On bivalent semantics and natural deduction for some infectious logics

In this work, we propose a variant of so-called informational semantics, a technique elaborated by Voishvillo, for two infectious logics, Deutsch’s ${\mathbf{S}_{\mathbf{fde}}}$ and Szmuc’s $\mathbf{dS}_{\mathbf{fde}}$. We show how the machinery of informational semantics can be effectively used to analyse truth and falsity conditions of disjunction and conjunction. Using this technique, it is possible to claim that disjunction and conjunction can be rightfully regarded as such, a claim which was disputed in the recent literature. Both ${\mathbf{S}_{\mathbf{fde}}}$ and $\mathbf{dS}_{\mathbf{fde}}$ are formalized in terms of natural deduction. This allows us to solve several problems: to develop a natural deduction calculus for ${\mathbf{S}_{\mathbf{fde}}}$ containing the standard form of disjunction elimination (in contrast to the calculus by Petrukhin), to introduce the first natural deduction calculus for $\mathbf{dS}_{\mathbf{fde}}$ and to reflect the fundamental symmetry between ${\mathbf{S}_{\mathbf{fde}}}$ and $\mathbf{dS}_{\mathbf{fde}}$ on proof-theoretical level forming a convenient basis for obtaining their well-known extensions $\mathbf{K}^{\mathbf{w}}_{\mathbf{3}}$ and $\mathbf{PWK}$.

Introduction

This chapter offers a breezy introduction to the content question, the question of what determines the content of a mental representation. Existing approaches are outlined: informational semantics, inferential role semantics, correspondence theories, ascriptionism and the intentional stance, and teleosemantics. This discussion highlights the major issues that the book’s positive account must address if it is to succeed.

Standard Objections

Varitel semantics has several resources for dealing with indeterminacy. It gives rise to more determinate contents than informational semantics or consumer-based teleosemantics. The remaining indeterminacy is a virtue: it is what we should expect in simpler systems with fewer interacting components. Some of the non-conceptual representations in our case studies exhibit some features exemplified by concepts: semantically significant constituent structure; unsaturated components; and limited, domain-specific generality. A historical component is needed to bring into view the explanandum to which representational explanation is directed, namely successful and unsuccessful behaviour. We should not expect representational explanation to get a grip, in these simple cases, without some period in which behavioural outcomes have been stabilized. Even a short period of interaction will establish some task functions and contents. Varitel semantics does not reduce misrepresentation to malfunction. Misrepresentation does not imply failure to perform a task function, nor the converse.

What has Natural Information to do with Intentional Representation?

‘According to informational semantics, if it's necessary that a creature can't distinguish Xs from Ys, it follows that the creature can't have a concept that applies to Xs but not Ys.’ (Fodor, 1994, p. 32)There is, indeed, a form of informational semantics that has this verificationist implication. The original definition of information given in Dretske'sKnowledge and the Flow of Information(1981, hereafter KFI), when employed as a base for a theory of intentional representation or ‘content,’ has this implication. I will argue that, in fact, most of what an animal needs to know about its environment is not available as natural information of this kind. It is true, I believe, that there is one fundamental kind of perception that depends on this kind of natural information, but more sophisticated forms of inner representation do not. It is unclear, however, exactly what ‘natural information’ is supposed to mean, certainly in Fodor's, and even in Dretske's writing. In many places, Dretske seems to employ a softer notion than the one he originally defines. I will propose a softer view of natural information that is, I believe, at least hinted at by Dretske, and show that it does not have verificationist consequences. According to this soft informational semantics, a creature can perfectly well have a representation of Xs without being able to discriminate Xs from Ys.

Double Disjunctivitis

Direct Informational Semantics, according to which [X]s represent (express/mean) X if ‘Xs cause [X]s’ is a law, and Fodorian naturalistic semantics both suffer from double disjunctivitis. I argue that robustness, properly construed, characterizes both represented properties and representing symbols: two or more properties normally regarded as non-disjunctive may each be nomologically connected to a non-disjunctive symbol, and two or more non-disjunctive symbols may each be nomologically connected to a property. This kind of robustness bifurcates the so-called disjunction problem into a Represented-Disjunction Problem, of which Fodor was aware, and a Representer-Disjunction Problem, of which he was on the whole oblivious. Fodor fails to solve these problems: his solution to the former, the Asymmetric Dependence Condition, presupposes a successful solution to the latter, while possible responses that Fodor might make to the latter either beg the former or cannot be met or else flout the Naturalistic Requirement and the Atomistic Requirement. Even setting the Representer-Disjunction Problem aside, the Represented-Disjunction Problem does not get solved, because the robustness involving phonological/orthographic sequences (tokens and types) guarantees that nothing can meet the Asymmetrical Dependence Condition. Indeed there is a serious problem of individuating phonological/orthographic tokens and types in a manner that satisfies Fodor’s expectations. This is made manifest by the presence of orthographic tokens embedded in larger tokens.