The Anthropocene has been observed as an opportunity to generate new legal imaginaries capable of revising incumbent assumptions of legal and political thought. What opportunities do such ambitions afford for communication between geological and legal thought? Responding to Birrell & Matthews attempt to ‘re-story a law for, rather than of, the Anthropocene,’ I wish to describe some ways in which the Anthropocene Working Group, who are pursuing formalisation of the Anthropocene as an official geological unit, are involved in a similar (...) exercise of re-storying geology. The Anthropocene theme is brought to bear as a geological reality through material practices of measurement and correlation, as well as through the invocation of previous judgements of the evaluative committees associated with the formalisation of new geological unit. This effort amounts to a redefinition of the practices of geological observation, i.e. what counts as geologically relevant and why. In keeping with the theme of an ‘ethics of encounter’, as encouraged by Birrell and Matthews, this article suggests that the AWG’s effort provides a model with which the elaboration of ‘laws for the Anthropocene’ might correspond. (shrink)

Persistence in Time No person ever steps into the same river twice—or so goes the Heraclitean maxim. Obscure as it is, the maxim is often taken to express two ideas. The first is that everything always changes, and nothing remains perfectly similar to how it was just one instant before. The second is that nothing … Continue reading Persistence in Time →.

This collection offers a set of new readings on the history, meanings, and cultural innovations of the grotesque as defined by various current critical theories and practices. Since the grotesque frequently manifests itself as striking incongruities, ingenious hybrids, and creative deformities of nature and culture, it is profoundly implicated in early modern debates on the theological, philosophical, and ethical role of images. This consideration serves as the central focus from which the articles in the collection then move outward along different (...) lines of conceptualization, chronology, cultural relevance, place, and site. They cover a wide spectrum of artistic media, from prints to drawings, from sculptures to gardens, from paintings to stuccos. As they do this, they engage with, and bring together, theoretical perspectives from writers as diverse as Plato and Paleotti, Vitruvius and Vasari, Molanus to Montaigne. Whether travelling a short distance from Nero's Domus Aurea to Raphael's Vatican logge, or across the ocean from Italy to New Spain, this volume goes further than any previous study in defining the historic understanding of grotesque and, in so doing, providing us with a more nuanced resource for our understanding of an art form once viewed as peripheral. (shrink)

A supplemental document for "Metalinguistic Gradability".

L’esame di un passo della Vita di Platone laerziana (III 2) – e di luoghi paralleli riferibili alla medesima tradizione – permette di mettere a fuoco un motivo mitico cruciale nei racconti sulla concorrenza tra essere umano e divinità nel gamos con una mortale: il divieto, che il nume impone al ‘rivale’ di inferiore natura, di congiungersi con la donna che reca in grembo il suo seme, finché l’eroina non abbia portato a termine la gravidanza. Le storie di personaggi femminili (...) colpevoli di duplice gamos – prima con il dio e poi, a breve distanza di tempo, con il mortale – si focalizzano sulle conseguenze nefaste del secondo contaminante connubio: uno per tutti il caso di Coronide madre di Asclepio (e forse il motivo era associato anche ad altre note madri mitiche, come Arianna, Semele e Alcmena). In questi esempi, tuttavia, in genere non è esplicitato il tema della proibizione divina, come invece accade nel bios di Diogene Laerzio. Qui infatti Apollo, dopo aver concepito Platone con Perictione, appare ad Aristone per vietargli il rapporto sessuale con la parthenos. (shrink)

Sahlqvist theory is extended to the fragments of the intuitionistic propositional calculus that include the conjunction connective. This allows us to introduce a Sahlqvist theory of intuitionistic character amenable to arbitrary protoalgebraic deductive systems. As an application, we obtain a Sahlqvist theorem for the fragments of the intuitionistic propositional calculus that include the implication connective and for the extensions of the intuitionistic linear logic.

