Epistemic Paradoxes

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)

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)

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)

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)

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)

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)

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 ‘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)

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)

According to a captivating picture, epistemic justification is essentially a matter of epistemic or evidential likelihood. While certain problems for this view are well known, it is motivated by a very natural thought—if justification can fall short of epistemic certainty, then what else could it possibly be? In this paper I shall develop an alternative way of thinking about epistemic justification. On this conception, the difference between justification and likelihood turns out to be akin to the more widely recognised difference (...) between ceteris paribus laws and brute statistical generalisations. I go on to discuss, in light of this suggestion, issues such as classical and lottery-driven scepticism as well as the lottery and preface paradoxes. (shrink)

According to deontological approaches to justification, we can analyze justification in deontic terms. In this paper, I try to advance the discussion of deontological approaches by applying recent insights in the semantics of deontic modals. Specifically, I use the distinction between weak necessity modals and strong necessity modals to make progress on a question that has received surprisingly little discussion in the literature, namely: ‘What’s the best version of a deontological approach?’ The two most obvious hypotheses are the Permissive View, (...) according to which justified expresses permission, and the Obligatory View, according to which justified expresses some species of obligation. I raise difficulties for both of these hypotheses. In light of these difficulties, I propose a new position, according to which justified expresses a property I call faultlessness, defined as the dual of weak necessity modals. According to this view, an agent is justified in phi-ing iff it’s not the case that she should [/ought] not phi. I argue that this ‘Faultlessness View’ gives us precisely what’s needed to avoid the problems facing the Permissive and Obligatory Views. (shrink)

I aim at dissolving Kripke's dogmatism paradox by arguing that, with respect to any particular proposition p which is known by a subject A, it is not irrational for A to ignore all evidence against p. Along the way, I offer a definition of 'A is dogmatic with respect to p', and make a distinction between an objective and a subjective sense of 'should' in the statement 'A should ignore all the evidence against p'. For the most part, I deal (...) with Kripke's original version of the paradox, wherein the subject wishes, above all else, to avoid losing her true belief or gaining a false one; in the final section I investigate the possibility of having a paradox for a subject who values knowledge above anything else. (shrink)

Translation of Mark Sainsbury: Paradoxes (Cambridge University Press 1988).

This paper considers clinical psychoanalysis together with developmental psychology (particularly attachment theory), evolution, and neuroscience in the context a Bayesian account of confirmation and disconfrimation. -/- In it I argue that these converging sources of support indicate that the combination of relatively low predictive power and broad explanatory scope that characterise the theories of both Freud and Darwin suggest that Freud's theory, like Darwin's, may strike deeply into natural phenomena. -/- The same argument, however, suggests that conclusive confirmation for Freudian (...) hypotheses, as in the case of Darwin's, will come from outside the original domain of explanation sketched out by Freud. As in Darwin's case conclusive confirmation came from understanding the physical mechanisms or reproduction, in Freud's case it will come from understanding the neural mechanisms that realise the phenomena described in psychoanalysis. (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.

Suppose you think that whether you believe some proposition A at some future time t might have a causal influence on whether A is true. For instance, maybe you think a woman can read your mind, and either (1) you think she will snap her fingers shortly after t if and only if you believe at t that she will, or (2) you think she will snap her fingers shortly after t if and only if you don't believe at t (...) that she will. Let A be the proposition that she snaps her fingers shortly after t. In case (1), theoretical rationality seems to leave it open whether you should believe A or not. Perhaps, for all it has to say, you could just directly choose whether to believe A. David Velleman seems to be committed to something close to that, but his view has been unpopular. In case (2), you seem to be in a theoretical dilemma, a situation where any attitude you adopt toward A will be self-undermining in a way that makes you irrational. Such theoretical dilemmas ought to be impossible, just as genuine moral dilemmas ought to be impossible, but it is surprisingly hard to show that they are (perhaps because they aren't). I study cases analogous to (1) and (2) in a probabilistic framework where degrees of belief rather than all-or-nothing beliefs are taken as basic. My principal conclusions are that Velleman's view is closer to the truth than it is generally thought to be, that case (2) type theoretical dilemmas only arise for hyperidealised agents unlike ourselves, and that there are related cases that can arise for agents like us that are very disturbing but might not quite amount to theoretical dilemmas. (shrink)

History and Philosophy of Logic, Volume 33, Issue 1, Page 101-104, February 2012.

