Epistemic Paradoxes

This work examines the structure of paradoxes, phenomena characterized by the apparent derivation of contradictions or counter-intuitive conclusions from acceptable premises using acceptable reasoning. Motivated by the recurrence of certain features across diverse paradoxes, a specific structural hypothesis regarding their generation is proposed and analyzed. The hypothesis posits that paradoxes frequently arise from the interaction of three components: (1) concepts that establish or interact with boundaries (such as those pertaining to scope, classification, truth, state, or definition); (2) the reflexive application (...) of these concepts or related rules (involving self-reference, self-inclusion, recursion, or causal/definitional circularity); and (3) the involvement of specific operational triggers – negation, limit (including infinity, extremes, or boundary values), or transformation (change of state, identity, position, or logical status) – within the reflexive structure. The study first provides a detailed conceptual analysis of these components – boundaries, reflexivity, and the triggers – outlining their definitions and potential roles based on discussions in logic, philosophy, and related fields. Subsequently, the hypothesis is examined against a wide range of paradoxes drawn from logic, set theory, semantics, physics, metaphysics, epistemology, and decision theory. This examination involves analyzing the structure of each paradox to identify the presence and interaction of the hypothesized components. The analysis indicated a recurrent correspondence between the structures of the examined paradoxes and the proposed pattern involving boundaries, reflexivity, and triggers. Further analysis explored the representation of this structural pattern using elements of logical and mathematical formalism, sketching how the interaction of boundary predicates/sets, reflexive constructions, and operators corresponding to negation, limits, or transformations can lead to derivations of inconsistency (e.g., P ↔ ¬P or P ∧ ¬P) within systems adhering to standard logical principles. The discussion also addressed the context and limitations surrounding the hypothesis, including the meaning of "often arise," the relationship between the identified structure and strategies for paradox resolution (which often involve modifying the system to restrict or manage components of the pattern), the distinction between the structure and its outcome in different systems, and the acknowledgment that the pattern may not be the sole source of all paradoxes and that its identification can involve interpretation. Finally, potential implications arising from the identification of this recurring structure were considered. These include the possibility of providing a unifying framework for paradox analysis across disciplines, offering insights relevant to the design of consistent conceptual and formal systems by highlighting potential points of instability, suggesting connections between the structure and characteristics of natural language or thought involving self-reference and boundary definition, and noting structural resonances with limitative results in mathematical logic, such as Gödel's incompleteness theorems. Potential directions for future work, including further categorization, analysis of non-paradoxical structures, cross-disciplinary applications, and exploration of cognitive aspects, were also outlined. (shrink)

One influential response to apparent higher-order dilemmas implies that agents can rationally both believe p on the basis of their evidence and simultaneously believe that their evidence does not support believing p. This possibility of rational epistemic akrasia seems to call into question the Enkratic Requirement, which prohibits believing a proposition p according to one’s lower-level evidence, while believing that one’s lower-level evidence does not support believing p. In this chapter, we explore two ways to defend the Enkratic Requirement. First, (...) evidentialists about epistemic justification are committed to holding that an ex post (or doxastically) justified belief, as part and parcel of being ex post justified, is accompanied by a corresponding higher-order belief that the first-order belief is supported by the evidence. In a dilemma case, this higher-order belief comes into direct rational conflict with the subject’s other higher-order belief, that her evidence does not support the belief – so the subject has contradictory beliefs. In this way, the so-called ‘level-splitting’ strategy for the claim that being akratic is not per se irrational is called into question. Our second argument for the Enkratic Requirement presupposes normativism about belief and appeals to the conditions of having epistemically permissible beliefs. We sketch an argument starting from an influential view about the normativity of belief: that irrational beliefs are impermissible beliefs. From this claim, together with some widely held as-sumptions about the notion of rationality, we show that agents who display akratic combi-nations of attitudes hold impermissible beliefs. (shrink)

