Epistemic Paradoxes, Misc

The aim of this paper is to present a constructive solution to Frege's puzzle (largely limited to the mathematical context) based on type theory. Two ways in which an equality statement may be said to have cognitive significance are distinguished. One concerns the mode of presentation of the equality, the other its mode of proof. Frege's distinction between sense and reference, which emphasizes the former aspect, cannot adequately explain the cognitive significance of equality statements unless a clear identity criterion for (...) senses is provided. It is argued that providing a solution based on proofs is more satisfactory from the standpoint of constructive semantics. (shrink)

This chapter provides a brief introduction to propositional epistemic logic and its applications to epistemology. No previous exposure to epistemic logic is assumed. Epistemic-logical topics discussed include the language and semantics of basic epistemic logic, multi-agent epistemic logic, combined epistemic-doxastic logic, and a glimpse of dynamic epistemic logic. Epistemological topics discussed include Moore-paradoxical phenomena, the surprise exam paradox, logical omniscience and epistemic closure, formalized theories of knowledge, debates about higher-order knowledge, and issues of knowability raised by Fitch’s paradox. The references (...) and recommended readings provide gateways for further exploration. (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)

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.

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 Marvin Backes (2019a) and Francesco Praolini (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 (2019b) has dubbed the ‘easy defeat’ problem for the normic theory. (shrink)

Philosophy and Phenomenological Research, EarlyView.

Instability occurs when the very fact of choosing one particular possible option rather than another affects the expected values of those possible options. In decision theory: An act is stable iff given that it is actually performed, its expected utility is maximal. When there is no stable choice available, the resulting instability can seem to pose a dilemma of practical rationality. A structurally very similar kind of instability, which occurs in cases of anti-expertise, can likewise seem to create dilemmas of (...) epistemic rationality. One possible line of response to such cases of instability, suggested by both Jeffrey (1983) and Sorensen (1987), is to insist that a rational agent can simply refuse to accept that such instability applies to herself in the first place. According to this line of thought it can be rational for a subject to discount even very strong empirical evidence that the anti-expertise condition obtains. I present a new variety of anti-expertise condition where no particular empirical stage-setting is required, since the subject can deduce a priori that an anti-expertise condition obtains. This kind of anti-expertise case is therefore not amenable to the line of response that Jeffrey and Sorensen recommend. (shrink)

Is it right to convict a person of a crime on the basis of purely statistical evidence? Many who have considered this question agree that it is not, posing a direct challenge to legal probabilism – the claim that the criminal standard of proof should be understood in terms of a high probability threshold. Some defenders of legal probabilism have, however, held their ground: Schoeman (1987) argues that there are no clear epistemic or moral problems with convictions based on purely (...) statistical evidence, and speculates that our aversion to such convictions may be nothing more than an irrational bias. More recently, Hedden and Colyvan (2019, section VI) describe our reluctance to convict on the basis of purely statistical evidence as an ‘intuition’, but suggest that there may be no ‘in principle’ problem with such convictions (see also Papineau, forthcoming, section 6). In this paper, I argue that there is, in some cases, an in principle problem with a conviction based upon statistical evidence alone – namely, it commits us to a precedent which, if consistently followed through, could lead to the deliberate conviction of an innocent person. I conclude with some reflections on the idea that the criminal justice system should strive to maximise the accuracy of its verdicts – and the related idea that we should each strive to maximise the accuracy of our beliefs. (shrink)

The surprise exam paradox is an apparently sound argument to the apparently absurd conclusion that a surprise exam cannot be given within a finite exam period. A closer look at the logic of the paradox shows the argument breaking down immediately. So why do the beginning stages of the argument appear sound in the first place? This paper presents an account of the paradox on which its allure is rooted in a common probabilistic mistake: the base rate fallacy. The account (...) predicts that the paradoxical argument should get less and less convincing as it goes along—a prediction I take to be welcome. On a bleaker note, the account suggests that the base rate fallacy may be more widespread than previously thought. (shrink)

Martin Smith has recently proposed, in this journal, a novel and intriguing approach to puzzles and paradoxes in evidence law arising from the evidential standard of the Preponderance of the Evidence. According to Smith, the relation of normic support provides us with an elegant solution to those puzzles. In this paper I develop a counterexample to Smith’s approach and argue that normic support can neither account for our reluctance to base affirmative verdicts on bare statistical evidence nor resolve the pertinent (...) paradoxes. Normic support is, as a consequence, not a successful epistemic anti-luck condition. (shrink)

