Sets are central to mathematics and its foundations, but what are they? In this book Luca Incurvati provides a detailed examination of all the major conceptions of set and discusses their virtues and shortcomings, as well as introducing the fundamentals of the alternative set theories with which these conceptions are associated. He shows that the conceptual landscape includes not only the naïve and iterative conceptions but also the limitation of size conception, the definite conception, the stratified conception and the (...) graph conception. In addition, he presents a novel, minimalist account of the iterative conception which does not require the existence of a relation of metaphysical dependence between a set and its members. His book will be of interest to researchers and advanced students in logic and the philosophy of mathematics. (shrink)

Paolo Bozzi developed his «experimental phenomenology» from the Gestalt psychology tradition, particularly from Gaetano Kanizsa’s method. The distinction between «phenomenal description» and «causal explanation» of the «perception» springs up from the analysis of Bozzi’s «S-D psychophysical scheme». What Frege, who was well-known by Bozzi, deals with in paragraph 71 of The Thought theoretically mirrors what is outlined in the Scheme and could also be intended as its source. The juxtaposition between a «science of observable things» or «experimental phenomenology» – conceived (...) as a science which is autonomous from what happens in the brain – and logics, which is set up autonomously from the thinking processes, is a programmatic element that is openly indicated by the author. Frege’s anti-psychologism and realism are both widely shared by Bozzi. The realism and the «naïve physics» Bozzi was a pioneer of lie at the basis of the so-called «New Realism». The following essay aims to localize and highlight some theoretical implications – up to their phenomenological origins – which can be detected particularly in paragraph 71 of The Thought. The present work tries to sketch out the boundaries and the autonomy of the «first person» perceptive experience and to define the scientific explanation that we can give of it. The distinction between science and experience, and the autonomy of experience from science and of the immediate experience of the content of consciousness from neuroscience, entail the impossibility of a naturalization of the phenomenological experience. In the examples taken from Frege can be found a theoretical bridge which connects the Gestalt perceptological tradition, Wittgenstein’s investigations of the philosophy of psychology, and the so called «New Realism». (shrink)

A comparative analysis of the different notions of ‘ways of thinking’ introduced by philosophers. A guiding thread running through historical epistemology in an attempt to unify the researches of its authors. A comprehensive study of Ian Hacking’s ‘project of styles of reasoning’ and its implications for the relativism.

According to constitutivism, we can justify the authority of aims and norms on the ground that they are inescapable. Constitutivist views divide between ambitious and modest ones. According to ambitious constitutivism, the inescapability of aims grounds their unconditional authority, whereas according to modest constitutivism, the inescapability of aims only grounds their conditional authority. Either way, both forms of constitutivism share the assumption that inescapability grounds authority, which in turn presupposes that at the foundation of normativity we find aims and norms (...) that can be evaluated as having or lacking authority. In this paper I shall defend a form of constitutivism that rejects this assumption. According to this view, which I shall call Hinge Constitutivism, at the foundation of epistemic normativity we find an aim, the truth-aim, that is altogether beyond the evaluation in terms of the ordinary notion of authority. Moreover, I shall argue that to aim at truth is a condition of possibility for justifying the authority of any other aims or norms. In this sense, to aim at truth is a hinge of deliberation. (shrink)

We present epistemic multilateral logic, a general logical framework for reasoning involving epistemic modality. Standard bilateral systems use propositional formulae marked with signs for assertion and rejection. Epistemic multilateral logic extends standard bilateral systems with a sign for the speech act of weak assertion (Incurvati and Schlöder 2019) and an operator for epistemic modality. We prove that epistemic multilateral logic is sound and complete with respect to the modal logic S5 modulo an appropriate translation. The logical framework developed provides the (...) basis for a novel, proof-theoretic approach to the study of epistemic modality. To demonstrate the fruitfulness of the approach, we show how the framework allows us to reconcile classical logic with the contradictoriness of so-called Yalcin sentences and to distinguish between various inference patterns on the basis of the epistemic properties they preserve. (shrink)

ABSTRACTLinguistic evidence supports the claim that certain, weak rejections are less specific than assertions. On the basis of this evidence, it has been argued that rejected sentences cannot be premisses and conclusions in inferences. We give examples of inferences with weakly rejected sentences as premisses and conclusions. We then propose a logic of weak rejection which accounts for the relevant phenomena and is motivated by principles of coherence in dialogue. We give a semantics for which this logic is sound and (...) complete, show that it axiomatizes the modal logic KD45 and prove that it still derives classical logic on its asserted fragment. Finally, we defend previous logics of strong rejection as being about the linguistically preferred interpretations of weak rejections. (shrink)