A whole text constituted by sentence parts is given verisimilitude as a whole IF verisimilitude constitutes utility AND utility implicates assigning a degree of significance to each sentence---such that its false sentences are semantically insignificant and true significant. Therefore there must be a literary-theoretic, in the most GENERAL sense, criterion for the text such that the significant sentences constitute semantic (truth-theoretic) content and insignificant sentences aesthetic forms which do not communicate their own sentential content but as communicative catalysis of the (...) semantic content by appealing to evocative emotive preparatory features. Then semantically insignificant sentences are not false but rather serve only poetic function in terms of Russian Formalism. If there is nothing outside text BUT there is more to text than just sentential content, text is the slippage of non-countable mental content into the abyss of countable sentential content. Textual retrieval is possible by attribution of literary functions. (shrink)

Whereas many philosophers accept the validity of 'probability' and confine themselves to interpreting it, this paper challenges its conceptual coherence by critically examining its use in the empirical world. While measure theory provides a rigorous mathematical framework for manipulating probability functions, we argue that applying precise probability measures to empirically uncertain outcomes introduces a fundamental contradiction. Probability measures claim to quantify uncertainty while simultaneously implying a degree of understanding about events that we do not fully possess. This inconsistency undermines the (...) idea that probability offers objective or reliable insights into reality. Moreover, we argue that it is impossible to assign a correct probability in the empirical world—neither deduction nor induction provides a justifiable basis for doing so. Therefore, despite probability appearing to work as a practical tool for managing uncertainty, its theoretical foundation collapses under scrutiny in empirical applications. (shrink)

The sentences ‘p but I don’t believe p’ (omissive form) and ‘p but I believe that not-p’ (comissive form) are typical examples of Moore’s paradox. When an agent (sincerely) asserts such sentences under normal circumstances, we consider his statements absurd. The Simple Solution (Moore, Heal, Wolgast, Kriegel, et al.) finds the source of absurdity for such statements in a certain formal contradiction (some kind of like ‘p & not-p’), the presence of which is lexically disguised. This solution is facing criticism (...) since it is obvious that the denial of the contradiction allegedly hidden in Moore’s paradox will not become an expression of tautology for us. Hintikka offers another solution to Moore’s paradox. In his view, the source of absurdity is the practical inconceivability of the situation, in which the agent would be able to hold mutually incompatible (inconsistent) beliefs. The sentences ‘p but I don’t believe that p’ and ‘p but I believe that not-p’ sound absurd because they express high-ordered beliefs that no rational agent can hold. A belief expressed in the sentence ‘he believes that p’, in order to be available to the agent, must be compatible with the truth of everything the agent believes. The problem with Hintikka’s solution is that it relies on an epistemic principle that does not correspond to our general intuitions about the notion of belief. According to this principle, there must be a close connection between the sentence ‘p but I don’t believe that p’ and the sentence ‘I believe that is the case is that p but I don’t believe that p’. However, it is not difficult to imagine the context for situations when the agent asserts the sentence ‘p but I don’t believe that p’ when s/he believes that p, but in parallel does not hold any high-ordered belief about his/her belief in p. For example, the agent does not recognize oneself in a photograph after a hard plastic surgery, and when one asks him ‘who is this?’ it would not be absurd for him/her to accept the following description of his/her beliefs ‘I believe that {I am me} but I don’t believe that I believe that {I am me}’. Wittgenstein provides an alternative solution based on a descriptive analysis of the grammar of verbs we use to express, attribute, and understand each other’s psychological states. In his view, the everyday practice of using the verb ‘believe’ demonstrates a characteristic asymmetry in the semantic and logical properties of the usage of this verb in the first person. The expression ‘I believe falsely’ has no real meaning since no one can meaningfully say the sentence ‘Now I believe falsely that p’ on their own behalf. Therefore, the genuine source of absurdity is associated with situations of self-attribution of false belief by the agent. Despite its originality, Wittgenstein’s solution faces objections. For example, in a certain context, it would not be absurd to assert the sentence ‘There are no beliefs, but I don’t believe in it’, unlike the sentence ‘There are no beliefs and I believe that it is so’. The solution proposed by Wittgenstein does not allow us to correct the situation since one could assert quite reasonably and without any absurdity a sentence like ‘In fact, there are no beliefs and now I falsely believe that it is so’. Based on Evans’ principle of epistemic transparency, some researchers (Atlas, Chan, Kwon, et al.) offer another strategy for solving Moore’s paradox, in which peculiar attention is paid to the dependence of understanding and evaluating the meaning of the sentences ‘p but I do not believe that p’ and ‘p but I believe that not-p’ from the immediate context of their usage. The source of absurdity should be looked for in the established practice of the self-referential use of the pronoun ‘I’. In the researchers’ view, Moore’s paradox arises only in the context of situations where the agent asserting such sentences is conscious speaking about oneself. Therefore, there is an obvious structural analogy between the sentences of the Liar family (‘This very sentence is false’, ‘Now I am lying’, etc.) and Moore’s paradox (‘p but I don’t believe that p’, ‘p but I believe that not-p’) – self-reference is constitutive for both families of paradoxical statements. (shrink)

