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

The 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)

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

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

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)

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

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)

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.

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

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.

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

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

Reconciling the existence of a perfectly good God with the reality of evil in the world seems to be an impossible - or rather an unimaginable endeavour for some scholars. J. L. Mackie, for instance, maintains a logical incompatibility thesis, stating that three of the essential attributes of God, namely: omnipotence, omniscience and omnibenevolence can not be consistently upheld like the theists maintain, in the face of the reality of evil and human suffering in the world. Scholars like (...) William Rowe, David Hume and J. S. Mill also contend that every instance or trace of evil and suffering in the actual human world makes the existence of the creator of the world who is also perfectly good at best, probable. However, some scholars have attempted to explain the compatibility of the existence of a perfectly good God with the reality of evil in the world. This very endeavour is known in philosophy of religion and theology as theodicy. There are four traditional types of theodicy: The Augustinian tradition, the Irananaean tradition, the Hickian Soul making tradition and process theodicy. Using the methods of analysis and critical argumentation, we attempt a critical re-evaluation of these theodicies in this paper. Our critical investigation reveals that these theodicies inhere some weaknesses which render them insufficient in the rationalisation of the compatibility of the existence of a perfectly good God with the reality of evil in the world. The problems with each of the theodicies are meticulously explained in the paper. (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)

Whereas Bayesians have proposed norms such as probabilism, which requires immediate and permanent certainty in all logical truths, I propose a framework on which credences, including credences in logical truths, are rational because they are based on reasoning that follows plausible rules for the adoption of credences. I argue that my proposed framework has many virtues. In particular, it resolves the problem of logical omniscience.

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

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)

An organizing theme of the dissertation is the issue of how to make philosophical theories useful for scientific purposes. An argument for the contention is presented that it doesn’t suffice merely to theoretically motivate one’s theories, and make them compatible with existing data, but that philosophers having this aim should ideally contribute to identifying unique and hard to vary predictions of their theories. This methodological recommendation is applied to the ranking-theoretic approach to conditionals, which emphasizes the epistemic relevance and the (...) expression of reason relations as part of the semantics of the natural language conditional. As a first step, this approach is theoretically motivated in a comparative discussion of other alternatives in psychology of reasoning, like the suppositional theory of conditionals, and novel approaches to the problems of compositionality and accounting for the objective purport of indicative conditionals are presented. In a second step, a formal model is formulated, which allows us to derive quantitative predictions from the ranking-theoretic approach, and it is investigated which novel avenues of empirical research that this model opens up for. Finally, a treatment is given of the problem of logical omniscience as it concerns the issue of whether ranking theory (and other similar approaches) makes too idealized assumptions about rationality to allow for interesting applications in psychology of reasoning. Building on the work of Robert Brandom, a novel solution to this problem is presented, which both opens up for new perspectives in psychology of reasoning and appears to be capable of satisfying a range of constraints on bridge principles between logic and norms of reasoning, which would otherwise stand in a tension. (shrink)

Some philosophers advance the claim that the phenomena of logical omniscience and of the indiscernibility of metaphysical statements, which arise in (certain) interpretations of normal modal logic, provide strong reasons in favour of impossible world approaches. These two specific lines of argument will be presented and discussed in this paper. Contrary to the recent much-held view that the characteristics of these two phenomena provide us with strong reasons to adopt impossible world approaches, the view defended here is that (...) no such ‘knock-down arguments’ do emanate on those grounds. This is not to rule out that there cannot be any other good reasons for assuming impossible world semantics. However, the discussion of a further argument for impossible worlds will suggest that different attempts to argue for them likely present intertwined problems. (shrink)

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 most widespread models of rational reasoners (the model based on modal epistemic logic and the model based on probability theory) exhibit the problem of logical omniscience. The most common strategy for avoiding this problem is to interpret the models as describing the explicit beliefs of an ideal reasoner, but only the implicit beliefs of a real reasoner. I argue that this strategy faces serious normative issues. In this paper, I present the more fundamental problem (...) of logical omnipotence, which highlights the normative content of the problem of logical omniscience. I introduce two developments of the notion of implicit belief (accessible and stable belief ) and use them in two versions of the most common strategy applied to the problem of logical omnipotence. (shrink)

