Criteria of acceptability for mathematical proofs are field-dependent. In topology, though not in most other domains, it is sometimes acceptable to appeal to visual intuition to support inferential steps. In previous work :829–842, 2014; Lolli, Panza, Venturi From logic to practice, Springer, Berlin, 2015; Larvor Mathematical cultures, Springer, Berlin, 2016) my co-author and I aimed at spelling out how topological proofs work on their own terms, without appealing to formal proofs which might be associated with them. In this article, I (...) address two criticisms that have been raised in Tatton-Brown against our approach: that it leads to a form of relativism according to which validity is equated with social agreement and that it implies an antiformalizability thesis according to which it is not the case that all rigorous mathematical proofs can be formalized. I reject both criticisms and suggest that our previous case studies provide insight into the plausibility of two related but quite different theses. (shrink)

Rigorous proof is supposed to guarantee that the premises invoked imply the conclusion reached, and the problem of rigor may be described as that of bringing together the perspectives of formal logic and mathematical practice on how this is to be achieved. This problem has recently raised a lot of discussion among philosophers of mathematics. We survey some possible solutions and argue that failure to understand its terms properly has led to misunderstandings in the literature.

In this paper I intend to grapple with the idea of philosophy as rigorous science from the point of view of Husserl‟s phenomenology in order to show that this idea may have an important contribution to the way in which the scientific character of sciences in general, and of human and social sciences in particular, is being conceived. As rigorous science, phenomenology emphasizes and investigates the a priori context of other sciences. In this way, it plays a vital role in (...) the development of every particular eidetic upon which any sciences rely. This eidetic (or the eidetic layer of any mature science) embraces the goal and strives to reach the objective of determining the valid sense of the fundamental notions used by the scientist in his research, without, nevertheless, stirring a radical questioning of this sense and of the ultimate validity of these notions. To define them requires passing from the usual level of inquiring of that particular science (the processes of dealing with facts and experiments) to the level (or meta-level) of a radical reflection on the sense or the meaning of the basic notions of the science in question (its own foundations). Philosophy as rigorous science connects the researcher´s assertions not only to the empirical state of affairs envisaged by his work, but, moreover and in a fundamental way, to their noematic content, to their intrinsic intentional meaning. Therefore, the idea of rigorous science elaborated in Husserl‟s phenomenology is heavy with the potential of clarifying the foundations and stakes of the research undertaken by the other sciences. (shrink)

Since philosophy is a notoriously difficult subject, one may think that the concept of adding rigor to a philosophy course is misguided. Isn’t reading difficult texts by Immanuel Kant or Friedrich Nietzsche enough to categorize a class as academically rigorous? This question is based on the misguided assumption that academic rigor has only to do with course content. While course content is a component of academic rigor, other aspects such as higher-order thinking, as well as how an instructor designs and (...) grades assignments, contribute to the level of academic rigor in a course. The author provides several ways to increase the level of academic rigor in a philosophy course based upon Bloom’s Taxonomy using examples from an introductory ethics course and then provides recommendations as to how to grade to promote academic rigor. (shrink)

A principle, according to which any scientific theory can be mathematized, is investigated. Social science, liberal arts, history, and philosophy are meant first of all. That kind of theory is presupposed to be a consistent text, which can be exhaustedly represented by a certain mathematical structure constructively. In thus used, the term “theory” includes all hypotheses as yet unconfirmed as already rejected. The investigation of the sketch of a possible proof of the principle demonstrates that it should be accepted rather (...) a metamathematical axiom about the relation of mathematics and reality. The main statement is formulated as follows: Any scientific theory admits isomorphism to some mathematical structure in a way constructive. Its investigation needs philosophical means. Husserl’s phenomenology is what is used, and then the conception of “bracketing reality” is modelled to generalize Peano arithmetic in its relation to set theory in the foundation of mathematics. The obtained model is equivalent to the generalization of Peano arithmetic by means of replacing the axiom of induction with that of transfinite induction. The sketch of the proof is organized in five steps: a generalization of epoché; involving transfinite induction in the transition between Peano arithmetic and set theory; discussing the finiteness of Peano arithmetic; applying transfinite induction to Peano arithmetic; discussing an arithmetical model of reality. Accepting or rejecting the principle, two kinds of mathematics appear differing from each other by its relation to reality. Accepting the principle, mathematics has to include reality within itself in a kind of Pythagoreanism. These two kinds are called in paper correspondingly Hilbert mathematics and Gödel mathematics. The sketch of the proof of the principle demonstrates that the generalization of Peano arithmetic as above can be interpreted as a model of Hilbert mathematics into Gödel mathematics therefore showing that the former is not less consistent than the latter, and the principle is an independent axiom. The present paper follows a pathway grounded on Husserl’s phenomenology and “bracketing reality” to achieve the generalized arithmetic necessary for the principle to be founded in alternative ontology, in which there is no reality external to mathematics: reality is included within mathematics. That latter mathematics is able to self-found itself and can be called Hilbert mathematics in honour of Hilbert’s program for self-founding mathematics on the base of arithmetic. The principle of universal mathematizability is consistent to Hilbert mathematics, but not to Gödel mathematics. Consequently, its validity or rejection would resolve the problem which mathematics refers to our being; and vice versa: the choice between them for different reasons would confirm or refuse the principle as to the being. An information interpretation of Hilbert mathematics is involved. It is a kind of ontology of information. The Schrödinger equation in quantum mechanics is involved to illustrate that ontology. Thus the problem which of the two mathematics is more relevant to our being is discussed again in a new way A few directions for future work can be: a rigorous formal proof of the principle as an independent axiom; the further development of information ontology consistent to both kinds of mathematics, but much more natural for Hilbert mathematics; the development of the information interpretation of quantum mechanics as a mathematical one for information ontology and thus Hilbert mathematics; the description of consciousness in terms of information ontology. (shrink)

