The strict-tolerant approach to paradox promises to erect theories of naïve truth and tolerant vagueness on the firm bedrock of classical logic. We assess the extent to which this claim is founded. Building on some results by Girard we show that the usual proof-theoretic formulation of propositional ST in terms of the classical sequent calculus without primitive Cut is incomplete with respect to ST-valid metainferences, and exhibit a complete calculus for the same class of metainferences. We also argue that the (...) latter calculus, far from coinciding with classical logic, is a close kin of Priest’s LP. (shrink)

We group the existing variants of the familiar set-theoretical and truth-theoretical paradoxes into two classes: connective paradoxes, which can in principle be ascribed to the presence of a contracting connective of some sort, and structural paradoxes, where at most the faulty use of a structural inference rule can possibly be blamed. We impute the former to an equivocation over the meaning of logical constants, and the latter to an equivocation over the notion of consequence. Both equivocation sources are tightly related, (...) and can be cleared up by adopting a particular substructural logic in place of classical logic. We then argue that our perspective can be justified via an informational semantics of contraction-free substructural logics. (shrink)

The following is an attempt to read Anselm’s treatise De veritate in accordance with its immanent intention by considering the question: to what extent and in which sense does it, in unfolding the concept of truth, more concretely determine the concept of God—and accordingly also the concept of man and his relationship to God? The question of whether and to what extent Anselm argues sola ratione will not be raised, but instead in what way his ratio is capable of developing (...) out of the data of belief a conceptuality that is binding for the intellectus credens. (shrink)

Paraconsistent Weak Kleene Logic is the 3-valued propositional logic defined on the weak Kleene tables and with two designated values. Most of the existing proof systems for PWK are characterised by the presence of linguistic restrictions on some of their rules. This feature can be seen as a shortcoming. We provide a cut-free calculus for PWK that is devoid of such provisos. Moreover, we introduce a Priest-style tableaux calculus for PWK.

The aim of the present book is to give a comprehensive account of the ‘state of the art’ of substructural logics, focusing both on their proof theory and on their semantics (both algebraic and relational. It is for graduate students in either philosophy, mathematics, theoretical computer science or theoretical linguistics as well as specialists and researchers.

Proof-theoretic semantics is an alternative to model-theoretic semantics. It aims at explaining the meaning of the logical constants in terms of the inference rules that govern their behaviour in proofs. We argue that this must be construed as the task of explaining these meanings relative to a logic, i.e., to a consequence relation. Alas, there is no agreed set of properties that a relation must have in order to qualify as a consequence relation. Moreover, the association of a consequence relation (...) to a logical calculus is not as straightforward as it may seem. We show that these facts are problematic for the proof-theoretic project but the problems can be solved. Our thesis is that the consequence relation relevant for proof-theoretic semantics is the one given by the sequent-to-sequent derivability relation in Gentzen systems. (shrink)

In recent years, bioethical discourse around the topic of ‘genetic enhancement’ has become increasingly politicized. We fear there is too much focus on the semantic question of whether we should call particular practices and emerging bio-technologies such as CRISPR ‘eugenics’, rather than the more important question of how we should view them from the perspective of ethics and policy. Here, we address the question of whether ‘eugenics’ can be defended and how proponents and critics of enhancement should engage with each (...) other. (shrink)

Here, we discuss historical, philosophical and technical problems associated with relating logic and relating semantics. To do so, we proceed in three steps. First, Section 1 is devoted to providing an introduction to both relating logic and relating semantics. Second, we address the history of relating semantics and some of the main research directions and their philosophical applications. Third, we discuss some technical problems related to relating semantics, particularly whether the direct incorporation of the relation into the language of relating (...) logic is needed. The starting point for our considerations presented here is the 1st Workshop On Relating Logic and the selected papers for this issue. (shrink)

Es innegable que la noción de epoché fue crucial para el surgimiento y el posterior desarrollo de la tradición fenomenológica. Si bien la resignificación que Husserl hace de ésta es sumamente original, él mismo se detiene a reconocer en la filosofía antigua el mérito de haber encontrado el camino idóneo para acceder a la subjetividad trascendental. En el siguiente trabajo buscaré, por un lado, definir la epoché tal como se origina en el pensamiento de los sofistas para luego pasar a (...) analizar el modo en el que Husserl logra reversionar dicha noción hasta convertirla en el método predilecto que nos permite arribar a la esfera trascendental. Por otro lado, continuaré rastreando la evolución de la epoché para llegar a su abandono en la filosofía de Sartre. En relación con esto último, me interesa preguntarme si el existencialismo reniega de la suspensión del juicio por considerarla inapropiada o si, más bien, se trata de una supresión parcial del método fenomenológico. Me propongo defender esta segunda tesis, alegando que, en realidad, la epoché no es una noción que esté totalmente ausente en la filosofía de Sartre sino que se mantiene vigente en términos de angustia existencial. (shrink)

