An Introduction to Proof Theory provides an accessible introduction to the theory of proofs, with details of proofs worked out and examples and exercises to aid the reader's understanding. It also serves as a companion to reading the original pathbreaking articles by Gerhard Gentzen. The first half covers topics in structural proof theory, including the Gödel-Gentzen translation of classical into intuitionistic logic, natural deduction and the normalization theorems, the sequent calculus, including cut-elimination and mid-sequent theorems, and various applications of these (...) results. The second half examines ordinal proof theory, specifically Gentzen's consistency proof for first-order Peano Arithmetic. The theory of ordinal notations and other elements of ordinal theory are developed from scratch, and no knowledge of set theory is presumed. The proof methods needed to establish proof-theoretic results, especially proof by induction, are introduced in stages throughout the text. Mancosu, Galvan, and Zach's introduction will provide a solid foundation for those looking to understand this central area of mathematical logic and the philosophy of mathematics. (shrink)

Knowing is an activity through which agents and world produce themselves. This is often expressed by the enactive claim that agents bring forth a world. I analyse this idea for different modes of agent–environment engagement: interactional, transactional, and constitutional. Something is produced in each case. Bringing forth a world is not only an epistemic but an ontological claim. Acts in their fine structure result from a process of fact production, or f/acts. F/acts co-emerge with their 'preconditions', e.g.intentions, affordances, across the (...) subject/object divide. F/acts define their inner temporality and affectivity, comprising both event and experience. A plurality of worlds is admitted in this enactive view, without entailing antirealism. We cannot bring forth just any world. World resistance organizes action and experience. I touch on the implications for objectivity and free will and discuss the primordiality of activity, community, and relationality. From a notion of groundlessness in early enactive work, I suggest that a participatory universe is better conceived as a meshwork of groundless grounds. (shrink)

Past research on recruitment has shown that employer image predicts job seekers’ perceptions of organizational attractiveness. We contribute to this body of work by examining job seekers’ reactions to a market-dominant employer that has suffered from a case of corporate social irresponsibility (CSI). We show that job seekers’ reaction is buffered in the case of dominant employers’ wrongdoing. This effect is stronger for job seekers who are very interested in working in the dominant employers’ industry. Market dominance, however, reduces the (...) negative impact of CSI only under certain circumstances. We find that market dominance provides a buffer against the negative effect of CSI only when (1) CSI is directly relevant to the domain of performance of the organization and (2) job seekers feel very certain about their attitudes toward the organization. In two experiments with participants actively looking for employment at the time of study, we tested a model of moderated mediation examining how market dominance and CSI influence perceived employer ethicality and perceived employer competence. These two variables, in turn, explain how job seekers form perceptions of organizational attractiveness. This is the first study to explore how job seekers react to potential employers that are dominant in a market but have suffered from a CSI incident. The study identifies the boundary conditions that explain why sometimes market-dominant employers can emerge relatively unscathed in the eyes of job seekers following CSI. The research opens important managerial implications concerning the recruitment efforts of organizations that have suffered from CSI. (shrink)

Large Language Models (LLMs) are generative AI systems capable of producing original texts based on inputs about topic and style provided in the form of prompts or questions. The introduction of the outputs of these systems into human discursive practices poses unprecedented moral and political questions. The article articulates an analysis of the moral status of these systems and their interactions with human interlocutors based on the Habermasian theory of communicative action. The analysis explores, among other things, Habermas's inquiries into (...) the analogy between human minds and computers, and into the status of atypical participants in the linguistic community such as genetically modified subjects and animals. Major conclusions are the LLMs seem to qualify as authors that originally participate in discursive practices but do display only a structurally derivative form of communicative competence and fail to meet the status of communicative agents. In this sense, while the contribution of AI writing systems in public discourse and deliberation can support the process of mutual understanding within the community of speakers, the human actors involved in the development, use, and diffusion of these systems share a collective responsibility for the disclosure of AI authorship and verification and adjudication of validity claims. (shrink)

