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  1. Intuition, Iteration, Induction.Mark van Atten - 2024 - Philosophia Mathematica 32 (1):34-81.
    Brouwer’s view on induction has relatively recently been characterised as one on which it is not only intuitive (as expected) but functional, by van Dalen. He claims that Brouwer’s ‘Ur-intuition’ also yields the recursor. Appealing to Husserl’s phenomenology, I offer an analysis of Brouwer’s view that supports this characterisation and claim, even if assigning the primary role to the iterator instead. Contrasts are drawn to accounts of induction by Poincaré, Heyting, and Kreisel. On the phenomenological side, the analysis provides an (...)
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  • Validity as a thick concept.Sophia Arbeiter - 2023 - Philosophical Studies 180 (10):2937-2953.
    This paper presents a novel position in the philosophy of logic: I argue that _validity_ is a thick concept. Hence, I propose to consider _validity_ in analogy to other thick concepts, such as _honesty_, _selfishness_ or _justice_. This proposal is motivated by the debate on the normativity of logic: while logic textbooks seem simply descriptive in their presentation of logical truths, many have argued that logic has consequences for how we ought to reason, for what we ought to believe, or (...)
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  • The Logical and Philosophical Foundations for the Possibility of True Contradictions.Ben Martin - 2014 - Dissertation, University College London
    The view that contradictions cannot be true has been part of accepted philosophical theory since at least the time of Aristotle. In this regard, it is almost unique in the history of philosophy. Only in the last forty years has the view been systematically challenged with the advent of dialetheism. Since Graham Priest introduced dialetheism as a solution to certain self-referential paradoxes, the possibility of true contradictions has been a live issue in the philosophy of logic. Yet, despite the arguments (...)
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  • Connecting the revolutionary with the conventional: Rethinking the differences between the works of Brouwer, Heyting, and Weyl.Kati Kish Bar-On - 2023 - Philosophy of Science 90 (3):580–602.
    Brouwer’s intuitionism was a far-reaching attempt to reform the foundations of mathematics. While the mathematical community was reluctant to accept Brouwer’s work, its response to later-developed brands of intuitionism, such as those presented by Hermann Weyl and Arend Heyting, was different. The paper accounts for this difference by analyzing the intuitionistic versions of Brouwer, Weyl, and Heyting in light of a two-tiered model of the body and image of mathematical knowledge. Such a perspective provides a richer account of each story (...)
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  • Evidence in Logic.Ben Martin & Ole Thomassen Hjortland - 2024 - In Maria Lasonen-Aarnio & Clayton Littlejohn (eds.), The Routledge Handbook of the Philosophy of Evidence. New York, NY: Routledge.
    The historical consensus is that logical evidence is special. Whereas empirical evidence is used to support theories within both the natural and social sciences, logic answers solely to a priori evidence. Further, unlike other areas of research that rely upon a priori evidence, such as mathematics, logical evidence is basic. While we can assume the validity of certain inferences in order to establish truths within mathematics and test scientifi c theories, logicians cannot use results from mathematics or the empirical sciences (...)
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  • David Makinson on Classical Methods for Non-Classical Problems.Sven Ove Hansson (ed.) - 2013 - Dordrecht, Netherland: Springer.
    The volume analyses and develops David Makinson’s efforts to make classical logic useful outside its most obvious application areas. The book contains chapters that analyse, appraise, or reshape Makinson’s work and chapters that develop themes emerging from his contributions. These are grouped into major areas to which Makinsons has made highly influential contributions and the volume in its entirety is divided into four sections, each devoted to a particular area of logic: belief change, uncertain reasoning, normative systems and the resources (...)
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  • Constructivity and Computability in Historical and Philosophical Perspective.Jacques Dubucs & Michel Bourdeau (eds.) - 2014 - Dordrecht, Netherland: Springer.