Relativity theory is often said to support something called ‘the four-dimensional view of reality’. But there are at least three different views that sometimes go by this name. One is ‘spacetime unitism’, according to which there is a spacetime manifold, and if there are such things as points of space or instants of time, these are just spacetime regions of different sorts: thus space and time are not separate manifolds. A second is the B-theory of time, according to which the (...) past, present, and future are all equally real and there is nothing metaphysically special about the present. A third is perdurantism, according to which persisting material objects are made up of different temporal parts located at different times. We sketch routes from relativity to unitism and to the B-theory. We then discuss some routes to perdurantism, via the B-theory and via unitism. (shrink)

Current theories propose that our sense of curiosity is determined by the learning progress or information gain that our cognitive system expects to make. However, few studies have explicitly tried to quantify subjective information gain and link it to measures of curiosity. Here, we asked people to report their curiosity about the intrinsically engaging perceptual ‘puzzles’ known as Mooney images, and to report on the strength of their aha experience upon revealing the solution image (curiosity relief). We also asked our (...) participants (279) to make a guess concerning the solution of the image, and used the distribution of these guesses to compute the crowdsourced semantic entropy (or ambiguity) of the images, as a measure of the potential for information gain. Our results confirm that curiosity and, even more so, aha experience is substantially associated with this semantic information gain measure. These findings support the expected information gain theory of curiosity and suggest that the aha experience or intrinsic reward is driven by the actual information gain. In an unannounced memory part, we also established that the often reported influence of curiosity on memory is fully mediated by the aha experience or curiosity relief. We discuss the implications of our results for the burgeoning fields of curiosity and psychoaesthetics. (shrink)

Multiple states are at risk of becoming uninhabitable due to climate change, forcing their populations to flee. While the 1951 Refugee Convention provides the gold standard of international protection, it is only applied to a limited subset of people fleeing their countries, those who suffer persecution, which most people fleeing climate change cannot establish. While many journalists and non-lawyers freely use the term “climate refugees,” governments, and courts, as well as UNHCR and many refugee experts, have excluded most climate refugees (...) from the Convention as a matter of legal interpretation. In our 2015 paper, “Unable to Return in the 1951 Refugee Convention: Stateless Refugees and Climate Change”, we sought to reopen the debate on “climate refugees” by arguing that some climate refugees qualify under the 1951 Convention as it is currently written (even if they are not persecuted): those who are stateless and are unable to return to their country of origin because climate change has rendered it uninhabitable. Our interpretation, however, has been rejected by Goodwin-Gill and McAdam (2021) and by Foster and Lambert (2019), which explicitly responds to our paper. Here, we address and respond to their arguments, and develop a new supplementary one, drawing on the principle of systemic integration, as enshrined in Article 31(3)(c) of the Vienna Convention on the Law of Treaties. (shrink)

When is a belief or judgment justified? One might be forgiven for thinking the search for single answer to this question to be hopeless. The concept of justification is required to fulfil several tasks: to evaluate beliefs epistemically, to fill in the gap between truth and knowledge, to describe the virtuous organization of one’s beliefs, to describe the relationship between evidence and theory (and thus relate to confirmation and probabilification). While some of these may be held to overlap, the prospects (...) for fulfilling all may well seem poor. Furthermore the internalist requires that justification be an introspectible property of beliefs and a fundamental epistemic concept, while the externalist is often happy to ignore the concept altogether or at best regard it as an embarrassing add-on to their epistemology. In the light of this one might reasonably give up on justification altogether or adopt pluralist approach, denying that justification is any single property of beliefs of judgments. (shrink)

In this paper we discuss how Causal Decision Theory should be modified to handle a class of problematic cases involving deterministic laws. Causal Decision Theory, as it stands, is problematically biased against your endorsing deterministic propositions (for example it tells you to deny Newtonian physics, regardless of how confident you are of its truth). Our response is that this is not a problem for Causal Decision Theory per se, but arises because of the standard method for assessing the truth of (...) certain counterfactuals. The truth of deterministic laws is `modally fragile' on the standard semantics for counterfactuals: if determinism is true and you were to do otherwise, the laws would be different. We provide two ways of avoiding this problem: 1) supplement the standard semantics for counterfactuals with impossible worlds, or 2) introduce rigid designators into the description of problematic decision situations. We argue that both of these approaches are well-motivated and can be readily incorporated into Lewisian Causal Decision Theory. (shrink)

