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77 results on '"Intuitionism"'

7. The Paradox of Knowability

Author

Usberti, Gabriele, Rahman, Shahid, Series Editor, Clerbout, Nicolas, Managing Editor, Symons, John, Founding Editor, van Bendegem, Jean Paul, Editorial Board Member, Benis Sinaceur, Hourya, Editorial Board Member, van Benthem, Johan, Editorial Board Member, Chemla, Karine, Editorial Board Member, Dubucs, Jacques, Editorial Board Member, Fagot-Largeault, Anne, Editorial Board Member, Van Fraassen, Bas C, Editorial Board Member, Gabbay, Dov M., Editorial Board Member, McNamara, Paul, Editorial Board Member, Priest, Graham, Editorial Board Member, Sandu, Gabriel, Editorial Board Member, Smets, Sonja, Editorial Board Member, Street, Tony, Editorial Board Member, Sundholm, Göran, Editorial Board Member, Wansing, Heinrich, Editorial Board Member, Williamson, Timothy, Editorial Board Member, Zarepour, Mohammad Saleh, Editorial Board Member, and Usberti, Gabriele

Published
2023
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8. Truth and Truth-Recognition

Author

Usberti, Gabriele, Rahman, Shahid, Series Editor, Clerbout, Nicolas, Managing Editor, Symons, John, Founding Editor, van Bendegem, Jean Paul, Editorial Board Member, Benis Sinaceur, Hourya, Editorial Board Member, van Benthem, Johan, Editorial Board Member, Chemla, Karine, Editorial Board Member, Dubucs, Jacques, Editorial Board Member, Fagot-Largeault, Anne, Editorial Board Member, Van Fraassen, Bas C, Editorial Board Member, Gabbay, Dov M., Editorial Board Member, McNamara, Paul, Editorial Board Member, Priest, Graham, Editorial Board Member, Sandu, Gabriel, Editorial Board Member, Smets, Sonja, Editorial Board Member, Street, Tony, Editorial Board Member, Sundholm, Göran, Editorial Board Member, Wansing, Heinrich, Editorial Board Member, Williamson, Timothy, Editorial Board Member, Zarepour, Mohammad Saleh, Editorial Board Member, and Usberti, Gabriele

Published
2023
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9. Belief, Synonymy, and the De Dicto/De Re Distinction

Author

Usberti, Gabriele, Rahman, Shahid, Series Editor, Clerbout, Nicolas, Managing Editor, Symons, John, Founding Editor, van Bendegem, Jean Paul, Editorial Board Member, Benis Sinaceur, Hourya, Editorial Board Member, van Benthem, Johan, Editorial Board Member, Chemla, Karine, Editorial Board Member, Dubucs, Jacques, Editorial Board Member, Fagot-Largeault, Anne, Editorial Board Member, Van Fraassen, Bas C, Editorial Board Member, Gabbay, Dov M., Editorial Board Member, McNamara, Paul, Editorial Board Member, Priest, Graham, Editorial Board Member, Sandu, Gabriel, Editorial Board Member, Smets, Sonja, Editorial Board Member, Street, Tony, Editorial Board Member, Sundholm, Göran, Editorial Board Member, Wansing, Heinrich, Editorial Board Member, Williamson, Timothy, Editorial Board Member, Zarepour, Mohammad Saleh, Editorial Board Member, and Usberti, Gabriele

Published
2023
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10. -Justifications for Logically Complex Sentences

Author

Usberti, Gabriele, Rahman, Shahid, Series Editor, Clerbout, Nicolas, Managing Editor, Symons, John, Founding Editor, van Bendegem, Jean Paul, Editorial Board Member, Benis Sinaceur, Hourya, Editorial Board Member, van Benthem, Johan, Editorial Board Member, Chemla, Karine, Editorial Board Member, Dubucs, Jacques, Editorial Board Member, Fagot-Largeault, Anne, Editorial Board Member, Van Fraassen, Bas C, Editorial Board Member, Gabbay, Dov M., Editorial Board Member, McNamara, Paul, Editorial Board Member, Priest, Graham, Editorial Board Member, Sandu, Gabriel, Editorial Board Member, Smets, Sonja, Editorial Board Member, Street, Tony, Editorial Board Member, Sundholm, Göran, Editorial Board Member, Wansing, Heinrich, Editorial Board Member, Williamson, Timothy, Editorial Board Member, Zarepour, Mohammad Saleh, Editorial Board Member, and Usberti, Gabriele

