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  1. Introduction.Tim Crane & Brian P. McLaughlin - 2009 - Synthese 170 (2):211-15.
    Jerry Fodor, by common agreement, is one of the world’s leading philosophers. At the forefront of the cognitive revolution since the 1960s, his work has determined much of the research agenda in the philosophy of mind and the philosophy of psychology for well over 40 years. This special issue dedicated to his work is intended both as a tribute to Fodor and as a contribution to the fruitful debates that his work has generated. One philosophical thesis that has dominated Fodor’s (...)
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  2. Introduction: Formal Approaches to Multi-Agent Systems: Special Issue of Best Papers of FAMAS 2007.B. Dunin-Keplicz & R. Verbrugge - 2013 - Logic Journal of the IGPL 21 (3):309-310.
    Over the last decade, multi-agent systems have come to form one of the key tech- nologies for software development. The Formal Approaches to Multi-Agent Systems (FAMAS) workshop series brings together researchers from the fields of logic, theoreti- cal computer science and multi-agent systems in order to discuss formal techniques for specifying and verifying multi-agent systems. FAMAS addresses the issues of logics for multi-agent systems, formal methods for verification, for example model check- ing, and formal approaches to cooperation, multi-agent planning, communication, (...)
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  3. Is Leibnizian Calculus Embeddable in First Order Logic?Piotr Błaszczyk, Vladimir Kanovei, Karin U. Katz, Mikhail G. Katz, Taras Kudryk, Thomas Mormann & David Sherry - 2017 - Foundations of Science 22 (4):73 - 88.
    To explore the extent of embeddability of Leibnizian infinitesimal calculus in first-order logic (FOL) and modern frameworks, we propose to set aside ontological issues and focus on pro- cedural questions. This would enable an account of Leibnizian procedures in a framework limited to FOL with a small number of additional ingredients such as the relation of infinite proximity. If, as we argue here, first order logic is indeed suitable for developing modern proxies for the inferential moves found in Leibnizian infinitesimal (...)
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  4. Assertion, Denial, Content, and (Logical) Form.Jack Woods - 2016 - Synthese 193 (6):1667-1680.
    I discuss Greg Restall’s attempt to generate an account of logical consequence from the incoherence of certain packages of assertions and denials. I take up his justification of the cut rule and argue that, in order to avoid counterexamples to cut, he needs, at least, to introduce a notion of logical form. I then suggest a few problems that will arise for his account if a notion of logical form is assumed. I close by sketching what I take to be (...)
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  5. Book Review Of: M. Schagrin, R. Dipert, and W. Rapaport, Logic: A Computer Approach. [REVIEW]Gary James Jason - 1987 - Philosophia 17 (4):557-558.
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  6. Objectivity And Proof In A Classical Indian Theory Of Number.Jonardon Ganeri - 2001 - Synthese 129 (3):413-437.
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  7. Decidable Formulas Of Intuitionistic Primitive Recursive Arithmetic.Saeed Salehi - 2002 - Reports on Mathematical Logic 36 (1):55-61.
    By formalizing some classical facts about provably total functions of intuitionistic primitive recursive arithmetic (iPRA), we prove that the set of decidable formulas of iPRA and of iΣ1+ (intuitionistic Σ1-induction in the language of PRA) coincides with the set of its provably ∆1-formulas and coincides with the set of its provably atomic formulas. By the same methods, we shall give another proof of a theorem of Marković and De Jongh: the decidable formulas of HA are its provably ∆1-formulas.
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  8. Erratum to “The Ricean Objection: An Analogue of Rice's Theorem for First-Order Theories” Logic Journal of the IGPL, 16: 585–590. [REVIEW]Igor Oliveira & Walter Carnielli - 2009 - Logic Journal of the IGPL 17 (6):803-804.
    This note clarifies an error in the proof of the main theorem of “The Ricean Objection: An Analogue of Rice’s Theorem for First-Order Theories”, Logic Journal of the IGPL, 16(6): 585–590(2008).
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  9. Classes and Theories of Trees Associated with a Class of Linear Orders.Valentin Goranko & Ruaan Kellerman - 2011 - Logic Journal of the IGPL 19 (1):217-232.
    Given a class of linear order types C, we identify and study several different classes of trees, naturally associated with C in terms of how the paths in those trees are related to the order types belonging to C. We investigate and completely determine the set-theoretic relationships between these classes of trees and between their corresponding first-order theories. We then obtain some general results about the axiomatization of the first-order theories of some of these classes of trees in terms of (...)
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  10. Expanding the Universe of Universal Logic.James Trafford - 2014 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 29 (3):325-343.
