We review several of de Finetti’s fundamental contributions where these have played and continue to play an important role in the development of imprecise probability research. Also, we discuss de Finetti’s few, but mostly critical remarks about the prospects for a theory of imprecise probabilities, given the limited development of imprecise probability theory as that was known to him.

Constrained coherence is compared to coherence and its role in the behavioural interpretation of coherence is discussed. The equivalence of these two notions is proven for coherent conditional previsions, showing that the same course of reasoning applies to several similar concepts developed in the realm of imprecise probability theory.

Several authors have made claims about the compatibility between the Free Energy Principle and theories of autopoiesis and enaction. Many see these theories as natural partners or as making similar statements about the nature of biological and cognitive systems. We critically examine these claims and identify a series of misreadings and misinterpretations of key enactive concepts. In particular, we notice a tendency to disregard the operational definition of autopoiesis and the distinction between a system’s structure and its organization. Other misreadings (...) concern the conflation of processes of self-distinction in operationally closed systems and Markov blankets. Deeper theoretical tensions underlie some of these misinterpretations. FEP assumes systems that reach a non-equilibrium steady state and are enveloped by a Markov blanket. We argue that these assumptions contradict the historicity of sense-making that is explicit in the enactive approach. Enactive concepts such as adaptivity and agency are defined in terms of the modulation of parameters and constraints of the agent-environment coupling, which entail the possibility of changes in variable and parameter sets, constraints, and in the dynamical laws affecting the system. This allows enaction to address the path-dependent diversity of human bodies and minds. We argue that these ideas are incompatible with the time invariance of non-equilibrium steady states assumed by the FEP. In addition, the enactive perspective foregrounds the enabling and constitutive roles played by the world in sense-making, agency, development. We argue that this view of transactional and constitutive relations between organisms and environments is a challenge to the FEP. Once we move beyond superficial similarities, identify misreadings, and examine the theoretical commitments of the two approaches, we reach the conclusion that far from being easily integrated, the FEP, as it stands formulated today, is in tension with the theories of autopoiesis and enaction. (shrink)

Enactive cognitive science combines questions in epistemology, ontology, and ethics by conceiving of bodies as open-ended and mutually transforming through activity. While enaction is not a theory of ethics, it can contribute to its foundations. We present a schematization of enactive ideas that underlie traditional distinctions between Being, Knowing, and Doing. Ethics in this scheme begins in the relation between knowing and becoming. Critical of dichotomous thinking, we approach the questions of alterity and ethical reality. Alterity is relevant to the (...) enactive approach, but not in the radical sense of transcendental arguments. We propose difference, instead, as a more generative concept. Following Simondon, we see norms and values manifest in webs of past and future acts together with their potentialities for becoming. We propose a transindividual concept of moral attunement that includes ethical know-how and consciousness raising. Through generative difference and attunement to configurations of becoming, enaction underpins an ethics of participation linking virtue ethics and ethics of care. (shrink)

European Journal of Philosophy, Volume 29, Issue 4, Page 937-947, December 2021.

In a recent paper, Christian List (2014) has argued for the compatibilism of free will and determinism. Drawing on a distinction between physical possibility (used in defining determinism) and agential possibility (used in defining free will), List constructs a formal two-level model in which the two concepts are consistent. This paper's first contribution is to show that though List's model is formally consistent, philosophically it falls short of establishing a satisfactory compatibilist position. Ensuingly, an analysis of the shortcomings of the (...) model leads to the identification of a controversial epistemological assumption implicit in the statements of both compatibilist and incompatibilist positions. Arguing that this assumption is not currently satisfied, the paper's second contribution is to show that neither the compatibilist nor the incompatibilist position is presently well-founded. (shrink)

