Incompatibility Semantics from Agreement

My aim in this paper is to present a pluralist thesis about the inferential role of the logical constants, which embraces classical, relevant, linear and ordered linear logic. That is, I defend that a logical constant c has more than one correct inferential role. The thesis depends on a particular interpretation of substructural logics vocabulary, according to which classical logic captures the literal meaning of the logical constants and substructural logics enrich their meaning pragmatically. The paper is divided into four parts: first, I introduce the motivation for the pluralist thesis of the paper; second I introduce the calculus for the different logics endorsed in the pluralist thesis; third, I motivate how the different behaviors of the logical vocabulary of these logics can be pragmatically interpreted, and fourth, I motivate how the different inferential roles that each substructural logic attribute to the logical constants can coexist, and how we should reason with a logical constant c given this plurality.

In this dissertation, we argue for a Pragmatic Logical Pluralism, a pluralist thesis about logic which endorses Classical, Relevant, Linear, and Ordered logic. We justify that the formal languages of these four logics are legitimate codifications of the logical vocabulary and capture legitimate senses of logical consequence. This will be justified given a particular interpretation of the four formal languages: logical consequence and conditional, disjunction, and conjunction of the four different logics codify different and legitimate senses of ‘follows from’, ‘if...then’, ‘or’ and ‘and’ which diverge in their different pragmatic enrichments. The dissertation is twofold. First, we will explore the effect that the lack of structural rules has on logical connectives, in four substructural logics, and its connection with certain pragmatic enrichments. Second, we will defend a pluralist thesis according to which pragmatics has an important role for capturing the inferential role of logical vocabulary, both of the notions of ‘follows from’ and the logical constants, although classical logic preserves truth and captures their literal meaning. In sum, we defend a version of logical pluralism based on the plurality of legitimate translations from natural language to formal languages, arguing that more than one translation is legitimate for logical vocabulary, which makes it possible to adopt more than one logic.

Linguistics and Philosophy, 2006

In this paper an approach to the exhaustive interpretation of answers is developed. It builds on a proposal brought forward by . We will use the close connection between their approach and predicate circumscription to describe exhaustive interpretation as an instance of interpretation in minimal models, well-known from work on counterfactuals (see for instance ). It is shown that by combining this approach with independent developments in semantics/pragmatics one can overcome certain limitations of Groenenedijk & Stokhof's (1984) proposal. In the last part of the paper we will provide a Gricean motivation for exhaustive interpretation building on work of van . The names are listed in alphabetical order.

Journal of Indian Philosophy, 1992

Philosophia, 2012

We investigate the relations among Brandom's three dimensions of semantic inferential articulation, namely, incompatibility entailments, committive consequences, and permissive consequences. In his unpublished manuscript "Conceptual Content and Discursive Practice" Brandom argues that (1) incompatibility entailment implies committive consequence, and that (2) committive consequence in turn implies permissive consequence. We criticize this hierarchy both on internal and external grounds. Firstly, we prove that, using Brandom's own definitions, the reverse of (1) also holds, and that the reverse of (2) may hold (but the proof relies on substantive assumptions). This suggests that there are no three different notions of inference emerging from Brandom's definitions, but at most two, and perhaps even just one. Secondly, this result puts into question the connections between the three inferential relations and the familiar notions of deduction and induction.

2003

Abstract We reexamine the foundations of linear logic, developing a system of natural deduction following Martin-Löf's separation of judgments from propositions. Our construction yields a clean and elegant formulation that accounts for a rich set of multiplicative, additive, and exponential connectives, extending dual intuitionistic linear logic but differing from both classical linear logic and Hyland and de Paiva's full intuitionistic linear logic.

Academicus International Scientific Journal

A pragmatist conception of logic rejects any kind of logical constructionism, based on the appeal to privileged ontological and epistemological items and to a perfect language supposedly provided by mathematical logic. Even in logic, “pluralism” must be the key-word if one does not want to be locked in the cage of conceptions that become rapidly outdated. Dealing with the dichotomy Absolutism/Relativism in logic, it may be observed that the enterprise of logic can be considered in several - and substantially different - perspectives, among which we find (1) the psychologistic, (2) the Platonistic, and (3) the instrumentalistic viewpoints. According to (1) logic is viewed as fundamentally descriptive, and its task is taken to be that of outlining a “theory of reasoning,” i.e. a systematic account of how we humans proceed when reasoning successufully. According to (3), instead, logic’s task is that of constructing rigorous systems codifying not only actual, but also possible instrumen...

Synthese, 2001

Preprint of the paper published in Synthese 127: 105–139, 2001 ABSTRACT: Many of the discussions about conditionals can best be put as follows: can those conditionals that involve an entailment relation be formulated within a formal system? The reasons for the failure of the classical approach to entailment have usually been that they ignore the meaning connection between antecedent and consequent in a valid entailment. One of the first theories in the history of logic about meaning connection resulted from the stoic discussions on tightening the relation between the If- and the Then-parts of conditionals, which in this context was called synartesis (connection). This theory gave a justification for the validity of what we today express through the formulae ~(a=>~a) and ~(~a=>a). Hugh MacColl and, more recently, Storrs McCall (from 1877 to 1906 and from 1963 to 1975 respectively) searched for a formal system in which the validity of these formulae could be expressed. Unfortunately neither of the resulting systems is very satisfactory. In this paper we introduce dialogical games with the help of a new connexive If-Then =>), the structural rules of which allow the Proponent to develop (formal) winning strategies for the above-mentioned connexive theses . Further on, we develop the corresponding tableau systems and conclude with some remarks on possible perspectives and consequences of the dialogical approach to connexivity including the loss of uniform substitution leading to a new concept of logical form.

Log. J. IGPL, 2020

The logics of formal inconsistency are logics tolerant to some amount of contradiction, but in which some versions of explosion still hold. The main result of this paper is a reconstruction of two such logics in the dialogical framework. By doing so, we achieve two things. On the one hand, we provide a formal approach to argumentative situations where some contradictions may occur while keeping the idea that there may still be situations in which some propositions are ‘safe’ in the sense of immunity to the contradictions. On the other hand, we open a new line of study on these logics, in the context of the game-theoretical approach to semantics born in the 1960s, with various interesting perspectives, some of which are discussed at the end of this article.

2010

The original article of Thomason pursues two goals: first to outline the central logical issues of non-monotonic reasoning, and second to indicate possible applications of nonmonotonic reasoning techniques in linguistics. This appendix will follow up on Thomason’s second goal and show that linguists have taken up his invitation to use nonmonotonic logic as a formal tool. Particularly in the new and very vivid area of formal pragmatics and at the intersection of semantics and cognitive psychology nonmonotonic logics are playing an important role. The paper is structured as follows. The purpose of its first part is to present the recent progress made in formal pragmatics by using nonmonotonic logic to describe pragmatic meaning. We will show how minimal models can be used to describe and explain inferences of language use, in particular Gricean conversational implicatures. After this we will discuss how nonmonotonic logic can be used at the semantic-pragmatic interface to account for ...