The purpose of this paper is to provide a new solution to the radical sceptical paradox. A sceptical paradox purports to indicate the inconsistency within our fundamental epistemological commitments that are all seemingly plausible. Typically, sceptics employ an intuitively appealing epistemic principle to derive the sceptical conclusion. This paper will reveal a dilemma intrinsic to the sceptical paradox, which I refer to as the self-hollowing problem of radical scepticism. That is, on the one hand, if the sceptical conclusion turns out (...) to be true, then the epistemic principle employed by sceptics would lose its foundation of plausibility; on the other hand, if the sceptical conclusion does not follow, then the sceptical problem would not arise. In either case, the so-called sceptical paradox cannot be a genuine paradox. This new solution has three theoretical merits: it is undercutting, less theory-laden, and widely applicable. (shrink)

This paper elaborates a new solution to the lottery paradox, according to which the paradox arises only when we lump together two distinct states of being confident that p under one general label of ‘belief that p’. The two-state conjecture is defended on the basis of some recent work on gradable adjectives. The conjecture is supported by independent considerations from the impossibility of constructing the lottery paradox both for risk-tolerating states such as being afraid, hoping or hypothesizing, and for risk-averse, (...) certainty-like states. The new proposal is compared to views within the increasingly popular debate opposing dualists to reductionists with respect to the relation between belief and degrees of belief. (shrink)

The strong law of large numbers and considerations concerning additional information strongly suggest that Beauty upon awakening has probability 1/3 to be in a heads-awakening but should still believe the probability that the coin landed heads in the Sunday toss to be 1/2. The problem is that she is in a heads-awakening if and only if the coin landed heads. So, how can she rationally assign different probabilities or credences to propositions she knows imply each other? This is the problem (...) I address in this article. I suggest that ‘p whenever q and vice versa’ may be consistent with p and q having different probabilities if one of them refers to a sample space containing ordinary possible worlds and the other to a sample space containing centred possible worlds, because such spaces may fail to combine into one composite probability space and, as a consequence, ‘whenever’ may not be well defined; such is the main contribution of this article. 1The Sleeping Beauty Game2Groisman’s and Peter Lewis’s Approaches3Discussing Beauty’s Credences4The Principle of Equivalence's Failure5Making Sense of the Principle of Equivalence's Failure6Elga’s and Lewis’s Approaches7ConclusionAppendix. (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)

Fitch’s Paradox shows that if every truth is knowable, then every truth is known. Standard diagnoses identify the factivity/negative infallibility of the knowledge operator and Moorean contradictions as the root source of the result. This paper generalises Fitch’s result to show that such diagnoses are mistaken. In place of factivity/negative infallibility, the weaker assumption of any ‘level-bridging principle’ suffices. A consequence is that the result holds for some logics in which the “Moorean contradiction” commonly thought to underlie the result is (...) in fact consistent. This generalised result improves on the current understanding of Fitch’s result and widens the range of modalities of philosophical interest to which the result might be fruitfully applied. Along the way, we also consider a semantic explanation for Fitch’s result which answers a challenge raised by Kvanvig. (shrink)

मैं Wittgenstein और विकासवादी मनोविज्ञान के एक एकीकृत परिप्रेक्ष्य से Noson Yanofsky द्वारा 'कारण की बाहरी सीमा' की एक विस्तृत समीक्षा दे. मैं संकेत मिलता है कि भाषा और गणित में विरोधाभास के रूप में इस तरह के मुद्दों के साथ कठिनाई, अपूर्णता, अनिर्णयीयता, computability, मस्तिष्क और कंप्यूटर आदि के रूप में ब्रह्मांड, सभी विफलता से उठता है उचित में भाषा के हमारे उपयोग को ध्यान से देखने के लिए संदर्भ और इसलिए कैसे भाषा काम करता है के मुद्दों से (...) वैज्ञानिक तथ्य के मुद्दों को अलग करने में विफलता. मैं अधूरापन, paraconsistency और undecidability और गणना करने के लिए सीमा पर Wolpert के काम पर Wittgenstein के विचारों पर चर्चा की. यह योग अप करने के लिए: ब्रह्मांड ब्रुकलीन के अनुसार---अच्छा विज्ञान, नहीं तो अच्छा दर्शन. आधुनिक दो systems दृश्यसे मानव व्यवहार के लिए एक व्यापक अप करने के लिए तारीख रूपरेखा इच्छुक लोगों को मेरी पुस्तक 'दर्शन, मनोविज्ञान, मिनडी और लुडविगमें भाषा की तार्किक संरचना से परामर्श कर सकते हैं Wittgenstein और जॉन Searle '2 एड (2019). मेरे लेखन के अधिक में रुचि रखने वालों को देख सकते हैं 'बात कर रहेबंदर- दर्शन, मनोविज्ञान, विज्ञान, धर्म और राजनीति पर एक बर्बाद ग्रह --लेख और समीक्षा 2006-2019 3 एड (2019) और आत्मघाती यूटोपियान भ्रम 21st मेंसदी 4वें एड (2019) . (shrink)

