Anti-realist epistemic conceptions of truth imply what is called the knowability principle: All truths are possibly known. The principle can be formalized in a bimodal propositional logic, with an alethic modality ${\diamondsuit}$ and an epistemic modality ${\mathcal{K}}$, by the axiom scheme ${A \supset \diamondsuit \mathcal{K} A}$. The use of classical logic and minimal assumptions about the two modalities lead to the paradoxical conclusion that all truths are known, ${A \supset \mathcal{K} A}$. A Gentzen-style reconstruction of the Church–Fitch paradox is presented (...) following a labelled approach to sequent calculi. First, a cut-free system for classical bimodal logic is introduced as the logical basis for the Church–Fitch paradox and the relationships between ${\mathcal {K}}$ and ${\diamondsuit}$ are taken into account. Afterwards, by exploiting the structural properties of the system, in particular cut elimination, the semantic frame conditions that correspond to KP are determined and added in the form of a block of nonlogical inference rules. Within this new system for classical and intuitionistic “knowability logic”, it is possible to give a satisfactory cut-free reconstruction of the Church–Fitch derivation and to confirm that OP is only classically derivable, but neither intuitionistically derivable nor intuitionistically admissible. Finally, it is shown that in classical knowability logic, the Church–Fitch derivation is nothing else but a fallacy and does not represent a real threat for anti-realism. (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)

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.

Using quantitative methods, we investigate the role of logic in analytic philosophy from 1941 to 2010. In particular, a corpus of five journals publishing analytic philosophy is assessed and evaluated against three main criteria: the presence of logic, its role and level of technical sophistication. The analysis reveals that logic is not present at all in nearly three-quarters of the corpus, the instrumental role of logic prevails over the non-instrumental ones, and the level of technical sophistication increases in time, although (...) it remains relatively low. These results are used to challenge the view, widespread among analytic philosophers and labeled here “prevailing view”, that logic is a widely used and highly sophisticated method to analyze philosophical problems. (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.

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 article investigates what happens when philosophy meets and begins to establish connections with two formal research methods such as game theory and network science. We use citation analysis to identify, among the articles published in Synthese and Philosophy of Science between 1985 and 2021, those that cite the specialistic literature in game theory and network science. Then, we investigate the structure of the two corpora thus identified by bibliographic coupling and divide them into clusters of related papers by automatic (...) community detection. Lastly, we construct by the same bibliometric techniques a reference map of philosophy, on which we overlay our corpora to map the diffusion of game theory and network science in the various sub-areas of recent philosophy. Three main results derive from this study. Philosophers are interested not only in using and investigating game theory as a formal method belonging to applied mathematics and sharing many relevant features with social choice theory, but also in considering its applications in more empirically oriented disciplines such as social psychology, cognitive science, or biology. Philosophers focus on networks in two research contexts and in two different ways: in the debate on causality and scientific explanation, they consider the results of network science; in social epistemology, they employ network science as a formal tool. In the reference map, logic—whose use in philosophy dates back to a much earlier period—is distributed in a more uniform way than recently encountered disciplines such as game theory and network science. We conclude by discussing some methodological limitations of our bibliometric approach, especially with reference to the problem of field delineation. (shrink)

This paper extends the axiomatic treatment of intuitionistic mereology introduced in Maffezioli and Varzi (_Synthese, 198_(S18), 4277–4302 2021 ) by examining the behavior of constructive notions of overlap and disjointness. We consider both (i) various ways of defining such notions in terms of other intuitionistic mereological primitives, and (ii) the possibility of treating them as mereological primitives of their own.

This paper develops sequent calculi for several classical modal logics. Utilizing a polymodal translation of the standard modal language, we are able to establish a base system for the minimal classical modal logic E from which we generate extensions in a modular manner. Our systems admit contraction and cut admissibility, and allow a systematic proof-search procedure of formal derivations.

Building on previous scholarly work on the mathematical roots of assertoric syllogistic we submit that for Aristotle, the semantic value of the copula in universal affirmative propositions is the relation of divisibility on positive integers. The adequacy of this interpretation, labeled here ‘arithmetical dictum’, is assessed both theoretically and textually with respect to the existing interpretations, especially the so-called ‘mereological dictum’.

