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.

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)

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 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)

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)

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)

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)

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)

Woke ideologues commandeered academia by invoking a trinity of buzzwords. Rallying around freedom, rigor, and merit, it is time for us non-woke to do the same.

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)

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)

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)

Theoretically rigorous approach to the key problems of Molinism.

Rigorous evaluations of the effects of vertical public health enterprises on the health systems of low-income countries usefully identify the public health and ethical costs of those initiatives. They reveal that such narrowly focused public health ventures undermine the efforts of those countries to establish and maintain adequately resourced and well-developed national health systems, including comprehensive primary care programs. This paper argues that the scope of assessments of vertical public health ventures should be broadened to include gender as an additional (...) axis of analysis. When members of socio-economically marginalized populations are sick with conditions that are not covered by fragmented and inadequate public health programs or disease-specific vertical public health schemes, their untreated illnesses add to the gendered familial caregiving responsibilities of the female members of their households. Those women and girls have to perform their ‘normal’ familial care work, work outside the home for pay, and take care of the unwell family members for whom the household cannot afford treatment. Given that women and girls from low-income households already shoulder a disproportionate amount of care work for their families, their health and life prospects are further affected by the amplification of their caregiving responsibilities. This paper argues that analyses of the impact of vertical public health initiatives should also track this gendered consequence of those enterprises because it is a crucial public health and ethical matter. (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)

The central topic of this essay consists into establishing a relation between two dimensions of formation: the conceptual process of creating philo- sophical toys - that is of reelaborating existing philosophical concepts, mainly deriving from the thought of Gilles Deleuze and Félix Guattari, in terms of their potential as ‘operative constructs' - and their parallel redeployment towards the specific problem of analyz- ing a recent transdisciplinary artwork. By means of this strategical shift, theory looses its character of explanation and illustration. (...) Philosophy as toy becomes rather the matter of evaluating the com- plexity of a specific artistic composition in terms of its aesthetic potential. It contributes towards developing meta- stable conditions of mutual resonance between heterogeneous modalities of creation. (shrink)

Clinical ethics consultants (CECs) are not moral authorities. Standardization of CECs’ professional role does not confer upon them moral authority. Certification of particular CECs does not confer upon them moral authority (nor does it reflect such authority). Or, so we will argue. This article offers a distinctly Orthodox Christian response to those who claim that CECs—or any other academically trained bioethicist—retain moral authority (i.e., an authority to know and recommend the right course of action). This article proceeds in three parts. (...) First, we discuss recent movements toward the certification of CECs in the United States, focusing primarily on proposals and programs put forth by the American Society for Humanities and Bioethics (ASBH). Second, we outline two secular reasons to be concerned about the relevant trends toward certification. For one thing, certification is currently being advanced via political dominance, rather than gaining authority by reliance on rigorous philosophical argument or reason. For another, the trends operate on the assumption that there exists a secular, content-full, canonical, morality. There is no such morality. Next, we argue that Orthodox Christians should resist the current trends toward certification of CECs. Specifically, we unpack ways in which the ASBH’s certification program (and those like it) conflict with Orthodox claims about moral authority and the moral life more generally. We conclude that Orthodox Christians should resist the current certification trends. (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)

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 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)

Gonzalo Rodriguez-Pereyra offers a fresh philosophical account of properties. How is it that two different things (such as two red roses) can share the same property (redness)? According to resemblance nominalism, things have their properties in virtue of resembling other things. This unfashionable view is championed with clarity and rigor.

A theoretically rigorous approach to the key problems of Molinism leads to a clear distinction between semantic and metaphysical problems. Answers to semantic problems do not provide answers to metaphysical problems that arise from the theory of middle knowledge. The so-called ‘grounding objection’ to Molinism raises a metaphysical problem. The most promising solution to it is a revised form of the traditional ‘essence solution’. Inspired by Leibniz’s idea of a ‘notio completa’ (complete concept), we propose a mathematical model of ‘possibilistic’ (...) (Molinist) complete concepts. They ground middle knowledge within the very being of the agents themselves. Molinist Complete Concepts can thus serve to reject consequence-style arguments against Molinism. They also allow the Molinist to safeguard a robustly libertarian notion of the ability to do otherwise. (shrink)

After a long hiatus, psychology and philosophy are returning to formal study of imagination. While excellent work is being done in the current environment, this article argues for a stronger thesis than usually adopted. Imagination is not just a peripheral feature of cognition or a domain for aesthetic research. It is instead the core operating system or cognitive capacity for humans and has epistemic and therapeutic functions that ground all our sense-making activities. A sketch of imagination as embodied cognition is (...) offered, followed by suggestions of how to organize imagination studies into a more rigorous science–humanities research area. (shrink)

