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)

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)

An exchange between Patrick Grim and Alvin Plantinga regarding Cantorian arguments against the possibility of an omniscient being.

In this paper I present two new arguments against the possibility of an omniscient being. My new arguments invoke considerations of cardinality and resemble several arguments originally presented by Patrick Grim. Like Grim, I give reasons to believe that there must be more objects in the universe than there are beliefs. However, my arguments will rely on certain mereological claims, namely that Classical Extensional Mereology is necessarily true of the part-whole relation. My first argument is an instance of a problem (...) first noted by Gideon Rosen and requires an additional assumption about the mereological structure of certain beliefs. That assumption is that an omniscient being’s beliefs are mereological simples. However, this assumption is dropped when I present my second argument. Thus, I hope to show that if Classical Extensional Mereology is true of the part-whole relation, there cannot be an omniscient being. (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.

The epistemicist theory aims to explain ignorance due to vagueness by semantic plasticity: the shiftiness of intensions across close possible worlds resulting from shiftiness in usage. This explanation is challenged by the Omniscient Speaker Puzzle (Sennet in Philos Stud 161(2):273–285, 2012). Suppose that an omniscient speaker, Barney, who knows all the facts about usage and how these facts determine the intensions of expressions, cooks up a scheme to stabilise the intension of a normally semantically plastic term like ‘rich’. It (...) seems that ‘rich’ would display all the phenomena associated with vagueness without being semantically plastic, thus making the epistemicist explanation of ignorance due to vagueness insufficient. In this paper, I present a few choice points for epistemicism that arise as a result of the puzzle. (shrink)

In this paper I examine an argument that has been made by Patrick Grim for the claim that de se knowledge is incompatible with the existence of an omniscient being. I claim that the success of the argument depends upon whether it is possible for someone else to know what I know in knowing (F), where (F) is a claim involving de se knowledge. I discuss one reply to this argument, proposed by Edward Wierenga, that appeals to first-person propositions (...) and argue that this response is unsuccessful. I then consider David Lewis’s theory of de se attitudes involving the self-ascription of properties. I claim that, according to this theory, there are two senses in which someone else can know what I know in knowing (F). I then argue that the second sense allows for the compatibility of de se knowledge with the existence of an omniscient being. (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)

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)

Arguments against our free will pose a serious problem. Although there are not very many philosophers who call themselves fatalists, quite a few are convinced that fatalism follows from common assumptions. Assuming that most believe themselves to be free, identifying ways to avoid the conclusion of such fatalist arguments is quite an important task. I begin by dealing specifically with theological fatalism. I present many versions of theological fatalism, but come to the conclusion that only one version constitutes a genuine (...) problem. That version, I argue, is reducible to a deeper fatalist dilemma that follows from assumptions so common that it must be faced by even the atheist: the mutually incompatibility of human freedom, the principle of alternate possibilities and bi-valance. After considering other objections to my argument, I conclude that the only way to avoid the fatalist conclusion is to either deny the principle of alternate possibilities or deny bi-valance. I argue that, although each option is somewhat problematic, denying bivalence is the more defensible of the two options. (shrink)

A knowledge argument is offered that presents unique difficulties for Christians who wish to assert that God is essentially omniscient. The difficulties arise from the doctrine of the incarnation. Assuming that God the Son did not necessarily have to become incarnate, then God cannot necessarily have knowledge de se of the content of a non-divine mind. If this is right, then God’s epistemic powers are not fixed across possible worlds and God is not essentially omniscient. Some options for Christian (...) theists are discussed, including rejecting traditional theism in favour of some version of pantheism or panentheism. (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)

A simple argument against Lewisian modal realism as portrayed in On the Plurality of World arises from its treatment of doxastic modalities. It is easily shown that if it is true, it is impossible to doubt the theory on ontological grounds, or, that, if it is possible to maintain doubt about modal realism’s existential postulate, it has to be false. The argument hinges on the fact that modal realism’s main ontological hypothesis, if true, is necessarily true.

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.