An influential proposal is that knowledge involves safe belief. A belief is safe, in the relevant sense, just in case it is true in nearby metaphysically possible worlds. In this paper, I introduce a distinct but complementary notion of safety, understood in terms of epistemically possible worlds. The main aim, in doing so, is to add to the epistemologist’s tool-kit. To demonstrate the usefulness of the tool, I use it to advance and assess substantive proposals concerning knowledge and justification.

The primary objective of this paper is to introduce a new epistemic paradox that puts pressure on the claim that justification is closed under multi premise deduction. The first part of the paper will consider two well-known paradoxes—the lottery and the preface paradox—and outline two popular strategies for solving the paradoxes without denying closure. The second part will introduce a new, structurally related, paradox that is immune to these closure-preserving solutions. I will call this paradox, The Paradox of the Pill. (...) Seeing that the prominent closure-preserving solutions do not apply to the new paradox, I will argue that it presents a much stronger case against the claim that justification is closed under deduction than its two predecessors. Besides presenting a more robust counterexample to closure, the new paradox also reveals that the strategies that were previously thought to get closure out of trouble are not sufficiently general to achieve this task as they fail to apply to similar closure-threatening paradoxes in the same vicinity. (shrink)

This paper introduces and defends a new position regarding the question of whether it is possible to have conflicting moral obligations. In doing so, it focuses on what I call a moral pickle. By “moral pickle” I mean a set of actions such that you ought to perform each and cannot perform all. Typically, when people discuss conflicting moral obligations, they focus on the notion of a moral dilemma, which is a type of moral pickle involving two conflicting actions. In (...) other words, a moral dilemma is a pair of actions such that you ought to perform each and cannot perform both. As of yet, there is no debate about the possibility of moral pickles over and above the possibility of moral dilemmas. But as I show, there is good reason to think that moral pickles are possible and moral dilemmas are not. (shrink)

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)

This paper contains an argument to the effect that possible worlds semantics renders semantic knowledge impossible, no matter what ontological interpretation is given to possible worlds. The essential contention made is that possible worlds semantic knowledge is unsafe and this is shown by a parallel with the preface paradox.

It is commonly thought that Impossibility, Incompleteness, Paraconsistency, Undecidability, Randomness, Computability, Paradox, Uncertainty and the Limits of Reason are disparate scientific physical or mathematical issues having little or nothing in common. I suggest that they are largely standard philosophical problems (i.e., language games) which were mostly resolved by Wittgenstein over 80years ago. -/- “What we are ‘tempted to say’ in such a case is, of course, not philosophy, but it is its raw material. Thus, for example, what a mathematician is (...) inclined to say about the objectivity and reality of mathematical facts, is not a philosophy of mathematics, but something for philosophical treatment.” Wittgenstein PI 234 -/- "Philosophers constantly see the method of science before their eyes and are irresistibly tempted to ask and answer questions in the way science does. This tendency is the real source of metaphysics and leads the philosopher into complete darkness." Wittgenstein -/- I provide a brief summary of some of the major findings of two of the most eminent students of behavior of modern times, Ludwig Wittgenstein and John Searle, on the logical structure of intentionality (mind, language, behavior), taking as my starting point Wittgenstein’s fundamental discovery –that all truly ‘philosophical’ problems are the same—confusions about how to use language in a particular context, and so all solutions are the same—looking at how language can be used in the context at issue so that its truth conditions (Conditions of Satisfaction or COS) are clear. The basic problem is that one can say anything, but one cannot mean (state clear COS for) any arbitrary utterance and meaning is only possible in a very specific context. -/- I dissect some writings of a few of the major commentators on these issues from a Wittgensteinian viewpoint in the framework of the modern perspective of the two systems of thought (popularized as ‘thinking fast, thinking slow’), employing a new table of intentionality and new dual systems nomenclature. I show that this is a powerful heuristic for describing the true nature of these putative scientific, physical or mathematical issues which are really best approached as standard philosophical problems of how language is to be used (language games in Wittgenstein’s terminology). -/- It is my contention that the table of intentionality (rationality, mind, thought, language, personality etc.) that features prominently here describes more or less accurately, or at least serves as an heuristic for, how we think and behave, and so it encompasses not merely philosophy and psychology, but everything else (history, literature, mathematics, politics etc.). Note especially that intentionality and rationality as I (along with Searle, Wittgenstein and others) view it, includes both conscious deliberative linguistic System 2 and unconscious automated prelinguistic System 1 actions or reflexes. (shrink)

