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  1. Axiomatizations of Arithmetic and the First-Order/Second-Order Divide.Catarina Dutilh Novaes - 2019 - Synthese 196 (7):2583-2597.
    It is often remarked that first-order Peano Arithmetic is non-categorical but deductively well-behaved, while second-order Peano Arithmetic is categorical but deductively ill-behaved. This suggests that, when it comes to axiomatizations of mathematical theories, expressive power and deductive power may be orthogonal, mutually exclusive desiderata. In this paper, I turn to Hintikka’s :69–90, 1989) distinction between descriptive and deductive approaches in the foundations of mathematics to discuss the implications of this observation for the first-order logic versus second-order logic divide. The descriptive (...)
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  2. Second-Order Logic: Properties, Semantics, and Existential Commitments.Bob Hale - 2019 - Synthese 196 (7):2643-2669.
    Quine’s most important charge against second-, and more generally, higher-order logic is that it carries massive existential commitments. The force of this charge does not depend upon Quine’s questionable assimilation of second-order logic to set theory. Even if we take second-order variables to range over properties, rather than sets, the charge remains in force, as long as properties are individuated purely extensionally. I argue that if we interpret them as ranging over properties more reasonably construed, in accordance with an abundant (...)
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  3. On the Existence of Large Subsets of [Λ] Κ Which Contain No Unbounded Non-Stationary Subsets.Saharon Shelah - 2002 - Archive for Mathematical Logic 41 (3):207-213.
    Here we deal with some problems posed by Matet. The first section deals with the existence of stationary subsets of [λ]<κ with no unbounded subsets which are not stationary, where, of course, κ is regular uncountable ≤λ. In the second section we deal with the existence of such clubs. The proofs are easy but the result seems to be very surprising. Theorem 1.2 was proved some time ago by Baumgartner (see Theorem 2.3 of [Jo88]) and is presented here for the (...)
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  4. Alter ego. Les paradoxes de l’identité démocratique. [REVIEW]Idil Boran - 2001 - Dialogue 40 (3):638-641.
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  5. Mathematical Logic. Proceedings of the Heyting '88 Summer School.Petio Petrov Petkov (ed.) - 1990
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  6. The Jena System, 1804–5: Logic and Metaphysics.Georg Wilhelm Friedrich Hegel - 1986 - McGill-Queen's Press.
    Translated into English for the first time in this edition, The Jena System, 1804-5: Logic and Metaphysics is an essential text in the study of the development of Hegel's thought. It is the climax of Hegel's efforts to construct a neutral theory of the categories of finite cognition as the necessary bridge to the theory of infinite, or philosophical, cognition.
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  7. Retreat From Non-Being: Graham Priest, Towards Non-Being: The Logic and Metaphysics of Intentionality, Oxford: Clarendon Press, 2005, Pp. Xv + 190, £30. [REVIEW]Terry Horgan - 2006 - Australasian Journal of Philosophy 84 (4):615-627.
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  8. What Logics Mean: From Proof Theory to Model-Theoretic Semantics, by James W. Garson: Cambridge: Cambridge University Press, 2013, Pp. Xv + 285, £10.99. [REVIEW]Jaroslav Peregrin - 2015 - Australasian Journal of Philosophy 93 (3):613-616.
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  9. The Set of Better Quasi Orderings is ∏21.Alberto Marcone - 1995 - Mathematical Logic Quarterly 41 (3):373-383.
    In this paper we give a proof of the II12-completeness of the set of countable better quasi orderings . This result was conjectured by Clote in [2] and proved by the author in his Ph.d. thesis [6] . Here we prove it using Simpson's definition of better quasi ordering and as little bqo theory as possible.
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  10. The Unseen Déjà-Vu: From Erkki Huhtamo’s Topoi to Ken Jacobs’ Remakes: Commentary to Edwin Carels “Revisiting Tom Tom: Performative Anamnesis and Autonomous Vision in Ken Jacobs’ Appropriations of Tom Tom the Piper’s Son”.Wanda Strauven - 2018 - Foundations of Science 23 (2):231-236.
    This commentary on Edwin Carels’ essay “Revisiting Tom Tom: Performative anamnesis and autonomous vision in Ken Jacobs’ appropriations of Tom Tom the Piper’s Son” broadens up the media-archaeological framework in which Carels places his text. Notions such as Huhtamo’s topos and Zielinski’s “deep time” are brought into the discussion in order to point out the difficulty to see what there is to see and to question the position of the viewer in front of experimental films like Tom Tom the Piper’s (...)
