Paradoxes have played an important role both in philosophy and in mathematics and paradox resolution is an important topic in both fields. Paradox resolution is deeply important because if such resolution cannot be achieved, we are threatened with the charge of debilitating irrationality. This is supposed to be the case for the following reason. Paradoxes consist of jointly contradictory sets of statements that are individually plausible or believable. These facts about paradoxes then give rise to a deeply troubling (...) epistemic problem. Specifically, if one believes all of the constitutive propositions that make up a paradox, then one is apparently committed to belief in every proposition. This is the result of the principle of classical logical known as ex contradictione (sequitur) quodlibetthat anything and everything follows from a contradiction, and the plausible idea that belief is closed under logical or material implication (i.e. the epistemic closure principle). But, it is manifestly and profoundly irrational to believe every proposition and so the presence of even one contradiction in one’s doxa appears to result in what seems to be total irrationality. This problem is the problem of paradox-induced explosion. In this paper it will be argued that in many cases this problem can plausibly be avoided in a purely epistemic manner, without having either to resort to non-classical logics for belief (e.g. paraconsistent logics) or to the denial of the standard closure principle for beliefs. The manner in which this result can be achieved depends on drawing an important distinction between the propositional attitude of belief and the weaker attitude of acceptance such that paradox constituting propositions are accepted but not believed. Paradox-induced explosion is then avoided by noting that while belief may well be closed under material implication or even under logical implication, these sorts of weaker commitments are not subject to closure principles of those sorts. So, this possibility provides us with a less radical way to deal with the existence of paradoxes and it preserves the idea that intelligent agents can actually entertain paradoxes. (shrink)

Why can testimony alone be enough for findings of liability? Why statistical evidence alone can’t? These questions underpin the “Proof Paradox” (Redmayne 2008, Enoch et al. 2012). Many epistemologists have attempted to explain this paradox from a purely epistemic perspective. I call it the “Epistemic Project”. In this paper, I take a step back from this recent trend. Stemming from considerations about the nature and role of standards of proof, I define three requirements that any successful (...) account in line with the Epistemic Project should meet. I then consider three recent epistemic accounts on which the standard is met when the evidence rules out modal risk (Pritchard 2018), normic risk (Ebert et al. 2020), or relevant alternatives (Gardiner 2019 2020). I argue that none of these accounts meets all the requirements. Finally, I offer reasons to be pessimistic about the prospects of having a successful epistemic explanation of the paradox. I suggest the discussion on the proof paradox would benefit from undergoing a ‘value-turn’. (shrink)

Epistemic theories of truth, such as those presumed to be typical for anti-realism, can be characterised as saying that what is true can be known in principle: p → ◊Kp. However, with statements of the form “p & ¬Kp”, a contradiction arises if they are both true and known. Analysis of the nature of the paradox shows that such statements refute epistemic theories of truth only if the the anti-realist motivation for epistemic theories of truth is (...) not taken into account. The motivation in a link of understandability ans meaningful- ness suggests to change the above principle and to restrict the theory to logically simple sentences, in which case the paradox does not arise. This suggestion also allows to see the deep philosophical problems for anti-realism those counterexamples are pointing at. (shrink)

This short paper offers a skeptical solution to Åqvist's paradox of epistemic obligation. The solution is based on the contention that in SDL/KDT logics the externalist features of knowledge, about which we cannot have obligations, are obscured.

Chalmers and Hájek argue that on an epistemic reading of Ramsey’s test for the rational acceptability of conditionals, it is faulty. They claim that applying the test to each of a certain pair of conditionals requires one to think that one is omniscient or infallible, unless one forms irrational Moore-paradoxical beliefs. I show that this claim is false. The epistemic Ramsey test is indeed faulty. Applying it requires that one think of anyone as all-believing and if one is (...) rational, to think of anyone as infallible-if-rational. But this is not because of Moore-paradoxical beliefs. Rather it is because applying the test requires a certain supposition about conscious belief. It is important to understand the nature of this supposition. (shrink)

By pooling together exhaustive analyses of certain philosophical paradoxes, we can prove a series of fascinating results regarding philosophical progress, agreement on substantive philosophical claims, knockdown arguments in philosophy, the wisdom of philosophical belief, the epistemic status of metaphysics, and the power of philosophy to refute common sense. As examples, this Element examines the Sorites Paradox, the Liar Paradox, and the Problem of the Many – although many other paradoxes can do the trick too.

Thomas Kroedel argues that the lottery paradox can be solved by identifying epistemic justification with epistemic permissibility rather than epistemic obligation. According to his permissibility solution, we are permitted to believe of each lottery ticket that it will lose, but since permissions do not agglomerate, it does not follow that we are permitted to have all of these beliefs together, and therefore it also does not follow that we are permitted to believe that all tickets will (...) lose. I present two objections to this solution. First, even if justification itself amounts to no more than epistemic permissibility, the lottery paradox recurs at the level of doxastic obligations unless one adopts an extremely permissive view about suspension of belief that is in tension with our practice of doxastic criticism. Second, even if there are no obligations to believe lottery propositions, the permissibility solution fails because epistemic permissions typically agglomerate, and the lottery case provides no exception to this rule. (shrink)

We shall evaluate two strategies for motivating the view that knowledge is the norm of belief. The first draws on observations concerning belief's aim and the parallels between belief and assertion. The second appeals to observations concerning Moore's Paradox. Neither of these strategies gives us good reason to accept the knowledge account. The considerations offered in support of this account motivate only the weaker account on which truth is the fundamental norm of belief.

