Lorenzo Peña

Three (apparent ) deontic antinomies are discussed: the paradoxes of the watchman and the praiser, as weIl as deontic dilemmas. A paraconsistent deontic logic, Ad, is put forward whose underlying 1st-order calculus is an infinite-valued tensorial logic. Several arguments are offered bearing out be existence of deontic contradictions, while two ways of dealing with conditional obligation paradoxes within the framework of Ad are canvassed. While the aggregation rule and the ought-implies-can principle are upheld, sundry schemata are shown not to obtain which involve iterated deontic operators (most conspicuously: that whatever ought to be obligatory is obligatory; and that it is obligatory that whatever ought to be the case should in fact be the case).

Este libro presenta el sistema ontofántico, un tratamiento de todas las cuestiones centrales de la métafísica articulado gracias a una lógica contradictorial, no aristotélica, inspirada en el gradualismo alético de Platón. El libro comporta dos partes: la una, histórica, examina el problema de la esencia y la existencia desde Platón hasta el primer Wittgenstein. La segunda parte, sistemática, propone una solución nueva a las dificultades, identificando a cada ente con su acto de existir y subsumiendo a todos los mundos posibles en un mundo real omniabarcador, del cual serían aspectos.

This essay belongs to a series of papers whose aim is to show that some differing accounts of relations in contemporary philosophy are flawed because they resort to what can be labelled `hylomorphism'. Some standard difficulties of Aristotelianism reappear in these analytical approaches. All of them resort to «form» as playing the role of `«ctualizing» a given «matter» by making it into another entity. In these accounts the actualizing or structuring form lacks the quality it bestows upon the matter it clings to. The puzzle lies in those forms' baffling slipperiness; for they cannot be meant or intended outside their role of actualizing or informing some matter. But, when we point to their playing such a role, we cannot mean or intend the form itself, but only the informed matter -- or, if you please, the result of its being thus informed. For some approaches, a problem also arises concerning matter itself, one closely resembling Aristotelian problems with prime matter -- problems which have prompted some interpreters to deny that Aristotle posited any such entity Foot note 1_1. What in these approaches plays the role of Aristotelian matter, when taken «prior to» or outside of its being «informed» by a form, lacks sufficient self being and endowment with qualities and ontological profile to be an entity directly meant as such. Such a problem e.g. affects Tractarian «objects», which are both form and content, but which can be meant as neither separately. It follows that their ipseity always eludes us and evades being meant or signified. As we are about to see, a similar problem affects Bergmann's new ontology

The main claim of this paper is that the boundary between scientific and non scientific knowledge does exist -- which means several things. First, it's not the case that anything goes: some irrationalists have been mistaken into acceptance of that wrong conclusion because they have remarked that, however the boundary might be drawn, some important scientific developments would fall afoul of the standards entitling a research practice to count as scientific. Second, the boundary is not an imaginary one, that is to say besides what is scientific and what is unscientific there also is what lies at the boundary, certain research practices which are neither wholly scientific nor fully unscientific. Third, studying what is science is itself a kind of research belonging to the boundary, since the methods available in that research are not as strictly rigorous as those used in science proper; in fact, all of philosophy is included in the boundary in question. Fourth, the boundary (and in fact science itself) displays a characteristic structure pertaining to what are by now usually called «non wellfounded sets» -- sets, that is, which are somehow or other involved in themselves, whether as members, or as members of members or so on; the significance of the last thesis is that the best way of approaching philosophy of science is not standard set theory, but theories allowing non wellfounded sets are preferable. Fifth, and last, admission of the boundary's existence compels us to go beyond standard classical logic and to look for a more suitable logic, as for instance some kind of fuzzy paraconsistent logic.

Raúl Orayen's Lógica, significado y ontología Foot note is a profound book, a thorough inquiry into several important issues in the philosophy of logic. Raúl Orayen is one of the outstanding analytical philosophers in the Spanish speaking world. As in his other publications, he displays a masterly reasoning power. No patched up solutions in this book. Orayen is not going to let what he takes to be unsatisfactory treatments off the hook with vague considerations of their being able to cope «somehow or other» with such difficulties as beset them.

