are important differences in connection with the identification of argument places and the significance of the identity relation.
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Second-Order Logic
  1. Logicism, Ontology, and the Epistemology of Second-Order Logic.Richard Kimberly Heck - 2018 - In Ivette Fred-Rivera & Jessica Leach (eds.), Being Necessary: Themes of Ontology and Modality from the Work of Bob Hale. Oxford: Oxford University Press. pp. 140-169.
    In two recent papers, Bob Hale has attempted to free second-order logic of the 'staggering existential assumptions' with which Quine famously attempted to saddle it. I argue, first, that the ontological issue is at best secondary: the crucial issue about second-order logic, at least for a neo-logicist, is epistemological. I then argue that neither Crispin Wright's attempt to characterize a `neutralist' conception of quantification that is wholly independent of existential commitment, nor Hale's attempt to characterize the second-order domain in terms (...)
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  2. Overgeneration in the Higher Infinite.Salvatore Florio & Luca Incurvati - manuscript
    The Overgeneration Argument is a prominent objection against the model-theoretic account of logical consequence for second-order languages. In previous work we have offered a reconstruction of this argument which locates its source in the conflict between the neutrality of second-order logic and its alleged entanglement with mathematics. Some cases of this conflict concern small large cardinals. In this article, we show that in these cases the conflict can be resolved by moving from a set-theoretic implementation of the model-theoretic account to (...)
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  3. Resonances of the Unknown.Claudia Westermann - 2011 - Kybernetes 40 (7/8):1189-1195.
    Purpose – The purpose of this paper is to discuss the relevance of second-order cybernetics for a theory of architectural design and related discourse. -/- Design/methodology/approach – First, the relation of architectural design to the concept of “poiesis” is clarified. Subsequently, selected findings of Gotthard Günther are revisited and related to an architectural poetics. The last part of the paper consists of revisiting ideas mentioned previously, however, on the level of a discourse that has incorporated the ideas and offers a (...)
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  4. Metalogic and the Overgeneration Argument.Salvatore Florio & Luca Incurvati - 2019 - Mind 128 (511):761-793.
    A prominent objection against the logicality of second-order logic is the so-called Overgeneration Argument. However, it is far from clear how this argument is to be understood. In the first part of the article, we examine the argument and locate its main source, namely, the alleged entanglement of second-order logic and mathematics. We then identify various reasons why the entanglement may be thought to be problematic. In the second part of the article, we take a metatheoretic perspective on the matter. (...)
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  5. On Delight: Thoughts for Tomorrow.Claudia Westermann - 2018 - Technoetic Arts 16 (1):43-51.
    The article introduces the problematics of the classical two-valued logic on which Western thought is generally based, outlining that under the conditions of its logical assumptions the subject I is situated in a world that it cannot address. In this context, the article outlines a short history of cybernetics and the shift from first- to second-order cybernetics. The basic principles of Gordon Pask’s 1976 Conversation Theory are introduced. It is argued that this second-order theory grants agency to others through a (...)
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  6. Neutrosophy in Arabic Philosophy (Arabic version).Salah Osman & Florentin Smarandache - 2007 - Alexandria, Egypt: Al Maaref Establishment Press.
    لأننا نعيش في عالم يكتنفه الغموض من كل جانب؛ عالم تتسم معرفتنا لأحداثه ووقائعه بالتناقض واللاتحديد، وتُفصح قضايانا اللغوية الواصفة له عن الصدق تارة وعن الكذب تارة أخرى، فنحن في حاجة إلى فلسفة جديدة تعكس حقيقة رؤيتنا النسبية لهذا العالم وقصور معرفتنا به؛ ونحن في حاجة إلى نسقٍِ منطقي يُلائم معطياته غير المكتملة ويُشبع معالجاتنا لها، سواء على مستوى ممارسات الحياة اليومية أو على مستوى الممارسة العلمية بمختلف أشكالها. والفلسفة التي يقترحها هذا الكتاب هي «النيوتروسوفيا»؛ تلك النظرية التي قدمها الفيلسوف (...)
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  7. Reply to Fritz.Timothy Williamson - 2016 - Canadian Journal of Philosophy 46 (4-5):610-612.
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  8. Reply to Goodman.Timothy Williamson - 2016 - Canadian Journal of Philosophy 46 (4-5):640-653.
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  9. Logic, Essence, and Modality — Review of Bob Hale's Necessary Beings. [REVIEW]Christopher Menzel - 2015 - Philosophia Mathematica 23 (3):407-428.
    Bob Hale’s distinguished record of research places him among the most important and influential contemporary analytic metaphysicians. In his deep, wide ranging, yet highly readable book Necessary Beings, Hale draws upon, but substantially integrates and extends, a good deal his past research to produce a sustained and richly textured essay on — as promised in the subtitle — ontology, modality, and the relations between them. I’ve set myself two tasks in this review: first, to provide a reasonably thorough (if not (...)
