Working in constructive set theory we formulate notions of constructive topological space and set-generated locale so as to get a good constructive general version of the classical Galois adjunction between topological spaces and locales. Our notion of constructive topological space allows for the space to have a class of points that need not be a set. Also our notion of locale allows the locale to have a class of elements that need not be a set. Class sized mathematical structures need (...) to be allowed for in constructive set theory because the powerset axiom and the full separation scheme are necessarily missing from constructive set theory. We also consider the notion of a formal topology, usually treated in Intuitionistic type theory, and show that the category of set-generated locales is equivalent to the category of formal topologies. We exploit ideas of Palmgren and Curi to obtain versions of their results about when the class of formal points of a set-presentable formal topology form a set. (shrink)

ABSTRACTThe general assumption that people fail to notice discrepancy between their answer and the normative answer in the conjunction fallacy task has been challenged by the theory of Logical Intuition. This theory suggests that people can detect the conflict between the heuristic and normative answers even if they do not always manage to inhibit their intuitive choice. This theory gained support from the finding that people report lower levels of confidence in their choice after they commit the conjunction fallacy compared (...) to when their answer is not in conflict with logic. In four experiments we asked the participants to give probability estimations to the options of the conflict and no-conflict versions of the tasks in the original set-up of the experiment or in a three-option design. We found that participants perceive probabilities for the options of the conflict version less similar than for the no-conflict version. As people are less confident when choosing between more similar options, this simil.. (shrink)

From the end of the 19th century until his death, one of history's most brilliant mathematicians languished in an asylum. The Mystery of the Aleph tells the story of Georg Cantor (1845-1918), a Russian-born German who created set theory, the concept of infinite numbers, and the "continuum hypothesis," which challenged the very foundations of mathematics. His ideas brought expected denunciation from established corners - he was called a "corruptor of youth" not only for his work in mathematics, but for his (...) larger attempts to meld spirituality and science. (shrink)

In this note a T1 formal space is a formal space whose points are closed as subspaces. Any regular formal space is T1. We introduce the more general notion of a formal space, and prove that the class of points of a weakly set-presentable formal space is a set in the constructive set theory CZF. The same also holds in constructive type theory. We then formulate separation properties for constructive topological spaces , strengthening separation properties discussed elsewhere. Finally we relate (...) the properties for ct-spaces with corresponding properties of formal spaces. (shrink)

We introduce a new axiom scheme for constructive set theory, the Relation Reflection Scheme . Each instance of this scheme is a theorem of the classical set theory ZF. In the constructive set theory CZF–, when the axiom scheme is combined with the axiom of Dependent Choices , the result is equivalent to the scheme of Relative Dependent Choices . In contrast to RDC, the scheme RRS is preserved in Heyting-valued models of CZF– using set-generated frames. We give an application (...) of the scheme to coinductive definitions of classes. (shrink)

Working in the weakening of constructive Zermelo-Fraenkel set theory in which the subset collection scheme is omitted, we show that the binary refinement principle implies all the instances of the exponentiation axiom in which the basis is a discrete set. In particular binary refinement implies that the class of detachable subsets of a set form a set. Binary refinement was originally extracted from the fullness axiom, an equivalent of subset collection, as a principle that was sufficient to prove that the (...) Dedekind reals form a set. Here we show that the Cauchy reals also form a set. More generally, binary refinement ensures that one remains in the realm of sets when one starts from discrete sets and one applies the operations of exponentiation and binary product a finite number of times. (shrink)