Introducción a la lógica matemática que se diferencia de los textos estándar que presuponen la verdad o la validez incuestionables de la lógica clásica o aristotélica (la que no admite grados de verdad ni contradicciones). Con este libro el estudiante se adentra en la lógica sin tener que presuponer nada en ese sentido; va descubriendo paulatinamente un abanico de lógicas, de las cuales la clásica es una de ellas, la más simple. El lector va así vislumbrando una inagotable pluralidad de lógicas posibles, algunas de las cuales vienen desarrolladas sintáctica y semánticamente.

Three (apparent ) deontic antinomies are discussed: the paradoxes of the watchman and the praiser, as weIl as deontic dilemmas. A paraconsistent deontic logic, Ad, is put forward whose underlying 1st-order calculus is an infinite-valued tensorial logic. Several arguments are offered bearing out be existence of deontic contradictions, while two ways of dealing with conditional obligation paradoxes within the framework of Ad are canvassed. While the aggregation rule and the ought-implies-can principle are upheld, sundry schemata are shown not to obtain which involve iterated deontic operators (most conspicuously: that whatever ought to be obligatory is obligatory; and that it is obligatory that whatever ought to be the case should in fact be the case).

Desde la perspectiva abierta por este libro no puede ya el estudio del Ser considerarse patrimonio de aquellas concepciones que lo entienden exento de contradicción, de gradualidad y de inserción en el devenir. Perfilase ahora una visión del Ser y de los seres que, a la vez que reconoce la absoluta realidad de aquél, concibe todo lo real con determinaciones mutuamente contradictorias, en un entretejimiento de ser y no-ser; visión que viene defendida adoptando el estilo de pensamiento de la filosofía analítica: un proceder, hasta donde quepa, por argumentos formalizables y por definiciones rigurosas. Van desfilando ante esa instancia metodológica los grandes problemas de la metafísica, desembocándose en un racionalismo ontológico consecuente, a la vez que dialéctico. Pruébase, con un argumento trascendental, un principio de inteligibilidad de lo real, del cual van resultando los de razón suficiente, no-contradicción y tercio excluso; explicándose cómo, y en qué medida, coexiste su vigencia con la de lo contradictorio, en una realidad donde se cumple el principio de gradualidad: todas las diferencias son de grado.

It is widely known that Plato seems to be committed in a number of dialogues to the view that all perfections are “united” — whether such unity is construed as identity, which doesn’t lack textual evidence, or, more probably, as some kind of mutual “supervenience”. (See for instance Laches 199e3-4, Alcib. I 114d-116d, Protag. 329c-333d & 349a-c. Whatever the solution to those interpretive problems is, what anyway can be ascertained is that, when writing the Statesman, our philosopher is keen on maintaining that not only is it not the case that all perfections are identical, but, moreover, some perfections do in fact clash with others, which means that a thing can possess one of them only to the extent it lacks the opposite perfection. However, as we’re going to see straight away, the Statesman’s main purpose and thrust is likely to be that of emphasizing the necessity of some unity among opposite qualities. The significance of such a contention can be set off against what will become the Aristotelian (and in effect the commonly received) view on the topic. In the Statesman Plato recognizes that in each case there is some desirable mean between the extremes, but where it lies changes according to circumstances. Trying to secure that convenient mean doesn’t debar us from loking upon the extremes under consideration as virtues or perfections themselves. Thus, when the Statesman is drawing towards its conclusion, the Foreigner abruptly brings up the issue of υπερβολην και την ελλειψιν (283c3-4), and thereby that of the art of measuring (η µετρητικη). Immediately the problem arises of the relations between the opposite extremes. In Theaet. 152d, 157a, 160b-c, it appears that Plato distinguishes relative from non-relative properties or determinations in the same way as he does between empirical, earthly, changeable things and the Forms. Yet in his later dialogues Plato is clearly committed to holding the view that the Forms themselves enter a number of relations, and even that some Forms partake of others. Since very early onwards he seems to have been concerned about some reciprocal relativity of opposite qualities (there are many places where such relativity is stressed, as Charm. 168b5-169a5, Phaed..

Arthur Lovejoy's masterful, highly influential interpretation of Leibniz's philosophy has been almost neglected for decades now. This paper tries to rehabilitate Lovejoy's construal (with a number of adaptations) by delving into the underlying logical links connecting Leibniz's principles of order and gradation (the latter also called `law of continuity', `principle of transition' or `principle of the jumpless change': natura non facit saltus ) with other fundamental principles of his mature philosophy