This study aimed to outline the profile of retractions of scientific articles on COVID-19 published in journals indexed in the Scopus database between 2020 and 2021. To analyze the data, we used a bibliometric technique, with the Bibliometrix package in the R-Studio software, and descriptive statistics. Twenty-nine retractions were analyzed, and we found that the most common reasons for retraction were related to ethical issues and that 68.97% of authors have previously retracted articles. We concluded that there appears to have (...) been a change in the publication policies of journals, which resulted in an increase in scientific retractions related to COVID-19 during the study period. (shrink)

This paper argues that we should solve paradoxes for propositions (such as the Russell–Myhill paradox) in essentially the same way that we solve Russellian paradoxes for sets. That is, the standard, iterative approach to sets is extended to include properties, and then the resulting hierarchy of sets and properties is used to construct propositions. Propositions on this account are structured in the sense of mirroring the sentences that express them, and they would seem to serve the needs of philosophers of (...) language and metaphysicians who rely on such propositions. The resulting account has limitations, comparable to those faced by the iterative approach to sets, but it is argued to be in important ways preferable to others that have been proposed. (shrink)

The aim of the paper is to argue that all—or almost all—logical rules have exceptions. In particular, it is argued that this is a moral that we should draw from the semantic paradoxes. The idea that we should respond to the paradoxes by revising logic in some way is familiar. But previous proposals advocate the replacement of classical logic with some alternative logic. That is, some alternative system of rules, where it is taken for granted that these hold without exception. (...) The present proposal is quite different. According to this, there is no such alternative logic. Rather, classical logic retains the status of the ‘one true logic’, but this status must be reconceived so as to be compatible with (almost) all of its rules admitting of exceptions. This would seem to have significant repercussions for a range of widely held views about logic: e.g. that it is a priori, or that it is necessary. Indeed, if the arguments of the paper succeed, then such views must be given up. (shrink)

Plausibly, mathematical claims are true, but the fundamental furniture of the world does not include mathematical objects. This can be made sense of by providing mathematical claims with paraphrases, which make clear how the truth of such claims does not require the fundamental existence of mathematical objects. This paper explores the consequences of this type of position for explanatory structure. There is an apparently straightforward relationship between this sort of structure, and the logical sort: i.e. logically complex claims are explained (...) by logically simpler ones. For example, disjunctions are explained by their (true) disjuncts, while generalizations are explained by their (true) instances. This would seem as plausible in the case of mathematics as elsewhere. Also, it would seem to be something that the anti-realist approaches at issue would want to preserve. It will be argued, however, that these approaches cannot do this: they lead not merely to violations of the familiar principles relating logical and explanatory structure, but even to reversals of these. That is, there are cases where generalizations explain their instances, or disjunctions their disjuncts. (shrink)

This paper examines David Hull’s and Peter Godfrey-Smith’s accounts of biological individuality using the case of biofilms. Biofilms fail standard criteria for individuality, such as having reproductive bottlenecks and forming parent-offspring lineages. Nevertheless, biofilms are good candidates for individuals. The nature of biofilms shows that Godfrey-Smith’s account of individuality, with its reliance on reproduction, is too restrictive. Hull’s interactor notion of individuality better captures biofilms, and we argue that it offers a better account of biological individuality. However, Hull’s notion of (...) interactor needs more precision. We suggest some ways to make Hull’s notion of interactor and his account of individuality more precise. Generally, we maintain that biofilms are a good test case for theories of individuality, and a careful examination of biofilms furthers our understanding of biological individuality. (shrink)

In this book Bruno Latour brings together these different approaches to provide a lively and challenging analysis of science, demonstrating how social context..

de Queiroz (1995), Griffiths (1999) and LaPorte (2004) offer a new version of essentialism called "historical essentialism". According to this version of essentialism, relations of common ancestry are essential features of biological taxa. The main type of argument for this essentialism proposed by Griffiths (1999) and LaPorte (2004) is that the dominant school of classification, cladism, defines biological taxa in terms of common ancestry. The goal of this paper is to show that this argument for historical essentialism is unsatisfactory: cladism (...) does not assume that relations of common ancestry are essential attributes of biological taxa. Therefore, historical essentialism is not justified by cladism. (shrink)