We prove a generalization of Maehara’s lemma to show that the extensions of classical and intuitionistic first-order logic with a special type of geometric axioms, called singular geometric axioms, have Craig’s interpolation property. As a corollary, we obtain a direct proof of interpolation for (classical and intuitionistic) first-order logic with identity, as well as interpolation for several mathematical theories, including the theory of equivalence relations, (strict) partial and linear orders, and various intuitionistic order theories such as apartness and positive partial (...) and linear orders. (shrink)

A combination of epistemic logic and dynamic logic of programs is presented. Although rich enough to formalize some simple game-theoretic scenarios, its axiomatization is problematic as it leads to the paradoxical conclusion that agents are omniscient. A cut-free labelled Gentzen-style proof system is then introduced where knowledge and action, as well as their combinations, are formulated as rules of inference, rather than axioms. This provides a logical framework for reasoning about games in a modular and systematic way, and to give (...) a step-by-step reconstruction of agents omniscience. In particular, its semantic assumptions are made explicit and a possible solution can be found in weakening the properties of the knowledge operator. (shrink)

We investigate in intuitionistic first-order logic various principles of preference relations alternative to the standard ones based on the transitivity and completeness of weak preference. In particular, we suggest two ways in which completeness can be formulated while remaining faithful to the spirit of constructive reasoning, and we prove that the cotransitivity of the strict preference relation is a valid intuitionistic alternative to the transitivity of weak preference. Along the way, we also show that the acyclicity axiom is not finitely (...) axiomatizable in first-order logic. (shrink)

I investigate Bocheński's first-order logic formalization of the argument for the incorruptibility of the human soul given by Aquinas in Summa Theologiae (Ia,75,6). I suggest a slightly different axiomatization that reflect better Aquinas' informal argument. Along the way, I also fix a mistake in Bocheński's derivation that the human soul is not corruptible per se.

I focus on the commonly shared view that Hume’s monetary theory is inconsistent. I review several attempts to solve the alleged inconsistency in Hume’s monetary theory, including the consensus interpretation according to which Hume was committed to the neutrality of money only in the long run, while he conceded that money can be non-neutral in the short run. Then, building on a monetary version of the logical fallacy of monotonic counterfactuals in the essay Of the Balance of Trade, I argue (...) for the consistency of Hume’s theory of money by ascribing to Hume a distinction between money as collectively neutral and distributively non-neutral. (shrink)

The paper explores the proof theory of non-wellfounded mereology with binary fusions and provides a cut-free sequent calculus equivalent to the standard axiomatic system.

I provide a mereological analysis of Zeno of Sidon’s objection that in Euclid’s Elements we need to supplement the principle that there are no common segments of straight lines and circumferences. The objection is based on the claim that such a principle is presupposed in the proof that the diameter cuts the circle in half. Against Zeno, Posidonius attempts to prove against Zeno the bisection of the circle without resorting to Zeno’s principle. I show that Posidonius’ proof is flawed as (...) it fails to account for the case in which one of the two circumferences cut by the diameter is a proper part of the other. When such a case is considered, then either the bisection of the circle is false or it presupposes Zeno’s principle, as claimed by Zeno. (shrink)

From Brouwer To Hilbert: The Debate on the Foundations of Mathematics in the 1920s offers the first comprehensive introduction to the most exciting period in the foundation of mathematics in the twentieth century. The 1920s witnessed the seminal foundational work of Hilbert and Bernays in proof theory, Brouwer's refinement of intuitionistic mathematics, and Weyl's predicativist approach to the foundations of analysis. This impressive collection makes available the first English translations of twenty-five central articles by these important contributors and many others. (...) The articles have been translated for the first time from Dutch, French, and German, and the volume is divided into four sections devoted to (1) Brouwer, (2) Weyl, (3) Bernays and Hilbert, and (4) the emergence of intuitionistic logic. Each section opens with an introduction which provides the necessary historical and technical context for understanding the articles. Although most contemporary work in this field takes its start from the groundbreaking contributions of these major figures, a good, scholarly introduction to the area was not available until now. Unique and accessible, From Brouwer To Hilbert will serve as an ideal text for undergraduate and graduate courses in the philosophy of mathematics, and will also be an invaluable resource for philosophers, mathematicians, and interested non-specialists. (shrink)