I give an interpretation according to which Meno’s paradox is an epistemic regress problem. The paradox is an argument for skepticism assuming that acquired knowledge about an object X requires prior knowledge about what X is and any knowledge must be acquired. is a principle about having reasons for knowledge and about the epistemic priority of knowledge about what X is. and jointly imply a regress-generating principle which implies that knowledge always requires an infinite sequence of (...) known reasons. Plato’s response to the problem is to accept but reject : some knowledge is innate. He argues from this to the conclusion that the soul is immortal. This argument can be understood as a response to an Eleatic problem about the possibility of coming into being that turns on a regress-generating causal principle analogous to the regress-generating principle presupposed by Meno’s paradox. (shrink)

This paper defends the heretical view that, at least in some cases, we ought to assign legal liability based on purely statistical evidence. The argument draws on prominent civil law litigation concerning pharmaceutical negligence and asbestos-poisoning. The overall aim is to illustrate moral pitfalls that result from supposing that it is never appropriate to rely on bare statistics when settling a legal dispute.

Epistemic modal operators give rise to something very like, but also very unlike, Moore's paradox. I set out the puzzling phenomena, explain why a standard relational semantics for these operators cannot handle them, and recommend an alternative semantics. A pragmatics appropriate to the semantics is developed and interactions between the semantics, the pragmatics, and the definition of consequence are investigated. The semantics is then extended to probability operators. Some problems and prospects for probabilistic representations of content and context (...) are explored. (shrink)

1) We will begin by offering a short introduction to Epistemic Logic and presenting Fitch’s paradox in an epistemic‑modal logic. (2) Then, we will proceed to presenting three Epistemic Temporal logical frameworks creat‑ ed by Hoshi (2009) : TPAL (Temporal Public Announcement Logic), TAPAL (Temporal Arbitrary Public Announcement Logic) and TPAL+P ! (Temporal Public Announcement Logic with Labeled Past Operators). We will show how Hoshi stated the Verificationist Thesis in the language of TAPAL and analyze his (...) argument on why this version of it is immune from paradox. (3) Edgington (1985) offered an interpretation of the Verificationist Thesis that blocks Fitch’s paradox and we will propose a way to formulate it in a TAPAL‑based lan‑ guage. The language we will use is a combination of TAPAL and TPAL+P ! with an Indefinite (Unlabeled) Past Operator (TAPAL+P !+P). Using indexed satisfi‑ ability relations (as introduced in (Wang 2010 ; 2011)) we will offer a prospec ‑ tive semantics for this language. We will investigate whether the tentative re‑ formulation of Edgington’s Verificationist Thesis in TAPAL+P !+P is free from paradox and adequate to Edgington’s ideas on how „all truths are knowable“ should be interpreted. (shrink)

According to Kierkegaard, truth is superimposed on the objective character that encompasses historical investigation and speculative exercise, dialoguing with subjectivity and the limit-condition of interiority. Focusing on such existential-hermeneutic principle, the article points out spirituality as an epistemic-existential experience involving truth as a paradox in Kierkegaard, that overlaps the logical-discursive mediation and implies a dialectical-subjective construction that transcends reason historical-objective. Thus, characterizing spirituality as an epistemic-existential experience that contains non-rational evidence, the article resorts to Rudolf Otto's phenomenology (...) to underline the sacred and its absolute distinction from natural reality and its perceptible character, emphasizing the non-rational element and its supra-rational nature in the numinous, which escapes logical-rational processes and converges to the apprehension of the rational and the non-rational in the notion of Divinity. Therefore, if the relationship with God overlaps subjectivity and objectivity and overcomes the aforementioned epistemic structural scheme, the article, based on the philosophical theology of Paul Tillich, focuses on the concept of Spiritual Presence and on life without ambiguity, which implies the union transcendent and correlates agape and gnosis in an ecstatic-religious movement that encompasses the self-manifestation, self-revelation and self-communication of the Absolute and Transcendent. (shrink)

According to Kierkegaard, truth is superimposed on the objective character that encompasses from a historical investigation to a speculative exercise, keeping a correspondence with subjectivity in a movement that implies the limit-condition of interiority. Focusing on such existential-hermeneutic principle, the article points out spirituality as an epistemic-existential experience involving truth as a paradox in Kierkegaard, that overlaps the logical-discursive mediation and implies a dialectical-subjective construction that transcends reason historical-objective (or finite). In this way, characterizing spirituality as an (...) class='Hi'>epistemic-existential experience thatconverges to the borders that contain non-rational evidence as the only type of evidence, the article resorts to Rudolf Otto's phenomenological perspective, that emphasizes the sacred and its absolute distinction in relation to natural reality and its perceptible character in a construction that emphasizes the non-rational element and its supra-rational nature and implies the numinous, which escapes logical-rational processes and, emerging as a priori, converges to the apprehension of the rational and the non-rational in the notion of Divinity. Thus, if the relationship with God overlaps the borders that enclose subjectivity and objectivity, converging to overcome the aforementioned epistemic structural scheme, the article, based on Paul Tillich's theological-philosophical perspective, focuses on the concept of Spiritual Presence that, characterizing life without ambiguity, implies a transcendent unión, correlatingagape and gnosis as an epistemic-existential experience involving the relationship with the sacred as the presence of God through an ecstatic-religious movement that converges to self-manifestation, self-revelation and the self-communication of the Absolute and Transcendent as God. (shrink)

I describe epistemic versions of the contrast between causal and conventionally probabilistic decision theory, including an epistemic version of Newcomb's paradox.

