Paradoxical Aspects of the Russellian Conception of Existence

In this paper, the authors try to clarify the relations between Meinong’s and Russell's thoughts on the ontological ideas of existence. The Meinongian theory on non-existent objects does not in itself violate the principle of non-contradiction, since the problem that this hypothesis offers to the theory of definite descriptions is not so much a logical problem as an ontological problem. To demonstrate this we will establish what we believe are the two main theses basic to the theory of descriptions: the epistemological thesis and logical thesis.

GARDNER'S PARADOX AND THEORY OF DESCRIPTIONS

Martin Gardner's two-children paradox posits two scenarios, in one we know that of two children one is a girl, and in the other we know that of two children the older one is a girl. The chances of the other child being a girl is not the same in these two scenarios, in the first being 1 in 3 while in the second they are 1 in 2. Gardner himself believed that the problem of this paradox lies in the ambiguous way the scenarios are articulated. However, it is possible to show that the original version of the paradox provides sufficient content for a meaningful explanation of these unexpected results. Inspired by comments by Leonard Mlodinow, we attempt to provide a comprehensible explanation for this counterintuitive change with help of Bertrand Russell's theory of descriptions. The difference between the two scenarios then boils down to the difference between indefinite and definite descriptions.

Understanding the Welby-Russell Correspondence

ABSTRACTA shallow reading of the 1905 correspondence between Victoria Welby and Bertrand Russell yields the impression that Welby has misunderstood Russell's “On Denoting.” I argue that a deeper reading reveals that Welby should be understood, not as misunderstanding Russell, but as bringing a pragmatic attitude to bear on Russell's theory of descriptions in order to expose the limits of his strictly logical analysis.

REFERENCES OF PROPER NAMES AS THE PROBLEM OF CONTEMPORARY PHILOSOPHY OF LANGUAGE

This article investigates the idea that meanings of proper names are their references which is popular in the philosophy of language. The aim is to show, first, that there is no satisfactory answer to the question “How references as stable relations between words and objects appear, due to accomplishment of what conditions these properties of linguistic expressions may be produced?”, and, second, that we can still use the notion of reference in our explanations of some effects of communication if we treat reference as pragmatic rather than semantic phenomenon. The actuality of this research is provided by the fact that the identification of meanings of certain types of terms, proper names first of all, with their references is still very influential account in the philosophy of language. The author uses the methods of historical exposition and philosophical analysis of the main theories of reference, such as theory of descriptions and causal theory of reference. It is shown that these theories in their different modifications fail to explain how references as semantic relations between proper names and their bearers may be produced in the course of communication and social interaction. But although there are alternative concepts of the nature meanings of proper names it is concluded that we still may apply the notion of reference in our explanations of natural language communication if we treat reference as pragmatic effect caused by mutual coordination of actions achieved by the participants of certain communicative situation.

The Predicate of Existence

Kant famously declared that existence is not a (real) predicate. This famous dictum has been seen as echoed in the doctrine of the founders of modern logic, Gottlob Frege and Bertrand Russell, that existence isn’t a first-order property possessed by individuals, but rather a second-order property expressed by the existential quantifier. Russell in 1905 combined this doctrine with his new theory of descriptions and declared the paradox of nonexistence to be resolved without resorting to his earlier distinction between existence and being. In recent years, however, logicians and philosophers like Saul Kripke, David Kaplan, and Nathan Salmon have argued that there is no defensible reason to deny that existence is a property of individuals. Kant’s dictum has also been re-evaluated, the result being that the paradox of nonexistence has not, after all, disappeared. Yet it’s not clear how exactly Kripke et al. propose to resolve the paradox.

