This category needs an editor. We encourage you to help if you are qualified.
Volunteer, or read more about what this involves.
Related categories

239 found
Order:
1 — 50 / 239
Material to categorize
  1. Conversation with John P. Burgess.Silvia De Toffoli - 2022 - Aphex 25.
    John P. Burgess is the John N. Woodhull Professor of Philosophy at Princeton University. He obtained his Ph.D. from the Logic and Methodology program at the University of California at Berkeley under the supervision of Jack H. Silver with a thesis on descriptive set theory. He is a very distinguished and influential philosopher of mathematics. He has written several books: A Subject with No Object (with G. Rosen, Oxford University Press, 1997), Computability and Logic (with G. Boolos and R. Jeffrey, (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  2. Against the Countable Transitive Model Approach to Forcing.Matteo de Ceglie - 2021 - In Martin Blicha & Igor Sedlár (eds.), The Logica Yearbook 2020.
    In this paper, I argue that one of the arguments usually put forward in defence of universism is in tension with current set theoretic practice. According to universism, there is only one set theoretic universe, V, and when applying the method of forcing we are not producing new universes, but only simulating them inside V. Since the usual interpretation of set generic forcing is used to produce a “simulation” of an extension of V from a countable set inside V itself, (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  3. All Worlds in One: Reassessing the Forest-Armstrong Argument.Phillip Bricker - 2020 - In Modal Matters: Essays in Metaphysics. Oxford: pp. 278-314.
    The Forrest-Armstrong argument, as reconfigured by David Lewis, is a reductio against an unrestricted principle of recombination. There is a gap in the argument which Lewis thought could be bridged by an appeal to recombination. After presenting the argument, I show that no plausible principle of recombination can bridge the gap. But other plausible principles of plenitude can bridge the gap, both principles of plenitude for world contents and principles of plenitude for world structures. I conclude that the Forrest-Armstrong argument, (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark   1 citation  
  4. The Quantum Strategy of Completeness: On the Self-Foundation of Mathematics.Vasil Penchev - 2020 - Cultural Anthropology eJournal (Elsevier: SSRN) 5 (136):1-12.
    Gentzen’s approach by transfinite induction and that of intuitionist Heyting arithmetic to completeness and the self-foundation of mathematics are compared and opposed to the Gödel incompleteness results as to Peano arithmetic. Quantum mechanics involves infinity by Hilbert space, but it is finitist as any experimental science. The absence of hidden variables in it interpretable as its completeness should resurrect Hilbert’s finitism at the cost of relevant modification of the latter already hinted by intuitionism and Gentzen’s approaches for completeness. This paper (...)
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  5. Reflections on the Foundations of Mathematics: Univalent Foundations, Set Theory and General Thoughts.Stefania Centrone, Deborah Kant & Deniz Sarikaya (eds.) - 2019 - Springer Verlag.
    This edited work presents contemporary mathematical practice in the foundational mathematical theories, in particular set theory and the univalent foundations. It shares the work of significant scholars across the disciplines of mathematics, philosophy and computer science. Readers will discover systematic thought on criteria for a suitable foundation in mathematics and philosophical reflections around the mathematical perspectives. The first two sections focus on the two most prominent candidate theories for a foundation of mathematics. Readers may trace current research in set theory, (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  6. 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 (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  7. Dummett on Indefinite Extensibility.Øystein Linnebo - 2018 - Philosophical Issues 28 (1):196-220.
    Dummett’s notion of indefinite extensibility is influential but obscure. The notion figures centrally in an alternative Dummettian argument for intuitionistic logic and anti-realism, distinct from his more famous, meaning-theoretic arguments to the same effect. Drawing on ideas from Dummett, a precise analysis of indefinite extensibility is proposed. This analysis is used to reconstruct the poorly understood alternative argument. The plausibility of the resulting argument is assessed.
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark   2 citations  
  8. Constructive Set Theory with Operations.Andrea Cantini & Laura Crosilla - 2008 - In Logic Colloquium 2004.
    We present an extension of constructive Zermelo{Fraenkel set theory [2]. Constructive sets are endowed with an applicative structure, which allows us to express several set theoretic constructs uniformly and explicitly. From the proof theoretic point of view, the addition is shown to be conservative. In particular, we single out a theory of constructive sets with operations which has the same strength as Peano arithmetic.
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark   3 citations  
  9. Elementary Constructive Operational Set Theory.Andrea Cantini & Laura Crosilla - 2010 - In Ways of Proof Theory.
    We introduce an operational set theory in the style of [5] and [16]. The theory we develop here is a theory of constructive sets and operations. One motivation behind constructive operational set theory is to merge a constructive notion of set ([1], [2]) with some aspects which are typical of explicit mathematics [14]. In particular, one has non-extensional operations (or rules) alongside extensional constructive sets. Operations are in general partial and a limited form of self{application is permitted. The system we (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark   1 citation  