The possibility of multi-location—of one entity having more than one exact location—is required by several metaphysical theories such as the immanentist theory of universals and three-dimensionalism about persistence. One of the most pressing challenges for multi-location theorists is that of making sense of exact location—in that extant definitions of exact location entail a principle called ‘functionality’, according to which nothing can have more than one exact location. Recently in a number of promising papers, Antony Eagle has proposed and defended a (...) definition of exact location in terms of weak location that does not entail functionality. This paper provides the first thorough assessment of Eagle’s proposal. In particular, we argue that it cannot account for the location of immanent universals, the multi-location of mereologically changing three-dimensional objects, the multi-location of mereologically complex objects, and that it makes extended simples impossible. (shrink)

I provide an argument against the Aristotelian view of universals, according to which universals depend for their existence on their exemplifiers. The argument consists in a set of five jointly inconsistent assumptions. As such, the argument can be used to argue in favour of other conclusions, such as that exemplification is no relation or that plausible principles concerning ontological dependence or grounding do not hold.

We discuss the fate of the correspondence principle beyond quantum mechanics, specifically in quantum field theory and quantum gravity, in connection with the intrinsic limitations of the human ability to observe the external world. We conclude that the best correspondence principle is made of unitarity, locality, proper renormalizability (a refinement of strict renormalizability), combined with fundamental local symmetries and the requirement of having a finite number of fields. Quantum gravity is identified in an essentially unique way. The gauge interactions are (...) uniquely identified in form. Instead, the matter sector remains basically unrestricted. The major prediction is the violation of causality at small distances. (shrink)

The correspondence principle made of unitarity, locality and renormalizability has been very successful in quantum field theory. Among the other things, it helped us build the standard model. However, it also showed important limitations. For example, it failed to restrict the gauge group and the matter sector in a powerful way. After discussing its effectiveness, we upgrade it to make room for quantum gravity. The unitarity assumption is better understood, since it allows for the presence of physical particles as well (...) as fake particles (fakeons). The locality assumption is applied to an interim classical action, since the true classical action is nonlocal and emerges from the quantization and a later process of classicization. The renormalizability assumption is refined to single out the special role of the gauge couplings. We show that the upgraded principle leads to an essentially unique theory of quantum gravity. In particular, in four dimensions, a fakeon of spin 2, together with a scalar field, is able to make the theory renormalizable while preserving unitarity. We offer an overview of quantum field theories of particles and fakeons in various dimensions, with and without gravity. (shrink)

We define life as the amplification of quantum uncertainty up to macroscopic scales. A living being is any amplifier that achieves this goal. We argue that everything we know about life can be explained from this idea. We study a ladder mechanism to estimate the probability that the amplification occurs spontaneously in nature. The amplification mechanism is so sensitive to small variations of its own parameters that it acts as a bifurcation itself, i.e. it implies that the universe is either (...) everywhere dead or alive wherever possible. Since the first option is excluded by the existence of life on earth, we infer that the universe hosts a huge number of inhabited planets (possibly one per star on average). We also investigate models of conscious and unconscious learning processes, as well as the structure of the brain and evolution. Finally, we address the problem of creating artificial life. (shrink)

Several particles are not observed directly, but only through their decay products. We consider the possibility that they might be fakeons, i.e. fake particles, which mediate interactions but are not asymptotic states. A crucial role to determine the true nature of a particle is played by the imaginary parts of the one-loop radiative corrections, which are affected in nontrivial ways by the presence of fakeons in the loop. The knowledge we have today is sufficient to prove that most non directly (...) observed particles are true physical particles. However, in the case of the Higgs boson the possibility that it might be a fakeon remains open. The issue can be resolved by means of precision measurements in existing and future accelerators. (shrink)

The Monster Objection has often been considered one of the main reasons to explore non-standard mereological views, such as hylomorphism. Still, it has been rarely discussed and then only in a cursory fashion. This paper fills this gap by offering the first thorough assessment of the objection. It argues that different metaphysical stances, such as presentism and three- and four-dimensionalism, provide different ways of undermining the objection.

