Paul Horwich (1990) once suggested restricting the T-Schema to the maximally consistent set of its instances. But Vann McGee (1992) proved that there are multiple incompatible such sets, none of which, given minimal assumptions, is recursively axiomatizable. The analogous view for set theory---that Naïve Comprehension should be restricted according to consistency maxims---has recently been defended by Laurence Goldstein (2006; 2013). It can be traced back to W.V.O. Quine(1951), who held that Naïve Comprehension embodies the only really intuitive conception of (...) set and should be restricted as little as possible. The view might even have been held by Ernst Zermelo (1908), who,according to Penelope Maddy (1988), subscribed to a ‘one step back from disaster’ rule of thumb: if a natural principle leads to contra-diction, the principle should be weakened just enough to block the contradiction. We prove a generalization of McGee’s Theorem, anduse it to show that the situation for set theory is the same as that for truth: there are multiple incompatible sets of instances of Naïve Comprehension, none of which, given minimal assumptions, is recursively axiomatizable. This shows that the view adumbrated by Goldstein, Quine and perhaps Zermelo is untenable. (shrink)

Discussion of new axioms for set theory has often focused on conceptions of maximality, and how these might relate to the iterative conception of set. This paper provides critical appraisal of how certain maximality axioms behave on different conceptions of ontology concerning the iterative conception. In particular, we argue that forms of multiversism (the view that any universe of a certain kind can be extended) and actualism (the view that there are universes that cannot be extended in particular ways) face (...) complementary problems. The latter view is unable to use maximality axioms that make use of extensions, where the former has to contend with the existence of extensions violating maximality axioms. An analysis of two kinds of multiversism, a Zermelian form and Skolemite form, leads to the conclusion that the kind of maximality captured by an axiom differs substantially according to background ontology. (shrink)

In this paper, I confront Parfit’s Mixed Maxims Objection. I argue that recent attempts to respond to this objection fail, and I argue that their failure is compounded by the failure of recent attempts to show how the Formula of Universal Law can be used to demarcate the category of obligatory maxims. I then set out my own response to the objection, drawing on remarks from Kant’s Metaphysics of Morals for inspiration and developing a novel account of how the Formula (...) of Universal Law can be employed to determine the deontic status of action tokens, action types, and maxims. (shrink)

It is standard in set theory to assume that Cantor's Theorem establishes that the continuum is an uncountable set. A challenge for this position comes from the observation that through forcing one can collapse any cardinal to the countable and that the continuum can be made arbitrarily large. In this paper, we present a different take on the relationship between Cantor's Theorem and extensions of universes, arguing that they can be seen as showing that every set is countable and that (...) the continuum is a proper class. We examine several principles based on maximality considerations in this framework, and show how some (namely Ordinal Inner Model Hypotheses) enable us to incorporate standard set theories (including ZFC with large cardinals added). We conclude that the systems considered raise questions concerning the foundational purposes of set theory. (shrink)

A Cantorian argument that there is no set of all truths. There is, for the same reason, no possible world as a maximal set of propositions. And omniscience is logically impossible.

This work presents a novel formulation of quantum mechanics as the solution to an entropy maximization problem constrained by empirical measurement outcomes. By treating the complete set of possible measurement outcomes as an optimization constraint, our entropy maximization problem derives the axioms of quantum mechanics as theorems, demonstrating that the theory's mathematical structure is the least biased probability measure consistent with the observed data. This approach reduces the foundation of quantum mechanics to a single axiom, the measurement constraint, from which (...) the full theory emerges through entropy maximization. In contrast to the conventional axiomatic approach, the framework grounds the axioms directly in empirical data, substantially restricting the interpretational landscape ruling out interpretations inconsistent with this empirical foundation. (shrink)

I want to distinguish between maxims at three levels of abstraction. At the first level are what I shall call individual maxims, or i‐maxims: maxim tokens as adopted by particular rational beings. At the second level are abstract maxims, or a‐maxims: abstract principles distinct from any individual who adopts them. At the third level are maxim kinds, or k‐maxims: sets of various action‐guiding principles that are grouped on the basis of their content. In this paper, I argue for the (...) thesis that i‐maxims are the locus of assessment in Kant's ethics. (shrink)

Proposals for allocating scarce lifesaving resources in the face of the Covid-19 pandemic have aligned in some ways and conflicted in others. This paper attempts a kind of priority setting in addressing these conflicts. In the first part, we identify points on which we do not believe that reasonable people should differ—even if they do. These are (i) the inadequacy of traditional clinical ethics to address priority-setting in a pandemic; (ii) the relevance of saving lives; (iii) the flaws of first-come, (...) first-served allocation; (iv) the relevance of post-episode survival; (v) the difference between age and other factors that affect life-expectancy; and (vi) the need to avoid quality-of-life judgments. In the second part, we lay out some positions on which reasonable people can and do differ. These include (i) conflicts between maximizing benefits and priority to the worst off; (ii) role-based priority; and (iii) whether patients’ existing lifesaving resources should be subject to redistribution. (shrink)

Recently theorists have demonstrated a growing interest in the ethical aspects of resource allocation in international non-governmental humanitarian, development and human rights organizations (INGOs). This article provides an analysis of Thomas Pogge's proposal for how international human rights organizations ought to choose which projects to fund. Pogge's allocation principle states that an INGO should govern its decision making about candidate projects by such rules and procedures as are expected to maximize its long-run cost-effectiveness, defined as the expected aggregate moral value (...) of the projects it undertakes divided by the expected aggregate cost of these projects? I critique Pogge's argument on two fronts: (1) I demonstrate that his view is problematic on his own terms, even if we accept the cost-effectiveness framework he employs. (2) I take issue with his overall approach because it generates results which can undermine the integrity of INGOs. Further, his approach mis-characterizes the nature of INGOs, and this mistake is at the root of his problematic view of INGO priority-setting. Ultimately, I argue for a conception of INGOs in which they are understood as ?organizations of principle?, in the sense that they are independent moral agents and so should be permitted a fairly wide sphere of autonomy within reasonable moral constraints. (shrink)