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  10. Second-Order Logic.John Corcoran - 2001 - In M. Zeleny (ed.), Logic, Meaning, and Computation: Essays in Memory of Alonzo Church. KLUKER. pp. 61–76.
    “Second-order Logic” in Anderson, C.A. and Zeleny, M., Eds. Logic, Meaning, and Computation: Essays in Memory of Alonzo Church. Dordrecht: Kluwer, 2001. Pp. 61–76. -/- Abstract. This expository article focuses on the fundamental differences between second- order logic and first-order logic. It is written entirely in ordinary English without logical symbols. It employs second-order propositions and second-order reasoning in a natural way to illustrate the fact that second-order logic is actually a familiar part of our traditional intuitive logical framework and (...)
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  11. Neo-Logicism and Its Logic.Panu Raatikainen - 2019 - History and Philosophy of Logic 41 (1):82-95.
    The rather unrestrained use of second-order logic in the neo-logicist program is critically examined. It is argued in some detail that it brings with it genuine set-theoretical existence assumptions and that the mathematical power that Hume’s Principle seems to provide, in the derivation of Frege’s Theorem, comes largely from the ‘logic’ assumed rather than from Hume’s Principle. It is shown that Hume’s Principle is in reality not stronger than the very weak Robinson Arithmetic Q. Consequently, only a few rudimentary facts (...)
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  12. CORCORAN'S 27 ENTRIES IN THE 1999 SECOND EDITION.John Corcoran - 1999 - In Robert Audi (ed.), The Cambridge Dictionary of Philosophy. CAMBRIDGE UP. pp. 65-941.
    Corcoran’s 27 entries in the 1999 second edition of Robert Audi’s Cambridge Dictionary of Philosophy [Cambridge: Cambridge UP]. -/- ancestral, axiomatic method, borderline case, categoricity, Church (Alonzo), conditional, convention T, converse (outer and inner), corresponding conditional, degenerate case, domain, De Morgan, ellipsis, laws of thought, limiting case, logical form, logical subject, material adequacy, mathematical analysis, omega, proof by recursion, recursive function theory, scheme, scope, Tarski (Alfred), tautology, universe of discourse. -/- The entire work is available online free at more than (...)
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  13. Strong Normalization of a Symmetric Lambda Calculus for Second-Order Classical Logic.Yoriyuki Yamagata - 2002 - Archive for Mathematical Logic 41 (1):91-99.
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  14. String Theory.John Corcoran, William Frank & Michael Maloney - 1974 - Journal of Symbolic Logic 39 (4):625-637.
    For each positive n , two alternative axiomatizations of the theory of strings over n alphabetic characters are presented. One class of axiomatizations derives from Tarski's system of the Wahrheitsbegriff and uses the n characters and concatenation as primitives. The other class involves using n character-prefixing operators as primitives and derives from Hermes' Semiotik. All underlying logics are second order. It is shown that, for each n, the two theories are definitionally equivalent [or synonymous in the sense of deBouvere]. It (...)
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  15. A Logic for Frege's Theorem.Richard Heck - 2011 - In Frege’s Theorem: An Introduction. Oxford University Press.
    It has been known for a few years that no more than Pi-1-1 comprehension is needed for the proof of "Frege's Theorem". One can at least imagine a view that would regard Pi-1-1 comprehension axioms as logical truths but deny that status to any that are more complex—a view that would, in particular, deny that full second-order logic deserves the name. Such a view would serve the purposes of neo-logicists. It is, in fact, no part of my view that, say, (...)
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Higher-Order Logic, Misc
  1. Philosophy of Logic – Reexamining the Formalized Notion of Truth.Pete Olcott - manuscript
    Because formal systems of symbolic logic inherently express and represent the deductive inference model formal proofs to theorem consequences can be understood to represent sound deductive inference to true conclusions without any need for other representations such as model theory.
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  2. Grounding, Essence, And Identity.Fabrice Correia & Alexander Skiles - 2019 - Philosophy and Phenomenological Research 98 (3):642-670.
    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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  3. We Belong Together? A Plea for Modesty in Modal Plural Logic.Simon Hewitt - manuscript
    It is often assumed that pluralities are rigid, in the sense of having all and only their actual members necessarily. This assumption is operative in standard approaches to modal plural logic. I argue that a sceptical approach towards the assumption is warranted.
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  4. Storrs McCall's Tree of The Universe and Counterfactuals شجرة الكون وقضايا مناقضة الواقع عند ستورس مكال.Salah Osman - 1999 - Journal of the Faculty of Arts, Menoufia University 2956-2090 39:83 – 128.
