A metafísica de 'Os Princípios da Matemática' de Russell e a controvérsia à respeito da suposta semelhança entre essa metafísica e a ontologia meinongiana

Resumo: No presente artigo, objetiva-se apresentar as principais características da metafísica do realismo lógico, desenvolvido por Russell em Os Princípios da Matemática, de 1903, e, principalmente, analisar a controvérsia sobre se os princípios dessa metafísica podem realmente ser interpretados como semelhantes aos princípios da ontologia meinongiana. São comparados os pontos de vista opostos dessa controvérsia à luz dos trechos de Os Princípios da Matemática que supostamente comprometeram Russell de ter elaborado uma gramática filosófica na qual todo e qualquer nome próprio ou descrição definida, ocupando a posição de sujeito lógico nas proposições, referem-se a objetos com alguma categoria de Ser. Ao realizar tal análise, conclui-se que o problema central diz respeito aos nomes próprios vazios e que, portanto, a metafísica de Os Princípios da Matemática expressa uma perspectiva instável da teoria da denotação de Russell. Palavras-chave: Russell; Ser; Existência; Significado. Russell’s The Principles of Mathematics metaphysics and the controversy over the supposed similarity between this metaphysics and the meinongian ontology Abstract: This article aims to present the main characteristics of the metaphysics of logical realism, developed by Russell in The Principles of Mathematics, of 1903, and, mainly, to analyze the controversy about whether the principles of this metaphysics can really be interpreted as similar to the principles of meinongian ontology. The opposing points of view of this controversy are compared in the light of the excerpts from The Principles of Mathematics that supposedly committed Russell to having elaborated a philosophical grammar in which all and any proper names or definite descriptions, occupying the position of logical subject in the propositions, refer to objects with some category of Being. In carrying out such an analysis, it is concluded that the central problem concerns empty proper names and that, therefore, the metaphysics of The Principles of Mathematics expresses an unstable perspective of Russell’s theory of denotation. Keywords: Russell; Being; Existence; Meaning. La metafísica de Los Principios de las Matemáticas de Russell y la controversia sobre la supuesta similitud entre esta metafísica y la ontología meinongiana Resumen: Este artículo tiene como objetivo presentar las principales características de la metafísica del realismo lógico, desarrollada por Russell en Los Principios de las Matemáticas, de 1903, y, principalmente, analizar la controversia sobre si los principios de esta metafísica pueden realmente interpretarse como similares a los principios de la ontología meinongiana. Los puntos de vista opuestos de esta controversia se comparan a la luz de los extractos de Los Principios de las Matemáticas que supuestamente comprometieron Russell a haber elaborado una gramática filosófica en la que todos y cualquier nombre propio o descripción definida, ocupando la posición de sujeto lógico en las proposiciones, se refieren a objetos con alguna categoría de Ser. Al realizar tal análisis, se concluye que el problema central concierne a los nombres propios vacíos y que, por lo tanto, la metafísica de Los Principios de las Matemáticas expresa una perspectiva inestable de la teoría de la denotación de Russell. Palabras clave: Russell; Ser; Existencia; Significado. Data de registro: 10/04/2020 Data de aceite: 08/12/2020

Ontological Pluralism and Notational Variance

Ontological pluralism is the view that there are different ways to exist. It is a position with deep roots in the history of philosophy, and in which there has been a recent resurgence of interest. In contemporary presentations, it is stated in terms of fundamental languages: as the view that such languages contain more than one quantifier. For example, one ranging over abstract objects, and another over concrete ones. A natural worry, however, is that the languages proposed by the pluralist are mere notational variants of those proposed by the monist, in which case the debate between the two positions would not seem to be substantive. Jason Turner has given an ingenious response to this worry, in terms of a principle that he calls ‘logical realism’. This paper offers a counter-response on behalf of the ‘notationalist’.

Property theory

Traditionally, a property theory is a theory of abstract entities that can be predicated of things. A theory of properties in this sense is a theory of predication – just as a theory of classes or sets is a theory of membership. In a formal theory of predication, properties are taken to correspond to some (or all) one-place predicate expressions. In addition to properties, it is usually assumed that there are n-ary relations that correspond to some (or all) n-place predicate expressions (for n≥ 2). A theory of properties is then also a theory of relations. In this entry we shall use the traditional labels ‘realism’ and ‘conceptualism’ as a convenient way to classify theories. In natural realism, where properties and relations are the physical, or natural, causal structures involved in the laws of nature, properties and relations correspond to only some predicate expressions, whereas in logical realism properties and relations are generally assumed to correspond to all predicate expressions. Not all theories of predication take properties and relations to be the universals that predicates stand for in their role as predicates. The universals of conceptualism, for example, are unsaturated concepts in the sense of cognitive capacities that are exercised (saturated) in thought and speech. Properties and relations in the sense of intensional Platonic objects may still correspond to predicate expressions, as they do in conceptual intensional realism, but only indirectly as the intensional contents of the concepts that predicates stand for in their role as predicates. In that case, instead of properties and relations being what predicates stand for directly, they are what nominalized predicates denote as abstract singular terms. It is in this way that concepts – such as those that the predicate phrases ‘is wise’, ‘is triangular’ and ‘is identical with’ stand for – are distinguished from the properties and relations that are their intensional contents – such as those that are denoted by the abstract singular terms ‘wisdom’, ‘triangularity’ and ‘identity’, respectively. Once properties are represented by abstract singular terms, concepts can be predicated of them, and, in particular, a concept can be predicated of the property that is its intensional content. For example, the concept represented by ‘is a property’ can be predicated of the property denoted by the abstract noun phrase ‘being a property’, so that ‘Being a property is a property’ (or, ‘The property of being a property is a property’) becomes well-formed. In this way, however, we are confronted with Russell’s paradox of (the property of) being a non-self-predicable property, which is the intensional content of the concept represented by ‘is a non-self-predicable property’. That is, the property of being a non-self-predicable property both falls and does not fall under the concept of being a non-self-predicable property (and therefore both falls and does not fall under the concept of being self-predicable).