Epistemic luck is a generic notion used to describe any of a number of ways in which it can be accidental, coincidental, or fortuitous that a person has a true belief. For example, one can form a true belief as a result of a lucky guess, as when one believes through guesswork that “C” is the right answer to a multiple-choice question and one’s belief just happens to be correct. One can form a true belief via wishful thinking; for (...) example, an optimist’s belief that it will not rain may luckily turn out to be correct, despite forecasts for heavy rain all day. One can reason from false premises to a belief that coincidentally happens to be true. One can accidentally arrive at a true belief through invalid or fallacious reasoning. And one can fortuitously arrive at a true belief from testimony that was intended to mislead but unwittingly reported the truth. In all of these cases, it is just a matter of luck that the person has a true belief. -/- Until the twenty-first century, there was nearly universal agreement among epistemologists that epistemic luck is incompatible with knowledge. Call this view “the incompatibility thesis.” In light of the incompatibility thesis, epistemic luck presents epistemologists with three distinct but related challenges. The first is that of providing an accurate analysis of knowledge (in terms of individually necessary and jointly sufficient conditions for “S knows that p,” where ‘S’ represents the knower and ‘p’ represents the proposition known). An adequate analysis of knowledge must succeed in specifying conditions that rule out all instances of knowledge-destroying epistemic luck. The second challenge is to resolve the skeptical paradox that the ubiquity of epistemic luck generates: As will become clear in section 2c, epistemic luck is an all-pervasive phenomenon. Coupling this fact with the incompatibility thesis entails that we have no propositional knowledge. The non-skeptical epistemologist must somehow reconcile the strong intuition that epistemic luck is not compatible with knowledge with the equally evident observation that it must be. The third challenge concerns the special skeptical threat that epistemic luck seems to pose for more reflective forms of knowledge, such as knowing that one knows. Each of these challenges will be explored in the present article. (shrink)

This paper generalises the classical Condorcet jury theorem from majority voting over two options to plurality voting over multiple options. The paper further discusses the debate between epistemic and procedural democracy and situates its formal results in that debate. The paper finally compares a number of different social choice procedures for many-option choices in terms of their epistemic merits. An appendix explores the implications of some of the present mathematical results for the question of how probable majority cycles (...) (as in Condorcet's paradox) are in large electorates. (shrink)

Clayton Littlejohn claims that the permissibility solution to the lottery paradox requires an implausible principle in order to explain why epistemic permissions don't agglomerate. This paper argues that an uncontentious principle suffices to explain this. It also discusses another objection of Littlejohn's, according to which we’re not permitted to believe lottery propositions because we know that we’re not in a position to know them.

The idea that knowledge can be extended by inference from what is known seems highly plausible. Yet, as shown by familiar preface paradox and lottery-type cases, the possibility of aggregating uncertainty casts doubt on its tenability. We show that these considerations go much further than previously recognized and significantly restrict the kinds of closure ordinary theories of knowledge can endorse. Meeting the challenge of uncertainty aggregation requires either the restriction of knowledge-extending inferences to single premises, or eliminating epistemic (...) uncertainty in known premises. The first strategy, while effective, retains little of the original idea—conclusions even of modus ponens inferences from known premises are not always known. We then look at the second strategy, inspecting the most elaborate and promising attempt to secure the epistemic role of basic inferences, namely Timothy Williamson’s safety theory of knowledge. We argue that while it indeed has the merit of allowing basic inferences such as modus ponens to extend knowledge, Williamson’s theory faces formidable difficulties. These difficulties, moreover, arise from the very feature responsible for its virtue- the infallibilism of knowledge. (shrink)

The coordinated attack scenario and the electronic mail game are two paradoxes of common knowledge. In simple mathematical models of these scenarios, the agents represented by the models can coordinate only if they have common knowledge that they will. As a result, the models predict that the agents will not coordinate in situations where it would be rational to coordinate. I argue that we should resolve this conflict between the models and facts about what it would be rational to do (...) by rejecting common knowledge assumptions implicit in the models. I focus on the assumption that the agents have common knowledge that they are rational, and provide models to show that denying this assumption suffices for a resolution of the paradoxes. I describe how my resolution of the paradoxes fits into a general story about the relationship between rationality in situations involving a single agent and rationality in situations involving many agents. (shrink)

The problem analysed in this paper is whether we can gain knowledge by using valid inferences, and how we can explain this process from a model-theoretic perspective. According to the paradox of inference (Cohen & Nagel 1936/1998, 173), it is logically impossible for an inference to be both valid and its conclusion to possess novelty with respect to the premises. I argue in this paper that valid inference has an epistemic significance, i.e., it can be used by an (...) agent to enlarge his knowledge, and this significance can be accounted in model-theoretic terms. I will argue first that the paradox is based on an equivocation, namely, it arises because logical containment, i.e., logical implication, is identified with epistemological containment, i.e., the knowledge of the premises entails the knowledge of the conclusion. Second, I will argue that a truth-conditional theory of meaning has the necessary resources to explain the epistemic significance of valid inferences. I will explain this epistemic significance starting from Carnap’s semantic theory of meaning and Tarski’s notion of satisfaction. In this way I will counter (Prawitz 2012b)’s claim that a truth-conditional theory of meaning is not able to account the legitimacy of valid inferences, i.e., their epistemic significance. (shrink)

Conciliatory theories of disagreement require that one lower one’s confidence in a belief in the face of disagreement from an epistemic peer. One question about which people might disagree is who should qualify as an epistemic peer and who should not. But when putative epistemic peers disagree about epistemic peerhood itself, then Conciliationism makes contradictory demands and paradoxes arise.