To reconcile the standard possible worlds model of knowledge with the intuition that ordinary agents fall far short of logical omniscience, a Stalnakerian strategy appeals to two components. The first is the idea that mathematical and logical knowledge is at bottom metalinguistic knowledge. The second is the idea that non-ideal minds are often fragmented. In this paper, we investigate this Stalnakerian reconciliation strategy and argue, ultimately, that it fails. We are not the first to complain about the Stalnakerian (...) strategy. But in contrast to existing complaints, we want to cause trouble for the strategy directly on its home turf. That is, we will advance our objection while granting both the plausibility of the fragmentation component—save for an extreme version of it—and that of the metalinguistic component. Once our central objection to the Stalnakerian strategy is in place, we will show how it negatively affects Adam Elga and Augustín Rayo’s recent attempt to apply the Stalnakerian strategy in the context of Bayesian decision theory. (shrink)

According to egalitarians, there is no privileged now-possible history. Egalitarianism seems to provide an attractive way to reconcile openness and omniscience, but, I argue, it does not.

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)

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)

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)

The article analyzes and criticizes the assumptions of Peter Van Inwagen’s argument for the alleged contradiction of the foreknowledge of God and human freedom. The argument is based on the sine qua non condition of human freedom defined as access to possible worlds containing such a continuation of the present in which the agent implements a different action than will be realized de facto in the future. The condition also contains that in every possible continuation of the present (...) state of affairs, the same propositions about the ‘present past’ (the past before the present moment) are true as are true in the present state of affairs. The paper argues that Van Inwagen’s reasoning is inconclusive, it contains the type of mistake of confusing conditional impossibility with unconditional and presents a methodologically wrong method of solving a philosophical problem. It is because in the very construction of the problem determining the available solution. The article points to the possibility that the human freedom of some action is not excluded by the fact that specific past facts logically entail that this event will occur. (shrink)

Information is often modelled as a set of relevant possibilities, treated as logically possible worlds. However, this has the unintuitive consequence that the logical consequences of an agent's information cannot be informative for that agent. There are many scenarios in which such consequences are clearly informative for the agent in question. Attempts to weaken the logic underlying each possible world are misguided. Instead, I provide a genuinely psychological notion of epistemic possibility and show how it can be captured (...) in a formal model, which I call a fan. I then show how to use fans to build formal models of being informed, as well as knowledge, belief and information update. (shrink)

// tl;dr A Proposition is a Way of Thinking // -/- This chapter is about type-theoretic approaches to propositional content. Type-theoretic approaches to propositional content originate with Hintikka, Stalnaker, and Lewis, and involve treating attitude environments (e.g. "Nate thinks") as universal quantifiers over domains of "doxastic possibilities" -- ways things could be, given what the subject thinks. -/- This chapter introduces and motivates a line of a type-theoretic theorizing about content that is an outgrowth of the recent literature on epistemic (...) modality, according to which contentful thought is broadly "informational" in its nature and import. The general idea here is that an object of thought is not a way *the world* could be, but rather a way *one's perspective* could be (with respect to a relevant representational question). I will spend the middle part of this chapter motivating and developing a version of this strategy that is, I’ll argue, well-suited to explaining clear phenomena concerning the attribution of perspectival attitudes -- in particular, attitudes towards loosely information-sensitive propositions -- with which extant approaches struggle. My overarching goal here will be to motivate a distinctive version of the "informational" approach -- the "Flexible Types" approach, which is based on the theory proposed in Charlow (2020). According to the Flexible Types approach, propositional attitude verbs are quantifiers over sets of possibilities, but a possibility is a type-flexible notion -- sometimes a possible world, sometimes a perspective, sometimes a set of possible worlds, sometimes a set of perspectives. -/- After introducing the Flexible Types approach, this chapter circles back to more traditional concerns for the analysis of propositions as types of possibilities -- Frege's Puzzle and the problem of Logical Omniscience. Here too the Flexible Types approach bears fruit. Although there are certainly significant differences -- I note some in the concluding section -- the gist of this theory is Hinitkkan or Lewisian in spirit (if not quite in letter). We can make progress on addressing the challenges for the analysis of propositional content in terms of types of possibilities, through empirically driven refinement of our notion of what kind of thing a "doxastic possibility" is. (shrink)

