Recently, several philosophers have moved from a classical account of divine omniscience according to which God knows all truths to a restricted account of divine omniscience according to which God knows all knowable truths. But an important objection offered by Alexander Pruss threatens to show that if God knows all knowable truths, God must also know all truths. In this paper, I show that there is a way out of Pruss’s objection for the advocate of restricted (...) omniscience if she will define her view in terms of ways of knowing rather than in terms of logical possibilities. (shrink)

Some, notably Peter van Inwagen, in order to avoid problems with free will and omniscience, replace the condition that an omniscient being knows all true propositions with a version of the apparently weaker condition that an omniscient being knows all knowable true propositions. I shall show that the apparently weaker condition, when conjoined with uncontroversial claims and the logical closure of an omniscient being's knowledge, still yields the claim that an omniscient being knows all true propositions.

The problem of the fictional truthfulness of deviant evaluations is a description of a paradox that has become the subject of debate in the philosophy of literature of the analytical tradition in the last thirty years. Philosophers such as Walton, Tanner, Moran, Gendler, and others have constructed “mini-stories” in order to show that the authors of fiction, regardless of the almost unlimited powers of what they can make true in their fictional storyworlds cannot successfully construct a fiction in which an (...) objectively false evaluation would nevertheless be fictionally true in the story. For example, someone comes up with a fictional account in which a brutal unmotivated murder takes place. The author merely postulates such an event, and then readers accept it as true in the story. But let us imagine that the description of the murder also contains the evaluation of such an act as a morally right thing to do. We do not accept an evaluation that we consider “deviant” in relation to our current (moral) beliefs as an integral part of the fictional world, even though the author asks us to do so. The paradox is that it seems to be a basic convention of fiction that all third-person narrative statements that cannot be attributed to fictional characters are always fictionally true. This seems to constitute a major restriction to the narratorial authority prompting us to question our usual understanding of the phenomenon of fiction. However, by analysing specific “mini-fictions”, the article argues that (i) there is no good reason to assume that deviant evaluations in these mini-stories are uttered by some thirdperson narratorial voice that cannot be identified with a fictional character; (ii) that deviant evaluations must always be voiced by a personal narrator; (iii) that such personal narrators are never sensu stricto “omniscient” and that we do not need to trust them unquestioningly when, for example, they evaluate a murder as “the right thing to do”. The whole paradox, we claim, is just a pseudo-problem generated by ignoring concrete reading practices and a simplified understanding of narrative conventions. (shrink)

This paper argues that there is a conflict between divine omniscience and the human right to privacy. The right to privacy derives from the right to moral autonomy, which human persons possess even against a divine being. It follows that if God exists and persists in knowing all things, his knowledge is a non-justifiable violation of a human right. On the other hand, if God exists and restricts his knowing in deference to human privacy, it follows that he cannot (...) fulfill the traditional function of being the perfect and final judge of all things. (shrink)

This paper argues that there is a conflict between divine omniscience and the human right to privacy. The right to privacy derives from the right to moral autonomy, which human persons possess even against a divine being. It follows that if God exists and persists in knowing all things, his knowledge is a non-justifiable violation of a human right. On the other hand, if God exists and restricts his knowing in deference to human privacy, it follows that he cannot (...) fulfill the traditional function of being the perfect and final judge of all things. (shrink)

The knowability paradox derives from a proof by Frederic Fitch in 1963. The proof purportedly shows that if all truths are knowable, it follows that all truths are known. Antirealists, wed as they are to the idea that truth is epistemic, feel threatened by the proof. For what better way to express the epistemic character of truth than to insist that all truths are knowable? Yet, if that insistence logically compels similar assent to some omniscience claim, antirealism is in (...) jeopardy. Response to the paradox has drifted toward a common theme, a theme I will argue is a non-starter in resolving the paradox. Seeing this point will also make clear the philosophical inadequacy of simply viewing the paradox as a refutation of a wide range of antirealisms. (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)

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)

This is the second part of a two-part series on the logic of hyperlogic, a formal system for regimenting metalogical claims in the object language (even within embedded environments). Part A provided a minimal logic for hyperlogic that is sound and complete over the class of all models. In this part, we extend these completeness results to stronger logics that are sound and complete over restricted classes of models. We also investigate the logic of hyperlogic when the language is (...) enriched with hyperintensional operators such as counterfactual conditionals and belief operators. (shrink)

Recently, Coquand and Palmgren considered systems of intuitionistic arithmetic in a finite types together with various forms of the axiom of choice and a numerical omniscience schema which implies classical logic for arithmetical formulas. Feferman subsequently observed that the proof theoretic strength of such systems can be determined by functional interpretation based on a non-constructive μ-operator and his well-known results on the strength of this operator from the 70's. In this note we consider a weaker form LNOS of NOS (...) which suffices to derive the strong form of binary König's lemma studied by Coquand/Palmgren and gives rise to a new and mathematically strong semi-classical system which, nevertheless, can proof theoretically be reduced to primitive recursive arithmetic PRA. The proof of this fact relies on functional interpretation and a majorization technique developed in a previous paper. (shrink)