In §201 of Philosophical Investigations, Ludwig Wittgenstein puts forward his famous "rule-following paradox". The paradox is how can one follow in accord with a rule - the applications of which are potentially infinite - when the instances from which one learns the rule and the instances in which one displays that one has learned the rule are only finite? How can one be certain of rule-following at all? In Wittgenstein: On Rules and Private Language, Saul Kripke concedes the skeptical position (...) that there are no facts that we follow a rule but that there are still conditions under which we are warranted in asserting of others that they are following a rule. In this paper, I explain why Kripke's solution to the rule-following paradox fails. I then offer an alternative. (shrink)

Argumentations are at the heart of the deductive and the hypothetico-deductive methods, which are involved in attempts to reduce currently open problems to problems already solved. These two methods span the entire spectrum of problem-oriented reasoning from the simplest and most practical to the most complex and most theoretical, thereby uniting all objective thought whether ancient or contemporary, whether humanistic or scientific, whether normative or descriptive, whether concrete or abstract. Analysis, synthesis, evaluation, and function of argumentations are described. Perennial philosophic (...) problems, epistemic and ontic, related to argumentations are put in perspective. So much of what has been regarded as logic is seen to be involved in the study of argumentations that logic may be usefully defined as the systematic study of argumentations, which is virtually identical to the quest of objective understanding of objectivity. (shrink)

In some lottery situations, the probability that your ticket's a loser can get very close to 1. Suppose, for instance, that yours is one of 20 million tickets, only one of which is a winner. Still, it seems that (1) You don't know yours is a loser and (2) You're in no position to flat-out assert that your ticket is a loser. "It's probably a loser," "It's all but certain that it's a loser," or even, "It's quite certain that it's (...) a loser" seem quite alright to say, but, it seems, you're in no position to declare simply, "It's a loser." (1) and (2) are closely related phenomena. In fact, I'll take it as a working hypothesis that the reason "It's a loser" is unassertable is that (a) You don't seem to know that your ticket's a loser, and (b) In flat-out asserting some proposition, you represent yourself as knowing it.1 This working hypothesis will enable me to address these two phenomena together, moving back and forth freely between them. I leave it to those who reject the hypothesis to sort out those considerations which properly apply to the issue of knowledge from those germane to that of assertability. Things are quite different when you report the results of last night's basketball game. Suppose your only source is your morning newspaper, which did not carry a story about the 1 game, but simply listed the score, "Knicks 83, at Bulls 95," under "Yesterday's Results." Now, it doesn't happen very frequently, but, as we all should suspect, newspapers do misreport scores from time to time. On several occasions, my paper has transposed a result, attributing to each team the score of its opponent. In fact, that your paper's got the present result wrong seems quite a bit more probable than that you've won the lottery of the above paragraph. Still, when asked, "Did the Bulls win yesterday?", "Probably" and "In all likelihood" seem quite unnecessary. "Yes, they did," seems just fine.. (shrink)

This paper proposes a new framework to solve the surprise examination paradox. I survey preliminary the main contributions to the literature related to the paradox. I introduce then a distinction between a monist and a dichotomic analysis of the paradox. With the help of a matrix notation, I also present a dichotomy that leads to distinguish two basically and structurally different notions of surprise, which are respectively based on a conjoint and a disjoint structure. I describe then how Quine's solution (...) and Hall's reduction apply to the version of the paradox corresponding to the conjoint structure. Lastly, I expose a solution to the version of the paradox based on the disjoint structure. (shrink)