The philosophy of mind is traditionally concerned with the study of mental processes, language, the representation of knowledge and the relation of the mind shares with the body; computational complexity theory is related to the classification of computationally solvable problems (be it via execution time, storage requirements, etc...). While there are well-established links between computer science in general & the philosophy of mind, many possible solutions to traditional problems in the philosophy of mind have not yet been analyzed from (...) the more specific lens of computational complexity theory. In his paper "Why Philosophers Should Care about Computational Complexity", Scott Aaronson argues that many conventional theories of epistemology & mind implicitly make the presupposition of omniscience (by supposing that knowing base facts means a knower necessarily understands derivative facts) - he proposes that computational complexity theory could explain why this is not the case. In this paper, I argue for a theory of mental representation & epistemology compatible with Aaronson's observations on complexity theory, overcoming that presupposition of omniscience. (shrink)

This is a system of pure speculative reason in answer to the challenge issued by Immanuel Kant, in his "Critique of Pure Reason," with regard to metaphysics; the challenge being clearly mentioned in the Appendix to his "Prolegomena..." wherein he asks his Reviewer to take any one of his four sets of contradictory propositions, and offer an a priori judgment/proposition of his own that would overturn the antinomy, and thus, allow room for the possibility of raising metaphysics to the level (...) of a science, meaning a synthesis of judgments, from pure reason, self-evidently a priori, therefore, necessary; and that as a synthesis of pure understanding, would relate to and help us make sense of reality, that is, the world of our experience. (shrink)

A Cantorian argument that there is no set of all truths. There is, for the same reason, no possible world as a maximal set of propositions. And omniscience is logically impossible.

The concept of knowledge can be modelled in epistemic modal logic and, if modelled by using a standard modal operator, it is subject to the problem of logical omniscience. The classical solution to this problem is to distinguish between implicit and explicit knowledge and to construe the knowledge operator as capturing the concept of implicit knowledge. In addition, since a proposition is said to be implicitly known just in case it is derivable from the set of propositions that are (...) explicitly known by using a certain set of logical rules, the concept of implicit knowledge is definable on the basis of the concept of explicit knowledge. In any case, both implicit and explicit knowledge are typically characterized as factive, i.e. such that it is always the case that what is known is also true. The aim of the present paper is twofold: first, we will develop a dynamic system of explicit intersubjective knowledge that allows us to introduce the operator of implicit knowledge by definition; secondly, we will show that it is not possible to hold together the following two theses: (1) the concept of implicit knowledge is definable along the lines indicated above and (2) the concept of implicit knowledge is factive. (shrink)

The topic of divine omniscience is well-trodden ground, with philosophers and theologians having asked virtually every question there is to ask about it. The questions regarding God's omniscience to be addressed here are as follows. First, is omniscience best understood as maximal propositional knowledge along with maximal experiential knowledge? I argue that it is. Second, is it possible for God to be essentially omniscient? I argue that it is not.

I present an approach to our conceiving absolute impossibilities—things which obtain at no possible world—in terms of ceteris paribus intentional operators: variably restricted quantifiers on possible and impossible worlds based on world similarity. The explicit content of a representation plays a role similar in some respects to the one of a ceteris paribus conditional antecedent. I discuss how such operators invalidate logical closure for conceivability, and how similarity works when impossible worlds are around. Unlike what happens with ceteris (...) paribus counterfactual conditionals, the closest worlds are relevantly closest belief-worlds: closest to how things are believed to be, rather than to how they are. Also, closeness takes into account apriority and the opacity of intentional contexts. (shrink)

In the recent debate on Christian theism, the position called Open Theism (OT) tries to solve the dilemma of omniscience and human freedom. In OT, the key word of the human-divine relationship is “risk”: in his relationship with us, God is a risk-taker in that he adapts his plan to human decisions and to the situations that arise from them. “Risk” is the fundamental characteristic of any true love relationship. According to OT, God has no exhaustive knowledge of how (...) humans will use their will, and the divine plan for this world is not seen as fixed for eternity. OT distinguishes between meticulous providence and general providence and denies that the former can exist. After illustrating these positions and a particular view of OT called essential kenosis, I highlight some of their weaknesses and conclude by asking whether the concept of mystery (at least in some of its possible interpretations: I outline four “solutions”) can enable a reconciliation between classical theism and OT. By applying an approach to the notion of mystery usually connected to the Trinity, I show that the dilemma of omniscience, human freedom and providence does not compromise the plausibility of theism. (shrink)

Though my ultimate concern is with issues in epistemology and metaphysics, let me phrase the central question I will pursue in terms evocative of philosophy of religion: What are the implications of our logic-in particular, of Cantor and G6del-for the possibility of omniscience?