In a rigorous systematic review, Dukhanin and colleagues categorize metrics and evaluative tools of the engagement of patient, public, consumer, and community in decision-making in healthcare institutions and systems. The review itself is ably done and the categorizations lead to a useful understanding of the necessary elements of engagement, and a suite of measures relevant to implementing engagement in systems. Nevertheless, the question remains whether the engagement of patient representatives in institutional or systemic deliberations will lead to improved clinical outcomes (...) or increased engagement of individual patients themselves in care. Attention to the conceptual foundations of patient engagement would help make this systematic review relevant to the clinical care of patients. (shrink)

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

'The arrow of time' refers to the curious asymmetry that distinguishes the future from the past. Reversing the Arrow of Time argues that there is an intimate link between the symmetries of 'time itself' and time reversal symmetry in physical theories, which has wide-ranging implications for both physics and its philosophy. This link helps to clarify how we can learn about the symmetries of our world, how to understand the relationship between symmetries and what is real, and how to overcome (...) pervasive illusions about the direction of time. Roberts explains the significance of time reversal in a way that intertwines physics and philosophy, to establish what the arrow of time means and how we can come to know it. This book is both mathematically and philosophically rigorous yet remains accessible to advanced undergraduates in physics and the philosophy of physics. This title is also available as Open Access on Cambridge Core. (shrink)

In this paper I present a precise version of Stalnaker's thesis and show that it is both consistent and predicts our intuitive judgments about the probabilities of conditionals. The thesis states that someone whose total evidence is E should have the same credence in the proposition expressed by 'if A then B' in a context where E is salient as they have conditional credence in the proposition B expresses given the proposition A expresses in that context. The thesis is formalised (...) rigorously and two models are provided that demonstrate that the new thesis is indeed tenable within a standard possible world semantics based on selection functions. Unlike the Stalnaker-Lewis semantics the selection functions cannot be understood in terms of similarity. A probabilistic account of selection is defended in its place. -/- I end the paper by suggesting that this approach overcomes some of the objections often leveled at accounts of indicatives based on the notion of similarity. (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)

Miranda Fricker's original presentation of Hermeneutical Injustice left open theoretical choice points leading to criticisms and subsequent clarifications with the resulting dialectic appearing largely verbal. The absence of perspicuous exposition of hallmarks of Hermeneutical Injustice might suggest scenarios exhibiting some – but not all – such hallmarks are within its purview when they are not. The lack of clear hallmarks of Hermeneutical Injustice, moreover, obscures both the extent to which Fricker's proposed remedy Hermeneutical Justice – roughly, virtuous communicative practices – (...) adequately addresses the injustice, and the accuracy of criticisms suggesting that Hermeneutical Justice is insufficient to the task. In what follows, after briefly defending necessary and sufficient conditions for what I take to be the best candidate interpretation of Hermeneutical Injustice, I build on recent work on moral responsibility to construct and defend a rigorous explication of Hermeneutical Justice. (shrink)

I propose an idealist ontology that makes sense of reality in a more parsimonious and empirically rigorous manner than mainstream physicalism, bottom-up panpsychism, and cosmopsychism. The proposed ontology also offers more explanatory power than these three alternatives, in that it does not fall prey to the hard problem of consciousness, the combination problem, or the decombination problem, respectively. It can be summarized as follows: there is only cosmic consciousness. We, as well as all other living organisms, are but dissociated alters (...) of cosmic consciousness, surrounded by its thoughts. The inanimate world we see around us is the extrinsic appearance of these thoughts. The living organisms we share the world with are the extrinsic appearances of other dissociated alters. (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)

Abstract: Accurate stock price prediction is essential for informed investment decisions and financial planning. In this research, we introduce an innovative approach to forecast stock prices using an Artificial Neural Network (ANN). Our dataset, consisting of 5582 samples and 6 features, including historical price data and technical indicators, was sourced from Yahoo Finance. The proposed ANN model, composed of four layers (1 input, 1 hidden, 1 output), underwent rigorous training and validation, yielding remarkable results with an accuracy of 99.84% and (...) an average error of 0.005. Additionally, we conducted a feature importance analysis, identifying the key drivers of stock price prediction, such as "High," "Low," "Open," "Volume"," and "Date." This study not only offers a highly accurate stock price prediction model but also contributes valuable insights into the influential factors affecting stock prices, enhancing the field of financial analysis and investment decision-making that are suitable for the task. (shrink)

