On the Explanatory Power of Truth in Logic

2025

This work proposes a structural-ontological foundation for logic based on the principle of self-contradicted identity, formulated as a relational tension within being itself. Rejecting both pragmatic and formalist approaches, the theory advances a second-order metalogical function, Φ, which operates on the set of relational structures over a given language and generates a class of stable configurations. Logic is not grounded in epistemic utility or inferential practices, but emerges from the iterability of a primary metaphysical contrariety, where identity and difference coexist as a generative tension. Through a formal definition of Φ and its convergence properties, the theory provides an account of logic as a manifestation of the structure of being, prior to any axiomatic system or linguistic articulation. The work engages with contemporary logical theories (e.g., Leitgeb, Da Costa) and classical foundations (e.g., Frege, Hilbert), offering a unified framework capable of encompassing both classical and non-classical logics. Ultimately, logic is redefined not as a tool of thought, but as an ontological-metaphysical necessity.

Studies in Logic, College Publications, King's College, London, 2013

This book is an attempt to renegotiate the notion of truth by bringing together perspectives generally seen as alternatives into a coherent whole. The perspectives include formal and informal logic, argumentation theory, scientific inquiry and epistemology. The guiding inspiration is the work of Stephen Toulmin, reflecting both his contribution to the theory of argument and his abiding concern with scientific inquiry. It thus bridges between the work of informal and formal logicians and the more general concern with the epistemological basis of inquiry. At the center is an insight, described in formalist terms, drawn from physical science. This moves epistemology from a purely abstract science to a partially empirical one and addresses the relationship between epistemologically relevant practices and basic epistemological concerns, The core of the book, a model of emerging truth (MET), is a metamathematical structure that envisions truth as the outcome of inquiry. It offers criteria by which the epistemological nature of such inquiry may be ascertained as it progresses towards the goal. The intuition for the construction is found in the development of physical chemistry, a scientific discipline of enormous reach and among the most firmly grounded of all of the fruits of human inquiry. The approach points away from the recent focus on dialogical criteria in argumentation theory and returns to an epistemological concern with truth, and the indicators of truthlikeness that govern inquiry short of its ideal conclusion. This requires an analysis of the substance of argumentational support, in particular, an account of the strength of warrants as an index of their ability to support inferences. In addition, it moves the focus from ordinary argument to argument as found in the special disciplines. This has consequences for the theory of logic, both formal and informal, as well as the application of logic in practical contexts such as teaching for critical thinking.

Natural Language Engineering, 1997

Logic and Information is an accessible introduction to situation theory and an insightful extension to Barwise and Perry's (1983) original work. It aims to develop the mathematics required for a science of information. So, this is indeed mostly a mathematical logic text, but an interdisciplinary one. There are topics that appeal to philosophers, linguists, computer scientists and cognitive scientists. The clear and illustrative style of the book makes it understandable both to students and more advanced researchers taking new interdisciplinary directions. Devlin states that the basic ideas of situation theory have not changed much since the first hardback edition of the book in 1991. (This paperback edition is the same as the original except for correction of typos.) However, he suggests various additional reading paths for those who want to pursue the recent mathematical developments in the field. Chapter 1 starts with an examination of how one can go about understanding information in the '' Age of Information ''. Devlin emphasizes an empirical approach, developing the mathematical devices when needed as opposed to adopting a form of logic top-down for the same purpose. A historical and critical account of classical logic, based on truth, is given from this point of view. Classical first-order predicate logic is foreseen as a constrained version of the logic of information to be developed. Two important concepts of the theory are introduced : Infons, discrete items of information ; and situations, some limited portion of the whole world linked with constraints. Analogies with other branches of mathematics and science are made liberally throughout the book. An account of cognition in terms of information is given in chapter 2, where the basic ontology of the theory is introduced. This chapter forms, if you like, a requirements specification of the theory being designed. The basic capability of agents to individuate (or discriminate) objects in their environment leads to the definition of a unit of information (an infon) as a tuple that shows whether a number of objects do or do not stand as arguments to a relation. An item of information can be true of a situation, hence is said to be supported by it. Individuation of a situation does not require its exact description to be known, however. Various theory-internal abstractions are underlined in this chapter. Taking representationconstraint pairs related with information as equivalence classes that denote an infon is one such point. Models (in this case set-theoretic) are not to be confused with the real world. More complex concepts of the theory are introduced in chapter 3. One such concept is the introduction of types as a way of detecting higher-order uniformities across situations and other objects of the theory. Related with this are parameters to denote arbitrary objects of a given type, and anchors to assign values to parameters. Examples of parameters in natural language are given in the form of pronouns or proper names. With the introduction of typeabstraction, a situation supporting a set of infons is shown to be a proposition : a claim about the world that a certain object is of a certain type. Also introduced is the concept of an oracle : a special situation that concerns a certain object within a set of related parametric infons. Between accounts of types and oracles, a rather lengthy (and probably redundant) digression is made to question and explain the nature of abstraction and formalism in mathematics.

Journal of Philosophy, 2015