  10. Note on the Significance of the New Logic.Frederique Janssen-Lauret - 2018 - The Reasoner 6 (12):47-48.
    Brief note explaining the content, importance, and historical context of my joint translation of Quine's The Significance of the New Logic with my single-authored historical-philosophical essay 'Willard Van Orman Quine's Philosophical Development in the 1930s and 1940s'.
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  11. The Foundations of Mathematics in the Theory of Sets. [REVIEW]Roy T. Cook - 2003 - British Journal for the Philosophy of Science 54 (2):347-352.
  12. J.P. Mayberry: The Foundations of Mathematics in the Theory of Sets. [REVIEW]W. W. Tait - 2002 - Bulletin of Symbolic Logic 8 (3):424-426.
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark   23 citations  
  13. The Ins and Outs of Frege's Way Out.Gregory Landini - 2006 - Philosophia Mathematica 14 (1):1-25.
    Confronted with Russell's Paradox, Frege wrote an appendix to volume II of his _Grundgesetze der Arithmetik_. In it he offered a revision to Basic Law V, and proclaimed with confidence that the major theorems for arithmetic are recoverable. This paper shows that Frege's revised system has been seriously undermined by interpretations that transcribe his system into a predicate logic that is inattentive to important details of his concept-script. By examining the revised system as a concept-script, we see how Frege imagined (...)
    Remove from this list   Direct download (8 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  14. What is the Infinite?Øystein Linnebo - 2013 - The Philosophers' Magazine 61:42-47.
    The paper discusses some different conceptions of the infinity, from Aristotle to Georg Cantor (1845-1918) and beyond. The ancient distinction between actual and potential infinity is explained, along with some arguments against the possibility of actually infinite collections. These arguments were eventually rejected by most philosophers and mathematicians as a result of Cantor’s elegant and successful theory of actually infinite collections.
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  15. The Foundations of Mathematics and Other Logical Essays.Frank Plumpton Ramsey - 1925 - London, England: Routledge & Kegan Paul.
  16. Russell Bektrand, Logical Positivism. Polemic , No. 1 , Pp. 6–13.Max Black - 1947 - Journal of Symbolic Logic 12 (1):24-24.
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  17. The Strength of Abstraction with Predicative Comprehension.Sean Walsh - 2016 - Bulletin of Symbolic Logic 22 (1):105–120.
    Frege's theorem says that second-order Peano arithmetic is interpretable in Hume's Principle and full impredicative comprehension. Hume's Principle is one example of an abstraction principle, while another paradigmatic example is Basic Law V from Frege's Grundgesetze. In this paper we study the strength of abstraction principles in the presence of predicative restrictions on the comprehension schema, and in particular we study a predicative Fregean theory which contains all the abstraction principles whose underlying equivalence relations can be proven to be equivalence (...)
    Remove from this list   Direct download (5 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  18. The Potential Hierarchy of Sets.Øystein Linnebo - 2013 - Review of Symbolic Logic 6 (2):205-228.
    Some reasons to regard the cumulative hierarchy of sets as potential rather than actual are discussed. Motivated by this, a modal set theory is developed which encapsulates this potentialist conception. The resulting theory is equi-interpretable with Zermelo Fraenkel set theory but sheds new light on the set-theoretic paradoxes and the foundations of set theory.
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark   68 citations  
  19. The Barber, Russell's Paradox, Catch-22, God, Contradiction, and More.Laurence Goldstein - 2004 - In Graham Priest, J. C. Beall & Bradley Armour-Garb (eds.), The Law of Non-Contradiction. Clarendon Press. pp. 295--313.
    outrageous remarks about contradictions. Perhaps the most striking remark he makes is that they are not false. This claim first appears in his early notebooks (Wittgenstein 1960, p.108). In the Tractatus, Wittgenstein argued that contradictions (like tautologies) are not statements (Sätze) and hence are not false (or true). This is a consequence of his theory that genuine statements are pictures.
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  20. Essay on Russell on Modalities and Frege on Judgement.Shahid Rahman - forthcoming - History and Philosophy of Logic.
  21. Anselm and Russell.Maciej Nowicki - 2006 - Logic and Logical Philosophy 15 (4):355-368.
    In his paper “St. Anselm’s ontological argument succumbs to Russell’s paradox” Christopher Viger presents a critique of Anselm’s Argument from the second chapter of Proslogion. Viger claims there that he manages to show that the greater than relation that Anselm used in his proof leads to inconsistency. I argue firstly, that Viger does not show what he maintains to show, secondly, that the flaw is not in the nature of Anselm’s reasoning but in Viger’s (mis)understanding of Anselm as well as (...)
    Remove from this list   Direct download (6 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  22. Review: Hugh J. Tallon, Russell's Doctrine of the Logical Proposition. [REVIEW]A. Wedberg - 1940 - Journal of Symbolic Logic 5 (2):74-74.
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  23. I Think, Therefore I Exist; I Belong, Therefore I Am.Juan José Luetich - 2012 - Transactions of The Luventicus Academy (3):1-4.
    The actions of perceiving and grouping are the two that the human being carries out when thinking in entities different from himself. In this article “The Mirror Problem” and “The Peer Problem”, which correspond respectively to self-perception and the perception of others, are studied. By solving these two problems, the thinker arrives to the following conclusions: “I exist” and “I am”.
    Remove from this list   Direct download  
    Translate
     
