The main goal of this paper is to investigate what explanatory resources Robert Brandom’s distinction between acknowledged and consequential commitments affords in relation to the problem of logical omniscience. With this distinction the importance of the doxastic perspective under consideration for the relationship between logic and norms of reasoning is emphasized, and it becomes possible to handle a number of problematic cases discussed in the literature without thereby incurring a commitment to revisionism about logic. One such case (...) in particular is the preface paradox, which will receive an extensive treatment. As we shall see, the problem of logical omniscience not only arises within theories based on deductive logic; but also within the recent paradigm shift in psychology of reasoning. So dealing with this problem is important not only for philosophical purposes but also from a psychological perspective. (shrink)

This paper looks at three ways of addressing probabilism’s implausible requirement of logical omniscience. The first and most common strategy says it’s okay to require an ideally rational person to be logically omniscient. I argue that this view is indefensible on any interpretation of ‘ideally rational’. The second strategy says probabilism should be formulated not in terms of logically possible worlds but in terms of doxastically possible worlds, ways you think the world might be. I argue that, on (...) the interpretation of this approach that lifts the requirement of certainty in all logical truths, the view becomes vacuous, issuing no requirements on rational believers at all. Finally, I develop and endorse a new solution to the problem. This view proposes dynamic norms for reasoning with credences. The solution is based on an old proposal of Ian Hacking’s that says you’re required to be sensitive to logical facts only when you know they are logical facts. (shrink)

The traditional possible-worlds model of belief describes agents as ‘logically omniscient’ in the sense that they believe all logical consequences of what they believe, including all logical truths. This is widely considered a problem if we want to reason about the epistemic lives of non-ideal agents who—much like ordinary human beings—are logically competent, but not logically omniscient. A popular strategy for avoiding logical omniscience centers around the use of impossible worlds: worlds that, in one way (...) or another, violate the laws of logic. In this paper, we argue that existing impossible-worlds models of belief fail to describe agents who are both logically non-omniscient and logically competent. To model such agents, we argue, we need to ‘dynamize’ the impossible-worlds framework in a way that allows us to capture not only what agents believe, but also what they are able to infer from what they believe. In light of this diagnosis, we go on to develop the formal details of a dynamic impossible-worlds framework, and show that it successfully models agents who are both logically non-omniscient and logically competent. (shrink)

We propose a solution to the problem of logical omniscience in what we take to be its fundamental version: as concerning arbitrary agents and the knowledge attitude per se. Our logic of knowledge is a spin-off from a general theory of thick content, whereby the content of a sentence has two components: an intension, taking care of truth conditions; and a topic, taking care of subject matter. We present a list of plausible logical validities and invalidities (...) for the logic of knowledge per se for arbitrary agents, and isolate three explanatory factors for them: the topic-sensitivity of content; the fragmentation of knowledge states; the defeasibility of knowledge acquisition. We then present a novel dynamic epistemic logic that yields precisely the desired validities and invalidities, for which we provide expressivity and completeness results. We contrast this with related systems and address possible objections. (shrink)

At least since Aristotle’s famous 'sea-battle' passages in On Interpretation 9, some substantial minority of philosophers has been attracted to the doctrine of the open future--the doctrine that future contingent statements are not true. But, prima facie, such views seem inconsistent with the following intuition: if something has happened, then (looking back) it was the case that it would happen. How can it be that, looking forwards, it isn’t true that there will be a sea battle, while also being true (...) that, looking backwards, it was the case that there would be a sea battle? This tension forms, in large part, what might be called the problem of future contingents. A dominant trend in temporal logic and semantic theorizing about future contingents seeks to validate both intuitions. Theorists in this tradition--including some interpretations of Aristotle, but paradigmatically, Thomason (1970), as well as more recent developments in Belnap, et. al (2001) and MacFarlane (2003, 2014)--have argued that the apparent tension between the intuitions is in fact merely apparent. In short, such theorists seek to maintain both of the following two theses: (i) the open future: Future contingents are not true, and (ii) retro-closure: From the fact that something is true, it follows that it was the case that it would be true. It is well-known that reflection on the problem of future contingents has in many ways been inspired by importantly parallel issues regarding divine foreknowledge and indeterminism. In this paper, we take up this perspective, and ask what accepting both the open future and retro-closure predicts about omniscience. When we theorize about a perfect knower, we are theorizing about what an ideal agent ought to believe. Our contention is that there isn’t an acceptable view of ideally rational belief given the assumptions of the open future and retro-closure, and thus this casts doubt on the conjunction of those assumptions. (shrink)