Some theories of rational belief assume that beliefs should be closed under conjunction. I motivate the rejection of the conjunction closure, and point out that the consequences of this rejection are not as severe as it is usually thought. An often raised objection is that without the conjunction closure people are unable to reason. I outline an approach in which we can – in usual cases – reason using conjunctions without accepting the closure in its whole generality. This solution is (...) based on the notion of confidence levels, which can be defined using probabilities. Moreover, on this approach, reasoning has a scalable computational complexity adaptable to cognitive abilities of both rationally bounded and perfectly rational agents. I perform a simulation to assess its error rate, and compare it to reasoning with conjunction closure. (shrink)

I will explore the paradoxical nature of epistemic access. By critiquing the traditional conception of mental states that are labelled as ’knowledge’, I demonstrate the susceptibility of these states to an infinite regress, thus, challenging their existence and validity. I scrutinise the assumption that an epistemic agent can have complete epistemic access to all facts about a given object while simultaneously being ignorant of certain truths that impact the very knowledge claims about the object. I further analyse the implications of (...) this paradox when attempting to fine-grain the parameters of epistemic access, which happens to reveal the vacuity of such definitions and the inevitability of the regress. (shrink)

The proof paradox results from conflicting intuitions concerning different types of fallible evidence in a court of law. We accept fallible individual evidence but reject fallible statistical evidence even when the conditional probability that the defendant is guilty given the evidence is the same, a seeming inconsistency. This paper defends a solution to the proof paradox, building on a sensitivity account of checking and settling a question. The proposed sensitivity account of legal proof not only requires sensitivity simpliciter but sensitivity (...) of each relevant step of the proof procedure and/or sensitivity concerning all relevant alternatives. This account avoids problems that have been identified for other sensitivity views of legal proof. Moreover, it is argued that sensitivity, rather than safety, is the crucial modal condition for legal proof. It is, finally, shown that the provided account can fruitfully support very different existing views on the relationship between knowledge and legal proof. (shrink)

This paper generalizes the preface paradox beyond the conjunctive aggregation of beliefs and constructs an analogous paradox for deontic reasoning. The analysis of the deontic case suggests a systematic restriction of intuitive rules for reasoning with obligations. This proposal can be transferred to the epistemic case: it avoids the preface and the lottery paradox and saves one of the two directions of the Lockean Thesis (i.e., high credence is sufficient, but not necessary for rational belief). The resulting account compares favorably (...) to competing proposals; in particular, we can formulate the rules of correct doxastic reasoning without reference to probabilistic features of the involved propositions. (shrink)

The essay aims to discuss a global skepticism about epistemic justification called Agrippa's Trilemma. Based on its exposition, the article will deal with the infinitist alternative of justification, traditional foundationalism and the hypothesis of the infallibility of introspection. It concludes that introspection beliefs are not verifiable propositional attitudes, representing an advantage to the infinitist theory. Keywords: Skepticism; Infinitism; Agrippa’s Trilemma; Epistemic Justification.