This paper investigates the link between informational consequence and credence. I first suggest a natural constraint, namely that informational consequence should preserve certainty: on any rational credence distribution, when the premises of an informational inferences have credence 1, the conclusion also has credence 1. Then I show that the certainty‐preserving constraint leads to triviality. In particular, the following three claims are incompatible: (i) informational consequence is extensionally distinct from classical consequence; (ii) informational inferences preserve certainty; (iii) credences obey (a subset (...) of) classical Bayesian constraints. The proof is straightforward, but the theoretical implications are substantial. Informational theorists need to either give up the idea that credence applies to epistemic discourse, or develop a nonclassical theory of credence and credal update. Moreover, the result also suggests that there is a connection between informational consequence and triviality results, including classical triviality results like Lewis's. (shrink)

In a previous paper we investigated the extraction of proof-theoretic properties of natural deduction derivations from their impredicative translation into System F. Our key idea was to introduce an extended equational theory for System F codifying at a syntactic level some properties found in parametric models of polymorphic type theory. A different approach to extract proof-theoretic properties of natural deduction derivations was proposed in a recent series of papers on the basis of an embedding of intuitionistic propositional logic into a (...) predicative fragment of System F, called atomic System F. In this paper we show that this approach finds a general explanation within our equational study of second-order natural deduction, and a clear semantic justification in terms of parametricity. (shrink)

Recently discovered correspondence from Oskar Becker to Hermann Weyl sheds new light on Weyl's engagement with Husserlian transcendental phenomenology in 1918-1927. Here the last two of these letters, dated July and August, 1926, dealing with issues in the philosophy of mathematics are presented, together with background and a detailed commentary. The letters provide an instructive context for re-assessing the connection between intuitionism and phenomenology in Weyl's foundational thought, and for understanding Weyl's term ‘symbolic construction’ as marking his own considered position (...) in the foundational controversy of the 1920s. In addition, they reveal Weyl's hitherto unknown objections to Becker's detailed attempt (Mathematische Existenz, 1927) to ground the transfinite phenomenologically. (shrink)

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)

Two mereological theories are presented based on a primitive apartness relation along with binary relations of mereological excess and weak excess, respectively. It is shown that both theories are acceptable from the standpoint of constructive reasoning while remaining faithful to the spirit of classical mereology. The two theories are then compared and assessed with regard to their extensional import.

In this essay I intend to analyze the issue of good government in the works of Adam Smith, the importance of which seems to have not received due attention. The reconstruction is driven by three hermeneutical hypotheses concerning the role played by the idea of good government in the development of Smith's speculation: 1) the «good government» has a synthetic character, holding together the different aspects – moral, legal, economic and political – of his reflection; 2) it emerges against the (...) backdrop of the first acquisitions of the Theory of Moral Sentiments about the ‘mediating’ role of the middle class, and especially during the reflection that goes from the Lectures on Jurisprudence to the Wealth of Nations, and then feeds back into the subsequent rewritings of the Theory; 3) From the moment the «good government» appears, it becomes a descriptive and prescriptive idea of the social order. In the conclusions I will show how these hermeneutical hypotheses might have implications in the history of political, legal and economic thought. (shrink)

An algebraization of the notion of topology has been proposed more than 70 years ago in a classical paper by McKinsey and Tarski, leading to an area of research still active today, with connections to algebra, geometry, logic and many applications, in particular, to modal logics. In McKinsey and Tarski’s setting the model theoretical notion of homomorphism does not correspond to the notion of continuity. We notice that the two notions correspond if instead we consider a preorder relation \( \sqsubseteq (...) \) defined by \(a \sqsubseteq b\) if _a_ is contained in the topological closure of _b_, for _a_, _b_ subsets of some topological space. A _specialization poset_ is a partially ordered set endowed with a further coarser preorder relation \( \sqsubseteq \). We show that every specialization poset can be embedded in the specialization poset naturally associated to some topological space, where the order relation corresponds to set-theoretical inclusion. Specialization semilattices are defined in an analogous way and the corresponding embedding theorem is proved. Specialization semilattices have the amalgamation property. Some basic topological facts and notions are recovered in this apparently very weak setting. The interest of these structures arises from the fact that they also occur in many rather disparate contexts, even far removed from topology. (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)