The incredible achievements of modern scientific theories lead most of us to embrace scientific realism: the view that our best theories offer us at least roughly accurate descriptions of otherwise inaccessible parts of the world like genes, atoms, and the big bang. In Exceeding Our Grasp, Stanford argues that careful attention to the history of scientific investigation invites a challenge to this view that is not well represented in contemporary debates about the nature of the scientific enterprise. The historical record (...) of scientific inquiry, Stanford suggests, is characterized by what he calls the problem of unconceived alternatives. Past scientists have routinely failed even to conceive of alternatives to their own theories and lines of theoretical investigation, alternatives that were both well-confirmed by the evidence available at the time and sufficiently serious as to be ultimately accepted by later scientific communities. Stanford supports this claim with a detailed investigation of the mid-to-late 19th century theories of inheritance and generation proposed in turn by Charles Darwin, Francis Galton, and August Weismann. He goes on to argue that this historical pattern strongly suggests that there are equally well-confirmed and scientifically serious alternatives to our own best theories that remain currently unconceived. Moreover, this challenge is more serious than those rooted in either the so-called pessimistic induction or the underdetermination of theories by evidence, in part because existing realist responses to these latter challenges offer no relief from the problem of unconceived alternatives itself. Stanford concludes by investigating what positive account of the spectacularly successful edifice of modern theoretical science remains open to us if we accept that our best scientific theories are powerful conceptual tools for accomplishing our practical goals, but abandon the view that the descriptions of the world around us that they offer are therefore even probably or approximately true. (shrink)

The place of the emotions among the passions -- The analytic of the emotions I -- The analytic of the emotions II -- The dialectic of the emotions -- Pride, arrogance, and humility -- Shame, embarrassment, and guilt -- Envy -- Jealousy -- Anger -- Love -- Friendship -- Sympathy and empathy.

The axiom of choice ensures precisely that, in ZFC, every set is projective: that is, a projective object in the category of sets. In constructive ZF (CZF) the existence of enough projective sets has been discussed as an additional axiom taken from the interpretation of CZF in Martin-Löf’s intuitionistic type theory. On the other hand, every non-empty set is injective in classical ZF, which argument fails to work in CZF. The aim of this paper is to shed some light on (...) the problem whether there are (enough) injective sets in CZF. We show that no two element set is injective unless the law of excluded middle is admitted for negated formulas, and that the axiom of power set is required for proving that “there are strongly enough injective sets”. The latter notion is abstracted from the singleton embedding into the power set, which ensures enough injectives both in every topos and in IZF. We further show that it is consistent with CZF to assume that the only injective sets are the singletons. In particular, assuming the consistency of CZF one cannot prove in CZF that there are enough injective sets. As a complement we revisit the duality between injective and projective sets from the point of view of intuitionistic type theory. (shrink)

The aim of this paper is to formulate and study two weak axiom systems for the conceptual framework of constructive set theory . Arithmetical CST is just strong enough to represent the class of von Neumann natural numbers and its arithmetic so as to interpret Heyting Arithmetic. Rudimentary CST is a very weak subsystem that is just strong enough to represent a constructive version of Jensenʼs rudimentary set theoretic functions and their theory. The paper is a contribution to the study (...) of formal systems for CST that capture significant stages in the development of constructive mathematics in CST. (shrink)

In this study, we investigated whether control of the conflict between incongruent heuristic and analytical answer options in a reasoning task is modulated by the presence of conflict on previous trials. In two experiments, we found that the incongruency of the previous trial has a significant effect on the control exhibited on the current trial. Our data also showed that this adaptation effect is modulated by the incongruency of the previous series of trials. These results demonstrate the same control adaptation (...) effects for a reasoning task as observed for standard response interference tasks. Coinciding control effects in the two research areas suggest that cognitive control might be an important mechanism underlying performance on reasoning tasks. Based on these results we argue that the study of cognitive control in reasoning could potentially facilitate the refinement of empirical predictions and provide a new tool to explore the exertion of top-down control in human thinking. (shrink)

We present a generalisation of the type-theoretic interpretation of constructive set theory into Martin-Löf type theory. The original interpretation treated logic in Martin-Löf type theory via the propositions-as-types interpretation. The generalisation involves replacing Martin-Löf type theory with a new type theory in which logic is treated as primitive. The primitive treatment of logic in type theories allows us to study reinterpretations of logic, such as the double-negation translation.