    In [5], Béziau provides a means by which Gentzen’s sequent calculus can be combined with the general semantic theory of bivaluations. In doing so, according to Béziau, it is possible to construe the abstract “core” of logics in general, where logical syntax and semantics are “two sides of the same coin”. The central suggestion there is that, by way of a modification of the notion of maximal consistency, it is possible to prove the soundness and completeness for any normal logic. (...)
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  11. Il Carteggio Fra Peano E Camillo Berneri.Enrico Pasini - 2001 - In Clara Silvia Roero (ed.), Giuseppe Peano. Matematica, Cultura E Società. L’Artistica. pp. 49-59.
    Between Giuseppe Peano and Camillo Berneri, a foremost protagonist of the Italian anarchist movement, an interesting correspondence was exchanged in the years 1925-1929. Along with a presentation of the correspondence, Peano's political attitude and the role of his international language projects in early 20th century Italian left are discussed.
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  12. On Graph-Theoretic Fibring of Logics.A. Sernadas, C. Sernadas, J. Rasga & M. Coniglio - 2009 - Journal of Logic and Computation 19 (6):1321-1357.
    A graph-theoretic account of fibring of logics is developed, capitalizing on the interleaving characteristics of fibring at the linguistic, semantic and proof levels. Fibring of two signatures is seen as a multi-graph (m-graph) where the nodes and the m-edges include the sorts and the constructors of the signatures at hand. Fibring of two models is a multi-graph (m-graph) where the nodes and the m-edges are the values and the operations in the models, respectively. Fibring of two deductive systems is an (...)
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  13. The Axiom of Infinity: A New Presupposition of Thought.Cassius Jackson Keyser - 1903 - Hibbert Journal 2:532-552.
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  14. Modal Logics for Topological Spaces.Konstantinos Georgatos - 1993 - Dissertation, City University of New York
    In this thesis we present two logical systems, $\bf MP$ and $\MP$, for the purpose of reasoning about knowledge and effort. These logical systems will be interpreted in a spatial context and therefore, the abstract concepts of knowledge and effort will be defined by concrete mathematical concepts.
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  15. Uniformly Convex Banach Spaces Are Reflexive—Constructively.Douglas S. Bridges, Hajime Ishihara & Maarten McKubre-Jordens - 2013 - Mathematical Logic Quarterly 59 (4-5):352-356.
    We propose a natural definition of what it means in a constructive context for a Banach space to be reflexive, and then prove a constructive counterpart of the Milman-Pettis theorem that uniformly convex Banach spaces are reflexive.
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  16. Elementary Canonical Formulae: Extending Sahlqvist’s Theorem.Valentin Goranko & Dimiter Vakarelov - 2006 - Annals of Pure and Applied Logic 141 (1):180-217.
    We generalize and extend the class of Sahlqvist formulae in arbitrary polyadic modal languages, to the class of so called inductive formulae. To introduce them we use a representation of modal polyadic languages in a combinatorial style and thus, in particular, develop what we believe to be a better syntactic approach to elementary canonical formulae altogether. By generalizing the method of minimal valuations à la Sahlqvist–van Benthem and the topological approach of Sambin and Vaccaro we prove that all inductive formulae (...)
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  17. A Path to the Epistemology of Mathematics: Homotopy Theory.Jean-Pierre Marquis - 2006 - In Jeremy Gray & Jose Ferreiros (eds.), The Architecture of Modern Mathematics: Essays in History and Philosophy. Oxford University Press. pp. 239--260.
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  18. A Proof of the Impossibility of Completing Infinitely Many Tasks.Jeremy Gwiazda - 2012 - Pacific Philosophical Quarterly 93 (1):1-7.
    In this article, I argue that it is impossible to complete infinitely many tasks in a finite time. A key premise in my argument is that the only way to get to 0 tasks remaining is from 1 task remaining, when tasks are done 1-by-1. I suggest that the only way to deny this premise is by begging the question, that is, by assuming that supertasks are possible. I go on to present one reason why this conclusion (that supertasks are (...)
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  19. From Traditional Set Theory – That of Cantor, Hilbert , Gödel, Cohen – to Its Necessary Quantum Extension.Edward G. Belaga - manuscript
    The original purpose of the present study, 2011, started with a preprint «On the Probable Failure of the Uncountable Power Set Axiom», 1988, is to save from the transfinite deadlock of higher set theory the jewel of mathematical Continuum — this genuine, even if mostly forgotten today raison d’être of all traditional set-theoretical enterprises to Infinity and beyond, from Georg Cantor to David Hilbert to Kurt Gödel to W. Hugh Woodin to Buzz Lightyear.