Despite having been solved numerous times, the surprise quiz paradox persists in the intellectual imagination as a riddle. This dialogue aims to dispel the fallacies of the paradox in an intuitive way through the causal format of a dialogue. Along the way, two contributions are made to the literature. Even if the student knew there would be a quiz at the end of a quizless Thursday, the fact that the quiz will be a surprise Friday would provide a Gettier-style defeater (...) for his supposed knowledge that he will have a quiz Friday. In addition, pace Sorensen (1988), the dialogue explains why the temporal retention of knowledge is essential to the puzzle and not a mere accident. (shrink)

This is an opinionated guide to the literature on epistemic dilemmas. It discusses seven kinds of situations where epistemic dilemmas appear to arise; dilemmic, dilemmish, and non-dilemmic takes on them; and objections to dilemmic views along with dilemmist’s replies to them.

There are many ways in which a speaker can confuse their audience. In this paper, I will focus on one such way, namely, a way of talking that seems to manifest a cross-level kind of cognitive dissonance on the part of the speaker. The goal of the paper is to explain why such ways of talking sound so twisted. The explanation is two-pronged, since their twisted nature may come either from the very mental states that the speaker thereby makes manifest, (...) or from how the speaker chooses to express themselves (even if there is nothing wrong with their mental states). So-called ‘Moore-paradoxical’ utterances are but one example of the phenomenon, and the explanation of what is wrong about them is subsumed under a more general explanation here—one that captures also the twisted-ness of utterances whereby questions are raised or intentions expressed. (shrink)

This research explores the incorporation of narrative perspectives in economics as a social science and its implications for rethinking epistemology. By examining the role of narratives in economic analysis, the study highlights the advantages of narratives in providing contextualized accounts of human experiences, connecting economic concepts to real-world phenomena, and exploring diverse perspectives. It emphasizes the importance of interdisciplinary collaboration between philosophers, economists, and social scientists to gain a comprehensive understanding of narratives' influence on economic decision-making, market dynamics, and consumer (...) behaviour. The research suggests that narratives offer a means to challenge the notion of a single, objective truth and contribute to a more inclusive and robust framework for analyzing economic phenomena. The implications extend beyond economics, urging a broader perspective on epistemology by embracing narrative perspectives and engaging in interdisciplinary collaboration across disciplines. Overall, this research calls for a rethinking of epistemology, recognising the significance of narratives and their role in knowledge production. (shrink)

I offer a new, limited solution to divine hiddenness based on a particular epistemic paradox: sometimes, knowing about a desired outcome or relevant features of that desired outcome would prevent the outcome in question from occurring. I call these cases epistemically self-defeating situations. This solution, in essence, says that divine hiddenness or silence is a necessary feature of at least some morally excellent or desirable states of affairs. Given the nature of the paradox, an omniscient being cannot completely eliminate hiddenness, (...) just as an omnipotent being cannot create a rock so heavy that they cannot lift it. Epistemically self-defeating situations provide an undercutting defeater for the assumption that any nonresistant nonbeliever could always, at any time, be in conscious relationship with a perfectly loving God. Thankfully, silence is a temporary feature of epistemically self-defeating situations: once the outcome is achieved, agents can know in full. (shrink)

Self-verifying judgments like _I exist_ seem rational, and self-defeating ones like _It will rain, but I don’t believe it will rain_ seem irrational_._ But one’s evidence might support a self-defeating judgment, and fail to support a self-verifying one. This paper explains how it can be rational to defy one’s evidence if judgment is construed as a mental performance or act, akin to inner assertion. The explanation comes at significant cost, however. Instead of causing or constituting beliefs, judgments turn out to (...) be mere epiphenomena, and self-verification and self-defeat lack the broader philosophical import often claimed for them. (shrink)