    Ranging from Alan Turing’s seminal 1936 paper to the latest work on Kolmogorov complexity and linear logic, this comprehensive new work clarifies the relationship between computability on the one hand and constructivity on the other. The authors argue that even though constructivists have largely shed Brouwer’s solipsistic attitude to logic, there remain points of disagreement to this day. Focusing on the growing pains computability experienced as it was forced to address the demands of rapidly expanding applications, the content maps the (...)
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  • Bishop's Mathematics: a Philosophical Perspective.Laura Crosilla - forthcoming - In Handbook of Bishop's Mathematics. CUP.
    Errett Bishop's work in constructive mathematics is overwhelmingly regarded as a turning point for mathematics based on intuitionistic logic. It brought new life to this form of mathematics and prompted the development of new areas of research that witness today's depth and breadth of constructive mathematics. Surprisingly, notwithstanding the extensive mathematical progress since the publication in 1967 of Errett Bishop's Foundations of Constructive Analysis, there has been no corresponding advances in the philosophy of constructive mathematics Bishop style. The aim of (...)
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  • Brouwer’s Weak Counterexamples and the Creative Subject: A Critical Survey.Peter Fletcher - 2020 - Journal of Philosophical Logic 49 (6):1111-1157.
    I survey Brouwer’s weak counterexamples to classical theorems, with a view to discovering what useful mathematical work is done by weak counterexamples; whether they are rigorous mathematical proofs or just plausibility arguments; the role of Brouwer’s notion of the creative subject in them, and whether the creative subject is really necessary for them; what axioms for the creative subject are needed; what relation there is between these arguments and Brouwer’s theory of choice sequences. I refute one of Brouwer’s claims with (...)
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  • (1 other version)Dag Prawitz on Proofs and Meaning.Heinrich Wansing (ed.) - 2014 - Cham, Switzerland: Springer.
    This volume is dedicated to Prof. Dag Prawitz and his outstanding contributions to philosophical and mathematical logic. Prawitz's eminent contributions to structural proof theory, or general proof theory, as he calls it, and inference-based meaning theories have been extremely influential in the development of modern proof theory and anti-realistic semantics. In particular, Prawitz is the main author on natural deduction in addition to Gerhard Gentzen, who defined natural deduction in his PhD thesis published in 1934. The book opens with an (...)
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  • Debunking, supervenience, and Hume’s Principle.Mary Leng - 2019 - Canadian Journal of Philosophy 49 (8):1083-1103.
    Debunking arguments against both moral and mathematical realism have been pressed, based on the claim that our moral and mathematical beliefs are insensitive to the moral/mathematical facts. In the mathematical case, I argue that the role of Hume’s Principle as a conceptual truth speaks against the debunkers’ claim that it is intelligible to imagine the facts about numbers being otherwise while our evolved responses remain the same. Analogously, I argue, the conceptual supervenience of the moral on the natural speaks presents (...)
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  • Intuitionistic mereology.Paolo Maffezioli & Achille C. Varzi - 2021 - Synthese 198 (Suppl 18):4277-4302.
    Two mereological theories are presented based on a primitive apartness relation along with binary relations of mereological excess and weak excess, respectively. It is shown that both theories are acceptable from the standpoint of constructive reasoning while remaining faithful to the spirit of classical mereology. The two theories are then compared and assessed with regard to their extensional import.
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  • Reply to Øystein Linnebo and Stewart Shapiro.Ian Rumfitt - 2019 - Inquiry: An Interdisciplinary Journal of Philosophy 62 (7):842-858.
    ABSTRACTIn reply to Linnebo, I defend my analysis of Tait's argument against the use of classical logic in set theory, and make some preliminary comments on Linnebo's new argument for the same conclusion. I then turn to Shapiro's discussion of intuitionistic analysis and of Smooth Infinitesimal Analysis. I contend that we can make sense of intuitionistic analysis, but only by attaching deviant meanings to the connectives. Whether anyone can make sense of SIA is open to doubt: doing so would involve (...)
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  • Five Observations Concerning the Intended Meaning of the Intuitionistic Logical Constants.Gustavo Fernández Díez - 2000 - Journal of Philosophical Logic 29 (4):409-424.