The aim of this paper is to investigate Nishida Kitarō’s way of philosophizing in the light of the concept of “transition” in order to deepen our understanding of both Nishida’s philosophy and our thinking about and in transitions, using the concept of “boundary” or “border” (Grenze) as a catalyst. For that purpose, we focus on Nishida’s essay “Place” (「場所」), passing through different parts of the text as if through successive gates on a path of transition between one place and the (...) next, until we reach the final place of “absolute nothingness.” Dwelling on this place, we turn our attention to its internal structure and try to depict it along the outlines of a boundary, following the movements taking place in Nishida’s essay. The second part proposes an interpretation of the place of nothingness as an interminable practice of boundary-crossing that doesn’t come to a halt in a final, all-encompassing place, but dynamically situates itself on countless intersecting planes. After a more or less abstract analysis of the concept of “boundary,” we will apply and concretize this approach by using the example of the skin. To this end, we expose five main features of the skin as boundary: permeability, enclosure, excessiveness, interstitiality and reciprocal self-formation. (shrink)

This paper focuses on the role of punishment as a critical social mechanism for cheating prevention in MMORPGs. The role of punishment is empirically investigated in a case study of the MMORPG Tibia and by focusing on the use of bots to cheat. We describe the failure of punishment in Tibia, which is perceived by players as one of the elements facilitating the proliferation of bots. In this process some players act as a moral enterprising group contributing to the reform (...) of the game rules and in particular to the reform of the Tibia punishment system by the game company. In the conclusion we consider the ethical issues raised by our findings and we propose some general reflections on the role of punishment and social mechanisms for the governance of online worlds more generally. (shrink)

The aim of this article is to discuss pure variable inclusion logics, that is, logical systems where valid entailments require that the propositional variables occurring in the conclusion are included among those appearing in the premises, or vice versa. We study the subsystems of Classical Logic satisfying these requirements and assess the extent to which it is possible to characterise them by means of a single logical matrix. In addition, we semantically describe both of these companions to Classical Logic in (...) terms of appropriate matrix bundles and as semilattice-based logics, showing that the notion of consequence in these logics can be interpreted in terms of truth (or non-falsity) and meaningfulness (or meaninglessness) preservation. Finally, we use Płonka sums of matrices to investigate the pure variable inclusion companions of an arbitrary finitary logic. -/- . (shrink)

Dave Ripley has recently argued against the plausibility of multiset consequence relations and of contraction-free approaches to paradox. For Ripley, who endorses a nontransitive theory, the best arguments that buttress transitivity also push for contraction—whence it is wiser for the substructural logician to go nontransitive from the start. One of Ripley’s allegations is especially insidious, since it assumes the form of a trivialisation result: it is shown that if a multiset consequence relation can be associated to a closure operator in (...) the expected way, then it necessarily contracts. We counter Ripley’s objection by presenting an approach to multiset consequence that escapes this trap. This approach is multiple-conclusioned in a heterodox way, for multiple succedents are given a conjunctive, rather than a disjunctive reading. Finally, we address a further objection by French and Ripley to the effect that the informational interpretation of sequents in linear logic does not motivate cut. (shrink)

Metaphor has been considered as a cognitive process, independent of the verbal versus visual mode, through which an unknown conceptual domain is understood in terms of another known conceptual domain. Metaphor might instead be viewed as a cognitive process, dependent on the mode, which leads to genuinely new knowledge via ignorance. First, I argue that there are two main senses of ignorance at stake when we understand a metaphor: we ignore some existing properties of the known domain in the sense (...) that we disregard or neglect them; we ignore some “non-existing” properties of the known domain in the sense that they are not a piece of information belonging to the known domain, but emerge in metaphor interpretation. Secondly, I consider a metaphor as a reasoning device, guiding the interpreters along a path of inferences to a conclusion, which attributes to the target some properties of the source. In this path, interpreters might discover the ignored existing properties of the known domain and/or recover the “non-existing” properties, inferring or imagining the missing piece of information. Finally, I argue that, especially in visual metaphors, this process is guided by a “sentiment of rationality”, tracking a disruption of existing familiar conceptualisations of objects and/or actions and a recovery of ignored properties. (shrink)

I discuss paradoxes of implication in the setting of a proof-conditional theory of meaning for logical constants. I argue that a proper logic of implication should be not only relevant, but also constructive and nonmonotonic. This leads me to select as a plausible candidate LL, a fragment of linear logic that differs from R in that it rejects both contraction and distribution.