     
    Export citation  
     
    Bookmark  
  24. Early Russell on Types and Plurals.Kevin Klement - 2014 - Journal for the History of Analytical Philosophy 2 (6):1-21.
    In 1903, in The Principles of Mathematics (PoM), Russell endorsed an account of classes whereupon a class fundamentally is to be considered many things, and not one, and used this thesis to explicate his first version of a theory of types, adding that it formed the logical justification for the grammatical distinction between singular and plural. The view, however, was short-lived; rejected before PoM even appeared in print. However, aside from mentions of a few misgivings, there is little evidence about (...)
    Remove from this list   Direct download (6 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  25. The Foundations of Mathematics in the Theory of Sets.John P. Mayberry - 2000 - Cambridge University Press.
    This book will appeal to mathematicians and philosophers interested in the foundations of mathematics.
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark   28 citations  
  26. The Consistency of Predicative Fragments of Frege’s Grundgesetze der Arithmetik.Richard G. Heck - 1996 - History and Philosophy of Logic 17 (1):209-220.
    As is well-known, the formal system in which Frege works in his Grundgesetze der Arithmetik is formally inconsistent, Russell?s Paradox being derivable in it.This system is, except for minor differences, full second-order logic, augmented by a single non-logical axiom, Frege?s Axiom V. It has been known for some time now that the first-order fragment of the theory is consistent. The present paper establishes that both the simple and the ramified predicative second-order fragments are consistent, and that Robinson arithmetic, Q, is (...)
    Remove from this list   Direct download (6 more)  
     