The rise of experimental philosophy has placed metaphilosophical questions, particularly those concerning concepts, at the center of philosophical attention. X-phi offers empirically rigorous methods for identifying conceptual content, but what exactly it contributes towards evaluating conceptual content remains unclear. We show how x-phi complements Rudolf Carnap’s underappreciated methodology for concept determination, explication. This clarifies and extends x-phi’s positive philosophical import, and also exhibits explication’s broad appeal. But there is a potential problem: Carnap’s account of explication was limited to empirical and (...) logical concepts, but many concepts of interest to philosophers are essentially normative. With formal epistemology as a case study, we show how x-phi assisted explication can apply to normative domains. (shrink)

If there is an area of discourse in which disagreement is virtually absent, it is mathematics. After all, mathematicians justify their claims with deductive proofs: arguments that entail their conclusions. But is mathematics really exceptional in this respect? Looking at the history and practice of mathematics, we soon realize that it is not. First, deductive arguments must start somewhere. How should we choose the starting points (i.e., the axioms)? Second, mathematicians, like the rest of us, are fallible. Their ability to (...) recognize whether a putative proof is correct is not infallible. In most cases, disagreement over the correctness of a putative proof is, however, evanescent. Once an error is spotted and communicated, the disagreement disappears. But this is not always the case. Sometimes it is recalcitrant; that is, it persists over time. In order to zoom in on this type of disagreement and explain its very possibility, we focus on a single case study: a decades-long (1921-1949) controversy between Federigo Enriques and Francesco Severi, two prominent exponents of the Italian school of algebraic geometry. We suggest that the instability of the mathematical community to which they belonged can be explained by the gap between an abstract criterion of rigor and local criteria of acceptability. It is this instability that made the existence of recalcitrant disagreement over putative proofs possible. We do not condemn speculative mathematics but rather its pretense of being rigorous mathematics. In this respect, we show that the overly self-confident Severi and the more intuitive, visionary Enriques had a completely different attitude. (shrink)

Measuring the effectiveness of medical interventions faces three epistemological challenges: the choice of good measuring instruments, the use of appropriate analytic measures, and the use of a reliable method of extrapolating measures from an experimental context to a more general context. In practice each of these challenges contributes to overestimating the effectiveness of medical interventions. These challenges suggest the need for corrective normative principles. The instruments employed in clinical research should measure patient-relevant and disease-specific parameters, and should not be sensitive (...) to parameters that are only indirectly relevant. Effectiveness always should be measured and reported in absolute terms (using measures such as 'absolute risk reduction'), and only sometimes should effectiveness also be measured and reported in relative terms (using measures such as 'relative risk reduction')-employment of relative measures promotes an informal fallacy akin to the base-rate fallacy, which can be exploited to exaggerate claims of effectiveness. Finally, extrapolating from research settings to clinical settings should more rigorously take into account possible ways in which the intervention in question can fail to be effective in a target population. (shrink)

Far from being rigorously defined, the concept of species in a biologicalsense has suffered from imprecision since Charles Darwin. This is mainlydue to the absence of a definition that allows to combine within eachspecies the organisms that are considered part of it. The objective of thiswork is to show, on the one hand, the diversity of characterizations of theconcept of species as well as their respective problems and, on the other,the different sustainable ontological positions. As a consequence of theaforementioned imprecision, (...) the ethical consequences that this entails inthe debate about speciesism are analyzed. (shrink)

According to factive accounts of the norm of belief and decision-making, you should not believe or base decisions on a falsehood. Even when the evidence misleadingly suggests that a false proposition is true, you should not believe it or base decisions on it. Critics claim that factive accounts are counterintuitive and badly mischaracterize our ordinary practice of evaluating beliefs and decisions. This paper reports four experiments that rigorously test the critic’s accusations and the viability of factive accounts. The results undermine (...) the accusations and provide the best evidence yet of factive norms of belief and decision-making. The results also help discriminate between two leading candidates for a factive norm: truth and knowledge. Knowledge is the superior candidate. (shrink)

Mainstream teleosemantics is the view that mental representation should be understood in terms of biological functions, which, in turn, should be understood in terms of selection processes. One of the traditional criticisms of teleosemantics is the problem of novel contents: how can teleosemantics explain our ability to represent properties that are evolutionarily novel? In response, some have argued that by generalizing the notion of a selection process to include phenomena such as operant conditioning, and the neural selection that underlies it, (...) we can resolve this problem. Here, we do four things: we develop this suggestion in a rigorous way through a simple example, we draw on recent neurobiological research to support its empirical plausibility, we defend the move from a host of objections in the literature, and we sketch how the picture can be extended to help us think about more complex “conceptual” representations and not just perceptual ones. (shrink)

