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In this paper I try to answer four basic questions: (1) How the concept of God is to be represented? (2) Are there any logical principles governing it? (3) If so, what kind of logic lies behind them? (4) Can there be a logic of the concept of God? I address them by presenting a formal-logical account to the concept of God. I take it as a methodological desideratum that this should be done within the simplest existing logical formalism. I start with first-order logic (FOL) with identity, and then show that its simplest modal extension (SQML, or the simplest quantified modal logic) is enough for us to formalize a minimally satisfactory theory of the concept of God. I focus exclusively on the monotheistic concept of God.

In this article I expound some of the main criticisms by David Hume and Immanuel Kant against the legitimacy of natural theology, the philosophical activity of presenting arguments for or against the existence of God. The aim is not to contribute to the scholarship in history of philosophy, but as a starting point for describing the main lines of Richard Swinburne’s approach to natural theology in terms of inductive probabilistic arguments. His proposal has been part of a current philosophical movement of re-establishing the argumentative debate on the existence and nature of God, an area that has been growing in quantity and quality since the 1970’s.

The complex relations between Christianity and science seem to present a critical point in evolutionary theory, especially for the challenges it poses to the doctrine of original sin. I investigate the precise senses in which evolution threatens (or not) the Augustinian/Reformed formulation of original sin, analyzing each of the six tenets of the doctrine vis a vis nine evolutionary claims, as well as the supposed clash between the narratives of evolution and Christianity. I show that the threat is less impressive than it is usually assumed, and I highlight where the conflict really lies. I defend that it is possible to remain faithful to the core of the doctrine of original sin and to accept the reliability of evolution as a scientific theory. I present three scenarios for “Adam and Eve” and interpret them using two different models. I favor the understanding of Adam and Eve as the whole initial human bottleneck viewed through the lens of a multilevel model.

One of the few points of agreement between most theists and non-theists working on the problem of evil is that the existence of a perfect God is incompatible with the existence of pointless evil. In a series of influential papers, however, Peter van Inwagen has argued that careful attention to the reasoning behind this claim reveals fatal difficulties related to the Sorites Paradox. In this paper, I explain van Inwagen’s appeal to sorites reasoning, distinguish between two different arguments in his work, and argue that they both commit the same so-far-unnoticed mistake.

In this paper, we present an abductive argument for the existence of God from the experience of awe at natural beauty. If God’s creative work is a viable explanation for why we experience awe at natural beauty, and there is no satisfactory naturalistic explanation for the origins of such experiences, then we have defeasible evidence that God exists. To evaluate the argument's tenability, we assess the merits of the two main naturalistic frameworks that can be marshaled to answer the question of why human beings experience awe at natural beauty, Wilson's biophilia hypothesis, and Keltner and Haidt's prototype approach to awe. We show shortcomings of both accounts in explaining the relevant experiences and argue that the reliance of these accounts on an adaptationist reading of our aesthetic appreciation of nature entails a commitment to questionable hidden premises: that affordances themselves can figure in the subject's perceptual experience, and that experiences of awe have adaptive value. We maintain that the argument's “empirical” premise is tenable and conclude with directions for future research regarding the argument's “theological” premise.

In a recent paper, Jc Beall and A. J. Cotnoir proposed a bi-modal solution to the fundamental problem of Christology - the problem of reconciling the apparent contradiction implied by Christ’s divine and human natures. According to their solution, the contradiction could be resolved if one takes Christ’s dual nature as implying two different theological modal notions: one ranging over divine possibilities and the other over human possibilities. As a riposte, I argue that as novel and ingenious as Beall and Cotnoir’s solution may be, it still fails to account for the very crux of the fundamental problem, viz., the true (modal) proposition about Christ being God-incarnate.

Alvin Plantinga (1993a, 1993b, 2000) argues that de jure objections to theism depend on de facto objections: in order to say that belief in God is not warranted, one should first assume that this belief is false. Assuming Plantinga’s epistemology and his de facto/de jure distinction, In this essay, I argue that to show that belief in miracles is not warranted, one must suppose that belief in miracles is always false. Therefore, a person who holds a skeptical position regarding miracles must choose either to find evidence that all of the supposed miracles are false, or admit that one is assuming an areligious commitment as a starting point.