In this paper we explore the potential bearing of the extended mind thesis—the thesis that the mind extends into the world—on epistemology. We do three things. First, we argue that the combination of the extended mind thesis and reliabilism about knowledge entails that ordinary subjects can easily come to enjoy various forms of restricted omniscience. Second, we discuss the conceptual foundations of the extended mind and knowledge debate. We suggest that the theses of extended mind and extended knowledge (...) lead to a bifurcation with respect to the concepts of belief and knowledge. We suggest that this conceptual bifurcation supports a form of pluralism about these concepts. Third, we discuss whether something similar can be said at the metaphysical level. (shrink)

Patrick Grim advances arguments meant to show that the doctrine of divine omniscience—the classical doctrine according to which God knows all truths—is false. In particular, we here have in mind to focus on two such arguments: the set theoretic argument and the semantic argument. These arguments due to Grim run parallel to, respectively, familiar paradoxes in set theory and naive truth theory. It is beyond the purview of this article to adjudicate whether or not these are successful arguments against (...) the classical doctrine of omniscience. What we are here interested in is a way in which these arguments can be generalized. In particular, we show how generalizations of those arguments can target, explicitly, alternatives to the classical doctrine of omniscience, including what we here call 'restricted omniscience' and 'open future open theism'. As a corollary, considerations of Grim-style arguments do not support these alternatives to the classical doctrine of omniscience over the classical doctrine. We conclude that what is paradoxical is not the classical doctrine of omniscience just as such; rather, what is paradoxical is a core commitment shared by the classical doctrine and its more modest alternatives, namely, the thesis that God is a perfectly logical reasoner. (shrink)

Bradwardine’s solution to the the logical paradoxes depends on the idea that every sentence signifies many things, and its truth depends on things’ being wholly as it signifies. This idea is underpinned by his claim that a sentence signifies everything that follows from what it signifies. But the idea that signification is closed under entailment appears too strong, just as logical omniscience is unacceptable in the logic of knowledge. What is needed is a more restricted closure principle. A (...) clue can be found in speech act pluralism, whereby indirect speech reports are closed under intersubstitutivity of co-referential terms. The conclusion is that solving the semantic paradoxes does not require revision of logic, thus saving logic from paradox. (shrink)

We deal with a restricted form WC-N' of the weak continuity principle, a version BT' of Baire's theorem, and a boundedness principle BD-N. We show, in the spirit of constructive reverse mathematics, that WC-N'. BT' + ¬LPO and BD-N + ¬LPO are equivalent in a constructive system, where LPO is the limited principle of omniscience.

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 lieu of an abstract, here is a brief excerpt of the content:Isaac Barrow on the Mathematization of Nature: Theological Voluntarism and the Rise of Geometrical OpticsAntoni MaletIntroductionIsaac Newton’s Mathematical Principles of Natural Philosophy embodies a strong program of mathematization that departs both from the mechanical philosophy of Cartesian inspiration and from Boyle’s experimental philosophy. The roots of Newton’s mathematization of nature, this paper aims to demonstrate, are to be found in Isaac Barrow’s (1630–77) philosophy of the mathematical sciences.Barrow’s attitude (...) towards natural philosophy evolved from his earnest interest in medicine of around 1650, when a young Cambridge graduate, to natural philosophy (apparently under Henry More’s influence); from his thesis on the insufficiency of the Cartesian hypothesis to geometrical optics and the strong program of mathematization of natural philosophy of the middle 1660s; from Lucasian professor of Mathematics to Chaplain of his Majesty and eminent Restoration divine. Contemporary accounts of Barrow’s life suggest that he grew ever more skeptical about the worth of natural philosophy and mathematics. 1 In his last years he became a prolific [End Page 265] author of sermons and theological works. Published shortly after his death by John Tillotson (1630–94), later archbishop of Canterbury, they occupy over two thousand folio pages. Overloaded with involved philosophical arguments, Barrow’s sermons were apparently not very popular, but they were highly regarded by scholars and the Anglican hierarchy. 2 It is on certain of his sermons, as well as on the philosophical discussions contained in the Mathematical Lectures that our account of Barrow’s philosophy of the mathematical sciences will rest. 3 Barrow’s understanding of the mathematical sciences will allow us to discuss together three issues often analyzed independently: the theological background to English natural philosophy, the changing notion of mixed mathematical sciences during the seventeenth century, and finally the philosophical foundations of modern geometrical optics.It has long been recognized that significant relationships exist between theological voluntarism or intellectualism and views on natural philosophy. In particular Robert Boyle’s theological voluntarism is seen as grounding his experimentalist approach to natural philosophy. It is not quite so clear, however, how well theological voluntarism may relate to a strong program of mathematization such as the one embodied in Newton’s Principia Mathematica. In fact it has been suggested that the relationship is a negative one. This is derived from the necessary character of mathematical laws, which would put unwanted restrictions on God’s absolute dominion over nature, and also from the notion that theological intellectualism is conducive to a deductive, a priori science—the paradigm of which is of course geometry. However, Barrow’s theological voluntarism lead him to heighten the role of mathematics within natural philosophy.During the seventeenth century the so-called mixed or subalternate mathematical sciences changed profoundly. In the Enlightenment mixed mathematics—meaning above all rational mechanics—became one of the most prestigious and influential disciplines. The mixed mathematics of the Enlightenment, however, was markedly different from the Aristotelian [End Page 266] mixed mathematical sciences. The differences are noticeable both in the subject matter and in the substitution of mathematical infinitesimal analysis for geometrical synthesis, but also in the way of grounding mathematical theory on empirical evidence. Barrow’s Mathematical Lectures (delivered at Cambridge from 1664 to 1666) offer a fresh insight into the metamorphosis of these sciences just when Newton’s “mathematical principles” were in the making. Not the least interesting feature of Barrow’s discussion is that God’s omnipotence allows an evaluation of the truth of mathematical theories that do not apply to this world. Therefore, Barrow is led to introduce the distinction between the internal consistency, or mathematical truth, of a mathematical theory and its physical truth. This, in turn, leads him to the notion that theories need testing.Barrow on Matter and GodRecent literature has established significant correlations between theological voluntarism and empiricism, as well as between theological intellectualism and rationalism. As E. B. Davis writes, “the Christian doctrine of creation is a dialogue between God’s unconstrained will, which utterly transcends the bounds of human comprehension, and God’s orderly intellect, which serves as the model for the human mind.” Intellectualist theology considers God’s omniscience His... (shrink)

