Inductive Logic

Inductive Logic is a ‘thematic compilation’ by Avi Sion. It collects in one volume many (though not all) of the essays, that he has written on this subject over a period of some 23 years, which all demonstrate the possibility and conditions of validity of human knowledge, the utility and reliability of human cognitive means when properly used, contrary to the skeptical assumptions that are nowadays fashionable

Ancient Logic and its Modern Interpretations: Proceedings of the Buffalo Symposium on Modernist Interpretations of Ancient Logic, 21 and 22 April, 1972

Articles by Ian Mueller, Ronald Zirin, Norman Kretzmann, John Corcoran, John Mulhern, Mary Mulhern,Josiah Gould, and others. Topics: Aristotle's Syllogistic, Stoic Logic, Modern Research in Ancient Logic

LOGICAL AND PSYCHOLOGICAL PARTITIONING OF MIND: DEPICTING THE SAME MAP?

The aim of this paper is to demonstrate that empirically delimited structures of mind are also differentiable by means of systematic logical analysis. In the sake of this aim, the paper first summarizes Demetriou's theory of cognitive organization and growth. This theory assumes that the mind is a multistructural entity that develops across three fronts: the processing system that constrains processing potentials, a set of specialized structural systems (SSSs) that guide processing within different reality and knowledge domains, and a hypecognitive system that monitors and controls the functioning of all other systems. In the second part the paper focuses on the SSSs, which are the target of our logical analysis, and it summarizes a series of empirical studies demonstrating their autonomous operation. The third part develops the logical proof showing that each SSS involves a kernel element that cannot be reduced to standard logic or to any other SSS. The implications of this analysis for the general theory of knowledge and cognitive development are discussed in the concluding part of the paper

Probability Semantics for Aristotelian Syllogisms

We present a coherence-based probability semantics for (categorical) Aristotelian syllogisms. For framing the Aristotelian syllogisms as probabilistic inferences, we interpret basic syllogistic sentence types A, E, I, O by suitable precise and imprecise conditional probability assessments. Then, we define validity of probabilistic inferences and probabilistic notions of the existential import which is required, for the validity of the syllogisms. Based on a generalization of de Finetti's fundamental theorem to conditional probability, we investigate the coherent probability propagation rules of argument forms of the syllogistic Figures I, II, and III, respectively. These results allow to show, for all three Figures, that each traditionally valid syllogism is also valid in our coherence-based probability semantics. Moreover, we interpret the basic syllogistic sentence types by suitable defaults and negated defaults. Thereby, we build a knowledge bridge from our probability semantics of Aristotelian syllogisms to nonmonotonic reasoning. Finally, we show how the proposed semantics can be used to analyze syllogisms involving generalized quantifiers

Richard Whately\u27s Revitalization of Syllogistic Logic

This is an expanded version of the first chapter Richard Whately’s Revitalization of Syllogistic Logic in Aristotle’s Syllogism and the Creation of Modern Logic edited by Lukas M. Verburgt and Matteo Cosci (Bloomsbury, 2023). Drawing upon the author’s 1982 Ph. D. dissertation (https://digitalcollections.dordt.edu/faculty_work/230/ ) and more current scholarship, this essay traces the critical historical background to Whately’s work in more detail than could be done in the published version

Per Se Modality and Natural Implication – an Account of Connexive Logic in Robert Kilwardby

We present a formal reconstruction of the theories of the medieval logician Robert Kilwardby, focusing on his account of accidental and natural inferences and the underlying modal logic that gives rise to it. We show how Kilwardby’s use of an essentialist modality underpins his connexive account of implication