Real-world agents do not know all consequences of what they know. But we are reluctant to say that a rational agent can fail to know some trivial consequence of what she knows. Since every consequence of what she knows can be reached via chains of trivial cot be dismissed easily, as some have attempted to do. Rather, a solution must give adequate weight to the normative requirements on rational agents’ epistemic states, without treating those agents as mathematically ideal reasoners. I’ll (...) argue that agents can fail to know trivial consequences of what they know, but never determinately. Such cases are epistemic oversights on behalf of the agent in question, and the facts about epistemic oversights are always indeterminate facts. As a result, we are never in a position to assert that such-and-such constitutes an epistemic oversight for agent i (for we may rationally assert only determinate truths). I then develop formal epistemic models according to which epistemic accessibility relations are vague. Given these models, we can show that epistemic oversights always concern indeterminate cases of knowledge. (shrink)

The subject of this article is Modal-Epistemic Arithmetic (MEA), a theory introduced by Horsten to interpret Epistemic Arithmetic (EA), which in turn was introduced by Shapiro to interpret Heyting Arithmetic. I will show how to interpret MEA in EA such that one can prove that the interpretation of EA is MEA is faithful. Moreover, I will show that one can get rid of a particular Platonist assumption. Then I will discuss models for MEA in light of the problems of (...) class='Hi'>logical omniscience and logical competence. Awareness models, impossible worlds models and syntactical models have been introduced to deal with the first problem. Certain conditions on the accessibility relations are needed to deal with the second problem. I go on to argue that those models are subject to the problem of quantifying in, for which I will provide a solution. (shrink)

My purpose in this chapter is to take seriously the idea that problem of evil is an incompatibility between the proposition that the world was created and is ruled by an omnipotent, omniscient and unlimitedly good being and one that says that there is evil and suffering in our world. Besides being in accordance with much of the literature on the problem of evil, this idea takes the problem at face value, that is to say, it sees (...) it as a logical and incompatibility problem. More important than that, it allows for a comprehensive and elegant account of the key concepts involved in the debate: despite contrary appearances, the concept of problem of evil itself, the concept of argument from evil, the concepts of logical and evidential problems of evil and the concepts of theodicy and defense can be seen and defined from the standpoint of the same general idea about the problem of evil. (shrink)

This paper argues that the logical coherence of classical theism can be defended through the traditional free-will defense and argument from divine omniscience and human finitude, but only at the cost of moral scepticism. The above two-pronged defense entails moral scepticism because it demands that we construe clear and undeniable cases of morally unjustifiable evil as merely apparently unjustifiable evils which can be morally justified from some moral point of view. The paper argues that justification is impossible because (...) such basic evils can never be justified from any "moral" perspective. The very conditions necessary for having a moral perspective demand that one recognize certain evils as unjustifiable from any moral point of view. This is the case because moral theories are designed to give us insight into such evils. Moreover, I argue that even if one rejects the above argument, moral scepticism still follows because any intelligible account of moral knowledge requires that its proponents be able at least to point to certain cases of unjustifiable evil if their theory is to have any purchase in the real world and avoid the charge of moral irrelevance and moral scepticism. But this is precisely what the classical theist cannot do. If, however, the classical theist rejects this moral scepticism, then real cases of morally unjustifiable evil must be admitted to exist and a single one of these is sufficient to undermine the logical coherence of classical theism. (shrink)

Modal accounts of knowledge, mind, and language, as prominently defended by Lewis, leave no room for enquiry into non-contingent matters. According to Lewis, there is only one necessarily true proposition, and it is vacuously known by everyone. What, then, are we doing when we do metaphysics, which often seems to deal with non-contingent questions? Lewis never gave a satisfactory answer, or even acknowledged the problem. I explore some options. Can we understand the relevant parts of metaphysics as dealing with (...) contingent questions about our concepts? Can we understand them in terms of a hyperintensional conception of “explicit” knowledge? Both options have some promise. Ultimately, however, I don’t think they succeed at squaring Lewis’s empiricist epistemology with his metaphysical realism. (shrink)