No livro I da Ethica Eudemia, Aristóteles dedica um capítulo a considerações acerca de seu método. No entanto, analisando passagens de outros tratados do autor, é possível concluir que há algo comum que perpassa as diversas considerações acerca de seu método, a saber: que o ponto de partida de toda investigação é dado pelo que é mais cognoscível a nós, e todo o procedimento de investigação visa chegar ao que é mais cognoscível em si mesmo – o conhecimento estrito do (...) objeto, que inclui compreender suas causas. O objetivo deste trabalho é tentar compreender como esse procedimento acontece na investigação moral, que opera no âmbito do discurso e, portanto, das definições. Para isso, pretendemos analisar como acontece a passagem da análise do que é dado na experiência em direção ao conhecimento de suas causas, que é próprio de outros tratados aristotélicos, para a análise das opiniões vagas e imprecisas em direção às definições estritas com as quais a Ethica Eudemia pretende operar. (shrink)

The classification of algebraic surfaces by the Italian School of algebraic geometry is universally recognized as a breakthrough in 20th-century mathematics. The methods by which it was achieved do not, however, meet the modern standard of rigor and therefore appear dubious from a contemporary viewpoint. In this article, we offer a glimpse into the mathematical practice of the three leading exponents of the Italian School of algebraic geometry: Castelnuovo, Enriques, and Severi. We then bring into focus their distinctive conception of (...) rigor and intuition. Unlike what is often assumed today, from their perspective, rigor is neither opposed to intuition nor understood as a unitary phenomenon – Enriques distinguishes between small-scale rigor and large-scale rigor and Severi between formal rigor and substantial rigor. Finally, we turn to the notion of mathematical objectivity. We draw from our case study in order to advance a multi-dimensional analysis of objectivity. Specifically, we suggest that various types of rigor may be associated with different conceptions of objectivity: namely, objectivity as faithfulness to facts and objectivity as intersubjectivity. (shrink)

Some physicians, in their care of patients at risk of misusing opioids, use machine learning (ML)-based prediction drug monitoring programmes (PDMPs) to guide their decision making in the prescription of opioids. This can cause a conflict: a PDMP Score can indicate a patient is at a high risk of opioid abuse while a patient expressly reports oppositely. The prescriber is then left to balance the credibility and trust of the patient with the PDMP Score. Pozzi1 argues that a prescriber who (...) downgrades the credibility of a patient’s testimony based on a low PDMP Score is epistemically and morally unjustified and contributes to a form of testimonial injustice. This results in patients being silenced, excluded from decision-making processes and subjected to structural injustices. Additionally, the use of ML systems in medical practices raises concerns about perpetuating existing inequalities, overestimating their capabilities and displacing human authority. However, almost the very same critiques apply to human-based systems. Formalisation, ML systems included, should instead be viewed positively,2 and precisely as a powerful means to begin eroding these and other problems in ethically sensitive domains. In this case, the epistemic virtues of formalisation include promoting transparency, consistency and replicability in decision making. Rigorous ML systems can also help ensure that models …. (shrink)

Latin American rigorous thought has consisted of a reconstruction of western rigorous thought. This inflexion is not only limited to literary practice, it also, and most importantly, reaches all sciences, and here visibly touches the social sciences. As such, the relation between literature and t..

Abstract: Brentano’s conception of scientific philosophy had a strong influence on his students and on the intellectual atmosphere of Vienna in the late nineteenth century. The aim of this article is to expose Brentano’s conception and to contrast his views with that of two traditions he is said to have considerably influenced: phenomenology and analytic philosophy. I will shed light on the question of how and to what extent Brentano’s conception of philosophy as a rigorous science has had an impact (...) on these two traditions. The discussion will show that both took their liberties in the interpretation of the thesis, a move that allowed them to liberate themselves from Brentano’s inheritance and to fully develop their own philosophical positions. (shrink)

This manuscript presents an English translation of the work titled “Begründung Einer Strengen Implikation” by the German logician and mathematician Wilhelm Ackermann (1896-1962), first published in June 1956.