According to the principle of Conjunction Closure, if one has justification for believing each of a set of propositions, one has justification for believing their conjunction. The lottery and preface paradoxes can both be seen as posing challenges for Closure, but leave open familiar strategies for preserving the principle. While this is all relatively well-trodden ground, a new Closure-challenging paradox has recently emerged, in two somewhat different forms, due to Backes :3773–3787, 2019a) and Praolini :715–726, 2019). This paradox (...) synthesises elements of the lottery and the preface and is designed to close off the familiar Closure-preserving strategies. By appealing to a normic theory of justification, I will defend Closure in the face of this new paradox. Along the way I will draw more general conclusions about justification, normalcy and defeat, which bear upon what Backes :2877–2895, 2019b) has dubbed the ‘easy defeat’ problem for the normic theory. (shrink)

Certain situations seem to call for acknowledging the possibility that one’s own beliefs are biased or distorted. On the other hand, certain sorts of epistemic self-doubts (such as ‘I believe it’s raining, but it’s not’) seem paradoxical. And some have put forth epistemic principles requiring rational agents to regard their own credences as so-called ‘expert functions’. This paper examines the question of whether rationality requires agents to respect their own credences in a way in which they need not (...) respect the credences of others. (shrink)

This paper argues that justification is accessible in the sense that one has justification to believe a proposition if and only if one has higher-order justification to believe that one has justification to believe that proposition. I argue that the accessibility of justification is required for explaining what is wrong with believing Moorean conjunctions of the form, ‘p and I do not have justification to believe that p.’.

If I were to say, “Agnes does not know that it is raining, but it is,” this seems like a perfectly coherent way of describing Agnes’s epistemic position. If I were to add, “And I don’t know if it is, either,” this seems quite strange. In this chapter, we shall look at some statements that seem, in some sense, contradictory, even though it seems that these statements can express propositions that are contingently true or false. Moore thought it was (...) paradoxical that statements that can express true propositions or contingently false propositions should nevertheless seem absurd like this. If we can account for the absurdity, we shall solve Moore’s Paradox. In this chapter, we shall look at Moore’s proposals and more recent discussions of Moorean absurd thought and speech. (shrink)

This essay concerns the question of how we make genuine epistemic progress through conceptual analysis. Our way into this issue will be through consideration of the paradox of analysis. The paradox challenges us to explain how a given statement can make a substantive contribution to our knowledge, even while it purports merely to make explicit what one’s grasp of the concept under scrutiny consists in. The paradox is often treated primarily as a semantic puzzle. However, in (...) “Sect. 1” I argue that the paradox raises a more fundamental epistemic problem, and in “Sects.1 and 2” I argue that semantic proposals—even ones designed to capture the Fregean link between meaning and epistemic significance—fail to resolve that problem. Seeing our way towards a real solution to the paradox requires more than semantics; we also need to understand how the process of analysis can yield justification for accepting a candidate conceptual analysis. I present an account of this process, and explain how it resolves the paradox, in “Sect. 3”. I conclude in “Sect. 4” by considering the implications for the present account concerning the goal of conceptual analysis, and by arguing that the apparent scarcity of short and finite illuminating analyses in philosophically interesting cases provides no grounds for pessimism concerning the possibility of philosophical progress through conceptual analysis. (shrink)

Metaphysically possible worlds have many uses. Epistemically possible worlds promise to be similarly useful, especially in connection with propositions and propositional attitudes. However, I argue that there is a serious threat to the natural accounts of epistemically possible worlds, from a version of Russell’s paradox. I contrast this threat with David Kaplan’s problem for metaphysical possible world semantics: Kaplan’s problem can be straightforwardly rebutted, the problems I raise cannot. I argue that although there may be coherent accounts of epistemically (...) possible worlds with fruitful applications, any such an account must fundamentally compromise the basic idea behind epistemic possibility. (shrink)

Moore’s Paradox is a test case for any formal theory of belief. In Knowledge and Belief, Hintikka developed a multimodal logic for statements that express sentences containing the epistemic notions of knowledge and belief. His account purports to offer an explanation of the paradox. In this paper I argue that Hintikka’s interpretation of one of the doxastic operators is philosophically problematic and leads to an unnecessarily strong logical system. I offer a weaker alternative that captures in a (...) more accurate way our logical intuitions about the notion of belief without sacrificing the possibility of providing an explanation for problematic cases such as Moore’s Paradox. (shrink)

