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.

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.

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.

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)

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’.

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)

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.

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)

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)

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)

In Multi Agent Systems it is often the case that individual preferences are not compatible and coalitions compete to achieve a given result. The paper presents a language to talk about the conflict between coalitional choices and it expresses deontic notions to evaluate them. We will be specifically concerned with cases where the collective perspective is at odds with the individual perspective.

This article introduces a novel theoretical framework for addressing epistemic injustice—a phenomenon where certain groups or individuals are systematically excluded from knowledge creation and dissemination processes—by employing ontological relativity and conceptual analysis. “Ontological relativity” refers to a philosophical perspective that posits our understanding of reality as being shaped by our toolbox of concepts, categories, language, and social practices; “conceptual analysis” is a method of inquiry that involves the rigorous examination and deconstruction of a particular concept or set of concepts in (...) order to uncover their constituent elements, relationships, and underlying assumptions. To exemplify the effectiveness of the ontology‐based approach, two paradigmatic applications are explored: (a) educational practices and (b) clinical practice and access to health care. Through the presentation of these applications and the step‐by‐step illustration of the applied methodology, the aim of the article is to showcase the efficacy of ontology in tackling epistemic injustices, suggesting innovative paths for future research in this domain. (shrink)

The study of evil and the different forms in which it manifests itself has long been the interest of a significant number of scholars, mainly philosophers and theologians. Yet, following the libera...

Can taxation and the redistribution of wealth through the welfare state be conceived as a modern system of circulation of the gift? But once such a gift is institutionalized, regulated and sanctioned through legal mechanisms, does it not risk being perverted or corrupted, and/or not leaving room for genuinely altruistic motives? What is more: if the market’s utilitarian logic can corrupt or ‘crowd out’ altruistic feelings or motivations, what makes us think that the welfare state cannot also be a source (...) of corruption? To explain the standard answers to the abovementioned questions as well as their implications I will first re-examine two opposing positions assumed here as paradigmatic examples of other similar positions: on the one hand, Titmuss’s work and the never-ending debate about it; on the other, Godbout’s position, in-so-far as it shows how Titmuss’s arguments can easily be turned upside down. I will then introduce and reinterpret Einaudi’s “critical point” theory as a more complex and richer anthropological explanation of the problems and answers considered herein. Through the analysis of these paradigmatic positions I will develop two interrelated arguments. 1) The way these problems are posed as well as the standard answers to them are: a) subject to fallacies: the dichotomy fallacy and the fallacy of composition; b) too reductive and simplistic: we should at least try to clarify what kind of ‘gift’ or ‘corruption’ we are thinking about, and who or what the ‘giver’, the ‘corrupter’, the ‘receiver’ and/or the ‘corrupted’ party are. 2) The answers to these problems cannot be found by merely following a theoretical approach, nor can they be merely based on empirical evidence; instead, they need to take into account the forever troublesome, ambiguous and unpredictable matter of human freedom. (shrink)

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)

The publication of Guido Calabresi’s book “The Future of Law and Economics” has drawn a substantial amount of attention among law and economics scholars. We thought that the best way to devote special attention to this book was to devote a Special issue to it. This article situates Calabresi’s book among other reflections on the future of the discipline, introduces and explains the reasons behind this Special issue and discuss the organization and content of it. -/- We emphasize how Calabresi’s (...) historical-conceptual standpoint allows him to isolate the stakes of different future developments around the question of how could further appreciation of legal institutions that defy the standard economic assumptions help the field develop theoretically. Overall, the contributors all shared Calabresi’s attempt to restore the balance between Law and Economics and the need to better account for the “whole unanalysed experience of human race”, often neglected by the Economic Analysis of Law approach. Most disagreements are about the ‘how’. In any case, the search for the Law and Economics ‘not (yet) taken’ or for other “Law and … ” approaches is always open to the Future. (shrink)

This introduction explains the reasons behind this Special issue and discuss the organization and content of it. The difficulty of a genuine dialogue and understanding between economics, law and humanities, seems to be due not only to the fragmentation of reflections on man, but to a real ‘conflict of anthropologies’. What kind of conceptions of man and human values are presupposed by and / or privileged by economics, law, economic approaches to law and social sciences? How and when do these (...) conceptions come into conflict within and between disciplines? How do these conceptions of man and his values influence the conceptions of economics, law and institutions, and vice versa, how do these last conceptions influence the former? What are the normative, regulatory and practical implications of assuming an anthropological and / or axiological perspective instead of another? This Special issue aims at exploring the possibility of finding a common ground for discussion between economics, law and humanities, through the analysis and comparison of both the conceptions of man, human action and values assumed by economics, law and humanities, and their normative implications. The contributions to this Special issue and its organization are outlined at the end of this introduction. (shrink)

The paper aims to address the following two questions: what kind of discourse is that which attempt to found or defend the autonomy or the boundaries of a discipline? Why do such discourses tend to turn into normative, dogmatic-excommunicating discourses between disciplines, schools or scholars? I will argue that an adequate answer may be found if we conceive disciplines as dogmatics, where such discourses often take the form of a discourse on the foundation of a discipline, a foundation in the (...) name of which the scholar speaks and with which he/she entertains an identity relationship. To this purpose I will re-examine the methodological discourses of (and debates between) Pareto, Croce and Einaudi on the demarcation issue between philosophy, economics and value-judgments as highly instructive to understand such issues. (shrink)

According to McDowell, in Empiricism and the Philosophy of Mind the myth of Jones has the purpose of completing the account of experience that Sellars needs to argue against traditional empiricism. In particular, on McDowell's view the myth of Jones should explain how to conceive of non-inferentially knowable experiences as containing propositional claims. This article argues that the myth of Jones does not succeed in providing such an account, especially on McDowell's own terms: assuming McDowell's epistemological distinction between inferential and (...) non-inferential knowledge, it turns out that in Sellars' thought experiment perceptual experiences can contain propositional claims only at the price of being known inferentially rather than non-inferentially. Therefore McDowell's Sellars' attack fails against traditional empiricism. (shrink)

Aristote attribue à la poésie la faculté de représenter la réalité par l'intermédiaire du récit: on comprend le monde en le racontant. Cette doctrine a été reçue, modifiée, pliée à de nouvelles exigences au cours des siècles. Comment les préoccupations de l'Antiquité ont-elles survécu à l'âge moderne?