Intensional Models for the Theory of Types

In this paper we define intensional models for the classical theory of types, thus arriving at an intensional type logic ITL. Intensional models generalize Henkin's general models and have a natural definition. As a class they do not validate the axiom of Extensionality. We give a cut-free sequent calculus for type theory and show completeness of this calculus with respect to the class of intensional models via a model existence theorem. After this we turn our attention to applications. Firstly, it is argued that, since ITL is truly intensional, it can be used to model ascriptions of propositional attitude without predicting logical omniscience. In order to illustrate this a small fragment of English is defined and provided with an ITL semantics. Secondly, it is shown that ITL models contain certain objects that can be identified with possible worlds. Essential elements of modal logic become available within classical type theory once the axiom of Extensionality is given up.Comment: 25 page

The meaning of meaning-fallibilism

Much discussion of meaning by philosophers over the last 300 years has been predicated on a Cartesian first-person authority (i.e. ‘infallibilism’) with respect to what one’s terms mean. However this has problems making sense of the way the meanings of scientific terms develop, an increase in scientific knowledge over and above scientists’ ability to quantify over new entities. Although a recent conspicuous embrace of rigid designation has broken up traditional meaning-infallibilism to some extent, this new dimension to the meaning of terms such as ‘water’ is yet to receive a principled epistemological undergirding (beyond the deliverances of ‘intuition’ with respect to certain somewhat unusual possible worlds). Charles Peirce’s distinctive, naturalistic philosophy of language is mined to provide a more thoroughly fallibilist, and thus more realist, approach to meaning, with the requisite epistemology. Both his pragmatism and his triadic account of representation, it is argued, produce an original approach to meaning, analysing it in processual rather than objectual terms, and opening a distinction between ‘meaning for us’, the meaning a term has at any given time for any given community and ‘meaning simpliciter’, the way use of a given term develops over time (often due to a posteriori input from the world which is unable to be anticipated in advance). This account provocatively undermines a certain distinction between ‘semantics’ and ‘ontology’ which is often taken for granted in discussions of realism

Abductive two-dimensionalism: a new route to the a priori identification of necessary truths

Epistemic two-dimensional semantics, advocated by Chalmers and Jackson, among others, aims to restore the link between necessity and a priority seemingly broken by Kripke, by showing how armchair access to semantic intensions provides a basis for knowledge of necessary a posteriori truths. The most compelling objections to E2D are that, for one or other reason, the requisite intensions are not accessible from the armchair. As we substantiate here, existing versions of E2D are indeed subject to such access-based objections. But, we moreover argue, the difficulty lies not with E2D but with the typically presupposed conceiving-based epistemology of intensions. Freed from that epistemology, and given the right alternative—one where inference to the best explanation provides the operative guide to intensions—E2D can meet access-based objections, and fulfill its promise of restoring the desirable link between necessity and a priority. This result serves as a central application of Biggs and Wilson, according to which abduction is an a priori mode of inference

A Bridge from Semantic Value to Content

A common view relating compositional semantics and the objects of assertion holds the following: Sentences φ and ψ expresses the same proposition iff φ and ψ have the same modal profile. Following Dummett, Evans, and Lewis, Stanley argues that this view is fundamentally mistaken. According to Dummett, we must distinguish the semantic contribution a sentence makes to more complex expressions in which it occurs from its assertoric content. Stojnić insists that views which distinguish the roles of content and semantic value must nevertheless ensure a tight connection between the two. But, she contends, there is a crucial disanalogy between the views that follow Lewis and the views that follow Dummett. Stanley’s Dummettian view is argued to contain a fatal flaw: On such views, there is no way to secure an appropriate connection between semantic value and a theoretically motivated notion of assertoric content. I will review the background issues from Dummett, Evans, Lewis, and Stanley, and provide a principled way of bridging the gap between semantic value and a theoretically motivated notion of assertoric content

Predicativity, the Russell-Myhill Paradox, and Church's Intensional Logic

This paper sets out a predicative response to the Russell-Myhill paradox of propositions within the framework of Church's intensional logic. A predicative response places restrictions on the full comprehension schema, which asserts that every formula determines a higher-order entity. In addition to motivating the restriction on the comprehension schema from intuitions about the stability of reference, this paper contains a consistency proof for the predicative response to the Russell-Myhill paradox. The models used to establish this consistency also model other axioms of Church's intensional logic that have been criticized by Parsons and Klement: this, it turns out, is due to resources which also permit an interpretation of a fragment of Gallin's intensional logic. Finally, the relation between the predicative response to the Russell-Myhill paradox of propositions and the Russell paradox of sets is discussed, and it is shown that the predicative conception of set induced by this predicative intensional logic allows one to respond to the Wehmeier problem of many non-extensions.Comment: Forthcoming in The Journal of Philosophical Logi