Discussions related to the detection of objective reality, the truth and lie are still a heated topic in the domain of philosophical epistemology. While certain philosophical contexts and theories suggest that the notion "reality as an independent category" should not be engaged, instead, interpretations, including reciprocal, should be used, others hold it that philosophical discussion cannot continue without reference to the said notion. Different philosophers and scolars approach this problem from different angles. When discussing these topics, philosophers often resort (...) to certain thought experiments, engaging an important concept, which can broadly be identified as "the global observer." This concept has something in common with such concepts as the God's Eye, Omniscient Interpreter, Ultimate Observer (quantum physics), Agent of Logical omniscience (game theories), Ideal Observer (ethics and meta-ethics), God (analytic theology). Despite the abundance of works on the topic and scrupulosity of arguments, there still remain many uncertainties in such discussions, mostly related to a great number of logical paradoxes, associated with the problem. Therefore, in view of the current situation, the focus of the research paper is on the deliberation of consistency of the notion "global observer" from the standpoint of logic and philosophy. The results of the analysis of the issue at stake are expected to clarify the notion and to enrich current discussions on the topic. I examine certain difficulties in the philosophical assumptions concerning one of the philosophical concepts, which could be collectively named as the "global observer." The article below explores the notion of the global observer as the guarantor of the determinability and configuration of events in the world. There is explained the meaning of this concept and attempt to show that, despite variations in the wording, it is used in many philosophical contexts related to epistemology. The core issue of the present research paper is the analysis of the consistency of the notion "global observer" from the standpoint of logic and philosophy. The paper discusses why application of this notion in some contexts poses challenges and appears to be paradoxical. (shrink)

The purpose of this paper is to consider the explanatory resources that Robert Brandom‟s distinction between acknowledged and consequential commitments affords in relation to the problem of logical omniscience. With this distinction the importance of the doxastic perspective under consideration for the relationship between logic and norms of reasoning is emphasized, and it becomes possible to handle a number of problematic cases discussed in the literature without thereby incurring a commitment to revisionism about logic. 12.

Epistemic logics based on the possible worlds semantics suffer from the problem of logical omniscience, whereby agents are described as knowing all logical consequences of what they know, including all tautologies. This problem is doubly challenging: on the one hand, agents should be treated as logically non-omniscient, and on the other hand, as moderately logically competent. Many responses to logical omniscience fail to meet this double challenge because the concepts of knowledge and reasoning (...) are not properly separated. In this paper, I present a dynamic logic of knowledge that models an agent’s epistemic state as it evolves over the course of reasoning. I show that the logic does not sacrifice logical competence on the altar of logical non- omniscience. (shrink)

Logical theories for representing knowledge are often plagued by the so-called Logical Omniscience Problem. The problem stems from the clash between the desire to model rational agents, which should be capable of simple logical inferences, and the fact that any logical inference, however complex, almost inevitably consists of inference steps that are simple enough. This contradiction points to the fruitlessness of trying to solve the Logical Omniscience Problem qualitatively if the (...) rationality of agents is to be maintained. We provide a quantitative solution to the problem compatible with the two important facets of the reasoning agent: rationality and resource boundedness. More precisely, we provide a test for the logical omniscience problem in a given formal theory of knowledge. The quantitative measures we use are inspired by the complexity theory. We illustrate our framework with a number of examples ranging from the traditional implicit representation of knowledge in modal logic to the language of justification logic, which is capable of spelling out the internal inference process. We use these examples to divide representations of knowledge into logically omniscient and not logically omniscient, thus trying to determine how much information about the reasoning process needs to be present in a theory to avoid logical omniscience. (shrink)

Standard epistemic logic actually formalizes folk-psychology. The problem of logical omniscience shows that this logic is not adequate in a cognitivist setting. In order to describe realistic information-processing believers, we need both an ontology of particulars and a hyper-intensional taxonomy of representations. From this point of view, sub-structural logics, which do not overlook the syntaxic details of the processing of information, are an interesting alternative to possible worlds semantics.

It would be good to have a Bayesian decision theory that assesses our decisions and thinking according to everyday standards of rationality — standards that do not require logical omniscience (Garber 1983, Hacking 1967). To that end we develop a “fragmented” decision theory in which a single state of mind is represented by a family of credence functions, each associated with a distinct choice condition (Lewis 1982, Stalnaker 1984). The theory imposes a local coherence assumption guaranteeing that as (...) an agent's attention shifts, successive batches of "obvious" logical information become available to her. A rule of expected utility maximization can then be applied to the decision of what to attend to next during a train of thought. On the resulting theory, rationality requires ordinary agents to be logically competent and to often engage in trains of thought that increase the unification of their states of mind. But rationality does not require ordinary agents to be logically omniscient. (shrink)

