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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.

An analysis—in its simplest form—is an assertion aiming to capture a certain intimate link between a given concept (the analysandum) and another, typically more precise and fully explicit concept (the analysans). For instance, the following are classical examples of analyses proposed for the geometric concept of a circle and the epistemic concept of knowledge, respectively: (1) A circle is a locus of points in the same plane equidistant from some common point. (2) Knowledge is justified true belief. In some cases, even a whole theory may be regarded as a constituting an analysis. For example, Russell’s celebrated theory of definite descriptions may be viewed as an analysis of that formal concept which in natural language can be expressed by means of the definite article.1 Analyses are also called philosophical, real, or simply analyzing defi- nitions. This is appropriate, since analyses are implicitly assumed to fulfill the following Definition Constraint: (DC) An analysis must obey the laws governing definitions, where the expression standing for the analysans is viewed as a defi- niens and the expression standing for the analysandum as a corresponding definiendum. 2 1..

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.

Moore's paradox pits our intuitions about semantic oddnessagainst the concept of truth-functional consistency. Most solutions tothe problem proceed by explaining away our intuitions. But``consistency'' is a theory-laden concept, having different contours indifferent semantic theories. Truth-functional consistency is appropriateonly if the semantic theory we are using identifies meaning withtruth-conditions. I argue that such a framework is not appropriate whenit comes to analzying epistemic modality. I show that a theory whichaccounts for a wide variety of semantic data about epistemic modals(Update Semantics) buys us a solution to Moore's paradox as a corollary.It turns out that Moorean propositions, when looked at through the lenseof an appropriate semantic theory, are inconsistent after all.

It might be thought that vagueness precludes the possibility of classical conceptual analysis and, thus, that the classical or definitional view of the nature of complex concepts is incorrect. The present paper argues that classical analysis can be had for concepts expressed by vague language since (1) all of the general theories of vagueness are compatible with the thesis that all complex concepts have classical analyses and also that (2) the meaning of vague expressions can be analyzed by having the degree of vagueness of a given analysandum be mapped onto the vagueness of an analysans.

The term 'explicatum' has been suggested by the following two usages. Kant calls a judgment explicative if the predicate is obtained by analysis, of the subject. Husserl, in speaking about the synthesis of identification between a confused, nonarticulated sense and a subsequently intended distinct, articulated sense, calls the latter the 'Explikat' of the former. (For both uses see Dictionary Of Philosophy [1942], ed. D. Runes, p. 105). What I mean by 'explicandum' and 'explicatum' is to some extent similar to what C. H. Langford calls 'analysandum' and 'analysans': "the analysis then states an appropriate relation of equivalence between the analysandum and the analysans" ("The notion of analysis in Moore's philosophy", in The Philosophy of G. E. Moore [1943], ed. P. A. Schilpp, pp. 321-42; see p. 323); he says that the motive of an analysis "is usually that of supplanting a relatively vague idea by a more precise one" (ibid., p. 329).

Philosophy of Language Philosophy of Logic On a rather popular conception, the paradox of analysis suggests that the intersubstitutivity of analysans and analysandum should be restricted to non-psychological contexts. This is typically taken to be compatible with the idea that two sentences differing only in that one has the analysandum where the other has the analysans express exactly the same proposition. In this note we argue that this should be pondered upon in light of the view that many important ordinary concepts are circular. In particular, we submit that if there are correct analyses grounding circular definitions, then we are bound to further restrict the substitutivity principle, for we must admit that it might fail even in non- psychological contexts. Show Abstract..

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.

The very idea of informative analysis gives rise to a well-known paradox. Yet a parallel puzzle, herein called the paradox of synonymy, arises for statements which do not express analyses. The paradox of synonymy has a straightforward metalinguistic solution: certain words are referring to themselves. Likewise, the paradox of analysis can be solved by recognizing that certain expressions in an analysis statement are referring to their own semantic structures.

On a rather popular conception, the paradox of analysis suggests that the intersubstitutivity of analysans and analysandum should be restricted to non-psychological contexts. This is typically taken to be compatible with the idea that two sentences differing only in that one has the analysandum where the other has the analysans express exactly the same proposition. In this note we argue that this should be pondered upon in light of the view that many important ordinary concepts are circular. In particular, we submit that if there are correct analyses grounding circular definitions, then we are bound to further restrict the substitutivity principle, for we must admit that it might fail even in non- psychological contexts.