Husserl (a mathematician by education) remained a few famous and notable philosophical “slogans” along with his innovative doctrine of phenomenology directed to transcend “reality” in a more general essence underlying both “body” and “mind” (after Descartes) and called sometimes “ontology” (terminologically following his notorious assistant Heidegger). Then, Husserl’s tradition can be tracked as an idea for philosophy to be reinterpreted in a way to be both generalized and mathenatizable in the final analysis. The paper offers a pattern borrowed from the (...) theory of information and quantum information (therefore relating philosophy to both mathematics and physics) to formalize logically a few key concepts of Husserl’s phenomenology such as “epoché” “eidetic, phenomenological, and transcendental reductions” as well as the identification of “phenomenological, transcendental, and psychological reductions” in a way allowing for that identification to be continued to “eidetic reduction” (and thus to mathematics). The approach is tested by an independent and earlier idea of Husserl, “logical arithmetic” (parallelly implemented in mathematics by Whitehead and Russell’s Principia) as what “Hilbert arithmetic” generalizing Peano arithmetics is interpreted. A basic conclusion states for the unification of philosophy, mathematics, and physics in their foundations and fundamentals to be the Husserl tradition both tracked to its origin (in the being itself after Heidegger or after Husserl’s “zu Sache selbst”) and embodied in the development of human cognition in the third millennium. (shrink)

We offer philosophical motivations for a method we call Virtual World Cognitive Science (VW CogSci), in which researchers use virtual embodied agents that are embedded in virtual worlds to explore questions in the field of Cognitive Science. We focus on questions about mental and linguistic representation and the ways that such computational modeling can add rigor to philosophical thought experiments, as well as the terminology used in the scientific study of such representations. We find that this method forces researchers to (...) take a god’s-eye view when describing dynamical relationships between entities in minds and entities in an environment in a way that eliminates the need for problematic talk of belief and concept types, such as the belief that cats are silly, and the concept CAT, while preserving belief and concept tokens in individual cognizers’ minds. We conclude with some further key advantages of VW CogSci for the scientific study of mental and linguistic representation and for Cognitive Science more broadly. (shrink)

Computational tools might tempt us to renounce complete cer- tainty. By forgoing of rigorous proof, we could get (very) probable results for a fraction of the cost. But is it really true that proofs (as we know and love them) can lead us to certainty? Maybe not. Proofs do not wear their correct- ness on their sleeve, and we are not infallible in checking them. This suggests that we need help to check our results. When our fellow mathematicians will be (...) too tired or too busy to scrutinize our putative proofs, computer proof assistants could help. But feeding a mathematical argument to a computer is hard. Still, we might be willing to undertake the endeavor in view of the extra perks that formalization may bring—chiefly among them, an enhanced mathematical understanding. (shrink)

We are pleased to feature a video interview with Jonathan Sim, where he shares his ongoing journey of integrating artificial intelligence (AI) in his teaching, the challenges encountered along the way, and what educators can do to get their students to meaningfully engage with AI tools like ChatGPT to enhance their learning.

The hard problem of consciousness is generally approached from the distinct avenues of materialism, dualism or monism. We will examine the structure that is at the core of all matter that exists in the universe. This dynamic, mathematical description of the specific type of field oscillation that generates all particles that have any tactile substance to them amazingly seems to be a physical manifestation of the most fundamental aspects of the experience of being a conscious agent. By adopting this novel (...) description of consciousness where there is a quantum of potential for consciousness intrinsic to all matter particles, the distinctions between materialism, dualism and monism become an arbitrary matter of how this mechanism is described rather than distinct ideologies, competing against one another in a winner-take-all race to the bottom of consciousness. (shrink)

Our purpose in this article is to identify and suggest resolution for two core problematics of grounded theory. First, while grounded theory provides transparency to one part of the conceptualization process, where codes emerge directly from the data, it provides no such systematic or transparent way for gaining insight into the conceptual relationships between discovered codes. Producing a grounded theory depends not only on the definition of conceptual pieces, but the delineation of a relationship between at least two of those (...) pieces. Second, the conceptualization process of grounded theory is done in hierarchical fashion, where individual codes emerge from the data but then are used to generate insight into more general concepts and thematic statements. But various works on grounded theory have failed to provide any systematic way of using data specific levels of scale (the codes) to gain insight into more macro levels of scale (concepts and themes). We offer fractal concept analysis as a means of resolving both of these issues. By using a logic structure generator, fractal concept analysis delineates self-similar conceptual frameworks at various levels of abstraction, yielding a method for linking concepts together within and between levels of scale encountered in the grounded theory coding and categorization process. We conclude that this fractal analytic technique can bolster the aims of grounded theory as a formalized and systematic process for generating theory from empirical data. (shrink)