In this paper, I investigate whether we can use a world-involving framework to model the epistemic states of non-ideal agents. The standard possible-world framework falters in this respect because of a commitment to logical omniscience. A familiar attempt to overcome this problem centers around the use of impossible worlds where the truths of logic can be false. As we shall see, if we admit impossible worlds where “anything goes” in modal space, it is easy to model extremely (...) non-ideal agents that are incapable of performing even the most elementary logical deductions. A much harder, and considerably less investigated challenge is to ensure that the resulting modal space can also be used to model moderately ideal agents that are not logically omniscient but nevertheless logically competent. Intuitively, while such agents may fail to rule out subtly impossible worlds that verify complex logical falsehoods, they are nevertheless able to rule out blatantly impossible worlds that verify obvious logical falsehoods. To model moderately ideal agents, I argue, the job is to construct a modal space that contains only possible and non-trivially impossible worlds where it is not the case that “anything goes”. But I prove that it is impossible to develop an impossible-world framework that can do this job and that satisfies certain standard conditions. Effectively, I show that attempts to model moderately ideal agents in a world-involving framework collapse to modeling either logical omniscient agents, or extremely non-ideal agents. (shrink)

In his book The Problem of Evil, Van Inwagen aims to establish that the problem of evil is a failure. My article considers his response to the evidential problem of evil. His response relies on a fundamental assumption: “Every possible world God could have actualized contains patterns of suffering morally equivalent to those of the actual world, or else is massively irregular.” While it may not be unreasonable to suggest that it is logically possible that an omnipotent, (...) omniscient being is unable to actualize a better world, a world with somewhat less, prolonged animal suffering, this hardly amounts to an adequate response to the evidential problem of evil, an argument that endeavors to establish that it is more likely than not that an omniscient, omnipotent being could have created such a world. (shrink)

The morality of war has been debated from a variety of perspectives. However, it has rarely been intertwined with the topic of the existence of God. Sometimes anti-theists argue that the existence of a Western Judeo-Christian God who is omnipotent, omniscient and morally perfect is inconsistent with the existence of evils such as war. We will argue that there is no such logical inconsistency between the God of the African traditional religions and the evil of war. First, we contend (...) that such a logical inconsistency does not exist because God in African traditional religions is not seen as omnipotent, omniscient or morally perfect, and therefore, it would not be logically inconsistent for such a God to co-exist with the evil of war. This is mainly because African moral realism entails that war is a legitimate means for an imperfect being in an imperfect world to pursue morally permissible goals. Second, even if God is omniscient, omnipotent and morally perfect, when considered from the African religious viewpoint, a God of harmony, like the one in African traditional religions, can permit some evils for a greater good such as “harmony”. (shrink)