Merging of opinions results underwrite Bayesian rejoinders to complaints about the subjective nature of personal probability. Such results establish that sufficiently similar priors achieve consensus in the long run when fed the same increasing stream of evidence. Initial subjectivity, the line goes, is of mere transient significance, giving way to intersubjective agreement eventually. Here, we establish a merging result for sets of probability measures that are updated by Jeffrey conditioning. This generalizes a number of different merging results in the (...) literature. We also show that such sets converge to a shared, maximally informed opinion. Convergence to a maximally informed opinion is a (weak) Jeffrey conditioning analogue of Bayesian “convergence to the truth” for conditional probabilities. Finally, we demonstrate the philosophical significance of our study by detailing applications to the topics of dynamic coherence, imprecise probabilities, and probabilistic opinion pooling. (shrink)

The principle of maximal entropy (further abbreviated as “MaxEnt”) can be founded on the formal mechanism, in which future transforms into past by the mediation of present. This allows of MaxEnt to be investigated by the theory of quantum information. MaxEnt can be considered as an inductive analog or generalization of “Occam’s razor”. It depends crucially on choice and thus on information just as all inductive methods of reasoning. The essence shared by Occam’s razor and MaxEnt is for the (...) relevant data known till now to be postulated as an enough fundament of conclusion. That axiom is the kind of choice grounding both principles. Popper’s falsifiability (1935) can be discussed as a complement to them: That axiom (or axiom scheme) is always sufficient but never necessary condition of conclusion therefore postulating the choice in the base of MaxEnt. Furthermore, the abstraction axiom (or axiom scheme) relevant to set theory (e.g. the axiom scheme of specification in ZFC) involves choice analogically. (shrink)

This chapter argues that rather than viewing transparency as a right, we should regard it as a finite resource whose allocation involves tradeoffs. It then argues that those tradeoffs should be resolved by using a multi-principle approach to distributive justice. The relevant principles include maximizing welfare, maximizing autonomy, and giving priority to the worst off. Finally, it examines some of the implications for law of recognizing the tradeoffs presented by transparency proposals.

A central area of current philosophical debate in the foundations of mathematics concerns whether or not there is a single, maximal, universe of set theory. Universists maintain that there is such a universe, while Multiversists argue that there are many universes, no one of which is ontologically privileged. Often forcing constructions that add subsets to models are cited as evidence in favour of the latter. This paper informs this debate by analysing ways the Universist might interpret this discourse that (...) seems to necessitate the addition of subsets to V. We argue that despite the prima facie incoherence of such talk for the Universist, she nonetheless has reason to try and provide interpretation of this discourse. We analyse extant interpretations of such talk, and analyse various tradeoffs in naturality that might be made. We conclude that the Universist has promising options for interpreting different forcing constructions. (shrink)

Jeremy Waldron, among others, has forcefully argued that public hate speech assaults the dignity of its targets. Without denying this claim, I contend that it fails to establish that bans, rather than counterspeech, are the appropriate response. By articulating a more refined understanding of counterspeech, I suggest that counterspeech constitutes a better way of blocking hate speech’s dignitarian harm. In turn, I address two objections: according to the first, which draws on contemporary philosophy of language, counterspeech does not block enough (...) hate speech; according to the second, counterspeech blocks too much speech. Although these objections should qualify our optimism regarding counterspeech, I demonstrate that each can be turned, with even greater force, against hate speech bans. (shrink)

The purpose of this paper is to show that the mathematics of quantum mechanics is the mathematics of set partitions linearized to vector spaces, particularly in Hilbert spaces. That is, the math of QM is the Hilbert space version of the math to describe objective indefiniteness that at the set level is the math of partitions. The key analytical concepts are definiteness versus indefiniteness, distinctions versus indistinctions, and distinguishability versus indistinguishability. The key machinery to go from indefinite to more definite (...) states is the partition join operation at the set level that prefigures at the quantum level projective measurement as well as the formation of maximally-definite state descriptions by Dirac’s Complete Sets of Commuting Operators. This development is measured quantitatively by logical entropy at the set level and by quantum logical entropy at the quantum level. This follow-the-math approach supports the Literal Interpretation of QM—as advocated by Abner Shimony among others which sees a reality of objective indefiniteness that is quite different from the common sense and classical view of reality as being “definite all the way down”. (shrink)

An influential critique of anger holds that anger comes at an important epistemic cost. In particular, feeling angry typically makes risk less visible to us. This is anger’s ‘red mist.’ These epistemic costs, critics suggest, arguably outweigh the epistemic benefits commonly ascribed to anger. This essay argues that the epistemic critique of anger is importantly misleading. This is not because it underestimates anger’s epistemic benefits, but rather because it overlooks the fact that anger’s red mist performs a crucial moral function. (...) By concealing risk, the red mist helps protect the dignity and self-respect of those who live under severe and unchosen risk. This function is vitally important in non-ideal circumstances, where many are unjustly subjected to dignity-impairing risk. And it is irreplaceable, in that it cannot readily be performed by other political emotions, such as hope. Beyond providing a novel defence of anger, this argument has a broader upshot. Anger’s red mist reveals that ignorance is not always problematic in politics. Accordingly, it should not be treated—as has standardly been the case—as an unmitigated political evil. In the first instance, our efforts are better spent ascertaining when ignorance is a problem, and when, instead, it performs a felicitous function. (shrink)

Public opinion research has shown that voters accept many falsehoods about politics. This observation is widely considered troubling for democracy—and especially participatory ideals of democracy. I argue that this influential narrative is nevertheless flawed, because it misunderstands the nature of political understanding. Drawing on philosophical examinations of scientific modelling, I demonstrate that accepting falsehoods within one’s model of political reality is compatible with—and indeed can positively enhance—one’s understanding of that reality. Thus, the observation that voters accept many political falsehoods does (...) not necessarily establish that they lack political understanding. I then address three worries: that voters cannot generally engage in such political modelling; that political modelling obscures facts that are crucial to political understanding; and that successful political modelling would require knowing that one’s model contains falsehoods. My responses reveal how, going forward, we should measure political ignorance; and they highlight the standing importance of participatory democracy. (shrink)