Situation Theory and Its Applications, Vol. 1 . Robin Cooper, Kuniaki Mukai, and John Perry (Eds.). Lecture Notes No. 22. ...

This work is derived from the SERC "Logic for IT" Summer School Conference on Proof Theory held at Leeds University. The contributions come from acknowledged experts and comprise expository and research articles which form an invaluable introduction to proof theory aimed at both mathematicians and computer scientists.

Situation theory is the result of an interdisciplinary effort to create a full-fledged theory of information. Created by scholars and scientists from cognitive science, computer science and AI, linguistics, logic, philosophy, and mathematics, it aims to provide a common set of tools for the analysis of phenomena from all these fields. Unlike Shannon-Weaver type theories of information, which are purely quantitative theories, situation theory aims at providing tools for the analysis of the specific content of a situation. The question addressed (...) is not how much information is carried, but what information is carried. (shrink)

The concept of normal is so familiar that it can be hard to imagine contemporary life without it. Yet the term entered everyday speech only in the mid-twentieth century. Before that, it was solely a scientific term used primarily in medicine to refer to a general state of health and the orderly function of organs. But beginning in the middle of the twentieth century, normal broke out of scientific usage, becoming less precise and coming to mean a balanced condition to (...) be maintained and an ideal to be achieved. In Normality, Peter Cryle and Elizabeth Stephens offer an intellectual and cultural history of what it means to be normal. They explore the history of how communities settle on any one definition of the norm, along the way analyzing a fascinating series of case studies in fields as remote as anatomy, statistics, criminal anthropology, sociology, and eugenics. Cryle and Stephens argue that since the idea of normality is so central to contemporary disability, gender, race, and sexuality studies, scholars in these fields must first have a better understanding of the context for normality. This pioneering book moves beyond binaries to explore for the first time what it does—and doesn’t—mean to be normal. (shrink)

An Interdisciplinary Approach to Cognitive Modelling presents a new approach to cognition that challenges long-held views. It systematically develops a broad-based framework to model cognition, which is mathematically equivalent to the emerging 'quantum-like modelling' of the human mind. The book argues that a satisfactory physical and philosophical basis of such an approach is missing, a particular issue being the application of quantization to the mind for which there is no empirical evidence as yet. In response to this issue, the book (...) adopts a COM (classical optical modelling) approach, broad-based but mathematically equivalent to quantum-like modelling while avoiding its problematic features. It presents a philosophically informed and empirically motivated mathematical model of cognition, mainly concerning decision making processes. It also deals with applications to different areas of the social sciences. It will be of interest to scholars and research students interested in the mathematical modelling of cognition and decision making, and also interdisciplinary researchers interested in broader issues of cognition. (shrink)

This study concerns the ideas of one particular philosopher, Henri Bergson, whose views of time, intuition, and creativity have had a significant impact on art, literature, and the humanities, both in his time and in our own. Although it is generally recognized that Bergson's ideas have significantly impacted the arts and the humanities, it has not been recognized how they have also had a creative influence on the sciences as well. Nor has it been realized that this was one of (...) his most basic contentions. Bergson's conception of intuition--his fundamental insight into reality--was not limited to fugitive insights into human existence. By realizing previously unsuspected possibilities for research and discovery, his endeavors were also meant to make possible new advances in the sciences. If it enabled his cousin by marriage, Marcel Proust, to explore human memory in depth, it also inspired psychologists like Daniel Schachter to use Bergson's ideas to make real contributions to contemporary memory science. If his notion of creative evolution brought many thinkers to a belief in human creative freedom, it brought others (notably Alexis Carrel and Pierre Lecomte de Noüy) to a scientific study of biological time. Among his successful speculations was the theory of the Big Bang cosmology. 'Getting Bergson Straight' shows many points at which Bergson's ideas anticipated future developments in the sciences. This was seen clearly by the Nobel Prize-winning physicist Luis de Broglie who viewed Bergson's physics as presaging quantum physics. Thus, the text is well situated for arts, humanities, social science, and natural science classrooms studying creative thinking and/or intellectual history. (shrink)