Two sources of possible disagreement in bioethics may be associated with pessimism about what bioethics can achieve. First, pluralism implies that bioethics engages with interlocutors who hold divergent moral beliefs. Pessimists might believe that these disagreements significantly limit the extent to which bioethics can provide normatively robust guidance in relevant areas. Second, the interdisciplinary nature of bioethics suggests that interlocutors may hold divergent views on the nature of bioethics itself—particularly its practicality. Pessimists may suppose that interdisciplinary disagreements could frustrate the (...) goals of bioethics. In this article, I explore how wonder may alleviate the concerns of the first group of pessimists regarding problems associated with pluralism, provided that we are willing to accept some interdisciplinary frustrations. Then, I invite readers of this issue of The Journal of Medicine & Philosophy to test these intuitions by considering the role of wonder in these articles. (shrink)

I develop an expressivist account of verbal disagreements as practical disagreements over how to use words rather than factual disagreements over what words actually mean. This account enjoys several advantages over others in the literature: it can be implemented in a neo-Stalnakerian possible worlds framework; it accounts for cases where speakers are undecided on how exactly to interpret an expression; it avoids appeals to fraught notions like subject matter, charitable interpretation, and joint-carving; and it naturally extends to an analysis of (...) metalinguistic negotiations. (shrink)

A common objection to the very idea of conceptual engineering is the topic continuity problem: whenever one tries to “reengineer” a concept, one only shifts attention away from one concept to another. Put differently, there is no such thing as conceptual revision: there’s only conceptual replacement. Here, I show that topic continuity is compatible with conceptual replacement. Whether the topic is preserved in an act of conceptual replacement simply depends on what is being replaced (a conceptual tool or a conceptual (...) role) and what the topic under discussion is. Thus, the topic continuity problem only arises from a failure to specify these two things. (shrink)

Burnout is a well-documented entity in Care Workers population, affecting up to 50% of physicians, just as it is equally well established that managing an infectious disease outbreaks, such as confirmed in the COVID-19 pandemic, increases Post-Traumatic Stress Disorder and the psychological burden. Mental health support, in the form of formal or remote sessions, has been shown to be helpful to health care staff, despite the organizational difficulties in an emergency. During the first emergence of COVID-19 in Italy, the Scientific (...) Institute for Research, Hospitalization and Health Care Istituto di Ricovero e Cura a Carattere Scientifico Policlinico San Matteo Foundation, the Italian hospital that treated “patient 1,” has activated an agreement with the Soleterre Foundation, an international Non-Governmental Organization that manages health emergency projects, to provide psychological support. A task force of psychologists was created with the aim of designing and administering a Therapeutic Mental Health Assessment for COVID-19 Care Workers to evaluate and support health care workers’ mental health. The assessment battery was developed to evaluate symptoms and behaviors associated with trauma and the corresponding maladaptive behaviors. Once the TMHA COVID-19 CWs had been developed, the team of psychologists regularly visited healthcare staff in the ward to administer it. One hundred seven care workers across Intensive Care Units, the emergency room and medical ward were administered the TMHA COVID-19 CWs. PTSD symptoms were reported as severe by 13% of the population. Depressive symptoms as severe for 7% and Anxiety symptoms as severe for 14%. Severe psychotic symptoms were experienced by 2% and severe suicidal thoughts by 1% of the population. The possibility of acting upon the results of the TMHA COVID-19 CWs allowed an early intervention through individual session beyond the cut-off level for PTSD in NSESSS. In fact, 280 individual support sessions were offered. Therefore, we considered our project a protective and support factor for healthcare workers’ mental well-being and we recommend implementing a mental health screening program in ward involved in COVID-19 patients’ care. (shrink)