    Export citation  
     
    Bookmark   55 citations  
  27. Idealist and Realist Elements in Cantor's Approach to Set Theory.I. Jane - 2010 - Philosophia Mathematica 18 (2):193-226.
    There is an apparent tension between the open-ended aspect of the ordinal sequence and the assumption that the set-theoretical universe is fully determinate. This tension is already present in Cantor, who stressed the incompletable character of the transfinite number sequence in Grundlagen and avowed the definiteness of the totality of sets and numbers in subsequent philosophical publications and in correspondence. The tension is particularly discernible in his late distinction between sets and inconsistent multiplicities. I discuss Cantor’s contrasting views, and I (...)
    Remove from this list   Direct download (7 more)  
     
    Export citation  
     
    Bookmark   8 citations  
  28. An Introduction to the Foundations and Fundamental Concepts of Mathematics.Howard Whitley Eves - 1958 - New York: Holt, Rinehart and Winston.
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark   7 citations  
  29. Bertrand Russell on His Paradox and the Multiplicative Axiom. An Unpublished Letter to Philip Jourdain.Ivor Grattan-Guinness - 1972 - Journal of Philosophical Logic 1 (2):103 - 110.
  30. Pluralism and the Foundations of Mathematics.Geoffrey Hellman - 2006 - In ¸ Itekellersetal:Sp. pp. 65--79.
    A plurality of approaches to foundational aspects of mathematics is a fact of life. Two loci of this are discussed here, the classicism/constructivism controversy over standards of proof, and the plurality of universes of discourse for mathematics arising in set theory and in category theory, whose problematic relationship is discussed. The first case illustrates the hypothesis that a sufficiently rich subject matter may require a multiplicity of approaches. The second case, while in some respects special to mathematics, raises issues of (...)
    Remove from this list  
     
    Export citation  
     
    Bookmark   13 citations  
  31. What is Categorical Structuralism?Geoffrey Hellman - 2006 - In Johan van Benthem, Gerhard Heinzman, M. Rebushi & H. Visser (eds.), The Age of Alternative Logics. Springer. pp. 151--161.
  32. Reflections on Skolem's Relativity of Set-Theoretical Concepts.Ignagio Jane - 2001 - Philosophia Mathematica 9 (2):129-153.
    In this paper an attempt is made to present Skolem's argument, for the relativity of some set-theoretical notions as a sensible one. Skolem's critique of set theory is seen as part of a larger argument to the effect that no conclusive evidence has been given for the existence of uncountable sets. Some replies to Skolem are discussed and are shown not to affect Skolem's position, since they all presuppose the existence of uncountable sets. The paper ends with an assessment of (...)
    Remove from this list   Direct download (9 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  33. Philosophy, Mathematics, Science and Computation.Enrique V. Kortright - 1994 - Topoi 13 (1):51-60.
    Attempts to lay a foundation for the sciences based on modern mathematics are questioned. In particular, it is not clear that computer science should be based on set-theoretic mathematics. Set-theoretic mathematics has difficulties with its own foundations, making it reasonable to explore alternative foundations for the sciences. The role of computation within an alternative framework may prove to be of great potential in establishing a direction for the new field of computer science.Whitehead''s theory of reality is re-examined as a foundation (...)
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  34. The Consistency Problem for Set Theory: An Essay on the Cantorian Foundations of Mathematics (II).John Mayberry - 1977 - British Journal for the Philosophy of Science 28 (2):137-170.
  35. What is Required of a Foundation for Mathematics?John Mayberry - 1994 - Philosophia Mathematica 2 (1):16-35.
    The business of mathematics is definition and proof, and its foundations comprise the principles which govern them. Modern mathematics is founded upon set theory. In particular, both the axiomatic method and mathematical logic belong, by their very natures, to the theory of sets. Accordingly, foundational set theory is not, and cannot logically be, an axiomatic theory. Failure to grasp this point leads obly to confusion. The idea of a set is that of an extensional plurality, limited and definite in size, (...)
    Remove from this list   Direct download (7 more)  
     
