Simon Evnine examines various epistemic aspects of what it is to be a person. Persons are defined as finite beings that have beliefs, including second-order beliefs about their own and others' beliefs, and are agents, capable of making long-term plans. It is argued that for any being meeting these conditions, a number of epistemic consequences obtain. First, all such beings must have certain logical concepts and be able to use them in certain ways. Secondly, there are at least two principles (...) governing belief that it is rational for persons to satisfy and are such that nothing can be a person at all unless it satisfies them to a large extent. These principles are that one believe the conjunction of one's beliefs and that one treat one's future beliefs as, by and large, better than one's current beliefs. Thirdly, persons both occupy epistemic points of view on the world and show up within those views. This makes it impossible for them to be completely objective about their own beliefs. Ideals of rationality that require such objectivity, while not necessarily wrong, are intrinsically problematic for persons. This "aspectual dualism" is characteristic of treatments of persons in the Kantian tradition. In sum, these epistemic consequences support a traditional view of the nature of persons, one in opposition to much recent theorizing. (shrink)

An attractive approach to the semantic paradoxes holds that cases of semantic pathology give rise to indeterminacy. What attitude should a rational agent have toward a proposition that it takes to be indeterminate in this sense? Orthodoxy holds that rationality requires that an agent disbelieve such a proposition. I argue that a rational agent should be such that it is indeterminate whether it believes the proposition in question. For rational agents, indeterminacy in the objects of their attitudes will filter up (...) to the attitudes themselves. (shrink)

We identify a class of paradoxes that is neither set-theoretical nor semantical, but that seems to depend on intensionality. In particular, these paradoxes arise out of plausible properties of propositional attitudes and their objects. We try to explain why logicians have neglected these paradoxes, and to show that, like the Russell Paradox and the direct discourse Liar Paradox, these intensional paradoxes are recalcitrant and challenge logical analysis. Indeed, when we take these paradoxes seriously, we may need to rethink the commonly (...) accepted methods for dealing with the logical paradoxes. (shrink)

Propositions are central to at least most theorizing about the connection between our mental lives and the world: we use them in our theories of an array of attitudes including belief, desire, hope, fear, knowledge, and understanding. Unfortunately, when we press on these theories, we encounter a relatively neglected family of paradoxes first studied by Arthur Prior. I argue that these paradoxes present a fatal problem for most familiar resolutions of paradoxes. In particular, I argue that truth-value gap, contextualist, situation (...) theoretic, revision theoretic, ramified, and dialetheist approaches to the paradoxes must deny us the conceptual resources that they themselves make use of, on pain of contradiction. I then detail the costs of the extant strategies that avoid this issue: Hartry Field’s paracomplete approach; Andrew Bacon’s classical treatment of indeterminacy; a generalization of ideas from Prior, Nicholas J.J. Smith, and Hartley Slater; and free logics as recently explored by Bacon, John Hawthorne, and Gabriel Uzquiano. I argue that none of these is perfect, and that each restricts the theories we can endorse in a variety of areas of philosophy. I spell these restrictions out, showing, I hope, that the further investigation of these paradoxes must be a part of future research on propositional attitudes. (shrink)

Peter Slezak and William Boos have independently advanced a novel interpretation of Descartes's "cogito". The interpretation portrays the "cogito" as a diagonal deduction and emphasizes its resemblance to Godel's theorem and the Liar. I object that this approach is flawed by the fact that it assigns 'Buridan sentences' a legitimate role in Descartes's philosophy. The paradoxical nature of these sentences would have the peculiar result of undermining Descartes's "cogito" while enabling him to "disprove" God's existence.

This is a defense and extension of Stephen Yablo's claim that self-reference is completely inessential to the liar paradox. An infinite sequence of sentences of the form 'None of these subsequent sentences are true' generates the same instability in assigning truth values. I argue Yablo's technique of substituting infinity for self-reference applies to all so-called 'self-referential' paradoxes. A representative sample is provided which includes counterparts of the preface paradox, Pseudo-Scotus's validity paradox, the Knower, and other enigmas of the genre. I (...) rebut objections that Yablo's paradox is not a genuine liar by constructing a sequence of liars that blend into Yablo's paradox. I rebut objections that Yablo's liar has hidden self-reference with a distinction between attributive and referential self-reference and appeals to Gregory Chaitin's algorithmic information theory. The paper concludes with comments on the mystique of self-reference. (shrink)

In Category Mistakes, Ofra Magidor provides two arguments against the view that category mistakes express propositions that are not truth-evaluable at some world. I argue that her first, Williamsonian argument against this view begs the question, and that her second argument rests on a misleading conception of how semantic defect results in infelicity judgments. I conclude by conceding that she is still correct to stress that the view she opposes face noteworthy foundational and empirical challenges.