Let us sum up. The paradox of the Knower poses a direct and formal challenge to the coherence of common notions of knowledge and truth. We've considered a number of ways one might try to meet that challenge: propositional views of truth and knowledge, redundancy or operator views, and appeal to hierarchy of various sorts. Mere appeal to propositions or operators, however, seems to be inadequate to the task of the Knower, at least if unsupplemented by an auxiliary recourse to (...) hierarchy. But the cost of hierarchy appears to be an abandonment of any notion of all truth or of omniscience. What the contradictions of the Knower seem to demand, then, is at least an abandonment of these. As noted in the introduction, the argument is complicated enough that one must be wary of dogmatic and precipitate conclusions. One may legitimately wonder whether some new response, or some variation on an old one, will yet offer a way out.Far too often, however, it is asked what has gone wrong with paradox rather than what paradox may have to teach us. What the Knower may have to teach us, I think, is that there really can be no coherent notion of all truth and really can be no coherent notion of omniscience. In its own way that conclusion is perhaps as humbling as is any traditional notion of God. (shrink)

This paper starts by indicating the analysis of Hempel's conditions of adequacy for any relation of confirmation (Hempel, 1945) as presented in Huber (submitted). There I argue contra Carnap (1962, Section 87) that Hempel felt the need for two concepts of confirmation: one aiming at plausible theories and another aiming at informative theories. However, he also realized that these two concepts are conflicting, and he gave up the concept of confirmation aiming at informative theories. The main part of the paper (...) consists in working out the claim that one can have Hempel's cake and eat it too - in the sense that there is a logic of theory assessment that takes into account both of the two conflicting aspects of plausibility and informativeness. According to the semantics of this logic, a is an acceptable theory for evidence β if and only if a is both sufficiently plausible given β and sufficiently informative about β. This is spelt out in terms of ranking functions (Spohn, 1988) and shown to represent the syntactically specified notion of an assessment relation. The paper then compares these acceptability relations to explanatory and confirmatory consequence relations (Flach, 2000) as well as to nonmonotonic consequence relations (Kraus et al., 1990). It concludes by relating the plausibility-informativeness approach to Carnap's positive relevance account, thereby shedding new light on Carnap's analysis as well as solving another problem of confirmation theory. (shrink)

A fundamental question asked in modal logic is whether a given theory is consistent. But consistent with what? A typical way to address this question identifies a choice of background knowledge axioms (say, S4, D, etc.) and then shows the assumptions codified by the theory in question to be consistent with those background axioms. But determining the specific choice and division of background axioms is, at least sometimes, little more than tradition. This paper introduces generic theories for propositional modal logic (...) to address consistency results in a more robust way. As building blocks for background knowledge, generic theories provide a standard for categorical determinations of consistency. We argue that the results and methods of this paper help to elucidate problems in epistemology and enjoy sufficient scope and power to have purchase on problems bearing on modalities in judgement, inference, and decision making. (shrink)

The article presents the empirical confirmation to the black hole and white hole juxtapose theory. The author based the experiment on the multi- mission multi-spectral space telescope data conducted remotely with the NASA Data Challenge and Harvard- Smithsonian Micro-Observatory. Since the loss of the original manuscript, the author reformulated the mathematics during the research. The observation developed a resonance observation technique that observed the white hole to the moon’s direction with the sun. The data reduction of the white hole and (...) other observations provides an explanation for the undetected gravitons and some empirical physical features of the white hole. (shrink)

In Replacing Truth, Scharp takes the concept of truth to be fundamentally incoherent. As such, Scharp reckons it to be unsuited for systematic philosophical theorising and in need of replacement – at least for regions of thought and talk which permit liar sentences and their ilk to be formulated. This replacement methodology is radical because it not only recommends that the concept of truth be replaced, but that the word ‘true’ be replaced too. Only Tarski has attempted anything like it (...) before. I dub such a view Conceptual Marxism. In assessing this view, my goals are fourfold: to summarise the many components of Scharp’s theory of truth; to highlight what I take to be some of the excess baggage carried by the view; to assess whether, and to what extent, the extreme methodology on offer is at all called for; finally, to briefly propose a less radical replacement strategy for resolving the liar paradox. (shrink)

Translation of Mark Sainsbury: Paradoxes (Cambridge University Press 1988).

