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The history of ethics often presupposes rationalist thinking on moral issues. An alternative to rationalism has been proposed by the social intuitionist model. This model suggests the bulk of our moral decisions are ‘gut reactions’ or intuitions. Unlike the rationalists, which support reasons and deliberation to draw moral conclusions, intuitionists argue such reasoning is used to support preconceived ethical decisions. This paper provides the first investigation to determine if intuitionism has any validity within business ethics. Using data from the Defining Issues Test and individual journal entries, results indicate discussion-based pedagogy improved the moral reasoning of participants but had very little influence over their beliefs. In short, the social intuitionist model is supported by this study. Most importantly, ethics education that focuses on peer-to-peer discussion can change how students’ reason about moral problems and should be heavily incorporated into classrooms.

Resumen El actual sistema mundo ha presenciado diversos escenarios de confrontación desde los grupos subalternos que representan diversos modelos ideológicos frente a acciones generadas desde los centros de poder político estatal. Este artículo de reflexión busca analizar, desde una perspectiva psicopolítica, cuáles son los condicionamientos que se han impulsado, particularmente en Nuestra América, en las movilizaciones sociales contra diversas proyecciones políticas, independientes de su valoración ideológica. Se toma en cuenta el modelo del intuicionismo bergsoniano, recurriendo como criterio de análisis a los puntos convergentes que se han generado en los escenarios de protestas de la región. Se concluye que es necesario buscar alternativas para comprender los procesos de movilización y protesta social desde una perspectiva psicopolítica, así como la necesidad de reinterpretar los usos del poder en torno a estos fenómenos sociales en Nuestra América. Abstract The current world system has witnessed different confrontation scenarios from the subaltern groups, that represent various ideological models, facing the actions generated from the center of State political power. This reflection article tries to analyze, from a psycho-political approach, what are the conditioners that have propelled, particularly in the region of Our America, the social mobilization against diverse political range, independent of his ideological assessment. It takes into account the model of the Bergsonian intuitionism, resorting to the convergent points that have been generated in the scenes of protests in the region as a criterion of analysis. It concludes that it is necessary to look for alternatives in order to understand the processes of social mobilization and outburst from a psycho-political perspective, as well as the need to reinterpret the uses of power around these social phenomena in Our America.

In this paper, I present theoretical assumptions behind Teoria/Literatura, a multifaceted digital research and publishing project on 20th-century Polish literary thought. The point of departure is the conjecture that the tensions between the digital and the humanistic in present-day DH help bring out in full relief the cardinal conflict line in Polish literary theory – between formalism/structuralism on the one hand and phenomenology on the other. Conversely, the order of concepts in the corpus of Polish literary theory enables the researcher to pinpoint the relation of the humanistic and the digital (or formalist) within DH so that it might be challenged and/or upgraded. In the first section, I provide an overview of the project's strata and its wide-ranging goal, i.e., a corpus of Polish literary theory. In section two, I examine the way in which the structure of the corpus can help elucidate the general problem of the relation between the digital and the humanistic in DH. Specifically, I relate this issue to the quarrel in constructive mathematics between mathematical intuitionism and formalism. The third section is devoted to a synecdochal representation of the general problem of the duality of intuitionism and formalism – the visualisation of narrative temporality.

The classical interpretation of mathematical statements can be seen as comprising two separate but related aspects: a domain and a truth-schema. L. E. J. Brouwer’s intuitionistic project lays the groundwork for an alternative conception of the objects in this domain, as well as an accompanying intuitionistic truth-schema. Drawing on the work of Arend Heyting and Michael Dummett, I present two objections to classical mathematical semantics, with the aim of creating an opening for an alternative interpretation. With this accomplished, I then make the case for intuitionism as a suitable candidate to fill this void.

In 1928 Ivan Orlov published a remarkable paper which contains the first formulation of a relevant logic. The paper remained largely unknown to English-speakers until this discovery of relevant log...