Self-referential sentences have troubled our understanding of language for centuries. The most famous self-referential sentence is probably the Liar, a sentence that says of itself that it is false. The Liar Paradox has encouraged many philosophers to establish theories of truth that manage to give a proper account of the truth predicate in a formal language. Kripke’s Fixed Point Theory from 1975 is one famous example of such a formal theory of truth that aims at giving a plausible notion of (...) truth by allowing truth value gaps. However, not only the concept of truth gives rise to paradoxes. A syntactical treatment of epistemic notions like belief and knowledge leads to contradictions that very much resemble the Liar Paradox. Therefore, it seems to be fruitful to apply the established theories of truth to epistemic concepts. In this paper, I will present one such attempt of solving the epistemic paradoxes: I adapt Kripke’s Fixed Point Theory and interpret truth, knowledge and belief within the framework of a partial logic. Thereby I find not only the fixed point of truth but also the fixed points of knowledge and belief. In this fixed point, the predicates of truth, belief and knowledge find their definite interpretation and the paradoxes are avoided. (shrink)

The coherence of omniscience is sometimes challenged using self-referential sentences like, “No omniscient entity knows that which this very sentence expresses,” which suggest that there are truths which no omniscient entity knows. In this paper, I consider two strategies for addressing these challenges: The Common Strategy, which dismisses such self-referential sentences as meaningless, and The Conciliatory Strategy, which discounts them as quirky outliers with no impact on one’s status as being omniscient. I argue that neither strategy succeeds. The Common Strategy (...) fails because it is both unmotivated and impotent. The Conciliatory Strategy fails because it leads to embarrassing situations in which omniscient entities are epistemically inferior to non-omniscient entities: we can, for example, devise trivia-based drinking games that force omniscient entities into an intoxicated state; and, given plausible closure principles for belief, such entities are unable to have the sorts of beliefs that give them reason to refuse to play. (shrink)

We consider a language containing partial predicates for subjective knowability and truth. For this language, inductive hierarchy rules are proposed which build up the extension and anti-extension of these partial predicates in stages. The logical interaction between the extension of the truth predicate and the anti-extension of the knowability predicate is investigated.

The epistemic paradox of 'belief instability' has recently received notable attention from many philosophers. Understanding this paradox is very important because belief is a central notion of psychologically motivated semantic theories in philosophy, linguistics, and cognitive science, and this paradox poses serious problems for these theories. In this dissertation I criticize previous proposals and offer a new proposal, which I call a 'revision theory of belief'. ;My revision theory of belief is in many respects an application of Gupta's and Belnap's (...) revision theory of truth, which is proposed to deal with the Liar paradox. They argue that truth is a circular notion because Tarski biconditionals provide circular, partial definitions of truth. And this circularity of truth is the source of the Liar paradox. I offer a similar proposal for handling the paradox of belief instability. In particular, I argue that our notion of belief involved in the paradox of belief instability is circular, and that is why this paradox arises. ;If the notion of belief involved in the paradox is circular, we have to employ a hypothetical evaluation of the belief predicate, and if we do so through a revision process, we can avoid the contradiction which seems to be generated by some paradoxical belief sentences. But it is not easy to show that our notion of belief is circular. Especially, there is nothing like Tarski biconditionals in the case of belief. Nonetheless, I show in this dissertation that there is a certain schema, which I call the B-schema, whose instances can be taken as circular, partial definitions of a notion of belief, and it is that notion of belief which is involved in the paradox of belief instability. In this dissertation I also show that the revision approach can be extended for handling the Knower paradox. I argue that the Knower paradox arises because our notion of knowledge involved in the paradox is circular. (shrink)

In his papers ‘Semantic Paradox ’ and ‘The Liar Paradox: Tangles and Chains,’ Tyler Burge provides a hierarchical solution to the Liar paradox. And in his paper ‘Epistemic Paradox ’ Burge extends his hierarchy approach to the epistemic paradox of belief instability, which I shall explain shortly. Although Burge's views on the Liar paradox have been widely criticized, his views on the paradox of belief instability have not received notable attention. In this paper I shall argue that Burge's proposal is (...) inadequate as a solution to the paradox of belief instability. For this purpose, I shall criticize Burge's claim that a circular evaluation of a thought is impossible, which is crucial for his proposal. The question of whether or not a circular evaluation of belief is possible is of its own philosophical interest as well. (shrink)

This paper provides a new solution to the epistemic paradox of belief-instability, a problem of rational choice which has recently received considerable attention (versions of the problem have been discussed by — among others — Tyler Burge, Earl Conee, and Roy Sorensen). The problem involves an ideally rational agent who has good reason to believe the truth of something of the form:[Ap] p if and only if it is not the case that I accept or believe p.

