Grelling’s Paradox

Grelling’s Paradox is the paradox which results from considering whether heterologicality, the word-property which a designator has when and only when the designator does not bear the word-property it designates, is had by ‘ ȁ8heterologicality’. Although there has been some philosophical debate over its solution, Grelling’s Paradox is nearly uniformly treated as a variant of either the Liar Paradox or Russell’s Paradox, a paradox which does not present any philosophical challenges not already presented by the two better known paradoxes. The aims of this paper are, first, to offer a precise formulation of Grelling’s Paradox which is clearly distinguished from both the Liar Paradox and Russell’s Paradox; second, to offer a solution to Grelling’s Paradox which both resolves the paradoxical reasoning and accounts for unproblematic predications of heterologicality; and, third, to argue that there are two lessons to be drawn from Grelling’s Paradox which have not yet been drawn from the Liar or Russell’s Paradox. The first lesson is that it is possible for the semantic content of a predicate to be sensitive to the semantic context; i.e., it is possible for a predicate to be an indexical expression. The second lesson is that the semantic content of an indexical predicate, though unproblematic for many cases, can nevertheless be problematic in some cases.     

McTaggart’s Paradox and Crisp’s Presentism

In his review of The Ontology of Time, Thomas Crisp (Notre Dame Philosophical Reviews, 2005a) argues that Oaklander's version of McTaggart's paradox does not make any trouble for his version of presentism. The aim of this paper is to refute that claim by demonstrating that Crisp's version of presentism does indeed succumb to a version of McTaggart's argument. I shall proceed as follows. In Part I I shall explain Crisp's view and then argue in Part II that his analysis of temporal becoming, temporal properties and temporal relations is inadequate. Finally, in Part III, I shall demonstrate that his presentist ontology of time is susceptible to the paradox he so assiduously sought to avoid.     

Moore’s Paradox for God

Philosophia - I argue that ‘Moore’s paradox for God’. I do not believe this proposition shows that nobody can be both omniscient and rational in all her beliefs. I then anticipate...     

Curry’s Paradox and ω -Inconsistency

In recent years there has been a revitalised interest in non-classical solutions to the semantic paradoxes¹. In this paper I show that a number of logics are susceptible to a strengthened version of Curry’s paradox. This can be adapted to provide a proof theoretic analysis of the ω-inconsistency in ?ukasiewicz’s continuum valued logic, allowing us to better evaluate which logics are suitable for a naïve truth theory. On this basis I identify two natural subsystems of ukasiewicz logic which individually, but not jointly, lack the problematic feature.     

Distributed Knowability and Fitch’s Paradox

Recently predominant forms of anti-realism claim that all truths are knowable. We argue that in a logical explanation of the notion of knowability more attention should be paid to its epistemic part. Especially very useful in such explanation are notions of group knowledge. In this paper we examine mainly the notion of distributed knowability and show its effectiveness in the case of Fitch’s paradox. Proposed approach raised some philosophical questions to which we try to find responses. We also show how we can combine our point of view on Fitch’s paradox with the others. Next we give an answer to the question: is distributed knowability factive? At the end, we present some details concerning a construction of anti-realist modal epistemic logic.     

Fitch’s Paradox and Probabilistic Antirealism

Fitch’s paradox shows, from fairly innocent-looking assumptions, that if there are any unknown truths, then there are unknowable truths. This is generally thought to deliver a blow to antirealist positions that imply that all truths are knowable. The present paper argues that a probabilistic version of antirealism escapes Fitch’s result while still offering all that antirealists should care for.     

Mereological Dominance and Simpson’s Paradox

Philosophia - Numerous papers have investigated the transitivity principle of ‘better-than.’ A recent argument appeals to the principle of mereological dominance for transitivity....     