1.1 The Concept of Evil The problem of evil, in the sense relevant here, concerns the question of the reasonableness of believing in the existence of a deity with certain characteristics. In most discussions, the deity is God, understood as an omnipotent, omniscient, and morally perfect person. But the problem of evil also arises, as Hume saw very clearly, for deities that are less than all-powerful, less than all-knowing, and less than morally perfect. What is the relevant concept (...) of evil, in this context? Here it is useful to distinguish between axiological concepts and deontological ones. First, there are judgments about whether certain states of affairs make the world better or worse, whether those states are good or bad, desirable or undesirable. Such normative concepts – of good and bad, or desirable and undesirable, states of affairs – are axiological concepts. Secondly, there are judgments about the rightness and wrongness of actions, about what one morally ought or ought not do, of what one’s duty is, of whether a certain action violates someone rights, and these concepts – of the rightness and wrongness of actions, of duties, of the rights of individuals, of what one should or should not do – are deontological concepts. Given this distinction, should the problem of evil be understood axiologically or deontologically? Often, and I think most commonly in this context, evils are equated with states of affairs that, all things considered, are bad or undesirable: they are states of affairs that make the world a worse place. But one can also interpret the problem of evil in a deontological fashion, equating evils with states of affairs that a person should have prevented, if he could have done so. Elsewhere (2008, 105-6), I have argued that the deontological interpretation is preferable. But for present purposes, either interpretation will be fine. 1.2 Evil and the Reasonableness of Belief in the Existence of God That many things in the world – tsunamis, earthquakes, the suffering of non-human animals and innocent children, human actions such as the carrying out of the Holocaust – certainly appear to be evil is not a controversial matter. But whether such things are really evils, all things considered, is disputed. Assume, however, that the world does continue genuine evils, and not merely apparent ones. How, then does the existence of such evils bear upon the reasonableness of belief in the existence of God? First, the existence of evils can be used to show that certain arguments for the existence of God cannot establish that conclusion, or even render it probable. For some arguments, of course, one need not appeal to evil to make that point. If someone argues for the existence of a first cause, or an unmoved mover, or a necessary being having its necessity of itself, and then claims that this is what everyone understands by the term “God”, one can point out that no reason has been offered for thinking that the entity in question is even a person, let alone omnipotent, omniscient, and perfectly good. By contrast, with the type of argument that Hume was concerned with when he discussed the problem of evil – namely, arguments from the existence of order in the world to the existence of a designer, or intelligent cause of that order – one does have a type of argument that, if sound, shows that there is a person who, even if not omnipotent and omniscient, is at least extremely powerful and very knowledgeable. But such arguments do not support for conclusions about the moral character of such a person, and so it is at this point that the existence of evils becomes crucial. For in providing a reason for holding that the one is not justified in attributing even moral goodness to such a being, let alone moral perfection, it supports the conclusion that that argument in question cannot be a successful argument for the existence of God. The existence of evils, then, can serve to block arguments for the existence of God. But a second, and very familiar possibility, is that the existence of evils can also provide the basis of arguments against the existence of God. A very important distinction here is between deductive, or logical incompatibility, versions of the argument from evil, and inductive, or evidential, or probabilistic versions of the argument. According to the former, there are facts about the existence of evils in the world that are logically incompatible with the existence of God. Thus, some have held that the mere existence of any evil whatsoever is incompatible with the existence of God; others, that that certain types of evil – such as natural evils – are incompatible with the existence of God; and others, that it is the amount of evil in the world, or the fact that some people suffer horrendous evils, that logically precludes the existence of God. Inductive (or evidential, or probabilistic) versions of the argument from evil, by contrast, do not claim that there are facts about the evils in the world that are logically incompatible with the existence of God. The claim is rather that there are facts about the evils found in the world that render the existence of God at the very least unlikely, and perhaps extremely so. 1.3 Hume’s Use of the Existence of Evils The preceding discussion suggests two very different ways in which Hume might be employing the existence of evils. First, he might be appealing to the existence of evils simply to undercut certain arguments for the existence of God. In particular, he might be appealing to evils to show that, whatever the merits of the argument from order to design may be, it can nether establish, nor render probable, the existence of a morally good deity. Secondly, Hume might be advancing a version of the argument from evil, and that in turn could take the form either of an argument that claims that facts about evil are logically incompatible with the existence of God, or of an argument that claims, more modestly, that the apparent evils found in the world render the existence of God unlikely. (shrink)

The logical problem of evil centers on the apparent inconsistency of the following two propositions: God is omnipotent, omniscient, and wholly good, and There is evil in the world. This is the problem that Alvin Plantinga takes to task in his celebrated response to the problem of evil. Plantinga denies that and are inconsistent, arguing that J.L. Mackie's principle - that there are no limits to what an omnipotent thing can do - is false. We challenge (...) Plantinga, and defend Mackie's view. (shrink)

Discussions related to the detection of objective reality, the truth and lie are still a heated topic in the domain of philosophical epistemology. While certain philosophical contexts and theories suggest that the notion "reality as an independent category" should not be engaged, instead, interpretations, including reciprocal, should be used, others hold it that philosophical discussion cannot continue without reference to the said notion. Different philosophers and scolars approach this problem from different angles. When discussing these topics, philosophers often resort (...) to certain thought experiments, engaging an important concept, which can broadly be identified as "the global observer." This concept has something in common with such concepts as the God's Eye, Omniscient Interpreter, Ultimate Observer (quantum physics), Agent of Logical omniscience (game theories), Ideal Observer (ethics and meta-ethics), God (analytic theology). Despite the abundance of works on the topic and scrupulosity of arguments, there still remain many uncertainties in such discussions, mostly related to a great number of logical paradoxes, associated with the problem. Therefore, in view of the current situation, the focus of the research paper is on the deliberation of consistency of the notion "global observer" from the standpoint of logic and philosophy. The results of the analysis of the issue at stake are expected to clarify the notion and to enrich current discussions on the topic. I examine certain difficulties in the philosophical assumptions concerning one of the philosophical concepts, which could be collectively named as the "global observer." The article below explores the notion of the global observer as the guarantor of the determinability and configuration of events in the world. There is explained the meaning of this concept and attempt to show that, despite variations in the wording, it is used in many philosophical contexts related to epistemology. The core issue of the present research paper is the analysis of the consistency of the notion "global observer" from the standpoint of logic and philosophy. The paper discusses why application of this notion in some contexts poses challenges and appears to be paradoxical. (shrink)

