Intentionality may be dealt with in two different ways: either ontologically, as an ordinary relation to some extraordinary objects, or epistemologically, as an extraordinary relation to some ordinary objects. This paper endorses the epistemological view in order to provide a model of semiotic intentionality defined as the meaning-and-cognizing process that constitutes to power of the mind to be about something on the basis of a semiotic system. After a short introduction that presents the components of semiotic intentionality (viz. sign, act, (...) content, referent) along with their division into an intending and a fulfilling side (Sect. 1), the first main part of the paper analyzes semiotic intentionality at its primary level (a.k.a. 'concrete intentionality') as a real and subjective relation between meaning-intending and meaning-fulfilling acts grounded in the manipulation of some semiotic system (Sect. 2). Then, building on such concrete intentionality, the second main part of the paper analyzes semiotic intentionality at its secondary level (a.k.a. 'abstract intentionality') as an ideal and objective relation between intentional and fulfillment contents, which in turn: (i) proceed from an abstraction performed on the intending and fulfilling acts, respectively, and (ii) retroactively categorize the intending and fulfilling acts, respectively (Sect. 3). Finally, from this combination of an act-based conception of content with a presentationalist account of intentionality, the conclusion of this paper produces the intended model of semiotic intentionality in such a way that knowledge and truth are then respectively defined in it as the subjective correspondence between the two acts of concrete intentionality and as the objective correspondence between the two contents of abstract intentionality (Sect. 4). (shrink)

Argumentation schemes can be described as abstract structures representing the most generic types of argument, constituting the building blocks of the ones used in everyday reasoning. This paper investigates the structure, classification, and uses of such schemes. Three goals are pursued: 1) to describe the schemes, showing how they evolved and how they have been classified in the traditional and the modern theories; 2) to propose a method for classifying them based on ancient and modern developments; and 3) to outline (...) and show how schemes can be used to describe and analyze or produce real arguments. To this purpose, we will build on the traditional distinctions for building a dichotomic classification of schemes, and we will advance a modular approach to argument analysis, in which different argumentation schemes are combined together in order to represent each step of reasoning on which a complex argument relies. Finally, we will show how schemes are applied to formal systems, focusing on their applications to Artificial Intelligence, AI & Law, argument mining, and formal ontologies. (shrink)

This paper deals with a collection of concerns that, over a period of time, led the author away from the Routley–Meyer semantics, and towards proof- theoretic approaches to relevant logics, and indeed to the weak relevant logic MC of meaning containment.

This paper has two aims. First, it sets out an interpretation of the relevant logic E of relevant entailment based on the theory of situated inference. Second, it uses this interpretation, together with Anderson and Belnap’s natural deduc- tion system for E, to generalise E to a range of other systems of strict relevant implication. Routley–Meyer ternary relation semantics for these systems are produced and completeness theorems are proven. -/- .

We discuss the philosophical implications of formal results showing the con- sequences of adding the epsilon operator to intuitionistic predicate logic. These results are related to Diaconescu’s theorem, a result originating in topos theory that, translated to constructive set theory, says that the axiom of choice (an “existence principle”) implies the law of excluded middle (which purports to be a logical principle). As a logical choice principle, epsilon allows us to translate that result to a logical setting, where one can (...) get an analogue of Diaconescu’s result, but also can disentangle the roles of certain other assumptions that are hidden in mathematical presentations. It is our view that these results have not received the attention they deserve: logicians are unlikely to read a discussion because the results considered are “already well known,” while the results are simultaneously unknown to philosophers who do not specialize in what most philosophers will regard as esoteric logics. This is a problem, since these results have important implications for and promise signif i cant illumination of contem- porary debates in metaphysics. The point of this paper is to make the nature of the results clear in a way accessible to philosophers who do not specialize in logic, and in a way that makes clear their implications for contemporary philo- sophical discussions. To make the latter point, we will focus on Dummettian discussions of realism and anti-realism. Keywords: epsilon, axiom of choice, metaphysics, intuitionistic logic, Dummett, realism, antirealism. (shrink)

This paper compares Hilbert’s -terms and Russell’s approach to indefinite descriptions, Russell’s indefinites for short. Despite the fact that both accounts are usually taken to express indefinite descriptions, there is a number of dissimilarities. Specifically, it can be shown that Russell indefinites - expressed in terms of a logical ρ-operator - are not directly representable in terms of their corresponding -terms. Nevertheless, there are two possible translations of Russell indefinites into epsilon logic. The first one is given in a language (...) with classical -terms. The second translation is based on a refined account of epsilon terms, namely indexed -terms. In what follows we briefly outline these approaches both syntactically and semantically and discuss their respective connections; in particular, we establish two equivalence results between the epsilon calculus and the proposed ρ-term approach to Russell’s indefinites. (shrink)

It is shown that the classes of Routley-Meyer models which are axiomatizable by a theory in a propositional relevant language with fusion and the Ackermann constant can be characterized by their closure under certain model-theoretic operations involving prime filter extensions, relevant directed bisimulations and disjoint unions.