Epistemic logic in the tradition of Hintikka provides, as one of its many applications, a toolkit for the precise analysis of certain epistemological problems. In recent years, dynamic epistemic logic has expanded this toolkit. Dynamic epistemic logic has been used in analyses of well-known epistemic “paradoxes”, such as the Paradox of the Surprise Examination and Fitch’s Paradox of Knowability, and related epistemic phenomena, such as what Hintikka called the “anti-performatory effect” of Moorean announcements. In this paper, we explore a variation (...) on basic dynamic epistemic logic—what we call sequential epistemic logic—and argue that it allows more faithful and fine-grained analyses of those epistemological topics. (shrink)

Epistemic logic in the tradition of Hintikka provides, as one of its many applications, a toolkit for the precise analysis of certain epistemological problems. In recent years, dynamic epistemic logic has expanded this toolkit. Dynamic epistemic logic has been used in analyses of well-known epistemic “paradoxes”, such as the Paradox of the Surprise Examination and Fitch’s Paradox of Knowability, and related epistemic phenomena, such as what Hintikka called the “anti-performatory effect” of Moorean announcements. In this paper, we explore a variation (...) on basic dynamic epistemic logic—what we call sequential epistemic logic—and argue that it allows more faithful and fine-grained analyses of those epistemological topics. (shrink)

This paper defends the permissibility solution to the lottery paradox against an objection by Anna-Maria Asunta Eder. Eder argues that the permissibility solution should also be applicable to the preface paradox, but conflicts with a plausible principle about epistemic permissions when so applied. This paper replies by first criticizing Eder’s considerations in defense of her principle; in particular, it argues that the plausibility of her principle is to a large extent parasitic on the spurious plausibility of the principle of factual (...) detachment. The paper then presents a direct argument against Eder’s principle, which shows that her principle conflicts with a Pareto-style condition on permissible belief. (shrink)

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)

The lottery and preface paradoxes pose puzzles in epistemology concerning how to think about the norms of reasonable or permissible belief. Contextualists in epistemology have focused on knowledge ascriptions, attempting to capture a set of judgments about knowledge ascriptions and denials in a variety of contexts (including those involving lottery beliefs and the principles of closure). This article surveys some contextualist approaches to handling issues raised by the lottery and preface, while also considering some of the difficulties encountered by those (...) approaches. (shrink)

The paper takes a closer look at the role of knowledge and evidence in legal theory. In particular, the paper examines a puzzle arising from the evidential standard Preponderance of the Evidence and its application in civil procedure. Legal scholars have argued since at least the 1940s that the rule of the Preponderance of the Evidence gives rise to a puzzle concerning the role of statistical evidence in judicial proceedings, sometimes referred to as the Problem of Bare Statistical Evidence. While (...) this puzzle has led to the development of a multitude of accounts and approaches in the legal literature, I argue here that the problem can be resolved fairly straightforwardly within a knowledge-first framework. (shrink)

The Preface Paradox apparently shows that it is sometimes rational to believe logically incompatible propositions. In this paper, I propose a way out of the paradox based on the ideas of fallibilism and verisimilitude. More precisely, I defend the view that a rational inquirer can fallibly believe or accept a proposition which is false, or likely false, but verisimilar; and I argue that this view makes the Preface Paradox disappear. Some possible objections to my proposal, and an alternative view of (...) fallible belief, are briefly discussed in the final part of the paper. (shrink)