How promising is Bitcoin as a currency? This paper discusses four claims on the advantages of Bitcoin: a more stable currency than state-backed ones; a secure and efficient payment system; a credible alternative to the central management of money; and a better protection of transaction privacy. We discuss these arguments by relating them to their philosophical roots in libertarian and neoliberal theories, and assess whether Bitcoin can effectively meet these expectations. We conclude that despite its advocates’ enthusiasm, there are good (...) reasons to doubt that Bitcoin can fulfill its promises and act as a functioning currency, rather than as a mere speculative asset. (shrink)

Contemporary public discourse is saturated with speech that vilifies and incites hatred or violence against vulnerable groups. The term “hate speech” has emerged in legal circles and in ordinary language to refer to these communicative acts. But legal theorists and philosophers disagree over how to define this term. This paper makes the case for, and subsequently develops, the first corpus-based analysis of the ordinary meaning of “hate speech.” We begin by demonstrating that key interpretive and moral disputes surrounding hate speech (...) laws—in particular, surrounding their compatibility with the rule of law, democracy, and free speech—depend crucially on the ordinary meaning of “hate speech.” Next, we argue, drawing on recent developments in legal philosophy, that corpus linguistics constitutes a distinctively promising tool for ascertaining the ordinary meaning of “hate speech.” Finally, we offer a proof of concept, by outlining, and analyzing the interpretive and moral implications of, the first such study. (shrink)

The proliferation of conspiracy theories poses a significant threat to democratic decision-making. To counter this threat, many political theorists advocate countering conspiracy theories with ‘more speech’ (or ‘counterspeech’). Yet conspiracy theories are notoriously resistant to counterspeech. This article aims to conceptualise and defend a novel form of counterspeech – narrative counterspeech – that is singularly well-placed to overcome this resistance. My argument proceeds in three steps. First, I argue that conspiracy theories pose a special problem for counterspeech for three interconnected (...) reasons relating to salience, emotion and internal coherence. Drawing on recent work in social epistemology, philosophy of emotion and cognitive science, I then demonstrate that narrative forms of counterspeech constitute an apt response to this diagnosis. Finally, I forestall two objections: the first questions the likely effectiveness of narrative counterspeech; the second insists that, even if it were effective, it would remain unacceptably manipulative. Neither objection, I contend, is ultimately compelling. (shrink)

Does intellectual property satisfy the requirements of the Lockean proviso, that the appropriator leave “enough and as good” or that he at least not “deprive others”? If an author's appropriation of a work he has just created is analogous to a drinker “taking a good draught” in the flow of an inexhaustible river, or to someone magically “causing springs of water to flow in the desert,” how could it not satisfy the Lockean proviso?

Counterspeech is communication that tries to counteract potential harm brought about by other speech. Theoretical interest in counterspeech partly derives from a libertarian ideal – as captured in the claim that the solution to bad speech is more speech – and partly from a recognition that well-meaning attempts to counteract harm through speech can easily misfire or backfire. Here we survey recent work on the question of what makes counterspeech effective at remedying or preventing harm, in those cases where it (...) is effective, as well as work investigating when and why there is a duty to engage in counterspeech. We suggest that the most fruitful area for philosophical inquiry on this topic, currently, relates to the questions about efficacy. Specifically, we argue that there is a need for better frameworks for conceptualizing the efficacy of counterspeech. Philosophers have collaborative work to do, alongside social scientists, in developing these frameworks. (shrink)

Yefremov’s personal characteristics exemplify the characteristic features of the Ukrainian revolution. He was an argumentative, pugnacious man, and the revolution was characterized by infighting. He was an institution builder, and that’s a key element of the Ukrainian revolution. He was ideologically an advocate of Ukrainian identity (sooner than social rights or state building) and that too was a feature of the Ukrainian revolution. His diaries and ego writing offer a variety of evidence of these aspects of his personality.

Do laypeople think that moral responsibility is compatible with determinism? Recently, philosophers and psychologists trying to answer this question have found contradictory results: while some experiments reveal people to have compatibilist intuitions, others suggest that people could in fact be incompatibilist. To account for this contradictory answers, Nichols and Knobe (2007) have advanced a ‘performance error model’ according to which people are genuine incompatibilist that are sometimes biased to give compatibilist answers by emotional reactions. To test for this hypothesis, we (...) investigated intuitions about determinism and moral responsibility in patients suffering from behavioural frontotemporal dementia. Patients suffering from bvFTD have impoverished emotional reaction. Thus, the ‘performance error model’ should predict that bvFTD patients will give less compatibilist answers. However, we found that bvFTD patients give answers quite similar to subjects in control group and were mostly compatibilist. Thus, we conclude that the ‘performance error model’ should be abandoned in favour of other available model that best fit our data. (shrink)

This paper analyses three centuries of developing German-language philosophy journals, from the first journals published in 1665 to those from the first decade of post-WWII recovery. Relying upon two bibliographies of philosophical journals collected in the 1970s, one by Joachim Kirchner and one by Wolfram Hogrebe, Rudolf Kamp, and Gert König, we attained a dataset of 607 journals. To analyse the population of periodicals, we identified three key components: the longevity of each journal and the growth rate and the continuity (...) of the body of the journal population. The most puzzling finding is that there was a rapid growth in the number of journals at the end of the eighteenth century followed by a long decline in numbers that lasted almost a century. This paper analyses the structure of the boom in philosophical periodicals after 1888, followed by the effects of both World Wars, and identifies the communication crisis that occurred at the height of the Weimar Republic. (shrink)

A thought experiment demonstrates that physicalism about consciousness entails a para- doxical duplication of physical information. Moreover, objective existence acquires the status of a physical property. To avoid this paradox, one requires a concept of objectivity in which individuation is finite and incomplete. Finite individuation requires objective uncertainty and is thus corroborated by the contemporary sciences. Finite individuation and objective uncer- tainty prevent existence from becoming a physical property, thus defeating physicalism about consciousness and resolving the paradox.