    Export citation  
     
    Bookmark   21 citations  
  36. Sets, Wholes, and Limited Pluralitiest.Stephen Pollard - 1996 - Philosophia Mathematica 4 (1):42-58.
    This essay defends the following two claims: (1) liraitation-of-size reasoning yields enough sets to meet the needs of most mathematicians; (2) set formation and mereological fusion share enough logical features to justify placing both in the genus composition (even when the components of a set are taken to be its members rather than its subsets).
    Remove from this list   Direct download (8 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  37. Foundations: Essays in Philosophy, Logic, Mathematics, and Economics.Frank Plumpton Ramsey & D. H. Mellor (eds.) - 1978 - Humanties Press; Routledge.
  38. Review of G. Boolos, Logic, Logic, and Logic.Michael D. Resnik - 1999 - Philosophia Mathematica 7 (3):328-335.
Russell's Paradox
  1. Semantyczna teoria prawdy a antynomie semantyczne [Semantic Theory of Truth vs. Semantic Antinomies].Jakub Pruś - 2021 - Rocznik Filozoficzny Ignatianum 1 (27):341–363.
    The paper presents Alfred Tarski’s debate with the semantic antinomies: the basic Liar Paradox, and its more sophisticated versions, which are currently discussed in philosophy: Strengthen Liar Paradox, Cyclical Liar Paradox, Contingent Liar Paradox, Correct Liar Paradox, Card Paradox, Yablo’s Paradox and a few others. Since Tarski, himself did not addressed these paradoxes—neither in his famous work published in 1933, nor in later papers in which he developed the Semantic Theory of Truth—therefore, We try to defend his concept of truth (...)
    Remove from this list   Direct download  
    Translate
     
     
    Export citation  
     
    Bookmark  
  2. Aboutness Paradox.Giorgio Sbardolini - 2021 - Journal of Philosophy 118 (10):549-571.
    The present work outlines a logical and philosophical conception of propositions in relation to a group of puzzles that arise by quantifying over them: the Russell-Myhill paradox, the Prior-Kaplan paradox, and Prior's Theorem. I begin by motivating an interpretation of Russell-Myhill as depending on aboutness, which constrains the notion of propositional identity. I discuss two formalizations of of the paradox, showing that it does not depend on the syntax of propositional variables. I then extend to propositions a modal predicative response (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  3. In Defense of Countabilism.David Builes & Jessica M. Wilson - forthcoming - Philosophical Studies:1-38.
    Inspired by Cantor's Theorem (CT), orthodoxy takes infinities to come in different sizes. The orthodox view has had enormous influence in mathematics, philosophy, and science. We will defend the contrary view---Countablism---according to which, necessarily, every infinite collection (set or plurality) is countable. We first argue that the potentialist or modal strategy for treating Russell's Paradox, first proposed by Parsons (2000) and developed by Linnebo (2010, 2013) and Linnebo and Shapiro (2019), should also be applied to CT, in a way that (...)
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  4. Application of "A Thing Exists If It's A Grouping" to Russell's Paradox and Godel's First Incompletness Theorem.Roger Granet - manuscript
    A resolution to the Russell Paradox is presented that is similar to Russell's “theory of types” method but is instead based on the definition of why a thing exists as described in previous work by this author. In that work, it was proposed that a thing exists if it is a grouping tying "stuff" together into a new unit whole. In tying stuff together, this grouping defines what is contained within the new existent entity. A corollary is that a thing, (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  5. The Barber, Russell's Paradox, Catch-22, God, Contradiction, and More.Laurence Goldstein - 2006 - In Graham Priest, J. C. Beall & Bradley Armour-Garb (eds.), The Law of Non-Contradiction: New Philosophical Essays. Clarendon Press.
    Remove from this list  
     