Published
2023
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11. Varieties of Semantical Anti-realism

Author

Usberti, Gabriele, Rahman, Shahid, Series Editor, Clerbout, Nicolas, Managing Editor, Symons, John, Founding Editor, van Bendegem, Jean Paul, Editorial Board Member, Benis Sinaceur, Hourya, Editorial Board Member, van Benthem, Johan, Editorial Board Member, Chemla, Karine, Editorial Board Member, Dubucs, Jacques, Editorial Board Member, Fagot-Largeault, Anne, Editorial Board Member, Van Fraassen, Bas C, Editorial Board Member, Gabbay, Dov M., Editorial Board Member, McNamara, Paul, Editorial Board Member, Priest, Graham, Editorial Board Member, Sandu, Gabriel, Editorial Board Member, Smets, Sonja, Editorial Board Member, Street, Tony, Editorial Board Member, Sundholm, Göran, Editorial Board Member, Wansing, Heinrich, Editorial Board Member, Williamson, Timothy, Editorial Board Member, Zarepour, Mohammad Saleh, Editorial Board Member, and Usberti, Gabriele

Published
2023
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12. Logic Discovered and Logic Imposed (A Purim Story)

Author

Franks, Curtis, Shenker, Orly, Series Editor, Boneh, Nora, Series Editor, Lamm, Ehud, Editorial Board Member, Leicht, Reimund, Editorial Board Member, Harman, Oren, Editorial Board Member, Corry, Leo, Editorial Board Member, Hemmo, Meir, Editorial Board Member, Belkind, Ori, Editorial Board Member, Katzir, Shaul, Editorial Board Member, Hon, Giora, Editorial Board Member, Fisch, Menachem, Editorial Board Member, Ben-Menahem, Yemima, Editorial Board Member, Posy, Carl, Editorial Board Member, Levy, Arnon, Editorial Board Member, Shagrir, Oron, Editorial Board Member, Shavit, Ayelet, Editorial Board Member, Miller, Boaz, Editorial Board Member, Dolev, Yuval, Editorial Board Member, Chen-Morris, Raz, Editorial Board Member, Even-Ezra, Ayelet, Editorial Board Member, and Gissis, Snait, Editorial Board Member

Published
2023
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13. Platonism and the Proto-ontology of Mathematics: Learning from the Axiom of Choice

Author

Posy, Carl J., Shenker, Orly, Series Editor, Boneh, Nora, Series Editor, Lamm, Ehud, Editorial Board Member, Leicht, Reimund, Editorial Board Member, Harman, Oren, Editorial Board Member, Corry, Leo, Editorial Board Member, Hemmo, Meir, Editorial Board Member, Belkind, Ori, Editorial Board Member, Katzir, Shaul, Editorial Board Member, Hon, Giora, Editorial Board Member, Fisch, Menachem, Editorial Board Member, Ben-Menahem, Yemima, Editorial Board Member, Posy, Carl, Editorial Board Member, Levy, Arnon, Editorial Board Member, Shagrir, Oron, Editorial Board Member, Shavit, Ayelet, Editorial Board Member, Miller, Boaz, Editorial Board Member, Dolev, Yuval, Editorial Board Member, Chen-Morris, Raz, Editorial Board Member, Even-Ezra, Ayelet, Editorial Board Member, and Gissis, Snait, Editorial Board Member

Published
2023
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14. Axioms and Intuitions

