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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 practicing philosophy in the age of artificial intelligence. [ABSTRACT FROM AUTHOR]

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In a recent paper, Nicolas Gisin suggests that by conducting physics with intuitionistic rather than classical mathematics, rich temporality—that is, passage and tense, and specifically the future's openness—can be incorporated into physics. Physics based on classical mathematics is tenseless and deterministic, and that, so he holds, renders it incongruent with experience. According to Gisin, physics ought to represent the indeterminate nature of reality, and he proposes that intuitionistic mathematics is the key to succeeding in doing so. While I share his insistence on the reality of passage and tense and on the future being real and open, I argue that the amendment he offers does not work. I show that, its attunement to time notwithstanding, intuitionistic mathematics is as tenseless as classical mathematics and that physics is bound to remain tenseless regardless of the math it employs. There is much to learn about tensed time, but the task belongs to phenomenology and not to physics. [ABSTRACT FROM AUTHOR]

TT□C is a generic family of effectful, extensional type theories with a forcing interpretation parameterized by modalities. This paper identifies a subclass of TT□C theories that internally realizes continuity principles through stateful computations, such as reference cells. The principle of continuity is a seminal property that holds for a number of intuitionistic theories such as System T. Roughly speaking, it states that functions on real numbers only need approximations of these numbers to compute. Generally, continuity principles have been justified using semantical arguments, but it is known that the modulus of continuity of functions can be computed using effectful computations such as exceptions or reference cells. In this paper, the modulus of continuity of the functionals on the Baire space is directly computed using the stateful computations enabled internally in the theory. [ABSTRACT FROM AUTHOR]

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

Copyright of Estudios Filosóficos is the property of Estudios Filosoficos and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We present four different approaches to prove the soundness theorem for variants with t-truth of functional interpretations. To showcase our different methods we focus on the intuitionistic nonstandard bounded functional interpretation of the nonstandard extensional Heyting arithmetic in all finite types because a version with t-truth for this interpretation has not been given before. Also, because it is a more involved interpretation than others since it includes both nonstandard principles and majorisability. This leads us to believe that if the approaches work for this more complicated functional interpretation, then they should also work for simpler functional interpretations (and realisabilities). [ABSTRACT FROM AUTHOR]

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.

Copyright of Studia Historiae Scientiarum is the property of Jagiellonian University Press and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The category of ethics is traditionally divided among researchers in this field in to three branches: applied ethics, normative ethics and meta-ethics. Despite the three branches, each of these branches has both an effect on the other. Medical ethics as a branch of applied ethics on the one hand is influenced by the views of ethics philosophers and on the other hand due to the importance of the medical profession requires special attention. The present article uses a descriptive and analytical method to apply the philosophy of Ṣadrīan ethics with one of the important views of medical ethics, namely Principalism. The authors of this study, by examining the relevant texts, have argued the following results that are stated briefly. Principalism is in line with Ṣadrīan moral view in that according to Mullā Ṣadrā's view of moral realism, moral concepts have an existential and external meaning, and therefore moral behavior and advice must be reflected in the world. Principalism also emphasizes the improvement of the moral performance of physicians and clinicians during medical interventions. However, the emphasis on Principalism should not lead to the molding of the clinician's mind, and according to Mullā Ṣadrā's moral Intuitionism, the moral conscience of the physician and those involved in medicine should always show their role during treatment. Based on the study of Mullā Ṣadrā 's views, it is inferred that among the four principles of medical ethics, the two principles of beneficence and non-maleficence are the first priority, and the principles of justice and respect for autonomy are considered a means of profitability and non-prejudicial. [ABSTRACT FROM AUTHOR]

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.

I model the version of Wilfrid Sellars' Myth of the Given argument that John McDowell presents in Mind and World along the lines of one of Graham Priest's inclosure paradoxes, with McDowell's "spinning of the wheels" worry being a worry about denial of Transcendence and his "exculpation not justification" worry being a worry about denial of Closure. This exercise reveals much, importantly: (1) McDowell's conceptualism does not in fact, resolve the paradox, and (2) on the other hand, with insights from Graham Harman, Hilan Bensusan, and the Rinzai tradition of Zen Buddhism, a non-conceptualist, indexicalist, epistemology can. [ABSTRACT FROM AUTHOR]