This paper develops an endurantist theory of persistence. The theory is built around one basic tenet, which concerns existence at a time – the relation between an object and the times at which that object is present. According to this tenet, which I call transcendentism, for an object to exist at a time is for it to participate in events that are located at that time. I argue that transcendentism is a semantically grounded and metaphysically fruitful. It is semantically grounded, (...) insofar as a semantic analysis of our temporal talk favors it over rivals. It is metaphysically fruitful, insofar as the theory of persistence that can be built around it – the transcendentist theory of persistence, to give it a name – requires neither temporal parts nor the problematic commitments to which all extant forms of endurantism are committed, such as the possibility of extended simples or multilocation. (shrink)

"Cover " -- "Title Page " -- "Copyright " -- "Contents " -- "Preface to the English Edition" -- "Introduction" -- "1. The Substitute" -- "2. Animals, Machines, Cyborgs, and the Taxi " -- "3. Mind, Emotions, and Artificial Empathy " -- "4. The Other Otherwise " -- "5. From Moral and Lethal Machines to Synthetic Ethics " -- "Notes" -- "Works Cited" -- "Acknowledgments" -- "Credits.

This paper commences by making a case for a naturalized approach to knowledge‐first epistemology. On this basis it then goes on to describe and defend a naturalized, functionalist account of group knowledge. It then contrasts this with Jennifer Lackey's (2021) account of the epistemological status of groups.

The essay explores the possibilities afforded by Heidegger’s thought for addressing the question of the reality of the phenomenon within the framework of the theory of quantum mechanics. Heidegger’s conception of the task of phenomenology is seen to provide a crucial axis along which the phenomenon of quantum physics can be connected both to its appearance in language and to the historical unfolding of the horizon that grounds the possibility of an encounter with the phenomenon itself. The determinations of this (...) horizon, i.e. of the order of “phenomenality” that makes the appearance of the phenomenon possible, are analyzed in the instance of quantum mechanics, and compared to the ones presented by Heidegger in his considerations concerning the appearing of the phenomenon in Aristotelian and classical physics. The three main directives that structure the analysis of this order of phenomenality are the determinations of the conditions of experience of the phenomenon, of the function of language that makes this appearance possible, and of the subject function that constitutes, and is in turn constituted by, this experience. (shrink)

Until recently, an almost perfect parallelism seemed to hold between theories of identity through time and across possible worlds,as every account in the temporal case(endurantism,perdurantism, exdurantism) was mirrored by a twin account in the modal case (trans-world identity, identity-via-parts, identity-via-counterparts). Nevertheless, in the recent literature, this parallelism has been broken because of the implementation in the debate of the relation of location. In particular, endurantism has been subject to a more in-depth analysis, and different versions of it, corresponding to different (...) ways an entity can be located in time, emerged. In this article, we provide a precise map of the conceptions at stake, complete the debate by introducing a version of endurantism not yet considered in the debate — we call transcendentism — and show that it allows us to provide an effective interpretation of the relation of trans-world identity and an intuitive solution in the temporal case. (shrink)

Aim of this paper is to support the view that all human practical identities are contingent by arguing against the view that there is at least one necessary practical identity shared by all human beings, namely Humanity. The view that Humanity is a necessary practical identity is explicitly defended by Christine M. Korsgaard (Korsgaard, C. M. 1996. The Sources of Normativity, edited by O. O’Neill. Cambridge: Cambridge University Press; Korsgaard, C. M. 2009. Self-Constitution: Agency, Identity, and Integrity. New York: Oxford (...) University Press) and indirectly by Marya Schechtman (Schechtman, M. 2014. Staying Alive: Personal Identity, Practical Concerns, and the Unity of a Life. New York: Oxford University Press). Korsgaard understands Humanity both in terms of pure self-legislation, and as deep sociality. In the first case, Humanity as self-legislation faces what I call ‘Existential dilemma’: either Humanity has specific content, typical of contingent practical identities, but stops being necessary for all human beings; or Humanity is emptied of its content and is conceived of as necessary self-legislation, but stops being a practical identity. In the second case, i.e., Humanity as deep sociality, Korsgaard confuses the necessary natural fact that human beings are social creatures, with contingent contexts of human socialization, which are the true sources of specifically human practical identities. I articulate this confusion in the guise of what I call ‘Nature/nurture dilemma’, which also applies to the morally neutral account of human personhood advocated by Schechtman (Schechtman, M. 2014. Staying Alive: Personal Identity, Practical Concerns, and the Unity of a Life. Oxford University Press). In conclusion, I address the worry that without the necessary practical identity of Humanity we might not be able to extend our practical and moral concerns to distant fellow human beings by sketching an alternative path to extend such concerns. (shrink)