    This paper contains five observations concerning the intended meaning of the intuitionistic logical constants: (1) if the explanations of this meaning are to be based on a non-decidable concept, that concept should not be that of `proof"; (2) Kreisel"s explanations using extra clauses can be significantly simplified; (3) the impredicativity of the definition of → can be easily and safely ameliorated; (4) the definition of → in terms of `proofs from premises" results in a loss of the inductive character of (...)
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  • Safe Contraction Revisited.Hans Rott & Sven Ove Hansson - 2014 - In Sven Ove Hansson (ed.), David Makinson on Classical Methods for Non-Classical Problems (Outstanding Contributions to Logic, Vol. 3). Springer. pp. 35–70.
    Modern belief revision theory is based to a large extent on partial meet contraction that was introduced in the seminal article by Carlos Alchourrón, Peter Gärdenfors, and David Makinson that appeared in 1985. In the same year, Alchourrón and Makinson published a significantly different approach to the same problem, called safe contraction. Since then, safe contraction has received much less attention than partial meet contraction. The present paper summarizes the current state of knowledge on safe contraction, provides some new results (...)
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  • Towards a philosophical understanding of the logics of formal inconsistency.Walter Carnielli & Abílio Rodrigues - 2015 - Manuscrito 38 (2):155-184.
    In this paper we present a philosophical motivation for the logics of formal inconsistency, a family of paraconsistent logics whose distinctive feature is that of having resources for expressing the notion of consistency within the object language in such a way that consistency may be logically independent of non-contradiction. We defend the view according to which logics of formal inconsistency may be interpreted as theories of logical consequence of an epistemological character. We also argue that in order to philosophically justify (...)
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  • On Dummett’s verificationist justification procedure.Wagner de Campos Sanz & Hermógenes Oliveira - 2016 - Synthese 193 (8):2539-2559.
    We examine the proof-theoretic verificationist justification procedure proposed by Dummett. After some scrutiny, two distinct interpretations with respect to bases are advanced: the independent and the dependent interpretation. We argue that both are unacceptable as a semantics for propositional intuitionistic logic.
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  • A pragmatic interpretation of intuitionistic propositional logic.Carlo Dalla Pozza & Claudio Garola - 1995 - Erkenntnis 43 (1):81-109.
    We construct an extension P of the standard language of classical propositional logic by adjoining to the alphabet of a new category of logical-pragmatic signs. The well formed formulas of are calledradical formulas (rfs) of P;rfs preceded by theassertion sign constituteelementary assertive formulas of P, which can be connected together by means of thepragmatic connectives N, K, A, C, E, so as to obtain the set of all theassertive formulas (afs). Everyrf of P is endowed with atruth value defined classically, (...)
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  • Nāgārjuna’s Catuṣkoṭi.Jan Westerhoff - 2006 - Journal of Indian Philosophy 34 (4):367-395.
    The catuṣkoṭi or tetralemma is an argumentative figure familiar to any reader of Buddhist philosophical literature. Roughly speaking it consists of the enumeration of four alternatives: that some propositions holds, that it fails to hold, that it both holds and fails to hold, that it neither holds nor fails to hold. The tetralemma also constitutes one of the more puzzling features of Buddhist philosophy as the use to which it is put in arguments is not immediately obvious and certainly not (...)
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  • (1 other version)Constructively Complete Finite Sets.Mark Mandelkern - 1988 - Mathematical Logic Quarterly 34 (2):97-103.
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  • The continuum as a formal space.Sara Negri & Daniele Soravia - 1999 - Archive for Mathematical Logic 38 (7):423-447.
    A constructive definition of the continuum based on formal topology is given and its basic properties studied. A natural notion of Cauchy sequence is introduced and Cauchy completeness is proved. Other results include elementary proofs of the Baire and Cantor theorems. From a classical standpoint, formal reals are seen to be equivalent to the usual reals. Lastly, the relation of real numbers as a formal space to other approaches to constructive real numbers is determined.