    Export citation  
     
    Bookmark   2 citations  
  6. Sets, Lies, and Analogy: A New Methodological Take.Giulia Terzian - 2020 - Philosophical Studies 178 (9):2759-2784.
    The starting point of this paper is a claim defended most famously by Graham Priest: that given certain observed similarities between the set-theoretic and the semantic paradoxes, we should be looking for a ‘uniform solution’ to the members of both families. Despite its indisputable surface attractiveness, I argue that this claim hinges on a problematic reasoning move. This is seen most clearly, I suggest, when the claim and its underlying assumptions are examined by the lights of a novel, quite general (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  7. Frege's Intellectual Life As a Logicist Project. [REVIEW]Joan Bertran-San Millán - 2020 - Teorema: International Journal of Philosophy 39:127-138.
    I critically discuss Dale Jacquette’s Frege: A Philosophical Biography. First, I provide a short overview of Jacquette’s book. Second, I evaluate Jacquette’s interpretation of Frege’s three major works, Begriffsschrift, Grundlagen der Arithmetik and Grundgesetze der Arithmetik; and conclude that the author does not faithfully represent their content. Finally, I offer some technical and general remarks.
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  8. The Many and the One: A Philosophical Study of Plural Logic.Salvatore Florio & Øystein Linnebo - 2021 - Oxford, England: Oxford University Press.
    Plural expressions found in natural languages allow us to talk about many objects simultaneously. Plural logic — a logical system that takes plurals at face value — has seen a surge of interest in recent years. This book explores its broader significance for philosophy, logic, and linguistics. What can plural logic do for us? Are the bold claims made on its behalf correct? After introducing plural logic and its main applications, the book provides a systematic analysis of the relation between (...)
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  9. The Completeness: From Henkin's Proposition to Quantum Computer.Vasil Penchev - 2018 - Логико-Философские Штудии 16 (1-2):134-135.
    The paper addresses Leon Hen.kin's proposition as a " lighthouse", which can elucidate a vast territory of knowledge uniformly: logic, set theory, information theory, and quantum mechanics: Two strategies to infinity are equally relevant for it is as universal and t hus complete as open and thus incomplete. Henkin's, Godel's, Robert Jeroslow's, and Hartley Rogers' proposition are reformulated so that both completeness and incompleteness to be unified and thus reduced as a joint property of infinity and of all infinite sets. (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  10. Numbers, Empiricism and the A Priori.Olga Ramirez Calle - 2020 - Logos and Episteme: An International Journal of Epistemology 11 (2):149-177.
    The present paper deals with the ontological status of numbers and considers Frege ́s proposal in Grundlagen upon the background of the Post-Kantian semantic turn in analytical philosophy. Through a more systematic study of his philosophical premises, it comes to unearth a first level paradox that would unset earlier still than it was exposed by Russell. It then studies an alternative path, that departin1g from Frege’s initial premises, drives to a conception of numbers as synthetic a priori in a more (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  11. The Significance of Evidence-Based Reasoning for Mathematics, Mathematics Education, Philosophy and the Natural Sciences.Bhupinder Singh Anand - forthcoming
    In this multi-disciplinary investigation we show how an evidence-based perspective of quantification---in terms of algorithmic verifiability and algorithmic computability---admits evidence-based definitions of well-definedness and effective computability, which yield two unarguably constructive interpretations of the first-order Peano Arithmetic PA---over the structure N of the natural numbers---that are complementary, not contradictory. The first yields the weak, standard, interpretation of PA over N, which is well-defined with respect to assignments of algorithmically verifiable Tarskian truth values to the formulas of PA under the interpretation. (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark   1 citation  
  12. Some Highs and Lows of Hylomorphism: On a Paradox About Property Abstraction.Teresa Robertson Ishii & Nathan Salmón - 2020 - Philosophical Studies 177 (6):1549-1563.
    We defend hylomorphism against Maegan Fairchild’s purported proof of its inconsistency. We provide a deduction of a contradiction from SH+, which is the combination of “simple hylomorphism” and an innocuous premise. We show that the deduction, reminiscent of Russell’s Paradox, is proof-theoretically valid in classical higher-order logic and invokes an impredicatively defined property. We provide a proof that SH+ is nevertheless consistent in a free higher-order logic. It is shown that the unrestricted comprehension principle of property abstraction on which the (...)
    Remove from this list   Direct download (2 more)  
    Translate
     
     
    Export citation  
     
    Bookmark   2 citations  
1 — 50 / 239