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In this article, we will consider the application of intuitionistic tense logics to construct logical systems in which the thesis of logical determinism cannot be expressed.

The interests of the Chilean engineer and philosopher Manuel Atria Ramírez cover a variety of subjects and disciplines, but most of his published work focuses on philosophy of mathematics and physics. After a first phase of youth, of evident Thomistic inclination, his mature thought shows the influence of the great epistemological schools that thrive during the first half of the 20th century. Beyond illustrating the reception that was given in those years in the Latin American academic scene to the new European philosophical tendencies, we think that the concise expository style of the author and his deep understanding of mathematical physics and its history, have the merit to pose with freshness and originality the question referring to the ultimate foundation of mathematics, and its connection with reality. In this article we present and analyze the fundamental lines of Professor Atria`s philosophy of mathematics and physics, as well as those questions open for further research.

The article is devoted to selected new trends in metaethics, ethics, political philosophy, and the practice of philosophy with the use of artificial intelligence. It consists of five parts. In the first part, I analyze the meaning of the question about new trends in analytical philosophy. In the second part, I present the latest trends in metaethics. In the third part, I briefly characterize the ethics of artificial intelligence. The fourth part, devoted to political philosophy, includes a presentation of the latest publications on meritocracy. The article concludes with considerations about practising philosophy in the age of artificial intelligence

When it comes to the relation of modern mathematics and philosophy, most people tend to think of the three major schools of thought—i.e. logicism, formalism, and intuitionism—that emerged as profound researches on the foundations and nature of mathematics in the beginning of the 20th century and have shaped the dominant discourse of an autonomous discipline of analytic philosophy, generally known under the rubric of “philosophy of mathematics” since then. What has been completely disregarded by these philosophical attitudes, these foundational researches which seek to provide pure mathematics with a philosophically plausible justification by founding it on firm logico-philosophical bases, is that the genuine self-foundation of pure mathematics had been done before, namely during the 19th century, when it was developing into an entirely new and independent discipline as a concomitant of the continuous dissociation of mathematics from the physical world. This self-foundation of the 19th-century pure mathematics, however, was more akin to the German-idealist interpretations of Kant’s transcendental philosophy, than the post-factum, retrospective 20th-century researches on the foundations of mathematics. This article aims to demonstrate this neglected historical fact via delving into the philosophical inclinations of the three major founders of the 19th-century pure mathematics, Riemann, Dedekind and Cantor. Consequently, pure mathematics, with respect to its idealist origins, proves to be a formalization and idealization of certain activities specific to a self-conscious transcendental subjectivity.

The foundations of mathematics cover mathematical as well as philosophical problems. At the turn of the 20th century logicism, formalism and intuitionism, main foundational schools were developed. A natural problem arose, namely of how much the foundations of mathematics influence the real practice of mathematicians. Although mathematics was and still is declared to be independent of philosophy, various foundational controversies concerned some mathematical axioms, e.g. the axiom of choice, or methods of proof (particularly, non-constructive ones) and sometimes qualified them as admissible (or not) in mathematical practice, relatively to their philosophical (and foundational) content. Polish Mathematical School was established in the years 1915–1920. Its research program was outlined by Zygmunt Janiszewski (the Janiszewski program) and suggested that Polish mathematicians should concentrate on special branches of studies, including set theory, topology and mathematical logic. In this way, the foundations of mathematics became a legitimate part of mathematics. In particular, the foundational investigations should be conducted independently of philosophical assumptions and apply all mathematically accepted methods, finitary or not, and the same concerns other branches of mathematics. This scientific ideology contributed essentially to the remarkable development of logic, set theory and topology in Poland.