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  • A Cognitive Approach to Benacerraf's Dilemma.Luke Jerzykiewicz - 2009 - Dissertation, University of Western Ontario
    One of the important challenges in the philosophy of mathematics is to account for the semantics of sentences that express mathematical propositions while simultaneously explaining our access to their contents. This is Benacerraf’s Dilemma. In this dissertation, I argue that cognitive science furnishes new tools by means of which we can make progress on this problem. The foundation of the solution, I argue, must be an ontologically realist, albeit non-platonist, conception of mathematical reality. The semantic portion of the problem can (...)
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  • The Crisis in the Foundations of Mathematics.J. Ferreiros - 2008 - In T. Gowers (ed.), Princeton Companion to Mathematics. Princeton University Press.
    A general introduction to the celebrated foundational crisis, discussing how the characteristic traits of modern mathematics (acceptance of the notion of an “arbitrary” function proposed by Dirichlet; wholehearted acceptance of infinite sets and the higher infinite; a preference “to put thoughts in the place of calculations” and to concentrate on “structures” characterized axiomatically; a reliance on “purely existential” methods of proof) provoked extensive polemics and alternative approaches. Going beyond exclusive concentration on the paradoxes, it also discusses the role of the (...)
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  • Mathematics and reality.Stewart Shapiro - 1983 - Philosophy of Science 50 (4):523-548.
    The subject of this paper is the philosophical problem of accounting for the relationship between mathematics and non-mathematical reality. The first section, devoted to the importance of the problem, suggests that many of the reasons for engaging in philosophy at all make an account of the relationship between mathematics and reality a priority, not only in philosophy of mathematics and philosophy of science, but also in general epistemology/metaphysics. This is followed by a (rather brief) survey of the major, traditional philosophies (...)
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  • Pragmatism, intuitionism, and formalism.Henry A. Patin - 1957 - Philosophy of Science 24 (3):243-252.
    “… there is no distinction of meaning so fine as to consist in anything but a possible difference of practice.”“… Consider what effects, that might conceivably have practical bearings, we conceive the object of our conception to have. Then, our conception of these effects is the whole of our conception of the object.”One example which Peirce chose to illustrate his pragmatic maxim as thus stated was the familiar theological distinction between transubstantiation and consubstantiation. Now since these two doctrines agree in (...)
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  • Wilson on relativism and teaching.Jim Mackenzie - 1987 - Journal of Philosophy of Education 21 (1):119–130.
    Jim Mackenzie; Wilson on Relativism and Teaching, Journal of Philosophy of Education, Volume 21, Issue 1, 30 May 2006, Pages 119–130, https://doi.org/10.1111/j.
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  • Poincaré's conception of the objectivity of mathematics.Janet Folina - 1994 - Philosophia Mathematica 2 (3):202-227.
    There is a basic division in the philosophy of mathematics between realist, ‘platonist’ theories and anti-realist ‘constructivist’ theories. Platonism explains how mathematical truth is strongly objective, but it does this at the cost of invoking mind-independent mathematical objects. In contrast, constructivism avoids mind-independent mathematical objects, but the cost tends to be a weakened conception of mathematical truth. Neither alternative seems ideal. The purpose of this paper is to show that in the philosophical writings of Henri Poincaré there is a coherent (...)
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  • The meaning of mathematical expressions: Does philosophy shed any light on psychology?Paul Ernest - 1990 - British Journal for the Philosophy of Science 41 (4):443-460.
    Mathematicians and physical scientists depend heavily on the formal symbolism of mathematics in order to express and develop their theories. For this and other reasons the last hundred years has seen a growing interest in the nature of formal language and the way it expresses meaning; particularly the objective, shared aspect of meaning as opposed to subjective, personal aspects. This dichotomy suggests the question: do the objective philosophical theories of meaning offer concepts which can be applied in psychological theories of (...)
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  • (1 other version)Constructive mathematics in theory and programming practice.Douglas Bridges & Steeve Reeves - 1999 - Philosophia Mathematica 7 (1):65-104.