I present a systematic interpretation of the foundational purpose of constructions in ancient Greek geometry. I argue that Greek geometers were committed to an operationalist foundational program, according to which all of mathematics—including its entire ontology and epistemology—is based entirely on concrete physical constructions. On this reading, key foundational aspects of Greek geometry are analogous to core tenets of 20th-century operationalist/positivist/constructivist/intuitionist philosophy of science and mathematics. Operationalism provides coherent answers to a range of traditional philosophical problems regarding classical mathematics, such as the epistemic warrant and generality of diagrammatic reasoning, superposition, and the relation between constructivism and proof by contradiction. Alleged logical flaws in Euclid (implicit diagrammatic reasoning, superposition) can be interpreted as sound operationalist reasoning. Operationalism also provides a compelling philosophical motivation for the otherwise inexplicable Greek obsession with cube duplication, angle trisection, and circle quadrature. Operationalism makes coherent sense of numerous specific choices made in this tradition, and suggests new interpretations of several solutions to these problems. In particular, I argue that: Archytas’s cube duplication was originally a single-motion machine; Diocles’s cissoid was originally traced by a linkage device; Greek conic section theory was thoroughly constructive, based on the conic compass; in a few cases, string-based constructions of conic sections were used instead; pointwise constructions of curves were rejected in foundational contexts by Greek mathematicians, with good reason. Operationalism enables us to view the classical geometrical tradition as a more unified and philosophically aware enterprise than has hitherto been recognised.

We investigate which part of Brouwer’s Intuitionistic Mathematics is finitistically justifiable or guaranteed in Hilbert’s Finitism, in the same way as similar investigations on Classical Mathematics (i.e., which part is equiconsistent with $\textbf {PRA}$ or consistent provably in $\textbf {PRA}$ ) already done quite extensively in proof theory and reverse mathematics. While we already knew a contrast from the classical situation concerning the continuity principle, more contrasts turn out: we show that several principles are finitistically justifiable or guaranteed which are classically not. Among them are: (i) fan theorem for decidable fans but arbitrary bars; (ii) continuity principle and the axiom of choice both for arbitrary formulae; and (iii) $\Sigma _2$ induction and dependent choice. We also show that Markov’s principle MP does not change this situation; that neither does lesser limited principle of omniscience LLPO (except the choice along functions); but that limited principle of omniscience LPO makes the situation completely classical.

We try to translate the intuitionistic propositional logic INT into Brouwer's modal logic KTB. Our translation is motivated by intuitions behind Brouwer's axiom p →☐◊p The main idea is to interpret intuitionistic implication as modal strict implication, whereas variables and other positive sentences remain as they are. The proposed translation preserves fragments of the Rieger-Nishimura lattice which is the Lindenbaum algebra of monadic formulas in INT. Unfortunately, INT is not embedded by this mapping into KTB.

EnglishThe contribution pursues two interrelated aims: the first one is to interpret the transition from Morality to Ethical Life in the Elements of the Philosophy of Right as a theory of moral justification; the second one is to show the meaning of this theory for contemporary philosophy. The essay thus seeks to turn to Hegel’s conception in order to shed light on the limits of the current discussion in moral epistemology and then to present a possible alternative. To this end, Hegel’s text is confronted with the main theses of intuitionism, on the one hand, and Kantian constructivism, on the other, as the most prominent contemporary forms, respectively, of ethical foundationalism and coherentism. portuguesO artigo tem dois objetivos mutuamente interligados: o primeiro e interpretar a transicao da moralidade para a etica nas Linhas fundamentais da filosofia do direito como uma teoria da justificacao moral; o segundo e mostrar o significado dessa teoria para a filosofia contemporânea. Dessa forma, o artigo procura retomar a reflexao hegeliana para lancar luz sobre alguns limites do debate contemporâneo acerca da epistemologia moral e, a seguir, apresentar uma possivel alternativa. Para tanto, o texto hegeliano e posto em dialogo com as teses centrais do intuicionismo, de um lado, e do construtivismo kantiano, de outro, na medida em que representam as formas contemporâneas que tem mais autoridade, respectivamente, a do fundacionalismo e a do coerentismo etico.

espanolEl presente texto trata de la teoria de Charles Larmore, mas precisamente, de las relaciones entre las concepciones de desacuerdo razonable, de pluralismo y de liberalismo. Tal teoria tiene como caracteristicas el intuicionismo racional, contextualismo y defiende una posicion realista de la moralidad. EnglishThe present text deals with Charles Larmore’s theory, more precisely, of the relations between the conceptions of reasonable disagreement, pluralism and liberalism. Such a theory has as its characteristics rational intuitionism, contextualism and defends a realistic position of morality.