Author

Patras, Frédéric, Bueno, Otávio, Editor-in-Chief, Brogaard, Berit, Editorial Board Member, French, Steven, Editorial Board Member, Dutilh Novaes, Catarina, Editorial Board Member, Rowbottom, Darrell P., Editorial Board Member, Ruttkamp, Emma, Editorial Board Member, Miller, Kristie, Editorial Board Member, and Patras, Frédéric

Published
2023
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15. Tri-simplicial Contradiction: The 'Pascalian 3D Simplex' for the Oppositional Tri-segment

Author

Moretti, Alessio, Andréka, Hajnal, Editorial Board Member, Beziau, Jean-Yves, Series Editor, Burgin, Mark, Editorial Board Member, Diaconescu, Răzvan, Editorial Board Member, Herzig, Andreas, Editorial Board Member, Koslow, Arnold, Editorial Board Member, Lee, Jui-Lin, Editorial Board Member, Maksimova, Larissa, Editorial Board Member, Malinowski, Grzegorz, Editorial Board Member, Paoli, Francesco, Editorial Board Member, Sarenac, Darko, Editorial Board Member, Schröder-Heister, Peter, Editorial Board Member, Vasyukov, Vladimir, Editorial Board Member, Zamansky, Anna, Editorial Board Member, Giovagnoli, Raffaela, Editorial Board Member, and Vandoulakis, Ioannis, editor

Published
2022
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16. Two Convergences to Dynamic Formalism: Bakhtin’s Dialogism and Brouwer’s Creating Subject

Author

Chakraborty, Ravi, Lion, Clément, Rahman, Shahid, Series Editor, Redmond, Juan, Managing Editor, van Eemeren, Frans H., Editorial Board Member, McConaughey, Zoe, Editorial Board Member, Street, Tony, Editorial Board Member, Woods, John, Editorial Board Member, Galvez-Behar, Gabriel, Editorial Board Member, Gazziero, Leone, Editorial Board Member, Laks, André, Editorial Board Member, Webb, Ruth, Editorial Board Member, Dubucs, Jacques, Editorial Board Member, Chemla, Karine, Editorial Board Member, Hansson, Sven Ove, Editorial Board Member, Coello, Yann, Editorial Board Member, Prakken, Henry, Editorial Board Member, Recanati, François, Editorial Board Member, Heinzmann, Gerhard, Editorial Board Member, Smets, Sonja, Editorial Board Member, Sundholm, Göran, Editorial Board Member, Benis-Sinaceur, Hourya, Editorial Board Member, Gabbay, Dov, Editorial Board Member, Tulenheimo, Tero, Editorial Board Member, Contamin, Jean-Gabriel, Editorial Board Member, Fischer, Franck, Editorial Board Member, Ober, Josh, Editorial Board Member, Pichard, Marc, Editorial Board Member, Crubellier, Michel, Editorial Board Member, Gregoire, Eric, Editorial Board Member, and Lopez-Soto, Teresa, editor

Published
2021
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17. In Defense of Unilateralism

Author

Santos, Gonçalo, Rahman, Shahid, Series Editor, Redmond, Juan, Managing Editor, van Eemeren, Frans H., Editorial Board Member, McConaughey, Zoe, Editorial Board Member, Street, Tony, Editorial Board Member, Woods, John, Editorial Board Member, Galvez-Behar, Gabriel, Editorial Board Member, Gazziero, Leone, Editorial Board Member, Laks, André, Editorial Board Member, Webb, Ruth, Editorial Board Member, Dubucs, Jacques, Editorial Board Member, Chemla, Karine, Editorial Board Member, Hansson, Sven Ove, Editorial Board Member, Coello, Yann, Editorial Board Member, Prakken, Henry, Editorial Board Member, Recanati, François, Editorial Board Member, Heinzmann, Gerhard, Editorial Board Member, Smets, Sonja, Editorial Board Member, Sundholm, Göran, Editorial Board Member, Benis-Sinaceur, Hourya, Editorial Board Member, Gabbay, Dov, Editorial Board Member, Tulenheimo, Tero, Editorial Board Member, Contamin, Jean-Gabriel, Editorial Board Member, Fischer, Franck, Editorial Board Member, Ober, Josh, Editorial Board Member, Pichard, Marc, Editorial Board Member, Crubellier, Michel, Editorial Board Member, Gregoire, Eric, Editorial Board Member, and Lopez-Soto, Teresa, editor