Maimonides looks for the true axiom for a demonstration of the existence of God, and he finds it in the universal fact of movement. His logical argumentation is as follows: given the hypothesis of the eternity of the Universe, of its eternal movement, if we can think of a First Mover, that Mover has all the characteristics of the First Principle according to Aristotle; the characteristics of eternity and to be essentially moving. Maimonides' contribution to the Aristotelian theory of the (...) First Principle is precisely the crossing of the invisible barrier between the physical proof of the First Mover and the metaphysical proof of the First Principle. By transforming Aristotle's corollary into the postulate that supports the whole proof, Maimonides avoids the aporia of the First Principle being confused with the First Mover. But setting a postulate, that is, a proposition whose opposite is equally possible, at the foundations of the theory, transforms what was meant to be "a true and indubitable proof" into a scientific theory in the modern sense of the term: a theory that can be accepted as true only regarding certain parameters or system of propositions. If there was creation of the world in time, then no doubt there is a Creator. If the world is eternally moving, then it has a Mover that is essentially moving, incorporeal, one and eternal itself, namely the divinity. (shrink)

In a fair, infinite lottery, it is possible to conclude that drawing a number divisible by four is strictly less likely than drawing an even number; and, with apparently equal cogency, that drawing a number divisible by four is equally as likely as drawing an even number.

Fitch's Paradox and the Paradox of the Knower both make use of the Factivity Principle. The latter also makes use of a second principle, namely the Knowledge-of-Factivity Principle. Both the principle of factivity and the knowledge thereof have been the subject of various discussions, often in conjunction with a third principle known as Closure. In this paper, we examine the well-known Surprise Examination paradox considering both the principles on which this paradox rests and some formal characterisations of the surprise notion, (...) crucial in this paradox. Standard formalizations of the Surprise Examination paradox in modal logic do not seem, at first glance, to depend on either factivity or knowledge-of-factivity, but we will argue that both factivity and knowledge-of-factivity play a key implicit role in the paradox. Namely, they are implicitly, perhaps unintentionally, used in order to simplify the definition of surprise. We analyze modal logical formalizations of three versions of the paradox concluding that the Surprise Examination paradox is the result of two flaws: the assumption of knowledge-of-factivity, and the over-simplification of the definition of "surprise" accordingly. By fixing these two flaws, the Surprise Examination paradox vanishes. (shrink)

One challenge for cognitive, evolutionary and anthropological studies of religion is to offer descriptions and explanatory models of the morphology and functions of supernatural dreaming, and of the religiosity, use of experience, and cultural transmission that are associated with these representations. The anthropological and religious studies literature demonstrates that dreaming, dream experience and narrative are connected with religious ideas and practices in traditional societies. Scholars have even proposed that dreaming is a primary source of religious beliefs and practice. Using Barrett’s (...) coding system, we measured a high frequency of minimally counterintuitive dream content among Hindu Nepalese, and we aim to quantify the relation between counterintuitive imagery and reported likelihood to communicate dreams in general and to religious experts, the relation between counterintuitive imagery and reported religiosity, and the proclivity to communicate SA dreams among those who are more or less religious. These aims will then be related to the broader topic of possible explanatory value of DPSR theory, or versions thereof, by framing the issue at the level of cultural transmission, religiosity and credibility of religious dream representations in relation to MCI theory. The article mainly draws upon data from ethnographic research among Hindu Nepalese. (shrink)