Suppose that it is metaphysically possible that the mereological fusion of all contingent states of affairs has a cause. Whatever the nature of the state of affairs that causes such mereological fusion, it should be metaphysically necessary because, otherwise, it could be part of the mereological fusion it causes. It is possible, then, that there is at least one necessary state of affairs. This state of affairs is a causal relatum, so it must include at least one concrete necessary object. But if something is possibly necessary, then it is necessary because it is not metaphysically contingent whether something is necessary or doesn't. Then, it results that it is metaphysically necessary that there is, at least, a concrete necessary object. This work presents and discusses this argument.

J.M. Bocheński (1902-1995) together with J. Salamucha, B. Sobociński, and J.F. Drewnowski formed the so-called Cracow Circle in the 30s of the previous century. Its main aim was to utilize contemporary logic in theology and philosophy of God. The first work in this area was Salamucha’s formal analysis of the prima via, published in 1934. The article was reviewed by Bocheński, who provided a number of remarks concerning Salamucha’s analysis. At that time he did not decide to conduct a holistic research into the prima via. That was done by him only at the end of his life as part of the logical analysis of the quinque viae. This paper aims at presenting Bocheński’s unpublished formal analysis of the prima via from 1953 and proving that it constitutes a valuable completion of his published formal analyses, which come from the 1980s and 1990s. Above all, they provide a more insightful analysis of the notion of movement in the prima via, as well as the form of axiom expressing the lack of regress into infinity. In the formalizations of 1953 there are also interesting analyses concerning the ancestral closure of three-argument relations.

In this paper, we discuss a family of arguments that show the inconsistency of the concept of omniscience, which is one of the central attributes of the theistic God. We introduce three member of this family: Grim’s Divine Liar Paradox, Milne’s Paradox and our own Divine Curry. They can be seen as theological counterparts of well-known semantic paradoxes. We argue that the very simple dialetheist response to these paradoxes doesn’t work well and then introduce our own response based on a framework that we call Logic of Impossible Truths (LIT). LIT is a non-dialetheist paraconsistent logic designed to represent divine ominiscience and to preserve the transparency of the truth predicate and which semantics rests on the concept of situation. Since some rules of classical logic are not valid in LIT, we are in a position to block the derivation of the paradoxes. Thus, LIT offers a way out of the dilemma of accepting that there are true contradictions (dialetheism) or giving up the idea that there is an all-powerful, omniscient and perfectly good being (atheism).

Beall has given more or less convincing arguments to the effect that neither classical logic, nor K3, nor LP, nor S3 can play the role he expects from logic: to be the basement theory for all true theories, including true theology. However, he has not considered all the pertinent competitors, and he has not given any reassurance that he has not gone too low in the hierarchy of logics to find his desired “universal closure of all true theories”. In this paper, I put forward those additional arguments to show the superiority of FDE with respect to logics that include a detachable conditional but that are very much like FDE otherwise. I also discuss the problem that theological consequence might not contrapose even if theological consequence is supposed to extend FDE consequence and the latter does contrapose.

We introduce a class of neighbourhood frames for graded modal logic embedding Kripke frames into neighbourhood frames. This class of neighbourhood frames is shown to be first-order definable but not modally definable. We also obtain a new definition of graded bisimulation with respect to Kripke frames by modifying the definition of monotonic bisimulation., Comment: removed journal template

In this review I provide a brief analysis of the main features of the collective volume Shifting Concepts (Oxford University Press, 2020), edited by Teresa Marques and Asa Wikforss. The volume addresses several related topics, and it contains contributions from psychologists and philosophers. It deals with the topic of concept variation understood in a broad sense, for it tackles diachronic, contextual, interpersonal and even intrapersonal variation; besides, the second part of the book is devoted to the topic of concept revision and amelioration. I provide a brief description of the book and then I critically assess each of the contributions.