The theory of possible worlds has permeated analytic philosophy in recent decades, and its best versions have a consequence which has gone largely unnoticed: in addition to the panoply of possible worlds, there are a great many impossible worlds. A uniform ontological method alone should bring the friends of possible worlds to adopt impossible worlds, I argue, but the theory's applications also provide strong incentives. In particular, the theory facilitates an account of counterfactuals which avoids several of (...) the implausible results of David Lewis's account, and it paves the way for the analogues of Kripkean semantics for epistemic and relevant logics. On the theories of possible worlds as abstract objects, worlds bear a strong resemblance to propositions. I contend that if there are distinct necessarily false propositions, then there are likewise distinct impossible worlds. However, one who regards possible worlds as concrete objects must not recognize impossible worlds, in part because concrete worlds cannot misrepresent certain features of reality, as some impossible worlds must. Accordingly, I defend and develop a theory of impossible worlds as maximal impossible states of affairs. Impossible worlds perform admirably in the analysis of counterfactuals with impossible antecedents. I argue that, contrary to standard accounts, not all counterpossibles are trivially true, and I develop a Lewis-style semantics which allows this result. The point is crucial, since many views presuppose that some counterpossibles are substantive philosophical truths. Finally, I show that impossible worlds hold great promise for doxastic and relevant logics. Epistemic logic needs a domain of propositions which is not closed under strict implication to avoid the problem of logical omniscience, and relevant logic needs such a domain to avoid the famous paradoxes of implication. In sum, impossible world theory promises natural, elegant solutions to philosophical problems in numerous areas where possible worlds alone flounder. These solutions come to most possible world theorists at no cost, since the existence of impossible worlds is entailed by theses they already hold. (shrink)

One response to the problem of logical omniscience in standard possible worlds models of belief is to extend the space of worlds so as to include impossible worlds. It is natural to think that essentially the same strategy can be applied to probabilistic models of partial belief, for which parallel problems also arise. In this paper, I note a difficulty with the inclusion of impossible worlds into probabilistic models. Under weak assumptions about the space of worlds, most of (...) the propositions which can be constructed from possible and impossible worlds are in an important sense inexpressible; leaving the probabilistic model committed to saying that agents in general have at least as many attitudes towards inexpressible propositions as they do towards expressible propositions. If it is reasonable to think that our attitudes are generally expressible, then a model with such commitments looks problematic. (shrink)

Is Divine Knowledge Incompatible with Human Freedom? An Analysis of Some Arguments The problem that divine omniscience or divine foreknowledge makes free will impossible belongs to notoriously difficult to solve. In XX century one of the most important interpretation of this difficulty was provided by Nelson Pike. If God believes infallibly and in advance how Smith will act, this fact about the past excludes out all alternatives for Smith. But libertarian account of free will requires alternatives possibilities, so, it (...) could be argue that God’s foreknowledge is incompatible with our free will. This paper carefully criticizes Pike’s argumentation and suggests that because God’s foreknowledge doesn’t eliminate future alternatives through causal means, it is compatible with free will and that Pike’s argument and two briefly analyzed standard arguments for fatalism presented by Zagzebski failed. (shrink)

This paper argues that, with certain provisos, predicting one's future actions is incompatible with rationally deliberating about whether to perform those actions. It follows that fully rational omniscient agents are impossible, since an omniscient being could never rationally deliberate about what to do . Consequently, theories that explain practical reasons in terms of the choices of a perfectly rational omniscient agent must fail. The paper considers several ways of defending the possibility of an omniscient agent, and concludes that while some (...) of these may work, they are inconsistent with the aim of explaining practical normativity by appeal to such an agent. (shrink)

Nāgārjuna’s Middle Way (Madhyamaka) doctrine met with the objection that it is a mere verbal attack (vitaṇḍā) against other philosophical positions. As one of the Madhyamaka critics pointed out: because Nāgārjuna does not hold own position, he is not able to justify his criticism of the essence (svabhāva). The article is an answer to the question whether, in the context of Indian philosophy, it is possible to know things devoid of essences. Theory of knowledge of this kind, i.e. the (...) concept of omniscience (sarvajña) was presented in Aṣṭasāhasrikāprajñāpāramitā sutra. Associations between Nāgārjuna’s texts and the sutra suggest that omniscience could be a substrate for epistemological position of the Middle Way. (shrink)