A novel solution to the knowability paradox is proposed based on Kant’s transcendental epistemology. The ‘paradox’ refers to a simple argument from the moderate claim that all truths are knowable to the extreme claim that all truths are known. It is significant because anti-realists have wanted to maintain knowability but reject omniscience. The core of the proposed solution is to concede realism about epistemic statements while maintaining anti-realism about non-epistemic statements. Transcendental epistemology supports such a view by providing for (...) a sharp distinction between how we come to understand and apply epistemic versus non-epistemic concepts, the former through our capacity for a special kind of reflective self-knowledge Kant calls ‘transcendental apperception’. The proposal is a version of restriction strategy: it solves the paradox by restricting the anti-realist’s knowability principle. Restriction strategies have been a common response to the paradox but previous versions face serious difficulties: either they result in a knowability principle too weak to do the work anti-realists want it to, or they succumb to modified forms of the paradox, or they are ad hoc. It is argued that restricting knowability to non-epistemic statements by conceding realism about epistemic statements avoids all versions of the paradox, leaves enough for the anti-realist attack on classical logic, and, with the help of transcendental epistemology, is principled in a way that remains compatible with a thoroughly anti-realist outlook. (shrink)

ARISTOTLE’S chapter-long digression in the Peri Hermenias to remark a restriction of the law of the excluded middle has touched off reams of commentary, logical, metaphysical and theological. For the theologian, God’s omniscience and human freedom were each at stake; for the metaphysician, the status of time; and logicians professed to find here an application for their remote exercises in trivalent logics. But whatever be the concern of the commentator, a glance at any one of them is likely to (...) discourage a student from pursuing a question which seems destined only to further entangle itself. (shrink)

The purpose is to study the strength of Ramsey’s Theorem for pairs restricted to recursive assignments ofk-many colors, with respect to Intuitionistic Heyting Arithmetic. We prove that for every natural number$k \ge 2$, Ramsey’s Theorem for pairs and recursive assignments ofkcolors is equivalent to the Limited Lesser Principle of Omniscience for${\rm{\Sigma }}_3^0$formulas over Heyting Arithmetic. Alternatively, the same theorem over intuitionistic arithmetic is equivalent to: for every recursively enumerable infinitek-ary tree there is some$i < k$and some branch with (...) infinitely many children of indexi. (shrink)

Jeremy Gwiazda has criticized my claim that God, understood as an omnipotent, omniscient, and perfectly free person is a person ’of the simplest possible kind’ on the grounds that omnipotence, etc., as spelled out by me are omnipotence, etc., of restricted kinds, and so less simple forms of these properties than maximal forms would be. However, the account which I gave of these properties in ’The Christian God’ (although not in ’The Coherence of Theism’) shows that, when they are (...) defined in certain ways, they all follow from one property of ’pure, limitless, intentional power’. I argue here that a person who has these properties so defined is a person ’of the simplest possible kind’. (shrink)

Classical epistemic logic describes implicit knowledge of agents about facts and knowledge of other agents, based on semantic information. The latter is produced by acts of observation or communication, that are described well by dynamic epistemic logics. What these logics do not describe, however, is how significant information is also produced by acts of inference – and key axioms of the system merely postulate “deductive closure”. In this paper, we take the view that all information is produced by acts, and (...) hence we also need a dynamic logic of inference steps showing what effort on the part of the agent makes a conclusion explicit knowledge. Strong omniscience properties of agents should be seen not as static idealizations, but as the result of dynamic processes that agents engage in. This raises two questions: (a) how to define suitable information states of agents and matching notions of explicit knowledge, (b) how to define natural processes over these states that generate new explicit knowledge. To this end, we extend earlier epistemic “awareness models” into a dynamic system that includes acts of public observation, but also adding and dropping formulas from the currently ‘entertained’ set, we give a completeness theorem, and we show how this dynamics updates explicit knowledge. Similar ideas have been proposed before, but they were restricted to update with factual propositions; our new dynamic system applies to arbitrary formulas. We also extend our approach to multi-agent scenarios where awareness changes may happen privately. Finally, we mention further directions and related approaches. (shrink)

