Lorenzo Peña

A Fuzzy-Set Theoretical Framework -resting on a paraconsistent infinite-valued logic- is sketched, wherein a thorough ontological-reduction program can be carried out. The framework includes formulae of the form “x comprises z in the time-interval e”. Reducing aggregates to sets thus handled is shown to escape usual objections. Likewise, systems generally can be regarded as aggregates, hence as (fuzzy) sets -the purported nonextensionality of systems objection being disposed of owing to our system’s recognizing infinitely many membership degrees. So do bodies, too, which enables us to find a solutionto Unger’s sorites concerning ordinary material bodies

This paper develops several insights put forward in the book Republican Studies. It goes into the difference between republicanism as a concept pertaining to legal theory, i.e. a system free from dynastic power, and the political-philosophy trend which currently goes by the same name, also known as `civicism', hinging upon the notion of freedom as non-domination. As against such a view, the value of a classical notion of liberty is maintained. Further grounds to choose a republic rather than a monarchy are analyzed. A Parlamentarian Republic is shown to offer a reasonable balance of powers. International implications of this conception are also sketched out, opening the prospect of a universal republic. Reparations for past grievances are advanced as a means to approach a system of international relations oriented towards a just integration of Planet Earth

Orayen proposes some kind of intensional approach in philosophy of logic, with meanings playing a central role in implementing the notion of logical truth. Orayen regards Quine as his main interlocutor. The major topic gone into through the book is logical form, validity and logical truth. As an outgrowth, Quine's operationalist view of language receives an extensive coverage and discussion. The investigation into the notion of logical truth and validity leads to a critical assessment of the relevantist challenge to the classical conception. This critical notice casts doubt on Orayen's defence of analyticity as a requirement for logical truth

La filosofía analítica ha contribuido a esclarecer la cuestión de los dilemas morales, sobre todo gracias a la utilización de la lógica deóntica. Vienen aquí examinados los debates recientes en el seno de dicha corriente filosófica sobre los conflictos de obligaciones.. Se pone de manifiesto cuán difícil es admitir conflictos- morales sin pagar el precio de aceptar contradicciones verdaderas. Pero, a la inversa de lo habitual en quienes sostienen esa tesis, el artículo, en vez de pronunciarse en contra de que haya conflictos morales, trata de mostrar que sí los hay y, a tenor de ello, aboga por el reconocimiento de contradicciones verdaderas en la vida moral. Tales contradicciones pueden entenderse en el marco de una metafísica a la vez gradualista y aspectualista.

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 concept of every real thing from all eternity contains the unavoidability of its existence before the divine decision. Thus every complete concept of a real thing contains the property of being such that the thing will exist if a created universe exists. Then a thing's existence cannot be external to its concept. There is bound to be more in the concept of something that exists than in that of "something" that does not-since existence is explained through the quidditative property of being an essence that constitutes an integral part of the most perfect series of things. Such an essential, quidditative perfection explains the divine decision, and hence existence. Therefore, existence can be deduced from that essential perfection. The essence-as-such, the mere possible, contains something from which existence follows. What Leibniz never manages to explain is what distinguishes existence from the quidditative perfection it unavoidably stems from. (edited)

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..

Da Costa's paraconsistent systems of the series Cm (for finite m) (see [C1], [C2], and esp. [C3], pp. 237ff.) share important features with transitive logic, TL (which has been gone into in [P1] and [P2]), namely, they all coincide in that: (c1) they possess a strong negation, `¬', a conditional, `⊃', a conjunction, `∧', and a disjunction, `∨', with respect to which they are conservative extensions of CL or Classical Logic; (c2) they possess a non strong negation, `N' (notations are different for systems C) which does not possess all properties of classical negation, but for which the following schemata are theorematic (I use the letters `p', `q', etc as schematic letters; my notational conventions are basically Church's: associativity leftwards; a dot stands for..