O presente texto observa a teoria crítica da sociedade desenvolvida por Habermas a partir da análise das duas teses apresentadas na Teoria da Ação Comunicativa, sobre a modernidade seletiva e sobre o desacoplamento das esferas socais tematizáveis, pretendendo compreender como o avanço dos imperativos funcionais do sistema (a burocracia administrativa estatal e a economia capitalista) têm extrapolado suas áreas de atuação e aumentado ainda mais sua dinâmica sistêmica sobre o ambito da reprodução simbólica nas sociedades capitalistas do século XXI. A (...) discussão que se segue analisará esta ampliação considerando que as interferências e alterações sobre os padrões de integração social são questões que se encontram em um desenvolvimento constante desde as mudanças pelas quais passaram a alterar os critérios de legitimação da modernidade capitalista. Ainda que de um modo não inteiramente distinto daquele tematizado por Habermas no contexto social do início dos anos 1980, pretende-se observar que que no atual estágio do capitalismo internacional esta interferência, assim como as alterações daí promovidas, tem provocado uma maior fragmentação social e gerado bloqueios que perturbam ainda mais a integração social (que ameaçam inviabilizar qualquer efetivação da emancipação social quanto mais são deturpados os critérios de legitimação e reconhecimento social). Circunscrito a este horizonte, pretende-se sustentar que tais fatores possam ser melhor compreendidos mediante uma investigação sobre as patologias sociais, especifiamente quando estas são compreendidas como parâmetros que proporcionariam identificar certa resistência a uma integração social orientada por imperativos sistêmicos. (shrink)

Cooperative behaviors within a group face the risk of being exploited by `free-riders,' individuals that reap the benefits produced by cooperators without paying the costs of cooperating. Free-riders are often perceived as a burden to the group, since the group's survival depends on tasks performed by cooperators. However, this paper challenges this perspective, arguing that an excess of cooperators may actually lower the efficiency and persistence of groups. The perspective presented in this paper has ramifications to broader issues in philosophy, (...) particularly the challenge of how to balance self-interest with the collective interests of the group. Ultimately, this paper seeks to highlight some of the subtle ways free-riders positively impact their groups, an aspect of free-riding that is often overlooked in discussions about cooperation. (shrink)

Nature is replete with borderline cases that fall somewhere between organisms and communities, such as lichens, biofilms, and the Portuguese Man-of-War. At first glance, the existence of such borderline cases might suggest that the concept of what constitutes an organism is too fuzzy to be useful in evolutionary biology. Yet, the notion of organisms is entrenched within central debates in evolution, including discussions over how fitness should be measured, what the bearers of adaptations and fitness are, and the status of (...) holobionts. Finally, accounts of organisms can set the stage for explanations of how multicellularity evolved. In particular, characterizing multicellular organisms in terms of the level of cooperation between their cells suggests that their evolution required the presence of mechanisms that could suppress conflict between cells. (shrink)

Kripke argues for origin essentialism, the view that the same individual cannot have multiple origins. Sober hypothesises that Kripke's origin essentialism applies to biological species. This paper shows that Sober's hypothesis fails. Because Kripke's original argument is invalid, it cannot vindicate Sober's proposal. Salmon offers an influential reformulation of Kripke's argument but his argument fails to extend to species: the notion of an individual's origin is too narrow to apply to species, and Salmon's argument rests on a thought experiment that (...) conflicts with how species evolve. Thus, Sober and others are wrong to think that Kripke's origin essentialism can save species essentialism. (shrink)

Doolittle :351–378, 2013) and Ereshefsky and Pedroso argue that selection can act at the level of biofilms and other microbial communities. Clarke is skeptical and argues that selection acts on microbial cells rather than microbial communities. Her main criticism is that biofilms lack one of the ingredients required for selection to operate: heritability. This paper replies to her concern by elaborating how biofilm-level traits can be inheritable.