In previous work by Baaz and Iemhoff, a Gentzen calculus for intuitionistic logic with existence predicate is presented that satisfies partial cut elimination and Craig's interpolation property; it is also conjectured that interpolation fails for the implication-free fragment. In this paper an equivalent calculus is introduced that satisfies full cut elimination and allows a direct proof of interpolation via Maehara's lemma. In this way, it is possible to obtain much simpler interpolants and to better understand and overcome the failure of (...) interpolation for the implication-free fragment. (shrink)

Hippogriffs and unicorns have a fixed role in philosophical reflection: they serve as interchangeable examples of fictional objects. The purpose of this article is to show that there are many different forms of imaginary objects and that drawing a taxonomy of these objects actually means rethinking the relation that binds imaginative products to our world – a relation that is far from being univocal.

We devise exact conditions under which a join semilattice with a weak contact relation can be semilattice embedded into a Boolean algebra with an overlap contact relation, equivalently, into a distributive lattice with additive contact relation. A similar characterization is proved with respect to Boolean algebras and distributive lattices with weak contact, not necessarily additive, nor overlap.

Pierre de Fermat is known as the inventor of modern number theory. He invented–improved many methods useful in this discipline. Fermat often claimed to have proved his most difficult theorems thanks to a method of his own invention: the infinite descent. He wrote of numerous applications of this procedure. Unfortunately, he left only one almost complete demonstration and an outline of another demonstration. The outline concerns the theorem that every prime number of the form 4n + 1 is the sum (...) of two squares. In this paper, we analyse a recent proof of this theorem. It is interesting because: it follows all the elements of which Fermat wrote in his outline; it represents a good introduction to all logical nuances and mathematical variants concerning this method of which Fermat spoke. The assertions by Fermat will also be framed inside their historical context. Therefore, the aims of this paper are related to the history of mathematics and to the logic of proof-methods. (shrink)

In the lively discussions on Galileo's laws of motion after the Pisan's death, we observe what might be called a new “Galilean affair.” That is, a trial brought against his new science of motion mainly by French and Italian Jesuits with the substantial adherence of M. Mersenne. This new trail was originated by Gassendi's presentation of Galileo's de motu not simply as a perfectly coherent doctrine, but also as a convincing argument in favor of the truth of Copernicanism.

This article provides an overview of philosophical interpretations of Dostoevsky, focusing on readings that pay particular attention to his representation of the battle between good and evil, and postulating that said representation constitutes the essence of his works. The analysis maps this history of interpretations as developing within a specific framework: the dispute between interpreters who argue that good triumphs in Dostoevsky’s works and those who maintain that nihilism prevails in the end. In this context, the article submits its own (...) thesis: that a fundamental contradiction haunts the offer, in Dostoevsky’s works, of Christian salvation, and condemns Dostoevsky to defeat at the hands of his nihilists. (shrink)

We present a sequent calculus for extensional mereology. It extends the classical first-order sequent calculus with identity by rules of inference corresponding to well-known mereological axioms. Structural rules, including cut, are admissible.

Ce texte examine l’affirmation d’Aristote qui se trouve dans les Seconds Analytiques II 19, que la perception porte sur l’universel. L’examen s’effectuera par le biais du De Anima II 6 et III 6-8 où Aristote décrit les objets de la perception et de l’intellect. L’auteur soutient que selon Aristote, la perception humaine porte toujours sur l’universel contenu dans le particulier parce que l’unité de la substance individuelle est garante de l’unité de l’acte de perception. Par conséquent, l’analyse en termes de (...) trois objets de perception n’est que le résultat de la méthode analytique qu’Aristote emploie afin d’étudier l’acte de perception. (shrink)