We propose a nonmonotonic Description Logic of typicality able to account for the phenomenon of the combination of prototypical concepts. The proposed logic relies on the logic of typicality ALC + TR, whose semantics is based on the notion of rational closure, as well as on the distributed semantics of probabilistic Description Logics, and is equipped with a cognitive heuristic used by humans for concept composition. We first extend the logic of typicality ALC + TR by typicality inclusions of the (...) form p :: T(C) v D, whose intuitive meaning is that “we believe with degree p about the fact that typical Cs are Ds”. As in the distributed semantics, we define different scenarios containing only some typicality inclusions, each one having a suitable probability. We then exploit such scenarios in order to ascribe typical properties to a concept C obtained as the combination of two prototypical concepts. We also show that reasoning in the proposed Description Logic is EXPTIME-complete as for the underlying standard Description Logic ALC. (shrink)

As systems based on opaque Artificial Intelligence (AI) continue to flourish in diverse real-world applications, understanding these black box models has become paramount. In response, Explainable AI (XAI) has emerged as a field of research with practical and ethical benefits across various domains. This paper not only highlights the advancements in XAI and its application in real-world scenarios but also addresses the ongoing challenges within XAI, emphasizing the need for broader perspectives and collaborative efforts. We bring together experts from diverse (...) fields to identify open problems, striving to synchronize research agendas and accelerate XAI in practical applications. By fostering collaborative discussion and interdisciplinary cooperation, we aim to propel XAI forward, contributing to its continued success. Our goal is to put forward a comprehensive proposal for advancing XAI. To achieve this goal, we present a manifesto of 27 open problems categorized into nine categories. These challenges encapsulate the complexities and nuances of XAI and offer a road map for future research. For each problem, we provide promising research directions in the hope of harnessing the collective intelligence of interested stakeholders. (shrink)

In this paper I intend to demonstrate how Merleau-Ponty develops in his late thought an insightful account of reality. In opposition to the ontological primacy Husserl and Heidegger bestow to man, Merleau-Ponty’s late perspective is based on a dynamic ontology, namely on a philosophical understanding of the strict relation between nature and consciousness. With this respect, Merleau- Ponty approaches the problem of negativity, in order to explain the differences within reality without adopting an Hegelian account of dialectic and, on the (...) other hand, avoiding a merely empirical view of contingency. (shrink)

In this work, we present some traits of the socio-political and economic thought of Giuseppe Toniolo, who lived in Italy at the turn of the XIX and XX century, with special reference to the contribution that the Italian economist and sociologist gave to the definition and implementation of the principle of subsidiarity and to the ethical foundation of economic science. After outlining the definition of the subsidiarity principle in the first paragraph, we sketch the historical background in which Toniolo lived (...) and operated. We then focus on the ethical factor and on the concept of subsidiary State emerging from Toniolo’s writings. Finally, we present some of the main elements of Toniolo’s legacy with reference to the current economic and socio-political debate. (shrink)

We present an inferentialist account of the epistemic modal operator might. Our starting point is the bilateralist programme. A bilateralist explains the operator not in terms of the speech act of rejection ; we explain the operator might in terms of weak assertion, a speech act whose existence we argue for on the basis of linguistic evidence. We show that our account of might provides a solution to certain well-known puzzles about the semantics of modal vocabulary whilst retaining classical logic. (...) This demonstrates that an inferentialist approach to meaning can be successfully extended beyond the core logical constants. (shrink)

HSimulator is a multithread simulator for mass-action biochemical reaction systems placed in a well-mixed environment. HSimulator provides optimized implementation of a set of widespread state-of-the-art stochastic, deterministic, and hybrid simulation strategies including the first publicly available implementation of the Hybrid Rejection-based Stochastic Simulation Algorithm. HRSSA, the fastest hybrid algorithm to date, allows for an efficient simulation of the models while ensuring the exact simulation of a subset of the reaction network modeling slow reactions. Benchmarks show that HSimulator is often considerably (...) faster than the other considered simulators. The software, running on Java v6.0 or higher, offers a simulation GUI for modeling and visually exploring biological processes and a Javadoc-documented Java library to support the development of custom applications. HSimulator is released under the COSBI Shared Source license agreement. (shrink)

La tesi di Alfred Korzybski secondo cui «la mappa non è il territorio» non è semplice come appare. Seguendo le idee di Bateson al riguardo, potremmo comparare il «territorio» alla kantiana «cosa in sé», sfondo inaccessibile della percezione e della conoscenza, soggetta a procedure di oggettazione interminabili; ma se il «territorio» è concepito come inaccessibile in senso stretto, le nostre mappe possono fare riferimento soltanto ad altre mappe. Trattando l’argomento, questo articolo considera alcune varianti del problema mappa-territorio ed argomenta che (...) un osservatore umano conosce ed elabora le proprie credenze in una dimensione intermedia tra le mappe simbolico-concettuali e i territori percettivi. (shrink)