Bu makalenin konusunu 19. yüzyıl Britanya’sının en önemli entelektüel figürlerinden birisi olan William Whewell’in ahlaki gelişim ideali oluşturmaktadır. Whewell’e göre ahlak bir gelişim idealini ifade eder. Bu gelişim ideali, sonunda gerçek mutluluğun bulunduğu, insan yaşamı boyunca devam eden bir süreçtir. Çünkü yaşadığımız her an daha erdemli, daha iyi bir insan olma imkânımız vardır. Ona göre insanın en önemli görevi, bu gelişim idealini gerçekleştirmektir. Bu gelişim idealinin altında Whewell’in ahlak, bilim ve dini birbirleriyle uyumlu olacak şekilde rasyonel bir sistem içerisinde bir araya getirme motivasyonu yatar. Bu motivasyonun kaynağı ise o dönemde en önemli muhalifleri olan faydacı düşünürlerin özellikle de John Stuart Mill’in sezgici ahlaka yönelttiği gayri rasyonellik ve tutarsızlık eleştirileridir. Bu üç alanı birbirleriyle tutarlı hale getirmenin yolu olarak Whewell, tıpkı dinde olduğu gibi ahlak ve bilimi de teolojik bir temele dayandırmakta görür. Buna göre evrenin ve insanın yaratıcısı olan Tanrı, hem doğayı hem de insanların eylemlerini düzenleyecek belirli ilkeler vaz etmiştir. Burada ahlak ve bilime düşen görev bu ilkeleri keşfetmektir. Bu nedenle ahlak ve bilim temelde bir keşif sürecini ifade eder. Whewell, ahlakın temel ilkelerinin ancak sezgisel olarak bilinebileceğini savunur. Whewell’in sezgici ahlak geleneği içerisinde değerlendirilmesinin temel nedeni de bu kabulüdür. Fakat temel ilkelerin bu bilinme aşaması, herhangi bir şekilde gayri rasyonel bir süreci ifade etmez. Bu ilkeleri sezgisel olarak kavrayan temel yeti akıldır. Vicdan ise aklın yargılarını onaylayan bir yetidir. Ancak Whewell’in sisteminde vicdan, akıldan ayrı bir yeti olmaktan ziyade aklın bir yönüne tekabül eder. Böylelikle Whewell, vicdanı ahlakın temel ilkelerini kavrayan akıldan ayrı bir yeti olarak kabul eden sezgici ahlak düşünürlerinden ayrılır. Whewell’e göre vicdan insanın rehberidir fakat vicdanın yargıları zaman zaman yanılabilir. Bu nedenle de vicdanın sürekli olarak akıl tarafından kontrol edilip geliştirilmesi gerekir. İşte Whewell’in ahlaki gelişim idealini temellendirdiği nokta da burasıdır. Çünkü insana düşen görev, vicdanını sürekli olarak geliştirip tüm yargılarını en üstün kurala uygun hale getirmektir. İşte bu da ahlaki gelişime tekabül eder. Ahlaki gelişimde en yüksek iyi, ödev ve erdem kavramları son derece önemlidir. Whewell’in sisteminde en üstün kural ise Tanrı iradesini ifade eder. Tanrı’nın emirlerine itaat etme yükümlülüğü ödev, ödevi yerine getirmek ise erdeme karşılık gelir. Bu nedenle ödevin ihlali bir anlamda Tanrı’nın emrinin ihlalidir. Ödevi yerine getirmemek, Tanrı’nın iradesine karşı gelmektir. Dinî bağlamda ise bu, günaha tekabül eder. Fakat Whewell, ahlaki gelişim idealini aklın tek başına gerçekleştiremeyeceğini savunur. Bunun temel nedeni, aklın sınırlı yapısıdır. Bu nedenle akıl, bu süreçte vahyin yardımına ihtiyaç duyar. Fakat Whewell, sisteminin rasyonel zeminini muhafaza edebilmek için vahiy karşısında akla, vahyedilmiş din karşısında akla dayanan doğal dine öncelik verir. Ancak Whewell, yine de gelişim idealinin tamamlaması için vahyin yardımını zorunlu görür. Hatta öyle ki vahyin bu yardımını kabul etmeyen, vahye inanmayan kişilerin kınanması gerektiğini söyler. Çünkü ona göre bu gelişim ideali, aklın ulaşamayacağı ve ancak vahiy tarafından verilebilecek bilgilerle tamamlanabilecektir. Whewell, bu noktada o kadar ileri gider ki İsa Mesih’in yeryüzüne inişinden önce hiçbir insanın ahlaki tekamülünü tamamlayamadığını ileri sürer. Buna da gerekçe olarak vahyin o dönemlerde olmamasını gösterir. Whewell’in bu iddiasının kendi sisteminin rasyonelliğini etkileyip etkilemediği makalenin temel tartışma alanını oluşturmaktadır. Kanaatimizce Whewell’in vahyin yardımı olmaksızın ahlaki gelişim idealinin tamamlanamayacağı şeklindeki yaklaşımı, ahlak teorisinin rasyonel zeminini tamamen ortadan kaldırmasa bile ciddi biçimde tartışmalı hale getirmektedir.

