When faced with the charge that a given concept of God is contradictory, the standard move among philosophers and theologians has been to try to explain away the contradiction and show that the concept of God in question is consistent. This has to do, of course, with the Law of Non-Contradiction (LNC). Another option, which has recently generated interest among logicians and analytic philosophers of religion, is to reject such a move as unnecessary and defend what might be called the (...) contradictory God thesis. To be sure, something close to that can be found in philosophers such as Pseudo-Dionysius, Thomas Aquinas and Nicolaus de Cusa. However, it is only recently that this approach has gained momentum, certainly driven by the contemporary advance of dialetheism and glut theoretic approaches in general, and paraconsistent logic. Needless to say, a standard move among defenders of the contradictory God thesis is to challenge the LNC. The argumentation, however, is seldomly framed in conceptual terms. Instead, it is mostly framed in ontological terms, as God being a contradictory entity. From this perspective, the contradictory God thesis is the thesis that God is a contradictory object. My goal in this paper is to provide a conceptual assessment of the discussion surrounding the contradictory God thesis. To achieve this, I make use of a general and hopefully non-controversial meta-theory of concepts and adopt a semantic approach rather than a metaphysical one. Within this framework, I address the following questions: What are the different ways we can understand the contradictory God thesis? What grounds are there for rejecting a contradictory concept of God? What standard moves are available to defend oneself from such criticisms and how do they relate to the LNC? What challenges do they present? As a secondary goal, the paper introduces a novel defense of the contradictory God thesis, drawing on a specific interpretation of the theology of the 16th-century Indian thinker Jīva Gosvāmī, which avoids the need to challenge the LNC. I term this approach ‘non-dialetheic mystical contradictory theism.’. (shrink)

It has been an open question whether or not we can define a belief revision operation that is distinct from simple belief expansion using paraconsistent logic. In this paper, we investigate the possibility of meeting the challenge of defining a belief revision operation using the resources made available by the study of dynamic epistemic logic in the presence of paraconsistent logic. We will show that it is possible to define dynamic operations of belief revision in a paraconsistent (...) setting. (shrink)

A logic is called 'paraconsistent' if it rejects the rule called 'ex contradictione quodlibet', according to which any conclusion follows from inconsistent premises. While logicians have proposed many technically developed paraconsistent logical systems and contemporary philosophers like Graham Priest have advanced the view that some contradictions can be true, and advocated a paraconsistent logic to deal with them, until recent times these systems have been little understood by philosophers. This book presents a comprehensive overview on paraconsistent (...) logical systems to change this situation. The book includes almost every major author currently working in the field. The papers are on the cutting edge of the literature some of which discuss current debates and others present important new ideas. The editors have avoided papers about technical details of paraconsistent logic, but instead concentrated upon works that discuss more 'big picture' ideas. Different treatments of paradoxes takes centre stage in many of the papers, but also there are several papers on how to interpret paraconistent logic and some on how it can be applied to philosophy of mathematics, the philosophy of language, and metaphysics. (shrink)

Paraconsistency is the study of logical systems with a non-explosive negation such that a pair of contradictory formulas (with respect to such negation) does not necessarily imply triviality, discordant to what would be expected by contemporary logical orthodoxy. From a purely logical point of view, the significance of paraconsistency relies on the meticulous distinction between the general notions of contradictoriness and triviality of a theory—respectively, the fact that a given theory proves a proposition and its negation, and the fact that (...) a given theory proves any proposition (in the language of its underlying logic). Aside from this simple rationale, the formal techniques and approaches that meet the latter definitional requirement are manifold. Furthermore, it is not solely the logical-mathematical properties of such systems that are open to debate. Rather, there are several foundational and philosophical questions worth studying, including the very question about the nature of the contradictions allowed by paraconsistentists. This entry aims to advance a brief account of some distinct approaches to paraconsistency, providing a panorama on the development of paraconsistent logic. (shrink)