The modern university and the academic profession itself are facing new challenges: First, the increasing complexity of labor markets and globalization are undermining the structure of the academic profession, and secondly, the rise in cost of university research calls into question the autonomy of the university. The internationalization of the academic labor market encourages rethinking the structure of academic professions that have historically been focused on national (regional) contexts. The university is too expensive for the state and/or for students. One (...) way to preserve the autonomy of the university is to offer society, the state, and businesses a wide range of services. This study seeks to answer the following questions: Can bureaucratic (self-)management effectively regulate the growing body of the university? Is it necessary to relinquish part of the university’s autonomy to a hired manager? Can “soft managerialism” and new economic instruments help unleash the modern university’s potential for society and sustain its autonomy? (shrink)

Two-step proportionality-balancing [TSPB] has become the standard method for human and constitutional rights decision-making. The first step consists in determining whether a rights-provision has been infringed/limited; if the answer to that first question is positive, the second step consists in determining whether the infringement/limit is reasonable or justified according to a proportionality analysis. TSPB has regularly been the target of some criticism. Critiques have argued that both its ‘two-step’ and ‘proportionality’ elements distort reality by promoting a false picture of rights (...) and constitutional decision-making. This would cause negative moral consequences. This article seeks to defend TSPB against these criticisms and to depict it in a more appropriate and favourable light. First, it is argued that both aspects of TSPB do not have the dire moral consequences that opponents suggest they have. Second, it is argued that TSPB, deploying notions such as burdens, presumptions and prima facie/defeasible propositions, constitutes a valuable framework for public argumentation and authoritative decision-making. (shrink)

Abstract. Death seems to be a permanent event, but there is no actual proof of its irreversibility. Here we list all known ways to resurrect the dead that do not contradict our current scientific understanding of the world. While no method is currently possible, many of those listed here may become feasible with future technological development, and it may even be possible to act now to increase their probability. The most well-known such approach to technological resurrection is cryonics. Another method (...) is indirect mind uploading, or digital immortality, namely the preservation of data about a person to allow for future reconstruction by powerful AI. More speculative ways to immortality include combinations of future superintelligence on a galactic scale, which could use simulation to resurrect all possible people, and new physical laws, which may include time-travel or obtaining information from the past. Acausal trade with parallel worlds could help combine random resurrection and reconstruction based on known data without loss of share of worlds where I exist (known as existence measure). Quantum immortality could help to increase the probability of success for cryonics and digital immortality. There many possible approaches to technological resurrection and thus if large-scale future technological development occurs, some form of resurrection is inevitable. (shrink)

In the last decade Open Science principles, such as Open Access, study preregistration, use of preprints, making available data and code, and open peer review, have been successfully advocated for and are being slowly adopted in many different research communities. In response to the COVID-19 pandemic many publishers and researchers have sped up their adoption of some of these Open Science practices, sometimes embracing them fully and sometimes partially or in a sub-optimal manner. In this article, we express concerns about (...) the violation of some of the Open Science principles and its potential impact on the quality of research output. We provide evidence of the misuses of these principles at different stages of the scientific process. We call for a wider adoption of Open Science practices in the hope that this work will encourage a broader endorsement of Open Science principles and serve as a reminder that science should always be a rigorous process, reliable and transparent, especially in the context of a pandemic where research findings are being translated into practice even more rapidly. (shrink)

Allen s has proposed a new approach to possible worlds, designed explicitly to overcome Cantorian difficulties for possible worlds construed as maximal consistent set of propositions. I emphasize some of the distinctive features of Hazenworlds, some of their weaknesses, and some further Cantorian problems for worlds against which they seem powerless.

The Hyperuniverse Programme, introduced in Arrigoni and Friedman (2013), fosters the search for new set-theoretic axioms. In this paper, we present the procedure envisaged by the programme to find new axioms and the conceptual framework behind it. The procedure comes in several steps. Intrinsically motivated axioms are those statements which are suggested by the standard concept of set, i.e. the `maximal iterative concept', and the programme identi fies higher-order statements motivated by the maximal iterative concept. The satisfaction of (...) these statements (H-axioms) in countable transitive models, the collection of which constitutes the `hyperuniverse' (H), has remarkable 1st-order consequences, some of which we review in section 5. (shrink)

Let's suppose you think that there are no uncountable sets. Have you adopted a restrictive position? It is certainly tempting to say yes---you've prohibited the existence of certain kinds of large set. This paper argues that this intuition can be challenged. Instead, I argue that there are some considerations based on a formal notion of restrictiveness which suggest that it is restrictive to hold that there are uncountable sets.

The independence phenomenon in set theory, while pervasive, can be partially addressed through the use of large cardinal axioms. A commonly assumed idea is that large cardinal axioms are species of maximality principles. In this paper, I argue that whether or not large cardinal axioms count as maximality principles depends on prior commitments concerning the richness of the subset forming operation. In particular I argue that there is a conception of maximality through absoluteness, on which large cardinal axioms are restrictive. (...) I argue, however, that large cardinals are still important axioms of set theory and can play many of their usual foundational roles. (shrink)

A central area of current philosophical debate in the foundations of mathematics concerns whether or not there is a single, maximal, universe of set theory. Universists maintain that there is such a universe, while Multiversists argue that there are many universes, no one of which is ontologically privileged. Often model-theoretic constructions that add sets to models are cited as evidence in favour of the latter. This paper informs this debate by developing a way for a Universist to interpret (...) talk that seems to necessitate the addition of sets to V. We argue that, despite the prima facie incoherence of such talk for the Universist, she nonetheless has reason to try and provide interpretation of this discourse. We present a method of interpreting extension-talk (V-logic), and show how it captures satisfaction in `ideal' outer models and relates to impredicative class theories. We provide some reasons to regard the technique as philosophically virtuous, and argue that it opens new doors to philosophical and mathematical discussions for the Universist. (shrink)

