This article examines the traditional and modern doctrines of categorical propositions and argues that both doctrines have serious problems. While the doctrines disagree about existential imports...

Contrary to received opinion, the Aristotelian Square of Opposition (square) is logically sound, differing from standard modern predicate logic (SMPL) only in that it restricts the universe U of cognitively constructible situations by banning null predicates, making it less unnatural than SMPL. U-restriction strengthens the logic without making it unsound. It also invites a cognitive approach to logic. Humans are endowed with a cognitive predicate logic (CPL), which checks the process of cognitive modelling (world construal) for consistency. The square is (...) considered a first approximation to CPL, with a cognitive set-theoretic semantics. Not being cognitively real, the null set Ø is eliminated from the semantics of CPL. Still rudimentary in Aristotle’s On Interpretation (Int), the square was implicitly completed in his Prior Analytics (PrAn), thereby introducing U-restriction. Abelard’s reconstruction of the logic of Int is logically and historically correct; the loca (Leaking O-Corner Analysis) interpretation of the square, defended by some modern logicians, is logically faulty and historically untenable. Generally, U-restriction, not redefining the universal quantifier, as in Abelard and loca, is the correct path to a reconstruction of CPL. Valuation Space modelling is used to compute the effects of U-restriction. (shrink)

Geach's account of the Aristotelian logic of categorical sentences supplemented the views shared by Frege, Russell, Quine and others. I argue that this particular predicate logic approach and Geach's points apply to only one variety of natural language categorical sentences. For example, it takes the universal categorical as a universal conditional “If anything is a man, then it is mortal”. A different natural language form can and should be invoked: “Every man is a mortal.” Employing special restricted quantifiers in a (...) version of predicate logic, we justify a full square of opposition and the rules of quality and quantity that Geach rejected. (shrink)

The paper shows that in the Art of Thinking (The Port Royal Logic) Arnauld and Nicole introduce a new way to state the truth-conditions for categorical propositions. The definition uses two new ideas: the notion of distributive or, as they call it, universal term, which they abstract from distributive supposition in medieval logic, and their own version of what is now called a conservative quantifier in general quantification theory. Contrary to the interpretation of Jean-Claude Parienté and others, the truth-conditions do (...) not require the introduction of a new concept of ‘indefinite’ term restriction because the notion of conservative quantifier is formulated in terms of the standard notion of term intersection. The discussion shows the following. Distributive supposition could not be used in an analysis of truth because it is explained in terms of entailment, and entailment in terms of truth. By abstracting from semantic identities that underlie distribution, the new concept of distributive term is definitionally prior to truth and can, therefore, be used in a non-circular way to state truth-conditions. Using only standard restriction, the Logic’s truth-conditions for the categorical propositions are stated solely in terms of (1) universal (distributive) term, (2) conservative quantifier, and (3) affirmative and negative proposition. It is explained why the Cartesian notion of extension as a set of ideas is in this context equivalent to medieval and modern notions of extension. (shrink)

El Problema de la Adopción afirma que ciertas leyes lógicas no pueden ser adoptadas. El argumento constituye un desafío al antiexcepcionalismo lógico, en la medida en que este último debe poder justificar su afirmación de que la teoría lógica en ejercicio puede revisarse. El propósito de este artículo es responder al desafío, utilizando como unidad de análisis el concepto de Taxonomía Lexical propuesto por Kuhn. Como mostraremos, una visión sociológicamente enriquecida de las teorías científicas y la naturaleza de sus cambios (...) permite dar cuenta de un antiexcepcionalismo lógico que evita el Problema de la Adopción. (shrink)

An account of Aristotle's syllogistic (including a full square of opposition and allowing for empty nouns) as an integral part of first-order predicate logic is lacking. Some say it is not possible. It is not found in the tradition stemming from ukasiewicz's attempt nor in less formal approaches such as Strawson's. The ukasiewicz tradition leaves Aristotle's syllogistic as an autonomous axiomatized system. In this paper Aristotle's syllogistic is presented within first-order predicate logic with special restricted quantifiers. The theory is not (...) motivated primarily by historical considerations but as an accurate account of categorical sentences along lines suggested by recent work on natural language quantifiers and themes from supposition theory. It provides logical forms which conform to grammatical ones and is intended as a rival to accounts of quantifiers in natural language that appeal to binary quantifiers, for example, Wiggins or to restricted quantifiers, for example, Neale. (shrink)

This entry traces the historical development of the Square of Opposition, a collection of logical relationships traditionally embodied in a square diagram. This body of doctrine provided a foundation for work in logic for over two millenia. For most of this history, logicians assumed that negative particular propositions ("Some S is not P") are vacuously true if their subjects are empty. This validates the logical laws embodied in the diagram, and preserves the doctrine against modern criticisms. Certain additional principles ("contraposition" (...) and "obversion") were sometimes adopted along with the Square, and they genuinely yielded inconsistency. By the nineteenth century an inconsistent set of doctrines was widely adopted. Strawson's 1952 attempt to rehabilitate the Square does not apply to the traditional doctrine; it does salvage the nineteenth century version but at the cost of yielding inferences that lead from truth to falsity when strung together. (shrink)

This paper advances an approach to presupposition rooted in the concept of commitment, a dialectical notion weaker than truth and belief. It investigates ancient medieval dialectical theories and develops the insights thereof for analyzing how presuppositions are evaluated and why a proposition is presupposed. In particular, at a pragmatic level, presuppositions are reconstructed as the conclusions of implicit arguments from presumptive reasoning, grounded on presumptions of different type and nature. A false (or rather unaccepted) presupposition can be thus represented as (...) the outcome of a conflict of presumptions – the ones used by the Speaker and the ones commonly accepted or backed by evidence. From an interpretative perspective, this defaulted presumptive reasoning can be explained by comparing the available presumptions and repaired by replacing the weaker and unacceptable ones. (shrink)