Fix \(2 < n < \omega\). Let \(L_n\) denote first order logic restricted to the first n variables. Using the machinery of algebraic logic, positive and negative results on omitting types are obtained for \(L_n\) and for infinitary variants and extensions of \(L_{\omega, \omega}\).

The falling shadow theory is applied to subhoops and filters in hoops. The notions of falling fuzzy subhoops and falling fuzzy filters in hoops are introduced, and several properties are investigated. Relationship between falling fuzzy subhoops and falling fuzzy filters are discussed, and conditions for a falling fuzzy subhoop to be a falling fuzzy filter are provided. Also conditions for a falling shadow of a random set to be a falling fuzzy filter are displayed.

Let \(A_{0},A_{1},...,A_{n}\) be (possibly) distintict wffs, \(n\) being an odd number equal to or greater than 1. Intuitionistic Propositional Logic IPC plus the axiom \((A_{0}\rightarrow A_{1})\vee ...\vee (A_{n-1}\rightarrow A_{n})\vee (A_{n}\rightarrow A_{0})\) is equivalent to Gödel-Dummett logic LC. However, if \(n\) is an even number equal to or greater than 2, IPC plus the said axiom is a sublogic of LC.

In this article, I review the new book by C. D. Novaes, The Dialogical Roots of Deduction: Historical, Cognitive, and Philosophical Perspectives on Reasoning (2020). I reconstruct the main themes and arguments presented in the work and critically assess its results.

The goal of the article is twofold. The first one is to provide logics based on positional semantics which will be suitable for the analysis of epistemic modalities such as ‘agent ... knows/beliefs that ...’. The second one is to define tableau systemsfor such logics. Firstly, we present the minimal positional logic MR. Then, we change the notion of formulas and semantics in order to consider iterations of the operator of realization and “free” classical formulas. After that, we move on to weaker logics in order to avoid the well known problem of logical omniscience. At the same time, we keep the positional counterparts of modal axioms (T), (4) and (5). For all of the considered logics we present sound and complete tableau systems.

We articulate a distinction between ontology, understood as involving existence questions, and metaphysics, understood as either providing for metaphysical profiles of entities or else as dealing with fundamentality and/or grounding and dependence questions. The distinction, we argue, allows a better understanding of the roles of metaontology and metametaphysics when it comes to discussing the relations between ontology and science on the one hand, and metaphysics and science on the other. We argue that while ontology, as understood in this paper, may have reasonable perspectives for naturalization, given its relation to science, the same cannot be said for metaphysics, given that it is typically understood as an additional theoretical layer over science, not participating in the scientific investigation. That may result either in skepticism over metaphysics, or else on accepting that metaphysics is an autonomous branch of investigation, depending on one’s concern for metaphysics.

Argumentation that uses the beliefs of one’s opponents to refute them is well known (ad hominem in the classical sense). This paper proposes that there is a hitherto unnoticed counterpart to it, to be called ab homine, in which speakers/writers argue through the manner in which they deliver a message. Since the manner of delivery can never be turned into a premise or premises, this form of argumentation—although somewhat resembling Aristotle’s ethos—is much closer to the peculiar force of Socratic elenchos., L’argumentation qui utilise les croyances de ses adversaires pour les réfuter est bien connue (ad hominem au sens classique). Cet article propose qu'il y ait une contrepartie jusqu'ici inaperçue, appelée ab homine, dans laquelle les orateurs / écrivains raisonnent par la manière dont ils délivrent un message. Puisque le mode de livraison ne peut jamais être transformé en une ou plusieurs prémisses, cette forme d’argumentation - bien qu’elle ressemble quelque peu à l’éthos d’Aristote - est beaucoup plus proche de la force particulière de l’élenchos socratique.