Set aside fanciful doomsday speculations about AI. Even lower-level AIs, while otherwise friendly and providing us a universal basic income, would be able to do all our jobs. Also, we would over-rely upon AI assistants even in our personal lives. Thus, John Danaher argues that a human crisis of moral passivity would result However, I argue firstly that if AIs are posited to lack the potential to become unfriendly, they may not be intelligent enough to replace us in all our (...) jobs. If instead they are intelligent enough to replace us, the risk they become unfriendly increases, given that they would not need us and humans would just compete for valuable resources. Their hostility will not promote our moral passivity. Secondly, the use of AI assistants in our personal lives will become a problem only if we rely on them for almost all our decision-making and motivation. But such a (maximally) pervasive level of dependence raises the question of whether humans would accept it, and consequently whether the crisis of passivity will arise. (shrink)

“Probably Peirce’s best-known works are the first two articles in a series of six that originally were collectively entitled Illustrations of the Logic of Science and published in Popular Science Monthly from November 1877 through August 1878. The first is entitled ‘The Fixation of Belief’ and the second is entitled ‘How to Make Our Ideas Clear.’ In the first of these papers Peirce defended, in a manner consistent with not accepting naive realism, the superiority of the scientific method over other (...) methods of overcoming doubt and ‘fixing belief.’” — Robert Burch, “Charles Sanders Peirce,” entry in the Stanford Encyclopedia of Philosophy (2021 revision) -/- “Pragmatist epistemologies often explore how we can carry out inquiries in a self-controlled and fruitful way. (Where much analytic epistemology centres around the concept of knowledge, considered as an idealised end-point of human thought, pragmatist epistemology centres around the concept of inquiry, considered as the process of knowledge-seeking and how we can improve it.) So pragmatists often provide rich accounts of the capacities or virtues that we must possess in order to inquire well, and the rules or guiding principles that we should adopt. A canonical account is Peirce’s classic early paper ‘The Fixation of Belief‘. Here Peirce states that inquiry is a struggle to replace doubt with “settled belief“, and that the only method of inquiry that can make sense of the fact that at least some of us are disturbed by inconsistent beliefs, and will subsequently reflect upon which methods of fixing belief are correct is the Method of Science, which draws on the Pragmatic Maxim described above. This contrasts with three other methods of fixing belief: i) refusing to consider evidence contrary to one’s favored beliefs (the Method of Tenacity), ii) accepting an institution’s dictates (the Method of Authority), iii) developing the most rationally coherent or elegant-seeming belief-set (the A Priori Method).“ — Catherine Legg, “Pragmatism,” entry in the Stanford Encyclopedia of Philosophy (2021 revision). (shrink)