    لم يكن العلم يومًا غريبًا عن الفلسفة، بل لقد أدت العلاقة الجدلية المستمرة بينهما إلى مزيد من المصداقية والقبول لبعض النماذج التفسيرية، سواء منها ما كان في الأصل نموذجًا فلسفيًا ثم وجد دعمًا علميًا – كنموذج الذرات والفـراغ عند «ديمرقــريطس» وتبنى النظرية الذرية الحديثة لإطاره العام – أو ما كان منها نموذجًا علميًا تم تداوله فلسفيًا – كنموذج النقاط المادية المتجاذبة عند »نيوتن« وتبنى معظم فلاسفة الحقبة الحديثة له. وفي هذا المقال يهتم الدكتور صلاح عثمان بمناقشة نموذج شجرة الكون لفيلسوف (...)
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  5. Many-Valued Logic between the Degrees of Truth and the Limits of Knowledge.Salah Osman - 2002 - Alexandria, Egypt: Al Maaref Establishment Press.
    هو أول كتاب باللغة العربية يعرض لمراحل وآليات تطور المنطق الرمزي المعاصر متعدد القيم بأنساقه المختلفة، مركزًا على مشكلة الغموض المعرفي للإنسان بأبعادها اللغوية والإبستمولوجية والأنطولوجية، والتي تتجلى – على سبيل المثال – فيما تحفل به الدراسات الفلسفية والمنطقية والعلمية من مفارقات تمثل تحديًا قويًا لثنائية الصدق والكذب الكلاسيكية، وكذلك في اكتشاف «هيزنبرج» لمبدأ اللايقين، وتأكيده وعلماء الكمّ على ضرورة التفسيرات الإحصائية في المجال دون الذري، الأمر الذي يؤكد عدم فعالية قانون الثالث المرفوع في التعامل مع معطيات الواقع الفعلي، واستحالة (...)
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  6. Neutrosophy in Arabic Philosophy (Arabic version).Salah Osman & Florentin Smarandache - 2007 - Alexandria, Egypt: Al Maaref Establishment Press.
    لأننا نعيش في عالم يكتنفه الغموض من كل جانب؛ عالم تتسم معرفتنا لأحداثه ووقائعه بالتناقض واللاتحديد، وتُفصح قضايانا اللغوية الواصفة له عن الصدق تارة وعن الكذب تارة أخرى، فنحن في حاجة إلى فلسفة جديدة تعكس حقيقة رؤيتنا النسبية لهذا العالم وقصور معرفتنا به؛ ونحن في حاجة إلى نسقٍِ منطقي يُلائم معطياته غير المكتملة ويُشبع معالجاتنا لها، سواء على مستوى ممارسات الحياة اليومية أو على مستوى الممارسة العلمية بمختلف أشكالها. والفلسفة التي يقترحها هذا الكتاب هي «النيوتروسوفيا»؛ تلك النظرية التي قدمها الفيلسوف (...)
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  7. 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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  8. 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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  9. Reply to Linnebo.Timothy Williamson - 2016 - Canadian Journal of Philosophy 46 (4-5):677-682.
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  10. Reply to Goodman.Timothy Williamson - 2016 - Canadian Journal of Philosophy 46 (4-5):640-653.
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  11. 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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  12. Semantics and the Plural Conception of Reality.Salvatore Florio - 2014 - Philosophers' Imprint 14:1-20.
    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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  13. Semantic Paradoxes and Transparent Intensional Logic.Jiri Raclavsky - 2012 - The Logica Yearbook 2011 (College Publications):239-252.
    The paper describes the solution to semantic paradoxes pioneered by Pavel Tichý and further developed by the present author. Its main feature is an examination (and then refutation) of the hidden premise of paradoxes that the paradox-producing expression really means what it seems to mean. Semantic concepts are explicated as relative to language, thus also language is explicated. The so-called ‘explicit approach’ easily treats paradoxes in which language is explicitly referred to. The residual paradoxes are solved by the ‘implicit approach’ (...)
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  14. Higher Order Modal Logic.Reinhard Muskens - 2006 - In Patrick Blackburn, Johan Van Benthem & Frank Wolter (eds.), Handbook of Modal Logic. Elsevier. pp. 621-653.
    A logic is called higher order if it allows for quantification over higher order objects, such as functions of individuals, relations between individuals, functions of functions, relations between functions, etc. Higher order logic began with Frege, was formalized in Russell [46] and Whitehead and Russell [52] early in the previous century, and received its canonical formulation in Church [14].1 While classical type theory has since long been overshadowed by set theory as a foundation of mathematics, recent decades have shown remarkable (...)
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