Spinoza’s epistemology is complex, with both a rationalist and an intuitionist side. The key to understanding Spinoza’s epistemology is to focus on the notion of intuitive knowledge (scientia intui...

In this essay we consider the moral claims of one branch of non-realist theory known as linguistic narrativism theory. By highlighting the moral implications of linguistic narrativism theory, we argue that the “moral vision” expressed by this theory can entail, at worst, undesirable moral agnosticism if not related to a transcendental and supra-personal normativity in our moral life. With its appeal to volitionism and intuitionism, the ethical sensitivity of this theory enters into difficulties brought about by several internal tensions as to what morality and moral judgements involve. We contend that the proponents of linguistic narrativism theory must strongly recognize and take responsibility for the “moral vison” their theory professes, in so far as they want to think of their theory as a morally responsible one.

The debate between Einstein and Bergson is a salient episode in the history of modern physics and a telling example of the interaction between science and philosophy. This paper initially discusses five reasons why Bergson criticised Einstein for giving up absolute time. The most important one was Bergson’s commitment to an intuitionist, anti-Kantian metaphysics informed by common sense. Apart from that, he knew that the theory of special relativity permits “duration” (durée) in the form of the passage of proper time, to which Bergson referred as “real time”. Neither static eternalism (which excludes temporal passage) nor dynamic eternalism (which, like the former, claims the existence of the future) are acceptable from Bergson’s philosophical perspective, which acknowledges the role of temporal experience and everyday thinking in addition to science and metaphysics. He understood temporal passage as creation of new existence, anticipating what later became known as the growing block theory of time. The pointy relativistic variant of this theory, which divides the universe into blocks of growing past light cones, does justice to large parts of his philosophy, including the distinction between the actual and the virtual. Supporters of Bergson’s account of duration should adopt this theory of time.

In this article, after clarifying aspects of the claim to objectivity in the common moral judgments and general aspects of moral epistemology, I present and analyze the possibility of the existence and attainment of true moral beliefs, firstly, in skeptical positions contrary to this, as in the nihilistic perspective of error theory and in the subjectivist perspective of relativistic theories (social and individual), then, secondly, I present and analyze the traditional concept of moral knowledge in two favorable realist positions, the naturalist realism and the non-naturalist realism or intuitionism. A perspective normally considered contrary to obtaining true moral beliefs is the expressivist one, but I suggest and outline here how it, or at least some of its more sophisticated versions, can be epistemically friendly in the search for moral knowledge, in a more weak meaning of the concept.

The aim of this paper is to establish a phenomenological mathematical intuitionism that is based on fundamental phenomenological-epistemological principles. According to this intuitionism, mathematical intuitions are sui generis mental states, namely experiences that exhibit a distinctive phenomenal character. The focus is on two questions: what does it mean to undergo a mathematical intuition and what role do mathematical intuitions play in mathematical reasoning? While I crucially draw on Husserlian principles and adopt ideas we find in phenomenologically minded mathematicians such as Hermann Weyl and Kurt Gödel, the overall objective is systematic in nature: to offer a plausible approach towards mathematics.