Traditional views about God and about deliberation seem to imply that we need a deliberation restriction on the concept of divine omniscience. I will argue, however, that this deliberation restriction is both irrelevant and unnecessary. It is irrelevant because there is no time at which God needs to deliberate; and it is unnecessary because even if God does deliberate, it’s possible for him to do so while knowing what the results of that deliberation will be. And because this (...) possibility of deliberating despite knowing the results holds for deliberation in general, my argument provides useful (and perhaps surprising) results not only for discussions of the divine attributes, but also for broader discussions of deliberation itself. (shrink)

A number of philosophers and theologians have argued that if God has knowledge of future human actions then human agents cannot be free. This argument rests on the assumption that, since God is essentially omniscient, God cannot be wrong about what human agents will do. It is this assumption that I challenge in this paper. My aim is to develop an interpretation of God’s essential omniscience according to which God can be wrong even though God never is wrong. If (...) this interpretation of essential omniscience is coherent, as I claim it is, then there is a logically consistent position according to which God is essentially omniscient, God foreknows what human agents will do, and yet it is possible for human agents to do otherwise. Thus, the argument for theological fatalism fails. (shrink)

In the following essay I will describe the cultural and disciplinary areas in which Open Theism has been developing and deal with the main authors, who has defended this new doctrine, and their main works. In the second section I will analyse their main theses about divine attributes, some theological questions, several objections to this new non-standard theism and their rebuttals. In the conclusion I will highlight the problems still open and evaluate the overall Open Theism’s theoretical work. At the (...) end, also the text "Omniscience, Freedom, and Mystery", a part of the article TRANSLATED into english. The issue of omniscience is one of the most debated in contemporary Analytical Philosophy of Religion. However, what is often lacking in this discussion is a deep understanding of the dilemma of omniscience and human freedom within a complete epistemological (what can we really say about the divine and the world), metaphysical and theological framework. For example, it is often forgotten to frame some issues within a clear definition of the notion of mystery. I defined what we can mean by “mystery” in this forthcoming article: "Trinity and Mystery. Three Models: Aquinas, Leibniz, and Hegel" In the same article (and also in the first article mentioned above) can be found a reflection on the analogical use of terms, which involve the terms (the notions) of “freedom” and “omniscience”. This use, therefore, could make possible to develop the argument I propose. (shrink)

World semantics for relevant logics include so-called non-normal or impossible worlds providing model-theoretic counterexamples to such irrelevant entailments as (A ∧ ¬A) → B, A → (B∨¬B), or A → (B → B). Some well-known views interpret non-normal worlds as information states. If so, they can plausibly model our ability of conceiving or representing logical impossibilities. The phenomenon is explored by combining a formal setting with philosophical discussion. I take Priest’s basic relevant logic N4 and extend it, on the syntactic (...) side, with a representation operator, (R), and on the semantic side, with particularly anarchic non-normal worlds. This combination easily invalidates unwelcome “logical omniscience” in- ferences of standard epistemic logic, such as belief-consistency and closure under entailment. Some open questions are then raised on the best strategies to regiment (R) in order to express more vertebrate kinds of conceivability. (shrink)

We explore some possibilities for developing epistemic logic using truthmaker semantics. We identify three possible targets of analysis for the epistemic logician. We then list some candidate epistemic principles and review the arguments that render some controversial. We then present the classic Hintikkan approach to epistemic logic and note—as per the ‘problem of logical omniscience’—that it validates all of the aforementioned principles, controversial or otherwise. We then lay out a truthmaker framework in the style of Kit Fine and (...) present six different ways of extending this semantics with a conditional knowledge operator, drawing on notions of implication and content that are prominent in Fine’s work. We demonstrate that different logics are thereby generated, bearing on the aforementioned epistemic principles. Finally, we offer preliminary observations about the prospects for each logic. (shrink)

