Editors’ note: These four interrelated discussions of the role of the cerebellum in coordinating emotional and higher cognitive functions developed out of a workshop presented by the four authors for the 2000 Conference of the Cognitive Science Society at the University of Pennsylvania. The four interrelated discussions explore the implications of the recent explosion of cerebellum research suggesting an expanded cerebellar role in higher cognitive functions as well as in the coordination of emotional functions with learning, logical thinking, perceptual consciousness, (...) and action planning. (shrink)

An introduction to the model-theoretic approach in the philosophy of science is given and it is argued that this program is further enhanced by the introduction of partial structures. It is then shown that this leads to a natural and intuitive account of both "iconic" and mathematical models and of the role of the former in science itself.

We apply the recently elaborated notions of ‘pragmatic truth’ and ‘pragmatic probability’ to the problem of the construction of a logic of inductive inference. It is argued that the system outlined here is able to overcome many of the objections usually levelled against such attempts. We claim, furthermore, that our view captures the essentially cumulative nature of science and allows us to explain why it is indeed reasonable to accept and believe in the conclusions reached by inductive inference.

We conjecture that the existence of some fast-growing functions implies in a simple way the existence of some inaccessible cardinals. This note expands some previous work by the second author.

Schrödinger logics are logical systems in which the principle of identity is not true in general. The intuitive motivation for these logics is both Erwin Schrödinger's thesis (which has been advanced by other authors) that identity lacks sense for elementary particles of modern physics, and the way which physicists deal with this concept; normally, they understandidentity as meaningindistinguishability (agreemment with respect to attributes). Observing that these concepts are equivalent in classical logic and mathematics, which underly the usual physical theories, we (...) present a higher-order logical system in which these concepts are systematically separated. A classical semantics for the system is presented and some philosophical related questions are mentioned. One of the main characteristics of our system is that Leibniz' Principle of the Identity of Indiscernibles cannot be derived. This fact is in accordance with some authors who maintain that quantum mechanics violates this principle. Furthermore, our system may be viewed as a way of making sense some of Schrödinger's logical intuitions about the nature of elementary particles. (shrink)

This paper develops the first deontic logic in the context of paraconsistent logics.

Trois sortes de définitions sont présentées et discutées: les définitions nominales, les définitions contextuelles et les définitions amplificatrices. On insiste sur le fait que I’elimination des definitions n’est pas forcement un procede automatique en particulier dans le cas de la logique paraconsistante. Finalement on s’int’resse à la théorie des objets de Meinong et l’on montre comment elle peut êrre considéréecomme une théorie des descripteurs.Three kinds of definitions are presented and discussed: nominal definitions, contextual definitions, amplifying definitions. It is emphasized that (...) the elimination of definitions is not necessarily straightforward in particular in the case of paraconsistent logic. Finally we have a look at Meinong’s theory objects and we show how it can be considered as a theory of descriptors. (shrink)

We expose the main ideas, concepts and results about Jakowski's discussive logic, and apply that logic to the concept of pragmatic truth and to the Dalla Chiara-di Francia view of the foundations of physics.

I discuss some questions of quantum physics, for instance the validity and limitations of the basic language of set theory to deal with problems related to elementary particles. I also present a sketch of a formalization of a “metaphysics of structures”, which might be useful for a kind of “ontic structural realism”, and briefly review the concept of quasi-truth, which underlies my way of understanding scientific theories and the scientific activity.

We present some recent technical results of us on the incompleteness of classical analysis and then discuss our work on the Arnol'd decision problems for the stability of fixed points of dynamical systems.

Da Costa and French explore the consequences of adopting a 'pragmatic' notion of truth in the philosophy of science. Their framework sheds new light on issues to do with belief, theory acceptance, and the realism-antirealism debate, as well as the nature of scientific models and their heuristic development.

An introduction to the model-theoretic approach in the philosophy of science is given and it is argued that this program is further enhanced by the introduction of partial structures. It is then shown that this leads to a natural and intuitive account of both "iconic" and mathematical models and of the role of the former in science itself.

Physical superpositions exist both in classical and in quantum physics. However, what is exactly meant by ‘superposition’ in each case is extremely different. In this paper we discuss some of the multiple interpretations which exist in the literature regarding superpositions in quantum mechanics. We argue that all these interpretations have something in common: they all attempt to avoid ‘contradiction’. We argue in this paper, in favor of the importance of developing a new interpretation of superpositions which takes into account contradiction, (...) as a key element of the formal structure of the theory, “right from the start”. In order to show the feasibility of our interpretational project we present an outline of a paraconsistent approach to quantum superpositions which attempts to account for the contradictory properties present in general within quantum superpositions. This approach must not be understood as a closed formal and conceptual scheme but rather as a first step towards a different type of understanding regarding quantum superpositions. (shrink)

We formulate Suppes predicates for various kinds of space-time: classical Euclidean, Minkowski's, and that of General Relativity. Starting with topological properties, these continua are mathematically constructed with the help of a basic algebra of events; this algebra constitutes a kind of mereology, in the sense of Lesniewski. There are several alternative, possible constructions, depending, for instance, on the use of the common field of reals or of a non-Archimedian field. Our approach was inspired by the work of Whitehead, though our (...) philosophical stance is completely different from his. The structures obtained are idealized constructs underlying extant, physical space-time. (shrink)

This paper is a summary of a lecture in which I presented some remarks on Gödel’s incompleteness theorems and their meaning for the foundations of physics. The entire lecture will appear elsewhere.