    The first part of the paper introduces the varieties of modern constructive mathematics, concentrating on Bishop's constructive mathematics (BISH). it gives a sketch of both Myhill's axiomatic system for BISH and a constructive axiomatic development of the real line R. The second part of the paper focusses on the relation between constructive mathematics and programming, with emphasis on Martin-L6f 's theory of types as a formal system for BISH.
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  • Languages and Other Abstract Structures.Ryan Mark Nefdt - 2018 - In Martin Neef & Christina Behme (eds.), Essays on Linguistic Realism. Philadelphia: John Benjamins Publishing Company. pp. 139-184.
    My aim in this chapter is to extend the Realist account of the foundations of linguistics offered by Postal, Katz and others. I first argue against the idea that naive Platonism can capture the necessary requirements on what I call a ‘mixed realist’ view of linguistics, which takes aspects of Platonism, Nominalism and Mentalism into consideration. I then advocate three desiderata for an appropriate ‘mixed realist’ account of linguistic ontology and foundations, namely (1) linguistic creativity and infinity, (2) linguistics as (...)
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  • What is Intuitionistic Arithmetic?V. Alexis Peluce - 2024 - Erkenntnis 89 (8):3351-3376.
    L.E.J. Brouwer famously took the subject’s intuition of time to be foundational and from there ventured to build up mathematics. Despite being largely critical of formal methods, Brouwer valued axiomatic systems for their use in both communication and memory. Through the Dutch Mathematical Society, Gerrit Mannoury posed a challenge in 1927 to provide an axiomatization of intuitionistic arithmetic. Arend Heyting’s 1928 axiomatization was chosen as the winner and has since enjoyed the status of being the _de facto_ formalization of intuitionistic (...)
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  • Quine's challenge and Logical Pluralism.Antonio Negro - 2010 - Dissertation,
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  • Proofs, Grounds and Empty Functions: Epistemic Compulsion in Prawitz’s Semantics.Antonio Piccolomini D’Aragona - 2021 - Journal of Philosophical Logic 51 (2):249-281.
    Prawitz has recently developed a theory of epistemic grounding that differs in many respects from his earlier semantics of arguments and proofs. An innovative approach to inferences yields a new conception of the intertwinement of the notions of valid inference and proof. We aim at singling out three reasons that may have led Prawitz to the ground-theoretic turn, i.e.: a better order in the explanation of the relation between valid inferences and proofs; a notion of valid inference based on which (...)
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  • Epistemic logic: All knowledge is based on our experience, and epistemic logic is the cognitive representation of our experiential confrontation in reality.Dan Nesher - 2021 - Semiotica 2021 (238):153-179.
    Epistemic Logic is our basic universal science, the method of our cognitive confrontation in reality to prove the truth of our basic cognitions and theories. Hence, by proving their true representation of reality we can self-control ourselves in it, and thus refuting the Berkeleyian solipsism and Kantian a priorism. The conception of epistemic logic is that only by proving our true representation of reality we achieve our knowledge of it, and thus we can prove our cognitions to be either true (...)
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  • (1 other version)On Formalism Freeness: Implementing Gödel's 1946 Princeton Bicentennial Lecture.Juliette Kennedy - 2013 - Bulletin of Symbolic Logic 19 (3):351-393.
    In this paper we isolate a notion that we call “formalism freeness” from Gödel's 1946 Princeton Bicentennial Lecture, which asks for a transfer of the Turing analysis of computability to the cases of definability and provability. We suggest an implementation of Gödel's idea in the case of definability, via versions of the constructible hierarchy based on fragments of second order logic. We also trace the notion of formalism freeness in the very wide context of developments in mathematical logic in the (...)
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  • Some Obstacles Facing a Semantic Foundation for Constructive Mathematics.Michael R. Koss - 2015 - Erkenntnis 80 (5):1055-1068.