This book concerns the foundations of epistemic modality. I examine the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality relates to the computational theory of mind; metaphysical modality; the types of mathematical modality; to the epistemic status of large cardinal axioms, undecidable propositions, and abstraction principles in the philosophy of mathematics; to the modal profile (...) of rational intuition; and to the types of intention, when the latter is interpreted as a modal mental state. Chapter \textbf{2} argues for a novel type of expressivism based on the duality between the categories of coalgebras and algebras, and argues that the duality permits of the reconciliation between modal cognitivism and modal expressivism. I also develop a novel topic-sensitive truthmaker semantics for dynamic epistemic logic, and develop a novel dynamic epistemic two-dimensional hyperintensional semantics. Chapter \textbf{3} provides an abstraction principle for epistemic intensions. Chapter \textbf{4} advances a topic-sensitive two-dimensional truthmaker semantics, and provides three novel interpretations of the framework along with the epistemic and metasemantic. Chapter \textbf{5} applies the fixed points of the modal $\mu$-calculus in order to account for the iteration of epistemic states, by contrast to availing of modal axiom 4 (i.e. the KK principle). Chapter \textbf{6} advances a solution to the Julius Caesar problem based on Fine's `criterial' identity conditions which incorporate conditions on essentiality and grounding. Chapter \textbf{7} provides a ground-theoretic regimentation of the proposals in the metaphysics of consciousness and examines its bearing on the two-dimensional conceivability argument against physicalism. The topic-sensitive epistemic two-dimensional truthmaker semantics developed in chapter \textbf{4} is availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. Chapters \textbf{8-12} provide cases demonstrating how the two-dimensional intensions of epistemic two-dimensional semantics solve the access problem in the epistemology of mathematics. Chapter \textbf{8} examines the interaction between topic-sensitive epistemic two-dimensional truthmaker semantics, the axioms of epistemic set theory, large cardinal axioms, the Epistemic Church-Turing Thesis, the modal axioms governing the modal profile of $\Omega$-logic, Orey sentences such as the Generalized Continuum Hypothesis, and absolute decidability. Chapter \textbf{9} examines the modal profile of $\Omega$-logic in set theory. Chapter \textbf{8} examines the modal commitments of abstractionism, in particular necessitism, and epistemic modality and the epistemology of abstraction. Chapter \textbf{11} avails of modal coalgebras to interpret the defining properties of indefinite extensibility, and avails of epistemic two-dimensional semantics in order to account for the interaction of the interpretational and objective modalities thereof. Chapter \textbf{12} provides a modal logic for rational intuition and provides a hyperintensional semantics. Chapter \textbf{13} examines modal responses to the alethic paradoxes. Chapter \textbf{14} examines, finally, the modal semantics for the different types of intention and the relation of the latter to evidential decision theory. The multi-hyperintensional, topic-sensitive epistemic two-dimensional truthmaker semantics developed in chapters \textbf{2} and \textbf{4} is applied in chapters \textbf{7}, \textbf{8}, \textbf{10}, \textbf{11}, \textbf{12}, and \textbf{14}. (shrink)

According to a widely held view epistemic justification is a normative notion. According to another widely held assumption, epistemic justification comes in degrees. Given that gradability requires a context-sensitivity that normativity seems to lack, these two assumptions stand in tension. Giving up the assumption of gradability of justification represents a lesser theoretical cost.

In the preface paradox the posited author is supposed to know both that every sentence in a book is true and that not every sentence in that book is true. But, this result is paradoxically contradictory. The paradoxicality exhibited in such cases arises chiefly out of the recognition that large-scale and difficult tasks like verifying the truth of large sets of sentences typically involve errors even given our best efforts to be epistemically diligent. This paper introduces an argument designed (...) to resolve the preface paradox so understood by appeal to the safety condition on knowledge. (shrink)

In this paper I consider two paradoxes that arise in connection with the concept of demonstrability, or absolute provability. I assume—for the sake of the argument—that there is an intuitive notion of demonstrability, which should not be conflated with the concept of formal deducibility in a (formal) system or the relativized concept of provability from certain axioms. Demonstrability is an epistemic concept: the rough idea is that a sentence is demonstrable if it is provable from knowable basic (“self-evident”) premises (...) by means of simple logical steps. A statement that is demonstrable is also knowable and a statement that is actually demonstrated is known to be true. By casting doubt upon apparently central principles governing the concept of demonstrability, the paradoxes of demonstrability presented here tend to undermine the concept itself—or at least our understanding of it. As long as we cannot find a diagnosis and a cure for the paradoxes, it seems that the coherence of the concepts of demonstrability and demonstrable knowledge are put in question. There are of course ways of putting the paradoxes in quarantine, for example by imposing a hierarchy of languages a` la Tarski, or a ramified hierarchy of propositions and propositional functions a` la Russell. These measures, however, helpful as they may be in avoiding contradictions, do not seem to solve the underlying conceptual problems. Although structurally similar to the semantic paradoxes, the paradoxes discussed in this paper involve epistemic notions: “demonstrability”, “knowability”, “knowledge”... These notions are “factive” (e.g., if A is demonstrable, then A is true), but similar paradoxes arise in connection with “nonfactive” notions like “believes”, “says”, “asserts”.3 There is no consensus in the literature concerning the analysis of the notions involved—often referred to as “propositional attitudes”—or concerning the treatment of the paradoxes they give rise to. (shrink)

One type of argument to sceptical paradox proceeds by making a case that a certain kind of metaphysically “heavyweight or “cornerstone” proposition is beyond all possible evidence and hence may not be known or justifiably believed. Crispin Wright has argued that we can concede that our acceptance of these propositions is evidentially risky and still remain rationally entitled to those of our ordinary knowledge claims that are seemingly threatened by that concession. A problem for Wright’s proposal is the so-called (...) Leaching worry: if we are merely rationally entitled to accept the cornerstones without evidence, how can we achieve evidence-based knowledge of the multitude of quotidian propositions that we think we know, which require the cornerstones to be true? This paper presents a rigorous, novel explication of this worry within a Bayesian framework, and offers the Entitlement theorist two distinct responses. (shrink)

Epistemic approaches towards understanding ultimate reality proceed chiefly via the rational, the empirical, and the fideistic way, each yielding a theological view consistent to the approach chosen. Rational theologies tend to be ultimately monist in nature, while empirical theologies are pluralistic, e.g. polytheism. Fideism has its dangers as well where blind faith only hampers scientific research. However, Indian philosophy has suggested few criteria for verifying a source of authoritative testimony. This dissertation investigates why an authentic revelation would solve the (...) ultimate clash between reason and experience. (shrink)

