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.

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.

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.

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’.

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)

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)

Italian political thinker Paolo Virno argues that the category of "multitude" is a far better tool to analyze contemporary issues than the Hobbesian concept of "people." Globalization is forcing us to rethink some of the categories—such as "the people"—that traditionally have been associated with the now eroding state. Italian political thinker Paolo Virno argues that the category of "multitude," elaborated by Spinoza and for the most part left fallow since the seventeenth century, is a far better tool to (...) analyze contemporary issues than the Hobbesian concept of "people," favored by classical political philosophy. Hobbes, who detested the notion of multitude, defined it as shunning political unity, resisting authority, and never entering into lasting agreements. "When they rebel against the state," Hobbes wrote, "the citizens are the multitude against the people." But the multitude isn't just a negative notion, it is a rich concept that allows us to examine anew plural experiences and forms of nonrepresentative democracy. Drawing from philosophy of language, political economics, and ethics, Virno shows that being foreign, "not-feeling-at-home-anywhere," is a condition that forces the multitude to place its trust in the intellect. In conclusion, Virno suggests that the metamorphosis of the social systems in the West during the last twenty years is leading to a paradoxical "Communism of the Capital.". (shrink)

The philosophical analysis of mathematical explanations concerns itself with two different, although connected, areas of investigation. The first area addresses the problem of whether mathematics can play an explanatory role in the natural and social sciences. The second deals with the problem of whether mathematical explanations occur within mathematics itself. Accordingly, this entry surveys the contributions to both areas, it shows their relevance to the history of philosophy and science, it articulates their connection, and points to the philosophical pay-offs to (...) be expected by deepening our understanding of the topic. (shrink)

The temporality of intentions and actions in situations of social interaction can sometimes be paradoxical. I argue that in these situations it may sometimes be possible to conceive of individual acts that can, in a strong sense, be intended retroactively. This could happen when the relational patterns in social interaction literally alter the virtual structure of a participant's past corporeal intentions resulting in an odd experience of having intended something all along without knowing it. I propose that this possibility should (...) be interpreted as more than just a narrowly epistemic phenomenon. Examining this claim involves clarifying the enactive perspective on intentionality, which I do here. The enactive approach rejects the model of a causal relation between intention and action for one of an intrinsic qualitative relation between the two as facets of sense-making. I develop this idea and compare it with Merleau-Ponty's Fundierung model of the mutual relation between corporeal and reflexive intentionality to show that co-regulated moves/affections during social interaction may modulate both arcs of this relation, creating the possibility of a re-signification that alters not the actuality but the virtual tendencies that preceded the social act. (shrink)

This paper explores the epistemology of extrapolation from model organisms to humans in molecular medicine. We take into account two common views on the issue, the homology view and the disanalogy view. In response to both interpretations, we argue that the foundational basis of extrapolations cannot simply be provided by homology and that relevant disanalogies can, thanks to the techniques of molecular biology, be experimentally controlled and exploited to allow useful and reliable extrapolations. The case of "humanised mice" in the (...) context of cancer stem cell research provides evidence of how animal models can be construed to approximate bona fide causal analogue models of human diseases. To supplement this view we show how the epistemology of model organisms needs to take into account the engineering side of molecular medicine. Model organisms are often manipulated to create analogies or remove disanalogies with the target system. We maintain that highlighting this feature is fundamental to explain what warrants extrapolation in the search for the molecular causes of disease. (shrink)

A novel theoretical framework for an embodied, non-representational approach to language that extends and deepens enactive theory, bridging the gap between sensorimotor skills and language. -/- Linguistic Bodies offers a fully embodied and fully social treatment of human language without positing mental representations. The authors present the first coherent, overarching theory that connects dynamical explanations of action and perception with language. Arguing from the assumption of a deep continuity between life and mind, they show that this continuity extends to language. (...) Expanding and deepening enactive theory, they offer a constitutive account of language and the co-emergent phenomena of personhood, reflexivity, social normativity, and ideality. Language, they argue, is not something we add to a range of existing cognitive capacities but a new way of being embodied. Each of us is a linguistic body in a community of other linguistic bodies. The book describes three distinct yet entangled kinds of human embodiment, organic, sensorimotor, and intersubjective; it traces the emergence of linguistic sensitivities and introduces the novel concept of linguistic bodies; and it explores the implications of living as linguistic bodies in perpetual becoming, applying the concept of linguistic bodies to questions of language acquisition, parenting, autism, grammar, symbol, narrative, and gesture, and to such ethical concerns as microaggression, institutional speech, and pedagogy. (shrink)

Christ as symbol in Kant¿s religion -- Hegel's conception of God -- The reality of religion in Hegel's idealist metaphysics -- Hegel's version of the ontological argument for the existence of God -- The trinity and the I -- The death of God and recognition of the self -- Beyond subjectivism -- The relevance of Hegel's philosophy of religion today.

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)

Summary This article presents three hitherto unpublished letters by Frank Plumpton Ramsey on the foundations of mathematics with commentary. One of the letters was sent to Abraham Fraenkel and the other two letters to Heinrich Behmann. The transcription of the letters is preceded by an account that details the extent of Ramsey's known contacts with mathematical logicians on the Continent.

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)

Le but de cet ouvrage est de montrer la teneur philosophique unitaire de la pensée critique de Diderot par delà le caractère éclaté et dispersé de son œuvre. Diderot philosophe est présenté comme un penseur critique et systématique, c'est-à-dire un philosophe dont la réflexion, d'une part, s'inscrit dans le cadre du courant de pensée moderne qui vise à dépasser les perspectives du « premier regard géomètre de la raison », celui de Descartes, de Malebranche et des post-cartésiens. D'autre part, elle (...) atteint un « second regard critique », plus profond, jeté sur le monde de la nature et surtout, sur lui-même (une philosophie de l'aperception : Spinoza, Wolff, les Moralistes anglais et Kant), qui se rattache intimement à un matérialisme biologique tout à fait original, issu de la confrontation de Diderot avec les naturalistes et les médecins de son temps. C'est ce matérialisme élaboré dans l'usine encyclopédique qui met en cause la notion clé d'« individualité naturelle » (jouée en couplet avec une « communauté du désir ») - néologisme dont Le Neveu de Rameau et Le Rêve de D'Alembert développeront les tenants et les aboutissants philosophiques -, et qui témoigne de la nouveauté d'approche propre à cette philosophie, à l'intérieur de la pensée des Lumières européennes. Avec Diderot, c'est une nouvelle figure historique de la philosophie elle-même - celle de la subjectivité individuelle complexe, uni-totalité de penser-sentir-agir - qui monte sur la scène de la modernité, comme étant la substance première, incontournable et insaisissable, de la pensée critique de nos jours. (shrink)