    This paper discusses Michael Dummett’s attempt to base the use of intuitionistic logic in mathematics on a proof-conditional semantics. This project is shown to face significant obstacles resulting from the existence of variants of standard intuitionistic logic. In order to overcome these obstacles, Dummett and his followers must give an intuitionistically acceptable completeness proof for intuitionistic logic relative to the BHK interpretation of the logical constants, but there are reasons to doubt that such a proof is possible. The paper concludes (...)
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  • The significance of a non-reductionist ontology for the discipline of mathematics: A historical and systematic analysis. [REVIEW]D. F. M. Strauss - 2010 - Axiomathes 20 (1):19-52.
    A Christian approach to scholarship, directed by the central biblical motive of creation, fall and redemption and guided by the theoretical idea that God subjected all of creation to His Law-Word, delimiting and determining the cohering diversity we experience within reality, in principle safe-guards those in the grip of this ultimate commitment and theoretical orientation from absolutizing or deifying anything within creation. In this article my over-all approach is focused on the one-sided legacy of mathematics, starting with Pythagorean arithmeticism (“everything (...)
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  • Elementary intuitionistic theories.C. Smorynski - 1973 - Journal of Symbolic Logic 38 (1):102-134.
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  • An intuitionistic logic for preference relations.Paolo Maffezioli & Alberto Naibo - 2019 - Logic Journal of the IGPL 27 (4):434-450.
    We investigate in intuitionistic first-order logic various principles of preference relations alternative to the standard ones based on the transitivity and completeness of weak preference. In particular, we suggest two ways in which completeness can be formulated while remaining faithful to the spirit of constructive reasoning, and we prove that the cotransitivity of the strict preference relation is a valid intuitionistic alternative to the transitivity of weak preference. Along the way, we also show that the acyclicity axiom is not finitely (...)
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  • L’interaction sociale comme fondement de la signification logique.Adjoua Bernadette Dango - 2017 - Revista de Humanidades de Valparaíso 9:121-142.
    Our article aims to show, on the one hand, the preeminence of the interactive paradigm as a determining element in the process of constitution of logical meaning and, on the other hand, to examine the contents of the linguistic expressions of pragmatic semantics. To do this, we expose three major figures of the logic of mathematical obedience in particular those of Gottfreid Leibniz, George Boole and Gottlob Frege. If this approach to mathematical logic has seen meritorious progress, it should be (...)
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  • The Seeming Interdependence Between the Concepts of Valid Inference and Proof.Dag Prawitz - 2019 - Topoi 38 (3):493-503.
    We may try to explain proofs as chains of valid inference, but the concept of validity needed in such an explanation cannot be the traditional one. For an inference to be legitimate in a proof it must have sufficient epistemic power, so that the proof really justifies its final conclusion. However, the epistemic concepts used to account for this power are in their turn usually explained in terms of the concept of proof. To get out of this circle we may (...)
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  • Fitch's Paradox and the Problem of Shared Content.Thorsten Sander - 2006 - Abstracta 3 (1):74-86.
    According to the “paradox of knowability”, the moderate thesis that all truths are knowable – ... – implies the seemingly preposterous claim that all truths are actually known – ... –, i.e. that we are omniscient. If Fitch’s argument were successful, it would amount to a knockdown rebuttal of anti-realism by reductio. In the paper I defend the nowadays rather neglected strategy of intuitionistic revisionism. Employing only intuitionistically acceptable rules of inference, the conclusion of the argument is, firstly, not ..., (...)
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  • (1 other version)The roots of contemporary Platonism.Penelope Maddy - 1989 - Journal of Symbolic Logic 54 (4):1121-1144.
    Though many working mathematicians embrace a rough and ready form of Platonism, that venerable position has suffered a checkered philosophical career. Indeed the three schools of thought with which most of us began our official philosophizing about mathematics—Intuitionism, Formalism, and Logicism—all stand in fundamental disagreement with Platonism. Nevertheless, various versions of Platonistic thinking survive in contemporary philosophical circles. The aim of this paper is to describe these views, and, as my title suggests, to trace their roots.I'll begin with some preliminary (...)