Husserl endorses ideal verificationism, the claim that there is a necessary correlation between truth and the ideal possibility of experience. This puts him in the company of semantic anti-realists like Dummett, Tennant, and Wright who endorse the knowability thesis that all truths are knowable. Unfortunately, there is a simple, seductive, and troubling argument due to Alonzo Church and Frederic Fitch that the knowability thesis collapses into the omniscience thesis that all truths are known. Phenomenologists should be worried. I assess (...) the damage by surveying responses that may be open to Husserl. In particular, I explore whether Husserl ought to have adopted intuitionistic logic and motivate a restriction of ideal verificationism on phenomenological grounds. (shrink)

Norms provide a valuable mechanism for establishing coherent cooperative behaviour in decentralised systems in which there is no central authority. One of the most influential formulations of norm emergence was proposed by Axelrod :1095–1111, 1986). This paper provides an empirical analysis of aspects of Axelrod’s approach, by exploring some of the key assumptions made in previous evaluations of the model. We explore the dynamics of norm emergence and the occurrence of norm collapse when applying the model over extended durations. It (...) is this phenomenon of norm collapse that can motivate the emergence of a central authority to enforce laws and so preserve the norms, rather than relying on individuals to punish defection. Our findings identify characteristics that significantly influence norm establishment using Axelrod’s formulation, but are likely to be of importance for norm establishment more generally. Moreover, Axelrod’s model suffers from significant limitations in assuming that private strategies of individuals are available to others, and that agents are omniscient in being aware of all norm violations and punishments. Because this is an unreasonable expectation, the approach does not lend itself to modelling real-world systems such as online networks or electronic markets. In response, the paper proposes alternatives to Axelrod’s model, by replacing the evolutionary approach, enabling agents to learn, and by restricting the metapunishment of agents to cases where the original defection is observed, in order to be able to apply the model to real-world domains. This work can also help explain the formation of a “social contract” to legitimate enforcement by a central authority. (shrink)

Abstract: Michael Tooley’s Comments on James Sterba’s Book, Is a Good God Logically Possible? -/- My comments on Jim Sterba’s book, Is a Good God Logically Possible?, were divided into the following sections. In the first section, I listed some of the attractive features of Sterba’s discussion. These included, first of all, his use of the ideas of “morally constrained freedom” and “constrained intervention by God” to show the moral evils in our world cannot be justified by an appeal to (...) the idea of free will. Then secondly, there is his response to the claim that if God intervened to prevent horrendous evils, one would have a world without regularities. Thirdly, there are his responses to certain important religiously based attempts to answer arguments from evil, namely, those that appeal to either Christian or Jewish views that we have wronged God, and stand in need of redemption, along with his discussion, and criticism of, certain specific, central Christian doctrines. Fourthly, there are his criticisms, first, of the four solutions that Michael Murray offers for the problem posed by the suffering of non-human animals, and then, secondly, of Trent Dougherty’s use of “a version of John Hick’s theodicy of soul-making in an attempt to provide a God-justifying account of animal suffering” (Dougherty, The Problem of Animal Pain: A Theodicy For All Creatures Great And Small, 2014). -/- I then went on to offer critical comments on various aspects of Sterba’s discussion, where I discussed: (1) his negative view of the relevance of probabilistic epistemology to the problem of evil; (2) his failure, in attempting to rule out logical connections between goods and evil, to consider evils that are not moral evils, such as Peter van Inwagen’s claim that “Being massively irregular is a defect in a world, a defect at least as great as the defect of containing patterns of suffering mentally equivalent to those found in the actual world”; (3) his failure, in discussing Michael Bergmann’s skeptical theism, to point out the central weakness in the principles that Bergmann advances, namely, that they entail not only moral skepticism, but inductive skepticism as well; (4) his treatment of natural evils, where he mistakenly claims that, in contrast to the case of horrendous moral evils, all of which God could prevent, God could not eliminate all horrendous natural evils, and where he says noting about either the horrendous evils due to bacteria and viruses or those due to natural disasters, all of which could be prevented by an omnipotent and omniscient deity without our ever being aware that this was happening. -/- Finally, I concluded by raising the question of what the strongest way is of formulating a logical incompatibility argument from evil, and I argued that it should take the form of the argument I set out in The Problem of Evil (2019) so that first, it should be based on natural evils rather than on moral evils; secondly, that it should focus on the case of suffering endured by sentient non-persons; and thirdly, that a crucial part must be an argument restricting the logical connections between goods and evils, an argument based on the proposition that the only goods and evils that can exist involve properties of, and relations between, conscious beings. -/- . (shrink)