In this conceptual paper, the traditional conceptualization of sustainable entrepreneurship is challenged because of a fundamental tension between processes involved in sustainable development and processes involved in entrepreneurship: the concept of sustainable business models contains a paradox, because sustainability involves the reduction of information asymmetries, whereas entrepreneurship involves enhanced and secured levels of information asymmetries. We therefore propose a new and integrated theory of sustainable entrepreneurship that overcomes this paradox. The basic argument is that environmental problems have to (...) be conceptualized as wicked problems or sustainability-related ecosystem failures. Because all actors involved in the entrepreneurial process are characterized by their epistemic insufficiency regarding the solving of these problems, the role of information in the sustainable entrepreneurial process changes. On the one hand, the reduction of information asymmetries primarily aims to enable actors to become critical of sustainable entrepreneurs’ actual business models. On the other hand, the epistemic insufficiency of sustainable entrepreneurs guarantees that information asymmetries remain as a source of new sustainable business opportunities. Three further characteristics of sustainable entrepreneurs are distinguished: sustainability and entrepreneurship-related risk-taking; sustainability and entrepreneurship-related self-efficacy; and the development of satisficing and open-ended solutions, together with multiple stakeholders. (shrink)

Quine's holistic empiricist account of scientific inquiry can be characterized by three constitutive principles: *noncontradiction*, *universal revisability* and *pragmatic ordering*. We show that these constitutive principles cannot be regarded as statements within a holistic empiricist's scientific theory of the world. This claim is a corollary of our refutation of Katz's [1998, 2002] argument that holistic empiricism suffers from what he calls the Revisability Paradox. According to Katz, Quine's empiricism is incoherent because its constitutive principles cannot themselves be rationally revised. (...) Using Gärdenfors and Makinson's logic of belief revision based on epistemic entrenchment, we argue that Katz wrongly assumes that the constitutive principles are *statements* within a holistic empiricist's theory of the world. Instead, we show that constitutive principles are best seen as *properties* of a holistic empiricist's theory of scientific inquiry and we submit that, without Katz's mistaken assumption, the paradox cannot be formulated. We argue that our perspective on the status of constitutive principles is perfectly in line with Quinean orthodoxy. In conclusion, we compare our findings with van Fraassen's [2002] argument that we should think of empiricism as a stance, rather than as a doctrine. (shrink)

This paper considers two novel Bayesian responses to a well-known skeptical paradox. The paradox consists of three intuitions: first, given appropriate sense experience, we have justification for accepting the relevant proposition about the external world; second, we have justification for expanding the body of accepted propositions through known entailment; third, we do not have justification for accepting that we are not disembodied souls in an immaterial world deceived by an evil demon. The first response we consider rejects the (...) third intuition and proposes an explanation of why we have a faulty intuition. The second response, which we favor, accommodates all three intuitions; it reconciles the first and the third intuition by the dual component model of justification, and defends the second intuition by distinguishing two principles of epistemic closure. (shrink)

This paper intends to explain key differences between Aristotle’s understanding of the relationships between nous, epistêmê, and the art of syllogistic reasoning(both analytic and dialectical) and the corresponding modern conceptions of intuition, knowledge, and reason. By uncovering paradoxa that Aristotle’s understanding of syllogistic reasoning presents in relation to modern philosophical conceptions of logic and science, I highlight problems of a shift in modern philosophy—a shift that occurs most dramatically in the seventeenth century—toward a project of construction, a pervasive desire for (...) rational certainty, and a general insistence on the reducibility of the sciences. The major motivation of this analysis is my intention to show that modern attempts to reduce science/epistêmê to a single science/method of inquiry occlude dialectical and ethico-political dimensions of “reason” and, hence, also impoverish philosophy’s critical capacities. (shrink)

Harman’s lottery paradox, generalized by Vogel to a number of other cases, involves a curious pattern of intuitive knowledge ascriptions: certain propositions seem easier to know than various higher-probability propositions that are recognized to follow from them. For example, it seems easier to judge that someone knows his car is now on Avenue A, where he parked it an hour ago, than to judge that he knows that it is not the case that his car has been stolen and (...) driven away in the last hour. Contextualists have taken this pattern of intuitions as evidence that ‘knows’ does not always denote the same relationship; subject-sensitive invariantists have taken this pattern of intuitions as evidence that non-traditional factors such as practical interests figure in knowledge; still others have argued that the Harman Vogel pattern gives us a reason to abandon the principle that knowledge is closed under known entailment. This paper argues that there is a psychological explanation of the strange pattern of intuitions, grounded in the manner in which we shift between an automatic or heuristic mode of judgment and a controlled or systematic mode. Understanding the psychology behind the pattern of intuitions enables us to see that the pattern gives us no reason to abandon traditional intellectualist invariantism. The psychological account of the paradox also yields new resources for clarifying and defending the single premise closure principle for knowledge ascriptions. (shrink)