– We offer a new motivation for imprecise probabilities. We argue that there are propositions to which precise probability cannot be assigned, but to which imprecise probability can be assigned. In such cases the alternative to imprecise probability is not precise probability, but no probability at all. And an imprecise probability is substantially better than no probability at all. Our argument is based on the mathematical phenomenon of non-measurable sets. Non-measurable propositions cannot receive precise probabilities, but there is a natural (...) way for them to receive imprecise probabilities. The mathematics of non-measurable sets is arcane, but its epistemological import is far-reaching; even apparently mundane propositions are liable to be affected by non-measurability. The phenomenon of non-measurability dramatically reshapes the dialectic between critics and proponents of imprecise credence. Non-measurability offers natural rejoinders to prominent critics of imprecise credence. Non-measurability even reverses some of the critics’ arguments—by the very lights that have been used to argue against imprecise credences, imprecise credences are better than precise credences. (shrink)

A process-oriented model of belief is presented which permits the representation of nested propositional attitudes within first-order logic. The model (NIM, for nested intensional model) is axiomatized, sense-based (via intensions), and sanctions inferences involving nested epistemic attitudes, with different agents and different times. Because NIM is grounded upon senses, it provides a framework in which agents may reason about the beliefs of another agent while remaining neutral with respect to the syntactic forms used to express the latter agent's beliefs. Moreover, (...) NIM provides agents with a conceptual map, interrelating the concepts of knowledge, belief, truth, and a number of cognate concepts, such as infers, retracts, and questions. The broad scope of NIM arises in part from the fact that its axioms are represented in a novel extension of first-order logic, -FOL (presented herein). -FOL simultaneously permits the representation of truth ascriptions, implicit self-reference, and arbitrarily embedded sentences within a first-order setting. Through the combined use of principles derived from Frege, Montague, and Kripke, together with context-sensitive semantic conventions, -FOL captures the logic of truth inferences, while avoiding the inconsistencies exhibited by Tarski. Applications of -FOL and NIM to interagent reasoning are described and the soundness and completeness of -FOL are established herein. (shrink)

According to some philosophers, the Liar paradox arises because of a mistaken theory of truth. Its lesson is that we must reject some instances of the naive propositional truth-schema \It is true that \ if and only if \\. In this paper, I construct a novel semantic paradox in which no principle even analogous to the truth-schema plays any role. I argue that this undermines the claim that we ought to respond to the Liar by revising our theory of truth.

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 Lottery Paradox and the Preface Paradox both involve the thesis that high probability is sufficient for rational acceptability. The standard solution to these paradoxes denies that rational acceptability is deductively closed. This solution has a number of untoward consequences. The present paper suggests that a better solution to the paradoxes is to replace the thesis that high probability suffices for rational acceptability with a somewhat stricter thesis. This avoids the untoward consequences of the standard solution. The new solution will (...) be defended against a seemingly obvious objection. 1 The paradoxes of rational acceptability 2 The standard solution 3 A new solution to the paradoxes 4 Basic assumptions 5 The new solution defended 6 Conclusion 7 Appendix. (shrink)

G. F. Stout is famous as an early twentieth century proselyte for abstract particulars, or tropes as they are now often called. He advanced his version of trope theory to avoid the excesses of nominalism on the one hand and realism on the other. But his arguments for tropes have been widely misconceived as metaphysical, e.g. by Armstrong. In this paper, I argue that Stout’s fundamental arguments for tropes were ideological and epistemological rather than metaphysical. He moulded his scheme to (...) fit what is actually given to us in perception, arguing that our epistemic practices would break down in an environment where only universals were given to us. (shrink)

Many philosophers have claimed that “belief aims at the truth”. But is there any interpretation of this claim on which it counts as true? According to some philosophers, the best interpretation of the claim takes it as the normative thesis that belief is subject to a truth-norm. The goal of this essay is to clarify this normative interpretation of the claim. First, the claim can be developed so that it applies to partial beliefs as well as to flat-out full beliefs. (...) Secondly, an answer is given to the objection that has been raised against the claim that belief is subject to a truth-norm of this sort by Krister Bykvist and Anandi Hattiangadi; responding to this objection will involve careful reflection on the structure of normative concepts, and of how these normative concepts apply to belief. (shrink)

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