Knowledge is correct and reliable when its foundation is correct, but humans never have the correct beliefs and methodology. Thus, knowledge is unreliable and the foundation of knowledge needs to be reconstructed. A pure rationalist only believes in logic. Thus, all matter and experience must be propositions derived from logic. The logically necessary consequence of this belief is truth; logically possible consequences are phenomena, and logically impossible consequence are fallacies and evils. This paper introduces belief and its logical consequences, such (...) as discovering first knowledge, both logically and illogically, establishing logical methodology, deducing truths purely through logic, and discovering unprovable truths by imitating the Universe. Logic and illogic are undeniable beliefs, and the reality of the Universe is the ultimate cause of everything. (shrink)

This chapter argues for an interpretation of Kant's psychology of moral evil that accommodates the so-called excluded middle cases and allows for variations in the magnitude of evil. The strategy involves distinguishing Kant's transcendental psychology from his empirical psychology and arguing that Kant's character rigorism is restricted to the transcendental level. The chapter also explains how Kant's theory of moral evil accommodates 'the badass'; someone who does evil for evil's sake.

Questions about the morality of lying tend to be decided in a distinctive way early in discussions of Kant’s view on the basis of readings of the false promising example in his Groundwork of The metaphysics of morals. The standard deception-as-interference model that emerges typically yields a very general and strong presumption against deception associated with a narrow and rigorous model subject to a range of problems. In this paper, I suggest an alternative account based on Kant’s discussion of self-deception (...) in the Metaphysics of Morals. I argue that we make the concern with respect for our capacity for inner freedom seen in the case of self-deception the model for deception in general. Focusing on the case of paternalistic lying, I claim that this approach yields a subtle and integrated account that promises the kind of resources we need if we are to be able to make headway with hard cases where deception may seem permissible. (shrink)

The book introduces a conception of discourse ethics, an intersubjectivist version of Kantian ethics. Analysing contributions by Jürgen Habermas, Karl-Otto Apel, Wolfgang Kuhlmann, Albrecht Wellmer, Robert Alexy, Klaus Günther, Rainer Forst, Marcel Niquet and others, it reconstructs critical discussions of the justification of the principle of morality (Part I) and the various proposals for its application (Part II). It defends an alternative model of how discourse ethics can provide guidance in non-ideal circumstances and avoid both arbitrariness and rigorism.

More than 50 years ago, Glaser and Strauss constructed the grounded theory methodology to develop substantive and formal data-grounded theories. Grounded theory is a rigorous methodology for generating theory grounded in data. It incorporates compare-and-contrast and abductive reasoning as its intellectual engine. Whenever one of these cognitive processes is engaged, so is the other. However, there is a need for a systematic means to assess how rigorous the grounded theory research process was employed. This paper aims to start this conversation (...) among methodologists and practitioners by proposing three criteria to evaluate the trustworthiness of grounded theories’ research process. Grounded theory studies ought to include abductive discoveries, the results of variation-finding, and Tilly’s comparison framework. Examples from Forde’s macro-level grounded theory will be used to demonstrate the significance of adding evaluation criteria to assess the rigor of the research process. (shrink)

We, the proponents of the Philosophy of Ethical Empirical Rationalism, have reviewed Heather Cox Richardson’s Democracy Awakening: Notes on the State of America and find it a case study in how modern academic work has become far too entangled with media-driven narratives, ultimately sacrificing rigor in favor of ideological amplification. While Richardson’s historical analysis provides some value, it is clear that her failure to apply empirical methods to contemporary issues, coupled with her recent appearance on a popular media platform, reveals (...) a troubling trend in academic scholarship today. (shrink)

Methodologically rigorous description, analysis, and critique of postmodern phenomena presuppose a rigorous theory of postmodernity, for which the philosophy of Martin Heidegger holds great untapped promise. This essay explicates the basic content of Heidegger’s “metametaphysics,” since for Heidegger a “metaphysics” is the epochally prevailing projection of the meaning of being in general, and he offers a theory of Western metaphysics. I begin with Heidegger’s analysis of the “regional ontologies” of the sciences in his 1927 magnum opus Being and Time, since (...) the metametaphysical works of the “late middle” Heidegger in the 1930s–1940s extend this analytical framework to metaphysics as global ontology. I then explicate Heidegger’s views on modern metaphysics, focusing on his analyses of modern science and the philosophy of Descartes, before turning to his theory of postmodernity, which I extract from his analyses of modern technology and the philosophy of Nietzsche. (shrink)

Among historians of philosophy it is often taken for granted that the “Brentano school” was one of the influential philosophical movements at the end of the nineteenth and the beginning of the twentieth century – but Brentano’s own contributions are often eclipsed by that of his direct students. This invites to reflect on the nature of and the unity within the school. Since Brentano’s conception of a rigorous, scientific philosophy had a strong impact on his students, it has been argued (...) that this conception constitutes a unifying element in an otherwise heterogeneous group. The scope of this article is to shed light on this thesis and to show its limits. I argue for a differentiated view: the Brentano school is best seen not as a compact movement, but as a heterogeneous group of scholars who approached, in a given historical and geographical period, similar topics in very similar ways. (shrink)