The question of how, according to Aristotle, the principles of science are acquired remains contested among scholars. An aspect of this broader topic concerns the role of induction, and whether it is able to provide us with knowledge of natural necessity without the assistance of intuition. In a recent publication in this journal, David Botting argues in favour of the enumerative/empiricist interpretation of induction and criticizes the intuitive/rationalist interpretation of it, a version of which was defended in one of my (...) publications. He thinks that Aristotle is like Hume: both understand the cognitive process of induction similarly; and, both are equally skeptical about acquiring knowledge of natural necessity through induction. My reply argues that reading Aristotle’s induction in Humean terms is problematic in several respects. I argue, in addition, that natural necessity can be known through induction if nous is involved. My explanation of how this is possible relies on thinking of the act of noēsis in terms of an act of recognition. Botting claims, furthermore, that Aristotle only differs from Hume in that the former does have a non-inductive and non-intuitive method by which natural necessity may become known, and which Botting calls “the constructive proof of necessity”. My reply examines this method, showing how certain steps in it rely on cognitive acts that are really acts of intuition merely expressed in Humean terms. Despite the criticisms, I end with suggestions for how Botting’s account might offer original paths of research to Aristotle scholars seeking to answer the question of the acquisition of principles of science, particularly in the early stages of this process. (shrink)

This paper aims to foster an interdisciplinary dialogue between Ricoeur’s phenomenological- hermeneutical thought and human geography, in particular with respect to the issue of landscape interpretation. The connection draws on the idea that landscapes and lived spaces can be read as texts, not unfamiliar to human geography and semiotics from 1980s onward. In the first part of the paper I will briefly expound some theories of landscape which make use of the metaphors “landscape as cultural image” and “landscape as text” (...) in human and cultural geography. Then, I will discuss the main contribution of Ricoeur to the issue of space. The philosopher already envisioned a possible application of his “threefold mimesis” of Time and Narrative to architectural spaces. In the conclusion, I will propose to rejuvenate the geographical metaphor of “landscape as text” by introducing a possible application of the Ricoeurian notion of “meaningful action as text” to landscape. (shrink)

This paper is the first of a series of three articles that present the syntactic proof of the PA-completeness of the modal system G, by introducing suitable proof-theoretic objects, which also have an independent interest. We start from the syntactic PA-completeness of modal system GL-LIN, previously obtained in [7], [8], and so we assume to be working on modal sequents S which are GL-LIN-theorems. If S is not a G-theorem we define here a notion of syntactic metric d(S, G): we (...) calculate a canonical characteristic fomula H of S (char(S)) so that ⊢G ∼ H → (∼S) and ⊢GL-LIN ∼ H, and the complexity σ of ∼ H gives the distance d(S, G) of S from G. Then, in order to produce the whole completeness proof as an induction on this d(S, G), we introduce the tree-interpretation of a modal sequent Q into PA, that sends the letters of Q into PA-formulas describing the properties of a GL-LIN-proof P of Q: It is also a d(*, G)-metric linked interpretation, since it will be applied to a proof-tree T of ∼ H with H = char(S) and σ(∼ H) = d(S, G). (shrink)

In "The Measure of the Mental" (Davidson 1990), replying to a series of criticisms, that grow out of inadvertence or misunderstanding, Davidson has revisited his thesis concerning the physical and the mental, which he called "anomalous monism" (henceforth, AM). The thesis is subtle and elusive, as it is most often the case with Davidson: there is only one kind of event and state, which has a physical description (i.e., a description in physical terms) and may have a mental description too (...) (i.e., a description in mental terms) -- that shows the monism. But there is no strict law to go from a mental to a physical description of events and states or vice versa -- that shows the anomalousness.This sophisticated third way captures the intuition, generally shared today, that we are physical machines, whereas it acknowledges the mind a peculiarity: the mental is identical with a part of the physical, but no part of the mind is specifically identifiable with any part of the physical; or, more weakly, each mental event or state is identical with a physical one, though there is no systematic way to connect the mental and the physical. (shrink)

We present a cut-free sequent calculus for a class of first-order theories in negation normal form which include coherent and co-coherent theories alike. All structural rules, including cut, are admissible.