In light of the problem of logical omniscience, some scholars have argued that belief is question-sensitive: agents don't simply believe propositions but rather believe answers to questions. Hoek (2022) has recently developed a version of this approach on which a belief state is a "web" of questions and answers. Here, we present several challenges to Hoek's question-sensitive account of belief. First, Hoek's account is prone to very similar logical omniscience problems as those he claims to (...) address. Second, the link between belief and action he proposes is too rigid. We close by sketching a generalization of the account that can meet these challenges. (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)

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

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)

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)

Analyzing causation in terms of Woodward's interventionist theory and describing the structure of the world in terms of causal powers are usually regarded as quite different projects in contemporary philosophy. Interventionists aim to give an account of how causal relations can be empirically discovered and described, without committing themselves to views about what causation really is. Causal powers theorists engage in precisely the latter project, aiming to describe the metaphysical structure of the world. In this paper, I argue that interventionism (...) can benefit from incorporating considerations about causal powers. I describe a previously undiscussed problem for Woodward's definition of an intervention variable that arises when interventionist causal models include disjunctive variables. This problem is solved not by excluding disjunctive (or logically compound) variables per se, but by excluding variables whose values represent disjunctions of too different causal powers. This suggests that interventionism and causal powers theories may be less distant from each other than is often assumed. (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)

All reasoners described in the most widespread models of a rational reasoner exhibit logical omniscience, which is impossible for finite reasoners (real reasoners). The most common strategy for dealing with the problem of logical omniscience is to interpret the models using a notion of beliefs different from explicit beliefs. For example, the models could be interpreted as describing the beliefs that the reasoner would hold if the reasoner were able reason indefinitely (stable beliefs). Then the (...) models would describe maximum rationality, which a finite reasoner can only approach in the limit of a reasoning sequence. This strategy has important consequences for epistemology. If a finite reasoner can only approach maximum rationality in the limit of a reasoning sequence, then the efficiency of reasoning is epistemically (and not only pragmatically) relevant. In this paper, I present an argument to this conclusion and discuss its consequences, as, for example, the vindication of the principle 'no rationality through brute-force'. (shrink)

Rosenkranz (2021) devised two bimodal epistemic logics: an idealized one and a realistic one. The former is shown to be sound with respect to a class of neighborhood frames called i-frames. Rosenkranz designed a specific i-frame able to invalidate a series of undesired formulas, proving that these are not theorems of the idealized logic. Nonetheless, an unwanted formula and an unwanted rule of inference are not invalidated. Invalidating the former guarantees the distinction between the two modal operators characteristic of the (...) logic, while invalidating the latter is crucial in order to deal with the problem of logical omniscience. In this paper, I present an i-frame able to invalidate all the undesired formulas already invalidated by Rosenkranz, together with the missing formula and rule of inference. (shrink)

A survey of logical problems for the concept of omniscience.

Orthodox Bayesianism is a highly idealized theory of how we ought to live our epistemic lives. One of the most widely discussed idealizations is that of logical omniscience: the assumption that an agent’s degrees of belief must be probabilistically coherent to be rational. It is widely agreed that this assumption is problematic if we want to reason about bounded rationality, logical learning, or other aspects of non-ideal epistemic agency. Yet, we still lack a satisfying way to avoid (...) logical omniscience within a Bayesian framework. Some proposals merely replace logical omniscience with a different logical idealization; others sacrifice all traits of logical competence on the altar of logical non-omniscience. We think a better strategy is available: by enriching the Bayesian framework with tools that allow us to capture what agents can and cannot infer given their limited cognitive resources, we can avoid logical omniscience while retaining the idea that rational degrees of belief are in an important way constrained by the laws of probability. In this paper, we offer a formal implementation of this strategy, show how the resulting framework solves the problem of logical omniscience, and compare it to orthodox Bayesianism as we know it. (shrink)

