Logic Without Truth

Abstract

Between the two horns of Jsrgensen's dilemma, the authors opt for that according to which logic deals not only with truth and falsity but also with those concepts not possessing this semantic reference. Notwithstanding the "descriptive" prejudice, deontic logic has gained validity among modal logics. The technical foundation proposed consists in an abstract characterization of logical consequence. By identifying in the abstract notion of consequence the primitive from which to begin, it is possible to define the connectives -even those of obligation -by means of the rules of introduction or elimination in a context of derivation.

Epistemic formulae, argument structures, and a narrative on identity and deception: a formal representation from the AJIT subproject within AURANGZEB

“…The role of logic, in this notation, is for providing a syntax with connectives, and we are not as much interested in truth value (even though on occasion it does matter that the negation of a proposition is stated). This is in line with non-alethic logics; see 'Logic Without Truth' by Alchourrón and Martino [2]." [76,'Introduction'].…”

A Minimalist Solution to Jørgensen's Dilemma

“…Philosophers have of course developed several strategies to avoid this unpalatable conclusion. Current approaches to Jørgensen's Dilemma range from the flat denial that deontic logic has anything to do with truth and falsity (e.g., Alchourrón and Martino 1990) 1 to the definition of logical relations between norms in terms of the "rationality" of norm-giving activity (e.g., von Wright 1991), to the claim that sentences occurring in normative reasoning can be true or false either because there is a normative reality to which they can correspond or fail to correspond (e.g., Kalinowski 1972;Walter 1996), or because they are to be interpreted as descriptive sentences about norms (e.g., von Wright 1963).…”

“…This result is all the more valuable since the "minimal" sense in which normative propositions are ascribed the capability of being either true or false involves no questionable ontological commitment to the existence of a "world of norms" as opposed to the familiar world of objects and their properties. 1 The position of Alchourrón and Martino (1990) is in fact that any logic, and not merely the logic of normative reasoning, is uniquely concerned with the "abstract" notion of consequence, that is, with consequence understood as a class of operations on a set of sentences in a language, independently from the semantic notions of truth and falsity. The position of Alchourrón and Martino is thus more radical than the widespread opinion (see, e.g., Ross 1968) that deontic logic is not concerned with truth and falsity because its subject is the transmission of "validity" and "invalidity.…”

A Critical Appraisal of Karl Olivecrona's Legal Philosophy

“…As is well known, the received view is that the laws of logic apply only to statements (or propositions), which can be true or false. On this difficulty, seeRoss (1941);Alchourròn and Martino (1990).…”