One curious phenomenon of several social groups is that they are ‘redundant’ in the sense that they contain more cooperators than strictly needed to complete certain group tasks, such as foraging. Redundancy is puzzling because redundant groups are particularly susceptible to invasion by defectors. Yet, redundancy can be found in groups formed by a wide range of organisms, including insects and microbes. Birch ([2012]) has recently argued that coercive behaviours might account for redundancy using insect colonies as a case study. (...) However, microbial examples suggest redundancy can evolve without coercive behaviours. This paper formulates an explanation for redundancy that does not require targeted punishment of defectors; instead, it proposes that redundancy might be due to ignorance. Specifically, it is suggested that redundancy evolves as a by-product of selection when group members have to opt whether to cooperate or not while being blind to the strategies of others. Accordingly, possessing information about the strategies of the group members might undermine rather than facilitate cooperation within groups. (shrink)

Some mathematicians and philosophers contend that set theory plays a foundational role in mathematics. However, the development of category theory during the second half of the twentieth century has encouraged the view that this theory can provide a structuralist alternative to set-theoretical foundations. Against this tendency, criticisms have been made that category theory depends on set-theoretical notions and, because of this, category theory fails to show that set-theoretical foundations are dispensable. The goal of this paper is to show that these (...) criticisms are misguided by arguing that category theory is entirely autonomous from set theory. (shrink)

Microbes often live in association with dense multicellular aggregates, especially biofilms, and the construction of these aggregates typically requires microbial cells to produce public goods, such as enzymes and signaling molecules. Public-goods producers are, in turn, vulnerable to exploitation by free-rider cells that consume the public goods without paying for their production costs. The cell population of a biofilm or other microbial aggregates are expected to pass through bottlenecks due to a wide range of factors, such as antibiotic treatments and (...) dispersal. The goal of this article is to make the case for the relevance of population bottlenecks at shaping the social interactions within microbial aggregates. The effect of bottlenecks on microbial aggregates is complex in that bottlenecks can favor producers under certain circumstances, but not in others. The concept of the Volunteer’s Dilemma from game theory will be used to motivate the hypothesis that this partly occurs because of how bottlenecks alter the risk of being a producer in a microbial aggregate. Finally, the role of bottlenecks in the microbial world impacts key issues in evolutionary biology, including the importance of ecology at shaping social evolution, and the evolution of multicellularity from unicellular ancestors. (shrink)

Bruno Latour was once asked : "Do you believe in reality?" This text is an attempt to answer this question.

One curious phenomenon of several social groups is that they are ‘redundant’ in the sense that they contain more cooperators than strictly needed to complete certain group tasks, such as foraging. Redundancy is puzzling because redundant groups are particularly susceptible to invasion by defectors. Yet, redundancy can be found in groups formed by a wide range of organisms, including insects and microbes. Birch has recently argued that coercive behaviours might account for redundancy using insect colonies as a case study. However, (...) microbial examples suggest redundancy can evolve without coercive behaviours. This paper formulates an explanation for redundancy that does not require targeted punishment of defectors; instead, it proposes that redundancy might be due to ignorance. Specifically, it is suggested that redundancy evolves as a by-product of selection when group members have to opt whether to cooperate or not while being blind to the strategies of others. Accordingly, possessing information about the strategies of the group members might undermine rather than facilitate cooperation within groups. 1The Evolution of Redundancy 2Explaining Redundancy via Coercion 3Explaining Redundancy via Ignorance 3.1Cooperation behind the Darwinian veil of ignorance 3.2Modelling group tasks with a public goods game 3.3Group tasks under harsh environments 4Conclusion. (shrink)

General-elimination harmony articulates Gentzen’s idea that the elimination-rules are justified if they infer from an assertion no more than can already be inferred from the grounds for making it. Dummett described the rules as not only harmonious but stable if the E-rules allow one to infer no more and no less than the I-rules justify. Pfenning and Davies call the rules locally complete if the E-rules are strong enough to allow one to infer the original judgement. A method is given (...) of generating harmonious general-elimination rules from a collection of I-rules. We show that the general-elimination rules satisfy Pfenning and Davies’ test for local completeness, but question whether that is enough to show that they are stable. Alternative conditions for stability are considered, including equivalence between the introduction- and elimination-meanings of a connective, and recovery of the grounds for assertion, finally generalizing the notion of local completeness to capture Dummett’s notion of stability satisfactorily. We show that the general-elimination rules meet the last of these conditions, and so are indeed not only harmonious but also stable. (shrink)

Pocas personas habr n suscitado tan un nimemente la imagen del maestro como don Manuel Pedroso. Nadie que lo haya conocido ha dejado de mencionar ese ejemplar del magisterio que rebasaba ampliamente el mbito meramente universitario. Los pr logos a este libro, obra de disc pulos o amigos, dan fe, de la huella profunda que dej en ellos. Pero nos informan tambi n de la renuencia de Pedroso a rematar sus abundantes notas y esbozos y a publicar sus (...) resultados. Por eso es tan importante la labor realizada con estas p ginas, ordenadas por sus disc pulos y reimpresas ahora en esta colecci n dedicada a rescatar la labor in dita o desconocida en Espa a del exilio espa ol de 1939. (shrink)

German classicist's monumental study of the origins of European thought in Greek literature and philosophy. Brilliant, widely influential. Includes "Homer's View of Man," "The Olympian Gods," "The Rise of the Individual in the Early Greek Lyric," "Pindar's Hymn to Zeus," "Myth and Reality in Greek Tragedy," and "Aristophanes and Aesthetic Criticism.".