The so-called Preface Paradox seems to show that one can rationally believe two logically incompatible propositions. We address this puzzle, relying on the notions of truthlikeness and approximate truth as studied within the post-Popperian research programme on verisimilitude. In particular, we show that adequately combining probability, approximate truth, and truthlikeness leads to an explanation of how rational belief is possible in the face of the Preface Paradox. We argue that our account is superior to other solutions of the paradox, including (...) a recent one advanced by Hannes Leitgeb (Analysis 74.1). (shrink)

The preface paradox does not show that it can be rational to have inconsistent beliefs, because preface writers do not have inconsistent beliefs. I argue, first, that a fully satisfactory solution to the preface paradox would have it that the preface writer's beliefs are consistent. The case here is on basic intuitive grounds, not the consequence of a theory of rationality or of belief. Second, I point out that there is an independently motivated theory of belief – sensitivism – which (...) allows such a solution. I sketch a sensitivist account of the preface writer's doxastic state. (shrink)

This paper offers a new solution to the Surprise Test Paradox. The paradox arises thanks to an ingenious argument that seems to show that surprise tests are impossible. My solution to the paradox states that it relies on a questionable closure principle. This closure principle says that if one knows something and competently deduces something else, one knows the further thing. This principle has been endorsed by John Hawthorne and Timothy Williamson, among others, and I trace its motivation back to (...) work by Alvin Goldman. I provide counterexamples to the principle and explain the flaw in the reasoning of those who defend it. (shrink)

In this paper, we provide a Bayesian analysis of the well-known surprise exam paradox. Central to our analysis is a probabilistic account of what it means for the student to accept the teacher's announcement that he will receive a surprise exam. According to this account, the student can be said to have accepted the teacher's announcement provided he adopts a subjective probability distribution relative to which he expects to receive the exam on a day on which he expects not to (...) receive it. We show that as long as expectation is not equated with subjective certainty there will be contexts in which it is possible for the student to accept the teacher's announcement, in this sense. In addition, we show how a Bayesian modeling of the scenario can yield plausible explanations of the following three intuitive claims: (1) the teacher's announcement becomes easier to accept the more days there are in class; (2) a strict interpretation of the teacher's announcement does not provide the student with any categorical information as to the date of the exam; and (3) the teacher's announcement contains less information about the date of the exam the more days there are in class. To conclude, we show how the surprise exam paradox can be seen as one among the larger class of paradoxes of doxastic fallibilism, foremost among which is the paradox of the preface. (shrink)

It is already known that Fitch's paradox of knowability can be solved by typing knowledge. I differentiate two kinds of such typing, Tarskian and Russellian, and focus on the latter which is framed within the ramified theory of types. My main aim is to other a defence of the approach against recently raised criticism. The key justification is provided by the Vicious Circle Principle which governs the very formation of propositions and thus also intensional operators, including the operator of knowledge.

Hili Razinsky, free downlad at link. ABSTRACT: Emotional perceptions are objectivist (objectivity-directed or cognitive) and conscious, both attributes suggesting they cannot be ambivalent. Yet perceptions, including emotional perceptions of value, allow for strictly objectivist ambivalence in which a person unitarily perceives the object in mutually undermining ways. Emotional perceptions became an explicandum of emotion for philosophers who are sensitive to the unique conscious character of emotion, impressed by the objectivist character of perceptions, and believe that the perceptual account solves a (...) worry about the possibility of a conflict between an emotion and a judgement. Back into the 1980s Greenspan has argued that emotional ambivalence is possible, her reasons implying that objectivist accounts of emotion are inconsistent with ambivalence. Tappolet has more recently replied that perceptual accounts allow for emotional ambivalence since the opposed values seen in ambivalence are good or bad in different senses. The present paper identifies strict objectivist ambivalence between judgements and between emotional perceptions by contrasting them with such ambivalence of separate values such as evoked by Tappolet. (shrink)