In this paper two systems of AGM-like Paraconsistent Belief Revision are overviewed, both defined over Logics of Formal Inconsistency (LFIs) due to the possibility of defining a formal consistency operator within these logics. The AGM° system is strongly based on this operator and internalize the notion of formal consistency in the explicit constructions and postulates. Alternatively, the AGMp system uses the AGM-compliance of LFIs and thus assumes a wider notion of paraconsistency - not necessarily related to the notion of (...) formal consistency. (shrink)

Skeptical theism is a popular response to arguments from evil. Many hold that it undermines a key inference often used by such arguments. However, the case for skeptical theism is often kept at an intuitive level: no one has offered an explicit argument for the truth of skeptical theism. In this article, I aim to remedy this situation: I construct an explicit, rigorous argument for the truth of skeptical theism.

In this paper paraconsistent first-order logic LP^{#} with infinite hierarchy levels of contradiction is proposed. Corresponding paraconsistent set theory KSth^{#} is discussed.Axiomatical system HST^{#}as paraconsistent generalization of Hrbacek set theory HST is considered.

In this paper, the notion of degree of inconsistency is introduced as a tool to evaluate the sensitivity of the Full Bayesian Significance Test (FBST) value of evidence with respect to changes in the prior or reference density. For that, both the definition of the FBST, a possibilistic approach to hypothesis testing based on Bayesian probability procedures, and the use of bilattice structures, as introduced by Ginsberg and Fitting, in paraconsistent logics, are reviewed. The computational and theoretical advantages of (...) using the proposed degree of inconsistency based sensitivity evaluation as an alternative to traditional statistical power analysis is also discussed. (shrink)

Skeptical theism (ST) may undercut the key inference in the evidential argument from evil, but it does so at a cost. If ST is true, then we lose our ability to assess the all things considered (ATC) value of natural events and states of affairs. And if we lose that ability, a whole slew of undesirable consequences follow. So goes a common consequential critique of ST. In a recent article, Anderson has argued that this consequential critique is flawed. Anderson (...) claims that ST only has the consequence that we lack epistemic access to potentially God-justifying reasons for permitting a prima facie “bad” (or “evil”) event. But this is very different from lacking epistemic access to the ATC value of such events. God could have an (unknowable) reason for not intervening to prevent E and yet E could still be (knowably) ATC-bad. Ingenious though it is, this article argues that Anderson’s attempted defence of ST is flawed. This is for two reasons. First, and most importantly, the consequential critique does not rely on the questionable assumption he identifies. Indeed, the argument can be made quite easily by relying purely on Anderson’s distinction between God-justifying reasons for permitting E and the ATC value of E. And second, Anderson’s defence of his position, if correct, would serve to undermine the foundations of ST. (shrink)

Arguments from evil purport to show that some fact about evil makes it (at least) probable that God does not exist. Skeptical theism is held to undermine many versions of the argument from evil: it is thought to undermine a crucial inference that such arguments often rely on. Skeptical objections to skeptical theism claim that it (skeptical theism) entails an excessive amount of skepticism, and therefore should be rejected. In this article, I show that skeptical objections to (...) skeptical theism have a very limited scope: only those who reject certain (apparently) popular epistemological theories will be threatened by them. (shrink)

This article is a preliminary presentation of conjunctive paraconsistency, the claim that there might be non-explosive true contradictions, but contradictory propositions cannot be considered separately true. In case of true ‘p and not p’, the conjuncts must be held untrue, Simplification fails. The conjunctive approach is dual to non-adjunctive conceptions of inconsistency, informed by the idea that there might be cases in which a proposition is true and its negation is true too, but the conjunction is untrue, Adjunction fails. While (...) non-adjunctivism is a well-known option, the other view is not so much studied nowadays, but it was not unknown in the tradition, and there are some positive suggestions, in recent literature, that the position is plausible and deserves to be developed. The article compares conjunctivism, non-adjunctivism and dialetheism, then focuses on some possible justifications, costs and benefits of the conjunctive view. (shrink)

