Off-campus access
Using PhilPapers from home?
Click here to configure this browser for off-campus access.
- Jay Newhard (2005). Grelling's Paradox. Philosophical Studies 126 (1):1 - 27.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.Reading list | Discuss | Edit | Categorize |My bibliography
| Export citation | Other links: jstor.org | Scholar | At my library 
Similar books and articles
The only passage from Aristotle's works that seemsto discuss the paradox of the liar is within chapter 25 of Sophistici Elenchi (180a34–b7). This passage raises several questions: Is it really about the paradox of the liar? If it is, is it addressing a strong version of the paradox or some weak strain of it? If it is addressing a strong version of the paradox, what solution does it propose? The conciseness of the passage does not enable one to answer these questions beyond doubt, and commentators have offered very different replies. However, a reasonable case can be made for claiming, first, that the passage in question is about the paradox of the liar, second, that it addresses a strong version of the paradox, and, third, that it attempts to solve it by assuming that someone uttering 'I am speaking falsely' (or whatever sentence-type the paradox turns on) is neither speaking truly nor speaking falsely absolutely.
Reading list
| Discuss | Edit | Categorize | My bibliography | Export citation | Scholar | At my library | More options ...
| | Scholar | At my library | More options ... There is a little known paradox the solution to which is a guide to a much more thoroughgoing solution to a whole range of classic paradoxes. This is shown in this paper with respect to Berrys Paradox, Heterologicality, Russells Paradox, and the Paradox of Predication, also the Liar and the Strengthened Liar, using primarily the epsilon calculus. The solutions, however, show not only that the first-order predicate calculus derived from Frege is inadequate as a basis for a clear science, and should be replaced with Hilbert and Bernays conservative extension. Standard second-order logic, and quantified propositional logic also must be substantially modified, to incorporate, in the first place, nominalizations of predicates, and whole sentences. And further modifications must be made, so as to insist that predicates are parts of sentences rather than forms of them, and that truth is a property of propositions rather than their sentential expressions. In all, a thorough reworking of what has been called logic in recent years must be undertaken, to make it more fit for use.
Reading list
| Discuss | Edit | Categorize | My bibliography | Export citation | Other links: jstor.org | Scholar | At my library | More options ...
| | Other links: jstor.org | Scholar | At my library | More options ... The Pinocchio paradox, devised by Veronique Eldridge-Smith in February 2001, is a counter-example to solutions to the Liar that restrict the use or definition of semantic predicates. Pinocchio’s nose grows if and only if what he is stating is false, and Pinocchio says ‘My nose is growing’. In this statement, ‘is growing’ has its normal meaning and is not a semantic predicate. If Pinocchio’s nose is growing it is because he is saying something false; otherwise, it is not growing. ‘Because’ stands here for a non-semantic relation; it might be supposed to be causal or of some other nature, but it is not semantic. The paradox is discussed in relation to Tarski’s and Kripke’s theories of truth. Although the paradox is not necessarily a counter-example to a theory of a truth predicate, it is a problem for a theory of truth of the kind preserved by validity.
Reading list
| Discuss | Edit | Categorize | My bibliography | Export citation | Other links: analysis.oxfordjournals.org dx.doi.org | Scholar | At my library | More options ...
| | Other links: analysis.oxfordjournals.org dx.doi.org | Scholar | At my library | More options ... This discusses a mistake (concerning what a definition is) in “Grelling’s revenge”, Analysis 64, 251-6 (2004), by Dale Jacquette, who claims that the simple theory of types is inconsistent.
No categories
Reading list
| Discuss | Edit | Categorize | My bibliography | Export citation | Other links: interscience.wiley.com hdl.handle.net jstor.org analysis.oxfordjournals.org dx.doi.org | Scholar | At my library | More options ...
| | Other links: interscience.wiley.com hdl.handle.net jstor.org analysis.oxfordjournals.org dx.doi.org | Scholar | At my library | More options ... In this paper, I examine a solution to the Liar paradox found in the work of Ockham, Burley, and Pseudo-Sherwood. I reject the accounts of this solution offered by modern commentators. I argue that this medieval line suggests a non-hierarchical solution to the Liar, according to which ?true? is analysed as an indexical term, and paradox is avoided by minimal restrictions on tokens of ?true?. In certain respects, this solution resembles the recent approaches of Charles Parsons and Tyler Burge; in other respects, it is related to a suggestion of Gödel. But, as a whole, it suggests an original solution to the Liar paradox, quite unlike any current proposals.