My paper examines the problem of evil in its logical form, and along lines of African philosophizing. I construe the problematic nature of this problem [of evil] (hereafter, λ) as arising from a Western logical structure, which takes the valuation of propositions as being marked by a rigid bivalence of only truth (T) and falsity (F). By this structure, values and propositions are diametrically pitted against each other such that it appears that choice is only restrained (...) to an ‘either’, ‘or’. My argument transcends and dismantles this bivalence and subscribes to the African system of Ezumezu logic, developed by Jonathan Okeke Chimakonam which permits the pursuit of a trivalent logical course of ‘either’, ‘or’, in addition to ‘and’. Employing the logical system of Ezumezu, I demonstrate a negative resolution to λ, showing via the ‘principle of value-complementarity’, that good and evil as observed and experienced, are not opposites, but rather complements. The conclusions I draw from my analysis bear some implication for the conception of the Supreme Being; for one, I argue that conceiving the Supreme Being in African philosophy through the categories of the superlative ‘omni’ properties is mistaken , and also, I argue that this Supreme Being is better conceived as a harmony of good and evil: an embodiment of balance. (shrink)

Stephen Yablo has argued that ascriptions of belief and knowledge are sensitive to _subject matter_ and that theorising in such terms may help resolve philosophical questions about the semantics of such ascriptions. _Truthmaker semantics_ offers a way of theorising about subject matters. My main aim in this paper is to investigate what a semantics for knowledge or belief ascriptions might look like within truthmaker semantics. I then discuss what the resulting account might have to say about the problem of (...) logical omniscience, the nature of concepts, and rational belief. (shrink)

The problem of communication in de se thoughts is the problem of communication of first-person or self-locating thoughts across the speakers of a conversation. The problem mainly stems from the lack of a proper account of attitude and content — an account that is supposed to explain whether or how the context of linguistic utterances is related to the semantic content of a sentence, assertion and belief. In this paper, after introducing two new semantic items, namely, almost-impossible (...) and almost-necessary propositions, that could be taken as theoretically primitive entities in the semantic framework I wish to draw, I propose an account of modified Lewisian-centered content and attitude based on the metaphysical framework of the Lewisian counterpart-theoretic semantics for quantified modal logic to the extent that the modification relies on those new semantic items. I then show that we can solve the problem by using our modified account. (shrink)

Various philosophers have long since been attracted to the doctrine that future contingent propositions systematically fail to be true—what is sometimes called the doctrine of the open future. However, open futurists have always struggled to articulate how their view interacts with standard principles of classical logic—most notably, with the Law of Excluded Middle. For consider the following two claims: Trump will be impeached tomorrow; Trump will not be impeached tomorrow. According to the kind of open futurist at issue, both of (...) these claims may well fail to be true. According to many, however, the disjunction of these claims can be represented as p ∨ ~p—that is, as an instance of LEM. In this essay, however, I wish to defend the view that the disjunction these claims cannot be represented as an instance of p ∨ ~p. And this is for the following reason: the latter claim is not, in fact, the strict negation of the former. More particularly, there is an important semantic distinction between the strict negation of the first claim [~] and the latter claim. However, the viability of this approach has been denied by Thomason, and more recently by MacFarlane and Cariani and Santorio, the latter of whom call the denial of the given semantic distinction “scopelessness”. According to these authors, that is, will is “scopeless” with respect to negation; whereas there is perhaps a syntactic distinction between ‘~Will p’ and ‘Will ~p’, there is no corresponding semantic distinction. And if this is so, the approach in question fails. In this paper, then, I criticize the claim that will is “scopeless” with respect to negation. I argue that will is a so-called “neg-raising” predicate—and that, in this light, we can see that the requisite scope distinctions aren’t missing, but are simply being masked. The result: a under-appreciated solution to the problem of future contingents that sees and as contraries, not contradictories. (shrink)