On abstraction in a Carnapian system

Rudolf Carnap (1891-1970) rejects two philosophical distinctions that have been made and admitted by Gottlob Frege (1848-1925), namely the object-concept and the sense-reference distinctions. In the analytic tradition and upon these distinctions, a family of analytic systems have been constructed and developed (which we call Fregean systems), within which a number of notions have been employed including the notion of abstraction. It has been claimed (by Neo- Fregeans) that the Fregean notion of abstraction has been captured by what is commonly known as the “principle of abstraction”. The goal of this dissertation is to present the notion of Carnapian abstraction, in particular, and the Carnapian system, in general, in distinction to the Fregean counterparts. We will argue that the admission and rejection of these distinctions will entail fundamentally different analytic systems. Hence, we will show how each system undertakes a different notion of abstraction. Abstraction in a Fregean system will be characterized as a mind-independent process subject to its own rules, whereas in a Carnapian system, abstraction will be characterized as a defined process of distancing from meaning in a linguistic framework. We will conclude that the Carnapian system has advantages over the Fregean one (among which is its simplicity), and that its technical aspect is yet to be developed.Rudolf Carnap (1891-1970) rejette deux distinctions philosophiques conçues par Gottlob Frege (1848-1925) : la distinction objet-concept et la distinction sens-référence. Dans la tradition analytique et parmi ces distinctions, une famille de systèmes analytiques a été construite et développée (appelée les « systèmes frégéen »), dans lesquels plusieurs notions ont été employées, incluant la notion d’abstraction. En fait, les néo- frégéen ont déclaré que la notion d’abstraction de Frege est capturée par ce qu’on appelle le « principe d’abstraction ». Le but de cette dissertation est de présenter la notion d’abstraction de Carnap en particulier et le système de Carnap en général, en comparaison aux notions de Frege. Nous allons argumenter que l’admission et le rejet de ces distinctions entraîneront des systèmes analytiques fondamentalement différents. Ainsi, nous allons démontrer comment chaque système utilise différentes notions d’abstraction. L’abstraction dans un système frégéen sera caractérisée comme un processus indépendant qui est confiné à ses propres règles, tandis que dans un système carnapien, l’abstraction sera caractérisée comme un processus défini d’éloignement du sens. Nous arriverons à la conclusion que le système carnapien a plus d’avantages que celui de Frege (comme la simplicité du système) et que son aspect technique a besoin d’être développé davantage

Intensions, types and existence

[ES] Esta es una disertación sobre dos preguntas: si y cómo los sentidos de las expresiones de un lenguaje pueden ser modelados matemáticamente; y sobre una respuesta: las intensiones son un medio necesario pero no suficiente para comprender totalmente los sentidos. Las intensiones no han aparecido de repente, tienen una historia enraizada en la lógica sobre Sentido y Denotación que comenzó con Frege, fue desarrollada sintáctica y axiomáticamente por Church, y semánticamente por Montague. Gracias a ellos, sentidos e intensiones son hoy en día nociones familiares para los lógicos. Y aunque los sentidos continúan siendo una noción más oscura, las intensiones, sin embargo, son un concepto bien definido: son funciones desde mundos posibles a objetos. El presente trabajo ofrece dos lenguajes formales con intensiones: una Lógica Híbrida Intensional de Primer Orden y una Teoría de Tipos Híbrida Intensional. Ambos lenguajes incluyen expresiones que denotan intensiones y también maquinaria híbrida para extensionalizar las intensiones en los diversos mundos de un modelo. Pero estos lenguajes no son puramente intensionales, ya que también incluyen expresiones para denotar extensiones. Se introduce también una poderosa notación de tipos que permite diferenciar entre expresiones intensionales y extensionales, predicación intensional y extensional, y entre fórmulas bien formadas y fórmulas incoherentes. La distinción entre predicación intensional y extensional equivale a defender la existencia de dos clases de conceptos de predicados: uno entendido como una función entre conceptos y el otro como una función entre un objeto y un concepto. Los temas tradicionales de lógica intensional—como modelos con un solo dominio o con varios dominios y las interpretaciones de dicto y de re—son analizados pero desde un punto de vista novedoso, dado que los lenguajes antes citados no sólo incluyen expresiones intensionales, sino también operadores híbridos y una notación de tipos para eliminar ambigüedades. El problema de los términos que no denotan se estudia asumiendo que las intensiones son funciones parciales; y el problema de la identidad de sentidos, aunque resuelto en el caso de contextos aléticos por medio de la identidad de intensiones, debería encontrar una mejor solución yendo más allá de las intensiones hasta llegar al reino de las hiperintensiones. Se han explorado algunas nociones filosóficas, como existencia y denotación, desde el punto de vista de nuestros lenguajes formales. Finalmente, la prueba de Gödel a favor de la existencia de Dios y el argumento de Caramuel en contra de la existencia de Dios, son analizados como dos ejercicios sugerentes tanto en lógica intensional como en ontología formal

A consideration of two attacks upon the sharp analytic-synthetic distinction

Thesis (M.A.)--Boston UniversityThe purpose of this essay is to reply to the attacks upon the sharp analytic-synthetic distinction made by Quine in "Two Dogmas of Empiricism" and by White in "The Analytic and the Synthetic: An Untenable Dualism". This essay attempts to show not only that these attacks are ill-conceived, but also that Carnap's semantic methods can be used to explain analytically in natural languages. The two attacks are, in effect, attacks upon the conception of the analytic as being definitely different from the synthetic. Quine's attack is directed primarily at three of Carnap's basic concepts -- state-description, explication, and semantic rule. These he regards as separate attempts to explain analytically. White attacks the claim that some natural language has the sharp analytic-synthetic distinction of an artificial language. He does this by considering primarily two imagined experiments [TRUNCATED