This paper is a historical companion to a previous one, in which it was studied the so-called abstract Galois theory as formulated by the Portuguese mathematician José Sebastião e Silva ). Our purpose is to present some applications of abstract Galois theory to higher-order model theory, to discuss Silva’s notion of expressibility and to outline a classical Galois theory that can be obtained inside the two versions of the abstract theory, those of Mark Krasner and of Silva. Some comments are (...) made on the universal theory of structures. (shrink)

We present some recent technical results of us on the incompleteness of classical analysis and then discuss our work on the Arnol'd decision problems for the stability of fixed points of dynamical systems.

The mathematical concept of pragmatic truth, first introduced in Mikenberg, da Costa and Chuaqui (1986), has received in the last few years several applications in logic and the philosophy of science. In this paper, we study the logic of pragmatic truth, and show that there are important connections between this logic, modal logic and, in particular, Jaskowski's discussive logic. In order to do so, two systems are put forward so that the notions of pragmatic validity and pragmatic truth can be (...) accommodated. One of the main results of this paper is that the logic of pragmatic truth is paraconsistent. The philosophical import of this result, which justifies the application of pragmatic truth to inconsistent settings, is also discussed. (shrink)

Contextual emergence was originally proposed as an inter-level relation between different levels of description to describe an epistemic notion of emergence in physics. Here, we discuss the ontic extension of this relation to different domains or levels of physical reality using the properties of temperature and molecular shape as detailed case studies. We emphasize the concepts of stability conditions and multiple realizability as key features of contextual emergence. Some broader implications contextual emergence has for the foundations of physics and cognitive (...) and neural sciences are given in the concluding discussion. Relevant facts about algebras of observables are found in the appendices along with an abstract definition of Kubo-Martin-Schwinger states. (shrink)

Provability, Computability and Reflection.

This paper is a summary of a lecture in which I presented some remarks on Gödel’s incompleteness theorems and their meaning for the foundations of physics. The entire lecture will appear elsewhere. doi: http://dx.doi.org/ 10.5007 / 1808-1711.2011v15n3p453.

We expose the main ideas, concepts and results about Jaśkowski's discussive logic, and apply that logic to the concept of pragmatic truth and to the Dalla Chiara-di Francia view of the foundations of physics.

An improvement on Horwich's so-called pseudo-proof of Russell 's principle of induction is offered, which, we believe, avoids certain objections to the former. Although strictly independent of our other work in this area, a connection can be made and in the final section we comment on this and certain questions regarding rationality, etc.

We apply the recently elaborated notions of 'pragmatic truth' and 'pragmatic probability' to the problem of the construction of a logic of inductive inference. It is argued that the system outlined here is able to overcome many of the objections usually levelled against such attempts. We claim, furthermore, that our view captures the essentially cumulative nature of science and allows us to explain why it is indeed reasonable to accept and believe in the conclusions reached by inductive inference.

We use Padoa's principle of independence of primitive symbols in axiomatic systems in order to show that time is dispensable in continuum thermodynamics, according to the axiomatic formulation of Gurtin and Williams. We also show how to define time by means of the remaining primitive concepts of Gurtin and Williams system. Finally, we introduce thermodynamics without time as a primitive concept.

In this work, the first of a series, we study the nature of informal inconsistency in physics, focusing mainly on the foundations of quantum theory, and appealing to the concept of quasi-truth. We defend a pluralistic view of the philosophy of science, grounded on the existence of inconsistencies and on quasi-truth. Here, we treat only the ‘classical aspects’ of the subject, leaving for a forthcoming paper the ‘non-classical’ part.

We discuss the hypothesis that the debate about the interpretation of the orthodox formalism of quantum mechanics might have been misguided right from the start by a biased metaphysical interpretation of the formalism and its inner mathematical relations. In particular, we focus on the orthodox interpretation of the congruence relation, '=', which relates equivalent classes of different mathematical representations of a vector in Hilbert space, in terms of metaphysical identity. We will argue that this seemingly "common sense" interpretation, at the (...) semantic level, has severe difficulties when considering the syntactic level of the theory. (shrink)

We expose the main ideas, concepts and results about Jaśkowski's discussive logic, and apply that logic to the concept of pragmatic truth and to the Dalla Chiara-di Francia view of the foundations of physics.