Dialectical Topoi

a) Topics and Objectives: Dialectical topoi constitute an essential component of Aristotelian logic and theory of argumentation (dialectics). These can be characterized as essential patterns of argumentation which allow us to found premises which are suited to the establishment of specific theses. Our research group concentrates on two themes: the first working focus consists of a precise investigation of the topos-based dialectical logic found in Aristotle. We are concerned in particular with the dialectical texts contained in the Organon (Topics, Rhetoric, Sophistical Refutations), and we are considering their relationship to the formal logic developed in the Prior Analytics. The second focus of our work is an investigation of the reception of Aristotelian dialectics in the Renaissance. Occurring in the 16th century was in intensive reception of the Aristotelian Topics, as suggested by numerous new translations and commentaries. We are concentrating on the relationship between veritas/scientia and opinio/probabilitas in the epistemology of the Renaissance. In particular, we are interested in the question of how the dialectics and rhetoric of the Renaissance were influenced by the form and genre of the dialogue, and in the role played in the Renaissance by the spatial dimension, which is contained both in Aristotle’s definition of the topos as the »place from which the attack comes«, as well as in Cicero’s definition of the locus as the »seat of the argument« (sedes argumentorum). b) Methods: Relevant passages from the texts of the Aristotelian Organon are analyzed and set into relationship with one another. Consulted in particular in interpreting these texts is the inventory of 20th century theories dealing with logic and argumentation; modern mereological and topological systems, for example, are used in reconstructing Aristotelian logic, albeit without overlooking the historical specificity of the problems that are bound up with these antique texts. c) State of the Discussion: The group has concluded that Aristotelian formal logic is dependent upon and was shaped in various ways by topos-based dialectical logic. Aristotelian predication theory, for example, plays a decisive role for various aspects of the Aristotelian syllogistic which is contained in the Prior Analytics. Beyond this, the group has demonstrated that interpretations of the Aristotelian Topics made an essential contribution to the emergence of a relativistic epistemology in the Renaissance. The status of opinio/probabilitas in the Renaissance, for example, was influenced by interpretations of the Aristotelian concept of endoxon

Aristotle's Foundationalism

For Aristotle, demonstrative knowledge is the result of what he calls ‘intellectual learning’, a process in which the knowledge of a conclusion depends on previous knowledge of the premises. Since demonstrations are ultimately based on indemonstrable principles (the knowledge of which is called ‘νοῦς’), Aristotle is often described as advancing a foundationalist doctrine. Without disputing the nomenclature, I shall attempt to show that Aristotle’s ‘foundationalism’ should not be taken as a rationalist theory of epistemic justification, as if the first principles of science could be known as such independently of their explanatory connections to demonstrable propositions. I shall argue that knowing first principles as such involves knowing them as explanatory of other scientific propositions. I shall then explain in which way noetic and demonstrative knowledge are in a sense interdependent cognitive states – even though νοῦς remains distinct from (and, in Aristotle’s words, more ‘accurate’ than) demonstrative knowledge

El programa de análisis aristotélico

In this paper, I submit an overall interpretation of Aristotle’s Analytics (Posterior as well as Prior) which I could express, to put it in a nutshell, by saying that the Analytics are analytic. That is, they do not lay out progressive or constructive processes, in which, given certain fundamental premises, terms or rules, one would go ahead and draw conclusions or even build a systematic body of knowledge on the basis of these principles. Rather they describe a backward movement, starting from a proposed or provisional conclusion and asking which premises could (or could best) be used in order to deduce, support, prove or explain it.En este documento, presento una interpretación general de los Primeros y Segundos Analíticos de Aristóteles que podría expresar, para decirlo en pocas palabras, el punto de vista de que los Analíticos de Aristóteles son analíticos. Es decir, no establecen procesos progresivos o constructivos, en los que, dadas ciertas premisas, términos o reglas fundamentales, uno podría avanzar y sacar conclusiones o incluso construir un cuerpo sistemático de conocimiento sobre la base de estos principios. Más bien, describen un retroceso, a partir de una conclusión propuesta o provisional y preguntando qué premisas podrían (o podrían mejor) ser utilizadas para deducir, apoyar, probar o explicar