Fil: Lassalle Casanave, Abel. Universidade Federal da Bahia; Brasil. Fil: Lassalle Casanave, Abel. Conselho Nacional de Desenvolvimento Científico e Tecnológico; Brasil. Fil: Pereira, Luiz Carlos. Pontifícia Universidade Católica do Rio de Janeiro; Brasil. Fil: Pereira, Luiz Carlos. Universidade do Estado do Rio de Janeiro; Brasil. Fil: Pereira, Luiz Carlos. Conselho Nacional de Desenvolvimento Científico e Tecnológico; Brasil. Lassalle Casanave, A. y Pereira, L. C. (2020). A propósito del formalismo de Johann von Neumann. Metatheoria, 10(2), 51-59. En 1930, Johann von Neumann, junto con Rudolf Carnap y Arend Heyting, participó de un evento realizado en Königsberg llamado “Segundo Seminario sobre Epistemología de las Ciencias Exactas”. La idea por detrás de la reunión de esos tres investigadores era presentar un cuadro suficientemente fiel de los tres programas de fundamentación de la matemática existentes al momento: el formalismo, el logicismo y el intuicionismo. El principal objetivo de este artículo es proponer un análisis del texto “La fundamentación formalista de la matemática” presentado por von Neumann en el mencionado seminario. Tratamos de mostrar como desde la perspectiva de von Neumann el problema de la consistencia de las teorías matemáticas es resultado de la transformación de una cuestión genuinamente filosófica en una genuina cuestión lógico-matemática y como una prueba de consistencia podía ser vista como la solución del problema fundacional. En la parte final del texto, presentamos algunas consideraciones acerca de las pruebas de consistencia de Gerhard Gentzen y su importancia para la teoría contemporánea de la demostración. In 1930, Johann von Neumann, together with Rudolf Carnap and Arend Heyting, participated in a conference held in Königsberg, called “Second Seminar on the Epistemology of Exact Sciences”. The idea behind the reunion of these three researchers was to compose a fairly faithful picture of the three main foundational programs of mathematics at the time: formalism, logicism, and intuitionism. The main objective of this paper is to propose an analysis of the text “The Formalist Foundation of Mathematics” presented by von Neumann in this conferenc e. We show how, from von Neumann's perspective, the problem of the consistency of mathematical theories results from the transformation of a genuinely philosophical question into a genuinely logical-mathematical question and how a proof of consistency could be seen as the solution to the foundational problem. In the final part of the text, we present some considerations about Gerhard Gentzen’s consistency proofs and their importance to contemporary proof theory.

Reflective equilibrium (RE) has been criticized for various reasons ever since the publication of Rawls’A Theory of Justice. Recent empirical research into moral decision-making poses new challenges to RE because it questions the reliability of moral intuitions. This research might discredit moral intuitionism in general and RE in particular insofar as it ascribes epistemic value to moral intuitions. These findings suggest, for instance, that moral intuitions vary with cultural background, gender or framing. If it could be shown that all or certain kinds of moral intuitions are unreliable, this would diminish the plausibility of the claim that they provide good reasons to believe in the truth of their content, especially given the growing evidence that professional philosophers are just as biased and susceptible to distorting factors as lay people. In this paper I critically discuss three recent defenses of RE against this unreliable intuitions objection (UIO). Two of these defenses argue that the UIO misses its target, because RE does not depend on intuitions, or because the relevant considered judgments in RE are not intuitions. The third defense grants that RE depends on intuitions and that some Rawlsian considered judgments are intuitions. But it argues that the notion of considered judgments can be revised, and that wide reflective equilibrium (WRE) has the means to adopt the criticism because it can use information about unreliable intuitions and exclude those from further consideration. I argue that the first two defenses do not succeed. The third defense is the most promising one. However, I argue that this defense also fails. In this defense, RE is not a distinctive moral epistemic theory: different versions of RE would be conceivable, all of which are deeply problematic. I conclude with a discussion of the broader philosophical implications of the UIO, specifically whether or not accepting the UIO would warrant skepticism regarding moral knowledge.

