- In Defense of the Implicit Commitment Thesis.Ethan Brauer - 2022 - Ergo: An Open Access Journal of Philosophy 9.details
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The Price of Mathematical Scepticism.Paul Blain Levy - 2022 - Philosophia Mathematica 30 (3):283-305.details
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Strict Finitism's Unrequited Love for Computational Complexity.Noel Arteche - manuscriptdetails
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(1 other version)The Significance of Evidence-based Reasoning in Mathematics, Mathematics Education, Philosophy, and the Natural Sciences (2nd edition).Bhupinder Singh Anand - 2024 - Mumbai: DBA Publishing (Second Edition).details
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The absorption law: Or: how to Kreisel a Hilbert–Bernays–Löb.Albert Visser - 2020 - Archive for Mathematical Logic 60 (3-4):441-468.details
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(1 other version)The Significance of Evidence-based Reasoning for Mathematics, Mathematics Education, Philosophy and the Natural Sciences.Bhupinder Singh Anand - forthcomingdetails
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Computational Complexity Theory and the Philosophy of Mathematics†.Walter Dean - 2019 - Philosophia Mathematica 27 (3):381-439.details
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Three Dogmas of First-Order Logic and some Evidence-based Consequences for Constructive Mathematics of differentiating between Hilbertian Theism, Brouwerian Atheism and Finitary Agnosticism.Bhupinder Singh Anand - manuscriptdetails
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The Truth Assignments That Differentiate Human Reasoning From Mechanistic Reasoning: The Evidence-Based Argument for Lucas' Goedelian Thesis.Bhupinder Singh Anand - 2016 - Cognitive Systems Research 40:35-45.details
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What is Mathematics: Gödel's Theorem and Around (Edition 2015).Karlis Podnieks - manuscriptdetails
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Wittgenstein Sobre as Provas Indutivas.André Porto - 2009 - Dois Pontos 6 (2).details
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Hilbert’s Finitism: Historical, Philosophical, and Metamathematical Perspectives.Richard Zach - 2001 - Dissertation, University of California, Berkeleydetails
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On the Concept of Finitism.Luca Incurvati - 2015 - Synthese 192 (8):2413-2436.details
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On the scheme of induction for bounded arithmetic formulas.A. J. Wilkie & J. B. Paris - 1987 - Annals of Pure and Applied Logic 35 (C):261-302.details
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Diophantine Induction.Richard Kaye - 1990 - Annals of Pure and Applied Logic 46 (1):1-40.details
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Bounded functional interpretation and feasible analysis.Fernando Ferreira & Paulo Oliva - 2007 - Annals of Pure and Applied Logic 145 (2):115-129.details
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Abelian groups and quadratic residues in weak arithmetic.Emil Jeřábek - 2010 - Mathematical Logic Quarterly 56 (3):262-278.details
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Combinatorial principles in elementary number theory.Alessandro Berarducci & Benedetto Intrigila - 1991 - Annals of Pure and Applied Logic 55 (1):35-50.details
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Quadratic forms in models of IΔ0+ Ω1, Part II: Local equivalence.Paola D’Aquino & Angus Macintyre - 2011 - Annals of Pure and Applied Logic 162 (6):447-456.details
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Homomorphisms and chains of Kripke models.Morteza Moniri & Mostafa Zaare - 2011 - Archive for Mathematical Logic 50 (3-4):431-443.details
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L'infinité des nombres premiers : une étude de cas de la pureté des méthodes.Andrew Arana - 2011 - Les Etudes Philosophiques 97 (2):193.details
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Provability logic-a short introduction.Per Lindström - 1996 - Theoria 62 (1-2):19-61.details
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The complexity of propositional proofs.Nathan Segerlind - 2007 - Bulletin of Symbolic Logic 13 (4):417-481.details
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On Infinite Number and Distance.Jeremy Gwiazda - 2012 - Constructivist Foundations 7 (2):126-130.details
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A universal approach to self-referential paradoxes, incompleteness and fixed points.Noson S. Yanofsky - 2003 - Bulletin of Symbolic Logic 9 (3):362-386.details