In a series of papers, 137–158; 1994, Midwest Studies in Philosophy, 23, 61–74, 1999) Fine develops his hylomorphic theory of embodiments. In this article, we supply a formal semantics for this theory that is adequate to the principles laid down for it in. In Section 1, we lay out the theory of embodiments as Fine presents it. In Section 2, we argue on Cantorian grounds that the theory needs to be stabilized, and sketch some ways forward, discussing various choice points (...) in modeling the view. In Section 3, we develop a formal semantics for the theory of embodiments by constructing embodiments in stages and restricting the domain of the second-order quantifiers. In Section 4 we give a few illustrative examples to show how the models deliver Finean hylomorphic consequences. In Section 5, we prove that Fine’s principles are sound with respect to this semantics. In Section 6 we present some inexpressibility results concerning Fine’s various notions of parthood and show that in our formal semantics these notions are all expressible using a single mereological primitive. In Section 7, we prove several mereological results stemming from the model theory, showing that the mereology is surprisingly robust. In Section 8, we draw some philosophical lessons from the formal semantics, and in particular respond to Koslicki’s main objection to Fine’s theory. In the appendix we present proofs of the inexpressibility results of Section 6. (shrink)

In this article I tease out a conception of reason in Pierre-Joseph Proudhon’s writings that is both decoupled from Enlightenment notions of human nature, progress, and transcendental truth, as well as auto-critically engaged with the anti-authoritarian Enlightenment ethos of anarchist thought. In so doing, I hope to reveal how the Proudhonian deployment of reason retained a healthy skepticism of foundationalism, philosophical systems-building, and the intellectualism bred of its dogmatic excesses as well as reconsider Proudhon’s relation to our most privileged faculty.

In this article I tease out a conception of reason in Pierre-Joseph Proudhon’s writings that is both decoupled from Enlightenment notions of human nature, progress, and transcendental truth, as well as auto-critically engaged with the anti-authoritarian Enlightenment ethos of anarchist thought. In so doing, I hope to reveal how the Proudhonian deployment of reason retained a healthy skepticism of foundationalism, philosophical systems-building, and the intellectualism bred of its dogmatic excesses as well as reconsider Proudhon’s relation to our most privileged faculty.

Multiple biological groups, such as ant colonies, appear to have a noteworthy inefficiency: they contain vast amounts of redundant members that are not strictly needed to maintain the group. Philosophers and biologists have proposed that such inefficiency is illusory because redundancy enhances the resilience of groups when living under harsh conditions. Still, this proposal is unsatisfactory in different respects. First, it is too vague to account for when redundancy is selectively advantageous. Furthermore, it overlooks cases in which redundancy fails to (...) increase the resilience of groups. This paper offers an account of group redundancy that addresses these difficulties. Specifically, it advances the hypothesis that the mere presence of harsh conditions is not what drives the evolution of redundancy; rather, it is the fact organisms are often unable to predict when they will face harsh conditions. Redundancy enables groups to properly respond to unpredictable circumstances without resorting to the unreliable detection systems of their members. A better understanding of the phenomenon of redundancy is likely to impact other key issues in philosophy of science, including the evolution of cooperation and transitions in individuality, and the role of redundancy in complex systems, be they biological or not. (shrink)

Resehna do livro O IMPÉRIO DO DIREITO de FRANZ NEUMANN.

