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  1. 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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  2. 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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  3. 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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  4. 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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  5. Assertion, Denial, Content, and 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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  6. 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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  7. Objectivity And Proof In A Classical Indian Theory Of Number.Jonardon Ganeri - 2001 - Synthese 129 (3):413-437.
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  8. The Future of the Concept of Infinite Number.Jeremy Gwiazda - unknown
    In ‘The Train Paradox’, I argued that sequential random selections from the natural numbers would grow through time. I used this claim to present a paradox. In response to this proposed paradox, Jon Pérez Laraudogoitia has argued that random selections from the natural numbers do not grow through time. In this paper, I defend and expand on the argument that random selections from the natural numbers grow through time. I also situate this growth of random selections in the context of (...)
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  9. 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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  10. 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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  11. 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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  12. 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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  13. 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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  14. The Axiom of Infinity: A New Presupposition of Thought.Cassius Jackson Keyser - 1903 - Hibbert Journal 2:532-552.
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  15. 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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  16. 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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  17. 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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  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. 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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  22. 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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  23. Book Review Of: R. Turner, Logics for AI. [REVIEW]Gary James Jason - 1989 - Philosophia 19 (1):73-83.
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Algebra
  1. 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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  2. 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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  3. ‘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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  4. 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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  5. Notes on Groups and Geometry, 1978-1986.Steven H. Cullinane - 2012 - Internet Archive.
    Typewritten notes on groups and geometry.
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  6. 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. 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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  2. 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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  3. 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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  4. 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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  5. 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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  6. 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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  7. 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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  8. 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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  9. 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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  10. 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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  11. 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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  12. 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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  13. 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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Category Theory
  1. Canonical Maps.Jean-Pierre Marquis - 2018 - In Elaine Landry (ed.), Categories for the Working Philosophers. Oxford, UK: pp. 90-112.
    Categorical foundations and set-theoretical foundations are sometimes presented as alternative foundational schemes. So far, the literature has mostly focused on the weaknesses of the categorical foundations. We want here to concentrate on what we take to be one of its strengths: the explicit identification of so-called canonical maps and their role in mathematics. Canonical maps play a central role in contemporary mathematics and although some are easily defined by set-theoretical tools, they all appear systematically in a categorical framework. The key (...)
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  2. The Cell and Protoplasm as Container, Object, and Substance, 1835–1861.Daniel Liu - 2017 - Journal of the History of Biology 50 (4):889-925.
    (Recipient of the 2020 Everett Mendelsohn Prize.) This article revisits the development of the protoplasm concept as it originally arose from critiques of the cell theory, and examines how the term “protoplasm” transformed from a botanical term of art in the 1840s to the so-called “living substance” and “the physical basis of life” two decades later. I show that there were two major shifts in biological materialism that needed to occur before protoplasm theory could be elevated to have equal status (...)
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  3. Brain Functors: A Mathematical Model for Intentional Perception and Action.David Ellerman - 2016 - Brain: Broad Research in Artificial Intelligence and Neuroscience 7 (1):5-17.
    Category theory has foundational importance because it provides conceptual lenses to characterize what is important and universal in mathematics—with adjunctions being the primary lens. If adjunctions are so important in mathematics, then perhaps they will isolate concepts of some importance in the empirical sciences. But the applications of adjunctions have been hampered by an overly restrictive formulation that avoids heteromorphisms or hets. By reformulating an adjunction using hets, it is split into two parts, a left and a right semiadjunction. Semiadjunctions (...)
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  4. A Brief Introduction to Transcendental Phenomenology and Conceptual Mathematics.Nicholas Lawrence - 2017 - Dissertation,
    By extending Husserl’s own historico-critical study to include the conceptual mathematics of more contemporary times – specifically category theory and its emphatic development since the second half of the 20th century – this paper claims that the delineation between mathematics and philosophy must be completely revisited. It will be contended that Husserl’s phenomenological work was very much influenced by the discoveries and limitations of the formal mathematics being developed at Göttingen during his tenure there and that, subsequently, the rôle he (...)
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  5. Grothendieck Universes and Indefinite Extensibility.Hasen Khudairi - manuscript
    This essay endeavors to define the concept of indefinite extensibility in the setting of category theory. I argue that the generative property of indefinite extensibility in the category-theoretic setting is identifiable with the Kripke functors of modal coalgebraic automata, where the automata model Grothendieck Universes and the functors are further inter-definable with the elementary embeddings of large cardinal axioms. The Kripke functors definable in Grothendieck universes are argued to account for the ontological expansion effected by the elementary embeddings in the (...)
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  6. Categorical Harmony and Path Induction.Patrick Walsh - 2017 - Review of Symbolic Logic 10 (2):301-321.
    This paper responds to recent work in the philosophy of Homotopy Type Theory by James Ladyman and Stuart Presnell. They consider one of the rules for identity, path induction, and justify it along ‘pre-mathematical’ lines. I give an alternate justification based on the philosophical framework of inferentialism. Accordingly, I construct a notion of harmony that allows the inferentialist to say when a connective or concept is meaning-bearing and this conception unifies most of the prominent conceptions of harmony through category theory. (...)
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  7. A Methodological Note on Proving Agreement Between the Elementary Process Theory and Modern Interaction Theories.Cabbolet Marcoen - manuscript
    The Elementary Process Theory (EPT) is a collection of seven elementary process-physical principles that describe the individual processes by which interactions have to take place for repulsive gravity to exist. One of the two main problems of the EPT is that there is no proof that the four fundamental interactions (gravitational, electromagnetic, strong, and weak) as we know them can take place in the elementary processes described by the EPT. This paper sets forth the method by which it can be (...)
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  8. The Logic of Partitions: Introduction to the Dual of the Logic of Subsets: The Logic of Partitions.David Ellerman - 2010 - Review of Symbolic Logic 3 (2):287-350.
    Modern categorical logic as well as the Kripke and topological models of intuitionistic logic suggest that the interpretation of ordinary “propositional” logic should in general be the logic of subsets of a given universe set. Partitions on a set are dual to subsets of a set in the sense of the category-theoretic duality of epimorphisms and monomorphisms—which is reflected in the duality between quotient objects and subobjects throughout algebra. If “propositional” logic is thus seen as the logic of subsets of (...)
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1 — 50 / 149