There have been several different and even opposed conceptions of the problem of logical constants, i.e. of the requirements that a good theory of logical constants ought to satisfy. This paper is in the first place a survey of these conceptions and a critique of the theories they have given rise to. A second aim of the paper is to sketch some ideas about what a good theory would look like. A third aim is to draw from (...) these ideas and from the preceding survey the conclusion that most conceptions of the problem of logical constants involve requirements of a philosophically demanding nature which are probably not satisfiable by any minimally adequate theory. (shrink)

We propose a model for belief which is free of presuppositions. Current models for belief suffer from two difficulties. One is the well known problem of logical omniscience which tends to follow from most models. But a more important one is the fact that most models do not even attempt to answer the question what it means for someone to believe something, and just what it is that is believed. We provide a flexible model which allows us (...) to give meaning to beliefs in general contexts, including the context of animal belief , and of human belief which is expressed in language. (shrink)

Famously, the Church–Fitch paradox of knowability is a deductive argument from the thesis that all truths are knowable to the conclusion that all truths are known. In this argument, knowability is analyzed in terms of having the possibility to know. Several philosophers have objected to this analysis, because it turns knowability into a nonfactive notion. In addition, they claim that, if the knowability thesis is reformulated with the help of factive concepts of knowability, then omniscience can be avoided. In (...) this article we will look closer at two proposals along these lines :557–568, 1985; Fuhrmann in Synthese 191:1627–1648, 2014a), because there are formal models available for each. It will be argued that, even though the problem of omniscience can be averted, the problem of possible or potential omniscience cannot: there is an accessible state at which all truths are known. Furthermore, it will be argued that possible or potential omniscience is a price that is too high to pay. Others who have proposed to solve the paradox with the help of a factive concept of knowability should take note :53–73, 2010; Spencer in Mind 126:466–497, 2017). (shrink)

One concern bothering ancient and medieval philosophers is the logical worry discussed in Aristotle's De Interpretatione 9, that if future contingent propositions are true, then they are settled in a way that is incompatible with freedom. Another is if we grant God foreknowledge of future contingent events then God's foreknowledge will determine those events in a way precluding freedom. ;I begin by discussing the standard compatibilist solution to these problems as represented in Boethius's Consolation of Philosophy and then examine (...) theories that allegedly deviate from the Boethian solution. Boethius's solution to these separate problems involves showing that both problems operate on an ambiguity in the scope of the modal operator 'necessarily' present in the articulation of the problem. Once the ambiguity is removed we see that both disambiguations fail to offer a sound argument against the compatibility of free action with either God's omniscience or future contingent proposition's being true. The only difference between the solutions is that before executing the scope distinction strategy in the theological problem, Boethius reminds us that God knows future contingents rather than foreknowing them, since God is timeless. ;The rest of my discussion examines positions that allegedly deviate from the Boethian solution: positions held by Peter de Rivo, William Ockham and Plotinus. I argue that Ockham doesn't in fact deviate from the Boethian solution to the theological problem as is commonly held. Instead of offering a compatibilist position where God's omniscience includes foreknowledge, Ockham denies that God foreknows the future advocating instead a more sophisticated Boethian position. The other two philosophers, Rivo and Plotinus, deviate from Boethius, but unfortunately neither position appears philosophically plausible. Rivo's incompatibilist solution to the logical problem is inconsistent with his retention of the Boethian solution to the theological problem and is probably implausible on its own. Plotinus's compatibilist account fails not because it claims that necessity and freedom are compatible, but because the account of moral responsibility Plotinus offers to justify the compatibility fails. (shrink)

I discuss three ways of responding to the logical omniscience problems faced by traditional ‘possible worlds’ epistemic logics. Two of these responses were put forward by Hintikka and the third by Cresswell; all three have been influential in the literature on epistemic logic. I show that both of Hintikka's responses fail and present some problems for Cresswell’s. Although Cresswell's approach can be amended to avoid certain unpalatable consequences, the resulting formal framework collapses to a sentential model of knowledge, (...) which defenders of the ‘possible worlds’ approach are frequently critical of. (shrink)