Em meio a uma disputa de fundamentos filosóficos que dura mais de uma centena de anos, a fundamentação intuicionista da matemática parece cada vez mais próxima de ser uma alternativa à fundamentação clássica. Interpretação de noções fundamentais e primitivas e consequências para a interpretação dos conectivos lógicos são algumas das questões a serem tratadas neste texto, em uma estrutura que pretende mostrar o papel fundamental e primitivo da noção de construção mental no Intuicionismo, desde a proposta de Brouwer até a Teoria Intuicionista dos Tipo de Martin-Löf. A discussão dos aspectos particulares da proposta de Martin-Löf não nos permite perder de vista que ela se trata essencialmente de um sistema formal, universal, porém, aberto, mas também uma linguagem para a prática da matemática intuicionista. Essas e outras características próprias do intuicionismo formal de Martin-Löf precisaram ir além das elucidações e conceitos do intuicionismo original de Brouwer, até então, considerado como mais especulativo e pouco viável do ponto de vista prático. Justamente, o aprofundamento conceitual do sistema de Martin-Löf trouxe luz ao intuicionismo e fazem dele único e tão importante, não apenas para a matemática, mas também para a lógica, filosofia e, até mesmo, para a computação. Com uma adequada compreensão da Teoria Intuicionista dos Tipos, especialmente a partir da interpretação intuicionista fundamental de provas como construções mentais, temos uma medida mais exata de o que se trata o intuicionismo e suas principais consequências. Algumas delas tratadas neste trabalho são a recusa do princípio do terceiro excluído, a interpretação de noções como “existência”, “construção”, “proposição” e “asserção”, além do caráter construtivo compulsório para provas matemáticas formais. Em se tratando especificamente do sistema de Martin-Löf, discutimos ainda as ideias de “verdade” e “bivalência das proposições”, “domínios primitivos” e “domínios proposicionais”, imprescindíveis para o sistema e distintas das concepções clássicas, apesar da coincidência terminológica. In the midst of a dispute over philosophical foundations that has lasted for over a hundred years, the intuitionistic foundations of mathematics seems ever closer to being an alternative to classical foundation. Interpretation of fundamental and primitive notions and consequences for the interpretation of logical connectives are some of the issues to be addressed in this text, in a framework that intends to show the fundamental and primitive role of the notion of mental construction in Intuitionism, from Brouwer's proposal to Martin-Löf's Intuitionistic Type Theory. The discussion of particular aspects of the Martin-Löf’s proposal does not allow us to lose sight of the fact that it is essentially a formal system, universal, however, open, but also a language for the practice of intuitionist mathematics. These and other characteristics of Martin-Löf’s formal intuitionism needed to go beyond the definitions and concepts of Brouwer's original intuitionism, until then, considered as more speculative and impractical from a practical point of view. Precisely, the conceptual deepening of the Martin-Löf’s system brought light to intuitionism and make it unique and so important, not only for mathematics, but also for logic, philosophy and even for computation. With an adequate understanding of the Intuitionistic Type Theory, especially from the fundamental intuitionist interpretation of proofs as mental constructions, we have a more accurate measure of what intuitionism is about and its main consequences. Some of them dealt with in this work are the refusal of the law of excluded middle, the interpretation of notions such as “existence”, “construction”, “proposition” and “assertion”, in addition to the compulsory constructive character for formal mathematical proofs. In the specific case of the Martin-Löf’s system, we also discuss the ideas of truth and bivalence of propositions, primitive domains and propositional domains, essential for the system and distinct from classical conceptions, despite the terminological coincidence. Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES Fundação de Amparo à Pesquisa do Estado de Goiás

Knjiga nastoji ponuditi doprinos razumijevanju i tumačenju Brouwerove šire filozofije, tj. njegove “teorije izlaska svijesti”. Donosimo najprije pojmovnu rekonstrukciju te filozofije, istražujući i neke termine koji su ostali bez mnogo analize u sekundarnoj literaturi. Potom iznosimo i logičku rekonstrukciju temeljnih dijelova Brouwerove teorije, predloživši aksiomatske sustave i modele dviju logika izlaska svijesti.

We provide a framework for understanding agnosticism. The framework accounts for the varieties of agnosticism while vindicating the unity of the phenomenon. This combination of unity and plurality is achieved by taking the varieties of agnosticism to be represented by several agnostic stances, all of which share a common core provided by what we call the minimal agnostic attitude. We illustrate the fruitfulness of the framework by showing how it can be applied to several philosophical debates. In particular, several philosophical positions can be aptly conceived of as instances of agnosticism whilst retaining their differences and distinguishing features.

Time-progressing expressions, i.e., expressions that compute to different values over time such as Brouwerian choice sequences or reference cells, are a common feature in many frameworks. For type theories to support such elements, they usually employ sheaf models. In this paper, we provide a general framework in the form of an extensional type theory incorporating various time-progressing elements along with a general possible-worlds forcing interpretation parameterized by modalities. The modalities can, in turn, be instantiated with topological spaces of bars, leading to a general sheaf model. This parameterized construction allows us to capture a distinction between theories that are "agnostic", i.e., compatible with classical reasoning in the sense that classical axioms can be validated, and those that are "intuitionistic", i.e., incompatible with classical reasoning in the sense that classical axioms can be proven false. This distinction is made via properties of the modalities selected to model the theory and consequently via the space of bars instantiating the modalities. We further identify a class of time-progressing elements that allows deriving "intuitionistic" theories that include not only choice sequences but also simpler operators, namely reference cells., LIPIcs, Vol. 228, 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022), pages 10:1-10:23