I show that the Lottery Paradox is just a version of the Sorites, and argue that this should modify our way of looking at the Paradox itself. In particular, I focus on what I call “the Cut-off Point Problem” and contend that this problem, well known by Sorites scholars, ought to play a key role in the debate on Kyburg’s puzzle. Very briefly, I show that, in the Lottery Paradox, the premises “ticket n°1 will lose”, “ticket n°2 will lose”… “ticket (...) n°1000 will lose” are equivalent to soritical premises of the form “~(the winning ticket is in {…, (tn)}) ⊃ ~(the winning ticket is in {…, tn, (tn + 1)})” (where “⊃” is the material conditional, “~” is the negation symbol, “tn” and “tn + 1” are “ticket n°n” and “ticket n°n + 1” respectively, and “{}” identify the elements of the lottery tickets’ set. The brackets in “(tn)” and “(tn + 1)” are meant to point out that in the antecedent of the conditional we do not always have a “tn” (and, as a result, a “tn + 1” in the consequent): consider the conditional “~(the winning ticket is in {}) ⊃ ~(the winning ticket is in {t1})”). As a result, failing to believe, for some ticket, that it will lose comes down to introducing a cut-off point in a chain of soritical premises. In this paper I explore the consequences of the different ways of blocking the Lottery Paradox with respect to the Cut-off Point Problem. A heap variant of the Lottery Paradox is especially relevant for evaluating the different solutions. One important result is that the most popular way out of the puzzle, i.e., denying the Lockean Thesis, becomes less attractive. Moreover, I show that, along with the debate on whether rational belief is closed under classical logic, the debate on the validity of modus ponens should play an important role in discussions on the Lottery 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.

In this paper, I present an outline of a paradox which is a variation on the lottery paradox and concerns whether we can ignore hesitant moral judgments.

Cognitive scientists claim to have discovered a large number of cognitive biases, which have a tendency to mislead reasoners. Might cognitive scientists themselves be subject to the very biases they purport to discover? And how should this alter the way they evaluate their research as evidence for the existence of these biases? In this paper, we posit a new paradox (the ‘Self-Reflexive Bias Paradox’), which bears a striking resemblance to some classical logical paradoxes. Suppose that research R appears to be (...) good evidence for the existence of bias B, but if B exists, then R would have been subject to B. Thus, it seems sensible for the researcher to reject R as good evidence for the existence of B. However, rejecting R for this reason admits the existence of B. We examine four putative cognitive biases and criticisms of them, each of which seem to be subject to self-reflexivity. In two cases, we argue, paradox is avoidable. In the remaining two, we cannot find a way to avoid the paradox, which poses a practical obstacle to scientific inquiry and results in an intriguing theoretical quandary. (shrink)

There is a very plausible principle linking abilities and possibilities: If S is able to Φ, then it is metaphysically possible that S Φ’s. Jack Spencer recently proposed a class of counterexamples to this principle involving the ability to know certain propositions. I renew an argument against these counterexamples based on the unknowability of Fitch propositions. In doing so, I provide a new argument for the unknowability of Fitch propositions and show that Spencer’s counterexamples are in tension with a principle (...) weaker than the one linking abilities and possibilities. (shrink)

A question, long discussed by legal scholars, has recently provoked a considerable amount of philosophical attention: ‘Is it ever appropriate to base a legal verdict on statistical evidence alone?’ Many philosophers who have considered this question reject legal reliance on bare statistics, even when the odds of error are extremely low. This paper develops a puzzle for the dominant theories concerning why we should eschew bare statistics. Namely, there seem to be compelling scenarios in which there are multiple sources of (...) incriminating statistical evidence. As we conjoin together different types of statistical evidence, it becomes increasingly incredible to suppose that a positive verdict would be impermissible. I suggest that none of the dominant views in the literature can easily accommodate such cases, and close by offering a diagnosis of my own. (shrink)

The paper explores applications of Kripke's theory of truth to semantics for anti-luck epistemology, that is, to subjunctive theories of knowledge. Subjunctive theories put forward modal or subjunctive conditions to rule out knowledge by mere luck as to be found in Gettier-style counterexamples to the analysis of knowledge as justified true belief. Because of the subjunctive nature of these conditions the resulting semantics turns out to be non-monotone, even if it is based on non-classical evaluation schemes such as strong Kleene (...) or FDE. This blocks the usual road to fixed-point results for Kripke's theory of truth within these semantics and consequently the paper is predominantly an exploration of fixed point results for Kripke's theory of truth within non-monotone semantics. Using the theory of quasi-inductive definitions we show that in case of the subjunctive theories of knowledge the so-called Kripke jump will have fixed points despite the non-monotonicity of the semantics: Kripke's theory of truth can be successfully applied in the framework of subjunctive theories of knowledge. (shrink)