Stance voluntarism highlights the role of the will in epistemic agency, claiming that agents can control the epistemic stances they assume in forming beliefs. It claims that radical belief changes are not compelled by the evidence; they are rationally permitted choices about which epistemic stances to adopt. However, terms like “will”, “choice”, and “stance” play a crucial role while being left as vague notions. This paper investigates what kind of control rational agents can have over epistemic stances. I argue that whether epistemic stances are voluntary depends on what kind of stance is being assessed. Sometimes epistemic stances are taken to be evaluative attitudes about how to produce knowledge. This kind of stance is not directly controllable, since it is essentially connected to beliefs, and believing is not voluntary. But sometimes epistemic stances are taken to be styles of reasoning and modes of engagement, expressing ways of approaching the world in order to produce knowledge, which can be voluntary. Overall, this supports a formulation of stance voluntarism as a dual-systems theory of epistemic agency, where epistemic rationality is compounded by a dynamic interplay between involuntary processes of belief formation and voluntary processes of cognitive guidance.

Building on a view of both narration and argumentation as dynamic concepts, this paper considers ways of assessing the credibility of narrative arguments constructed in empirical examples of conversational discourse. I argue that the key in any such exercise is to pay close attention to both structural and pragmatic details, particularly how conversational storytelling gets embedded in the surrounding discourse and how the way this is discursively accomplished vis-à-vis the narrators’ multilayered audience may be reflective of their argumentative goals., S'appuyant sur une vision à la fois de la narration et de l'argumentation en tant que concepts dynamiques, cet article examine les moyens d'évaluer la crédibilité des arguments narratifs, construits dans des exemples empiriques de discours conversationnel. Je soutiens que la clé de tout exercice de ce type est de prêter une attention particulière aux détails structurels et pragmatiques, en particulier comment la narration conversationnelle est intégrée dans le discours environnant et comment la façon dont cela est accompli discursivement vis-à-vis du public multicouche des narrateurs peut refléter leurs objectifs argumentatifs.

Social decisions are often made under great uncertainty - in situations where political principles, and even standard subjective expected utility, do not apply smoothly. In the first section, we argue that the core of this problem lies in decision theory itself - it is about how to act when we do not have an adequate representation of the context of the action and of its possible consequences. Thus, we distinguish two criteria to complement decision theory under ignorance - Laplace’s principle of insufficient reason and Wald’s maximin criterion. After that, we apply this analysis to political philosophy, by contrasting Harsanyi’s and Rawls’s theories of justice, respectively based on Laplace’s principle of insufficient reason and Wald’s maximin rule - and we end up highlighting the virtues of Rawls’s principle on practical grounds (it is intuitively attractive because of its computational simplicity, so providing a salient point for convergence) - and connect this argument to our moral intuitions and social norms requiring prudence in the case of decisions made for the sake of others.

For as long as there have been theories about common knowledge, they have been exposed to a certain amount of skepticism. Recent more sophisticated arguments question whether agents can acquire common attitudes and whether they are needed in social reasoning. I argue that this skepticism arises from assumptions about practical reasoning that, considered in themselves, are at worst implausible and at best controversial. A proper approach to the acquisition of attitudes and their deployment in decision making leaves room for common attitudes. Postulating them is no worse off than similar idealizations that are usefully made in logic and economics.

In this paper we present a concept of similarity in games, on which to ground alternative solution concepts, some of which differ from the classical notions in the field. In order to do this we impose a constraint on players’ beliefs that amounts to a variant of the well-known symmetry principle in classical bargaining theory. We show how this similarity relation helps to identify different Nash equilibria in games, and how these “similar Nash equilibria” can be extended to non-symmetric games. While the notion is normative, it is nonetheless inspired by phenomena in which similarities between players lead to outcomes detected in behavioral studies. We study the strategic properties of the concept of similarity and discuss its relationships with Hofstadter’ notion of superrationality.

In this paper, the notions of tense operators and tense filters in \(BL\)-algebras are introduced and several characterizations of them are obtained. Also, the relation among tense \(BL\)-algebras, tense \(MV\)-algebras and tense Boolean algebras are investigated. Moreover, it is shown that the set of all tense filters of a \(BL\)-algebra is complete sublattice of \(F(L)\) of all filters of \(BL\)-algebra \(L\). Also, maximal tense filters and simple tense \(BL\)-algebras and the relation between them are studied. Finally, the notions of tense congruence relations in tense \(BL\)-algebras and strict tense \(BL\)-algebras are introduced and an one-to-one correspondence between tense filters and tense congruences relations induced by tense filters are provided.