Published
2021
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21. Weyl and Intuitionistic Infinitesimals

Author

van Atten, Mark, French, Steven, Advisory Editor, Rasmussen, Nicholas, Advisory Editor, Schuster, John, Advisory Editor, Yeo, Richard, Advisory Editor, Gaukroger, Stephen, Advisory Editor, Ankeny, Rachel, Advisory Editor, Anstey, Peter, Advisory Editor, Montelle, Clemency, Advisory Editor, Gal, Ofer, Advisory Editor, Bernard, Julien, editor, and Lobo, Carlos, editor

Published
2019
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22. Mathematics as Intuition

Author

Ravn, Ole, Skovsmose, Ole, Ellerton, Nerida F., Series Editor, Clements, M.A. (Ken), Series Editor, Ravn, Ole, and Skovsmose, Ole

Published
2019
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23. Ontology of Logic and Mathematics in Lvov-Warsaw School

Author

Murawski, Roman, Andréka, Hajnal, Editorial board, Béziau, Jean-Yves, Series Editor, Burgin, Mark, Editorial board, Diaconescu, Razvan, Editorial board, Herzig, Andreas, Editorial board, Koslow, Arnold, Editorial board, Lee, Jui-Lin, Editorial board, Maksimova, Larisa, Editorial board, Malinowski, Grzegorz, Editorial board, Paoli, Francesco, Editorial Board Member, Sarenac, Darko, Editorial board, Schroeder-Heister, Peter, Editorial board, Vasyukov, Vladimir, Editorial board, Garrido, Ángel, editor, and Wybraniec-Skardowska, Urszula, editor

Published
2018
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27. Dependent Types for Pragmatics

Author

McAdams, Darryl, Sterling, Jonathan, Rahman, Shahid, Series editor, Symons, John, Series editor, Redmond, Juan, editor, Pombo Martins, Olga, editor, and Nepomuceno Fernández, Ángel, editor

Published
2016
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28. Perennial Intuitionism

Author

Granström, Johan G., Rahman, Shahid, Series editor, Symons, John, Series editor, Redmond, Juan, editor, Pombo Martins, Olga, editor, and Nepomuceno Fernández, Ángel, editor

Published
2016
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35. Degrees of Unsolvability: A Tutorial

Author

Simpson, Stephen G., Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Weikum, Gerhard, Series editor, Beckmann, Arnold, editor, Mitrana, Victor, editor, and Soskova, Mariya, editor

Published
2015
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36. Ramsey Theorem as an Intuitionistic Property of Well Founded Relations

Author

Berardi, Stefano, Steila, Silvia, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Kobsa, Alfred, editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Weikum, Gerhard, editor, and Dowek, Gilles, editor

Published
2014
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39. From Intuitionism to Many-Valued Logics Through Kripke Models

Author

Saeed Salehi

Subjects
Discrete mathematics, Intuitionism, Kripke models, Many-valued logic, Gödel, Propositional calculus, Mathematical proof, Symbol (formal), computer, Fuzzy logic, computer.programming_language, Mathematics
Abstract

Intuitionistic Propositional Logic is proved to be an infinitely many valued logic by Godel (Kurt Godel collected works (Volume I) Publications 1929–1936, Oxford University Press, pp 222–225, 1932), and it is proved by Jaśkowski (Actes du Congres International de Philosophie Scientifique, VI. Philosophie des Mathematiques, Actualites Scientifiques et Industrielles 393:58–61, 1936) to be a countably many valued logic. In this paper, we provide alternative proofs for these theorems by using models of Kripke (J Symbol Logic 24(1):1–14, 1959). Godel’s proof gave rise to an intermediate propositional logic (between intuitionistic and classical), that is known nowadays as Godel or the Godel-Dummett Logic, and is studied by fuzzy logicians as well. We also provide some results on the inter-definability of propositional connectives in this logic.