Jeremy Gwiazda has criticized my claim that God, understood as an omnipotent, omniscient, and perfectly free person is a person ‘of the simplest possible kind’ on the grounds that omnipotence etc. as spelled out by me are omnipotence etc. of restricted kinds, and so less simple forms of these properties than maximal forms would be. However the account which I gave of these properties in The Christian God shows that, when they are defined in certain ways, they all follow (...) from one property of ‘pure, limitless, intentional power’. I argue here that a person who has these properties so defined is a person ‘of the simplest possible kind’. (shrink)

The best and most popular argument for probabilism is the accuracy-dominance argument, which purports to show that alethic considerations alone support the view that an agent’s degrees of belief should always obey the axioms of probability. I argue that extant versions of the accuracy-dominance argument face a problem. In order for the mathematics of the argument to function as advertised, we must assume that every omniscient credence function is classically consistent; there can be no worlds in the set of dominance-relevant (...) worlds that obey some other logic. This restriction cannot be motivated on alethic grounds unless we’re also willing to accept that rationality requires belief in every metaphysical necessity, as the distinction between a priori logical necessities and a posteriori metaphysical ones is not an alethic distinction. To justify the restriction to classically consistent worlds, non-alethic motivation is required. And thus, if there is a version of the accuracy-dominance argument in support of probabilism, it isn’t one that is grounded in alethic considerations alone. (shrink)

Argument evaluation, one of the central problems in argumentation theory, consists in studying what makes an argument a good one. This paper proposes a formal approach to argument evaluation from the perspective of justification logic. We adopt a multi-agent setting, accepting the intuitive idea that arguments are always evaluated by someone. Two general restrictions are imposed on our analysis: non-deductive arguments are left out and the goal of argument evaluation is fixed: supporting a given proposition. Methodologically, our approach uses several (...) existing tools borrowed from justification logic, awareness logic, doxastic logic and logics for belief dependence. We start by introducing a basic logic for argument evaluation, where a list of argumentative and doxastic notions can be expressed. Later on, we discuss how to capture the mentioned form of argument evaluation by defining a preference operator in the object language. The intuitive picture behind this definition is that, when assessing a couple of arguments, the agent puts them to a test consisting of several criteria. As a result of this process, a preference relation among the evaluated arguments is established by the agent. After showing that this operator suffers a special form of logical omniscience, called preferential omniscience, we discuss how to define an explicit version of it, more suitable to deal with non-ideal agents. The present work exploits the formal notion of awareness in order to model several informal phenomena: awareness of sentences, availability of arguments and communication between agents and external sources. We discuss several extensions of the basic logic and offer completeness and decidability results for all of them. (shrink)

In this article I shall argue for an interpretation of Odyssey 19.393–466 as a flash-back taking place in the mind of Eurykleia at the moment she recognises Odysseus' scar. That Eurykleia somehow forms the connection between main story and digression has been suggested before, but so far other interpretations have been defended with more fervour. Most famous of these interpretations is the one given by E. Auerbach in the first chapter of his Mimesis. He had chosen 19.393–466 to illustrate his (...) thesis that in Homer everything is ‘fully externalized’ and that there is no background, only a ‘uniformly illuminated’ foreground. According to Auerbach the digression on the scar stands in complete isolation to its context. It is meant to ‘relax the tension’, to make the hearer/reader ‘forget what had just taken place during the footwashing’, and although it might have been presented as a recollection of Odysseus , this ‘subjectivisticperspectivistic procedure, creating a foreground and background’ was not chosen, being ‘entirely foreign to the Homeric style’. Some twenty years later this interpretation was challenged by A. Köhnken, who, however, stuck to the idea that the digression is not told from the restricted perspective of one of the characters but from the perspective of the omniscient narrator; he claims that foreground and background are marked as such through a difference in narrative style: ‘berichtende Erzählung’ for the digression itself and ‘szenische Darstellung’ for the context. I disagree with both points. (shrink)

The problem of hyperintensional contexts, and the problem of logical omniscience, shows the severe limitation of possible-worlds semantics which is employed also in standard epistemic logic. As a solution, we deploy here hyperintensional semantics according to which the meaning of an expression is an abstract structured algorithm, namely Tichý's construction. Constructions determine the denotata of expressions. Propositional attitudes are modelled as attitudes towards constructions of truth values. Such a model of belief is, of course, inferentially restrictive. We therefore also (...) propose a model of implicit knowledge, which is the collection of a possible agent's explicit beliefs which are related through a derivation system mastered by the agent. A derivation system consists of beliefs and derivation rules by means of which the agent may derive beliefs different from the beliefs she is actually related to. Conditions imposed on the set of base beliefs and the set of rules capture the limitations of the agent's deriving capabilities. (shrink)

Two proofs are given which show that if some set of truths fall under finitely many concepts (so-called Collectivity), then they all fall under at least one of them even if we do not know which one. Examples are given in which the result seems paradoxical. The first proof crucially involves Moorean propositions while the second is a reconstruction and generalization of a proof due to Humberstone free from any reference to such propositions. We survey a few solution routes including (...) Tennant-style restriction strategies. It is concluded that accepting Collectivity for some set of truths while also denying that any of the involved concepts in isolation capture all of them requires that one of these concepts cannot be closed under conjunction elimination. This is surprising since the paper surveys several applications in which Collectivity and the latter closure condition seemed jointly satisfiable for concepts of actual philosophical interest. (shrink)