This article focuses on the moral development ideal of William Whewell, one of the most important intellectual figures of the 19th century Britain. According to Whewell, morality is an ideal of development. This is a process that continues throughout human life in which there is true happiness at the end. In every moment we live, we have the opportunity to be a more virtuous and better person. According to him, the most important task of human beings is to realize this ideal of development. The motivation behind this ideal is to bring morality, science and religion together in a rational system in harmony with each other. The source of this motivation is the criticism of irrationality and inconsistency directed by utilitarian thinkers (especially, John Stuart Mill), the most important opponents of ethical intuitionism. As a way of making these three areas consistent with each other, Whewell bases morality and science on a theological basis. Accordingly, God, the creator of the universe and human beings, has laid down certain principles that will regulate both nature and human actions. The duty of morality and science is to discover these principles. Therefore, morality and science are simply a process of discovery. Whewell argues that the basic principles of morality can only be known intuitively. The main reason why Whewell is considered within the ethical intuitionist tradition is this view. But this process of knowing the basic principles does not in any way imply an irrationality. The basic power that intuitively perceives these principles is reason. Conscience is a faculty that approves the judgments of reason. However, in Whewell's philosophy, conscience corresponds to an aspect of reason rather than being a faculty separate from reason. Thus, Whewell is distinguished from the intuitive moral thinkers who regard conscience as a faculty separate from reason, which grasps the basic principles of morality. According to Whewell, conscience is the guide of a human being but the judgments of conscience can sometimes be mistaken. Therefore, conscience must be constantly controlled and developed by reason. This point is where Whewell bases his moral philosophy. Because one's duty is to continuously improve their conscience and make all their judgments in accordance with the highest rule. This corresponds to moral development. The concepts of the highest good, duty, and virtue are extremely important in moral development. The ultimate rule in Whewell's philosophy expresses the will of God. The obligation to obey God's commands corresponds to duty, and fulfilling the duty corresponds to virtue. Thus, any violation of duty is a violation of God's command. Failing to do the duty is to go against the will of God. In a religious context, this corresponds to sin. Whewell argues, however, that the ideal of moral progress cannot be fulfilled by reason alone. The main reason for this is the limited structure of reason. Therefore, reason needs the help of revelation in this process. Nevertheless, in order to preserve the rational ground of his moral philosophy Whewell prioritizes reason over revelation and natural religion over revealed religion. However, Whewell still argues the help of revelation necessary for the fulfillment of the ideal of progress. He even says that those who do not accept this help of revelation and do not believe in revelation should be condemned. Because, according to him, this ideal of development can be completed with the information beyond the reach of reason that can only be bestowed by revelation. Whewell goes so far as to argue that no one was able to complete their moral evolution before Jesus Christ descended on earth. He also shows that revelation did not occur at that time as a justification. The question of whether Whewell's claim has an impact on the rationality of his philosophy is the main problem of this article. Here I argue that Whewell's approach that the ideal of moral development cannot be completed without the help of revelation makes his philosophy controversial, even if it does not completely remove the rational ground of moral theory. [ABSTRACT FROM AUTHOR]

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.

Intuitionism had been one of the most prominent ethical approaches over two hundred years, especially on the British Isles. In the first third of the 20th century it started losing its power; however, in the last few years several philosophers have been trying to renew this approach, which has made it one of the most discussed topics of contemporary metaethics. Intuitionism is a foundationalist approach which regards basic moral beliefs, i.e., intuitions, as self-evident. Nonetheless, modern intuitionists have to cope with empirical evidence which shows that intuitions are not as reliable a source of moral knowledge as would be necessary in this case. The aim of the paper is to present and discuss contemporary critique of intuitionism. First, I introduce intuitionism and its basic assumptions, both ontological and epistemological. Second, I focus on the criticism itself, especially on its empirical aspects concerning the role and the reliability of intuitions. As some of the proponents of intuitionism try to react to these objections and create a less flawed version of this approach, in the third part, I describe one of these attempts, i.e., Michael Huemer's revisionary intuitionism. Finally, I try to explain why intuitionism -- despite these efforts -- remains a problematic approach and why ethics might be better off without it. [ABSTRACT FROM AUTHOR]

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 CCw. [ABSTRACT FROM AUTHOR]