Bus bunching is ostensibly regarded as a detrimental phenomenon in bus systems. We study a bus loop with two bus stops, one regular bus stop and one spike bus stop, where bunched buses can outperform staggered buses. The spike bus stop models a bus stop connected to a train or metro service, where passengers arrive in groups at periodic intervals. We introduce the configuration of synchronised bunched buses, where bunched buses wait for the spike in demand. For a wide range (...) of parameters, synchronised bunched buses outperform perfectly staggered buses in terms of minimising the waiting time of commuters. We present an analytical formulation of the average waiting time in the case of bunched buses, synchronised bunched buses, and perfectly staggered buses with the consideration of different passenger demands, number of buses, and bus capacity. We demonstrate the validity of our analytical results through an agent-based simulation of the bus loop system. (shrink)

We discuss a well-known puzzle about the lexicalization of logical operators in natural language, in particular connectives and quantifiers. Of the many logically possible operators, only few appear in the lexicon of natural languages: the connectives in English, for example, are conjunction _and_, disjunction _or_, and negated disjunction _nor_; the lexical quantifiers are _all, some_ and _no_. The logically possible nand (negated conjunction) and Nall (negated universal) are not expressed by lexical entries in English, nor in any natural language. Moreover, (...) the lexicalized operators are all upward or downward monotone, an observation known as the Monotonicity Universal. We propose a logical explanation of lexical gaps and of the Monotonicity Universal, based on the dynamic behaviour of connectives and quantifiers. We define update potentials for logical operators as procedures to modify the context, under the assumption that an update by \( \phi \) depends on the logical form of \( \phi \) and on the speech act performed: assertion or rejection. We conjecture that the adequacy of update potentials determines the limits of lexicalizability for logical operators in natural language. Finally, we show that on this framework the Monotonicity Universal follows from the logical properties of the updates that correspond to each operator. (shrink)

We show that if Ƒ is any "well-behaved" subset of the Borei functions and we assume the Axiom of Determinacy then the hierarchy of degrees on $P(^\omega \omega )$ induced by Ƒ turns out to look like the Wadge hierarchy (which is the special case where Ƒ is the set of continuous functions).

In the contemporary epistemological debate on social reality, characterized by the crisis of post-modern theories and the emergence of new forms of realism, are there any approaches not acknowledging some specific ontological character to the construction of social objects? The question is apparently rhetorical, but the implication of this problem are not obvious. In the sociological literature the opposition between reality and construction is not clearly defined. Sometimes it is considered a dichotomy, in other situations the synthesis of alternative theses (...) in a dialectical horizon. The more systematic attempt considers reality and construction as analytical macro-dimensions where the relation between social ontology and epistemology operates. From this stance, the acknowledgement of the role of social construction in a wider realist horizon is the true overtaking of postmodern philosophy. If it is true that facts exist beyond representations, it is also true that representations themselves have a specific effect on reality, who continually re-structures itself around specific relations of emergent power. Stating that reality is socially constructed is an evident limit of postmodern theories. On the other hand, stating that only facts exist constitute an impoverishment of realism and its replacement in neo-positivism. Social phenomena are real because they are based on specific properties of the inter-subjective construction of social reality. This thesis represents the revitalization of an advanced, anti-positivistic realism and the definition of the specificity of social objects. The aim of this essay is to search for a specific place of construction within the development of realist social ontology. (shrink)

; Some students in the audience liked the talk, but not all. The intuitive meaning of the sentences in (1) imposes restrictions (the material underlined in the glosses) that go beyond the meaning of logical disjunction or existential quantification: in formal logic, P ∨ Q is true if both disjuncts are, and ∃xP (x) is true if the P holds of all entities in the domain of quantification.

I review recent work on Phenomenal Conservatism, the position introduced by Michael Huemer according to which if it seems that P to a subject S, in the absence of defeaters S has thereby some degree of justification for believing P.