ExcerptDrawing on the quasi-legal human experimentation programs designed and implemented by the CIA between the 1950s and 1970s, the television series Severance envisions the possible corporate uses of brainwashing and mind control. The narrative centers on employees of a technology company, Lumon Industries, who agree to undergo a medical procedure (“severance”) that separates non-work memories from work memories by implanting a microchip into the brain. Unfolding like a science fiction psychological thriller, the narration falls somewhere between omniscient and restricted. (...) Viewers at the outset know only slightly more about the non-work lives and histories of the characters than the characters’ work-day versions, while the gradual increase of viewer knowledge parallels that of the characters’ paths toward self-discovery. (shrink)

We show that several logics of common belief and common knowledge are not only complete, but also strongly complete, hence compact. These logics involve a weakened monotonicity axiom, and no other restriction on individual belief. The semantics is of the ordinary fixed-point type.

At the close of the Cyclops adventure Odysseus piously sacrifices to Zeus the ram that has carried him out of Polyphemus' cave. Yet the god spurns his offering and ponders instead the destruction of Odysseus' ships and their crews :These lines need explaining, as they present two difficulties, one formal, the other thematic. How can Odysseus know what Zeus is pondering? As a first-person narrator Odysseus assumes temporarily the role of the epic poet, yet without being given the latter's (...) class='Hi'>omniscience. He retains therefore the restricted perspective of an epic character which precludes any precise knowledge of supernatural processes. (shrink)

Awareness logic is a type of belief logic in which an agent's beliefs are restricted to those sentences that the agent is aware of. Awareness logic is a successful way to circumvent the problem of omniscience so that actual belief is modelled in a reasonable way. In this paper, we suggest a new method modelling awareness and actual belief by using two-dimensional logics. We show that the two-dimensional logics are flexible tools. Different types of concepts of awareness can (...) be easily modelled by this method. (shrink)

We introduce a three-tiered framework for modelling and reasoning about agents who (i) can use possibly complete reasoning systems without any restrictions but who nevertheless are (ii) bounded in the sense that they never reach infinitely many results and, finally, who (iii) perform their reasoning in time. This last aspect does not concern so much the time it takes for agents to actually carry out their reasoning, as the time which can bring about external changes in the agents’ states such (...) as arriving of new information or discarding previously available information due to bounds of the agent’s resources. These three aspects are treated with the maximal possible degree of independence from each other. The treatment of layer (iii) can be combined with arbitrary logic at level (ii) which, in turn, can be combined with arbitrary agent logic at level (i). At the level (iii), we discuss briefly the duality (or rather, complementarity) of system descriptions based on actions and transitions, on the one hand, and states and their changes, on the other. We settle for the latter and present a simple language, for describing state changes, which is parameterized by an arbitrary language for describing properties of the states. The language can be viewed as a simple fragment of step logic, admitting however various extensions by appropriate choices of the underlying logic. Alternatively, it can be seen as a very specific fragment of temporal logic (with a variant of ‘until’ or ‘chop’ operator), and is interpreted over dense linear time. The reasoning system presented here is sound, as well as strongly complete and decidable (provided that so is the parameter logic for reasoning about single states). We give the main idea of the completeness proof and suggest a wide range of possible applications, which is a simple consequence of the parametric character of both the language and the reasoning system. We address then in more detail the case of non-omniscient rational agents, (ii). Their models are syntactic structures (sets of available formulae) similar in spirit, though not in the technical formulation, to the models used in other syntax oriented approaches and in active logic. We give a new sound, complete and decidable system for reasoning about such agents. Finally, we illustrate its extensions with the internal reasoning of agents, (i), by equipping them with some example logics. (shrink)

Wonderful Knowledge. Aquinas on the Immutability and Eternity of God’s Knowledge The general concept of knowledge is a kind of concept closely akin to transcententals: its use is not restricted to a certain kind of being, and it does not itself designate a kind of entity. Such concepts may be applied to God not as metaphors: when we grasp (through the analysis of cases of finite knowledge) some general traits of knowledge as such, we can show that God has (...) knowledge, and his knowledge, as opposed to ours, is infinitely perfect. We have no insight into this realization of knowledge as opposed to ours, but as far as we know what general traits of knowledge are, it is important to know that God has infinitely perfect knowledge. To grasp the general traits of knowledge, I focus on the topic of mutability and immutability of knowledge analyzed systematically by Aquinas, and thus on the topic of identity criteria specific for knowledge in general: the question of when knowledge that p and knowledge that q are (in a certain knower) one and the same knowledge; the criteria of identity of knowledge vary according to natures of knowers. I think that the problem of the criteria of identity of knowledge is rather neglected in omniscience-immutability discussions. I analyze Aquinas’ arguments for the thesis that human knowledge is mutable, and God’s knowledge is absolutely immutable (they concern the role of tense). The analysis sheds light on some general traits of knowledge: it is always something formulated by the knower which manifests some truth to him, and in general the way it is formulated corresponds to (i) the way it manifests some truth, (ii) its identity criteria, (iii) the way it is propositional, (iv) the way it is related to tense, and finally (v) the nature of the knower. Focusing on the criteria of the identity of knowledge shows that God’s knowledge is absolutely immutable, and that time and change in its objects are nevertheless undoubtedly real. Keywords: God’s knowledge, knowledge, criteria of identity of knowledge, immutability; tense; transcendentals; omniscience-immutability arguments. (shrink)