Constructivism is the metaethical position stating that although we cannot have direct access to moral facts, we can still come up with a set of principles that can be justified and that ought to be respected by individuals. The strength of these moral principles derives from the fact that they are the result of a procedure respecting certain desirable conditions. Constructivism concerns the methodology of political philosophy, being preoccupied with the process of generating and justifying moral principles. In this review article I present the main contentions of constructivism (focusing especially on the Kantian constructivism advanced by Rawls and Scanlon), describe its positioning on the realist-antirealist axis, and compare it with its main competitor in the field of metaethical views, intuitionism. I dedicate a separate section to the method of reflective equilibrium, which represents an important part of several metaethical accounts, be they constructivist, realist, or intuitionist. I show how reflective equilibrium represents the main instrument constructivists can employ in order to capture the appeal of relying on intuitions in moral theorizing, without leaning toward intuitionism. Toward the end of the article I present G. A. Cohen's (2003, 2008) criticism of constructivism. I focus on the replies Ronzoni and Valentini (2008), Hall (2013), de Maagt (2014, 2016) and Rossi (2016) give to Cohen, ending with a criticism of my own. [ABSTRACT FROM AUTHOR]

In their recent book Buchanan and Powell claim that there is moral progress. Their analysis focuses on increasing inclusiveness, yet they also suggest other dimensions as possible indicators-improvements in the concept of morality and refinements in moral motivation. In the following I present empirical data on changes in moral understanding that occurred during the second half of the 20th century in Germany. These changes concern an increasing delimitation of the moral realm, the rise of an ethics of responsibility, the displacement of an orientation to super ego dictates by a more ego-syntonic type of moral motivation. This research largely follows the 'cognitivist' paradigm which I start off defending against Haidt's counter proposal of moral intuitionism. Feasible explanatory factors for the changes documented are put forward-processes of secularization and changes in socialization styles-and their interpretation as indicators of moral progress is discussed. The paper ends with brief speculations concerning possible reasons for current moral regressions. [ABSTRACT FROM AUTHOR]

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.

Abstract Recently, a number of formal systems for Nonstandard Analysis restricted to the language of finite types, i.e. nonstandard arithmetic , have been proposed. We single out one particular system by Dinis–Gaspar, which is categorised by the authors as being part of intuitionistic nonstandard arithmetic. Their system is indeed in consistent with the Transfer axiom of Nonstandard Analysis, and the latter axiom is classical in nature as it implies (higher-order) comprehension. Inspired by this observation, the main aim of this paper is to provide answers to the following questions: (Q1) In the spirit of Reverse Mathematics , what is the minimal fragment of Transfer that is inconsistent with the Dinis–Gaspar system? (Q2) What other axioms are inconsistent with the Dinis–Gaspar system? Our answer to the first question suggests that the aforementioned inconsistency actually derives from the axiom of extensionality relative to the standard world, and that other (much stronger) consequences of Transfer are actually harmless. Perhaps surprisingly, our answer to the second question shows that the Dinis–Gaspar system is inconsistent with a number of (non-classical) continuity theorems which one would – in our opinion – categorise as intuitionistic in the sense of Brouwer. Finally, we show that the Dinis–Gaspar system involves a standard part map , suggesting this system also pushes the boundary of what still counts as 'Nonstandard Analysis' or 'internal set theory'. [ABSTRACT FROM AUTHOR]

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.

Frege writes in Numbers and Arithmetic about kindergarten-numbers and "an a priori mode of cognition" that they may have "a geometrical source." This resembles recent findings on arithmetical cognition. In my paper, I explore this resemblance between Gottlob Frege's later position concerning the geometrical source of arithmetical knowledge, and some current positions in the literature dedicated to arithmetical cognition, especially that of Stanislas Dehaene. In my analysis, I shall try to mainly see to what extent (Frege's) logicism is compatible with (Dehaene's) intuitionism. [ABSTRACT FROM AUTHOR]

We present a bounded modified realisability and a bounded functional interpretation of intuitionistic nonstandard arithmetic with nonstandard principles. The functional interpretation is the intuitionistic counterpart of Ferreira and Gaspar's functional interpretation and has similarities with Van den Berg, Briseid and Safarik's functional interpretation but replacing finiteness by majorisability. We give a threefold contribution: constructive content and proof-theoretical properties of nonstandard arithmetic; filling a gap in the literature; being in line with nonstandard methods to analyse compactness arguments. [ABSTRACT FROM AUTHOR]

In § 7 of the Critique of Practical Reason Kant presents his first definition of the universal law of morality--called the Categorical Imperative. In the same place, he affirms that being conscious of the law of morality is a Faktum of reason. The ambiguity of this statement has prompted some authors to argue that Kant does not deduce the moral law satisfactorily nor does he clarify how we become conscious of it. Nevertheless, they all forget in their analysis a relevant aspect of Kantian moral philosophy that turns out to be of great importance in contemporary studies of the philosophy of action--the self-constituting character of the rational subject and the role it plays within the foundation of morality. I claim that the Faktum of reason must be understood fundamentally as a self-constituting act. [ABSTRACT FROM AUTHOR]