Paraconsistent logics are logical systems that reject the classical principle, usually dubbed Explosion, that a contradiction implies everything. However, the received view about paraconsistency focuses only the inferential version of Explosion, which is concerned with formulae, thereby overlooking other possible accounts. In this paper, we propose to focus, additionally, on a meta-inferential version of Explosion, i.e. which is concerned with inferences or sequents. In doing so, we will offer a new characterization of paraconsistency by means of which a logic (...) is paraconsistent if it invalidates either the inferential or the meta-inferential notion of Explosion. We show the non-triviality of this criterion by discussing a number of logics. On the one hand, logics which validate and invalidate both versions of Explosion, such as classical logic and Asenjo–Priest’s 3-valued logic LP. On the other hand, logics which validate one version of Explosion but not the other, such as the substructural logics TS and ST, introduced by Malinowski and Cobreros, Egré, Ripley and van Rooij, which are obtained via Malinowski’s and Frankowski’s q- and p-matrices, respectively. (shrink)

Sceptical theists--e.g., William Alston and Michael Bergmann--have claimed that considerations concerning human cognitive limitations are alone sufficient to undermine evidential arguments from evil. We argue that, if the considerations deployed by sceptical theists are sufficient to undermine evidential arguments from evil, then those considerations are also sufficient to undermine inferences that play a crucial role in ordinary moral reasoning. If cogent, our argument suffices to discredit sceptical theist responses to evidential arguments from evil.

Is skeptical theism tenable once one acknowledges, as proponents of that view do, one's cognitive limitations vis-à-vis religious matters? In this article, I aim to answer that question both by examining the apparent radical skeptical implications of the skeptical component of skeptical theism and by comparing this view with fideism and Pyrrhonism, which also lay emphasis on our cognitive limitations. My ultimate purpose is to determine which of the three stances it makes more sense to adopt once the (...) limitations of human cognitive powers are recognized. (shrink)

This article is a response to Stephen Law's article ‘The evil-god challenge’. In his article, Law argues that if belief in evil-god is unreasonable, then belief in good-god is unreasonable; that the antecedent is true; and hence so is the consequent. In this article, I show that Law's affirmation of the antecedent is predicated on the problem of good (i.e. the problem of whether an all-evil, all-powerful, and all-knowing God would allow there to be as much good in the world (...) as there is), and argue that the problem of good fails. Thus, the antecedent is unmotivated, which renders the consequent unmotivated. Law's challenge for good-god theists is to show that good-god theism is not rendered unreasonable by the problem of evil in the same way that evil-god theism is rendered unreasonable by the problem of good. Insofar as the problem of good does not render belief in evil-god unreasonable, Law's challenge has been answered: since it is not unreasonable to believe in evil-god (at least for the reasons that Law gives) it is not unreasonable to believe in good-god. Finally, I show that – my criticism aside – the evil-god challenge turns out to be more complicated and controversial than it initially appears, for it relies on the (previously unacknowledged) contentious assumption that sceptical theism is false. (shrink)

In this paper, we present a non-trivial and expressively complete paraconsistent naïve theory of truth, as a step in the route towards semantic closure. We achieve this goal by expressing self-reference with a weak procedure, that uses equivalences between expressions of the language, as opposed to a strong procedure, that uses identities. Finally, we make some remarks regarding the sense in which the theory of truth discussed has a property closely related to functional completeness, and we present a sound (...) and complete three-sided sequent calculus for this expressively rich theory. (shrink)

The terms “model” and “model-building” have been used to characterize the field of formal philosophy, to evaluate philosophy’s and philosophical logic’s progress and to define philosophical logic itself. A model is an idealization, in the sense of being a deliberate simplification of something relatively complex in which several important aspects are left aside, but also in the sense of being a view too perfect or excellent, not found in reality, of this thing. Paraconsistent logic is a branch of philosophical (...) logic. It is however not clear how paraconsistent logic can be seen as model-building. What exactly is modeled? In this paper I adopt the perspective of looking at a particular instance of paraconsistent logic—paranormal modal logic—which might be seen as a model of a specific kind of agent: inductive agents. After ntroducing what I call the highlevel and low-level models of inductive agents, I analyze the extent to which the above-mentioned idealizing features of model-building appear in paranormal modal logic and how they affect its philosophical significance. (shrink)