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  • Lie-toe-tease: double negatives and unexcluded middles.Laurence Horn - 2017 - Philosophical Studies 174 (1):79-103.
    Litotes, “a figure of speech in which an affirmative is expressed by the negative of the contrary” has had some tough reviews. For Pope and Swift, litotes—stock examples include “no mean feat”, “no small problem”, and “not bad at all”—is “the peculiar talent of Ladies, Whisperers, and Backbiters”; for Orwell, it is a means to affect “an appearance of profundity” that we can deport from English “by memorizing this sentence: A not unblack dog was chasing a not unsmall rabbit across (...)
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  • A Burgessian Critique of Nominalistic Tendencies in Contemporary Mathematics and its Historiography.Karin Usadi Katz & Mikhail G. Katz - 2012 - Foundations of Science 17 (1):51-89.
    We analyze the developments in mathematical rigor from the viewpoint of a Burgessian critique of nominalistic reconstructions. We apply such a critique to the reconstruction of infinitesimal analysis accomplished through the efforts of Cantor, Dedekind, and Weierstrass; to the reconstruction of Cauchy’s foundational work associated with the work of Boyer and Grabiner; and to Bishop’s constructivist reconstruction of classical analysis. We examine the effects of a nominalist disposition on historiography, teaching, and research.
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  • On Logic in the Law: "Something, but not All".Susan Haack - 2007 - Ratio Juris 20 (1):1-31.
    In 1880, when Oliver Wendell Holmes (later to be a Justice of the U.S. Supreme Court) criticized the logical theology of law articulated by Christopher Columbus Langdell (the first Dean of Harvard Law School), neither Holmes nor Langdell was aware of the revolution in logic that had begun, the year before, with Frege's Begriffsschrift. But there is an important element of truth in Holmes's insistence that a legal system cannot be adequately understood as a system of axioms and corollaries; and (...)
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  • Encoding true second‐order arithmetic in the real‐algebraic structure of models of intuitionistic elementary analysis.Miklós Erdélyi-Szabó - 2021 - Mathematical Logic Quarterly 67 (3):329-341.
    Based on the paper [4] we show that true second‐order arithmetic is interpretable over the real‐algebraic structure of models of intuitionistic analysis built upon a certain class of complete Heyting algebras.
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  • Denotational Semantics for Languages of Epistemic Grounding Based on Prawitz’s Theory of Grounds.Antonio Piccolomini D’Aragona - 2021 - Studia Logica 110 (2):355-403.
    We outline a class of term-languages for epistemic grounding inspired by Prawitz’s theory of grounds. We show how denotation functions can be defined over these languages, relating terms to proof-objects built up of constructive functions. We discuss certain properties that the languages may enjoy both individually and with respect to their expansions. Finally, we provide a ground-theoretic version of Prawitz’s completeness conjecture, and adapt to our framework a refutation of this conjecture due to Piecha and Schroeder-Heister.
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  • Is There an Ontology of Infinity?Stathis Livadas - 2020 - Foundations of Science 25 (3):519-540.
    In this article I try to articulate a defensible argumentation against the idea of an ontology of infinity. My position is phenomenologically motivated and in this virtue strongly influenced by the Husserlian reduction of the ontological being to a process of subjective constitution within the immanence of consciousness. However taking into account the historical charge and the depth of the question of infinity over the centuries I also include a brief review of the platonic and aristotelian views and also those (...)
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  • On epistemic and ontological interpretations of intuitionistic and paraconsistent paradigms.Walter Carnielli & Abilio Rodrigues - 2021 - Logic Journal of the IGPL 29 (4):569-584.
    From the technical point of view, philosophically neutral, the duality between a paraconsistent and a paracomplete logic (for example intuitionistic logic) lies in the fact that explosion does not hold in the former and excluded middle does not hold in the latter. From the point of view of the motivations for rejecting explosion and excluded middle, this duality can be interpreted either ontologically or epistemically. An ontological interpretation of intuitionistic logic is Brouwer’s idealism; of paraconsistency is dialetheism. The epistemic interpretation (...)
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