In the present paper we discuss a recent suggestion of Schroeder-Heister concerning the possibility of defining an intensional notion of harmony using isomorphism in second-order propositional logic. The latter is not an absolute notion, but its definition is relative to the choice of criteria for identity of proofs. In the paper, it is argued that in order to attain a satisfactory account of harmony, one has to consider a notion of identity stronger than the usual one (based on β- and (...) η-conversions) that the authors have investigated in recent work. (shrink)

Recent developments in generalized probability theory have renewed a debate about whether regularity (i.e., the constraint that only logical contradictions get assigned probability 0) should be a necessary feature of both chances and credences. Crucial to this debate, however, are some mathematical facts regarding the interplay between the existence of regular generalized probability measures and various cardinality assumptions. We improve on several known results in the literature regarding the existence of regular generalized probability measures. In particular, we give necessary and (...) sufficient conditions for the existence of regular generalized probability measures defined on the whole powerset of any sample space. (shrink)

The present article aims at providing some clarification on the Horkheimer-Neurath 1937 debate, so as to make three main claims: (a) around 1937 (even though perhaps neither in the early 1930s, at the time of his review of Mannheim’s Ideology and Utopia, nor after the Second World War, at the time of Adorno’s disenchanted statement, “the whole is the false”), Horkheimer belonged to the Hegelian-Marxist tradition stemming from Lukács’s History and Class Conscioussness (1923); (b) notwithstanding Neurath’s semantic and epistemological holism, (...) his fallibilism, his rejection of Wertfreiheit in the social sciences, his commitment to socialism, there is still a gulf between his position and Horkheimer’s, for Neurath did not accept the main methodological claim made by the latter, namely, the Lukács-inspired view that what “constitutes the decisive difference between Marxism and bourgeois thought” is the Hegelian “point of view of totality”; (c) highlighting the main differences between Neurath’s and Lukács’s versions of Marxism – one concerning the very idea of dialectic, and the other concerning the epistemic privilege of the proletariat – can throw some light on and help understand better the distinctive features of Lukács’s Hegelianization of Marxism. (shrink)

The thesis argues that a basic ontology of dóxa and appearances (and more in general mental episodes) can be gleaned from a careful analysis of Plato's early dialogues. To this aim, the first part (chapter 1) discusses the main issues concerning Plato's language of dóxa and appearances, both from the linguistic and from the philosophical point of view, and argues that dóxa is best understood as judgement. The second part develops a three-stage argument: chapter 2 argues that dóxa and appearances (...) are for Plato affections (páthe); chapter 3 that affections are for Plato fundamentally relational events; chapter 4 that, therefore, appearances are for Plato fundamentally relational events. The third and last part (chapter 5) investigates Plato's ontology of evaluative appearances (and desire) by focussing on the interplay between the ontology of appearances and the ontology of values (“goods and evils”) as one can extract it from the dialogue Gorgias. The three parts are secluded within a general introduction and conclusions. Four appendices complement the thesis with: a philosophical glossary of mental events; a table of frequencies of terms for mental episodes in the Platonic corpus; a list of all the occurrences of 'phaínomai' and 'dokéo' in the early dialogues; and a semi-formal appendix discussing the logical form of Plato's statements about metaphysical explanations. (shrink)

Part one: the act of speaking -- The speaker as performing artist -- The absolute performative -- The repetition of anthropogenesis -- Part two: toward a critic of interiority -- Second-degree sensualism: a physiognomic project -- In praise of reification -- Part three: from the beginning and right now -- Natural history -- The multitude and the principle of individuation -- Appendix: Wittgenstein and the question of atheism.

This book addresses the various systems in place for collaborative e-research and how these practices serve to enhance the quality of research across disciplines, covering new networks available through social media as well as traditional methods such as mailing lists and forums.