Profoundly important ethical and political controversies turn on the question of whether biological life is an essential aspect of a human person, or only an extrinsic instrument. Lee and George argue that human beings are physical, animal organisms - albeit essentially rational and free - and examine the implications of this understanding of human beings for some of the most controversial issues in contemporary ethics and politics. The authors argue that human beings are animal organisms and that their personal identity (...) across time consists in the persistence of the animal organisms they are; they also argue that human beings are essentially rational and free and that there is a radical difference between human beings and other animals; criticize hedonism and hedonistic drug-taking; present detailed defenses of the prolife positions on abortion and euthanasia; and defend the traditional moral position on marriage and sexual acts. (shrink)

Do the ethical features of an artwork bear on its aesthetic value? This movie endorses misogyny, that song is a civil rights anthem, the clay constituting this statue was extracted with underpaid labor—are facts like these the proper bases for aesthetic evaluation? I argue that this debate has suffered from a false presupposition: that if the answer is yes (for at least some such ethical features), such considerations feature as pro tanto contributions to an artwork's overall aesthetic value, i.e., as (...) merits or flaws which make something have more or less overall aesthetic value. As the case of ethically laden, aesthetic evaluation makes clear, however, good aesthetic judgement is irreducibly multi-dimensional, e.g., "the movie has an engaging soundtrack, tasteful camera work, and takes a misogynistically prurient perspective on its female lead.'' Such a "non-summative" judgement refuses to reduce those various dimensions of aesthetic value to a single aggregate aesthetic evaluation, like "it's a 6/10" or "it's a pretty good movie!" I defend both the modest claim that such non-summative evaluations are not mistaken and the extremist claim that summative (i.e., unidimensional) aesthetic evaluation is defective by considering other domains of normative assessment in which summing seems inappropriate, notably including evaluations of people's character. (shrink)

This practical and essential text, co-authored by an engineer and an ethicist, covers ethical dilemmas that any engineer might encounter on the job, emphasizing the responsibility of a practicing engineer to act in an ethical manner. To illustrate the complexities involved, the authors present characters who encounter situations that test the engineering code of ethics. The dialogue between the characters highlights different perspectives of each dilemma. As they proceed through the book, students see how the code of ethics can help (...) in decision making, as well as the implications of various decisions. The philosophical theory that supports the ethical situations encountered is presented as boxed material following each section. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version. (shrink)

In worlds that lack life, there is no value. For all that, there is no mystery about 'the existence of values in a world of facts'. The world does not consist of facts, rather true descriptions of the world consist of statements of fact. It is as much a fact concerning the world that there are things that are of value to living things, that human beings value things and possess valuable characteristics, perform valuable deeds, stand in valuable relationships to (...) others, as it is a fact that there is life on earth. (shrink)

A critical note on Christopher Bartel and Jack M. C. Kwong, ‘Pluralism, Eliminativism, and the Definition of Art’, Estetika 58 (2021): 100–113. Art pluralism is the view that there is no single, correct account of what art is. Instead, art is understood through a plurality of art concepts and with considerations that are different for particular arts. Although avowed pluralists have retained the word ‘art’ in their discussions, it is natural to ask whether the considerations that motivate pluralism should lead (...) us to abandon art talk altogether; that is, should pluralism lead to eliminativism? This paper addresses arguments both for and against this move. We ultimately argue that pluralism allows one to retain the word ‘art’, if one wants it, but only in a loose, conversational sense. The upshot of pluralism is that talk of art in general cannot be asked to do theoretical and philosophical work. (shrink)