We continue the investigation of the first paper where we studied logics with various negations including empirical negation and co-negation. We established how such logics can be treated uniformly with R. Sylvan's CCω as the basis. In this paper we use this result to obtain cut-free labelled sequent calculi for the logics.

We investigate the relationship between M. De's empirical negation in Kripke and Beth Semantics. It turns out empirical negation, as well as co-negation, corresponds to different logics under different semantics. We then establish the relationship between logics related to these negations under unified syntax and semantics based on R. Sylvan's CCω.

Comparing Nietzsche’s moral psychology and the social intuitionist approach to moral judgment proposed by Jonathan Haidt, this paper reveals remarkable similarities between the two models. It also clarifies what implications Nietzsche drew from his description of human psychology and the perspective changes these entail for understanding ourselves as “moral beings”.

Recent developments in experimental research on decision-making have received attention from moral philosophers trying to explain classical moral dilemmas. The class of cognitive illusions known as framing effects have received particular attention because they appear to play a role in explaining the famous trolley-problem. Some philosophers maintain that cognitive illusions such as framing effects seriously undermine classical point of views in moral philosophy such as normative ethics and moral intuitionism. This essay investigates whether, in light of empirical research on framing effects, we can still maintain an intuitionist point of view, and what the available data imply in general for moral philosophy.

The conception of the paper is connected with bringing forward the reflection of Leon Petrażycki on intuitive law. For this purpose I analyze the genesis and dynamics of this phenomenon on the cultural-historical level, as well as with reference to issues belonging to the scope of positive law. In addition, I broaden the research field with the range of problems touching on intuitionism, morality, and also independent ethics of Janusz Kotarbinski. The starting point of the methodological optics I assume is constituted by the multi-aspectual transformations surrounding us in the sphere of axiology. Hence, if the pedagogical aspects are taken into account, it seems to me justified to undertake some actions in order to search for the logically consistent, sensible and universal solutions, which can become an ethical guide-post for the contemporary human being.

The paper focuses on cosmological ideas of a twentieth-century Russian philosopher Nikolay Lossky (1870-1965). It specifies the place of these ideas within the entire framework of his philosophical views, as well as in the context of his topology of philosophical systems, in particular ― the discrimination between organic and non-organic worldview. A historico-philosophical analysis of Lossky’s cosmology allows revealing the interaction of gnoseological and ontological principles of his system, e.g. explicating the difference of Lossky’s intuitionism from the one of Bergson. The key section of the organic worldview is the doctrine of the hierarchy of substantival agents: the hierarchical personalism, as well as the notions of transcreation, dynamic understanding of matter, and the doctrine of free will closely related to it. The paper specifies the peculiarities of Lossky’s interpretations of panvitalism and panpsychism, as well as the doctrine of reincarnation, which has a particular place in his system. The final stage of Lossky’s cosmological ideas development is his ontological aesthetics: on this stage he understands the world as an embodiment of beauty. The conclusion is drawn that Lossky’s cosmological doctrine is Christian and metaphysical in its nature.

A recognizable topological model construction shows that any consistent principles of classical set theory, including the validity of the law of the excluded third, together with a standard class theory, do not suffice to demonstrate the general validity of the law of the excluded third. This result calls into question the classical mathematician's ability to offer solid justifications for the logical principles he or she favors.

Jonathan Haidt is a moral psychologist whose influential book, The Righteous Mind: Why Good People are Divided by Politics and Religion, explains the origins of our political disagreements. The aim of the book is to encourage understanding and civility in our public life. Deliberative democrats also have a significant stake in understanding the sources of our disagreements and see rational deliberation as the key to civility and democratic legitimacy. However, Haidt’s empirical studies give reasons to suggest that the “faith” of deliberative democrats in reasoning may be misplaced, particularly as that faith tends be inflected in terms of a “Kantian” moral psychology.This article analyzes four different explanatory “stories” that Haidt weaves together: (1) a “causal” evolutionary account of the development of morality; (2) a “causal” story about the psychological mechanisms explaining human action; (3) a “causal” story about the historical and cultural determinants of our political attitudes; and (4) a “normative” story about the grounds and justification of human action. The article then examines these stories to discern how deliberative democrats might rearticulate their conception of public reasoning, and their normative hopes for it, in light of Haidt’s findings by introducing the “embedded” conception of public reasoning.