Published
2021
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40. Advanced Topics in Logic

Author

Gerard O’Regan

Subjects
Automated theorem proving, TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES, Intuitionism, Computer science, Law of excluded middle, Classical logic, Calculus, Temporal logic, Intuitionistic logic, Fuzzy logic, Logic programming, Hardware_LOGICDESIGN
Abstract

We consider some advanced topics in logic including fuzzy logic, temporal logic, intuitionist logic, undefined values in logic, logic and AI and theorem provers. Fuzzy logic is an extension of classical logic that acts as a mathematical model for vagueness. Temporal logic is concerned with the expression of properties that have time dependencies. Brouwer and others developed intuitionist logic as the logical foundation for intuitionism, which was a controversial theory of the foundations of mathematics based on a rejection of the law of the excluded middle and an insistence on constructive existence. We discuss several approaches that have been applied to dealing with undefined values that arise with partial functions including the logic of partial functions; Dijkstra’s approach with his cand and cor operators; and Parnas’s approach which preserves a classical two-valued logic.

Published
2021
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42. Moral Frames and Coronavirus

Author

Jonathan Charteris-Black

Subjects
Framing (social sciences), Dishonesty, Intuitionism, Metaphor, Honesty, media_common.quotation_subject, Face (sociological concept), Social intuitionism, Psychology, Rational planning model, media_common, Epistemology
Abstract

This book examines the metaphors and allegories of the Coronavirus pandemic and shows how they provide a better understanding of the moral framing of our decisions. Haidt’s social intuitionist model employs a metaphor: the elephant and the rider. The ‘rider’ is a metaphor for the rational mind in which control derives from language-based reasoning and the ‘elephant’ is a metaphor for the emotions and the intuitions that accompany such reasoning. When people face a moral dilemma, Haidt claims, they rely more on the elephant than on the rider, and decisions are based on an emotionally motivated moral intuition. In this book I argue that that during times of pandemic the role of the rational mind, the rider, should be restored intoa position of control over the elephant of emotional intuition and that to assist with rational decision making a moral frame of Honesty and Dishonesty needs to be established.

Published
2021
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43. Seneca’s Argumentation and Moral Intuitionism

Author

David Merry

Subjects
Argument, Intuitionism, Philosophy, Form of the Good, Epistemology, Argumentation theory
Abstract

Walter Sinnott-Armstrong argues that moral disagreement and widespread moral bias pose a serious problem for moral intuitionism. Seneca’s view that we just recognise the good could be criticised using a similar argument. His approach to argumentation offers a way out, one that may serve as a model for a revisionary intuitionism.

Published
2021
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44. Mathematics and Modernism

Author

Nina Engelhardt

Subjects
Literature, Formalism (philosophy), business.industry, Intuitionism, Poetics, Matrix (music), Modernism, business, Pound (mass)
Abstract

This chapter focuses on developments in nineteenth- and early twentieth-century mathematics, their reverberations in philosophy, and the interrelations with literary modernism and writers’ aims to “make it new”. Addressing changes in mathematics such as a developing non-representational understanding, sense of crisis, and split into the schools of formalism and intuitionism, the chapter locates these in the wider philosophical matrix of the time and examines mathematical imagery and poetics in modernist works such as by Ezra Pound, T. S. Eliot, Robert Musil, and Yevgeny Zamyatin.

Published
2020
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45. No Safe Sanctuary: Race, Space, and Time in Colson Whitehead’s Speculative Cities

Author

Anne-Marie Evans

Subjects
Race (biology), Politics, History, Spacetime, Aesthetics, Intuitionism, Underground Railroad, Space (commercial competition), Uncanny, Social activism
Abstract

This chapter explores representations of the city in three of Colson Whitehead’s novels—The Intuitionist (1999), Zone One (2011), and The Underground Railroad (2016)—and considers how Whitehead uses the construction of a speculative city space as a way of engaging with history and social activism. In each text, American cities are re-imagined as ‘new’ versions of the original, allowing Whitehead to rebuild and repurpose each urban literary space. The city is an uncanny and often unknowable space, from the imagined historical sites of The Underground Railroad, to the Gotham-like spaces of The Intuitionist, and the post-apocalyptic space of Manhattan in Zone One. Each of these spaces is fluid, flowing, and occasionally unnavigable. Whitehead positions these speculative urban sites as both in and outside time; they function as catalysts for his political polemic and are crucial components in Whitehead’s scathing social critique of contemporary American race relations.