What is paradoxical about the Socratic paradoxes is that they are not paradoxical at all. Socrates famously argued that knowledge is sufficient for virtue and that no one errs willingly. Both doctrines are discussed in the Protagoras between Socrates and the Abderian sophist, however the argumentative line that Socrates chooses to follow in order to refute ‘the many’ has raised a serious degree of controversy among scholars. Is Socrates upholding the hedonistic view? Or, is he only trying to show the (...) bankruptcy of the explanation of akrasia as ‘being overcome by pleasure’ which ‘the many’ advocate? Socrates intends to do the latter, showing that this hedonistic explanation of akrasia leads to absurdity. Plato’s and Socrates’ identification of goodness with pleasure would mark a sudden and unexplained departure from their moral theories, and would render the Socratic denial of akrasia an argument with limited range –only for those assuming hedonism. If we are correct to hold that Socrates does not intend to identify the good with the pleasant, then we are immediately put against a new and much more difficult challenge; that is, to suggest how the Socratic denial of akrasia could regain its catholic plausibility against the commonsensical stance to akrasia, namely that people act against their best judgment due to their impotence to resist to motivational forces such as pleasure, pain, fear, passion and love. Socrates does not offer any other explicit account –apart from the hedonistic one- of how his doctrine could be catholically defended; hence the task of decoding the Socratic line of thought is far from an easy one. The key move in order to decode the puzzling Socratic doctrine is to understand how Socrates treats the notion of ‘knowledge’. For Socrates, moral knowledge is distinguished from mere belief; in this sense, only knowledge has the commanding power which enables one to sustain his best evaluative judgment against other motivational forces and only knowledge is sufficient for the virtuous conduct. By contrast, as mere belief is susceptible to other motivational forces like pleasure, pain, fear, etc. its possessor will, in turn, be susceptible to the revision of his intentions which derive from his best value judgment. In the Protagoras, Socrates implies that intentions grounded on belief can be ‘dragged around’ by desire; and according to my view in this paper, this Socratic stance allows a non-epistemic interpretation of his thesis. According to the traditional epistemic interpretation of the Socratic denial of akrasia, one’s wrongdoing is always a miscalculation that takes place on his practical syllogism. However, my understanding of the Socratic denial of akrasia allows cases of one even going against his best judgment, when his judgment is based on belief. In that sense, a judgment grounded on belief has insufficient power to guarantee that the chosen action will follow, whereas only judgments grounded on knowledge have a commanding and lordly power. For Socrates, everyone always goes for the good but only those with knowledge can infallibly discover and act on the good. Those with mere belief can only reach an apparent good, which may be good or bad. The motivation for the good is not unshakeable for those with mere belief since the grounding of their belief is scarcely strong enough to hold on the correct intention. Socrates therefore holds that the grounding of knowledge influences the motivational state of the moral agent. Thereupon, my interpretation differs from others in suggesting that for Socrates not all the cases of akrasia are cognitive mistakes in their judgment. Rather I hold, in opposition to the received stance on akrasia, that Socrates allows that one could act against his best judgment, when the latter is grounded on mere belief. (shrink)

A dynamic epistemic logic is presented in which the single agent can reason about his knowledge stages before and after announcements. The logic is generated by reinterpreting multi agent private announcements in a single agent environment. It is shown that a knowability principle is valid for such logic: any initially true ϕ can be known after a certain number of announcements.

In this paper, I start by describing and examining the main results about the option of formalizing the Yablo Paradox in arithmetic. As it is known, although it is natural to assume that there is a right representation of that paradox in first order arithmetic, there are some technical results that give rise to doubts about this possibility. Then, I present some arguments that have challenged that Yablo’s construction is non-circular. Just like that, Priest (1997) has argued that (...) such formalization shows that Yablo’s Paradox involves implicit circularity. In the same direction, Beall (2001) has introduced epistemic factors in this discussion. Even more, Priest has also argued that the introduction of infinitary reasoning would be of little help. Finally, one could reject definitions of circularity in term of fixed-point adopting non-well-founded set theory. Then, one could hold that the Yablo paradox and the Liar paradox share the same non-well-founded structure. So, if the latter is circular, the first is too. In all such cases, I survey Cook’s approach (2006, forthcoming) on those arguments for the charge of circularity. In the end, I present my position and summarize the discussion involved in this volume. En este artículo, describo y examino los principales resultados vinculados a la formalización de la paradoja de Yablo en la aritmética. Aunque es natural suponer que hay una representación correcta de la paradoja en la aritmética de primer orden, hay algunos resultados técnicos que hacen surgir dudas acerca de esta posibilidad. Más aún, presento algunos argumentos que han cuestionado que la construcción de Yablo no sea circular. Así, Priest (1997) ha argumentado que la formalización de la paradoja de Yablo en la aritmética de primer orden muestra que la misma involucra implícitamente circularidad. En la misma dirección, Beall (2001) ha introducido factores epistémicos en esta discusión. Más aún, Priest ha también argumentado que la introducción de razonamiento infinitario como complemento de la formalización en la aritmética sería de poca ayuda. Finalmente, se podría rechazar todo intento de dar definiciones de circularidad en términos de puntos fijos adoptando teoría de conjuntos infundados. Entonces, se podría sostener que la paradoja de Yablo y la del mentiroso comparten la misma estructura infundada. Por eso, si la última es circular, también lo es la primera. En todos los casos, presento el enfoque de Roy Cook (2006, en prensa) sobre estos argumentos que atribuyen circularidad a la construcción de Yablo. En el final, presento mi posición y un breve resumen de la discusión involucrada en este volumen. (shrink)

Wittgenstein's paradoxical theses that unproved propositions are meaningless, proofs form new concepts and rules, and contradictions are of limited concern, led to a variety of interpretations, most of them centered on rule-following skepticism. We argue, with the help of C. S. Peirce's distinction between corollarial and theorematic proofs, that his intuitions are better explained by resistance to what we call conceptual omniscience, treating meaning as fixed content specified in advance. We interpret the distinction in the context of modern epistemic (...) logic and semantic information theory, and show how removing conceptual omniscience helps resolve Wittgenstein's paradoxes and explain the puzzle of deduction, its ability to generate new knowledge and meaning. (shrink)

To resolve the lottery paradox, the “no-justification account” proposes that one is not justified in believing that one's lottery ticket is a loser. The no-justification account commits to what I call “the Harman-style skepticism”. In reply, proponents of the no-justification account typically downplay the Harman-style skepticism. In this paper, I argue that the no-justification reply to the Harman-style skepticism is untenable. Moreover, I argue that the no-justification account is epistemically ad hoc. My arguments are based on a rather surprising (...) finding that the no-justification account implies that people living in Taiwan typically suffer from the Harman-style skepticism. (shrink)

In this essay I defend a solution to a skeptical paradox. The paradox I focus on concerns epistemic justification (rather than knowledge), and skeptical scenarios that entail that most of our ordinary beliefs about the external world are false. This familiar skeptical paradox hinges on a “closure” principle. The solution is to restrict closure, despite its first appearing as a fully general principle, so that it can no longer give rise to the paradox. This has (...) some extra advantages. First, it suggests a general strategy that provides solutions to other versions of the paradox, not just those that depend on closure. Second, it clarifies the relation between the paradox and other kinds of skeptical problem. (shrink)

According to the permissibility solution to the lottery paradox, the paradox can be solved if we conceive of epistemic justification as a species of permissibility. Clayton Littlejohn has objected that the permissibility solution draws on a sufficient condition for permissible belief that has implausible consequences and that the solution conflicts with our lack of knowledge that a given lottery ticket will lose. The paper defends the permissibility solution against Littlejohn's objections.