We present a novel approach to defining the mathematical constant π through the infinite den- sification of a sweeping net, which approximates a circle as the net becomes infinitely dense. By developing and enhancing notation related to sweeping nets and saddle maps, we establish a rigor- ous framework for expressing π in terms of the densification process using reverse integration. This method, inspired by the concept that numbers ”come from infinity,” leverages a reverse integral approach to model the transition from (...) infinite densification to the finite circle. Our work not only offers a new perspective on the geometric interpretation of π but also provides insights into reverse integration techniques and their applications in mathematical analysis. (shrink)

The rigor and precision of Leibniz's "possible world" evolved into the concept of Turing machine, and with the birth of the first computer and the physical realization of Turing machine, human cognitive and intelligent activities were optimistically considered by cognitive scientists to be convertible into computational programs for simulation by machines. Cognitive science then formed the research agenda of "cognitive computationalism", and our Chinese scholars have responded to this general view that "the essence of cognition is computation" and that the (...) human brain and computers are merely formal systems for manipulating and processing symbols in their respective fields. Professor Hong Dingguo used the concepts of "manifest order" and "hidden order", Professor Jin Gulun used the philosophical categories of "constitutive theory" and "generative theory", and Liu Yuesheng used the concept of "cognition". Professor Hong Dingguo reinterpreted the relationship between the "real world" and the "possible world" by using the concepts of "manifest sequence" and "hidden sequence", Professor Jin Wulun used the philosophical categories of "composition theory" and "generation theory", and Professor Liu Yuesheng used the generalized information paradigm of "structural information" and "exchange information". "This provides a profound elucidation of the nature of cognitive logic and the process of human cognitive activities becoming symbols through coding and puts forward theoretical limits. The current theoretical dilemma and practical difficulty of cognitive science lies in the fact that it has developed algorithmic concepts in the Turing sense that can only model the explicitly sequential part of cognitive and intellectual activity, forming a constitutive atomic abstraction, or in our terms, classical "structural information", which cannot fully explain the inner mechanisms of human mental activity and its embodied flexibility, selectivity and self-emergence. Wu Xuemou's pan-system theory does not simply rely on logic and Turing machine algorithms, but models human intelligence by treating structural information as a complex large system composed of a collection of elements and a collection of relations (exchange information: five mutual eight chips), in order to break through the narrow path of seeking only the local consistency of the system as currently done; while Wang Dekui's exploration of the three-spin biological and physical path and Huang Zhanji's abandonment of the artificial means of logic to seek the large logical natural mechanisms and Mr. Zhou Liquan's proposal of a schema for successful communication using natural language on the basis of concepts such as context and implicit connotation ("Logic — A Theory of Correct Thinking and Successful Communication"), all reflect the milestones of Chinese scholars who seek to address the deeper issues of cognitive science. We believe that along this series of explorations, combined with new results in recent years in the fields of artificial life and evolutionary computation, a new research agenda in cognitive science will emerge. (shrink)

El rigor en pensar la vida psíquica le lleva a Leibniz a disociar la percepción de la con­ciencia, rompiendo con la tradición filosófica, carente de la idea de una vida psíquica incons­ciente. Nuestro conocimiento no se limita a la “apercepción” o percepción consciente, sino que alcanza una mayor profundidad. Desarrolla Leibniz una teoría puntillista de la sensa­ción, un hormigueo incesante de innumerables percepciones individuales imperceptibles componen toda percepción consciente.

Theoretically rigorous approach to the key problems of Molinism.

To become more useful and efficient in sustaining the Earth's health, economics must undergo a paradigm shift in its thinking. From a humanistic perspective, humans should be the center of everything. However, from the standpoint of physics and the universe, this is not the case. As a species, having a planet among the millions in the universe where humans can survive and thrive is already a great fortune. Through this book, we also try to answer one of our long-standing questions: (...) why has economics learned so little from physics, the oldest and most rigorous academic discipline that studies nature? -/- Learning from the quantum and information theories, we also provide a new definition of value, which is expected to help economists relax assumptions and loosen established economic principles in order to change and evolve. The new definition is also expected to enable social scientists to address newly arising phenomena or events that are not accounted for by existing value systems, such as environmental crises, artificial intelligence (AI), and interdisciplinary information, more proactively and productively. (shrink)

A rigorous approach to the study of the mind–body problem is suggested. Since humans are able to talk about consciousness (produce phenomenal judgments), it is argued that the study of neural mechanisms of phenomenal judgments can solve the hard problem of consciousness. Particular methods are suggested for: (1) verification and falsification of materialism; (2) verification and falsification of interactionism; (3) falsification of epiphenomenalism and parallelism (verification is problematic); (4) verification of particular materialistic theories of consciousness; (5) a non-Turing test for (...) machine consciousness. A complex research program is constructed that includes studies of intelligent machines, numerical models of human and artificial creatures, language, neural correlates of con- sciousness, and quantum mechanisms in brain. (shrink)

This paper rigorously examines the primitive foundations of economic reasoning through an original framework based on symbolic logic. Extending previous work, it formalizes economic conceptions (\(\mathbb{C}\)), symbols (\(s_i\)), and introduces a structured language (\(\mathcal{L_{\mathbb{C}}}\)) to define their formation and interpretation. Organized as a continuous chain of declarations and illustrations, the paper offers a concise, systematic approach to understanding the philosophy of economic reasoning through formal representations.