René Girard's mimetic theory has been object of much interest in the last few years, both in the 'Continental' and in the 'English-speaking' philosophical areas. Nevertheless, Girard's thought is not always accepted in the academic circles. The main cause for this is that his theory is considered too 'philosophical' in the Human Sciences Departments, and it seems too close to cultural anthropology and literary criticism to be appreciated by philosophers. This is the reason why it could be fruitful to focus (...) the attention on the philosophical aspects of René Girard's thought. I clarify what is meant exactly by 'philosophy' within the mimetic theory of René Girard and I define the borders of the problem of the 'death of philosophy,' as it appears from Girard's work. Then, I focus on philosophical hermeneutics and its relationship with the mimetic theory. Finally, I try to answer a central question: is it still possible to speak of 'philosophy' within the Girardian universe? (shrink)

The institution is always a heteronomous construction which supposes the intervention of a “fiat” establishing a break in the continuum of the natural succession of events. This beginning is a sequence of acts leading to a practical judgment on a reality that exists only because of this qualification. This is the sense of the legal verb instituere. The paper tests this vision of the institution on the case of a widespread practice in the managerial world: the 360-degree feedback. A Jesuit (...) genealogy of this practice illustrates new cultures within the firm and the consequences on the subjectivity level. (shrink)

In this study, in the light of Xavier Zubiri’s Metaphysics, we want to pay attention to the nuances of the term “transcendental”, trying to grasp shades and developments of its use in Zubiri’s thought to understand its originality and to be able to offer some clarifications on essential aspects of his philosophical system, in order to redefine his philosophy of reality as trans-physics.

One of the innovative approaches in contemporary philosophical ontology consists in the assumption of a plurality of ontologies based on different metaphysical presuppositions. Such presuppositions involve, among others, the identification of relevant properties for the objects of our domain as a guiding principle in uncovering what it is to be considered intrinsic and what could be the mere effect of selection preferences based on objective or subjective criteria. A remarkable example of the application of a background metaphysical theory in astrophysics (...) is the problem of selection biases in detecting cosmological objects, such as supernovae, galaxies and gamma-ray bursts. We will show that it is valuable to be aware of the importance of uncovering this type of background theory to better understand selection effects and to promote a novel approach in scientific research. (shrink)

In European culture the sacred and the secular have existed in a dialectical relationship. Prodi sees the fifteenth-century crisis of Christianity as opening up three paths that eroded this dualism and tended towards modernity: civic-republican religion, sacred monarchy, and the territorial churches. Important counter-forces, which sought to maintain dualism, included the Roman-Tridentine Compromise, and those forms of Radical Christianity which rejected confessionalisation outright. During the Eighteenth Century, all these phenomena tended to contribute to one of two tendencies: towards civic religion, (...) or towards political religion. The former preserved a distinction between conscience and law; the latter comprised a state religion which sought to perfect all of human nature. It was civic religion which become embodied in the early USA, alienating God from worldly power, but leaving him as the guarantor of agreements between humans. Back in Europe, Prodi tracks the relationship between the Catholic Church and the new national states. He then turns to the political religions of the Twentieth Century. Prodi concludes by emphasising that this dualism of sacred and secular power lay at the centre of Western modernity, and expresses his fears about the collapse of civic religion into political religion, especially in the USA. (shrink)

Recent crises in Europe and beyond have renewed a longstanding debate on the status and treatment of refugees. Hannah Arendt famously questioned the limits of universalistic human rights discourse based on the widespread phenomena of statelessness and displacement that emerged during and after World War II. In this paper, we analyze recent patterns of inclusion and exclusion of refugees in Italy through the lens of Arendtian narrative and theorizing. We consider three cases of interaction between families, schools, and other public (...) institutions in light of the shifting normative framework before and during the war in Ukraine. Two major insights emerge from this analysis. From a pedagogical point of view, the most promising educational practices with refugees are those centered on enabling their agency and corresponding experiences of "natality". From an ethical-political perspective, these practices highlight a latent tension between the universalistic scope of human rights enshrined in the human rights declarations and their structural dependence on the particular norms and procedures enacted by nation states. The understanding and teaching of human rights within our political communities is inseparable from the practices that engage with refugees. In this sense, our practices of inclusion and exclusion affect the understanding of national borders as a barrier or threshold with other political communities, but also the interpretation of our own ethical-political principles. (shrink)