This essay centres on two contributions—Giorgio Agamben’s What is Real? and Karen Barad’s Meeting the Universe Halfway —that deal with what they see as the import the quantum turn has...

The Aristotelian view of universals, according to which each universal generically depends for its existence on its instantiations, has recently come under attack by a series of ground-theoretic arguments. The last such arguments, presented by Raven, promises to offer several significant improvements over its predecessors, such as avoiding commitment to the transitivity of ground and offering new reasons for the metaphysical priority of universals over their instantiations. In this paper, we argue that Raven's argument does not effectively avoid said commitment (...) and that Raven's new reasons fail. Moreover, we present a novel ground-theoretic interpretation of the Aristotelian view, referred to as strong immanence, and introduce a new argument against the Aristotelian view, intended to sidestep any commitment to the transitivity of ground. (shrink)

The ontology of Bohmian mechanics includes both the universal wave function and particles. Proposals for understanding the physical significance of the wave function in this theory have included the idea of regarding it as a physically-real field in its 3N-dimensional space, as well as the idea of regarding it as a law of nature. Here we introduce and explore a third possibility in which the configuration space wave function is simply eliminated—replaced by a set of single-particle pilot-wave fields living in (...) ordinary physical space. Such a re-formulation of the Bohmian pilot-wave theory can exactly reproduce the statistical predictions of ordinary quantum theory. But this comes at the rather high ontological price of introducing an infinite network of interacting potential fields which influence the particles’ motion through the pilot-wave fields. We thus introduce an alternative approach which aims at achieving empirical adequacy with a more modest ontological complexity, and provide some preliminary evidence for optimism regarding the program of trying to replace the configuration space wave function with a set of fields in ordinary physical space. (shrink)

Social robotics entertains a particular relationship with anthropomorphism, which it neither sees as a cognitive error, nor as a sign of immaturity. Rather it considers that this common human tendency, which is hypothesized to have evolved because it favored cooperation among early humans, can be used today to facilitate social interactions between humans and a new type of cooperative and interactive agents - social robots. This approach leads social robotics to focus research on the engineering of robots that activate anthropomorphic (...) projections in users. The objective is to give robots "social presence" and "social behaviors" that are sufficiently credible for human users to engage in comfortable and potentially long-lasting relations with these machines. This choice of ’applied anthropomorphism’ as a research methodology exposes the artifacts produced by social robotics to ethical condemnation: social robots are judged to be a "cheating" technology, as they generate in users the illusion of reciprocal social and affective relations. This article takes position in this debate, not only developing a series of arguments relevant to philosophy of mind, cognitive sciences, and robotic AI, but also asking what social robotics can teach us about anthropomorphism. On this basis, we propose a theoretical perspective that characterizes anthropomorphism as a basic mechanism of interaction, and rebuts the ethical reflections that a priori condemns "anthropomorphism-based" social robots. To address the relevant ethical issues, we promote a critical experimentally based ethical approach to social robotics, "synthetic ethics," which aims at allowing humans to use social robots for two main goals: self-knowledge and moral growth. (shrink)

