Bjørn Jespersen

Procedural Semantics for Hyperintensional Logic

The book is about logical analysis of natural language. Since we humans communicate by means of natural language, we need a tool that helps us to understand in a precise manner how the logical and formal mechanisms of natural language work. Moreover, in the age of computers, we need to communicate both with and through computers as well. Transparent Intensional Logic is a tool that is helpful in making our communication and reasoning smooth and precise. It deals with all kinds of linguistic context in a fully compositional and anti-contextual way.

PREDICATION AND EXTENSIONALIZATION

In his 2000 book Logical Properties Colin McGinn argues that predicates denote properties rather than sets or individuals. I support the thesis, but show that it is vulnerable to a type-incongruity objection, if properties are (modelled as) functions, unless a device for extensionalizing properties is added. Alternatively, properties may be construed as primitive intensional entities, as in George Bealer. However, I object to Bealer’s construal of predication as a primitive operation inputting two primitive entities and outputting a third primitive entity. Instead I recommend we follow Pavel Tichý in construing both predication and extensionalization as instances of the primitive operation of functional application.

How hyper are hyperpropositions

It is an old dispute among logicians and philosophers of language just how finely individuated propositions ought to be. Frege, for one, was torn between two criteria: logical equivalence, which is an exact, but probably also overly crude criterion, and cognitive significance, which is an inexact but arguably on the right track. Possible-world semantics, taking off around 1960, has gotten much technical and philosophical mileage out of the former criterion, but the insight is catching on that propositions need to be more finely individuated than in terms of mathematical mappings. Sophisticated theories of propositions embrace a three-tiered strategy, according to which fine-grained hyperpropositions apply to sentential senses, explicit attitudes, etc.; coarse-grained possible-world propositions apply to states-of-affairs, implicit attitudes, etc., while truth-values make up the third tier. This paper explains the rationale for hyperpropositions and outlines one particular theory maintaining that their right calibration is in terms of near-identity (isomorphism) among abstract procedures. This proposal tallies with the prevalent idea that hyperpropositions are structured meanings.

Are wooden tables necessarily wooden? : Intensional essentialism versus metaphysical modality ()

This paper defendsintensional essentialism: a property (intensional entity) is not essential relative to an individual (extensional entity), but relative to other properties (or intensional entities). Consequently, an individual can have a property only accidentally, but in virtue of having that property the individual has of necessity other properties. Intensional essentialism is opposed to various aspects of the Kripkean notion of metaphysical modality, eg, varying domains, existence as a property of individuals, and its category of properties which are both empirical and essential with respect to particular individuals and natural kinds. The key notion of intensional essentialism isrequisite. A requisite is explicated as a relation-in-extension between two intensions (functions from possible worlds and moments of time)X, Y such that wherever and wheneverX is instantiatedY is also instantiated. We predict three readings of the sentence. “Every wooden table is necessarily wooden”, one involving modalityde re and the other two modalityde dicto. The first reading claims that no individual which is a wooden table is necessarily wooden. The claim is backed up by bare particular anti-essentialism. The two other interpretations claim that it is necessary that whatever is a wooden table is wooden. However, as we try to show, one is logically far more perspicuous thanks to the concept of requisite and thus preferable to more standardde dicto formalizations.

Procedural isomorphism, analytic information and β-conversion by value

This article solves, in a logically rigorous manner, a problem originally advanced as a counterexample to Chomsky’s theory of binding and recently discussed in a 2004 paper by Stephen Neale. The example is this. John loves his wife, and so does Peter. Hence John and Peter share a property. But which one? (i) Loving John’s wife: then John and Peter love the same woman. (ii) Loving one’s own wife: then, unless they are married to the same woman, John loves one woman and Peter loves another woman. Since ‘John loves his wife’ is ambiguous between attributing (i) or (ii) to John, ‘So does Peter’ is also ambiguous between attributing (i) or (ii) to Peter. With unrestricted β-reduction, the lambda-term counterparts of the attributions of (i) and (ii) to John both β-reduce to (ii). Which, intuitively, they should not. With suitably restricted β-conversion, the two redexes do not reduce to the same contractum and can be reconstructed from their respective contracta. This article details how to apply this restricted rule of β-conversion to contexts containing anaphora such as ‘his’ and ‘so does’. The logical contribution of the article is a generally valid form of β-conversion ‘by value’ rather than ‘by name’. The philosophical application of β-conversion ‘by value’ to a context containing anaphora is another contribution of this article.

Two kinds of procedural semantics for privative modification

In this paper we present two kinds of procedural semantics for privative modification. We do this for three reasons. The first reason is to launch a tough test case to gauge the degree of substantial agreement between a constructivist and a realist interpretation of procedural semantics; the second is to extend Martin-Lofs Constructive Type Theory to privative modification, which is characteristic of natural language; the third reason is to sketch a positive characterization of privation.

A New Logic of Technical Malfunction

Aim of the paper is to present a new logic of technical malfunction. The need for this logic is motivated by a simple-sounding philosophical question: Is a malfunctioning corkscrew, which fails to uncork bottles, nonetheless a corkscrew? Or in general terms, is a malfunctioning F, which fails to do what Fs do, nonetheless an F? We argue that ‘malfunctioning’ denotes the modifier Malfunctioning rather than a property, and that the answer depends on whether Malfunctioning is subsective or privative. If subsective, a malfunctioning F is an F; if privative, a malfunctioning F is not an F. An intensional logic is required to raise and answer the question, because modifiers operate directly on properties and not on sets or individuals. This new logic provides the formal tools to reason about technical malfunction by means of a logical analysis of the sentence “a is a malfunctioning F”.

Anatomy of a proposition

This paper addresses the mereological problem of the unity of structured propositions. The problem is how to make multiple parts interact such that they form a whole that is ultimately related to truth and falsity. The solution I propose is based on a Platonist variant of procedural semantics. I think of procedures as abstract entities that detail a logical path from input to output. Procedures are modeled on a function/argument logic, but are not functions (mappings). Instead they are higher-order, fine-grained structures. I identify propositions with particular kinds of molecular procedures containing multiple sub-procedures as parts. Procedures are among the basic entities of my ontology, while propositions are derived entities. The core of a structured proposition is the procedure of predication, which is an instance of the procedure of functional application. The main thesis I defend is that procedurally conceived propositions are their own unifiers detailing how their parts interact so as to form a unit. They are not unified by one of their constituents, e.g., a relation or a sub-procedure, on pain of regress. The relevant procedural semantics is Transparent Intensional Logic, a hyperintensional, typed

Post-Fregean Thoughts on Propositional Unity

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