Axiomatization and Models of Scientific Theories

In this paper we discuss two approaches to the axiomatization of scien- tific theories in the context of the so called semantic approach, according to which (roughly) a theory can be seen as a class of models. The two approaches are associated respectively to Suppes’ and to da Costa and Chuaqui’s works. We argue that theories can be developed both in a way more akin to the usual mathematical practice (Suppes), in an informal set theoretical environment, writing the set theoretical predicate in the language of set theory itself or, more rigorously (da Costa and Chuaqui), by employing formal languages that help us in writing the postulates to define a class of structures. Both approaches are called internal, for we work within a mathematical framework, here taken to be first-order ZFC. We contrast these approaches with an external one, here discussed briefly. We argue that each one has its strong and weak points, whose discussion is relevant for the philosophical foundations of science

Paraconsistent transition systems

Often in Software Engineering, a modeling formalism has to support scenarios of inconsistency in which several requirements either reinforce or contradict each other. Paraconsistent transition systems are proposed in this paper as one such formalism: states evolve through two accessibility relations capturing weighted evidence of a transition or its absence, respectively. Their weights come from a specific residuated lattice. A category of these systems, and the corresponding algebra, is defined as providing a formal setting to model different application scenarios. One of them, dealing with the effect of quantum decoherence in quantum programs, is used for illustration purposes.publishe

Axiomatization and Models of Scientific Theories

In this paper we discuss two approaches to the axiomatization of scien- tific theories in the context of the so called semantic approach, according to which (roughly) a theory can be seen as a class of models. The two approaches are associated respectively to Suppes’ and to da Costa and Chuaqui’s works. We argue that theories can be developed both in a way more akin to the usual mathematical practice (Suppes), in an informal set theoretical environment, writing the set theoretical predicate in the language of set theory itself or, more rigorously (da Costa and Chuaqui), by employing formal languages that help us in writing the postulates to define a class of structures. Both approaches are called internal, for we work within a mathematical framework, here taken to be first-order ZFC. We contrast these approaches with an external one, here discussed briefly. We argue that each one has its strong and weak points, whose discussion is relevant for the philosophical foundations of science

Quasi-truth and defective knowledge in science: a critical examination

Quasi-truth (a.k.a. pragmatic truth or partial truth) is typically advanced as a framework accounting for incompleteness and uncertainty in the actual practices of science. Also, it is said to be useful for accommodating cases of inconsistency in science without leading to triviality. In this paper, we argue that the given developments do not deliver all that is promised. We examine the most prominent account of quasi-truth available in the literature, advanced by da Costa and collaborators in many places, and argue that it cannot legitimately account for incompleteness in science: we shall claim that it conflates paraconsistency and paracompleteness. It also cannot account for inconsistencies, because no direct contradiction of the form α ∧ ¬α can be quasi-true, according to the framework. Finally, we advance an alternative interpretation of the formalism in terms of dealing with distinct contexts where incompatible information is dealt with. This does not save the original program, but seems to make better sense of the formalism

Understanding Defective Theories: The case of Quantum Mechanics and non-individuality

Here, we deal with the question of under which circumstances can scientists achieve a legitimate understanding of defective theories qua defective. We claim that scientists understand a theory if they can recognize the theory’s underlying inference pattern(s) and if they can reconstruct and explain what is going on in specific cases of defective theories as well as consider what the theory would do if non-defective –even before finding ways of fixing it. Furthermore, we discuss the implications of this approach to understanding the meta-metaphysics of Quantum Mechanics, specifically with regard to Quasi-set theory. We illustrate this by employing Quasi-set theory to structure a defective scientific theory and make possible the understanding of the theory

Memorial de Atividades Acadêmicas

Memorial da trajetória acadêmica.Memorial de Atividades Acadêmicas apresentado para progressão para a Classe de Professor Titular do Departamento de Filosofia da UFSC em 2015

Abstract Consequence and Logics - Essays in Honor of Edelcio G. de Souza

Edelcio G. de Souza is a Brazilian logician and philosopher who has researches in the domains of abstract logic, non-classical systems, philosophy of science and the foundations of mathematics. This book is in his honor with the purpose of celebrating his 60th birthday. It contains some articles connected with the above topics and other subjects in logical investigations