Situated at the intersection of animal studies and literary theory, this book explores the remarkable and subtly pervasive web of animal imagery, metaphors, and concepts in the work of the Jewish-Italian writer, chemist, and Holocaust survivor Primo Levi. Relatively unexamined by scholars, the complex and extensive animal imagery Levi employed in his literary works offers new insights into the aesthetical and ethical function of testimony, as well as an original perspective on contemporary debates surrounding human-animal relationships and posthumanism. The three (...) main sections that compose the book mirror Levi’s approach to non-human animals and animality: from an unquestionable bio-ethical origin ; through an investigation of the relationships between writing, technology, and animality ; to a creative intellectual project in which literary animals both counterbalance the inevitable suffering of all creatures, and suggest a transformative image of interspecific community. (shrink)

From Hegel to Heidegger and Agamben, modern Western philosophy has been haunted by how to think the connections between death, humanness and animality. This article explores how these connections h...

Pope Gregory I, commonly known as Saint Gregory the Great, is celebrated for re-organizing both the institutional and liturgical life of the Roman Catholic Church; for instigating the first recorded large-scale mission from Rome to England; and for his writings. Among these, a distinct importance has been attributed to his “Dialogues,” a collection of four books of miracles, signs, wonders, and healings carried out by then little-known holy men, which represent a portion of central Italy as a sacred space where (...) the Christian God is present in both human and non-human form, while also interacting with the environment by performing landscaping functions. This article outlines the “Dialogues Bioregional Project,” a digital, interdisciplinary interface on Italian landscape ecology which would promote dialogues between scientists and humanists as well as provide a modeling tool for environmental and cultural awareness. Shaped around the “Dialogues” of Pope Gregory I, this digital humanities project explores continuities and discontinuities between the socio-political and ecological history of a specific section of Italian territory, a set of multidisciplinary environmental narratives, and local communities. My aim is to introduce readers to the ecological potentials of Gregory’s book and thus prompt scholars interested in the environmental humanities and the integration of biophysical and analytical approaches with humanistic and holistic perspectives to become part of the “Dialogues Bioregional Project” and collaborate in its further development. (shrink)

In the paper, a detailed analysis of some new logical aspects of Cantor’s diagonal proof of the uncountability of continuum is presented. For the first time, strict formal, axiomatic, and algorithmic definitions of the notions of potential and actual infinities are presented. It is shown that the actualization of infinite sets and sequences used in Cantor’s proof is a necessary, but hidden, condition of the proof. The explication of the necessary condition and its factual usage within the framework of Cantor’s (...) proof makes, Cantor’s proof invalid. It’s shown that traditional Cantor’s proof has a second necessary, but hidden as well, condition which is teleological by its nature, i.e., is not mathematical. The explication of the second necessary condition makes Cantor’s statement on the uncountability of continuum unprovable from the point of view of classical logic.One of the most dramatic facts in history of science is connected just with the notion of actual infinity and consists in the following. On the one hand, Aristotle, Berkeley, Locke, Descartes, Spinoza, Gauss, Kant, Cauchy, Kronecker, Hermite, Poincaré, Bair, Borel, Brouwer, Quine, Wittgenstein, Weyl, Luzin, and a lot of other outstanding creators of classical logic and classical mathematics, during millenniums, stated categorically and insistently warned about that the actual infinity is a self-contradictory notion and its usage in mathematics is inadmissible (e.g., according to Poincare, “There is no actual infinity. - Cantorians forgot that and fell into contradictions. Later generations will regard Mengenlehre (set theory) as a disease from which one has recovered”). On the other hand, a lot of outstanding scientists of the XX c.c., such as Hilbert, Church, Turing, Gödel, etc., and modern axiomatic set theory as a whole ignored this (intuitive though) opinion of genii and accepted Cantor’s “transfinite paradise”, based on the actual infinity. In the paper some logical, philosophical, and psychological aspects of this historical “favorable opposition” are analyzed, and the fact that the scientific intuition of genii has won the historical battle against the mytho-’logic’ of Cantor’s transfinite ‘paradise’ is explained and logically justified. (shrink)