In ‘Godel’s Way’ three eminent scientists discuss issues such as undecidability, incompleteness, randomness, computability and paraconsistency. I approach these issues from the Wittgensteinian viewpoint that there are two basic issues which have completely different solutions. There are the scientific or empirical issues, which are facts about the world that need to be investigated observationally and philosophical issues as to how language can be used intelligibly (which include certain questions in mathematics and logic), which need to be decided by looking at (...) how we actually use words in particular contexts. When we get clear about which language game we are playing, these topics are seen to be ordinary scientific and mathematical questions like any others. Wittgenstein’s insights have seldom been equaled and never surpassed and are as pertinent today as they were 80 years ago when he dictated the Blue and Brown Books. -/- Those wishing a comprehensive up to date framework for human behavior from the modern two systems view may consult my book ‘The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle’ 2nd ed (2019). Those interested in more of my writings may see ‘Talking Monkeys--Philosophy, Psychology, Science, Religion and Politics on a Doomed Planet--Articles and Reviews 2006-2019 3rd ed (2019), The Logical Structure of Human Behavior (2019), and Suicidal Utopian Delusions in the 21st Century 4th ed (2019). (shrink)

I illustrate with three classical examples the mistakes arising from using a modal operator admitting multiple interpretations in the same argument; the flaws arise especially easily if no attention is paid to the range of propositional variables. Premisses taken separately might seem convincing and a substitution for a propositional variable in a modal context might seem legitimate. But there is no single interpretation of the modal operators involved under which all the premisses are plausible and the substitution successful.

In this paper I argue that human beings should reason, not in accordance with classical logic, but in accordance with a weaker ‘reticent logic’. I characterize reticent logic, and then show that arguments for the existence of fundamental Gödelian limitations on artificial intelligence are undermined by the idea that we should reason reticently, not classically.

This thesis focuses on expressively rich languages that can formalise talk about probability. These languages have sentences that say something about probabilities of probabilities, but also sentences that say something about the probability of themselves. For example: (π): “The probability of the sentence labelled π is not greater than 1/2.” Such sentences lead to philosophical and technical challenges; but can be useful. For example they bear a close connection to situations where ones confidence in something can affect whether it is (...) the case or not. The motivating interpretation of probability as an agent's degrees of belief will be focused on throughout the thesis. -/- This thesis aims to answer two questions relevant to such frameworks, which correspond to the two parts of the thesis: “How can one develop a formal semantics for this framework?” and “What rational constraints are there on an agent once such expressive frameworks are considered?”. (shrink)

We’ve all been at parties where there's one cookie left on what was once a plate full of cookies, a cookie no one will eat simply because everyone is following a rule of etiquette, according to which you’re not supposed to eat the last cookie. Or at least we think everyone is following this rule, but maybe not. In this paper I present a new paradox, the Cookie Paradox, which is an argument that seems to prove that in any situation (...) in which everyone is truly following the rule, no one eats any cookies at all, no matter how many there are to be eaten. The ‘Cookie Argument’ resembles the more familiar argument that surprise exams are impossible, but it's not exactly the same. I argue that the biggest difference is that, unlike the surprise exam argument, the Cookie Argument is actually sound! I conclude the paper by explaining how it could be possible for a group of people to engage in behavior (eating cookies) that guarantees that at least one of the members of the group will violate a rule, even when it's common knowledge in the group that everyone is committed to following that very rule. (shrink)

Many philosophers have argued that "degree of belief" or "credence" is a more fundamental state grounding belief. Many other philosophers have been skeptical about the notion of "degree of belief", and take belief to be the only meaningful notion in the vicinity. This paper shows that one can take belief to be fundamental, and ground a notion of "degree of belief" in the patterns of belief, assuming that an agent has a collection of beliefs that isn't dominated by some other (...) collection in terms of the overall balance of truth and falsity that it could contain. (shrink)

One of Moore’s paradoxical sentence types is ‘P, but I believe ~P’. Mooreans have assumed that all tokens of that sentence type are absurd in some way: epistemically, pragmatically, semantically, or assertively. And then they proceed to debate what the absurdity really is. I argue that if one has the appropriate philosophical views, then one can rationally assert tokens of that sentence type, and one can be epistemically reasonable in the corresponding compound belief as well.