In a famous and controversial paper, B. H. Slater has argued against the possibility of paraconsistent logics. Our reply is centred on the distinction between two aspects of the meaning of a logical constant *c* in a given logic: its operational meaning, given by the operational rules for *c* in a cut-free sequent calculus for the logic at issue, and its global meaning, specified by the sequents containing *c* which can be proved in the same calculus. Subsequently, we use the (...) same strategy to counter Quine's meaning variance argument against deviant logics. In a nutshell, we claim that genuine rivalry between (similar) logics *L* and *L'* is possible whenever each constant in *L* has the same operational meaning as its counterpart in *L'* although differences in global meaning arise in at least one case. (shrink)

Proof-theoretic semantics is an alternative to model-theoretic semantics. It aims at explaining the meaning of the logical constants in terms of the inference rules that govern their behaviour in proofs. We argue that this must be construed as the task of explaining these meanings relative to a logic, i.e., to a consequence relation. Alas, there is no agreed set of properties that a relation must have in order to qualify as a consequence relation. Moreover, the association of a consequence relation (...) to a logical calculus is not as straightforward as it may seem. We show that these facts are problematic for the proof-theoretic project but the problems can be solved. Our thesis is that the consequence relation relevant for proof-theoretic semantics is the one given by the sequent-to-sequent derivability relation in Gentzen systems. (shrink)

We consider the class of pointed varieties of algebras having a lattice term reduct and we show that each such variety gives rise in a natural way, and according to a regular pattern, to at least three interesting logics. Although the mentioned class includes several logically and algebraically significant examples (e.g. Boolean algebras, MV algebras, Boolean algebras with operators, residuated lattices and their subvarieties, algebras from quantum logic or from depth relevant logic), we consider here in greater detail Abelian ℓ-groups, (...) where such logics respectively correspond to: i) Meyer and Slaney’s Abelian logic [31]; ii) Galli et al.’s logic of equilibrium [21]; iii) a new logic of “preservation of truth degrees”. (shrink)

Paraconsistent weak Kleene logic is the $3$-valued logic based on the weak Kleene matrices and with two designated values. In this paper, we investigate the poset of prevarieties of generalized involutive bisemilattices, focussing in particular on the order ideal generated by Α$\textrm{lg} $. Applying to this poset a general result by Alexej Pynko, we prove that, exactly like Priest’s logic of paradox, $\textrm{PWK}$ has only one proper nontrivial extension apart from classical logic: $\textrm{PWK}_{\textrm{E}}\textrm{,}$ PWK logic plus explosion. This $6$-valued logic, (...) unlike $\textrm{PWK} $, fails to be paraconsistent. We describe its consequence relation via a variable inclusion criterion and identify its Suszko-reduced models. (shrink)

In this paper we introduce a new natural deduction system for the logic of lattices, and a number of extensions of lattice logic with different negation connectives. We provide the class of natural deduction proofs with both a standard inductive definition and a global graph-theoretical criterion for correctness, and we show how normalisation in this system corresponds to cut elimination in the sequent calculus for lattice logic. This natural deduction system is inspired both by Shoesmith and Smiley's multiple conclusion systems (...) for classical logic and Girard's proofnets for linear logic. (shrink)

The basis for adoption of pro-environment behaviour is the understanding of causal passages within climate dynamics. The understanding of the causes of climate change is necessary in order _to be able_ to take mitigation actions. Conversely, the understanding of the consequences of climate change is essential in _motivating_ action. The case of ozone depletion confirms this view: the understanding of its causal dynamics played a determining role in people’s behavioural response.