We present a rigorous way to evaluate the visual perception of correlation in scatterplots, based on classical psychophysical methods originally developed for simple properties such as brightness. Although scatterplots are graphically complex, the quantity they convey is relatively simple. As such, it may be possible to assess the perception of correlation in a similar way. Scatterplots were each of 5.0 extent, containing 100 points with a bivariate normal distribution. Means were 0.5 of the range of the points, and standard deviations (...) 0.2 of this range. Precision was determined via an adaptive algorithm to find the just noticeable differences (jnds) in correlation, i.e., the difference between two side-by-side scatterplots that could be discriminated 75% of the time. Accuracy was measured by direct estimation, using reference scatterplots with fixed upper and lower values, with a test scatterplot adjusted so that its correlation appeared to be halfway between these. This process was recursively applied to yield several further estimates. Results of the discrimination tests show jnd(r) = k (1/b – r), where r is the Pearson correlation, and parameters 0 < k, b < 1. Integration yields a subjective estimate of correlation g(r) = ln(1 – br) / ln(1– b). The values of b found via discrimination closely match those found via direct estimation. As such, it appears that the perception of correlation in a scatterplot is completely described by two related performance curves, specified by two easily-measured parameters. (shrink)

This chapter sheds light on a response to experimental philosophy that has not yet received enough attention: the reflection defense. According to proponents of this defense, judgments about philosophical cases are relevant only when they are the product of careful, nuanced, and conceptually rigorous reflection. The chapter argues that the reflection defense is misguided: Five studies (N>1800) are presented, showing that people make the same judgments when they are primed to engage in careful reflection as they do in the conditions (...) standardly used by experimental philosophers. (shrink)

Is consciousness intrinsically valuable? Some theorists favor the positive view, according to which consciousness itself accrues intrinsic value, independent of the particular kind of experience instantiated. In contrast, I favor the neutral view, according to which consciousness is neither intrinsically valuable nor disvaluable. The primary purpose of this paper is to clarify what is at stake when we ask whether consciousness is intrinsically valuable, to carve out the theoretical space, and to evaluate the question rigorously. Along the way, I also (...) show why the neutral view is attractive and why certain arguments for the positive view do not work. (shrink)

This paper presents a survey of the literature on the problem of contingency in science. The survey is structured around three challenges faced by current attempts at understanding the conflict between “contingentist” and “inevitabilist” interpretations of scientific knowledge and practice. First, the challenge of definition: it proves hard to define the positions that are at stake in a way that is both conceptually rigorous and does justice to the plethora of views on the issue. Second, the challenge of distinction: some (...) features of the debate suggest that the contingency issue may not be sufficiently distinct from other philosophical debates to constitute a genuine, independent philosophical problem. And third, the challenge of decidability: it remains unclear whether and how the conflict could be settled on the basis of empirical evidence from the actual history of science. The paper argues that in order to make progress in the present debate, we need to distinguish more systematically between different expressions that claims about contingency and inevitability in science can take. To this end, it introduces a taxonomy of different contingency and inevitability claims. The taxonomy has the structure of an ordered quadruple. Each contingency and each inevitability claim contains an answer to the following four questions: (how) are alternatives to current science possible, what types of alternatives are we talking about, how should the alternatives be assessed, and how different are they from actual science? (shrink)

A brief but rigorous description of the logical structure of mathematical truth.

This article proposes a rigorous method to “map” the law on to the facts in the legal analysis of “sexual consent” using a series of mandatory questions of law designed to eliminate the legal errors often made by decision-makers who routinely rely on personal beliefs about and attitudes towards “normal sexual behavior” in screening and deciding cases. In Canada, sexual consent is affirmative consent, the communication by words or conduct of “voluntary agreement” to a specific sexual activity, with a specific (...) person. As in many jurisdictions, however, the sexual assault laws are often not enforced. Reporting is lowest and non-enforcement highest in cases involving the most common type of assailants, those who are not strangers but instead persons the complainant knows, often quite well -- acquaintances, supervisors or co-workers, and family members. Reliance on popular narratives about “seduction” and “stranger-danger” leads complainants, police, prosecutors, lawyers, and trial judges, to truncate legal analysis of the facts and leap to erroneous conclusions about “consent.” Wrongful convictions and perverse acquittals, questionable plea bargains and ill-considered decisions not to charge, result. This proposal is designed to curtail the impact of pre-judgments, assumptions, and biases in legal reasoning about voluntariness and affirmative agreement and produce decisions that are legally sound, based on the application of the rule of law to the material facts. Law has long had better tools than the age-old and popular tales of “ravishment” and “seduction.” Those tools can and should be used. (shrink)