This paper is about the alethic aspect of epistemic rationality. The most common approaches to this aspect are either normative (what a reasoner ought to/may believe?) or evaluative (how rational is a reasoner?), where the evaluative approaches are usually comparative (one reasoner is assessed compared to another). These approaches often present problems with blindspots. For example, ought a reasoner to believe a currently true blindspot? Is she permitted to? Consequently, these approaches often fail in describing a situation of alethic maximality, (...) where a reasoner fulfills all the alethic norms and could be used as a standard of rationality (as they are, in fact, used in some of these approaches). I propose a function α, which accepts a set of beliefs as inputand returns a numeric alethic value. Then I use this function to define a notion of alethic maximality that is satisfiable by finite reasoners (reasoners with cognitive limitations) and does not present problems with blindspots. Function α may also be used in alethic norms and evaluation methods (comparative and non-comparative) that may be applied to finite reasoners and do not present problems with blindspots. A result of this investigation isthat the project of providing purely alethic norms is defective. The use of function α also sheds light on important epistemological issues, such as the lottery and the preface paradoxes, and the principles of clutter avoidance and reflection. (shrink)

When a belief is self-fulfilling, having it guarantees its truth. When a belief is self-defeating, having it guarantees its falsity. These are the cases of “self-impacting” beliefs to be examined below. Scenarios of self-defeating beliefs can yield apparently dilemmatic situations in which we seem to lack sufficient reason to have any belief whatsoever. Scenarios of self-fulfilling beliefs can yield apparently dilemmatic situations in which we seem to lack reason to have any one belief over another. Both scenarios have been used (...) independently to challenge Evidentialism, on which what we may rationally believe is all and only what fits our current evidence. Here we tie the two scenarios together and explore what a knowledge-sensitive evidentialist approach to one implies for the other. (shrink)

Recent years have seen fresh impetus brought to debates about the proper role of statistical evidence in the law. Recent work largely centres on a set of puzzles known as the ‘proof paradox’. While these puzzles may initially seem academic, they have important ramifications for the law: raising key conceptual questions about legal proof, and practical questions about DNA evidence. This article introduces the proof paradox, why we should care about it, and new work attempting to resolve it.

Before the semester begins, a teacher tells his students: “There will be exactly one exam this semester. It will not take place on a day that is an immediate-successor of a day that you are currently in a position to know is not the exam-day”. Both the students and the teacher know – it is common knowledge – that no exam can be given on the first day of the semester. Since the teacher is truthful and reliable, it seems that (...) the students can know that what he says is true. However, in that case, assuming the students can know that they know whatever it is they know (KK) and assuming their knowledge is closed under entailment (closure), the students can reason from what they know to the conclusion that no exam will take place during the semester. This conclusion contradicts what they supposedly know: that there will be an exam. This puzzle, we argue, gives rise to a new consideration for the rejection of KK. We discuss unique features of the argument, especially in comparison to Timothy Williamson's rejection of KK in light of other versions of the surprise exam paradox. (shrink)

In virtue of Fitch-Church proof, also known as the knowability paradox, we are able to prove that if everything is knowable, then everything is known. I present two ‘onto-theological’ versions of the proof, one concerning collective omniscience and another concerning omnificence. I claim these arguments suggest new ways of exploring the intersection between logical and ontological givens that is a grounding theme of religious thought. What is more, they are good examples of what I call semi-paradoxes: apparently sound arguments whose (...) conclusion is not properly unacceptable, but simply arguable. (shrink)

Abstract: Using a critical review of the literature, we study a challenge from philosophical anarchism to J. Raz's theory of legal authority: it would be irrational to follow an order with which one disagrees, since it would mean acting against what is considered more justified. Through references from decision theory and epistemology, and deploying examples about tools for assisting in routine decision-making, we sketch two possible answers: first, it may be justifiable to put yourself in a situation that leads to (...) irrationally acting; second, according to the “blindspots” theory, we outline some restrictions from a theory of rationality to the authority. (shrink)

A number of philosophers deny that contradictions can be believed. Are they correct? In this note, I show that even in quite weak logics, on pain of inconsistency, if there are false beliefs, either there are propositions which are true but unbelievable or contradictions are believable. Since the antecedent clearly holds, I offer some considerations in favor of the latter disjunct. Objections and variants of the main argument are considered.

