This book contains an introduction to mathematical proofs, including fundamental material on logic, proof methods, set theory, number theory, relations, functions, cardinality, and the real number system. The book is divided into approximately fifty brief lectures. Each lecture corresponds rather closely to a single class meeting.

The 1927 Solvay conference was perhaps the most important meeting in the history of quantum theory. Contrary to popular belief, the interpretation of quantum theory was not settled at this conference, and no consensus was reached. Instead, a range of sharply conflicting views were presented and extensively discussed, including de Broglie's pilot-wave theory, Born and Heisenberg's quantum mechanics, and Schrödinger's wave mechanics. Today, there is no longer an established or dominant interpretation of quantum theory, so it is important to re-evaluate (...) the historical sources and keep the interpretation debate open. This book contains a complete translation of the original proceedings, with background essays on the three main interpretations of quantum theory presented at the conference, and an extensive analysis of the lectures and discussions in the light of current research in the foundations of quantum theory. The proceedings contain much unexpected material, including extensive discussions of de Broglie's pilot-wave theory (which de Broglie presented for a many-body system), and a theory of 'quantum mechanics' apparently lacking in wave function collapse or fundamental time evolution. This book will be of interest to graduate students and researchers in physics and in the history and philosophy of quantum theory. (shrink)

Given the metaphysical and explanatory stalemate between Embedded and Extended cognition, different authors proposed moral arguments to overcome such a deadlock in favor of EXT. Farina and Lavazza attribute to EXT and EMB a substantive moral content, arguing in favor of the former by virtue of its progressiveness and inclusiveness. In this treatment, I criticize four of their moral arguments. In Sect. 2, I focus on the argument from legitimate interventions and on the argument from extended agency. Section 3 concerns (...) the argument from better protection and the argument from better treatment. Sections 4 and 5 are dedicated to counterarguments against each respectively. By distinguishing between EXT and the extended view, I argue that it is sufficient to use this second version for directly addressing and evaluating moral problems on normative grounds, independently of the causal or constitutive cognitive influence of the external resource on the agents’ minds. Moreover, I argue that the arguments and assumptions used by EXT theorists do not foster values of progressiveness and inclusiveness. To conclude, in Sect. 6, I show that the analysis of each argument converges on the conclusion that EXT does not have substantive moral content and implications per se, since they always depend on further assumptions. (shrink)

According to virtue epistemology, the main aim of education is the development of the cognitive character of students (Pritchard, 2014, 2016). Given the proliferation of technological tools such as ChatGPT and other LLMs for solving cognitive tasks, how should educational practices incorporate the use of such tools without undermining the cognitive character of students? Pritchard (2014, 2016) argues that it is possible to properly solve this ‘technology-education tension’ (TET) by combining the virtue epistemology framework with the theory of extended cognition (...) (EXT) (Clark and Chalmers, 1998). He argues that EXT enables us to consider tools as constitutive parts of the students’ cognitive system, thus preserving their cognitive character from technologically induced cognitive diminishment. The first aim of this paper is to show that this solution is not sufficient to solve the TET. Second, I aim to offer a complementary and more encompassing framework of tool-use to address the TET. Then, I apply it to the educational uses of ChatGPT as the most notable example of LLM, although my arguments can be extended to other generative AI systems. To do so, in Sect. 1.1, I present Pritchard’s framework of cognitive character and virtue epistemology applied in education, to which I am committed in this treatment. In Sects. 2 and 3, I respectively illustrate Pritchard’s (2014) solution to the TET, and I highlight the general limitations of his proposal. Thus, in Sect. 4.1 I characterize ChatGPT as a computational cognitive artifact using Fasoli’s (2017, 2018) taxonomy of cognitive artifacts. In Sect. 4.2, I introduce my proposal, which combines Pritchard’s account of virtue epistemology with Fasoli’s (2017, 2018) taxonomy of cognitive artifacts to address the TET. Finally, in Sect. 5.1, I present some epistemically virtuous uses of ChatGPT in educational contexts. To conclude, I argue in favor of a multidisciplinary approach for analyzing educational activities involving AI technologies such as ChatGPT. (shrink)