This paper considers the time continuum of Brouwer in terms of the complex system physics. It is based upon a processual definition of real numbers which concern the measurement problem. The multiresolution hierarchy of the measurement process is represented by the time operator acting on continuous signals. The wavelet domain hidden Markov model, which recapitulates statistical properties of the hierarchy, is verified experimentally on a wide range of signal ensembles. It indicates a novel method that has already been proved to be tremendously useful in applied mathematics.

An interview with Charles McCarty by Piotr Urbańczyk concerning mathematical explanation.

At the end of the 19th century in the fundamentals of mathematics appeared a crisis. It was caused by the paradoxes found in Cantor’s set theory. One of the ideas a resolving the crisis was intuitionism – one of the constructivist trends in the philosophy of mathematics. Its creator was Brouwer, the main representative was Heyting. In this paper described will be attempt to construct a suitable logic for philosophical intuitionism theses. In second paragraph Heyting system will be present – its axioms and matrices truth-. Later Gödel theorem about the inadequacy of finite dimensional matrices for this system will be explained. At the end this paper an infinite sequence of matrices adequate for Heyting axioms proposed by Jaśkowski will be described.

Intuitionistic logic, as a non-classical logic, encompasses the principles of logical reasoning which were used by L. E. J. Brouwer in developing his intuitionistic mathematics. Brouwer rejected the principle of the excluded middle on the basis of his philosophy. In his philosophical view, logic is the application of mathematics to the language of mathematics. In other words, logic studies the patterns that characterize valid inference. The resulting linguistic system of logic may be studied mathematically, even independently of the mathematical activities that it was originally abstracted from. In this paper, the philosophical basis of Brouwer’s view about Logic and Mathematics is explained.

Intuitionistic logic, as a non-classical logic, encompasses the principles of logical reasoning which were used by L. E. J. Brouwer in developing his intuitionistic mathematics. Brouwer rejected the principle of the excluded middle on the basis of his philosophy. In his philosophical view, logic is the application of mathematics to the language of mathematics. In other words, logic studies the patterns that characterize valid inference. The resulting linguistic system of logic may be studied mathematically, even independently of the mathematical activities that it was originally abstracted from. In this paper, the philosophical basis of Brouwerâs view about Logic and Mathematics is explained.

Anti-realism was first introduced by Michael Dummett, the contemporary analytic philosopher. He has always preferred to discuss about statements and assertions (instead of entities), such as statements in the past tense, statements about the physical world, and so on. Based on his approach to metaphysical problems, we should initially choose an appropriate model of meaning and a proper conception of the notion of truth applicable to the statements. By doing so, the dispute between realism and anti-realism can be rendered to a disagreement on the kind of meaning the statements may have. After criticizing the realist approach, he goes on to claim that without having proper evidence, we cannot judge on meaning and truth or falsity of linguistic statements. To understand a sentence, Dummett says, is to have the capacity of recognizing what would be counted as evidence for or against it. Therefore, an anti-realist believes that there is no guarantee for every sentence to be certainly true (or false). Or, it cannot be approved for each statement to be necessarily true or false, independently of our knowledge and relevant abilities. An adherent of realism, by contrast, admits the principle of bivalence and acknowledges that sentences are true or false because of the reality existing independently of us. In this essay, after introducing Dummett’s anti-realist approach and his criticisms on realism, I am going to discuss about and explain the correlation between his desired theory of meaning and anti-realism.

In this paper, we present valuation semantics for the Propositional Intuitionistic Calculus (also called Heyting Calculus) and three important subcalculi: the Implicative, the Positive and the Minimal Calculus (also known as Kolmogoroff or Johansson Calculus). Algorithms based in our definitions yields decision methods for these calculi.

One of Da Costa’s motives when he constructed the paraconsistent logic C! was to dualise the negation of intuitionistic logic. In this paper I explore a different way of going about this task. A logic is defined by taking the Kripke semantics for intuitionistic logic, and dualising the truth conditions for negation. Various properties of the logic are established, including its relation to C!. Tableau and natural deduction systems for the logic are produced, as are appropriate algebraic structures. The paper then investigates dualising the intuitionistic conditional in the same way. This establishes various connections between the logic, and a logic called in the literature ‘Brouwerian logic’ or ‘closed-set logic’.