A significant body of research concludes that stable beliefs of perceived consumer effectiveness lead to sustainable consumption choices. Consumers who believe that their decisions can significantly affect environmental and social issues are more likely to behave sustainably. Little is known, however, about how perceived consumer effectiveness can be increased. We find that feelings of guilt and pride, activated by a single consumption episode, can regulate sustainable consumption by affecting consumers’ general perception of effectiveness. This paper demonstrates the impact that guilt (...) and pride have on perceived consumer effectiveness and shows how this effect rests on the ability of these emotions to influence perceptions of agency. After experiencing guilt or pride, consumers see themselves as the cause of relevant sustainability outcomes. The process of causal attribution associated with these emotions influences consumers’ use of neutralization techniques. Through the reduction in consumers’ ability to neutralize their sense of personal responsibility, guilt and pride positively influence perceived consumer effectiveness. The inability to rationalize-away their personal responsibility, persuades consumers that they affect sustainability outcomes through their decisions. The research advances our understanding of sustainable consumption and identifies a new avenue for the regulation of individual consumer behavior that has significant implications for the development of sustainable marketing initiatives. (shrink)

A growing body of literature documents the important role played by moral outrage or moral anger in stakeholders’ reactions to cases of corporate social irresponsibility. Existing research focuses more on the consequences of moral outrage than a systematic analysis of how appraisals of irresponsible corporate behavior can lead to this emotional experience. In this paper, we develop and test, in two field studies, an extended model of moral outrage that identifies the cognitions that lead to, and are associated with, this (...) emotional experience. This research contributes to the existing literature on reactions to corporate social irresponsibility by explaining how observers’ evaluation of irresponsible corporate behavior leads to reactions of moral anger. The paper also helps clarify the difference between moral outrage and other types of anger and offers useful insights for managers who have to confront public outrage following cases of irresponsible corporate behavior. Finally, the analysis of the causes of stakeholders’ anger at irresponsible corporations opens important avenues for future research that are presented in the paper. (shrink)

The seventeenth century saw dramatic advances in mathematical theory and practice. With the recovery of many of the classical Greek mathematical texts, new techniques were introduced, and within 100 years, the rules of analytic geometry, geometry of indivisibles, arithmatic of infinites, and calculus were developed. Although many technical studies have been devoted to these innovations, Mancosu provides the first comprehensive account of the relationship between mathematical advances of the seventeenth century and the philosophy of mathematics of the period. Starting with (...) the Renaissance debates on the certainty of mathematics, Mancosu leads the reader through the foundational issues raised by the emergence of these new mathematical techniques, including the influence of the Aristotelian conception of science in Cavalieri and Guldin, the foundational relevance of Descartes' Geometrie, the relation between geometrical and epistemological theories of the infinite, and the Leibnizian calculus and the opposition to infinitesimalist procedures. In the process Mancosu draws a sophisticated picture of the subtle dependencies between technical development and philosophical reflection in seventeenth century mathematics. (shrink)

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

That words express a conceptual content is uncontroversial. This does not entail that their content should break down neatly into a grammatical part, relevant for language and to be analyzed in linguistic terms, and a conceptual part, relevant for cognition and to be analyzed in psychological terms. Various types of empirical evidence are reviewed, showing that the conceptual content of words cannot be isolated from their linguistic properties, because it is affected and shaped by them. The view of words as (...) labels or containers for a non-linguistic conceptual content stems from a naive disregard of the complex and structured nature of lexical knowledge. On the contrary, knowledge of language is shown not just to organize and categorize conceptual content in a way not reducible to non-linguistic cognition, but also to affect its scope, as the range of verbalized concepts is both limited by abstract templates and expanded by productive word formation. This suggests that lexical knowledge is a distinctively linguistic dimension of conceptualization, and that words do not so much label or package concepts, as provide an inner form for conceptual knowledge. (shrink)

Il libro ricostruisce la vita e il pensiero di Jean Guitton (1901-1999), il grande amico di Paolo VI, a quasi ventʼanni dalla sua morte. La vicenda umana di questo scrittore e filosofo cristiano ha attraversato quasi integralmente il XX secolo quale testimone diretto di eventi epocali: i primi tentativi ecumenici, le due guerre mondiali, le radicalizzazioni ideologiche del secondo dopoguerra, lʼera atomica e il Concilio Vaticano II. Il primo capitolo del volume è dedicato alla ricostruzione della vita di Guitton (...) e alle sue prime sintesi accademiche; ed esso fanno seguito altri due capitoli che trattano della sua antropologia (il tempo, il pudore, l'amore umano) e della sua cristologia filosofica (le condizioni di possibilità della rivelazione, la filosofia della risurrezione, la sua innovativa mariologia). Ne viene il ritratto di un pensiero di impronta umanista, ben radicato nella tradizione francese e che forse, come già lamentava Yves Congar nel 1963, non ha avuto, fino ad oggi, quellʼattenzione e quellʼaccoglienza che sembra meritare. (shrink)