The discussion about deep disagreement has gained significant momentum in the last several years. This discussion often relies on the intuition that deep disagreement is, in some sense, rationally irresolvable. In this paper, I will provide a theory of rationally irresolvable disagreement. Such a theory is interesting in its own right, since it conflicts with the view that rational attitudes and procedures are paradigmatic tools for resolving disagreement. Moreover, I will suggest replacing discussions about deep disagreement with an analysis of (...) rationally irresolvable disagreement, since this notion can be more clearly defined than deep disagreement and captures the basic intuitions underlying deep disagreement. I will first motivate this project by critically assessing the current debate about deep disagreement. I then detail the notions of rationality and resolvable disagreement which are crucial for a suitable theory of rationally irresolvable disagreement before sketching various instances of rationally irresolvable disagreement. Finally, I argue for replacing theories of deep disagreement with theories of rationally irresolvable disagreement, an approach that has significant advantages over existing theories of deep disagreement which focus on hinge propositions or fundamental epistemic principles. (shrink)

What makes trust such a powerful concept? Is it merely that in trust the whole range of social forces that we know play together? Or is it that trust involves a peculiar element beyond those we can account for? While trust is an attractive and evocative concept that has gained increasing popularity across the social sciences, it remains elusive, its many facets and applications obscuring a clear overall vision of its essence. In this book, Guido Möllering reviews a broad (...) range of trust research and extracts three main perspectives adopted in the literature for understanding trust. Accordingly, trust is presented as a matter of reason, routine or reflexivity. While all these perspectives contribute something to our understanding of trust, Möllering shows that they imply, but cannot explain, ‘suspension’ – the leap of faith that is typical of trust. He therefore proposes a new direction in trust research that builds on existing perspectives but places the suspension of uncertainty and vulnerability at the heart of the concept of trust. Beyond a purely theoretical line of argument, the author discusses implications for empirical studies of trust and presents original case material that captures the experience of trust in terms of reason, routine, reflexivity and suspension. Möllering concludes by suggesting how the new approach can enhance the relevance of trust research and its contributions to broader research agendas concerning the constitution of positive expectations in the face of prevalent uncertainty and change at various levels in our economies and societies. The book is essential reading for anyone who wants to gain a thorough understanding of trust. It can serve as a general introduction for advanced students and scholars in the social sciences, especially in economics, sociology, psychology and management. For more experienced researchers, it is a challenging and provocative critique of the field and a new approach to understanding trust. (shrink)

The origin of the concept of “emotional sharing” can be traced back to the first edition of Sympathiebuch [1913/23], in which Max Scheler paved the way to a phenomenology of emotions and to social ontology. The importance of his findings is evident: consider the central role of emotional sharing in Michael Tomasello’s analysis and the lively debate on social ontology and collective intentionality.

Interference phenomena are a well-known and crucial feature of quantum mechanics, the two-slit experiment providing a standard example. There are situations, however, in which interference effects are (artificially or spontaneously) suppressed. We shall need to make precise what this means, but the theory of decoherence is the study of (spontaneous) interactions between a system and its environment that lead to such suppression of interference. This study includes detailed modelling of system-environment interactions, derivation of equations (‘master equations’) for the (reduced) state (...) of the system, discussion of time-scales etc. A discussion of the concept of suppression of interference and a simplified survey of the theory is given in Section 2, emphasising features that will be relevant to the following discussion (and restricted to standard non-relativistic particle quantum mechanics.[1] A partially overlapping field is that of decoherent histories, which proceeds from an abstract definition of loss of interference, but which we shall not be considering in any detail. (shrink)

Modal knowledge accounts that are based on standards possible-worlds semantics face well-known problems when it comes to knowledge of necessities. Beliefs in necessities are trivially sensitive and safe and, therefore, trivially constitute knowledge according to these accounts. In this paper, I will first argue that existing solutions to this necessity problem, which accept standard possible-worlds semantics, are unsatisfactory. In order to solve the necessity problem, I will utilize an unorthodox account of counterfactuals, as proposed by Nolan, on which we also (...) consider impossible worlds. Nolan’s account for counterpossibles delivers the intuitively correct result for sensitivity i.e. S’s belief is sensitive in intuitive cases of knowledge of necessities and insensitive in intuitive cases of knowledge failure. However, we acquire the same plausible result for safety only if we reject his strangeness of impossibility condition and accept the modal closeness of impossible worlds. In this case, the necessity problem can be analogously solved for sensitivity and safety. For some, such non-moderate accounts might come at too high a cost. In this respect, sensitivity is better off than safety when it comes to knowing necessities. (shrink)