Este estudo tem por objeto analisar um segmento do pensamento argentino da década de 1930, representado no ensaísmo sobre a "alma", ou o caráter nacional. Esse ensaísmo produziu alguns textos que se transformaram, por meio da crítica, em clássicos da reflexão sobre o país - tais como Radiografía de la pampa, de Ezequiel Martínez Estrada, e Historia de una pasión argentina, de Eduardo Mallea -, e que se gestaram sobre a base de uma crise política - sua primeira exteriorização foi o golpe de Estado de 1930 - e de uma desordem mais ampla dos pontos intelectuais de referência, em consequência da falência do positivismo entre as elites culturais. O dissabor provocado pelo contexto político nacional se mesclou ao mal-estar oriundo do pensamento europeu sobre a crise - crise do espírito, da ordem liberal e do capitalismo -, e esse amálgama alimentou um estado de descontentamento intelectual que ganhou forma na reflexão ensaística. De modo cada vez mais amplo, esse gênero dá início a uma rigorosa revisão da Argentina liberal, no âmbito de cuja produção destacam-se os referidos ensaios de Martínez Estrada e de Mallea, que serão analisados na parte final do presente estudo.This study analyzes a sector of Argentine thought from the 1930s, represented in the essays on the national 'soul' or character. This essay writing produced a number of texts that were transformed, through critical appraisal, into classics on the country itself - such as Radiografía de la pampa by Ezequiel Martínez Estrada, and Historia de una pasión argentina by Eduardo Mallea - and which emerged out of a political crisis - whose first notable effect was the 1930 coup d'état - and a more widespread disruption of the intellectual points of reference caused by the exhaustion of positivism as a paradigm among the cultural elites. The unease provoked by the national political context merged with the unease stemming from European thought concerning the crisis - the crisis of spirit, of the liberal order and of capitalism - and this amalgam fed a state of intellectual discontent that took concrete form in the essay. In an ever broader way, this genre stimulated a profound revision of liberal Argentina. Among the texts involved in this process we can highlight the essays by Martínez Estrada and Mallea, analyzed in the final part of the study.

The text shows a historical approach to the concept of logic in relation with mathematics. Therefore it exposes the contributions of ancient and medieval logic, and problematizes the approaches of logicism and intuitionism with the idea of providing aesthetic reasonableness based upon the theory of abduction of Charles Sanders Peirce. Later on, it demonstrates the fundamentals of a hermeneutic–approach qualitative research. Finally, it advances the development of aesthetic reasonableness based on the design and staging of a didactic strategy, supported on the analysis of fictional stories and research articles. The first results of the strategy show teachers in training, both in literature and mathematics, at the University of Antioquia, are unaware of the logical and creative possibilities that can be experienced and identified through literary and scientific texts. This difficulty suggests the importance of further progress in the teaching strategy design and experience.

Anti-realism was first introduced by Michael Dummett, the contemporary analytic philosopher. He has always preferred to discuss about statements and assertions (instead of entities), such as statements in the past tense, statements about the physical world, and so on. Based on his approach to metaphysical problems, we should initially choose an appropriate model of meaning and a proper conception of the notion of truth applicable to the statements. By doing so, the dispute between realism and anti-realism can be rendered to a disagreement on the kind of meaning the statements may have. After criticizing the realist approach, he goes on to claim that without having proper evidence, we cannot judge on meaning and truth or falsity of linguistic statements. To understand a sentence, Dummett says, is to have the capacity of recognizing what would be counted as evidence for or against it. Therefore, an anti-realist believes that there is no guarantee for every sentence to be certainly true (or false). Or, it cannot be approved for each statement to be necessarily true or false, independently of our knowledge and relevant abilities. An adherent of realism, by contrast, admits the principle of bivalence and acknowledges that sentences are true or false because of the reality existing independently of us. In this essay, after introducing Dummett’s anti-realist approach and his criticisms on realism, I am going to discuss about and explain the correlation between his desired theory of meaning and anti-realism.

In this article the initial discussion of the untenability of the distinction between “pure” and “applied" mathematics is followed by looking at alternative approaches regarding the relationship between mathematics and the “real world” - with intuitionism and Platonism representing the two opposite positions. The notions of infinity as well as the totality character of spatial continuity (and its implied infinite divisibility) turned out to occupy a central position in this context. In the final section brief attention is given - against the background of some perspectives on the history of mathematics - to an alternative approach in which both the uniqueness and the mutual irreducibility of number and space are conjectured.