The Paradox of the Surprise Examination has been a testing ground for a variety of frameworks in formal epistemology, from epistemic logic to probability theory to game theory and more. In this paper, I treat a related paradox, the Paradox of the Undiscoverable Position, as a test case for the possible-worlds style representation of epistemic states. I argue that the paradox can be solved in this framework, further illustrating the power of possible-worlds style modeling. The solution also illustrates an important (...) distinction between anti-performatory and unassimilable announcements of information. (shrink)

ABSTRACTMany discussions of the ‘preface paradox’ assume that it is more troubling for deductive closure constraints on rational belief if outright belief is reducible to credence. I show that this is an error: we can generate the problem without assuming such reducibility. All that we need are some very weak normative assumptions about rational relationships between belief and credence. The only view that escapes my way of formulating the problem for the deductive closure constraint is in fact itself a reductive (...) view: namely, the view that outright belief is credence 1. However, I argue that this view is unsustainable. Moreover, my version of the problem turns on no particular theory of evidence or evidential probability, and so cannot be avoided by adopting some revisionary such theory. In sum, deductive closure is in more serious, and more general, trouble than some have thought. (shrink)

ABSTRACTAccording to the Dogmatism Puzzle presented by Gilbert Harman, knowledge induces dogmatism because, if one knows that p, one knows that any evidence against p is misleading and therefore one can ignore it when gaining the evidence in the future. I try to offer a new solution to the puzzle by explaining why the principle is false that evidence known to be misleading can be ignored. I argue that knowing that some evidence is misleading doesn't always damage the credential of (...) the evidence, and therefore it doesn't always entitle one to ignore it. I also explain in what kind of cases and to what degree such knowledge allows one to ignore evidence. Hopefully, through the discussion, we can not only understand better where the dogmatism puzzle goes wrong, but also understand better in what sense rational believers should rely on their evidence and when they can ignore it. (shrink)

Recent attempts to resolve the Paradox of the Gatecrasher rest on a now familiar distinction between individual and bare statistical evidence. This paper investigates two such approaches, the causal approach to individual evidence and a recently influential (and award-winning) modal account that explicates individual evidence in terms of Nozick's notion of sensitivity. This paper offers counterexamples to both approaches, explicates a problem concerning necessary truths for the sensitivity account, and argues that either view is implausibly committed to the impossibility of (...) no-fault wrongful convictions. The paper finally concludes that the distinction between individual and bare statistical evidence cannot be maintained in terms of causation or sensitivity. We have to look elsewhere for a solution of the Paradox of the Gatecrasher. (shrink)

We present a semantics for a language that includes sentences that can talk about their own probabilities. This semantics applies a fixed point construction to possible world style structures. One feature of the construction is that some sentences only have their probability given as a range of values. We develop a corresponding axiomatic theory and show by a canonical model construction that it is complete in the presence of the ω-rule. By considering this semantics we argue that principles such as (...) introspection, which lead to paradoxical contradictions if naively formulated, should be expressed by using a truth predicate to do the job of quotation and disquotation and observe that in the case of introspection the principle is then consistent. (shrink)

We can make new progress on stalled debates in epistemology if we adopt a new practical approach, an approach concerned with the function served by epistemic evaluations. This paper illustrates how. I apply the practical approach to an important, unsolved problem: the problem of forgotten evidence. Section 1 describes the problem and why it is so challenging. Section 2 outlines and defends a general view about the function of epistemic evaluations. Section 3 then applies that view to solve the problem (...) of forgotten evidence. (shrink)

Yehoshua Bar-Hillel and Rudolph Carnap’s classical theory of semantic information entails the counterintuitive feature that inconsistent statements convey maximal information. Theories preserving Bar-Hillel and Carnap’s modal intuitions while imposing a veridicality requirement on which statements convey information—such as the theories of Fred Dretske or Luciano Floridi—avoid this commitment, as inconsistent statements are deemed not information-conveying by fiat. This paper produces a pair of paradoxical statements that such “veridical-modal” theories must evaluate as both conveying and not conveying information, although Bar-Hillel and (...) Carnap’s theory accommodates these statements without inconsistency. Moreover, the paradoxes are independently interesting as the mode in which they self-refer bears on their evaluation. (shrink)

The preface paradox can be motivated by appealing to a plausible inference from an author’s reasonable assertion that her book is bound to contain errors to the author’s rational belief that her book contains errors. By evaluating and undermining the validity of this inference, I offer a resolution of the paradox. Discussions of the preface paradox have surprisingly failed to note that expressions of fallibility made in prefaces typically employ terms such as surely, undoubtedly, and bound to be. After considering (...) what these terms mean, I show that the motivating inference is invalid. Moreover, I argue that a closer consideration of our expressions of fallibility suggest that epistemically responsible authors would not be rational to believe that their books contain errors. I conclude by considering alternative expressions of fallibility that employ terms such as possible and probable, and discuss the role that expressions of fallibility play in conversation. (shrink)