After outlining sceptical theism (ST) and the fine-tuning argument (FTA), I demonstrate how arguments for the former undercut the latter. I then consider and reject three recent proposals for ameliorating the conflict: positive ST, considerations about normative superiors, and appeal to theistic metaethics. I contend, however, that Kirk Durston’s complexity argument for ST does not undercut the FTA but in fact supports it. In defending that thesis, I respond to Climenhaga’s contention that ST undermines all warrant for theistic belief, (...) the FTA included. (shrink)

In the first section, I characterize skeptical theism more fully. This is necessary in order to address some important misconceptions and mischaracterizations that appear in the essays by Maitzen, Wilks, and O’Connor. In the second section, I describe the most important objections they raise and group them into four “families” so as to facilitate an orderly series of responses. In the four sections that follow, I respond to the objections.

We introduce a modal expansion of paraconsistent Nelson logic that is also as a generalization of the Belnapian modal logic recently introduced by Odintsov and Wansing. We prove algebraic completeness theorems for both logics, defining and axiomatizing the corresponding algebraic semantics. We provide a representation for these algebras in terms of twiststructures, generalizing a known result on the representation of the algebraic counterpart of paraconsistent Nelson logic.

Two systems of belief change based on paraconsistent logics are introduced in this article by means of AGM-like postulates. The first one, AGMp, is defined over any paraconsistent logic which extends classical logic such that the law of excluded middle holds w.r.t. the paraconsistent negation. The second one, AGMo , is specifically designed for paraconsistent logics known as Logics of Formal Inconsistency (LFIs), which have a formal consistency operator that allows to recover all the classical inferences. (...) Besides the three usual operations over belief sets, namely expansion, contraction and revision (which is obtained from contraction by the Levi identity), the underlying paraconsistent logic allows us to define additional operations involving (non-explosive) contradictions. Thus, it is defined external revision (which is obtained from contraction by the reverse Levi identity), consolidation and semi-revision, all of them over belief sets. It is worth noting that the latter operations, introduced by S. Hansson, involve the temporary acceptance of contradictory beliefs, and so they were originally defined only for belief bases. Unlike to previous proposals in the literature, only defined for specific paraconsistent logics, the present approach can be applied to a general class of paraconsistent logics which are supraclassical, thus preserving the spirit of AGM. Moreover, representation theorems w.r.t. constructions based on selection functions are obtained for all the operations. (shrink)

Recently there has been a good deal of interest in the relationship between common sense epistemology and Skeptical Theism. Much of the debate has focused on Phenomenal Conservatism and any tension that there might be between it and Skeptical Theism. In this paper I further defend the claim that there is no tension between Phenomenal Conservatism and Skeptical Theism. I show the compatibility of these two views by coupling them with an account of defeat – one that (...) is friendly to both Phenomenal Conservatism and Skeptical Theism. In addition, I argue that this account of defeat can give the Skeptical Theist what she wants – namely a response to the evidential argument from evil that can leave one of its premises unmotivated. In giving this account I also respond to several objections from Trent Dougherty (2011) and Chris Tucker (this volume) as well as to an additional worry coming from the epistemology of disagreement. (shrink)

In this essay, I investigate the implications for the discussion of theism in philosophy of religion for the beliefs of ordinary Christians and conclude that, in light of its historical development, those implications are minimal.

Given plausible assumptions about the nature of evidence and undercutting defeat, many believe that the force of the evidential problem of evil depends on sceptical theism’s being false: if evil is...