In the first chapter I have introduced Carnapian intensional logic against the background of Frege's and Quine's puzzles. The main body of the dissertation consists of two parts. In the first part I discussed Carnapian modal logic and arithmetic with descriptions. In the second chapter, I have described three Carnapian theories, CCL, CFL, and CNL. All three theories have three things in common. First, they are formulated in languages containing description terms. Second, they contain a system of modal logic. Third, (...) they do not contain the unrestricted classical substitution principle, but they do contain the classical substitution principle restricted to non-modal formulas and the Carnapian substitution principle, which says that two terms can be substituted salva veritate if they are necessarily coreferential. There are two major differences between the three theories. First, CCL and CFL allow universal instantiation with description terms, whereas CNL does not. Moreover, the quantificational theory of the CCL is classical, whereas the quantificational theory of CFL is a free logic. Another difference is that CCL and CFL contain different description principles. Most importantly, the description principle of CCL ensures that even improper descriptions have a denotation, whereas the description principle of CFL does not guarantee this. CNL does not have a description principle. In the third chapter, I have studied collapse arguments for CCL, CFL, and CNL. A collapse argument is an argument for the following statement: if p is true, then it is necessarily true. A crucial role in the proofs of these collapse results was played by so-called self-predication principles, which say that under certain conditions the predicate that expresses the descriptive condition can be combined by the description term formed out of that predicate with the result being a true sentence. In this chapter I have discussed a collapse argument for the extension of CCL with a self-predication principle, I have given a collapse argument for a similarly extended CFL, and most importantly, I have given a collapse argument for the extension of CNL with a self- predication principle. Finally, I have argued that the relevant self-predication principles are unsound under a Carnapian interpretation. In the fourth chapter, I have studied the extension of Peano Arithmetic with a Carnapian modal logic C, which is a dummy letter standing for either CCL or CFL. One can prove that the principle of the necessity of identity is a theorem of CPA. This implies that one gets a collapse result for CPA. The standard principle of weak induction was crucial for the proof. One can also prove that, if one assumes a particular self-predication principle, and if one assumes the principle of strong induction or, equivalently, the least-number principle, then one gets a partial collapse of de re modal truths in de dicto modal truths. I have argued that, if the box operator is interpreted as a metaphysical necessity operator, then Platonists would not be inimical to the collapse result. But if CPA is extended with a physical theory, then there is a threat that physical truths become physical necessiti es. It was shown that, under a Carnapian interpretation, the standard principle of weak induction is unsound, and that it can be replaced by a Carnapian principle of weak induction that is sound. The problem of logical and mathematical omniscience prevents ordinary Carnapian intensional logic from being taken seriously as a logic adequate for describing the principles of demonstrability. Yet many of the proof-theoretic results of the first part carry over to the part on Carnapian epistemic arithmetic with descriptions, since proof-theoretic results are independent of the informal reading of the operators. In the fifth chapter, I looked at extensions of arithmetic with a modal logic in which the box operator is interpreted as a demonstrability operator. A first extension in that sense is Shapiro s Epistemic Arithmetic. Shapiro himself offered the problem of mathematical omniscience as a reason why it is difficult to find a model theory for EA. Horsten attempted to provide a model theory via the detour of Modal-Epistemic Arithmetic. The attention of the reader was drawn to an incoherence in the model theory of. Two alternative solutions were presented and, after a short discussion of the problem of de re demonstrability one of those alternatives was chosen. The discussion of the problem of de re demonstrability made it clear that it would be interesting to study the epistemic properties of notation systems. Horsten himself provided a framework for this, viz. Carnapian Epistemic Arithmetic, and he started a systematic study of the epistemic properties of notation systems within that framework. However, he did not provide non-trivial but adequate models. To make a start with solving the problem of finding good models for CEA, I introduced Carnapian Modal-Epistemic Arithmetic In constructing CMEA I incorporated the lesson about the principle of weak induction learnt in the fourth chapter. In the sixth chapter, I gave a critical assessment of an argument concerning the limits of de re demonstrability about the natural numbers. The conclusion of the Description Argument is that it is undemonstrable that there is a natural number that has a certain property but of which it is undemonstrable that it has that property. A crucial step in the Description Argument involved a self-predication principle. Making good use of one of the results obtained in the third chapter, I proved a collapse result for the background theory against which the Description Argument was formulated. I concluded that either the either the Description Argument is sound but its conclusion is trivial, o r the Description Argument is unsound, or it is a cheapshot. As an appendix I included an article co-authored by prof. dr. Leon Horsten and me. The topic of the article is indirectly related to some other topics investigated in my dissertation. Also, it backs up one of the addition al theses I might be asked to publicly defend during my doctoral exam. T he topic of the appendix is the set of the so-called paradoxes of strict implication. Jonathan Lowe has argued that a particular variation on C.I. Lewis notion of strict implication avoids the paradoxes of strict implication. Pace Lowe, it is argued that Lowe s notion of implication does not achieve this aim. Moreover, a general argument is offered to the effect that no other variation on Lewis notion of constantly strict implication describes the logical behaviour of natural language conditional s in a satisfactory way. (shrink)