It is well-known that versions of the lottery paradox and of the preface paradox show that the following three principles are jointly inconsistent: (Sufficiency) very probable propositions are justifiably believable; (Conjunction Closure) justified believability is closed under conjunction introduction; (No Contradictions) propositions known to be contradictory are not justifiably believable. This paper shows that there is a hybrid of the lottery and preface paradoxes that does not require Sufficiency to arise, but only Conjunction Closure and No Contradictions; and it argues (...) that, given any plausible solution to this paradox, if one is not ready to deny Conjunction Closure (and analogous consistency principles), then one must endorse the thesis that justified believability is factive. (shrink)

A ‘lottery belief’ is a belief that a particular ticket has lost a large, fair lottery, based on nothing more than the odds against it winning. The lottery paradox brings out a tension between the idea that lottery beliefs are justified and the idea that that one can always justifiably believe the deductive consequences of things that one justifiably believes – what is sometimes called the principle of closure. Many philosophers have treated the lottery paradox as an argument against the (...) second idea – but I make a case here that it is the first idea that should be given up. As I shall show, there are a number of independent arguments for denying that lottery beliefs are justified. (shrink)

Lin and Kelly :957–981, 2012) and Leitgeb :1338–1389, 2013, Philos Rev 123:131–171, 2014), offer similar solutions to the Lottery Paradox, defining acceptance rules which determine a rational agent’s beliefs in terms of broader features of her credal state than just her isolated credences in individual propositions. I express each proposal as a method for obtaining an ordering over a partition from a credence function, and then a belief set from the ordering. Although these proposals avoid the original Lottery Paradox, I (...) raise a diachronic case which illustrates that neither satisfies both Lin and Kelly’s constraint that the update on orderings track the update on credence functions, and the intuitive constraint that credence of at least 0.5 is necessary for rational belief. I conclude by suggesting that we reformulate these proposals in terms of orderings over entire algebras based on partitions rather than orderings just over the partitions themselves. Reformulating both rules in this way yields acceptance rules which avoid the Lottery Paradox while satisfying both the tracking and likeliness constraints. (shrink)

Some attempts have been made to block the Knowability Paradox and other modal paradoxes by adopting a type-theoretic framework in which knowledge and necessity are regarded as typed predicates. The main problem with this approach is that when these notions are simultaneously treated as predicates, a new kind of paradox appears. I claim that avoiding this paradox either by weakening the Knowability Principle or by introducing types for both predicates is rather messy and unattractive. I also consider the prospect of (...) using the truth predicate to emulate other modal notions. It turns out that this idea works quite well. (shrink)

_Tell Me Something I Don’t Know_ is a collection of original dialogues in epistemology, suitable for student readers but also of interest to experts. Familiar problems, theories, and arguments are explored: second-order knowledge, epistemic closure, the preface paradox, skepticism, pragmatic encroachment, the Gettier problem, and more. New ideas on each of these issues are also offered, defended, and critiqued, often in humorous and entertaining ways.

Many epistemologists have responded to the lottery paradox by proposing formal rules according to which high probability defeasibly warrants acceptance. Douven and Williamson present an ingenious argument purporting to show that such rules invariably trivialise, in that they reduce to the claim that a probability of 1 warrants acceptance. Douven and Williamson’s argument does, however, rest upon significant assumptions – amongst them a relatively strong structural assumption to the effect that the underlying probability space is both finite and uniform. In (...) this paper, I will show that something very like Douven and Williamson’s argument can in fact survive with much weaker structural assumptions – and, in particular, can apply to infinite probability spaces. (shrink)