"Paraconsistent Belief Revision Based on a Formal Consistency Operator" delves into Belief Revision—a significant area of research in Formal Philosophy that uses logic to model the ways in which human and artificial agents modify their beliefs in response to new information and examines how these changes can be considered rational. -/- Originally authored as a PhD thesis (previously published in Portuguese), this work provides a novel epistemic interpretation of Paraconsistency through Paraconsistent Belief Revision systems. It explores the concept (...) of paraconsistency from the standpoint of epistemic attitudes of acceptance and rejection. -/- This work challenges the traditional notion that accepting a new belief requires retracting its negation from the current epistemic state. The author contends that such reflexive retraction goes against the principle of informational economy, which is a crucial aspect of rationality in the context of belief change. Consequently, the phenomenon of paraconsistency is further examined from this fresh perspective of belief change, shedding light on the complexities of the Logics of Formal Inconsistency (LFIs). These LFIs provide the foundational logic, offering a comprehensive framework for understanding and implementing paraconsistent principles within belief revision systems. -/- This thesis was supervised by Marcelo Esteban Coniglio and co-supervised by Márcio Moretto Ribeiro, as part of Rafael Rodrigues Testa's doctoral studies at the University of Campinas (Unicamp), Brazil. (shrink)

This paper considers whether theism is compatible with moral error theory. This issue is neglected, perhaps because it is widely assumed that these views are incompatible. I argue that this is mistaken. In so doing, I articulate the best argument for thinking that theism and moral error theory are incompatible. According to it, these views are incompatible because theism entails that God is morally good, and moral error theory entails that God is not. I reject this argument. (...) Since it is the best argument for thinking that theism and moral error theory are incompatible, I conclude that these views are compatible: one can coherently accept both views. (shrink)

I examine issues in the philosophy of religion at the intersection of what possibilities there are and what a God, as classically conceived in the theistic philosophical tradition, would be able to do. The discussion is centered around arguing for an incompatibility between theism and two principles about possibility and ability, and exploring what theists should say about these incompatibilities. -/- I argue that theism entails that certain kinds and amounts of evil are impossible. This puts theism (...) in conflict with popular principles of modal recombination. However, theists have plausible explanations for the violations of recombination that they posit, and can suitably amend these principles without giving up their usefulness in accounting for what possibilities there are. -/- I also argue that despite the impossibility of these evils, God is able to bring these evils about. This puts theism in conflict with the principle that no one is able to do the impossible. However, theists can give a plausible account of why God is unique in being able to do the impossible, and have distinctive resources to address the arguments in favor of the idea that no one is able to do the impossible. And by denying this principle, theists are able to resolve several otherwise difficult puzzles, including reconciling conflicts between the divine attributes. (shrink)

Inductive arguments from evil claim that evil presents evidence against the existence of God. Skeptical theists hold that some such arguments from evil evince undue confidence in our familiarity with the sphere of possible goods and the entailments that obtain between that sphere and God’s permission of evil. I argue that the skeptical theist’s skepticism on this point is inconsistent with affirming the truth of a given theodicy. Since the skeptical theist’s skepticism is best understood dialogically, I’ll begin by sketching (...) the kind of argument against which the skeptical theist’s skepticism is pitched. I will then define ‘skeptical theistic skepticism’, offer a precise definition of ‘theodicy’, and proceed with my argument. (shrink)

Skeptical theism, broadly construed, is an attempt to leverage our limited cognitive powers, in some specified sense, against “evidential” and “explanatory” arguments from evil. Since there are different versions of these kinds of arguments, there are correspondingly different versions of skeptical theism. In this paper, I consider four challenges to three central versions of skeptical theism: (a) the problem of generalized skepticism, (b) the problem of moral skepticism, (c) the problem of unqualified modal skepticism, and (d) the (...) challenge from Bayesian epistemology. (shrink)