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  11. Reflections on Relativism: From Momentous Tautology to Seductive Contradiction.Susan Haack - 1996 - Philosophical Perspectives 10:297-315.
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  12. Colloquium 8: Pros Hen and the Foundations of Aristotelian Metaphysics.Heike Sefrin-Weis - 2009 - Proceedings of the Boston Area Colloquium of Ancient Philosophy 24 (1):261-300.
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  13. Deductive Versus Expressive Power: A Pre-Godelian Predicament.Neil Tennant - 2000 - Journal of Philosophy 97 (5):257.
  14. Mathematical Logic. W. V. Quine.John M. Reiner - 1941 - Philosophy of Science 8 (1):136-136.
  15. Critique de la Mesure. G. Beneze.Karol Meisels - 1939 - Philosophy of Science 6 (2):258-259.
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  16. The Limits of Scientific Reasoning. David Faust.Andrew Lugg - 1987 - Philosophy of Science 54 (1):137-138.
  17. Ontology and the Vicious-Circle Principle. Charles S. Chihara.Fred Wilson - 1975 - Philosophy of Science 42 (3):339-341.
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  18. The Logical Structure of Mathematical Physics. Joseph D. Sneed.C. A. Hooker - 1973 - Philosophy of Science 40 (1):130-131.
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  19. Contributions to Mathematical Logic. H. Arnold Schmidt, Kurt Schütte, Ernst Jochen Thiele.Arthur Skidmore - 1970 - Philosophy of Science 37 (4):623-625.
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  20. Fundamentals of Logic. James D. Carney, Richard K. Scheer.Ivo Thomas - 1967 - Philosophy of Science 34 (1):76-77.
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  21. Reasoning and Logic. Richard B. Angell, Sterling P. Lamprecht.Milton Fisk - 1966 - Philosophy of Science 33 (1/2):85-87.
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  22. Axiomatic Set Theory. Patrick Suppes.Azriel Levy - 1962 - Philosophy of Science 29 (1):99-101.
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  23. Experience and the Analytic. Alan Pasch.Harry G. Frankfurt - 1960 - Philosophy of Science 27 (2):222-223.
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  24. Oneirics and Psychosomatics. Rolf Loehrich.Calvin S. Hall - 1955 - Philosophy of Science 22 (1):69-69.
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  25. From Euclid to Eddington. E. Whittaker.D. J. Struik - 1951 - Philosophy of Science 18 (1):88-91.
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  26. Logical Consequence for Nominalists.Marcus Rossberg & Daniel Cohnitz - 2009 - Theoria : An International Journal for Theory, History and Fundations of Science 24 (2):147-168.
    It is often claimed that nominalistic programmes to reconstruct mathematics fail, since they will at some point involve the notion of logical consequence which is unavailable to the nominalist. In this paper we use an idea of Goodman and Quine to develop a nominalistically acceptable explication of logical consequence.
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  27. Christopher Hollings, Mathematics Across the Iron Curtain: A History of the Algebraic Theory of Semigroups. Providence, RI: American Mathematical Society, 2014. Pp. Xi + 441. ISBN 978-1-4704-1493-1. £79.95. [REVIEW]Michael J. Barany - 2016 - British Journal for the History of Science 49 (1):140-141.
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  28. Why Axiomatize?Mario Bunge - 2017 - Foundations of Science 22 (4):695-707.
    Axiomatization is uncommon outside mathematics, partly for being often viewed as embalming, partly because the best-known axiomatizations have serious shortcomings, and partly because it has had only one eminent champion, namely David Hilbert. The aims of this paper are to describe what will be called dual axiomatics, for it concerns not just the formalism, but also the meaning of the key concepts; and to suggest that every instance of dual axiomatics presupposes some philosophical view or other. To illustrate these points, (...)
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  29. A Note on the Enumeration Degrees of 1-Generic Sets.Liliana Badillo, Caterina Bianchini, Hristo Ganchev, Thomas F. Kent & Andrea Sorbi - 2016 - Archive for Mathematical Logic 55 (3-4):405-414.
    We show that every nonzero Δ20\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta^{0}_{2}}$$\end{document} enumeration degree bounds the enumeration degree of a 1-generic set. We also point out that the enumeration degrees of 1-generic sets, below the first jump, are not downwards closed, thus answering a question of Cooper.
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  30. Neostability-Properties of Fraïssé Limits of 2-Nilpotent Groups of Exponent $${P > 2}$$ P > 2.Andreas Baudisch - 2016 - Archive for Mathematical Logic 55 (3-4):397-403.