Jakob Friedrich Fries (1773-1843): A Philosophy of the Exact Sciences -/- Shortened version of the article of the same name in: Tabula Rasa. Jenenser magazine for critical thinking. 6th of November 1994 edition -/- 1. Biography -/- Jakob Friedrich Fries was born on the 23rd of August, 1773 in Barby on the Elbe. Because Fries' father had little time, on account of his journeying, he gave up both his sons, of whom Jakob Friedrich was the elder, to the Herrnhut Teaching (...) Institution in Niesky in 1778. Fries attended the theological seminar in Niesky in autumn 1792, which lasted for three years. There he (secretly) began to study Kant. The reading of Kant's works led Fries, for the first time, to a deep philosophical satisfaction. His enthusiasm for Kant is to be understood against the background that a considerable measure of Kant's philosophy is based on a firm foundation of what happens in an analogous and similar manner in mathematics. -/- During this period he also read Heinrich Jacobi's novels, as well as works of the awakening classic German literature; in particular Friedrich Schiller's works. In 1795, Fries arrived at Leipzig University to study law. During his time in Leipzig he became acquainted with Fichte's philosophy. In autumn of the same year he moved to Jena to hear Fichte at first hand, but was soon disappointed. -/- During his first sojourn in Jenaer (1796), Fries got to know the chemist A. N. Scherer who was very influenced by the work of the chemist A. L. Lavoisier. Fries discovered, at Scherer's suggestion, the law of stoichiometric composition. Because he felt that his work still need some time before completion, he withdrew as a private tutor to Zofingen (in Switzerland). There Fries worked on his main critical work, and studied Newton's "Philosophiae naturalis principia mathematica". He remained a lifelong admirer of Newton, whom he praised as a perfectionist of astronomy. Fries saw the final aim of his mathematical natural philosophy in the union of Newton's Principia with Kant's philosophy. -/- With the aim of qualifying as a lecturer, he returned to Jena in 1800. Now Fries was known from his independent writings, such as "Reinhold, Fichte and Schelling" (1st edition in 1803), and "Systems of Philosophy as an Evident Science" (1804). The relationship between G. W. F. Hegel and Fries did not develop favourably. Hegel speaks of "the leader of the superficial army", and at other places he expresses: "he is an extremely narrow-minded bragger". On the other hand, Fries also has an unfavourable take on Hegel. He writes of the "Redundancy of the Hegelistic dialectic" (1828). In his History of Philosophy (1837/40) he writes of Hegel, amongst other things: "Your way of philosophising seems just to give expression to nonsense in the shortest possible way". In this work, Fries appears to argue with Hegel in an objective manner, and expresses a positive attitude to his work. -/- In 1805, Fries was appointed professor for philosophy in Heidelberg. In his time spent in Heidelberg, he married Caroline Erdmann. He also sealed his friendships with W. M. L. de Wette and F. H. Jacobi. Jacobi was amongst the contemporaries who most impressed Fries during this period. In Heidelberg, Fries wrote, amongst other things, his three-volume main work New Critique of Reason (1807). -/- In 1816 Fries returned to Jena. When in 1817 the Wartburg festival took place, Fries was among the guests, and made a small speech. 1819 was the so-called "Great Year" for Fries: His wife Caroline died, and Karl Sand, a member of a student fraternity, and one of Fries' former students stabbed the author August von Kotzebue to death. Fries was punished with a philosophy teaching ban but still received a professorship for physics and mathematics. Only after a period of years, and under restrictions, he was again allowed to read philosophy. From now on, Fries was excluded from political influence. The rest of his life he devoted himself once again to philosophical and natural studies. During this period, he wrote "Mathematical Natural Philosophy" (1822) and the "History of Philosophy" (1837/40). -/- Fries suffered from a stroke on New Year's Day 1843, and a second stroke, on the 10th of August 1843 ended his life. -/- 2. Fries' Work Fries left an extensive body of work. A look at the subject areas he worked on makes us aware of the universality of his thinking. Amongst these subjects are: Psychic anthropology, psychology, pure philosophy, logic, metaphysics, ethics, politics, religious philosophy, aesthetics, natural philosophy, mathematics, physics and medical subjects, to which, e.g., the text "Regarding the optical centre in the eye together with general remarks about the theory of seeing" (1839) bear witness. With popular philosophical writings like the novel "Julius and Evagoras" (1822), or the arabesque "Longing, and a Trip to the Middle of Nowhere" (1820), he tried to make his philosophy accessible to a broader public. Anthropological considerations are shown in the methodical basis of his philosophy, and to this end, he provides the following didactic instruction for the study of his work: "If somebody wishes to study philosophy on the basis of this guide, I would recommend that after studying natural philosophy, a strict study of logic should follow in order to peruse metaphysics and its applied teachings more rapidly, followed by a strict study of criticism, followed once again by a return to an even closer study of metaphysics and its applied teachings." -/- 3. Continuation of Fries' work through the Friesian School -/- Fries' ideas found general acceptance amongst scientists and mathematicians. A large part of the followers of the "Fries School of Thought" had a scientific or mathematical background. Amongst them were biologist Matthias Jakob Schleiden, mathematics and science specialist philosopher Ernst Friedrich Apelt, the zoologist Oscar Schmidt, and the mathematician Oscar Xavier Schlömilch. Between the years 1847 and 1849, the treatises of the "Fries School of Thought", with which the publishers aimed to pursue philosophy according to the model of the natural sciences appeared. In the Kant-Fries philosophy, they saw the realisation of this ideal. The history of the "New Fries School of Thought" began in 1903. It was in this year that the philosopher Leonard Nelson gathered together a small discussion circle in Goettingen. Amongst the founding members of this circle were: A. Rüstow, C. Brinkmann and H. Goesch. In 1904 L. Nelson, A. Rüstow, H. Goesch and the student W. Mecklenburg travelled to Thuringia to find the missing Fries writings. In the same year, G. Hessenberg, K. Kaiser and Nelson published the first pamphlet from their first volume of the "Treatises of the Fries School of Thought, New Edition". -/- The school set out with the aim of searching for the missing Fries' texts, and re-publishing them with a view to re-opening discussion of Fries' brand of philosophy. The members of the circle met regularly for discussions. Additionally, larger conferences took place, mostly during the holidays. Featuring as speakers were: Otto Apelt, Otto Berg, Paul Bernays, G. Fraenkel, K. Grelling, G. Hessenberg, A. Kronfeld, O. Meyerhof, L. Nelson and R. Otto. On the 1st of March 1913, the Jakob-Friedrich-Fries society was founded. Whilst the Fries' school of thought dealt in continuum with the advancement of the Kant-Fries philosophy, the members of the Jakob-Friedrich-Fries society's main task was the dissemination of the Fries' school publications. In May/June, 1914, the organisations took part in their last common conference before the gulf created by the outbreak of the First World War. Several members died during the war. Others returned disabled. The next conference took place in 1919. A second conference followed in 1921. Nevertheless, such intensive work as had been undertaken between 1903 and 1914 was no longer possible. -/- Leonard Nelson died in October 1927. In the 1930's, the 6th and final volume of "Treatises of the Fries School of Thought, New Edition" was published. Franz Oppenheimer, Otto Meyerhof, Minna Specht and Grete Hermann were involved in their publication. -/- 4. About Mathematical Natural Philosophy -/- In 1822, Fries' "Mathematical Natural Philosophy" appeared. Fries rejects the speculative natural philosophy of his time - above all Schelling's natural philosophy. A natural study, founded on speculative philosophy, ceases with its collection, arrangement and order of well-known facts. Only a mathematical natural philosophy can deliver the necessary explanatory reasoning. The basic dictum of his mathematical natural philosophy is: "All natural theories must be definable using purely mathematically determinable reasons of explanation." Fries is of the opinion that science can attain completeness only by the subordination of the empirical facts to the metaphysical categories and mathematical laws. -/- The crux of Fries' natural philosophy is the thought that mathematics must be made fertile for use by the natural sciences. However, pure mathematics displays solely empty abstraction. To be able to apply them to the sensory world, an intermediatory connection is required. Mathematics must be connected to metaphysics. The pure mechanics, consisting of three parts are these: a) A study of geometrical movement, which considers solely the direction of the movement, b) A study of kinematics, which considers velocity in Addition, c) A study of dynamic movement, which also incorporates mass and power, as well as direction and velocity. -/- Of great interest is Fries' natural philosophy in view of its methodology, particularly with regard to the doctrine "leading maxims". Fries calls these "leading maxims" "heuristic", "because they are principal rules for scientific invention". -/- Fries' philosophy found great recognition with Carl Friedrich Gauss, amongst others. Fries asked for Gauss's opinion on his work "An Attempt at a Criticism based on the Principles of the Probability Calculus" (1842). Gauss also provided his opinions on "Mathematical Natural Philosophy" (1822) and on Fries' "History of Philosophy". Gauss acknowledged Fries' philosophy and wrote in a letter to Fries: "I have always had a great predilection for philosophical speculation, and now I am all the more happy to have a reliable teacher in you in the study of the destinies of science, from the most ancient up to the latest times, as I have not always found the desired satisfaction in my own reading of the writings of some of the philosophers. In particular, the writings of several famous (maybe better, so-called famous) philosophers who have appeared since Kant have reminded me of the sieve of a goat-milker, or to use a modern image instead of an old-fashioned one, of Münchhausen's plait, with which he pulled himself from out of the water. These amateurs would not dare make such a confession before their Masters; it would not happen were they were to consider the case upon its merits. I have often regretted not living in your locality, so as to be able to glean much pleasurable entertainment from philosophical verbal discourse." -/- The starting point of the new adoption of Fries was Nelson's article "The critical method and the relation of psychology to philosophy" (1904). Nelson dedicates special attention to Fries' re-interpretation of Kant's deduction concept. Fries awards Kant's criticism the rationale of anthropological idiom, in that he is guided by the idea that one can examine in a psychological way which knowledge we have "a priori", and how this is created, so that we can therefore recognise our own knowledge "a priori" in an empirical way. Fries understands deduction to mean an "awareness residing darkly in us is, and only open to basic metaphysical principles through conscious reflection.". -/- Nelson has pointed to an analogy between Fries' deduction and modern metamathematics. In the same manner, as with the anthropological deduction of the content of the critical investigation into the metaphysical object show, the content of mathematics become, in David Hilbert's view, the object of metamathematics. -/-. (shrink)