European thought begins with the Greeks. Scientific and philosophic thinking--the pursuit of truth and the grasping of unchanging principles of life--is a historical development, an achievement; and, as Bruno Snell writes in The Discovery of the Mind, nothing less than a revolution. The Greeks did not take mental resources already at their disposal and merely map out new subjects for discussion and investigation. In poetry, drama, and philosophy they in fact discovered the human mind. The stages in man's gradual (...) understanding of himself are revealed in the course of ancient literature from Homer to Virgil. A rational view of the nature of man slowly established itself in the creations of epic and lyric poetry, tragedy and literary criticism, pre-Socratic thought, and early Greek ethics all the way to the discovery of humanitas and the spiritual landscape of Virgil's Arcadia. The Discovery of the Mind is a landmark work in tracing this evolution of consciousness--one of the distinguishing characteristics of the history of man. (shrink)

The emergence of modern sciences in the seventeenth century profoundly renewed our understanding of Nature. For the last three centuries new ideas of Nature have been continuously developed by theology, politics, economics, and science, especially the sciences of the material world. The situation is even more unstable today, now that we have entered an ecological mutation of unprecedented scale. Some call it the Anthropocene, but it is best described as a new climatic regime. And a new regime it certainly is, (...) since the many unexpected connections between human activity and the natural world oblige every one of us to reopen the earlier notions of Nature and redistribute what had been packed inside. So the question now arises: what will replace the old ways of looking at Nature? This book explores a potential candidate proposed by James Lovelock when he chose the name "Gaia" for the fragile, complex system through which living phenomena modify the Earth. The fact that he was immediately misunderstood proves simply that his readers have tried to fit this new notion into an older frame, transforming Gaia into a single organism, a kind of giant thermostat, some sort of New Age goddess, or even divine Providence. In this series of lectures on "natural religion", Bruno Latour argues that the complex and ambiguous figure of Gaia offers, on the contrary, an ideal way to disentangle the ethical, political, theological, and scientific aspects of the now obsolete notion of Nature. He lays the groundwork for a future collaboration among scientists, theologians, activists, and artists as they, and we, begin to adjust to the new climatic regime. (shrink)

Serious actualism is the prima facie plausible thesis that things couldn’t have been related while being nothing. The thesis plays an important role in a number of arguments in metaphysics, e.g., in Plantinga’s argument for the claim that propositions do not ontologically depend on the things that they are about and in Williamson’s argument for the claim that he, Williamson, is necessarily something. Salmon has put forward that which is, arguably, the most pressing challenge to serious actualists. Salmon’s objection is (...) based on a scenario intended to elicit the judgment that merely possible entities may nonetheless be actually referred to, and so may actually have properties. It is shown that predicativism, the thesis that names are true of their bearers, provides the resources for replying to Salmon’s objection. In addition, an argument for serious actualism based on Stephanou, 219–250 2007) is offered. Finally, it is shown that once serious actualism is conjoined with some minimal assumptions, it implies property necessitism, the thesis that necessarily all properties are necessarily something, as well as a strong comprehension principle for higher-order modal logic according to which for every condition there necessarily is the property of being a thing satisfying that condition. (shrink)

Are there ‘self-referential’ propositions? That is, propositions that say of themselves that they have a certain property, such as that of being false. There can seem reason to doubt that there are. At the same time, there are a number of reasons why it matters. For suppose that there are indeed no such propositions. One might then hope that while paradoxes such as the Liar show that many plausible principles about sentences must be given up, no such fate will befall (...) principles about propositions. But the existence of self-referential propositions would dash such hopes. Further, the existence of such propositions would also seem to challenge the widespread claim that Liar sentences fail to express propositions. The aim of this paper is thus to settle the question–at least given an assumption. In particular, I argue that if propositions are structured, then self-referential propositions exist. (shrink)

Ontological pluralism is the view that there are different ways to exist. It is a position with deep roots in the history of philosophy, and in which there has been a recent resurgence of interest. In contemporary presentations, it is stated in terms of fundamental languages: as the view that such languages contain more than one quantifier. For example, one ranging over abstract objects, and another over concrete ones. A natural worry, however, is that the languages proposed by the pluralist (...) are mere notational variants of those proposed by the monist, in which case the debate between the two positions would not seem to be substantive. Jason Turner has given an ingenious response to this worry, in terms of a principle that he calls ‘logical realism’. This paper offers a counter-response on behalf of the ‘notationalist’. I argue that, properly applied, the principle of logical realism is no threat to the claim that the languages in question are notational variants. Indeed, there seems to be every reason to think that they are. (shrink)