    Let L\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${L}$$\end{document} be the language of group theory with n additional new constant symbols c1,…,cn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${c_1,\ldots,c_n}$$\end{document}. In L\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${L}$$\end{document} we consider the class K\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathbb{K}}}$$\end{document} of all finite groups G of exponent p>2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${p > 2}$$\end{document}, where G′⊆⟨c1G,…,cnG⟩⊆Z\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} (...)
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  31. Reverse Mathematics, Well-Quasi-Orders, and Noetherian Spaces.Emanuele Frittaion, Matthew Hendtlass, Alberto Marcone, Paul Shafer & Jeroen Van der Meeren - 2016 - Archive for Mathematical Logic 55 (3-4):431-459.
    A quasi-order Q induces two natural quasi-orders on P\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{P}}$$\end{document}, but if Q is a well-quasi-order, then these quasi-orders need not necessarily be well-quasi-orders. Nevertheless, Goubault-Larrecq, pp. 453–462, 2007) showed that moving from a well-quasi-order Q to the quasi-orders on P\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{P}}$$\end{document} preserves well-quasi-orderedness in a topological sense. Specifically, Goubault-Larrecq proved that the upper topologies of the induced quasi-orders on P\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} (...)
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  32. The Classification of $${\Mathbb {Z}}P$$ Z P -Modules with Partial Decomposition Bases in $$L{\Infty \Omega }$$ L ∞ Ω.Carol Jacoby & Peter Loth - 2016 - Archive for Mathematical Logic 55 (7-8):939-954.
    Ulm’s Theorem presents invariants that classify countable abelian torsion groups up to isomorphism. Barwise and Eklof extended this result to the classification of arbitrary abelian torsion groups up to L∞ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_{\infty \omega }$$\end{document}-equivalence. In this paper, we extend this classification to a class of mixed Zp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {Z}}_p$$\end{document}-modules which includes all Warfield modules and is closed under L∞ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} (...)
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  33. An Induction Principle Over Real Numbers.Assia Mahboubi - 2017 - Archive for Mathematical Logic 56 (1-2):43-49.
    We give a constructive proof of the open induction principle on real numbers, using bar induction and enumerative open sets. We comment the algorithmic content of this result.
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  34. Univalent Foundations as Structuralist Foundations.Dimitris Tsementzis - 2017 - Synthese 194 (9):3583-3617.
    The Univalent Foundations of Mathematics provide not only an entirely non-Cantorian conception of the basic objects of mathematics but also a novel account of how foundations ought to relate to mathematical practice. In this paper, I intend to answer the question: In what way is UF a new foundation of mathematics? I will begin by connecting UF to a pragmatist reading of the structuralist thesis in the philosophy of mathematics, which I will use to define a criterion that a formal (...)
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  35. X—On The Logic Of Relations.Stephan Körner - 1977 - Proceedings of the Aristotelian Society 77 (1):149-164.
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  36. A Fixed Point, A Point of Interruption.Mark Hewson - 2006 - Cosmos and History : The Journal of Natural and Social Philosophy 2 (1-2):376-379.
    A review of Alain Badiou, emInfinite Thought: Truth and the Return to Philosophy/em, ed. and trans. Justin Clemens and Oliver Feltham, New Edition, London, Continuum, 2005. ISBN: 0826479294.br /.
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  37. On Axiom Systems of Słupecki for the Functionally Complete Three-Valued Logic.Mateusz Radzki - 2017 - Axiomathes 27 (4):403-415.
    The article concerns two axiom systems of Słupecki for the functionally complete three-valued propositional logic: W1–W6 and A1–A9. The article proves that both of them are inadequate—W1–W6 is semantically incomplete, on the other hand, A1–A9 governs a functionally incomplete calculus, and thus, it cannot be a semantically complete axiom system for the functionally complete three-valued logic.
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  38. Exploring the Tractability Border in Epistemic Tasks.Cédric Dégremont, Lena Kurzen & Jakub Szymanik - 2014 - Synthese 191 (3):371-408.
    We analyse the computational complexity of comparing informational structures. Intuitively, we study the complexity of deciding queries such as the following: Is Alice’s epistemic information strictly coarser than Bob’s? Do Alice and Bob have the same knowledge about each other’s knowledge? Is it possible to manipulate Alice in a way that she will have the same beliefs as Bob? The results show that these problems lie on both sides of the border between tractability (P) and intractability (NP-hard). In particular, we (...)
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  39. Infinite Lotteries, Large and Small Sets.Luc Lauwers - 2017 - Synthese 194 (6):2203-2209.