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  20. Topological Representations of Mereological Systems.Thomas Mormann - 2000 - Poznan Studies in the Philosophy of the Sciences and the Humanities 76:463 -486.
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  21. “Barriers to Implication”.Peter B. M. Vranas - unknown
    I was quite excited when I first read Restall and Russell’s (2010) paper. For two reasons. First, because the paper provides rigorous formulations and formal proofs of implication barrier theses, namely “theses [which] deny that one can derive sentences of one type from sentences of another”. Second (and primarily), because the paper proves a general theorem, the Barrier Construction Theorem, which unifies implication barrier theses concerning four topics: generality, necessity, time, and normativity. After thinking about the paper, I am satisfied (...)
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  22. Review of S. Feferman's in the Light of Logic. [REVIEW]Andrew Arana - 2005 - Mathematical Intelligencer 27 (4).
    We review Solomon Feferman's 1998 essay collection In The Light of Logic (Oxford University Press).
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  23. Epistemic Truth and Excluded Middle.Cesare Cozzo - 1998 - Theoria 64 (2-3):243-282.
    Can an epistemic conception of truth and an endorsement of the excluded middle (together with other principles of classical logic abandoned by the intuitionists) cohabit in a plausible philosophical view? In PART I I describe the general problem concerning the relation between the epistemic conception of truth and the principle of excluded middle. In PART II I give a historical overview of different attitudes regarding the problem. In PART III I sketch a possible holistic solution.
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  24. Logic and Limits of Knowledge and Truth.Patrick Grim - 1988 - Noûs 22 (3):341-367.
    Though my ultimate concern is with issues in epistemology and metaphysics, let me phrase the central question I will pursue in terms evocative of philosophy of religion: What are the implications of our logic-in particular, of Cantor and G6del-for the possibility of omniscience?
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  25. Book Review Of: R. Turner, Logics for AI. [REVIEW]Gary James Jason - 1989 - Philosophia 19 (1):73-83.
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Algebra
  1. Why Did Weyl Think That Emmy Noether Made Algebra the Eldorado of Axiomatics?Iulian D. Toader - forthcoming - Hopos: The Journal of the International Society for the History of Philosophy of Science:000-000.
    This paper argues that Noether's axiomatic method in algebra cannot be assimilated to Weyl's late view on axiomatics, for his acquiescence to a phenomenological epistemology of correctness led Weyl to resist Noether's principle of detachment.
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  2. Poincaré on the Foundation of Geometry in the Understanding.Jeremy Shipley - 2017 - In Maria Zack & Dirk Schlimm (eds.), Research in History and Philosophy of Mathematics: The CSHPM 2016 Annual Meeting in Calgary, Alberta. Springer. pp. 19-37.
    This paper is about Poincaré’s view of the foundations of geometry. According to the established view, which has been inherited from the logical positivists, Poincaré, like Hilbert, held that axioms in geometry are schemata that provide implicit definitions of geometric terms, a view he expresses by stating that the axioms of geometry are “definitions in disguise.” I argue that this view does not accord well with Poincaré’s core commitment in the philosophy of geometry: the view that geometry is the study (...)
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  3. A Survey of Geometric Algebra and Geometric Calculus.Alan Macdonald - 2017 - Advances in Applied Clifford Algebras 27:853-891.
    The paper is an introduction to geometric algebra and geometric calculus for those with a knowledge of undergraduate mathematics. No knowledge of physics is required. The section Further Study lists many papers available on the web.
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  4. ‘Chasing’ the Diagram—the Use of Visualizations in Algebraic Reasoning.Silvia de Toffoli - 2017 - Review of Symbolic Logic 10 (1):158-186.
    The aim of this article is to investigate the roles of commutative diagrams (CDs) in a specific mathematical domain, and to unveil the reasons underlying their effectiveness as a mathematical notation; this will be done through a case study. It will be shown that CDs do not depict spatial relations, but represent mathematical structures. CDs will be interpreted as a hybrid notation that goes beyond the traditional bipartition of mathematical representations into diagrammatic and linguistic. It will be argued that one (...)
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  5. Two Conjectures on the Arithmetic in ℝ and ℂ†.Apoloniusz Tyszka - 2010 - Mathematical Logic Quarterly 56 (2):175-184.
    Let G be an additive subgroup of ℂ, let Wn = {xi = 1, xi + xj = xk: i, j, k ∈ {1, …, n }}, and define En = {xi = 1, xi + xj = xk, xi · xj = xk: i, j, k ∈ {1, …, n }}. We discuss two conjectures. If a system S ⊆ En is consistent over ℝ, then S has a real solution which consists of numbers whose absolute values belong to (...)