The Bayesian maxim for rational learning could be described as conservative change from one probabilistic belief or credence function to another in response to newinformation. Roughly: ‘Hold fixed any credences that are not directly affected by the learning experience.’ This is precisely articulated for the case when we learn that some proposition that we had previously entertained is indeed true (the rule of conditionalisation). But can this conservative-change maxim be extended to revising one’s credences in response to entertaining propositions or (...) concepts of which one was previously unaware? The economists Karni and Vierø (2013, 2015) make a proposal in this spirit. Philosophers have adopted effectively the same rule: revision in response to growing awareness should not affect the relative probabilities of propositions in one’s ‘old’ epistemic state. The rule is compelling, but only under the assumptions that its advocates introduce. It is not a general requirement of rationality, or so we argue. We provide informal counterexamples. And we show that, when awareness grows, the boundary between one’s ‘old’ and ‘new’ epistemic commitments is blurred. Accordingly, there is no general notion of conservative change in this setting. (shrink)

In this paper, I argue that a naturalist approach in philosophy of mathematics justifies a pluralist conception of set theory. For the pluralist, there is not a Single Universe, but there is rather a Multiverse, composed by a plurality of universes generated by various set theories. In order to justify a pluralistic approach to sets, I apply the two naturalistic principles developed by Penelope Maddy (cfr. Maddy (1997)), UNIFY and MAXIMIZE, and analyze through them the potential of the set (...) theoretic multiverse to be the best framework for mathematical practice. According to UNIFY, an adequate set theory should be foundational, in the sense that it should allow one to represent all the currently accepted mathematical theories. As for MAXIMIZE, this states that any adequate set theory should be as powerful as possible, allowing one to prove as many results and isomorphisms as possible. In a recent paper, Maddy (2017) has argued that this two principle justify ZFC as the best framework for mathematical practice. I argue that, pace Maddy, these two principles justify a multiverse conception of set theory, more precisely, the generic multiverse with a core (GMH). (shrink)

There is a trade-off between specificity and accuracy in existing models of belief. Descriptions of agents in the tripartite model, which recognizes only three doxastic attitudes—belief, disbelief, and suspension of judgment—are typically accurate, but not sufficiently specific. The orthodox Bayesian model, which requires real-valued credences, is perfectly specific, but often inaccurate: we often lack precise credences. I argue, first, that a popular attempt to fix the Bayesian model by using sets of functions is also inaccurate, since it requires us (...) to have interval-valued credences with perfectly precise endpoints. We can see this problem as analogous to the problem of higher order vagueness. Ultimately, I argue, the only way to avoid these problems is to endorse Insurmountable Unclassifiability. This principle has some surprising and radical consequences. For example, it entails that the trade-off between accuracy and specificity is in-principle unavoidable: sometimes it is simply impossible to characterize an agent’s doxastic state in a way that is both fully accurate and maximally specific. What we can do, however, is improve on both the tripartite and existing Bayesian models. I construct a new model of belief—the minimal model—that allows us to characterize agents with much greater specificity than the tripartite model, and yet which remains, unlike existing Bayesian models, perfectly accurate. (shrink)

The assumption that procuring more organs will save more lives has inspired increasingly forceful calls to increase organ procurement. This project, in contrast, directly questions the premise that more organ transplantation means more lives saved. Its argument begins with the fact that resources are limited and medical procedures have opportunity costs. Because many other lifesaving interventions are more cost‐effective than transplantation and compete with transplantation for a limited budget, spending on organ transplantation consumes resources that could have been used to (...) save a greater number of other lives. This argument has not yet been advanced in debates over expanded procurement and could buttress existing concerns about expanded procurement. To support this argument, I review existing empirical data on the cost‐effectiveness of transplantation and compare them to data on interventions for other illnesses. These data should motivate utilitarians and others whose primary goal is maximizing population‐wide health benefits to doubt the merits of expanding organ procurement. I then consider two major objections: one makes the case that transplant candidates have a special claim to medical resources, and the other challenges the use of cost‐effectiveness to set priorities. I argue that there is no reason to conclude that transplant candidates’ medical interests should receive special priority, and that giving some consideration to cost‐effectiveness in priority setting requires neither sweeping changes to overall health priorities nor the adoption of any specific, controversial metric for assessing cost‐effectiveness. Before searching for more organs, we should first ensure the provision of cost‐effective care. (shrink)