What corresponds to the present-day ‘transcendental-pragmatic’ concept of ultimate grounding in Hegel is his claim to absoluteness of the logic. Hegel’s fundamental intuition is that of a ‘backward going grounding’ obtaining the initially unproved presuppositions, thereby ‘wrapping itself into a circle’ – the project of the self-grounding of logic, understood as the self-explication of logic by logical means. Yet this is not about one of the multiple ‘logics’ which as formal constructs cannot claim absoluteness. It is rather a fundamental (...) logic that only makes logical textures possible at all and so owns transcendental character. The non-contradiction-principle is an example for this. Es- sential is that it is ‘under-cover-effcient’ as soon as meaningful concepts are used. Self-explication of the fundamental logic then means explicating its implicit under-cover validity, in fact by means of the fundamental logic itself. As is shown this is the affair of dialectic which thereby is to be understood as ultimate grounding of the fundamental logic. This is analyzed in detail using the example of the being/non-being-dialectic. As is demonstrated each explication step generates a new implicit issue and therewith a new explication-discrepancy inducing an antinomical structure that anew forwards the explication procedure. So this is entirely determined by itself. Decisive for the ultimate grounding argumentation is that thereby an objectively verifyable procedure is found, which is apparently possible only in a Hegelian framework. In contrast the immediate evidence of a speech act claimed by the transcendental-pragmatic position has only private character, which is grounding-theoretically irrelevant. (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)

Non-cognitivists are known to face a problem in extending their account of straightforward predicative moral judgments to logically complex moral judgments. This paper presents a related problem concerning how non-cognitivists might extend their accounts of moral judgments to other kinds of moral attitudes, such as moral hopes and moral intuitions. Non-cognitivists must solve three separate challenges: they must explain the natures of these other attitudes, they must explain why they count as moral attitudes, and they must explain why (...) the moral attitudes are systematically correlated with ordinary propositional attitudes. After presenting the problem, this paper examines several contemporary theories with some initial promise for solving it, and argues that they are insufficient. (shrink)

Heinrich Behmann (1891-1970) obtained his Habilitation under David Hilbert in Göttingen in 1921 with a thesis on the decision problem. In his thesis, he solved - independently of Löwenheim and Skolem's earlier work - the decision problem for monadic second-order logic in a framework that combined elements of the algebra of logic and the newer axiomatic approach to logic then being developed in Göttingen. In a talk given in 1921, he outlined this solution, but also presented important programmatic (...) remarks on the significance of the decision problem and of decision procedures more generally. The text of this talk as well as a partial English translation are included. (shrink)

The problem of forgiveness may rightly be regarded as a perennial philosophical problem. But of what sort? Introducing his 1973 contribution to the discussion, entitled simply "Forgiveness"—an essay that remains the standard reference for contemporary discussions of the problem, especially in the Anglo-American philosophical community—Aurel Kolnai writes that while the ethical nature of the problem is indisputable, he intends his argument "to be chiefly logical in nature: the central question I wish to discuss is … (...) whether, and if so in what manner, [forgiveness] is logically possible at all."1 The problem, as Kolnai develops it in the first two sections of his essay, is that forgiveness seems to be either... (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)

In Appearance and Explanation, McCain and Moretti propose a novel internalist account of epistemic justification called phenomenal explanationism, which combines phenomenal conservatism and explanationism. I argue that the current version of phenomenal explanationism faces a dilemma: either it omits the awareness requirement but implies an implausible form of logical-mathematical omniscience, or it preserves the requirement but leads to a vicious regress. I suggest how phenomenal explanationism might be revised to avoid this dilemma.

I raise the following six moral objections to the way God evaluates us. (i) He violates the human right to free thought. (ii) He makes the dubious assumption that it is praiseworthy and blameworthy, respectively, to believe and disbelieve that he exists. (iii) He excessively rewards believers and excessively punishes disbelievers. (iv) He only assigns to his evaluatees the two extreme grades: eternal bliss and eternal damnation. (v) He overlooks diverse factors related to the belief of God. (vi) He is (...) silent on the issue of whether to evaluate animals. Therefore, God, who is allegedly omnipotent, omniscient, and omnibenevolent, does not exist. (shrink)