Moore’s Paradox and Moral Motivation

Assertions of statements such as ‘it’s raining, but I don’t believe it’ are standard examples of what is known as Moore’s paradox. Here I consider moral equivalents of such statements, statements wherein individuals affirm moral judgments while also expressing motivational indifference to those judgments (such as ‘hurting animals for fun is wrong, but I don’t care’). I argue for four main conclusions concerning such statements: 1. Such statements are genuinely paradoxical, even if not contradictory. 2. This paradoxicality can be traced to a form of epistemic self-defeat that also explains the paradoxicality of ordinary Moore-paradoxical statements. 3. Although a simple form of internalism about moral judgment and motivation can explain the paradoxicality of these moral equivalents, a more plausible explanation can be provided that does not rely on this simple form of internalism. 4. The paradoxicality of such statements suggests a more credible understanding of the thesis that those who are not motivated by their moral judgments are irrational.     

Yablo’s Paradox and ω-Inconsistency

It is argued that Yablo’s Paradox is not strictly paradoxical, but rather ‘ω-paradoxical’. Under a natural formalization, the list of Yablo sentences may be constructed using a diagonalization argument and can be shown to be ω-inconsistent, but nonetheless consistent. The derivation of an inconsistency requires a uniform fixed-point construction. Moreover, the truth-theoretic disquotational principle required is also uniform, rather than the local disquotational T-scheme. The theory with the local disquotation T-scheme applied to individual sentences from the Yablo list is also consistent.     

Can the Paradox of Forgiveness Be Dissolved?

The “paradox of forgiveness” can be described as follows: Forgiving, unlike forgetting, is tied to reasons. It is a response to considerations that lead us to think that we ought to forgive. On the other hand, acts of forgiveness, unlike excuses, are responses to instances of culpable wrongdoing. If, however, the wrongdoing is culpable, there is (or seems to be) no reason to forgive it. So two mutually exclusive theses about forgiveness both seem to be equally warranted: Forgiveness is related to reasons, but there can be no reasons for forgiveness. In this paper, I attempt to dissolve this paradox. I argue that the paradox arises as a result of a too narrow conception of “reason” and that it can be dissolved if we acknowledge different kinds of reasons for forgiveness. More specifically, I examine three kinds of reasons for forgiving an act of wrongdoing: (1) Moral reasons that make forgiveness morally mandatory. (2) Prudential reasons for forgiveness. (3) Moral reasons that pertain to the character of the forgiver and that favor forgiveness without making it morally mandatory. I show that while the paradox of forgiveness arises when we consider reasons of the first kind, it can be dissolved with recourse to reasons of the second and third kind. The upshot of the argument is that we can be rational in deciding to overcome our feelings of resentment towards an act of unjustified and unexcused wrongdoing—and this is a strong point in favor of forgiveness.     

Rescuing Poincaré from Richard’s Paradox

Poincaré in a 1909 lecture in Göttingen proposed a solution to the apparent incompatibility of two results as viewed from a definitionist perspective: on the one hand, Richard’s proof that the definitions of real numbers form a countable set and, on the other, Cantor’s proof that the real numbers make up an uncountable class. Poincaré argues that, Richard’s result notwithstanding, there is no enumeration of all definable real numbers. We apply previous research by Luna and Taylor on Richard’s paradox, indefinite extensibility and unrestricted quantification to evaluate Poincaré’s proposal. We emphasize that Poincaré’s solution involves an early recourse to indefinite extensibility and argue that his proposal, if it is to completely avoid Richard’s paradox, requires rejecting absolutely unrestricted quantification: Richard’s paradox provides a context in which paradox seems inescapable if unrestricted quantification is possible. In proposing his solution to the apparent conflict between Richard’s and Cantor’s results, Poincaré employs temporal expressions whose exact meaning he does not clarify. We suggest an interpretation of these expressions in terms of order of availability and briefly discuss its explanatory power in topics like paradoxes, limitation theorems and indefinite extensibility.     

A Principled Solution to Fitch’s Paradox

To save antirealism from Fitchs Paradox, Tennant has proposed to restrict the scope of the antirealist principle that all truths are knowable to truths that can be consistently assumed to be known. Although the proposal solves the paradox, it has been accused of doing so in an ad hoc manner. This paper argues that, first, for all Tennant has shown, the accusation is just; second, a restriction of the antirealist principle apparently weaker than Tennants yields a non-ad hoc solution to Fitchs Paradox; and third, the alternative is only apparently weaker than, and even provably equivalent to, Tennants. It is thereby shown that the latter is not ad hoc after all.     