Current research has documented how cases of irresponsible corporate behavior generate negative reactions from consumers and other stakeholders. Existing research, however, has not examined empirically whether the characteristics of the victims of corporate malfeasance contribute to shaping individual reactions. This study examines, through four experimental surveys, the role played by the national identity of the people affected on consumers’ intentions to spread negative word of mouth. It is shown that national identity influences individual reactions indirectly; mediated by perceived similarity and (...) sympathy. Consumers perceive foreign victims as different from the self and this reduces the sympathy experienced towards them. Sympathy is an emotion that shapes consumer reactions and regulates WOM. The study identifies two moderating processes of this effect. Individuals who score high on collective narcissism are most likely to be strongly biased against foreign victims. In-group bias is also moderated by the perceived severity of the crisis. When a case is perceived as very serious, perceived similarity plays a less important role in generating sympathy because consumers focus on the perceived suffering of the victims. Hence, in-group bias is stronger in cases perceived as having minor consequences. The paper contributes to the literature on corporate social irresponsibility and offers implications for both scholars and managers. (shrink)

On an influential line of thinking tracing back to Ramsey, conditionals are closely linked to the attitude of supposition. When applied to counterfactuals, this view suggests a subjunctive version of the so-called Ramsey test: the probability of a counterfactual If A, would B ought to be equivalent to the probability of B, under the subjunctive supposition that A. I present a collapse result for any view that endorses the subjunctive version of the Ramsey test. Starting from plausible assumptions, the result (...) shows that one’s rational credence in a would-counterfactual and in the corresponding might-counterfactual have to be identical. (shrink)

Meaningful places -- Fictional objects -- Migrant objects -- Multicultural and transcultural objects -- Objects as props -- Conclusion.

Suppose that you're certain that a certain sentence, e.g. "Frida is tall", lacks a determinate truth value. What cognitive attitude should you take towards it—reject it, suspend judgment, or what else? We show that, by adopting a seemingly plausible principle connecting credence in A and Determinately A, we can prove a very implausible answer to this question: i.e., all indeterminate claims should be assigned credence zero. The result is striking similar to so-called triviality results in the literature on modals and (...) conditionals. (shrink)

In this paper we investigate splitting algebras in varieties of logics, with special consideration for varieties of BL-algebras and similar structures. In the case of the variety of all BL-algebras a complete characterization of the splitting algebras is obtained.

Bringing together contributors from philosophy, international relations, security studies, and strategic studies, New Wars and New Soldiers offers a truly interdisciplinary analysis reflective of the nature of modern warfare. This comprehensive approach allows the reader to see the broad scope of modern military ethics, and to understand the numerous questions about modern conflict that require critical scrutiny. Aimed at both military and academic audiences, this paperback will be of significant interest to researchers and students in philosophy, sociology, military and strategic (...) studies, international relations, politics, and security studies, acting as an ideal course text or as supplementary reading. (shrink)

Heinrich Behmann (1891-1970) obtained his Habilitation under David Hilbert in Göttingen in 1921 with a thesis on the decision problem. In his thesis, he solved - independently of Löwenheim and Skolem's earlier work - the decision problem for monadic second-order logic in a framework that combined elements of the algebra of logic and the newer axiomatic approach to logic then being developed in Göttingen. In a talk given in 1921, he outlined this solution, but also presented important programmatic remarks on (...) the significance of the decision problem and of decision procedures more generally. The text of this talk as well as a partial English translation are included. (shrink)

At the same time, the book is a contribution to recent philosophical debates, in particular on the prospects for a successful nominalist reconstruction of .

In this paper we investigate splitting algebras in varieties of logics, with special consideration for varieties of BL-algebras and similar structures. In the case of the variety of all BL-algebras a complete characterization of the splitting algebras is obtained.