Negative Existentials

This chapter presents a critical discussion of the problem of negative existentials in the tradition of analytic philosophy of language. Firstly, it presents the problem as a compelling argument in support of the counterintuitive conclusion that sentences such as ‘Pegasus does not exist’ cannot be used to make true and informative assertions. Then, seven influential proposals for solving the problem are considered, each of which is construed as a response to this argument. The proposals considered are Russell’s (1905) theory of descriptions, Quine’s (1948) prescribed elimination of names, Donnellan’s (1974) ‘historical block’ view, Kripke’s (1973/2013) ‘no such proposition’ view, Salmon’s (1998) fictional entities view, Braun’s (1993) gappy proposition view, and Katz’s (1990) pure metalinguistic descriptivism. Though the official stance with regard to these proposals is neutral, the chapter concludes with a brief reactive summary that endorses a general pragmatic approach to the problem.

Descriptions

‘Definite descriptions’ are noun phrases of the form ‘the’ + noun complex (for example, ‘the finest Greek poet’, ‘the cube of five’) or of the form possessive + noun complex (for example, ‘Sparta’s defeat of Athens’). As Russell realized, it is important to philosophy to be clear about the semantics of such expressions. In the sentence ‘Aeschylus fought at Marathon’, the function of the subject, ‘Aeschylus’, is to refer to something; it is a referential noun phrase (or ‘singular term’). By contrast, in the sentence ‘Every Athenian remembers Marathon’, the subject noun phrase, ‘every Athenian’, is not referential but quantificational. Definite descriptions appear at first sight to be referential. Frege treated them referentially, but Russell held that they should be treated quantificationally in accordance with his theory of descriptions, and argued that certain philosophical puzzles were thereby solved.

Russell, Bertrand Arthur William (1872–1970)

Bertrand Russell divided his efforts between philosophy and political advocacy on behalf of a variety of radical causes. He did his most important philosophical work in logic and the philosophy of mathematics between 1900 and 1913, though later he also did important work in epistemology, metaphysics and the philosophy of mind, and continued to contribute to philosophy until the late 1950s. He wrote relatively little on ethics. His political work went on until his death. In the philosophy of mathematics his position was logicism, the view that all of mathematics can be derived from logical premises, which he attempted to establish in detail by actual derivations, creating in the process what is essentially now the standard formulation of classical logic. Early in this work he discovered the self- referential paradoxes which posed the main difficulty for logicism and which he eventually overcame by the ramified theory of types. Logic was central to Russell’s philosophy from 1900 onwards, and much of his fertility and importance as a philosopher came from his application of the new logic to old problems. Among his most important logical innovations were the modern theory of relations and the theory of descriptions. The latter enabled him to reparse sentences containing the phrase ‘the so-and-so’ into a form in which the phrase did not appear. The importance of this theory for subsequent philosophy was that it enabled one to recast sentences which apparently committed one to the existence of the so-and-so into sentences in which no such commitment was suggested. This laid the basis for a new method in metaphysics (widely pursued by Russell and others in the first half of the century) in which theories about items of a given kind are reformulated so as to avoid reference to items of that kind. Logicism itself offers just such a treatment of mathematics and in his later work Russell used the method repeatedly, though the reformulations he suggested were rarely so explicit as the ones he had offered in mathematics. In 1914 he proposed a solution to the problem of the external world by constructing matter out of sensibilia. After 1918 he proposed to construct both mind and matter out of events. After 1940 he treated all particulars as bundles of qualities. In each case his motivation was to avoid postulating anything that could be constructed, thereby eliminating ontological commitments which had no independent evidential support. Outside mathematics, his starting-point was the empirically given and he attempted to make his constructions depend as little as possible upon items not given in experience. He was not, however, a strict empiricist, since he did not think that empirical evidence alone would be sufficient for the constructions and he was always prepared to supplement it in order to obtain them. He wanted to construct, not those items which were empirically warranted, but those which were required by the relevant scientific theories, for he regarded science as the best available, though by no means an infallible, source of truth. The task, in each case, was therefore to reveal the least amount of apparatus that would have to be assumed in addition to the empirical data in order for the constructions required by science to be possible. This methodology, which he pursued throughout his career, gives an underlying unity to what, more superficially, appears as a series of abrupt changes of position.