Are there different sizes of infinity? That is, are there infinite sets of different sizes? This is one of the most natural questions that one can ask about the infinite. But it is of course generally taken to be settled by mathematical results, such as Cantor’s theorem, to the effect that there are infinite sets without bijections between them. These results settle the question, given an almost universally accepted principle relating size to the existence of functions. The principle is: for (...) any sets A and B, if A is the same size as B, then there is a bijection from A to B. The aim of the paper, however, is to argue that this question is in fact wide open: to argue that we are not in a position to know the answer, because we are not in one to know the principle. The aim, that is, is to argue that for all we know there is only one size of infinity. (shrink)

Theology as a science reflects the phenomena that in some way constitute the experience of faith in society, that is, looking at the world and the various periods of history with the help of the various sciences: anthropology, the sciences of religion and sociology. With the black traffic of the African continent, came the various customs lived in Africa: culture, religiosity, African myths, beliefs in the Orixás, all these elements constituted the Brazilian cultural imaginary. Thus syncretism arises as a form (...) of resistance and survival of faith. The Church with the Second Vatican Council and the post-conciliar declarations opens a new way of being in the world, valuing dialogue with other religions and cultures. (shrink)

I argue that dialetheists have a problem with the concept of logical consequence. The upshot of this problem is that dialetheists must appeal to a hierarchy of concepts of logical consequence. Since this hierarchy is akin to those invoked by more orthodox resolutions of the semantic paradoxes, its emergence would appear to seriously undermine the dialetheic treatments of these paradoxes. And since these are central to the case for dialetheism, this would represent a significant blow to the position itself.

I argue that dialetheists have a problem with the concept of logical consequence. The upshot of this problem is that dialetheists must appeal to a hierarchy of concepts of logical consequence. Since this hierarchy is akin to those invoked by more orthodox resolutions of the semantic paradoxes, its emergence would appear to seriously undermine the dialetheic treatments of these paradoxes. And since these are central to the case for dialetheism, this would represent a significant blow to the position itself.

This paper discusses three generic types or ways of understanding the common good found in the literature, and then describes the implications of the integral common good for seven key practices of humanistic management. In particular, compared to conventional management, an approach to humanistic management based on the integral common good tends to: 1) have institutional mission and vision statements that are developed by multiple stakeholders that emphasize social and ecological well-being ahead of financial well-being; 2) have a strategic orientation (...) that emphasizes collaboration, “minimizer” and “transformer” generic strategies, a Radical Resource Based View, and uses Porter’s five forces as a way to foster collaboration; 3) structure organizations based on experimentation, sensitization, dignification, and participation ; 4) develop control systems based on value loops that seek to enhance the flourishing of multiple stakeholders; 5) emphasize multi-directional multi-stakeholder communication; 6) invite all stakeholders to participate in making decisions, including developing and choosing alternatives; 7) foster leadership based on socialized power, a focus on SMART 2.0 goals, a desire to ensure everyone is treated fairly, and an emphasis on relationships that nurture community and the integral common good. Implications for research and teaching are discussed. (shrink)

This book provides a thoroughly worked out and systematic presentation of an interpretivist position in the philosophy of mind, of the view that having mental properties is a matter of interpretation. Bruno Mölder elaborates and defends a particular version of interpretivism, the ascription theory, which explicates the possession of mental states with contents in terms of their canonical ascribability, and shows how it can withstand various philosophical challenges. Apart from a defence of the ascription theory from the objections commonly (...) directed against interpretivism, the book provides a critical analysis of major alternative accounts of mental state possession as well as the interpretivist ideas originating from Donald Davidson and Daniel Dennett. The viability of the approach is demonstrated by showing how one can treat mental causation as well as the faculties closely connected with consciousness -- perception and the awareness of one’s own mental states -- in the interpretivist framework. (shrink)

This chapter challenges Cantor’s notion of the ‘power’, or ‘cardinality’, of an infinite set. According to Cantor, two infinite sets have the same cardinality if and only if there is a one-to-one correspondence between them. Cantor showed that there are infinite sets that do not have the same cardinality in this sense. Further, he took this result to show that there are infinite sets of different sizes. This has become the standard understanding of the result. The chapter challenges this, arguing (...) that we have no reason to think there are infinite sets of different sizes. It begins with an initial argument against Cantor’s claim that there are infinite sets of different sizes and then proceeds, by way of an analogy between Cantor’s mathematical result and Russell’s paradox, to a more direct argument. (shrink)