We develop a novel solution to the negation version of the Frege-Geach problem by taking up recent insights from the bilateral programme in logic. Bilateralists derive the meaning of negation from a primitive *B-type* inconsistency involving the attitudes of assent and dissent. Some may demand an explanation of this inconsistency in simpler terms, but we argue that bilateralism’s assumptions are no less explanatory than those of *A-type* semantics that only require a single primitive attitude, but must stipulate inconsistency elsewhere. Based (...) on these insights, we develop a version of B-type expressivism called *inferential expressivism*. This is a novel semantic framework that characterises meanings by inferential roles that define which *attitudes* one can *infer* from the use of terms. We apply this framework to normative vocabulary, thereby solving the Frege-Geach problem generally and comprehensively. Our account moreover includes a semantics for epistemic modals, thereby also explaining normative terms under epistemic modals. (shrink)

In this chapter, we investigate whether psychopathy is a mental disorder. We argue that addressing this question requires engaging, at least, with three principal issues that have conceptual, empirical, and normative dimensions. First, it must be established whether current measures of psychopathy individuate a unitary class of individuals. By this we mean that persons classifed as psychopaths should share some relevant similarities that support explanation, prediction, and treatment. Second, it must be proven that psychopathy harms the person who has it. (...) Third, it must be established that the harm associated with psychopathy is relevant for the ascription of disorder status. Regarding this latter issue, we argue that psychopathy should be considered a disorder if its harmfulness derives from certain incapacities or limited capacities. These incapacities should affect basic competences that are justifably required for conducting a preferable type of life. Within this framework, we tentatively advance the hypothesis that some normatively justifed conclusions and empirical evidence about psychopathy, that needs nonetheless to be further investigated, might support the claim that people with psychopathy have a mental disorder. (shrink)

In [9] we have considered a wide class of "well-behaved" reducibilities for sets of reals. In this paper we continue with the study of Borel reducibilities by proving a dichotomy theorem for the degree-structures induced by good Borel reducibilities. This extends and improves the results of [9] allowing to deal with a larger class of notions of reduction (including, among others, the Baire class ξ functions).

This edited volume systematically addresses the connection between Wilfrid Sellars and the history of modern philosophy, exploring both the content and method of this relationship. It intends both to analyze Sellars’s position in relation to singular thinkers of the modern tradition, and to inquire into Sellars’s understanding of philosophy as a field in reflective and constructive conversation with its past. The chapters in Part I cover Sellars’s interpretation and use of Descartes, Leibniz, Hume, Kant and Hegel. Part II features essays (...) on his relationship with Peirce, Frege, Carnap, Wittgenstein, American pragmatism, behaviorism and American realism, particularly his father, Roy Wood. Sellars and the History of Modern Philosophy features original contributions by many of the most renowned Sellars scholars throughout the world. It offers an exhaustive survey of Sellars’s views on the historical antecedents and metaphilosophical aspects of his thought. (shrink)

Antinaturalistic Strategies in Beyond Good and Evil. Naturalistic interpretations of Nietzsche’s thought ultimately appeal to two arguments. On the one hand, when tracing various human phenomena back to processes sufficiently explicable by the natural sciences, it would appear that Nietzsche was pursuing a de facto naturalization program. On the other hand, in BGE 230, the need for the naturalization of human beings as a whole is often interpreted as an argument de jure. After outlining some basic features of contemporary naturalism (...) and showing its incompatibility with Nietzsche’s philosophy, I argue in this paper that neither the de jure nor the de facto argument can be understood in a naturalistic sense. The task of “translating man back into nature” in BGE 230 is indeed turned against a point of view held by “old metaphysical bird-catchers.” An analysis of the manuscript and a comparison of it with the preface to HH I, in which this figure is used in the opposite sense, suggests rather that Nietzsche conceives of the renaturalization of the human in a deceptive way, that is, as one of those numerous “snares and nets for unwary birds” scattered throughout his works. Widening this view, a similar dynamic arises with respect to the de facto argument. In the concluding section, I highlight how, in On the Prejudices of Philosophers, certain naturalization operations are countered by as many arguments to the contrary. Such sudden shifts in perspective seem to indicate, at least in Beyond Good and Evil, a desire to subvert naturalism from within. (shrink)

Many classically valid meta-inferences fail in a standard supervaluationist framework. This allegedly prevents supervaluationism from offering an account of good deductive reasoning. We provide a proof system for supervaluationist logic which includes supervaluationistically acceptable versions of the classical meta-inferences. The proof system emerges naturally by thinking of truth as licensing assertion, falsity as licensing negative assertion and lack of truth-value as licensing rejection and weak assertion. Moreover, the proof system respects well-known criteria for the admissibility of inference rules. Thus, supervaluationists (...) can provide an account of good deductive reasoning. Our proof system moreover brings to light how one can revise the standard supervaluationist framework to make room for higher-order vagueness. We prove that the resulting logic is sound and complete with respect to the consequence relation that preserves truth in a model of the non-normal modal logic _NT_. Finally, we extend our approach to a first-order setting and show that supervaluationism can treat vagueness in the same way at every order. The failure of conditional proof and other meta-inferences is a crucial ingredient in this treatment and hence should be embraced, not lamented. (shrink)