In this chapter, I consider personal and impersonal anti-theism and personal and impersonal pro-theism. I show that skeptical theism undermines arguments for personal anti-theism and impersonal anti-theism. Next, I show that (at least some) arguments for personal and impersonal pro-theism are not undermined by skeptical theism. This throws a wrench in debates about the axiology of theism: if skeptical theism is true, then it is very difficult to establish certain positions in (...) answer to the axiological question about God. (shrink)

The most common charge against sceptical theism is that it is too sceptical, i.e. it committed to some undesirable form of scepticism or another. I contend that Michael Bergmann’s sceptical theism isn’t sceptical enough. I argue that, if true, the sceptical theses secure a genuine victory: they prevent, for some people, a prominent argument from evil from providing any justification whatsoever to doubt the existence of God. On the other hand, even if true, the sceptical theses fail to (...) prevent even the atheist from justifiably accepting it. (shrink)

Some moral realists have defended moral realism on the basis of the purported fact that moral facts figure as components in some good explanations of non-moral phenomena. In this paper I explore the relationship between theism and this sort of explanationist defense of moral realism. Theistic explanations often make reference to moral facts, and do so in a manner which is ineliminable in an important respect – remove the moral facts from those explanations, and they suffer as a result. (...) In this respect theistic moral explanations seem to differ from the sorts of moral explanations typically offered by moral explanationists. (shrink)

Skeptical theism is a family of responses to the evidential problem of evil. What unifies this family is two general claims. First, that even if God were to exist, we shouldn’t expect to see God’s reasons for permitting the suffering we observe. Second, the previous claim entails the failure of a variety of arguments from evil against the existence of God. In this essay, we identify three particular articulations of skeptical theism—three different ways of “filling in” those two (...) claims—and describes their role in responding to evidential arguments of evil due to William Rowe and Paul Draper. But skeptical theism has been subject to a variety of criticisms, several of which raise interesting issues and puzzles not just in philosophy of religion but other areas of philosophy as well. Consequently, we discuss some of these criticisms, partly with an eye to bringing out the connections between skeptical theism and current topics in mainstream philosophy. Finally, we conclude by situating skeptical theism within our own distinctive methodology for evaluating world views, what we call “worldview theory versioning.”. (shrink)

A logic is paraconsistent if it allows for non-trivial inconsistent theories. Given the usual definition of inconsistency, the notion of paraconsistent logic seems to rely upon the interpretation of teh sign '¬'. As paraconsistent logic challenges properties of negation taken to be basic in other contexts, it is disputable that an operator lacking those properties will count as real negation. The conclusion is that there cannot be genuine paraconsistent logics. This objection can be met from a (...) substructural perspective, since paraconsistent sequent calculi can be built from the same operational rules as classical logic but with slightly different structural rules. (shrink)

In this paper we present a philosophical motivation for the logics of formal inconsistency, a family of paraconsistent logics whose distinctive feature is that of having resources for expressing the notion of consistency within the object language in such a way that consistency may be logically independent of non- contradiction. We defend the view according to which logics of formal inconsistency may be interpreted as theories of logical consequence of an epistemological character. We also argue that in order to (...) philosophically justify paraconsistency there is no need to endorse dialetheism, the thesis that there are true contradictions. Furthermore, we argue that an intuitive reading of the bivalued semantics for the logic mbC, a logic of formal inconsistency based on classical logic, fits in well with the basic ideas of an intuitive interpretation of contradictions. On this interpretation, the acceptance of a pair of propositions A and ¬A does not mean that A is simultaneously true and false, but rather that there is conflicting evidence about the truth value of A. (shrink)

This paper briefly outlines some advancements in paraconsistent logics for modelling knowledge representation and reasoning. Emphasis is given on the so-called Logics of Formal Inconsistency (LFIs), a class of paraconsistent logics that formally internalize the very concept(s) of consistency and inconsistency. A couple of specialized systems based on the LFIs will be reviewed, including belief revision and probabilistic reasoning. Potential applications of those systems in the AI area of KRR are tackled by illustrating some examples that emphasizes the (...) importance of a fine-tuned treatment of consistency in modelling reputation systems, preferences, argumentation, and evidence. (shrink)

This chapter provides a quick sketch of the history of western philosophy of religion as it bears on theism.