In a possible world framework, an agent can be said to know a proposition just in case the proposition is true at all worlds that are epistemically possible for the agent. Roughly, a world is epistemically possible for an agent just in case the world is not ruled out by anything the agent knows. If a proposition is true at some epistemically possible world for an agent, the proposition is epistemically possible for the agent. If (...) a proposition is true at all epistemically possible worlds for an agent, the proposition is epistemically necessary for the agent, and as such, the agent knows the proposition. -/- This framework presupposes an underlying space of worlds that we can call epistemic space. Traditionally, worlds in epistemic space are identified with possible worlds, where possible worlds are the kinds of entities that at least verify all logical truths. If so, given that epistemic space consists solely of possible worlds, it follows that any world that may remain epistemically possible for an agent verifies all logical truths. As a result, all logical truths are epistemically necessary for any agent, and the corresponding framework only allows us to model logically omniscient agents. This is a well-known consequence of the standard possible world framework, and it is generally taken to imply that the framework cannot be used to model non-ideal agents that fall short of logical omniscience. -/- A familiar attempt to model non-ideal agents within a broadly world involving framework 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 epistemic space, it is easy to avoid logical omniscience. If any logical falsehood is true at some impossible world, then any logical falsehood may remain epistemically possible for some agent. As a result, we can use an impossible world involving framework to model extremely non-ideal agents that do not know any logical truths. -/- A much harder, and considerably less investigated challenge is to ensure that the resulting epistemic 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 impossible worlds that verify complex logical falsehoods, they are nevertheless able to rule out impossible worlds that verify obvious logical falsehoods. To model such agents, we need a construction of a non-trivial epistemic space that partly consists of impossible worlds where not "anything goes". This involves imposing substantive constraints on impossible worlds to eliminate from epistemic space, say, trivially impossible worlds that verify obvious logical falsehoods. -/- The central aim of this dissertation is to investigate the nature of such non-trivially impossible worlds and the corresponding epistemic spaces. To flag my conclusions, I argue that successful constructions of epistemic spaces that can safely navigate between the Charybdis of logical omniscience and the Scylla of of “anything goes” are hard, if not impossible to find. (shrink)

“There is no use in trying,” said Alice; “one can’t believe impossible things.” “I dare say you haven’t had much practice,” said the Queen. “When I was your age, I always did it for half an hour a day. Why, sometimes I’ve believed as many as six impossible things before breakfast”. Lewis Carroll, Through the Looking Glass. -/- It is a rather common view among philosophers that one cannot, properly speaking, be said to believe, conceive, imagine, hope for, or seek (...) what is impossible. -/- Some philosophers, for instance George Berkeley and the early Wittgenstein, thought that logically contradictory propositions lack cognitive meaning (informational content) and cannot, therefore, be thought or believed. Philosophers who do not go as far as Berkeley and Wittgenstein in denying that impossible propositions or states of affairs are thinkable, may still claim that it is impossible to rationally believe an impossible proposition. On a classical “Cartesian” view of belief, belief is a purely mental state of the agent holding true a proposition p that she “grasps” and is directly acquainted with. But if the agent is directly acquainted with an impossible proposition, then, presumably, she must know that it is impossible. But surely no rational agent can hold true a proposition that she knows is impossible. Hence, no rational agent can believe an impossible proposition. Thus it seems that on the Cartesian view of propositional attitudes as inner mental states in which proposition are immediately apprehended by the mind, it is impossible for a rational agent to believe, imagine or conceive an impossible proposition. -/- Ruth Barcan Marcus (1983) has suggested that a belief attribution is defeated once it is discovered that the proposition, or state of affairs that is believed is impossible. According to her intuition, just as knowledge implies truth, belief implies possibility. -/- It is commonplace that people claim to believe propositions that later turn out to be impossible. According to Barcan Marcus, the correct thing to say in such a situation is not: I once believed that A but I don’t believe it any longer since I have come to realize that it is impossible that A. What one should say is instead: It once appeared to me that I believed that A, but I did not, since it is impossible that A. Thus, Barcan Marcus defends what we might call Alice’s thesis: Necessarily, for any proposition p and any subject x, if x believes p, then p is possible. -/- Alice’s thesis that it is impossible to hold impossible beliefs, seems to come into conflict with our ordinary practices of attributing beliefs. Consider a mathematical example. Some mathematicians believe that CH (the continuum hypothesis) is true and others believe that it is false. But if CH is true, then it is necessarily true; and if it is false, then it is necessarily false. Regardless of whether CH is true or false, the conclusion seems to be that there are mathematicians who believe impossible propositions. -/- Examples of apparent beliefs in impossible propositions outside of mathematics are also easy to come by. Consider, for example, Kripke’s (1999) story of the Frenchman Pierre who without realizing it has two different names ‘London’ and ‘Londres’ for the same city, London. After having arrived in London, Pierre may assent to ‘Londres is beautiful and London is not beautiful’ without being in any way irrational. It seems reasonably to infer from this that Pierre believes that Londres is beautiful and London is not beautiful. But since ‘Londres’ and ‘London’ are rigid designators for the same city, it seems to follow from this that Pierre believes the inconsistent proposition that we may express as ‘London is both beautiful and not beautiful’. (shrink)

