Neuroscience has studied deductive reasoning over the last 20 years under the assumption that deductive inferences are not only de jure but also de facto distinct from other forms of inference. The objective of this research is to verify if logically valid deductions leave any cerebral electrical trait that is distinct from the trait left by non-valid deductions. 23 subjects with an average age of 20.35 years were registered with MEG and placed into a two conditions paradigm (100 trials for (...) each condition) which each presented the exact same relational complexity (same variables and content) but had distinct logical complexity. Both conditions show the same electromagnetic components (P3, N4) in the early temporal window (250–525 ms) and P6 in the late temporal window (500–775 ms). The significant activity in both valid and invalid conditions is found in sensors from medial prefrontal regions, probably corresponding to the ACC or to the medial prefrontal cortex. The amplitude and intensity of valid deductions is significantly lower in both temporal windows (p = 0.0003). The reaction time was 54.37% slower in the valid condition. Validity leaves a minimal but measurable hypoactive electrical trait in brain processing. The minor electrical demand is attributable to the recursive and automatable character of valid deductions, suggesting a physical indicator of computational deductive properties. It is hypothesized that all valid deductions are recursive and hypoactive. (shrink)

Our question is: can we embed minimal negation in implicative logics weaker than I→? Previous results show how to define minimal negation in the positive fragment of the logic of relevance R and in contractionless intuitionistic logic. Is it possible to endow weaker positive logics with minimal negation? This paper prooves that minimal negation can be embedded in even such a weak system as Anderson and Belnap’s minimal positive logic.

Minimal Negation is defined within the basic positive relevance logic in the relational ternary semantics: B+. Thus, by defining a number of subminimal negations in the B+ context, principles of weak negation are shown to be isolable. Complete ternary semantics are offered for minimal negation in B+. Certain forms of reductio are conjectured to be undefinable (in ternary frames) without extending the positive logic. Complete semantics for such kinds of reductio in a properly extended positive logic are offered.

Electrical brain activity modulation in terms of changes in its intensity and spatial distribution is a function of age and task demand. However, the dynamics of brain modulation is unknown when it depends on external factors such as training. The aim of this research is to verify the effect of deductive reasoning training on the modulation in the brain activity of healthy younger and older adults ( (mean age of 21 ± 3.39) and (mean age of 68.92 ± 5.72)). The (...) analysis reveals the benefits of training, showing that it lowers cerebral activation while increasing the number of correct responses in the trained reasoning task (). The brain source generators were identified by time-averaging low-resolution brain electromagnetic tomography (sLORETA) current density images. In both groups, a bilateral overactivation associated with the task and not with age was identified. However, while the profile of bilateral activation in younger adults was symmetrical in anterior areas, in the older ones, the profile was located asymmetrically in anterior and posterior areas. Consequently, bilaterality may be a marker of how the brain adapts to maintain cognitive function in demanding tasks in both age groups. However, the differential bilateral locations across age groups indicate that the tendency to brain modulation is determined by age. (shrink)

Hay doble pulsión en el centro de la discusión del razonamiento deductivo. Una conduce aparentemente a la abstracción y dominios arbitrarios, mientras que la otra conduce a la concreción y la dependencia del contenido. El objetivo de esta investigación es diseñar, aplicar y validar un instrumento de evaluación que nos permita corroborar si el razonamiento deductivo maneja reglas lógicas o contenidos. La muestra de estudio se compuso de 80 participantes (edad 18-77 años). El test consta de 60 ítems categorizados en: (...) formalidad, integrabilidad, complejidad y modalidad. Los resultados ponen de manifiesto la fiabilidad del test de razonamiento deductivo con un alpha de Cronbach. 775 y con un índice de validación. 850 para el índice de inteligencia no verbal (INV) del RIAS. Cómo conclusión inferimos que el razonador deductivo no dispone de un cuerpo preciso de reglas generales deductivas, sino que usa colecciones de reglas heurísticas cada vez menos abstractas. (shrink)

It is an intimate experience for us to think, to understand and to perceive things as being identical to themselves, and to suppose, consequently, that things are truly “what” they are. Something is always conceived as itself. The given is given full of itself in all its modifications. For instance, I can think or perceive partially some lips, I can see them almost in their whole or in some of their aspects, or just see them disappear. But it does not (...) seem to be possible to think or to perceive a given as almost itself, as an aspect or as part of itself. It is the aim of this work to study the assumptions and conditions for the original position of sameness in experience, just as it occurs in the synthesis of the datum singular and distinct. The polarization of single tone (einstimmig) intentional rays in an αvτó already contains the aporiae peculiar to the experience of the identical, whose revelation shall lead us, on the one hand, to one of the nuclei of the analysis of passive synthesis, and, on the other hand, to point up how critical revision of the numerical or extensional model of self-identity is for the unity of meaning. Then, it will be a question of pointing out the reasons why in a phenomenology of identity, the renunciation of the phenomenological legitimacy of the αvτó as a guarantee for the different positions of identity must be observed. DOI: 10.1007/978-94-011-3464-4_13 . (shrink)

Etude de l'extension par la negation semi-intuitionniste de la logique positive des propositions appelee logique C, developpee par A. Urquhart afin de definir une semantique relationnelle valable pour la logique des valeurs infinies de Lukasiewicz (Lw). Evitant les axiomes de contraction et de reduction propres a la logique classique de Dummett, l'A. propose une semantique de type Routley-Meyer pour le systeme d'Urquhart (CI) en tant que celle-la ne fournit que des theories consistantes pour la completude de celui-ci.