This book is primarily about checking and only derivatively about knowing. Checking is a very common concept for describing a subject’s epistemic goals and actions. Surprisingly, there has been no philosophical attention paid to the notion of checking. In Part I, I develop a sensitivity account of checking. To be more explicit, I analyze the internalist and externalist components of the epistemic action of checking which include the intentions of the checking subject and the necessary externalist features of the method (...) used. Crucially, successfully checking whether p is true requires using a method that is sensitive with respect to p, i.e. a method that would not indicate that p, if p were false. In Part II, I use the distinction between knowing and checking to explain central puzzles about knowledge, particularly puzzles centering on knowledge closure, puzzles concerning bootstrapping and the skeptical puzzle. Moreover, the book clarifies a dispute about modal epistemology, concerning the application of the sensitivity principle. By arguing that sensitivity is necessary for checking but not knowing, I explain where our persisting intuitions about sensitivity have their place in epistemology. (shrink)

En partant de la théorie des émotions développée par Mead et Dewey dans les années 1890, les aspects centraux de la théorie gestuelle de Mead, qui sous-tend sa théorie de l’émergence de la signification, du langage et de la cognition humaine, seront mis en évidence. L’article souligne, en outre, comment la théorie de Mead s’inscrit dans une perspective sociobiologique sur la naturalisation du langage qui gagne en intérêt aujourd’hui, notamment dans le domaine des théories évolutionnistes du langage et parmi les (...) neuroscientifiques. (shrink)

_Brill's Companion to Medieval and Early Platonism_ explores the impact exercised by Platonism on philosophy and many other fields of European culture, and the links it established with Christian, Jewish, Byzantine and Arabic traditions of thought during the Middle Ages and the early modern period.

In epistemology, the concept of knowledge is of distinctive interest. This fact is also reflected in the discussion of epistemic value, which focuses to a large extend on the value problem of knowledge. This discussion suggests that knowledge has an outstanding value among epistemic standings because its value exceeds the value of its constitutive parts. I will argue that the value of knowledge is not outstanding by presenting epistemic standings of checking, transferring knowledge, and proving in court, whose values exceed (...) the value of knowledge in certain contexts. Moreover, the values of these other epistemic standings do not always rely on the value of knowledge. In terms of value, knowledge is not an outstanding epistemic concept. Hence, in terms of value we cannot find support for the privileged position that knowledge enjoys in epistemology. (shrink)

An outstanding problem in so-called modal interpretations of quantum mechanics has been the specification of a dynamics for the properties introduced in such interpretations. We develop a general framework (in the context of the theory of stochastic processes) for specifying a dynamics for interpretations in this class, focusing on the modal interpretation by Vermaas and Dieks. This framework admits many empirically equivalent dynamics. We give some examples, and discuss some of the properties of one of them. This approach is applicable (...) to a wider class of theories, in particular, those using (discrete) strict effective—as in decoherence theory—superselection rules. (shrink)

The article argues in favour of a pragmatist enactive interpretation of the emergence of the symbolic and contentful mind from a basic form of social communicative interaction in which basic cognitive capacities are involved. Through a critical overview of Radical Enactivists (RECers)’ view about language, the article focuses on Mead’s pragmatist behavioural theory of meaning that refers to the gestural conversation as the origin of the evolution of linguistic conversation. The article develops as follows. After exposing the main elements of (...) REC’s theory of cognition and language that involve the construction of a theory of natural signs (teleosemiotics) and basic directionality (Ur-intentionality), some critical points of Hutto and Myin’s proposal will be highlighted. To foster a continuist perspective of language, the behavioural theory of meaning and language that Mead develops from the notion of gesture will be analysed. His theory is akin to REC and could augment the bare bones of REC’s sketched perspective, helping to include Ur-intentionality in a broader non-dualistic phylogenetic and ontogenetic theory of symbolic language from gestural communication, thus helping to overcome the distinction between a content-less intentionality and a content-involving intentionality, i.e., a semantic propositional intentionality. Furthermore, a recent revival of Mead’s theory testifies to its up-to-date relevance to explain the innate social dimension of human and non-human animals, and the human communicative capacity through the conditioning of bio-social canons and structures. (shrink)