This chapter traces how theism was developed by leading 19th and 20th century figures (Schleiermacher, Hegel, Kierkegaard, Nietzsche, Rahner, and Tillich) responding to Kant’s Copernican revolution in philosophy. Part one deals with the ontological nature of subjectivity itself and what it reveals about the conditions of the possibility of a subject’s relation to the Absolute. Part two explores the role of subjectivity and interiority in the individual’s relation to God, and part three takes a look at the theme of (...) the “unhappy consciousness,” how its development led to important attacks on theism, and the resources available to theology in countering these attacks. (shrink)

In his presidential address to the APA, Alvin Plantinga argues that the only sensible way to be an anti-realist is to be a theist. Anti-realism (AR) in this context is the epistemic analysis of truth that says, "(AR) necessarily, a statement is true if and only if it would be believed by an ideally [or sufficiently] rational agent/community in ideal [or sufficiently good] epistemic circumstances." Plantinga demonstrates, with modest modal resources, that AR entails that necessarily, ideal epistemic circumstances obtain. As (...) it is a contingent matter whether ideal epistemic circumstances obtain, Plantinga concludes that an anti-realist should be a theist. In this paper, we show that counterfactual analyses of truth as epistemic are instances of a more general problem of philosophical analysis. More specifically, without a radical revision of the logic, counterfactual analyses of truth as epistemic cannot avoid perpetrating some version of the conditional fallacy. Even so, we argue, anti-realists are not committed to the necessary existence of ideal epistemic circumstances and therefore need not be theists. (shrink)

Compares and contrasts Open Theism with Theological Determinism, Molinism, and Process Theism.

This chapter centers around the question of whether theism is rational. We begin by discussing different theories of rationality, and introducing some importantly related epistemic concepts and controversies. We then consider the possible sources of rational belief in God and argue that even if these provide some positive support, the fact of religious disagreement defeats the rationality of theism.

In this paper we consider the theory of predicate logics in which the principle of Bivalence or the principle of Non-Contradiction or both fail. Such logics are partial or paraconsistent or both. We consider sequent calculi for these logics and prove Model Existence. For L4, the most general logic under consideration, we also prove a version of the Craig-Lyndon Interpolation Theorem. The paper shows that many techniques used for classical predicate logic generalise to partial and paraconsistent logics once (...) the right set-up is chosen. Our logic L4 has a semantics that also underlies Belnap’s [4] and is related to the logic of bilattices. L4 is in focus most of the time, but it is also shown how results obtained for L4 can be transferred to several variants. (shrink)

God is usually taken to be a necessarily existing being who is unsurpassably powerful, knowledgeable and good. Theism is conceptualized in a single being that is monotheism in some religions and polytheism that is more than one being in some others. Yet some others see theism in everything of human concern that is pantheism. The doctrine of God is strong-minded by means of the religious experiences of men and evident in the conduct of such religious persons. This work (...) intends to show here, the points of similarities and dissimilarities between the concept of theism in Christianity, Islam and Sikhism. This work exposed among others that their major point of way out is that in Christianity, there is a distinctive and central teaching concerning Jesus Christ as unique incarnations, the word of God, pre-eminently manifested in a historic person, on the ground that his moral character perfectly represents the character and purpose of the invisible holy God. While Islam, and Sikhism, have no such doctrine, or theory of incarnation. (shrink)

Epistemological objections to moral realism allege that realism entails moral skepticism. Many philosophers have assumed that theistic moral realists can easily avoid such objections. In this article, I argue that things are not so easy: theists run the risk of violating an important constraint on replies to epistemological objections, according to which replies to such objections may not rely on substantive moral claims of a certain kind. Yet after presenting this challenge, I then argue that theists can meet it, successfully (...) replying to the objections without relying on the problematic kinds of substantive moral claims. Theists have a distinctive and plausible reply to epistemological objections to moral realism. (shrink)

I discuss J. P. Moreland's arguments from consciousness. I argue for the conclusion that considerations about consciousness favor naturalism over theism.