Published
2020
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46. Zhu Xi’s Ethical Theory: Virtue Ethics Considerations and Kantian Parallels

Author

Kirill O. Thompson

Subjects
Virtue ethics, Emotivism, Intuitionism, Moral agency, media_common.quotation_subject, Pragmaticism, Utilitarianism, Sociology, Form of the Good, Duty, media_common, Epistemology
Abstract

Throughout his scholarly career, Zhu Xi 朱熹 (1130–1200) pondered the hallowed Confucian project of self-cultivation in quest of moral realization (see Chan 1976, 1987; Schirokauer 1976). On one level, his understanding of this Confucian project has much in common with modern virtue ethics, which is receiving attention in the scholarship; on another level, he made additional philosophical efforts to justify and ramify Confucian cultivation and moral realization. In making these efforts, Zhu Xi in effect sought to set forth the grounds of genuine moral agency, which in turn led to the formation of what I consider to be his distinctive ethical theory, one that bears parallels with that of Immanuel Kant (1724–1804) and highlights the salience of Zhu’s contribution to ethical theory. The expression “ethical theory” covers a range of accounts of ethics. In the early twentieth century, ethical theorists in the Anglo-American philosophical tradition examined the meaning and uses of the key terms in moral and ethical discourse, such as “goodness” or “the good,” “right and wrong,” “duty,” “responsibility,” etc. The main approaches they took included intuitionism, emotivism, and prescriptivism. Subsequently, ethical theorists have tried more systematic approaches, such as utilitarianism, pragmaticism, deonotologism, and even Marxism in their efforts to explain the enterprise of ethics. In recent decades, virtue ethics has been touted as a truer to life approach to understanding people’s practical moral reflection and conduct.

Published
2020
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47. The Enlightenment’s Legacy

Author

Dafydd Mills Daniel

Subjects
Individualism, Meaning (philosophy of language), Intuitionism, media_common.quotation_subject, Rationalism, Secularization, Enlightenment, Theology, Conscience, media_common, Cicero
Abstract

Part 1 explores criticisms of Enlightenment rationalism from Lord Shaftesbury’s and William Blake’s interpretations of Thomas Hobbes and John Locke, to modern representations of Immanuel Kant and Jeremy Bentham. Three secular effects of the Enlightenment are identified: naturalisation of reason; individualism; privatisation of value.Part 2 introduces the British Enlightenment ethical rationalism of Samuel Clarke, John Balguy, and Richard Price.First, the Bangorian controversy, and the analogy between mathematics and morals, are referenced to explain why Clarke’s ethical rationalism (CER) has been interpreted as part of the Enlightenment’s secular legacy.Second, it is suggested that CER is a resource for responding to Enlightenment secularisation, as well as leading Humean and neo-Kantian criticisms of rational intuitionism, if we appreciate its conception of conscience and recta ratio (right reason).The meaning of conscience and recta ratio is established via a range of figures, including: Cicero, Aquinas, Richard Hooker, Cambridge Platonists, Anglican casuists.