Hassin recently proposed the “Yes It Can” (YIC) principle to describe the division of labor between conscious and unconscious processes in human cognition. According to this principle, unconscious processes can carry out every fundamental high-level cognitive function that conscious processes can perform. In our commentary, we argue that the author presents an overly idealized review of the literature in support of the YIC principle. Furthermore, we point out that the dissimilar trends observed in social and cognitive psychology, with respect to (...) published evidence of strong unconscious effects, can better be explained by the way how awareness is defined and measured in both research fields. Finally, we show that the experimental paradigm chosen by Hassin to rule out remaining objections against the YIC principle is unsuited to verify the new default notion that all high-level cognitive functions can unfold unconsciously. (shrink)

Leo Pardi was the initiator of ethological research in Italy. During more than 50 years of active scientific career, he gave groundbreaking contributions to the understanding of social life in insects, especially in Polistes wasps, an important model organism in sociobiology. In the 1940s, Pardi showed that Polistes societies are organized in a linear social hierarchy that relies on reproductive dominance and on the physiological and developmental mechanisms that regulate it, i.e. on the status of ovarian development of single wasps. (...) Pardi’s work set the stage for further research on the regulatory mechanisms governing social life in primitively eusocial organisms both in wasps and in other insect species. This article reconstructs Pardi’s investigative pathway between 1937 and 1952 in the context of European ethology and American animal sociology. This reconstruction focuses on the development of Pardi’s physiological approach and presents a new perspective on the interacting development of these two fields at the origins of our current understanding of animal social behavior. (shrink)

I discuss Edouard Machery’s claim that philosophers and psychologists when using the term ‘concept’ are really theorizing about different things. This view is not new, but it has never been developed or defended in detail. Once spelled out, we can see that Machery is right that the psychological literature uses a different notion of concept. However, Machery fails to acknowledge that the two notions are not only compatible but complementary. This fits more with the traditional view according to which philosophers (...) and psychologists are merely interested in different aspects of the same kind. The main aim of this paper is then to show how precisely the two notions of ‘concept’ relate. Distinguishing them resolves the long-standing debate on whether concepts can be prototypes and allows me to formulate success conditions of a theory of categorization that are independent of the success conditions of a theory of concepts. (shrink)

This paper provides a reinterpretation of some of the most influential skeptical arguments, Agrippa’s trilemma, meta-regress arguments, and Cartesian external world skepticism. These skeptical arguments are reasonably regarded as unsound arguments about the extent of our knowledge. However, reinterpretations of these arguments tell us something significant about the preconditions and limits of persuasive argumentation. These results contribute to the ongoing debates about the nature and resolvability of deep disagreement. The variety of skeptical arguments shows that we must distinguish different types (...) of deep disagreement. Moreover, the reinterpretation of skeptical arguments elucidates that deep disagreement cannot be resolved via argumentation. (shrink)

The aim of the article is to outline several valuable elements of Mead’s pragmatist theory of perception in action developed in his The Philosophy of the Act, in order to strengthen the pragmatist legacy of the enactivist approach. In particular, Mead’s theory of perception in action turns out to be a forerunner of sensorimotor enactivist theory. Unlike the latter, however, Mead explicitly refers to imagery as an essential capacity for agency. Nonetheless, the article argues that the ways in which Mead (...) refers to this capacity do not necessarily place it in opposition to enactivist non-representationalism. On the contrary, as a synthetic process of re-presenting of present and past sensorimotor elements, imagery can be seen as the hallmark of a pragmatically inspired sensorimotor enactivist approach that bypasses the opposition between representationalists and non-representationalists. (shrink)