There are two foundational, but not fully developed, ideas in paraconsistency, namely, the duality between paraconsistent and intuitionistic paradigms, and the introduction of logical operators that express meta-logical notions in the object language. The aim of this paper is to show how these two ideas can be adequately accomplished by the Logics of Formal Inconsistency (LFIs) and by the Logics of Formal Undeterminedness (LFUs). LFIs recover the validity of the principle of explosion in a paraconsistent scenario, while LFUs (...) recover the validity of the principle of excluded middle in a paracomplete scenario. We introduce definitions of duality between inference rules and connectives that allow comparing rules and connectives that belong to different logics. Two formal systems are studied, the logics mbC and mbD, that display the duality between paraconsistency and paracompleteness as a duality between inference rules added to a common core– in the case studied here, this common core is classical positive propositional logic (CPL + ). The logics mbC and mbD are equipped with recovery operators that restore classical logic for, respectively, consistent and determined propositions. These two logics are then combined obtaining a pair of logics of formal inconsistency and undeterminedness (LFIUs), namely, mbCD and mbCDE. The logic mbCDE exhibits some nice duality properties. Besides, it is simultaneously paraconsistent and paracomplete, and able to recover the principles of excluded middle and explosion at once. The last sections offer an algebraic account for such logics by adapting the swap-structures semantics framework of the LFIs the LFUs. This semantics highlights some subtle aspects of these logics, and allows us to prove decidability by means of finite non-deterministic matrices. (shrink)

There was a time when 'logic' just meant classical logic. The climate is slowly changing and non-classical logic cannot be dismissed off-hand. However, a metatheory used to study the properties of non-classical logic is often classical. In this paper, we will argue that this practice of relying on classical metatheories is problematic. In particular, we will show that it is a bad practice because the metatheory that is used to study a non-classical logic often rules out the very logic it (...) is designed to study. (shrink)

Following Hume’s lead, Paul Draper argues that, given the biological role played by both pain and pleasure in goal-directed organic systems, the observed facts about pain and pleasure in the world are antecedently much more likely on the Hypothesis of Indifference than on theism. I examine one by one Draper’s arguments for this claim and show how they miss the mark.

This paper attempts to delineate a kind of realism, which incorporates some anti-realistic insights regarding the perspective, situated, and historical character of our forms of knowing and being in the world, and which resonates with the basic tenets of Christian theism. The first part of the paper analyzes the challenges anti-realism poses to Christian theism, particularly regarding the role, which the doctrine of creation played in securing the correspondence theory of truth as well as the fundamental experience of (...) God as the foundation of order and meaning. Using Heidegger’s hermeneutics in the second part, it is shown that epistemic pluralism can be made compatible with realism. Given that this form of hermeneutic realism still has problems with integrating the transcendence of God, as well as his/ her presence and action in the “world,” the notion of continuous co-creation as the basis for a pluralist realism that is amenable to Christian theism is explored in the final part. (shrink)

This paper extends Fitting's epistemic interpretation of some Kleene logics, to also account for Paraconsistent Weak Kleene logic. To achieve this goal, a dualization of Fitting's "cut-down" operator is discussed, rendering a "track-down" operator later used to represent the idea that no consistent opinion can arise from a set including an inconsistent opinion. It is shown that, if some reasonable assumptions are made, the truth-functions of Paraconsistent Weak Kleene coincide with certain operations defined in this track-down fashion. Finally, (...) further reflections on conjunction and disjunction in the weak Kleene logics accompany this paper, particularly concerning their relation with containment logics. These considerations motivate a special approach to defining sound and complete Gentzen-style sequent calculi for some of their four-valued generalizations. (shrink)