We chart how neuroscience and philosophy have together advanced our understanding of moral judgment with implications for when it goes well or poorly. The field initially focused on brain areas associated with reason versus emotion in the moral evaluations of sacrificial dilemmas. But new threads of research have studied a wider range of moral evaluations and how they relate to models of brain development and learning. By weaving these threads together, we are developing a better understanding of the neurobiology of (...) moral judgment in adulthood and to some extent in childhood and adolescence. Combined with rigorous evidence from psychology and careful philosophical analysis, neuroscientific evidence can even help shed light on the extent of moral knowledge and on ways to promote healthy moral development. (shrink)

Robert Sinclair’s *Quine, Conceptual Pragmatism, and the Analytic-Synthetic Distinction* persuasively argues that Quine’s epistemology was deeply influenced by C. I. Lewis’s pragmatism. Sinclair’s account raises the question why Quine himself frequently downplayed Lewis’s influence. Looking back, Quine has always said that Rudolf Carnap was his “greatest teacher” and that his 1933 meeting with the German philosopher was his “first experience of sustained intellectual engagement with anyone of an older generation” (1970, 41; 1985, 97-8, my emphasis). Quine’s autobiographies contain only a (...) handful of biographical references to Lewis and he regularly soft-pedaled the latter’s influence in private correspondence. In this note, I discuss some archival evidence that helps us better understand Quine’s reluctance to acknowledge Lewis’s influence. I contextualize the relation between Lewis and Quine and argue that the latter viewed his teacher as a retrograde force in modern epistemology, impeding the more rigorous approach that Carnap had been developing in Europe. Next, I briefly discuss Lewis’s contribution to the development of scientific philosophy in the United States and argue that Quine underestimated his teacher’s role in this process. In doing so, I hope to show that Quine’s zealous commitment to Carnap’s approach negatively affected his assessment of Lewis’s influence, thereby supplementing Sinclair’s praiseworthy reconstruction with an explanation of why Quine himself underestimated Lewis’s role. (shrink)

Defenders of deontological constraints in normative ethics face a challenge: how should an agent decide what to do when she is uncertain whether some course of action would violate a constraint? The most common response to this challenge has been to defend a threshold principle on which it is subjectively permissible to act iff the agent's credence that her action would be constraint-violating is below some threshold t. But the threshold approach seems arbitrary and unmotivated: what would possibly determine where (...) the threshold should be set, and why should there be any precise threshold at all? Threshold views also seem to violate ought agglomeration, since a pair of actions each of which is below the threshold for acceptable moral risk can, in combination, exceed that threshold. In this paper, I argue that stochastic dominance reasoning can vindicate and lend rigor to the threshold approach: given characteristically deontological assumptions about the moral value of acts, it turns out that morally safe options will stochastically dominate morally risky alternatives when and only when the likelihood that the risky option violates a moral constraint is greater than some precisely definable threshold (in the simplest case, .5). I also show how, in combination with the observation that deontological moral evaluation is relativized to particular choice situations, this approach can overcome the agglomeration problem. This allows the deontologist to give a precise and well-motivated response to the problem of uncertainty. (shrink)

Skeptical theism is a popular response to arguments from evil. Many hold that it undermines a key inference often used by such arguments. However, the case for skeptical theism is often kept at an intuitive level: no one has offered an explicit argument for the truth of skeptical theism. In this article, I aim to remedy this situation: I construct an explicit, rigorous argument for the truth of skeptical theism.

Plato uses the most rigorous logic, stories, and analogies in an effort to show what appears to be a mystical vision. Indeed, this is affirmed if we consider his aim of turning the cave dweller towards the light. In essence, as we have seen, this is a turning inward--or the self-reflecting on itself, which ultimately leads to a subject-to-object merging. It is through the cognitive progression, however, from image, to belief, understanding and knowledge that enlightenment is achieved. This, we have (...) seen, corresponds to mystical experiences. Why is this occurring? If we follow Plato’s procession of knowledge, it follows logically that this must occur. The true nature of self (at the lower levels of the hierarchy) cannot be perceived unless directly perceived at the level of forms--where images dissolve. If we examine the dialogues closely, I believe clues can be found that point to the mystical experience. I propose that the merging into one with regard to the tripartite soul--with each component becoming aligned with the rational--which is really a way of “purifying us from the defilements of the passions…”as well as Socrates’ refutation of opinions or belief to find universals are both evidence of a synoptic perspective characteristic of mystics who have achieved a mystical experience. (shrink)