The present essay is a critical study of Barwise and Perry’s book, emphasizing the logical and model-theoretical aspects of their work. I begin by presenting the authors’ criticism of the classical view of logic and semantics within the tradition of Frege, Russell and Tarski. In this connection, I discuss the so-called Frege argument (“the slingshot”). I try to show that the argument appears inconclusive, not only from a situation-theoretic perspective, but also from such alternative perspectives as orthodox Fregean semantics or (...) Russellian semantics. I then discuss the ontology of situation semantics and the way it is modeled within set theory. In particular, I compare the notion of an abstract situation with that of a possible world. The last two sections concern the model-theoretic aspects of the authors’ theory. In Section 7, I discuss how the “partial” perspective of situation semantics differs from that of classical model theory. Finally, in Section 8, different model-theoretic accounts of attitude reports within situation semantics are discussed, in particular the “relations to situations”-approach presented by the authors in Chapter 9 of S & A. The usual problems of “logical omniscience” that appear in standard Hintikka-style epistemic logic are avoided in situation semantics. I argue, however, that situation semantics is faced with analogous counter-intuitive results, unless the expressive power of the language under study is suitably restricted. (shrink)

This book deals with an old conundrum: if God knows what we will choose tomorrow, how can we be free to choose otherwise? If all our choices are already written, is our freedom simply an illusion? This book provides a precise analysis of this dilemma using the tools of modern ontology and the logic of time. With a focus on three intertwined concepts - God's nature, the formal structure of time, and the metaphysics of time, including the relationship between temporal (...) entities and a timeless God - the chapters analyse various solutions to the problem of foreknowledge and freedom, revealing the advantages and drawbacks of each. Building on this analysis, the authors advance constructive solutions, showing under what conditions an entity can be omniscient in the presence of free agents, and whether an eternal entity can know the tensed futures of the world. The metaphysics of time, its topology and the semantics of future tensed sentences are shown to be invaluable topics in dealing with this issue. Combining investigations into the metaphysics of time with the discipline of temporal Logic this monograph brings about important advancements in the philosophical understanding of an ancient and fascinating problem. The answer, if any, is hidden in the folds of time, in the elusive nature of this feature of reality and in the infinite branching of our lives. (shrink)

I discuss the propositional knowledge of an omniscient being, knowledge of facts that can be represented by that-clauses in sentences such as ‘John knows that the world is round.’ I shall focus upon questions about a supposedly omniscient being who propositionally knows the truth about all current states of affairs. I shall argue that there is no such being.

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

At first glance, the properties being omniscient and being worthy of worship might appear to be perfectly co-instantiable. But there are reasons to be worried about this co-instantiability, as it turns out that, depending on our commitments with respect to certain kinds of knowledge and notions of personhood, it might be the case that no being—God included—could instantiate both. In this paper, I lay out and motivate this claim before going on to consider a variety of responses—some more plausible than (...) others—that may be offered by the theist. (shrink)

I argue that if deliberation is incompatible with (fore)knowing what one is going to do at the time of the deliberation, then God cannot deliberate. However, this thesis cannot be used to show either that God cannot act intentionally or that human persons cannot deliberate. Further, I have suggested that though omniscience is incompatible with deliberation, it is not incompatible with either some speculation or knowing something on the grounds of inference.

Does rationality require logical omniscience? Our best formal theories of rationality imply that it does, but our ordinary evaluations of rationality seem to suggest otherwise. This paper aims to resolve the tension by arguing that our ordinary evaluations of rationality are not only consistent with the thesis that rationality requires logical omniscience, but also provide a compelling rationale for accepting this thesis in the first place. This paper also defends an account of apriori justification for logical beliefs that (...) is designed to explain the rational requirement of logical omniscience. On this account, apriori justification for beliefs about logic has its source in logical facts, rather than psychological facts about experience, reasoning, or understanding. This account has important consequences for the epistemic role of experience in the logical domain. In a slogan, the epistemic role of experience in the apriori domain is not a justifying role, but rather an enabling and disabling role. (shrink)

A very weak omniscience principle is formulated, related omniscience principlesare considered, and the theorem that a function of bounded variation is the difference of two increasing functions is shown to be equivalent to the omniscience principle WLPO. It is a so shown that an arbitrary function with located variation on an interval is the difference of two increasing functions.

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)

Several theorists (Merricks, Westphal, and McCall) have recently claimed to offer a novel way to respond to the dilemma of freedom and foreknowledge, rooted in Molina's insight that God's beliefs depend on what we do, rather than the other way around. In this paper we argue that these responses either beg the question, or else are dressed-up versions of Ockhamism.