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(1 other version)Self-verifying axiom systems, the incompleteness theorem and related reflection principles.Dan Willard - 2001 - Journal of Symbolic Logic 66 (2):536-596.details
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Arithmetic without the successor axiom.Andrew Boucher - details
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Strict Finitism, Feasibility, and the Sorites.Walter Dean - 2018 - Review of Symbolic Logic 11 (2):295-346.details
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On me number of steps in proofs.Jan Krajíèek - 1989 - Annals of Pure and Applied Logic 41 (2):153-178.details
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Multifunction algebras and the provability of PH↓.Chris Pollett - 2000 - Annals of Pure and Applied Logic 104 (1-3):279-303.details
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A generalization of the Second Incompleteness Theorem and some exceptions to it.Dan E. Willard - 2006 - Annals of Pure and Applied Logic 141 (3):472-496.details
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Provably recursive functions of constructive and relatively constructive theories.Morteza Moniri - 2010 - Archive for Mathematical Logic 49 (3):291-300.details
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The unprovability of small inconsistency.Albert Visser - 1993 - Archive for Mathematical Logic 32 (4):275-298.details
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Polynomial local search in the polynomial hierarchy and witnessing in fragments of bounded arithmetic.Arnold Beckmann & Samuel R. Buss - 2009 - Journal of Mathematical Logic 9 (1):103-138.details
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Provability logic.Rineke Verbrugge - 2008 - Stanford Encyclopedia of Philosophy.details
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On the untenability of Nelson's predicativism.St Iwan - 2000 - Erkenntnis 53 (1-2):147-154.details
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Proof, Computation and Agency: Logic at the Crossroads.Johan van Benthem, Amitabha Gupta & Rohit Parikh (eds.) - 2011 - Dordrecht, Netherland: Springer.details
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Feasibly constructive proofs of succinct weak circuit lower bounds.Moritz Müller & Ján Pich - 2020 - Annals of Pure and Applied Logic 171 (2):102735.details
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Pell equations and exponentiation in fragments of arithmetic.Paola D'Aquino - 1996 - Annals of Pure and Applied Logic 77 (1):1-34.details
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A theory of hyperfinite sets.P. V. Andreev & E. I. Gordon - 2006 - Annals of Pure and Applied Logic 143 (1-3):3-19.details
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On interpretations of bounded arithmetic and bounded set theory.Richard Pettigrew - 2009 - Notre Dame Journal of Formal Logic 50 (2):141-152.details
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Number theory and elementary arithmetic.Jeremy Avigad - 2003 - Philosophia Mathematica 11 (3):257-284.details
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Infinity and continuum in the alternative set theory.Kateřina Trlifajová - 2021 - European Journal for Philosophy of Science 12 (1):1-23.details
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Another Look at Reflection.Martin Fischer - 2021 - Erkenntnis 88 (2):479-509.details
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Interpretability suprema in Peano Arithmetic.Paula Henk & Albert Visser - 2017 - Archive for Mathematical Logic 56 (5-6):555-584.details
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Arithmetizing Uniform NC.Bill Allen - 1991 - Annals of Pure and Applied Logic 53 (1):1-50.details
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Mathematically strong subsystems of analysis with low rate of growth of provably recursive functionals.Ulrich Kohlenbach - 1996 - Archive for Mathematical Logic 36 (1):31-71.details
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(2 other versions)reputation among logicians as being essentially trivial. I hope to convince the reader that it presents some of the most challenging and intriguing problems in modern logic. Although the problem of the complexity of propositional proofs is very natural, it has been investigated systematically only since the late 1960s. [REVIEW]Alasdair Urquhart - 1995 - Bulletin of Symbolic Logic 1 (4):425-467.details
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Upper and lower Ramsey bounds in bounded arithmetic.Kerry Ojakian - 2005 - Annals of Pure and Applied Logic 135 (1-3):135-150.details
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Preservation theorems and restricted consistency statements in bounded arithmetic.Arnold Beckmann - 2004 - Annals of Pure and Applied Logic 126 (1-3):255-280.details
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