Individuals’ propensity not to override the first answer that comes to mind is thought to be a crucial cause behind many failures in reasoning. In the present study, we aimed to explore the strategies used and the abilities employed when individuals solve the cognitive reflection test, the most widely used measure of this tendency. Alongside individual differences measures, protocol analysis was employed to unfold the steps of the reasoning process in solving the CRT. This exploration revealed that there are several (...) ways people solve or fail the test. Importantly, 77% of the cases in which reasoners gave the correct final answer in our protocol analysis, they started their response with the correct answer or with a line of thought which led to the correct answer. We also found that 39% of the incorrect responders reflected on their first response. The findings indicate that the suppression of the first answer may not be the only crucial feature of reflectivity in the CRT and that the lack of relevant knowledge is a prominent cause of the reasoning errors. Additionally, we confirmed that the CRT is a multi-faceted construct: both numeracy and reflectivity account for performance. The results can help to better apprehend the “whys and whens” of the decision errors in heuristics and biases tasks and to further refine existing explanatory models. (shrink)

" In a book that seeks to shift the ground of debate within theory of knowledge, William P. Alston finds that the century-lo.

In lieu of an abstract, here is a brief excerpt of the content:Burma’s Healthcare Under Fire: My Experience as an Exiled Medical ProfessionalP. P. KyawI used to work as a medical doctor in a less developed state than many big cities in Burma1 that experienced prolonged civil wars and current similar atrocities decades before the urban areas of the country experienced them. Before everything started, I was responsible for the medical management of the most vulnerable communities and had been struggling (...) with pandemic-related medical activities. Those were the happiest years of my life. I was with one of the best international organizations, where every effort I made was directly delivered to the patients with no unnecessary paperwork. The system was efficient, my colleagues were supportive, and I had a good work-life balance. I supported my family and whoever needed temporary financial support, played music weekly, met good friends who I hung out with every weekend, and [End Page 164] found hobbies like gardening and crocheting. I was content and happy. I even postponed my plans to get registered as a doctor in the Western world.Before moving to this beautiful ethnic state in 2019, I previously worked as a government medical doctor in Yangon, the capital. As much as I loved working in those civilian hospitals, I could not support myself with a monthly pay of $100-$150 USD. It was a hard decision to leave the service because it meant I could not pursue the medical specialty that I had always longed for and had to leave like-minded supportive colleagues. In Myanmar, unless you are a civil servant, you cannot pursue further clinical specialties. However, after leaving the government’s service to work in humanitarian medical assistance in hard-to-reach areas of Burma, I learned that life is still beautiful outside my comfort zone, until February 2021 when the coup began. Democratically elected members of the country’s ruling party were overthrown by the military, which then bestowed power in a military junta.I expected the election prior to the coup in November 2020 to be an uphill battle for Burma, but nothing more. I was still in denial when I first heard the news from one of the town’s NGO staff. The person had to travel on a motorbike to inform everyone that the junta had staged the coup. No telephone or internet was working at that time. My colleagues and I cried in our office, saying, “We are so young, and the future is still ahead. I don’t think this is going to last long. Maybe it will be over in a few days or, at most, a few weeks.” Once the peaceful protests started nationwide, my friends and I provided medical cover for the protesters, initially for minor medical problems such as low sugar, low blood pressure, injuries from accidental minor slips and falls, etc. Never in my life had I imagined that I would be taking care of bullet wounds and people injured by live rounds. While learning about gunshot wounds in forensic medicine, I thought, “Oh, this is not going to be very useful because Burma is not America, and I am not going there.” Then suddenly, it became too real and more useful than I would’ve liked it to be.I always think back to one especially bloody day when many people in the town were shot with live rounds. We assisted many patients. Usually, we would go around with the protest groups until they were over in the late afternoon. The protesters were always peaceful. There were no riots, no harmful acts, or vandalism. Only when the protesters were cruelly dispersed with tear gas, high-pressure pumps, rubber bullets, and live rounds (to the head) did they decide to defend themselves while still making their voices heard. The only defenses people had to counteract the live rounds were things like metal covers, firecrackers, and slingshots.One afternoon in March 2021, my team and I took an early break for lunch—unaware that some people would lose their lives that afternoon. We followed the local protests through Facebook Live while having lunch and started to hear firecracker sounds. A few seconds later, we knew... (shrink)