The “four-color” theorem seems to be generalizable as follows. The four-letter alphabet is sufficient to encode unambiguously any set of well-orderings including a geographical map or the “map” of any logic and thus that of all logics or the DNA plan of any alive being. Then the corresponding maximally generalizing conjecture would state: anything in the universe or mind can be encoded unambiguously by four letters. That admits to be formulated as a “four-letter theorem”, and thus one can search for (...) a properly mathematical proof of the statement. It would imply the “four colour theorem”, the proof of which many philosophers and mathematicians believe not to be entirely satisfactory for it is not a “human proof”, but intermediated by computers unavoidably since the necessary calculations exceed the human capabilities fundamentally. It is furthermore rather unsatisfactory because it consists in enumerating and proving all cases one by one. Sometimes, a more general theorem turns out to be much easier for proving including a general “human” method, and the particular and too difficult for proving theorem to be implied as a corollary in certain simple conditions. The same approach will be followed as to the four colour theorem, i.e. to be deduced more or less trivially from the “four-letter theorem” if the latter is proved. References are only classical and thus very well-known papers: their complete bibliographic description is omitted. (shrink)

Kant takes the idea of autonomy of the will to be his distinctive contribution to moral philosophy. However, this idea is more nuanced and complicated than one might think. In this chapter, I sketch the rough outlines of Kant’s idea of autonomy of the will while also highlighting contentious exegetical issues that give rise to various possible interpretations. I tentatively defend four basic claims. First, autonomy primarily features in Kant’s account of moral agency, as the condition of the possibility of (...) moral obligation. Second, autonomy amounts to a metaphysical property as well as a normative principle and a psychological capacity. Third, although there is legitimate scholarly disagreement about whether or not autonomy involves self-legislation of the moral law, there is good reason to believe it underwrites an ‘inside-out’ (as opposed to ‘outside-in’) conception of the relationship between the will and moral requirements. Fourth, persons have dignity because their autonomy makes them members in the set of beings over whom the categorical imperative requires us to universalise our maxims, not because autonomy is an independently important property. (shrink)

This paper sets out to show that Kant’s account of cognition can be used to defend epistemic responsibility against the double threat of either being committed to implausible versions of doxastic voluntarism, or failing to account for a sufficiently robust connection between the will and belief. To support this claim, I argue that whilst we have no direct control over our beliefs, we have two forms of indirect doxastic control that are sufficient to ground epistemic responsibility: first, the capacity (...) to judge and doubt; and second, the ability to choose our epistemic maxims. It is because we have direct control over our capacity to judge as well as the epistemic principles that govern belief-acquisition that we have indirect control over the beliefs we thereby acquire. The interpretation of Kant I defend here thus allows us to account for the possibility of epistemic responsibility by providing a robust account of indirect doxastic voluntarism and thereby rendering direct doxastic voluntarism unnecessary. (shrink)

In computer science, Artificial Intelligence (AI), sometimes called machine intelligence, is intelligence demonstrated by machines, in contrast to the natural intelligence displayed by humans and other animals. Computer science defines AI research as the study of "intelligent agents": any device that perceives its environment and takes actions that maximize its chance of successfully achieving its goals. Deep Learning is a new field of research. One of the branches of Artificial Intelligence Science deals with the creation of theories and algorithms that (...) allow the machine to learn by simulating neurons in the human body. Most in-depth learning research focuses on finding high-level methods. The strippers analyze a large data set using linear and nonlinear transformations. The method of deep learning is used in the detection of several diseases including blood cell diseases and their classification using the radiography of blood cells to help decision makers to know the type of blood cell and its associated diseases and the results will be presented in detail and discussed. This thesis is using python language and deep learning to detect blood cell diseases and their classifications. The proposed deep learning model was trained, validated and the tested. The accuracy of proposed model was 98.00%. (shrink)

Animal welfare scientists face an acute version of the problem of inductive risk, since they must choose whether to affirm attributions of mental states to animals in advisory contexts, knowing their decisions hold consequences for animal welfare. In such contexts, the burden of proof should be sensitive to the consequences of error, but a framework for setting appropriate burdens of proof is lacking. Through reflection on two cases—pain and cognitive enrichment—I arrive at a tentative framework based on the principle of (...) expected welfare maximization. I then discuss the limitations of this framework and the questions it leaves open. (shrink)

Two lines of evidence indicate that there exists a reciprocal inhibitory relationship between opposed brain networks. First, most attention-demanding cognitive tasks activate a stereotypical set of brain areas, known as the task-positive network and simultaneously deactivate a different set of brain regions, commonly referred to as the task negative or defaultmode network. Second, functional connectivity analyses show that these same opposed networks are anti-correlated in the resting state. Wehypothesize that these reciprocally inhibitory effects reflect two incompatible cognitive modes, each of (...) which may be directed towards understanding the external world. Thus, engaging onemode activates one set of regions and suppresses activity in the other.Wetest this hypothesis by identifying two types of problem-solving task which, on the basis of prior work, have been consistently associated with the task positive and task negative regions: tasks requiring social cognition, i.e., reasoning about the mental states of other persons, and tasks requiring physical cognition, i.e., reasoning about the causal/mechanical properties of inanimate objects. Social and mechanical reasoning tasks were presented to neurologically normal participants during fMRI. Each task type was presented using both text and video clips. Regardless of presentation modality, we observed clear evidence of reciprocal suppression: social tasks deactivated regions associated with mechanical reasoning and mechanical tasks deactivated regions associated with social reasoning. These findings are not explained by self-referential processes, task engagement, mental simulation,mental time travel or external vs. internal attention, all factors previously hypothesized to explain default mode network activity. Analyses of resting state data revealed a close match between the regions our tasks identified as reciprocally inhibitory and regions of maximal anti-correlation in the resting state. These results indicate the reciprocal inhibition is not attributable to constraints inherent in the tasks, but is neural in origin. Hence, there is a physiological constraint on our ability to simultaneously engage two distinct cognitive modes. Furtherwork is needed tomore precisely characterize these opposing cognitive domains. (shrink)