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  6. Fictionalism and Mathematical Objectivity.Iulian D. Toader - 2012 - In Metaphysics and Science. University of Bucharest Press. pp. 137-158.
    This paper, written in Romanian, compares fictionalism, nominalism, and neo-Meinongianism as responses to the problem of objectivity in mathematics, and then motivates a fictionalist view of objectivity as invariance.
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  7. Imagination in Mathematics.Andrew Arana - 2016 - In Amy Kind (ed.), Routledge Handbook on the Philosophy of Imagination. Routledge. pp. 463-477.
    This article will consider imagination in mathematics from a historical point of view, noting the key moments in its conception during the ancient, modern and contemporary eras.
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  8. Notes on Groups and Geometry, 1978-1986.Steven H. Cullinane - 2012 - Internet Archive.
    Typewritten notes on groups and geometry.
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  9. The Construction of Transfinite Equivalence Algorithms.Han Geurdes - manuscript
    Context: Consistency of mathematical constructions in numerical analysis and the application of computerized proofs in the light of the occurrence of numerical chaos in simple systems. Purpose: To show that a computer in general and a numerical analysis in particular can add its own peculiarities to the subject under study. Hence the need of thorough theoretical studies on chaos in numerical simulation. Hence, a questioning of what e.g. a numerical disproof of a theorem in physics or a prediction in numerical (...)
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Analysis
  1. Hermann Cohen’s Principle of the Infinitesimal Method: A Defense.Scott Edgar - 2020 - Hopos: The Journal of the International Society for the History of Philosophy of Science 10 (2):440-470.
    In Bertrand Russell's 1903 Principles of Mathematics, he offers an apparently devastating criticism of the neo-Kantian Hermann Cohen's Principle of the Infinitesimal Method and its History (PIM). Russell's criticism is motivated by his concern that Cohen's account of the foundations of calculus saddles mathematics with the paradoxes of the infinitesimal and continuum, and thus threatens the very idea of mathematical truth. This paper defends Cohen against that objection of Russell's, and argues that properly understood, Cohen's views of limits and infinitesimals (...)
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  2. Analisi - sintesi.Sergio Volodia Marcello Cremaschi - 1996 - In Virgilio Melchiorre (ed.), Enciclopedia della Filosofia e delle Scienze Umane. Novara: De Agostini. pp. 41-42.
    A short reconstruction of the analytic-synthetic method, a key idea in Medieval and Early Modern Logic.
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  3. The Idea of Continuity as Mathematical-Philosophical Invariant.Eldar Amirov - 2019 - “Metafizika” Journal 2 (8):p. 87-100.
    The concept of ‘ideas’ plays central role in philosophy. The genesis of the idea of continuity and its essential role in intellectual history have been analyzed in this research. The main question of this research is how the idea of continuity came to the human cognitive system. In this context, we analyzed the epistemological function of this idea. In intellectual history, the idea of continuity was first introduced by Leibniz. After him, this idea, as a paradigm, formed the base of (...)
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  4. What Is the Validity Domain of Einstein’s Equations? Distributional Solutions Over Singularities and Topological Links in Geometrodynamics.Elias Zafiris - 2016 - 100 Years of Chronogeometrodynamics: The Status of the Einstein's Theory of Gravitation in Its Centennial Year.
    The existence of singularities alerts that one of the highest priorities of a centennial perspective on general relativity should be a careful re-thinking of the validity domain of Einstein’s field equations. We address the problem of constructing distinguishable extensions of the smooth spacetime manifold model, which can incorporate singularities, while retaining the form of the field equations. The sheaf-theoretic formulation of this problem is tantamount to extending the algebra sheaf of smooth functions to a distribution-like algebra sheaf in which the (...)
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  5. A Survey of Geometric Algebra and Geometric Calculus.Alan Macdonald - 2017 - Advances in Applied Clifford Algebras 27:853-891.
    The paper is an introduction to geometric algebra and geometric calculus for those with a knowledge of undergraduate mathematics. No knowledge of physics is required. The section Further Study lists many papers available on the web.
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  6. Differential Calculus Based on the Double Contradiction.Kazuhiko Kotani - 2016 - Open Journal of Philosophy 6 (4):420-427.
    The derivative is a basic concept of differential calculus. However, if we calculate the derivative as change in distance over change in time, the result at any instant is 0/0, which seems meaningless. Hence, Newton and Leibniz used the limit to determine the derivative. Their method is valid in practice, but it is not easy to intuitively accept. Thus, this article describes the novel method of differential calculus based on the double contradiction, which is easier to accept intuitively. Next, the (...)