The main aim of this paper is to put Peano’s opinion about the unacceptability of the actual infinitesimal notion into evidence. First we briefly focus on the cultural environment where Peano’s considerations originated and developed. Then we examine Peano’s article of 1892, “Dimostrazione dell’impossibilità di segmenti infinitesimi costanti” [Peano 1892].

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)

The purpose of this paper is to contribute to shed some light on the early Stoics' practice of managing platonic suggestions to construct their epistemology. Instances of such a practice, which scholars have recently focussed on, are the Stoic reassessment of the account of phantasia Plato offers in the Sophist and the image of the wax block as discussed in the Theaetetus. In this work I put forward a comparison between the simile of the soul-book, as presented by Socrates in (...) the Philebus (39a1-c2), and the Stoic image of the soul as a sheet in which conceptions are inscribed. I try to show that a far-reaching investigation of the relationship between Plato and early Stoic epistemology should take such a comparison into due account. In section one, I go into the details of the comparison and argue that Plato's perceptual judgment (this is how I translate the term doxa as it is used in the relevant section of the Philebus) is compatible with Stoic phantasia. In section two, I try to show that the theorisation of assent enable the Stoics to reply to an objection Aristotle made to Plato's definition of phantasia as a mixture of perception and judgment. (shrink)

The aim of this paper is to say something significant about Stanley Cavell's style. To accomplish this task, we adopt a distant reading approach, quantifying what seems to be an idiosyncratic use of parentheses. After outlining our methodological approach and the choices of texts from Cavell's corpus, we will present the results of our quantitative analysis. Two kinds of results will be presented and interpreted: the result of a comparison between Cavell and other authors (i.e. why Cavell's use of parentheses (...) is exceptional) and the result of a quantitative analysis of Cavell's texts (i.e. how Cavell uses parentheses throughout his books). For both results, we will provide our own interpretation. In the conclusion, we will draw the moral of this parenthetical story, hoping to open future parentheses. (shrink)

The specific complexity of the question of genres depends on the plurality of the problems to which genre is pertinent and relevant. When Croce proclaimed, at the beginning of the century, the non-existence of the genre, he reduced the entire range of problems to the sole question relative to a work's belonging to a genre. In more recent times, there has been an attempt to reduce genre to the property of the linguistic act, in a methodological framework that understands poetics (...) exclusively as the science of literature. Against such reductionism, it is important to keep in mind a wider, more articulated idea of poetics as a pragmatic meditation, to investigate genres according to the multiple lines of systematization that are pertinent to them. (shrink)

Towards the end of The Coming Community (1993) [La comunità che viene, 1990], Giorgio Agamben writes something that may be interpreted as a paraphrase of Franz Kafka's famous statement that while t...

A default theory can be seen as a way for representing a set of formulae, i.e., its extensions. In this paper, we characterize the sets of formulae that can be expressed by a default theory according to various semantics: justified, constrained, rational, cumulative, QDL, CADL, and two semantics with priorities. These characterizations imply some non-translatability results between semantics.

This paper explores the death of God narrative through the lens of kenosis, drawing insights from thinkers such as Marcel, Heidegger, Vattimo, and Girard. It investigates the implications of kenotic thought for contemporary religious and philosophical discourse, exploring various interpretations of kenosis, ranging from Altizer and Žižek’s apocalyptic views to Vattimo’s more hopeful perspective. Through critical engagement with these viewpoints, this paper advocates for a nuanced understanding of kenosis inspired by Hegel, one that bypasses both radical theology and excessive optimism. (...) Methodologically, this study adopts a hermeneutic approach, analyzing key texts and engaging in philosophical dialogue. This paper concludes that rethinking kenotic thought could provide a robust framework for grappling with the death of God in the contemporary context, offering avenues for ethical reflection, social critique, and speculative renewal. (shrink)