In this article, we present the positional logic that is suitable for the formalization of reasoning about social phenomena. It is the effect of extending the Minimal Realisation (MR) logic with new expressions. These expressions allow, inter alia, to consider different points of view of social entities (humanistic coefficient). In the article, we perform a metalogical analysis of this logic. Finally, we present some simple examples of its application.

In 2004, C. Sanza, with the purpose of legitimizing the study of \(n\times m\)-valued Łukasiewicz algebras with negation (or \(\mathbf{NS}_{n\times m}\)-algebras) introduced \(3 \times 3\)-valued Łukasiewicz algebras with negation. Despite the various results obtained about \(\mathbf{NS}_{n\times m}\)-algebras, the structure of the free algebras for this variety has not been determined yet. She only obtained a bound for their cardinal number with a finite number of free generators. In this note we describe the structure of the free finitely generated \(NS_{3 \times 3}\)-algebras and we determine a formula to calculate its cardinal number in terms of the number of free generators. Moreover, we obtain the lattice \(\Lambda(\mathbf{NS}_{3\times 3})\) of all subvarieties of \(\mathbf{NS}_{3\times 3}\) and we show that the varieties of Boolean algebras, three-valued Łukasiewicz algebras and four-valued Łukasiewicz algebras are proper subvarieties of \(\mathbf{NS}_{3\times 3}\).

After putting forward a formal account of value disagreement via imprecise measures, I develop a logic of value attribution and of (dis)agreement based on (exact) truthmaker semantics.

The present article provides a taxonomic analysis of bimodal logics of normative ideality and normative awfulness, two notions whose meaning is here explained in terms of the moral values pursued by a given community. Furthermore, the article addresses the traditional problem of a reduction among deontic concepts: we explore the possibility of defining other relevant normative notions, such as obligation, explicit permission and Hohfeldian relations, in terms of ideality and awfulness. Some proposals in this respect, which have been formulated in the literature over the years, are here improved and discussed with reference to the various logics that we will introduce.

The paper argues that adopting a form of skepticism, Skeptical-Dogmatism, that recommends disbelieving each philosophical position in many multi-proposition disputes- disputes where there are three or more contrary philosophical views-leads to a higher ratio of true to false beliefs than the ratio of the “average philosopher” (as indicated by survey data). Hence, Skeptical-Dogmatists have more accurate beliefs than the average philosopher. As a corollary, most philosophers would improve the accuracy of their beliefs if they adopted Skeptical-Dogmatism.

Driven by an appreciation of the field’s early stage of development, I apply the concept of exploratory experimentation, originally put forward in the late 90s philosophy of biology, to current research in cognitive neuroscience. I concentrate on functional magnetic resonance imaging and how this wide-spread technique is used, from experimental design to data analysis. I claim that, although subject to certain significant modifications with respect to the concept’s original rendering, the exploratory character of neuroimaging experiments can be appreciated considering their goals, centered on the stabilization of experimental systems for phenomenological description, and the relevance of their methodological facet. Although I do not claim that there is a specific kind of experiment that one can single out as definitely exploratory, exploration can be seen as a general trait imbuing fMRI-based experimentation.

In the present paper we study the relationship between the notions of force, cause and subject of motion in Leibniz’s early dynamics. First, we specify the role that the problem of the subject and cause of motion played in the development of his dynamics. Second, we analyze the distinction between force and quantity of motion and the validity and limits of his proof. Third, we study and evaluate the limits of the arguments for establishing that forces are inherent to bodies. Our main goal is to show that between 1678 and 1686 Leibniz dissociates the problem of the subject from the problem of the cause of motion and, furthermore, that even though the problem of establishing that force is inherent to particular bodies played a major role in the discovery of his dynamics, it has no place in its justification.