Despite the remarkable advances in behavioral and brain sciences over the last decades, the mind/body (brain) problem is still an open debate and one of the most intriguing questions for both cognitive neuroscience and philosophy of mind. Traditional approaches have conceived this problem in terms of a contrast between physicalist monism and Cartesian dualism. However, since the late sixties, the landscape of philosophical views on the problem has become more varied and complex. The Multiple Realization Thesis (MRT) claims that mental (...) properties can be (or are) realized, and mental processes can be (or are) implemented by neural correlates of different kinds. Thus, MRT challenges the psychoneural type-identity theory and the corresponding reductionism. Many philosophers have acknowledged the a priori plausibility of MRT. However, the existence of empirical evidence in favor of intraspecific, human multiple realizations of mental processes and properties is still controversial. Here we illustrate some cases that provide empirical evidence in support of MRT. Recently, it has been proposed that foveal agnosic vision, like peripheral vision, can be restored by increasing object parts’ spacing (Strappini et al., 2017a; Crutch and Warrington, 2007). Agnosic fovea and normal periphery are both limited by crowding, that impairs object recognition, and provides the signature of visual integration. Here we define a psychological property of restored object identification and we cross-reference the data of visually-impaired patients with different etiologies. In particular, we compare the data of two stroke patients, two patients with posterior cortical atrophy (PCA), six cases of strabismic amblyopia, and one case with restored sight. We also compare these patients with unimpaired subjects tested in the periphery. We show that integration (i.e. restored recognition) seems to describe quite accurately the visual performance in all these cases. While the patients have different etiologies and different neural correlates, the unimpaired subjects have no neural damage. Thus similarity in the psychological property given the differences in the neural substrate can be interpreted in relation to MRT and provide evidence in its support. Finally, we will frame our contribution within the current debate concerning MRT providing new and compelling empirical evidence. (shrink)

In the tradition of substructural logics, it has been claimed for a long time that conjunction and inclusive disjunction are ambiguous:we should, in fact, distinguish between ‘lattice’ connectives (also called additive or extensional) and ‘group’ connectives (also called multiplicative or intensional). We argue that an analogous ambiguity affects the quantifiers. Moreover, we show how such a perspective could yield solutions for two well-known logical puzzles: McGee’s counterexample to modus ponens and the lottery paradox.

Criminal liability for acts committed by AI systems has recently become a hot legal topic. This paper includes three different contributions. The first contribution is an analysis of the extent to which an AI system can satisfy the requirements for criminal liability: accomplishing an actus reus, having the corresponding mens rea, possessing the cognitive capacities needed for responsibility. The second contribution is a discussion of criminal activity accomplished by an AI entity, with reference to a recent case involving an online (...) bot, the Random Darknet Shopper. This discussion will provide the context for the analysis of commonalities and differences between criminal activities by humans and by artificial systems. The third contribution concerns the evaluation of different ways of addressing criminal activities by AI systems in a regulatory perspective. (shrink)

What is a gene? Does it represent a natural kind, or is it just a tool for genomics? A clear answer to these questions has been challenged by postgenomic discoveries. In response, I will argue that the gene can be deemed a natural kind as it satisfies some requirements for genuine kindhood. Specifically, natural kinds are projectible categories in our best scientific theories, and they represent nodes in the causal network of the world (as in Khalidi. Natural Categories and Human (...) Kinds: Classification in the Natural and Social Sciences. Cambridge University Press, Cambridge, 2013; Khalidi. Synthese 195: 1379–1396, 2018; Khalidi. Are Sexes Natural Kinds, In: Dasgupta S, Weslake B (eds) Current Controversies in Philoso-phy of Science. Routledge, New York, 2020; Khalidi. Philos Sci 88:1–21, 2021). In Sect. 2, I will present a brief history of the gene and the controversy over its status. In Sect. 3, I will introduce the account of natural kinds considered in this paper. In Sect. 4, I will first present the relevant definition of genes and how they can be classified. Then, I will argue that the gene can be considered a natural kind as it satisfies the criteria for natural kindhood. Section 5 concludes. (shrink)

Portuguese translation of Aristotle’s _Prophecy in Sleep_, preceded by a short presentation of the text and accompanied by explanatory notes.

Grammar as a discipline devoted to the study of language was greatly advanced by the Alexandrian philologists, and especially by Aristarchus, as demonstrated by Stephanos Matthaios. In order to edit Homer and other literary authors, whose texts were often written in archaic Greek and presented many linguistic problems, the Alexandrians had to recognize linguistic grammatical categories and declensional patterns. In particular, to determine the correct orthography or accentuation of debated morphological forms they often employed analogy, which is generally defined as (...) the doctrine that grammatical forms must follow strict rules of declension. Modern scholars have often opposed the Alexandrian doctrine of analogy to the Pergamene doctrine of ‘anomaly’, which favoured spoken usage to determine debated forms. Detlev Fehling and David Blank, however, have shown that this strong opposition never really existed and it is mostly due to Varro. More correctly, ancient grammarians identified inflectional rules as well as forms derived from spoken usage or otherwise aberrant forms—however, respect for spoken usage in the latter case was not labelled ‘anomaly’, which was never a technical term of ancient grammar. Rather, and especially in the Roman period, grammarians used the term ‘pathology’ to account for and explain irregular forms. (shrink)