In the space of possible worlds, there might be a best possible world (a uniquely best world or a world tied for best with some other worlds). Or, instead, for every possible world, there might be a better possible world. Suppose that the latter is true, i.e., that there is no best world. Many have thought that there is then an argument against the existence of God, i.e., the existence of an omnipotent, omniscient and morally perfect (...) being; we will call such arguments no-best-world arguments. In this paper, we discuss ability-based objections to such arguments; an ability-based objection to a no-best world argument claims that the argument fails because one or more of its premises conflict with a plausible principle connecting the applicability of some type of moral evaluation to the agent’s possession of a relevant ability. In particular, we formulate and evaluate an important new ability-based objection to the most promising no-best world argument. (shrink)

We present a simple model to show the compossibility of middle knowledge, grounded truth, libertarian free will, predestination, evil, hell, a sin-free heaven, God being perfectly just, free, praiseworthy, and necessarily omnibenevolent, omniscient, and omnipotent, this world being both replete with injustice and the best of all possible worlds, heinous suffering, no-one unjustly suffering, God’s grace for the godly, the prospering of the godless, original sin, human responsibility, transworld depravity, irresistible grace, and Arminian human choice. The model is not (...) intended to be realistic, but its possibility argues for the possibility that a realistic model containing such compossibles could exist – and even be actual. (shrink)

In Indian philosophy, a pramāṇa is an epistemic instrument or doxastic practice that results in a veridical cognition (in an event of knowing). For just about all Indian thinkers, perception (pratyakṣa) and inference (anumāna) are the foundational pramāṇas, although they debated energetically over how to characterize the content of the resultant cognitions and how to explain the basis for the authority of these pramāṇas. Debate also includes the relationship of knowledge to religious liberation, the role of scripture in knowing, and (...) the possibility of omniscience. (shrink)

We argue that there is a conflict among classical theism's commitments to divine simplicity, divine creative freedom, and omniscience. We start by defining key terms for the debate related to classical theism. Then we articulate a new argument, the Aloneness Argument, aiming to establish a conflict among these attributes. In broad outline, the argument proceeds as follows. Under classical theism, it's possible that God exists without anything apart from Him. Any knowledge God has in such a world would (...) be wholly intrinsic. But there are contingent truths in every world, including the world in which God exists alone. So, it's possible that God contingently has wholly intrinsic knowledge. But whatever is contingent and wholly intrinsic is an accident. So, God possibly has an accident. This is incompatible with classical theism. Finally, we consider and rebut several objections. (shrink)

One problem for Molinism that critics of the view have pressed, and which Molinists have so far done little to address, is that even if there are true counterfactuals of freedom, it is puzzling how God could possibly know them. I defuse this worry by sketching a plausible model of the mechanics of middle knowledge which draws on William Alston’s direct acquaintance account of divine knowledge.

The standard position on moral perfection and gratuitous evil makes the prevention of gratuitous evil a necessary condition on moral perfection. I argue that, on any analysis of gratuitous evil we choose, the standard position on moral perfection and gratuitous evil is false. It is metaphysically impossible to prevent every gratuitously evil state of affairs in every possible world. No matter what God does—no matter how many gratuitously evil states of affairs God prevents—it is necessarily true that God coexists (...) with gratuitous evil in some world or other. Since gratuitous evil cannot be eliminated from metaphysical space, the existence of gratuitous evil presents no objection to essentially omnipotent, essentially omniscient, essentially morally perfect, and necessarily existing beings. (shrink)