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  7. Laplacian Growth Without Surface Tension in Filtration Combustion: Analytical Pole Solution.Oleg Kupervasser - 2016 - Complexity 21 (5):31-42.
    Filtration combustion is described by Laplacian growth without surface tension. These equations have elegant analytical solutions that replace the complex integro-differential motion equations by simple differential equations of pole motion in a complex plane. The main problem with such a solution is the existence of finite time singularities. To prevent such singularities, nonzero surface tension is usually used. However, nonzero surface tension does not exist in filtration combustion, and this destroys the analytical solutions. However, a more elegant approach exists for (...)
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  8. Review of Hintikka and Remes. The Method of Analysis (Reidel, 1974).John Corcoran - 1979 - MATHEMATICAL REVIEWS 58:3202-3.
    John Corcoran. 1979 Review of Hintikka and Remes. The Method of Analysis (Reidel, 1974). Mathematical Reviews 58 3202 #21388. -/- The “method of analysis” is a technique used by ancient Greek mathematicians (and perhaps by Descartes, Newton, and others) in connection with discovery of proofs of difficult theorems and in connection with discovery of constructions of elusive geometric figures. Although this method was originally applied in geometry, its later application to number played an important role in the early development of (...)
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  9. Zur Mathematischen Wissenschaftsphilosophie des Marburger Neukantianismus.Thomas Mormann - 2018 - In Christian Damböck (ed.), Philosophie und Wissenschaft bei Hermann Cohen, Veröffentlichungen des Instituts Wiener Kreis, Bd. 28. Wien: Springer. pp. 101 - 133.
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  10. Continuity for the Maximal Bochner-Riesz Operators on the Weighted Weak Hardy Spaces.Shihong Zhu - manuscript
    In this papers ,we generalize some results of other authors to weighted spaces and gain the boundedness of maximal Bochner-Riesz operator on weighted Herz-Hardy spaces,weighted Hardy spaces and weighted weak Hardy spaces ,where $\omega \in A_1.$.
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  11. Continuity of Higher Order Commutators Generated by Maximal Bochner-Riesz Operator on Morrey Space.Shihong Zhu - manuscript
    In this papers ,we use the control method of the maximal fractional integral and obtain the boundedness of higher order commutator generated by maximal Bochner-Riesz operator on Morrey space. Moreover , we get it's continuty from Morrey space to Lipschtz space and from Morrey space to BMO space.
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  12. Throwing Darts, Time, and the Infinite.Jeremy Gwiazda - 2013 - Erkenntnis 78 (5):971-975.
    In this paper, I present a puzzle involving special relativity and the random selection of real numbers. In a manner to be specified, darts thrown later hit reals further into a fixed well-ordering than darts thrown earlier. Special relativity is then invoked to create a puzzle. I consider four ways of responding to this puzzle which, I suggest, fail. I then propose a resolution to the puzzle, which relies on the distinction between the potential infinite and the actual infinite. I (...)
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  13. Three Concepts of Decidability for General Subsets of Uncountable Spaces.Matthew W. Parker - 2003 - Theoretical Computer Science 351 (1):2-13.
    There is no uniquely standard concept of an effectively decidable set of real numbers or real n-tuples. Here we consider three notions: decidability up to measure zero [M.W. Parker, Undecidability in Rn: Riddled basins, the KAM tori, and the stability of the solar system, Phil. Sci. 70(2) (2003) 359–382], which we abbreviate d.m.z.; recursive approximability [or r.a.; K.-I. Ko, Complexity Theory of Real Functions, Birkhäuser, Boston, 1991]; and decidability ignoring boundaries [d.i.b.; W.C. Myrvold, The decision problem for entanglement, in: R.S. (...)
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  14. The Construction of Transfinite Equivalence Algorithms.Han Geurdes - manuscript
    Context: Consistency of mathematical constructions in numerical analysis and the application of computerized proofs in the light of the occurrence of numerical chaos in simple systems. Purpose: To show that a computer in general and a numerical analysis in particular can add its own peculiarities to the subject under study. Hence the need of thorough theoretical studies on chaos in numerical simulation. Hence, a questioning of what e.g. a numerical disproof of a theorem in physics or a prediction in numerical (...)
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  15. Mathematics and the Theory of Multiplicities: Badiou and Deleuze Revisited.Daniel W. Smith - 2003 - Southern Journal of Philosophy 41 (3):411-449.
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  16. Deleuze on Leibniz : Difference, Continuity, and the Calculus.Daniel W. Smith - 2005 - In Current Continental Theory and Modern Philosophy. Northwestern University Press.
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