    One result of this note is about the nonconstructivity of countably infinite lotteries: even if we impose very weak conditions on the assignment of probabilities to subsets of natural numbers we cannot prove the existence of such assignments constructively, i.e., without something such as the axiom of choice. This is a corollary to a more general theorem about large-small filters, a concept that extends the concept of free ultrafilters. The main theorem is that proving the existence of large-small filters requires (...)
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  40. On the Use of Hilbert”s Varepsilon -Operator in Scientific Theories.Rudolf Carnap - 1961 - In Yehoshua Bar-Hillel (ed.), Essays on the Foundations of Mathematics. Magnes Press. pp. 156--164.
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  41. Set Partitions and the Meaning of the Same.R. Zuber - 2017 - Journal of Logic, Language and Information 26 (1):1-20.
    It is shown that the notion of the partition of a set can be used to describe in a uniform way the meaning of the expression the same, in its basic uses in transitive and ditransitive sentences. Some formal properties of the function denoted by the same, which follow from such a description are indicated. These properties indicate similarities and differences between functions denoted by the same and generalised quantifiers.
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  42. On Wright’s Inductive Definition of Coherence Truth for Arithmetic.Jeffrey Ketland - 2003 - Analysis 63 (1):6-15.
    In “Truth – A Traditional Debate Reviewed”, Crispin Wright proposed an inductive definition of “coherence truth” for arithmetic relative to an arithmetic base theory B. Wright’s definition is in fact a notational variant of the usual Tarskian inductive definition, except for the basis clause for atomic sentences. This paper provides a model-theoretic characterization of the resulting sets of sentences "cohering" with a given base theory B. These sets are denoted WB. Roughly, if B satisfies a certain minimal condition, then WB (...)
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  43. Adequacy and Consistency: A Second Reply to Dr Bar-Hillel.K. R. Popper - 1956 - British Journal for the Philosophy of Science 7 (27):249-256.
  44. The Foundations of Mathematics in the Theory of Sets.Roy T. Cook - 2003 - British Journal for the Philosophy of Science 54 (2):347-352.
  45. La natura e il futuro della filosofia.Donald Gillies - 2003 - British Journal for the Philosophy of Science 54 (3):501-507.
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  46. What is a Higher Level Set?Dimitris Tsementzis - 2016 - Philosophia Mathematica:nkw032.
    Structuralist foundations of mathematics aim for an ‘invariant’ conception of mathematics. But what should be their basic objects? Two leading answers emerge: higher groupoids or higher categories. I argue in favor of the former over the latter. First, I explain why to choose between them we need to ask the question of what is the correct ‘categorified’ version of a set. Second, I argue in favor of groupoids over categories as ‘categorified’ sets by introducing a pre-formal understanding of groupoids as (...)
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  47. Reply to Feferman, Koellner, Tait, and Sieg.Charles Parsons - 2016 - Journal of Philosophy 113 (5/6):286-307.
    I comment on Feferman’s views on set theory, in particular criticizing a priori arguments claiming that the continuum hypothesis has no determinate truth value and commenting on his responses to my paper on his skepticism about set theory. I respond to criticisms of his of the structuralism that I have advocated and comment on his view of proof theory. On Koellner’s paper, I register little disagreement but note a difference of sympathy about views such as constructivism. On Tait’s paper, I (...)
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  48. Frege Meets Aristotle: Points as Abstracts.Stewart Shapiro & Geoffrey Hellman - 2015 - Philosophia Mathematica:nkv021.
    There are a number of regions-based accounts of space/time, due to Whitehead, Roeper, Menger, Tarski, the present authors, and others. They all follow the Aristotelian theme that continua are not composed of points: each region has a proper part. The purpose of this note is to show how to recapture ‘points’ in such frameworks via Scottish neo-logicist abstraction principles. The results recapitulate some Aristotelian themes. A second agenda is to provide a new arena to help decide what is at stake (...)
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  49. Philosophy of the Matrix.A. C. Paseau - 2017 - Philosophia Mathematica 25 (2):246-267.
    A mathematical matrix is usually defined as a two-dimensional array of scalars. And yet, as I explain, matrices are not in fact two-dimensional arrays. So are we to conclude that matrices do not exist? I show how to resolve the puzzle, for both contemporary and older mathematics. The solution generalises to the interpretation of all mathematical discourse. The paper as a whole attempts to reinforce mathematical structuralism by reflecting on how best to interpret mathematics.
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  50. If P, Then Q: Conditionals and the Foundations of Reasoning.Vann McGee - 1992 - Philosophy and Phenomenological Research 53 (1):239-242.
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