Reading list
| Discuss | Edit | Categorize | My bibliography | Export citation | Other links: tandfonline.com dx.doi.org | Scholar | At my library | More options ...
| | Other links: tandfonline.com dx.doi.org | Scholar | At my library | More options ... The No-No Paradox consists of a pair of statements, each of which ?says? the other is false. Roy Sorensen claims that the No-No Paradox provides an example of a true statement that has no truthmaker: Given the relevant instances of the T-schema, one of the two statements comprising the ?paradox? must be true (and the other false), but symmetry constraints prevent us from determining which, and thus prevent there being a truthmaker grounding the relevant assignment of truth values. Sorensen's view is mistaken: situated within an appropriate background theory of truth, the statements comprising the No-No Paradox are genuinely paradoxical in the same sense as is the Liar (and thus, on Sorensen's view, must fail to have truth values). This result has consequences beyond Sorensen's semantic framework. In particular, the No-No Paradox, properly understood, is not only a new paradox, but also provides us with a new type of paradox, one which depends upon a general background theory of the truth predicate in a way that the Liar Paradox and similar constructions do not.
Reading list
| Discuss | Edit | Categorize | My bibliography | Export citation | Other links: tandfonline.com dx.doi.org | Scholar | At my library | More options ...
| | Other links: tandfonline.com dx.doi.org | Scholar | At my library | More options ... One recently proposed solution to the Liar paradox is the contextual theory of truth. Tyler Burge (1979) argues that truth is an indexical notion and that the extension of the truth predicate shifts during Liar reasoning. A Liar sentence might be true in one context and false in another. To many, contextualism seems to capture our pre-theoretic intuitions about the semantic paradoxes; this is especially due to its reliance on the so-called Revenge phenomenon. I, however, show that Super-Liar sentences (where a Super-Liar sentence is a sentence which says of itself that it is not true in any context) generate a significant problem for Burge’s contextual theory of truth.
Reading list
| Discuss | Edit | Categorize | My bibliography | Export citation | Scholar | At my library | More options ...
| | Scholar | At my library | More options ... Curry's paradox, so named for its discoverer, namely Haskell B. Curry, is a paradox within the family of so-called paradoxes of self-reference (or paradoxes of circularity). Like the liar paradox (e.g., ‘this sentence is false’) and Russell's paradox , Curry's paradox challenges familiar naive theories, including naive truth theory (unrestricted T-schema) and naive set theory (unrestricted axiom of abstraction), respectively. If one accepts naive truth theory (or naive set theory), then Curry's paradox becomes a direct challenge to one's theory of logical implication or entailment. Unlike the liar and Russell paradoxes Curry's paradox is negation-free; it may be generated irrespective of one's theory of negation. An intuitive version of the paradox runs as follows.
Reading list
| Discuss | Edit | Categorize | My bibliography | Export citation | Scholar | More options ...
| | Scholar | More options ... Graham Priest (1994) has argued that the following paradoxes all have the same structure: Russell’s Paradox, Burali-Forti’s Paradox, Mirimanoff’s Paradox, König’s Paradox, Berry’s Paradox, Richard’s Paradox, the Liar and Liar Chain Paradoxes, the Knower and Knower Chain Paradoxes, and the Heterological Paradox. Their common structure is given by Russell’s Schema: there is a property φ and function δ such that..
Reading list
| Discuss | Edit | Categorize | My bibliography | Export citation | Other links: jstor.org mind.oxfordjournals.org mind.oupjournals.org dx.doi.org | Scholar | At my library | More options ...
| | Other links: jstor.org mind.oxfordjournals.org mind.oupjournals.org dx.doi.org | Scholar | At my library | More options ... In this essay (for undergraduates) I introduce three of the famous semantic paradoxes: the Liar, Grelling’s, and the No-No. Collectively, they seem to show that the notion of truth is highly paradoxical, perhaps even contradictory. They seem to show that the concept of truth is a bit akin to the concept of a married bachelor—it just makes no sense at all. But in order to really understand those paradoxes one needs to be very comfortable thinking about how lots of interesting sentences talk about not dogs or cats or elections or baseball but sentences. That is, we need to get familiar analyzing sentences that talk about sentences.
Reading list
| Discuss | Edit | Categorize | My bibliography | Export citation | Scholar | More options ...
| | Scholar | More options ... Discussion of Jay Newhard, Grelling's Paradox
 Back
All discussions
Start a new thread
|
There are no threads in this forum |
Nothing in this forum yet.