The majority of philosophers of religion, at least since Plantinga’s reply to Mackie’s logical problem of evil, agree that it is logically possible for an omnibenevolent, omniscient, and omnipotent God to exist who permits some of the evils we see in the actual world. This is conceivable essentially because of the possible world known as heaven. That is, heaven is an imaginable world in a similar way that logically possible scenarios in any fiction are imaginable. However, like some (...) of the imaginable stories in fiction where we are asked to envision an immoral act as a moral one, we resist. I will employ the works of Tamar Gendler on imaginative resistance and Keith Buhler’s Virtue Ethics approach to moral imaginative resistance and apply them to the conception of heaven and the problem of evil. While we can imagine God as an omnibenevolent parent permitting evil to allow for morally significant freedom and the rewards in heaven or punishments in hell (both possible worlds), we should not. This paper is not intended to be a refutation of particular theodicies; rather it provides a very general groundwork connecting issues of horrendous suffering and imaginative resistance to heaven as a possible world. (shrink)

Logical omniscience states that the knowledge set of ordinary rational agents is closed for its logical consequences. Although epistemic logicians in general judge this principle unrealistic, there is no consensus on how it should be restrained. The challenge is conceptual: we must find adequate criteria for separating obvious logical consequences from non-obvious ones. Non-classical game-theoretic semantics has been employed in this discussion with relative success. On the one hand, with urn semantics [15], an expressive fragment of (...) classical game semantics that weakens the dependence relations between quantifiers occurring in a formula, we can formalize, for a broad array of examples, epistemic scenarios in which an individual ignores the validity of some first-order sentence. On the other hand, urn semantics offers a disproportionate restriction of logical omniscience. Therefore, an improvement of this system is needed to obtain a better solution of the problem. In this paper, I argue that our linguistic competence in using quantifiers requires a sort of basic hypothetical logical knowledge that can be formulated as follows: when inquiring after the truth-value of ∀xφ, an individual might be unaware of all substitutional instances this sentence accepts, but at least she must know that, if an element a is given, then ∀xφ holds only if φ is true. This thesis accepts game-theoretic formalization in terms of a refinement of urn semantics. I maintain that the system so obtained affords an improved solution of the logical omniscience problem. To do this, I characterize first-order theoremhood in US+. As a consequence of this result, we will see that the ideal reasoner depicted by US+ only knows the validity of first-order formulas whose Herbrand witnesses can be trivially found, a fact that provides strong evidence that our refinement of urn semantics captures a relevant sense of logical obviousness. (shrink)

Classical theists hold that God is omnipotent. But now suppose a critical atheologian were to ask: Can God create a stone so heavy that even he cannot lift it? This is the dilemma of the stone paradox. God either can or cannot create such a stone. Suppose that God can create it. Then there's something he cannot do – namely, lift the stone. Suppose that God cannot create the stone. Then, again, there's something he cannot do – namely, create it. (...) Either way, God cannot be omnipotent. Among the variety of known theological paradoxes, the paradox of the stone is especially troubling because of its logical purity. It purports to show that one cannot believe in both God and the laws of logic. In the face of the stone paradox, how should the contemporary analytic theist respond? Ought they to revise their belief in theology or their belief in logic? Ought they to lose their religion or lose their mind? (shrink)

The beliefs of the agents in a multi-agent system have been formally modelled in the last decades using doxastic logics. The possible worlds model and its associated Kripke semantics provide an intuitive semantics for these logics, but they commit us to model agents that are logically omniscient. We propose a way of avoiding this problem, using a new kind of entities called subjective situations. We define a new doxastic logic based on these entities and we show how the belief (...) operators have some desirable properties, while avoiding logical omniscience. A comparison with two well-known proposals (Levesque's logic of explicit and implicit beliefs and Thijsse's hybrid sieve systems) is also provided. (shrink)

The article is an attempt at explaining the category of logical form used by Ludwig Wittgenstein in his Tractatus logico-philosophicus by using concepts from Gottfried Wilhelm Leibniz’s The Monadology. There are many similarities and analogies between those works, and the key concept for them is the category of the inner and acknowledged importance of consideration based on basic categories of thinking about the world. The Leibnizian prospect allows for a broader look at Wittgenstein’s analysis of the relation between propositions (...) and facts, between language and the world. Using the Hanoverian philosopher’s terminology allows for the demonstration of the ambivalence of the concept of logical form in the philosophy of Wittgenstein and also the metaphysical nature of his first book. (shrink)