Group decisions must often obey exogenous constraints. While in a preference aggregation problem constraints are modelled by restricting the set of feasible alternatives, this paper discusses the modelling of constraints when aggregating individual yes/no judgments on interconnected propositions. For example, court judgments in breach-of-contract cases should respect the constraint that action and obligation are necessary and sufficient for liability, and judgments on budget items should respect budgetary constraints. In this paper, we make constraints in judgment aggregation explicit by relativizing (...) the rationality conditions of consistency and deductive closure to a constraint set, whose variation yields more or less strong notions of rationality. This approach of modelling constraints explicitly contrasts with that of building constraints as axioms into the logic, which turns compliance with constraints into a matter of logical consistency and thereby conflates requirements of ordinary logical consistency and requirements dictated by the environment . We present some general impossibility results on constrained judgment aggregation; they are immediate corollaries of known results on judgment aggregation. (shrink)

This academic paper provides a historical reflection on the problem of the origin of science in order to determine the reasons for differences in determining the date and content of the first scientific achievements. The application of historical-genetic research methods in the disciplinary aspect contributes to the distinction of particular scientific programs in the science body frame with a different relationship between the object and subject of cognition, the internal logic of ideas and worldviews. As a result, the existing (...) research concerned with the conditions of knowledge function in different types of society or with the relations between the structure of knowledge and its purpose, was supplemented by an explication of forms of the continuity of program components – ontological, epistemological and axiological basis of specific scientific cognition/knowledge. In particular, it is established that the ancient world atomistic and peripatetic programs follow the structural pattern of the scientific explanation of the Pythagorean one (scientific and philosophical at the same time), contributing a new subject content in it. (shrink)

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)

In he Problems of Philosophy and other works of the same period, Russell claims that every proposition must contain at least one universal. Even fully general propositions of logic are claimed to contain “abstract logical universals”, and our knowledge of logical truths claimed to be a species of a priori knowledge of universals. However, these views are in considerable tension with Russell’s own philosophy of logic and mathematics as presented in Principia Mathematica. Universals generally are qualities and relations, (...) but if, for example, PM’s disjunction (∨) is a relation, what is it a relation between? There is no obvious answer to this given Russell’s other philosophical commitments at this time, although hints are left in some of the pre-PM manuscripts. In this paper, I explore this tension in Russell's philosophy and relate it to developments both before and after Problems. (shrink)

[[[ (Here only the chapters 3 – 8, see *** ) First I argue that the prohibition of linguistic self-reference as a solution to the antinomy problem contains a pragmatic contradiction and is thus not only too restrictive, but just inconsistent (chap.1). Furthermore, the possibilities of non-restrictive strategies for antinomy avoidance are discussed, whereby the explicit inclusion of the – pragmatically presuposed – consistency requirement proves to be the optimal strategy (chap.2). ]]] The central question here is that about (...) the actual reason for antinomic structures. It turns out to be a form of negative self-conditioning (chap.3). This makes it necessary to clarify the status of negative concepts (chap.4). The generalization of these considerations (chap.5) leads to the actual analysis of the antinomic basic structure (chap.6): Decisively for the pragmatics of the concept is that it positively owns a meaning, so that positivity is always constituted by the concept qua concept. Thus a negative concept is characterized by a fundamental ambivalence: From a semantic point of view it has negative character, in its pragmatic status as a concept, however, it has positive character. If the meaning is especially that of a negative self-reference, the ambivalence leads to the antinomic constellation of a negative self-condition – that is the crux of the matter here! The concept thus possesses the property defined by it exactly when it does not possess it and vice versa. A closer analysis shows that the function of reflective structures for the occurrence of antinomies has to be judged much more differentiated than previous opinions suggest. Not only are four forms of reflectivity to be distinguished in this context – ontic, semantic, pragmatic reflectivity, and especially the form of negative self-condition; but it is also apparent that these are intertwined with each other in a way that is difficult to be understood. The astonishing variety of relationships associated with this makes the irritation that has always emanated from the antinomy problem appear more comprehensible. In the developed pragmatic perspective furtheron parallels to the structure of self-consciousness become visible (chap.7). I conclude with considerations about the significance of the antinomic structure for the problem of dialectics, especially for the synthesis formation of mutually exclusive terms (chap.8). (shrink)