Melnyk provides a rigorous analysis of the notion of realization with the aim of defining Physicalism. It is argued here that contrary to Melnyk's Realization Physicalism, the idea that mental phenomena are realized by physical phenomena fails to capture the physicalist belief that the former obtain in virtue of the latter. The conclusion is not that Physicalism is false, but that its truth is best explained with some notion other than realization in Melnyk's sense. I also argue that the problems (...) with Melnyk's brand of Realization Physicalism generalize to other potential attempts to express Physicalism in terms of realization. The burden of proof is on the Realization Physicalist to show that physicalist intuitions can be adequately captured with the notion of realization. (shrink)

The Problem of Iterated Ground is to explain what grounds truths about ground: if Γ grounds φ, what grounds that Γ grounds φ? This paper develops a novel solution to this problem. The basic idea is to connect ground to explanatory arguments. By developing a rigorous account of explanatory arguments we can equip operators for factive and non-factive ground with natural introduction and elimination rules. A satisfactory account of iterated ground falls directly out of the resulting logic: non- factive grounding (...) claims, if true, are zero-grounded in the sense of Fine. (shrink)

This article builds on ideas presented in Klein (2015a) concerning the importance of a more nuanced, conceptually rigorous approach to the scientific understanding and use of the construct “memory”. I first summarize my model, taking care to situate discussion within the terminological practices of contemporary philosophy of mind. I then elucidate the implications of the model for a particular operation of mind – the manner in which content presented to consciousness realizes its particular phenomenological character (i.e., mode of presentation). Finally, (...) I discuss how the model offers a reconceptualization of the technical language used by psychologists and neuroscientists to formulate and test ideas about memory. (shrink)

Public policymakers and institutional decision-makers routinely face questions about whether interventions “work”: does universal basic income improve people’s welfare and stimulate entrepreneurial activity? Do gated alleyways reduce burglaries or merely shift the crime burden to neighbouring communities? What is the most cost-effective way to improve students’ reading abilities? These are empirical questions that seem best answered by looking at the world, rather than trusting speculations about what will be effective. Evidence-based policy (EBP) is a movement that concretizes this intuition. It (...) maintains that policy should be based on evidence of “what works.” Not any evidence will do, however. Following on the heels of its intellectual progenitor, evidence-based medicine (EBM), EBP insists on the use of high-quality evidence produced in accordance with rigorous methodological standards. Though intuitively compelling, EBP has attracted significant criticism from methodologists, political scientists, and philosophers. This chapter provides a critical overview of EBP through a philosophical lens, reviewing and discussing some of the most pressing challenges that EBP faces and outlining some proposals for improving it. I first provide a brief overview of EBP and distinguish a broader and narrower understanding of it. I then review existing lines of criticism of EBP, two of which are considered in detail. The first elaborates how EBP struggles with extrapolation, that is, the use of evidence from study populations to make inferences about the effects of policies on novel target populations. The second maintains that EBP’s methodological tenets are deeply entwined with moral and political values, which can threaten EBP’s promise to promote objectivity in policymaking. Finally, I make some proposals for how EBP could be improved going forward. (shrink)

Extant literature suggests a positive correlation between social trust (also called generalized trust) and life satisfaction. However, the psychological pathways underlying this relationship can be complex. Using the Bayesian Mindsponge Framework (BMF), we examined the influence of social trust in a high-violence environment. Employing Bayesian analysis on a sample of 1237 adults in Cali, Colombia, we found that in a linear relationship, generalized trust is positively associated with life satisfaction. However, in a model including the interactions between trust and education (...) level as well as between trust and socioeconomic status, generalized trust is found to be negatively associated with life satisfaction. In this non-linear relationship, both education level and socioeconomic status have moderating effects against the negative association between generalized trust and life satisfaction. In other words, less educated people living in worse socioeconomic conditions are more likely to have lower life satisfaction when they have higher levels of social trust. In contrast, highly educated people living in better socioeconomic conditions are more likely to have higher life satisfaction when they have higher levels of social trust. Due to the facilitating function of trust in information processing, lowering the rigor of the filtering system in a high-violence social environment will likely put an individual at risk. Based on our findings, we suggest that policymakers should consider the impacts of social contexts when advocating for increasing social trust. We also recommend that researchers carefully examine the psychological mechanism underlying an observed association before making suggestions for policymaking. (shrink)

This paper explains how the practice of ‘no platforming’ can be reconciled with a liberal politics. While opponents say that no platforming flouts ideals of open public discourse, and defenders see it as a justifiable harm-prevention measure, both sides mistakenly treat the debate like a run-of-the-mill free speech conflict, rather than an issue of academic freedom specifically. Content-based restrictions on speech in universities are ubiquitous. And this is no affront to a liberal conception of academic freedom, whose purpose isn’t just (...) to protect the speech of academics, but also to give them the prerogative to determine which views and speakers have sufficient disciplinary credentials to receive a hearing in academic contexts. No platforming should therefore be acceptable to liberals, in principle, in cases where it is used to support a university culture that maintains rigorous disciplinary standards, by denying attention and credibility to speakers without appropriate disciplinary credentials. (shrink)