The literature on indicative conditionals contains two appealing views. The first is the selectional view: on this view, conditionals operate by selecting a single possibility, which is used to evaluate the consequent. The second is the informational view: on this view, conditionals don’t express propositions, but rather impose constraints on information states of speakers. Both views are supported by strong arguments, but they are incompatible on their standard formulations. Hence it appears that we have to choose between mutually exclusive options. (...) But the options are not exclusive. This paper develops a theory of the semantics and assertability of conditionals that is both selectional and informational. The theory vindicates the signature inferences of both selectional and informational theories, including so-called Conditionals Excluded Middle and principles about the interplay between conditionals and ‘might’. It also predicts some interesting and puzzling facts about the assertion of conditionals. (shrink)

The aim of this article is to tackle the sociosemiotic strategies through which the relation between power and visibility is articulated in today’s metropolitan São Paulo. Drawing on the theoretical-methodological framework of Greimasian and post-Greimasian semiotics, the following hypotheses are put forth: (1) contemporary São Paulo is characterized by a true visual hypertrophy, which manifests itself, all at once, in both its architectural and mediatic landscapes; (2) in São Paulo, power is hypervisible and apparently transparent; (3) the excess of images, (...) gazes, and perspectives produces, in São Paulo, dense and wide areas of topological, mediatic, and social invisibility; (4) the predominant visibility in São Paulo can be qualified as a “populist” visibility. Based on these assumptions, this article intends to contribute to the consolidation of a critical debate on the visual matrices of power and on social processes of exclusion and inclusion currently in place in global metropolises. Likewise, it is intended to contribute to the elaboration of a theoretical-methodological framework capable of understanding and addressing the complexity of the phenomena that characterize such debate. (shrink)

Este ensayo, dedicado a las doctrinas psicológicas de Alejandro, se divide en tres partes: la primera ilustra, a través de ejemplos tratados por el De anima, la concepción que tenía Alejandro de su actividad filosófica. Dado que Aristóteles ha transmitido las doctrinas más verdaderas, cree Alejandro, lo que hay que hacer es simplemente exponerlas de nuevo del modo más claro y completo, valiéndose de todo lo que dice Aristóteles respecto de las funciones psíquicas, incluso en obras diferentes del tratado principal. (...) La segunda parte del ensayo se centra en la sección inicial (1-26 Bruns) del tratado alejandrino, donde principalmente se prueba que el alma, como cualquier otra forma, es sólo la conjunción de las capacidades del cuerpo, cuya forma es el alma. Más aún, argumenta Accattino, tales capacidades anímicas nunca pueden expresarse independientemente del cuerpo, y menos aún con la desaparición del cuerpo. Por lo tanto, como forma del cuerpo, el alma es completamente mortal. La otra tesis célebre de Alejandro (la identificación del intelecto activo con el dios aristotélico de Metafísica Lambda) es tratada por Accattino en la tercera parte de su ensayo. Allí examina la noética del De intellectu de Alejandro y la sección dedicada a la noética en su De anima (80, 16-91, 6). En esta parte de su artículo el autor aclara, primero, los términos usados en la noética alejandrina (intelecto en potencia o intelecto “material”, intelecto entendido como “hábito”, intelecto “que viene de afuera”, el intelecto “agente”); luego ilustra el modo en que Alejandro da cuenta de la actividad intelectiva del intelecto humano y, finalmente, se concentra en el papel diferente que atribuye al intelecto agente (o el intelecto “que viene de afuera”, identificado por Alejandro con el intelecto divino) en el De intellectu y en la sección del De anima, respectivamente, de modo de mostrar que la posición más madura de Alejandro es la indicada en el De anima. (shrink)

This paper deals with a case of Virgilian ambiguity, namely the famous hemistich at Aen. 4.298 omnia tuta timens. By highlighting a plausible reading with a causal force (‘fearing everything too calm’, ‘because of the excessive calmness’), it seeks to demonstrate that this hemistich is an ambiguous passage. This view is confirmed through the imitation by Valerius Flaccus, who, in alluding to the Virgilian passage (Argonautica 8.408–12), highlights its ambiguity by including both of the most plausible readings.

Natural language conditionals seem to be subject to three logical requirements: they invalidate Antecedent Strengthening, they validate so-called Simplification of Disjunctive Antecedents, and they allow for the replacement of logically equivalent clauses in antecedent position. Unfortunately, these requirements are jointly inconsistent. Conservative solutions to the puzzle drop Simplification, treating it as a pragmatic inference. I show that pragmatic accounts of Simplification fail, and develop a truthmaker semantics for conditionals that captures all the relevant data. Differently from existing truthmaker semantics, my (...) semantics extends, rather than replaces, standard possible worlds semantics. The main innovation is the notion of a truthmaker in play: this notion is cognitive, rather than metaphysical, and can be defined in a purely syntactic way. (shrink)