The workshop took place in Leuven, Belgium, and was hosted by the KU Leuven's Centre for Logic and Analytic Philosophy. The workshop’s theme was the syntactical treatment of (alethic, epistemic, etc.) modalities. The standard view on modalities nowadays is that they are operators. Syntactic theories, however, treat modalities as predicates, and thus have to assume a background theory which is sufficiently strong to encode its own formulas (usually, one works with some system of arithmetic and Gödel coding). As a consequence, (...) such theories suffer from paradoxes of self-referentiality. For example, just as the liar sentence states of itself that it is false, the knower sentence states of itself that it is unknown. Kaplan and Montague (1960: 'A paradox regained', Notre Dame J. Formal Logic, vol. 1, pp. 79–90) famously showed that any sufficiently strong theory that contains the knower is inconsistent. (shrink)

Predicates are term-to-sentence devices, and operators are sentence-to-sentence devices. What Kaplan and Montague's Paradox of the Knower demonstrates is that necessity and other modalities cannot be treated as predicates, consistent with arithmetic; they must be treated as operators instead. Such is the current wisdom.A number of previous pieces have challenged such a view by showing that a predicative treatment of modalities neednot raise the Paradox of the Knower. This paper attempts to challenge the current wisdom in another way as well: (...) to show that mere appeal to modal operators in the sense of sentence-to-sentence devices is insufficient toescape the Paradox of the Knower. A family of systems is outlined in which closed formulae can encode other formulae and in which the diagonal lemma and Paradox of the Knower are thereby demonstrable for operators in this sense. (shrink)

The article discusses the main ideas of Alvin Goldman’s process reliabilism and related epistemological theories. A conceptual distinction between epistemic reliability and veritic effectiveness is introduced as a more parsimonious alternative to traditional arguments against reliabilism. The main ideas of reliabilism are examined in light of the notion of veritic effectiveness.

The principle of total evidence says that all relevant information should be considered when making an inference about a hypothesis. In this article, we argue that the criminalist’s paradox from the literature on the methodology of forensic science constitutes a counterexample against the principle of total evidence. The paradox arises, for example, when a forensic scientist uses the results from other forensic procedures to inform their own analysis. In such cases, their results can become more reliable, but at the same (...) time also dependent on those other forensic results and therefore less useful for decisions in court cases. Consequently, such influences are generally avoided in forensic science. We argue that structurally similar problems plague also other scientific disciplines, anticipate an objection to the counterexample, and propose two new versions of the principle of total evidence that do not fall prey to the criminalist’s paradox. (shrink)

David Chalmers argued against the claim that for all p, or even for all entertainable p, it is knowable a priori that p iff actually p. Instead of criticizing Chalmers’s argument, I suggest that it can be generalized, in a sense, and in interesting ways, concerning other principles about contingent a priori truths. In particular, I will argue that the puzzle presented by Chalmers runs parallel to others that do not turn on ‘actually’. Furthermore, stronger arguments can be presented that (...) do not turn on apriority either, though they do entail the conclusion of Chalmers’s argument. All such puzzles involve interactions between rigidifying sentence-forming devices with factive operators. (shrink)

The Preface Paradox is often discussed for its implications for rational belief. Much less discussed is a variant of the Preface Paradox for knowledge. In this paper, I argue that the most plausible closure-friendly resolution to the Preface Paradox for Knowledge is to say that in any given context, we do not know much. I call this view “Socraticism”. I argue that Socraticism is the most plausible view on two accounts—(1) this view is compatible with the claim that most of (...) our knowledge ascriptions are true, and (2) provided that (1) is true, the costs of accepting Socraticism are much less than the costs of accepting any other resolution to the Paradox. I argue for (1) in Section 2 by developing a question-sensitive contextualist model for knowledge that shows how Socraticism is compatible with the claim that most of our knowledge ascriptions are true. I also argue how this contextualist model can achieve this result where other contextualist models fail. I then consider other closure-friendly solutions to the paradox in Section 3 and show how accepting those solutions forces us to give up a number of plausible epistemic principles. (shrink)