Belief, assertion and Moore’s Paradox

In this article I argue that two received accounts of belief and assertion cannot both be correct, because they entail mutually contradictory claims about Moore’s Paradox. The two accounts in question are, first, the Action Theory of Belief (ATB), the functionalist view that belief must be manifested in dispositions to act, and second, the Belief Account of Assertion (BAA), the Gricean view that an asserter must present himself as believing what he asserts. It is generally accepted also that Moorean assertions are absurd, and that BAA explains why they are. I shall argue that ATB implies that some Moorean assertions are, in some fairly ordinary contexts, well justified. Thus BAA and ATB are mutually inconsistent. In the concluding section I explore three possible ways of responding to the dilemma, and what implications they have for the nature of the constitutive relationships linking belief, assent and behavioural dispositions.

The Paradox of Howard Becker’s Intellectual Identity

Howard S. Becker, best known as a sociologist of deviance, claims that he “never really did work on deviance as such.” Why does he say this? The fortuitous nature of his entry into the field, his belief that deviance is not an analytic category, and the amount of time, energy, and commitment he has invested in this as opposed to other fields, play a role in this stance. In all likelihood, contrary to his wish, Howard Becker will always be regarded as a deviance researcher.     

Rosser-Type Undecidable Sentences Based on Yablo’s Paradox

It is widely considered that Gödel’s and Rosser’s proofs of the incompleteness theorems are related to the Liar Paradox. Yablo’s paradox, a Liar-like paradox without self-reference, can also be used to prove Gödel’s first and second incompleteness theorems. We show that the situation with the formalization of Yablo’s paradox using Rosser’s provability predicate is different from that of Rosser’s proof. Namely, by using the technique of Guaspari and Solovay, we prove that the undecidability of each instance of Rosser-type formalizations of Yablo’s paradox for each consistent but not Σ₁-sound theory is dependent on the choice of a standard proof predicate.     

The Humean problem of induction and Carroll’s Paradox

Hume argued that inductive inferences do not have rational justification. My aim is to reject Hume’s argument. The discussion is partly motivated by an analogy with Carroll’s Paradox, which concerns deductive inferences. A first radically externalist reply to Hume (defended by Dauer and Van Cleve) is that justified inductive inferences do not require the subject to know that nature is uniform, though the uniformity of nature is a necessary condition for having the justification. But then the subject does not have reasons for believing what she believes. I defend a moderate externalist account that seeks to partly accommodate that objection to the radical externalist proposal. It is based on an extension of Peacocke’s theory of concepts: possession conditions for predicative concepts standing for natural properties include (fallible) dispositions to project them to new cases in accordance with inductive inferential patterns.

Moore’s Paradox is not just another pragmatic paradox

One version of Moore’s Paradox is the challenge to account for the absurdity of beliefs purportedly expressed by someone who asserts sentences of the form ‘p & I do not believe that p’ (‘Moorean sentences’). The absurdity of these beliefs is philosophically puzzling, given that Moorean sentences (i) are contingent and often true; and (ii) express contents that are unproblematic when presented in the third-person. In this paper I critically examine the most popular proposed solution to these two puzzles, according to which Moorean beliefs are absurd because Moorean sentences are instances of pragmatic paradox; that is to say, the propositions they express are necessarily false-when-believed. My conclusion is that while a Moorean belief is a pragmatic paradox, it is not just another pragmatic paradox, because this diagnosis does not explain all the puzzling features of Moorean beliefs. In particularly, while this analysis is plausible in relation to the puzzle posed by characteristic (i) of Moorean sentences, I argue that it fails to account for (ii). I do so in the course of an attempt to formulate the definition of a pragmatic paradox in more precise formal terms, in order to see whether the definition is satisfied by Moorean sentences, but not by their third-person transpositions. For only an account which can do so could address (ii) adequately. After rejecting a number of attempted formalizations, I arrive at a definition which delivers the right results. The problem with this definition, however, is that it has to be couched in first-person terms, making an essential use of ‘I’. Thus the problem of accounting for first-/third-person asymmetry recurs at a higher order, which shows that the Pragmatic Paradox Resolution fails to identify the source of such asymmetry highlighted by Moore’s Paradox.