The received view has it that Hans Reichenbach and his friends of the Berlin Group worked close together with the more prominent Vienna Circle. In the wake of this view, Reichenbach was often treated as a logical positivist – despite the fact that he decisively opposed it. In this chapter we follow another thread. We shall show the “third man”– besides Reichenbach and Walter Dubislav – of the Berlin Group, Kurt Grelling, as a man who could grasp the academic (...) trends of the time faster than anybody else, who was better informed about logic and philosophy of nature than his two prominent colleagues and thus, could better delineate, although tentatively, central threads of research of the Berlin Group. Grelling did this on several occasions, but most ostensibly in the last years of his life when he was focused on problems of formal ontology. On the basis of this analysis, we shall see that in the early 1920s, Reichenbach too was led by a project in ontology of science that he elaborated together with the psychologist Kurt Lewin. Moreover, Reichenbach’s later philosophy of nature was also shaped by this project. We present this direction of philosophy of science as a “road less travelled” which, however, if revived, can point to a new direction that will more closely connect philosophy and science. (shrink)

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. (shrink)

The paper discusses whether there are strictly inexpressible properties. Three main points are argued for: (i) Two different senses of ‘predicate t expresses property p ’ should be distinguished. (ii) The property of being a predicate that does not apply to itself is inexpressible in one of the senses of ‘express’, but not in the other. (iii) Since the said property is related to Grelling’s Antinomy, it is further argued that the antinomy does not imply the non-existence of that (...) property. (shrink)

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 'heterologicality'. 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. In Section 1, Grelling's Paradox is presented informally. After making some refinements, Grelling's Paradox is then presented formally. In Section 2, the formal version of Grelling's Paradox is evaluated, and several previously proposed solutions are discussed and argued to be inadequate. In Section 3, it is argued that the heterologicality predicate is an indexical expression. A semantics for the heterologicality predicate is given, and it is shown how this semantics accounts for the unproblematic predications of heterologicality, as well as the problematic cases, and therefore constitutes a satisfactory and complete solution to Grelling's Paradox. Objections to this solution are addressed in Section 4. The conclusions of this paper are summarized in Section 5. (shrink)

La solution des antinomies s’accomplit en 3 étapes. 1° La théorie des types de Russell avec l’axiome de réductibilité. 2° Ramsey divise les antinomies en deux groupes. Le premier groupe reçoit sa solution de la simple théorie des types ; seul, le groupe élargi exige l’axiome de réductibilité. 3° Hilbert fonde la théorie métamathématique de la preuve, que les logiciens polonais élargissent en une métalogique. Gödel découvre l’arithmétisation et il prouve l’existence de propositions insolubles. Tarski montre que le concept de (...) vérité ne peut être défini sans contradiction que dans un métalangage. Carnap généralise ce résultat, ce qui fait que les antinomies syntactiques sont sans dommage pour la science. (shrink)

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.

Tarski's argumentative use of the liar paradox is well-known, but officially it is the Grelling paradox that has final pride of place in Tarski's argument, not the Liar at all. Tarski explicitly gives argumentation that adverts to the liar argument, but it is an alternative argument—one he only hints at and which adverts to the Grelling—which he says has the advantage of removing any empirical element. In this paper, we will examine how the Grelling might be used (...) in place of the Liar in Tarski's argument for his exact indefinability thesis, and assess in what way the difference might be significant. If successful, Tarski's use of the Grelling puts pressure on how Convention T can be justified. (shrink)