Este estudo tem como objeto a recepção da teoria scotista da vontade no início do século 14. Interesse precípuo é o modo como autores, sobretudo franciscanos, a partir das Universidades de Paris e de Oxford, discutiram sobre a possibilidade de uma escolha livre ou de um ato da própria vontade, por parte dos bemaventurados, quando da visão de Deus. Para tanto, pressuposições gerais da teoria scotista da vontade são apresentadas, bem como as inovações dos filósofos influenciados por Scotus. PALAVRAS-CHAVE – (...) Teoria scotista da vontade. Visão beatífica. Liberdade. Influência do pensamento scotista no século 14. ABSTRACT This study aims to analyse the reception of Scotus’s theory of will in the beginning of the 14th Century. The main interest is the way some authors, specially Franciscan thinkers, departing from the Universities of Paris and Oxford, discussed about the possibility for the blessed of a free choice or an act of the will itself concerning the vision of God. For this purpose, general pressupositions of Scotus’s theory of will shall be presented, as well as the innovations of those philosophers influenced by Scotus. KEY WORDS – Scotus’s theory of will. Beatific vision. Freedom. Influence os Scotistic thought in the 14th Century. (shrink)

What is a race? Ernst Mayr (1904–2005) distinguishes between species in which biological change is continuous in space, and species in which groups of populations with different character combinations are separated by borders. In the latter species, the entities separated by borders are geographic races or subspecies. Many anthropology textbooks describe human races as discrete (or nearly discrete) clusters of individuals, geographically localized, each of which shares a set of ancestors, and hence can be distinguished from other races by their (...) common gene pool or by different alleles fixed in each. (shrink)

Modern society is challenged by a loss of efficiency in national governance systems values, and lifestyles. Corporate social responsibility (CSR) discourse builds upon a conception of organizational legitimacy that does not appropriately reflect these changes. The problems arise from the a-political role of the corporation in the concepts of cognitive and pragmatic legitimacy, which are based on compliance to national law and on relatively homogeneous and stable societal expectations on the one hand and widely accepted rhetoric assuming that all members (...) of society benefit from capitalist production on the other. We therefore propose a fundamental shift to moral legitimacy, from an output and power oriented approach to an input related and discursive concept of legitimacy. This shift creates a new basis of legitimacy and involves organizations in processes of active justification vis-à-vis society rather than simply responding to the demands of powerful groups. We consider this a step towards the politicization of the corporation and attempt to re-embed the debate on corporate legitimacy into its broader context of political theory, while reflecting the recent turn from a liberal to a deliberative concept of democracy. (shrink)

Discrimination is a central epistemic capacity but typically, theories of discrimination only use discrimination as a vehicle for analyzing knowledge. This paper aims at developing a self-contained theory of discrimination. Internalist theories of discrimination fail since there is no compelling correlation between discriminatory capacities and experiences. Moreover, statistical reliabilist theories are also flawed. Only a modal theory of discrimination is promising. Versions of sensitivity and adherence that take particular alternatives into account provide necessary and sufficient conditions on discrimination. Safety in (...) contrast is not sufficient for discrimination as there are cases of safety that are clearly instances of discrimination failure. The developed account of discrimination between objects will be extended to discrimination between kinds and between types. (shrink)

The orthodox view about sensitivity and induction has it that beliefs formed via induction are insensitive. Since inductive knowledge is highly plausible, this problem is usually regarded as a reductio argument against sensitivity accounts of knowledge. Some adherents of sensitivity defend sensitivity against this objection, for example by considering backtracking interpretations of counterfactuals. All these extant views about sensitivity and induction have to be revised, since the problem of sensitivity and induction is a different one. Regardless of whether we allow (...) backtracking interpretations of counterfactuals, some instances of induction yield insensitive beliefs whereas others yield sensitive ones. These results are too heterogenous for providing a plausible sensitivity-account of inductive knowledge. Induction remains a serious problem for sensitivity accounts of knowledge. (shrink)

In this paper, we discuss various aspects of Heisenberg’s thought on hidden variables in the period 1927–1935. We also compare Heisenberg’s approach to others current at the time, specifically that embodied by von Neumann’s impossibility proof, but also views expressed mainly in correspondence by Pauli and by Schroedinger. We shall base ourselves mostly on published and unpublished materials that are known but little-studied, among others Heisenberg’s own draft response to the EPR paper. Our aim will be not only to clarify (...) Heisenberg’s thought on the hidden-variables question, but in part also to clarify how this question was understood more generally at the time. (shrink)