Social norms are commonly understood as rules that dictate which behaviors are appropriate, permissible, or obligatory in different situations for members of a given community. Many researchers have sought to explain the ubiquity of social norms in human life in terms of the psychological mechanisms underlying their acquisition, conformity, and enforcement. Existing theories of the psychology of social norms appeal to a variety of constructs, from prediction-error minimization, to reinforcement learning, to shared intentionality, to domain-specific adaptations for norm acquisition. In (...) this paper, we propose a novel methodological and conceptual framework for the cognitive science of social norms that we call normative pluralism. We begin with an analysis of the explanatory aims of the cognitive science of social norms. From this analysis, we derive a recommendation for a reformed conception of its explanandum: a minimally psychological construct that we call normative regularities. Our central empirical proposal is that the psychological underpinnings of social norms are most likely realized by a heterogeneous set of cognitive, motivational, and ecological mechanisms that vary between norms and between individuals, rather than by a single type of process or distinctive norm system. This pluralistic approach, we suggest, offers a methodologically sound point of departure for a fruitful and rigorous science of social norms. (shrink)

We propose a qualitatively new kind of governance for the emerging need to efficiently guide the densely interconnected, ever more complex world development, which is based on explicit and openly presented problem solutions and their interactive implementation practice within the versatile, but unified professional analysis of complex real-world dynamics, involving both the powerful central units and the attached creative worldwide network of professional representatives. We provide fundamental and rigorous scientific arguments in favour of introduction of just that kind of governance (...) at the modern development stage, after the complexity threshold in the real world dynamics evolution (sometimes intuitively designated as "globalisation"), where the traditional spontaneous-empirical kind of development and related administrative governance lose dramatically and inevitably their efficiency and the necessity of explicit consistent understanding and guidance of complex real-world dynamics becomes evident. (shrink)

Recent methodological debates regarding the place of feasibility considerations in normative political theory are hindered for want of a rigorous model of the feasibility frontier. To address this shortfall, I present an analysis of feasibility that generalizes the economic concept of a production possibility frontier and then develop a rigorous model of the feasibility frontier using the familiar possible worlds technology. I then show that this model has significant methodological implications for political philosophy. On the Target View, a political ideal (...) presents a long-term goal for morally progressive reform efforts and, thus, serves as an important reference point for our specification of normative political principles. I use the model to show that we can- not reasonably expect that adopting political ideals as long-term reform objectives will guide us toward the realization of morally optimal feasible states of affairs. I conclude by proposing that political philosophers turn their attention to the analysis of actual social failures rather than political ideals. (shrink)

Within the framework of 'Temporalities and the Urban Fabric: Co-Producing Liminal Spaces in Transitional Epochs,' this rigorous examination unravels the multilayered nuances of temporality and its intimate relationship with urban spaces in times of transition. The research delineates the intricate interplay between public exhibitions, urban realms, and socio-political paradigms, particularly within the dynamic settings of the metropolitan entities of Houston and Amsterdam. These cities, as epitomes of temporal urban flux, become fertile grounds for exploring the ephemeral essence of liminal spaces (...) and their transformative manifestations. By weaving together diverse academic domains – from Design Computation and Fabrication to Urban Communities and Spatial Justice – this study underscores the symbiotic fusion of Augmented Reality (AR) and Gamification within the broader canvas of urban temporalities. Crucially, the research accentuates the transformative potential of Extended Reality (XR) in augmenting the theoretical and methodological contours of urban studies within these transitional epochs. (shrink)

Despite the recent proliferation of scientific, clinical, and narrative accounts of auditory verbal hallucinations, the phenomenology of voice hearing remains opaque and undertheorized. In this article, we outline an interdisciplinary approach to understanding hallucinatory experiences which seeks to demonstrate the value of the humanities and social sciences to advancing knowledge in clinical research and practice. We argue that an interdisciplinary approach to the phenomenology of AVH utilizes rigorous and context-appropriate methodologies to analyze a wider range of first-person accounts of AVH (...) at 3 contextual levels: cultural, social, and historical; experiential; and biographical. We go on to show that there are significant potential benefits for voice hearers, clinicians, and researchers. These include informing the development and refinement of subtypes of hallucinations within and across diagnostic categories; “front-loading” research in cognitive neuroscience; and suggesting new possibilities for therapeutic intervention. In conclusion, we argue that an interdisciplinary approach to the phenomenology of AVH can nourish the ethical core of scientific enquiry by challenging its interpretive paradigms, and offer voice hearers richer, potentially more empowering ways to make sense of their experiences. (shrink)