Published
2020
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48. Conscience, Normativity, and Rational Intuition

Author

Dafydd Mills Daniel

Subjects
Intuitionism, media_common.quotation_subject, Affection, Analogy, Normative, Enlightenment, Conscience, media_common, Epistemology, Intuition
Abstract

Part 1 explores David Hume’s and Francis Hutcheson’s criticisms of Clarkean ethical rationalism (CER). It also discusses modern criticisms of CER, and rational intuitionism more broadly, derived from Hutcheson and Hume, including: the fact/value distinction; moral ‘fetishism’; and, ‘queerness’Part 2 shows how CER can respond to Humean and Hutchesonian criticisms.Just as the Clarkeans have been associated with the secular legacy of Enlightenment rationalism, a thinned out conception of reason has been read back into CER.Factoring conscience and recta ratio (right reason) into CER contextualises the analogy between mathematics and morals, highlighting the distinction between ‘original obligations’ and ‘additional motivations’, and ‘tripartite’ conception of moral duty.In CER, the phrase ‘right in itself’ means ‘according to reason’ where reason is the law of divine and human nature. Consequently, the apparently circular claim ‘do what is right because it is right’ includes a normative role for God’s will and human affection.

Published
2020
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49. Understanding Unethical Decision-Making in Organizations and Proposals for Its Avoidance: The Contribution of Neuroscience

Author

J. Félix Lozano, Ministerio de Economía y Competitividad (España), and Generalitat Valenciana

Subjects
ComputingMilieux_THECOMPUTINGPROFESSION, Intuitionism, Rationalism, Ethical decision-making, Neuroethics, Psychology, Neuroscience, Rationalism (international relations)
Abstract

The aim of this chapter is to propose strategies for improving ethical decision-making in organizations by taking into consideration the contributions of neuroethics research. Our hypothesis is that results from research in neuroscience and cognitive science offer new insight and perspectives on ethical decision-making in organizations. This chapter has three main parts. The first part is descriptive, and we present the main factors affecting unethical decision-making in organizations. Understanding why good people make or contribute to unethical decisions in organizations is a first step. In the second part, we discuss the contribution of neuroscience research to ethical decision-making. Finally, we propose strategies and actions that managers should take into account to develop a more consistent ethical decision-making model for individuals and organizations., This research is part of the Project FFI2016-76753-C2-1-P, financed by the Spanish Ministry for Science, Innovation and Universities; and is part of the Excelence Research Group PROMETEO/2018/121 by Generalitat Valenciana.

Published
2019
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50. Foundations of Mathematics: From Hilbert and Wittgenstein to the Categorical Unity of Science

Author

Yoshihiro Maruyama

Subjects
Philosophy of mathematics, Intuitionism, media_common.quotation_subject, Logicism, Certainty, Gödel's incompleteness theorems, Finitism, Foundations of mathematics, Epistemology, Unity of science, media_common
Abstract

Wittgenstein’s philosophy of mathematics is often devalued due to its peculiar features, especially its radical departure from any of standard positions in foundations of mathematics, such as logicism, intuitionism, and formalism. We first contrast Wittgenstein’s finitism with Hilbert’s finitism, arguing that Wittgenstein’s is perspicuous or surveyable finitism whereas Hilbert’s is transcendental finitism. We then further elucidate Wittgenstein’s philosophy by explicating his natural history view of logic and mathematics, which is tightly linked with the so-called rule-following problem and Kripkenstein’s paradox, yielding vital implications to the nature of mathematical understanding, and to the nature of the certainty and objectivity of mathematical truth. Since the incompleteness theorems, foundations of mathematics have mostly lost their philosophical driving force, and anti-foundationalism has become prevalent and pervasive. Yet new foundations have nevertheless emerged and come into the scene, namely categorical foundations. We articulate the foundational significance of category theory by explicating three forms of foundations, i.e., global foundations (aka. reductive absolute foundations), local foundations (aka. structural relative foundations), and conceptual foundations. And we explore the possibility of categorical unified science qua pluralistic unified science, arguing for the categorical unity of science on both mathematical and philosophical grounds. We then turn to an issue in conceptual foundations of mathematics, namely the nature of the concept of space. We elucidate Wittgenstein’s intensional conception of space in relation to Brouwer’s theory of space continua and to the modern conception of space as point-free structure in category theory and algebraic geometry. We finally give a bird’s-eye view of mathematical philosophy from a Wittgensteinian perspective, and further sheds new light on Wittgenstein’s constructive structuralism and his view of incompleteness and contradictions in mathematics.

Published
2019
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