Assuming that a paralogism is an unintentionally invalid reasoning, we give an exampli.

A sorites argument is a symptom of the vagueness of the predicate with which it is constructed. A vague predicate admits of at least one dimension of variation (and typically more than one) in its intended range along which we are at a loss when to say the predicate ceases to apply, though we start out confident that it does. It is this feature of them that the sorites arguments exploit. Exactly how is part of the subject of this paper. (...) The majority of philosophers writing on vagueness take it to be a kind of semantic phenomenon. If we are right, they are correct in this assumption, which is surely the default position, but they have not so far provided a satisfactory account of the implications of this or a satisfactory diagnosis of the sorites arguments. Other philosophers have urged more exotic responses, which range from the view that the fault lies not in our language, but in the world, which they propose to be populated with vague objects which our semantics precisely reflects, to the view that the world and language are both perfectly in order, but that the fault lies with our knowledge of the properties of the words we use (epistemicism). In contrast to the exotica to which some philosophers have found themselves driven in an attempt to respond to the sorites puzzles, we undertake a defense of the commonsense view that vague terms are semantically vague. Our strategy is to take fresh look at the phenomenon of vagueness. Rather than attempting to adjudicate between different extant theories, we begin with certain pre-theoretic intuitions about vague terms, and a default position on classical logic. The aim is to see whether (i) a natural story can be told which will explain the vagueness phenomenon and the puzzling nature of soritical arguments, and, in the course of this, to see whether (ii) there arises any compelling pressure to give up the natural stance. We conclude that there is a simple and natural story to be told, and we tell it, and that there is no good reason to abandon our intuitively compelling starting point. The importance of the strategy lies in its dialectical structure. Not all positions on vagueness are on a par. Some are so incredible that even their defenders think of them as positions of last resort, positions to which we must be driven by the power of philosophical argument. We aim to show that there is no pressure to adopt these incredible positions, obviating the need to respond to them directly. If we are right, semantic vagueness is neither surprising, nor threatening. It provides no reason to suppose that the logic of natural languages is not classical or to give up any independently plausible principle of bivalence. Properly understood, it provides us with a satisfying diagnosis of the sorites argumentation. It would be rash to claim to have any completely novel view about a topic so well worked as vagueness. But we believe that the subject, though ancient, still retains its power to inform and challenge us. In particular, we will argue that taking seriously the central phenomenon of predicate vagueness—the “boundarylessness” of vague predicates—on the commonsense assumption that vagueness is semantic, leads ineluctably to the view that no sentences containing vague expressions (henceforth ‘vague sentences’) are truth-evaluable. This runs counter to much of the literature on vagueness, which commonly assumes that, though some applications of vague predicates to objects fail to be truth-evaluable, in clear positive and negative cases vague sentences are unproblematically true or false. It is clarity on this, and related points, that removes the puzzles associated with vagueness, and helps us to a satisfying diagnosis of why the sorites arguments both seem compelling and yet so obviously a bit of trickery. We give a proof that semantically vague predicates neither apply nor fail-to-apply to anything, and that consequently it is a mistake to diagnose sorites arguments, as is commonly done, by attempting to locate in them a false premise. Sorites arguments are not sound, but not unsound either. We offer an explanation of their appeal, and defend our position against a variety of worries that might arise about it. The plan of the paper is as follows. We first introduce an important distinction in terms of which we characterize what has gone wrong with vague predicates. We characterize what we believe to be our natural starting point in thinking about the phenomenon of vagueness, from which only a powerful argument should move us, and then trace out the consequences of accepting this starting point. We consider the charge that among the consequences of semantic vagueness are that we must give up classical logic and the principle of bivalence, which has figured prominently in arguments for epistemicism. We argue there are no such consequences of our view: neither the view that the logic of natural languages is classical, nor any plausible principle of bivalence, need be given up. Next, we offer a diagnosis of what has gone wrong in sorites arguments on the basis of our account. We then present an argument to show that our account must be accepted on pain of embracing (in one way or another) the epistemic view of “vagueness”, i.e., of denying that there are any semantically vague terms at all. Next, we discuss some worries that may arise about the intelligibility of our linguistic practices if our account is correct. We argue none of these worries should force us from our intuitive starting point. Finally, we cast a quick glance at other forms of semantic incompleteness. (shrink)

The sciences occasionally generate discoveries that undermine their own assumptions. Two such discoveries are characterized here: the discovery of apophenia by cognitive psychology and the discovery that physical systems cannot be locally bounded within quantum theory. It is shown that such discoveries have a common structure and that this common structure is an instance of Priest’s well-known Inclosure Schema. This demonstrates that science itself is dialetheic: it generates limit paradoxes. How science proceeds despite this fact is briefly discussed, as is (...) the connection between our results and the realism-antirealism debate. We conclude by suggesting a position of epistemic modesty. (shrink)