Originally published in 1941. Professor Ushenko treats of current problems in technical Logic, involving Symbolic Logic to a marked extent. He deprecates the tendency, in influential quarters, to regard Logic as a branch of Mathematics and advances the intuitionalist theory of Logic. This involves criticism of Carnap, Russell, Wittgenstein, Broad and Whitehead, with additional discussions on Kant and Hegel. The author believes that the union of Philosophy and Logic is a natural one, and that an exclusively mathematical treatment cannot give (...) an adequate account of Logic. A fundamental characteristic of Logic is comprehensiveness, which brings out the affinity between logic and philosophy, for to be comprehensive is the aim of philosophical ambition. (shrink)

Originally published in 1941. Professor Ushenko treats of current problems in technical Logic, involving Symbolic Logic to a marked extent. He deprecates the tendency, in influential quarters, to regard Logic as a branch of Mathematics and advances the intuitionalist theory of Logic. This involves criticism of Carnap, Russell, Wittgenstein, Broad and Whitehead, with additional discussions on Kant and Hegel. The author believes that the union of Philosophy and Logic is a natural one, and that an exclusively mathematical treatment cannot give (...) an adequate account of Logic. A fundamental characteristic of Logic is comprehensiveness, which brings out the affinity between logic and philosophy, for to be comprehensive is the aim of philosophical ambition. (shrink)

A recent approach to the problem of logical omniscience holds that belief is question-sensitive: what an agent believes depends on what question they try to answer (Pérez Carballo, 2016; Yalcin, 2018; Hoek, 2022). While the question-sensitive approach can avoid some logical omniscience problems, we argue that it suffers from nearby problems. First, these accounts all validate closure principles that are just as implausible as the ones it was designed to avoid. Second, question-sensitivity by itself isn’t (...) suitable for explaining many kinds of failures of logical omniscience. Recognizing the flaws of this approach, however, naturally leads to a more promising solution. Our account generalizes the question-sensitive approach by appealing to (1) the defeasible nature of dispositions toward action associated with belief and (2) the algorithms an agent uses to make decisions. On our view, then, believing that φ means being disposed to employ an algorithm which outputs acting on the information that φ in normal circumstances associated with φ. We argue that this account naturally generalizes the question-sensitive accounts while avoiding their faults. (shrink)

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James Sterba uses the Pauline Principle to argue that the occurrence of significant, horrendous evils is logically incompatible with the existence of a good God. The Pauline Principle states that (as a rule) one must never do evil so that good may come from it, and according to Sterba, this principle implies that God may not permit significant evils even if that permission would be necessary to secure other, greater goods. By contrast, I argue that the occurrence of significant evils (...) is logically compatible with the existence of a good God because victims of significant evils may themselves reasonably consent to their suffering. In particular, I argue that they may be able to accept their suffering if it turns out that there was no way for God to secure relevant greater goods (or prevent other, greater evils) except by way of allowing their suffering, and God also provides them with other compensating, heavenly comforts. After using this consent-based argument to address Sterba’s logical problem from evil, I briefly consider how this argument may also help address a related evidential problem from evil, which suggests that while it is possible that victims of significant evils would consent to their suffering, it is unlikely that they would do so. While I do not provide a definitive solution to this evidential problem of evil, I highlight one important example of a trade-off that God may need to make that would—along with the provision of compensating, heavenly comforts—potentially persuade victims of significant evils to consent to their suffering. Specifically, I argue that there may be a necessary trade-off that God needs to make between permitting significant evils (on the one hand) and protecting a certain, morally significant form of free will (on the other hand). (shrink)

In this paper, I defend the metalinguistic solution to the problem of mathematical omniscience for the possible-worlds account of propositions by combining it with a computational model of knowledge and belief. The metalinguistic solution states that the objects of belief and ignorance in mathematics are relations between mathematical sentences and what they express. The most pressing problem for the metalinguistic strategy is that it still ascribes too much mathematical knowledge under the standard possible-worlds model of knowledge and (...) belief on which these are closed under entailment. I first argue that Stalnaker's fragmentation strategy is insufficient to solve this problem. I then develop an alternative, computational strategy: I propose a model of mathematical knowledge and belief adapted from the algorithmic model of Halpern et al. which, when combined with the metalinguistic strategy, entails that mathematical knowledge and belief require computational abilities to access metalinguistic information, and thus aren't closed under entailment. As I explain, the computational model generalizes beyond mathematics to a version of the functionalist theory of knowledge and belief that motivates the possible-worlds account in the first place. I conclude that the metalinguistic and computational strategies yield an attractive functionalist, possible-worlds account of mathematical content, knowledge, and inquiry. (shrink)