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). (shrink)

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. (shrink)

7 pages.-- Delivered to: 5th International Conference on Argumentation, The International Society for the Study of Argumentation, University of Amsterdam, 25-28 June 2002.

A comparative study of a broad range of logical systems, showing that classical logic is just one among them and thate there are useful nonclassical logics which are conservative extensions of classical logic, by risorting to several negations and several implications. The book is oriented towards a defense of fuzzy logics.

Still, it is but fair for me to point out that several of the mainstays of the present proposal owe very little to the influence of the philosophers whose epistemological views have attracted me most — or for that matter to that of other analytical philosophers. I am referring to my acknowledging degrees of truth and existence and, consequently, degrees of knowledge, too.

Graham Priest's book In Contradiction is a bold defense of the existence of true contradictions. Although Priest's case is impressive, and many of his arguments are correct, his approach is not the only one allowing for true contradictions. As against Priest's, there is at least one contradictorialist approach which establishes a link between true contradictions and degrees of truth. All in all, such an alternative is more conservative, closer to mainstream analytical philosophy. The two approaches differ as regards the floodgate (...) problem. Priest espouses a confinement policy banning contradictions except in a few special domains, particularly those of pure semantics and set-theory , whereas the alternative approach admits two negations -- natural or weak negation and strong negation, the latter being classical; accordingly, the alternative approach prohibits any contradiction involving strong negation, thus providing a syntactic test of what contradictions have to be rejected. (shrink)

This is a critical discusssion of Professor da Costa's Essay on the foundations of logic which brings up issues of philosophy of logic, set theory, the foundations of mathematics, and paraconsistency.

The main starting point of many of the contributions collected into the book is the kind of Twin Earth considerations, along with meaning individualism. Is Putnam's claim about water in this world and a stuff in an alternative world being different materials?. Is meaning in the head? One seems allowed to be skeptical about the starting point of the debate between such as emphasize broad content and those who think that the basic semantic entities are narrow contents, which would fail (...) to be world-dependent or world-oriented. The kind of motivations prompting the essays collected into the book are likely to be regarded as in need of a deeper elucidation by such as have been more or less influenced by Quine. Pettit & McDowell's collection of essays is one of the books most scholars interested in the confines of philosophy of language and philosophy of mind will find worth reading. (shrink)

Many-Valued logics can harbour nonclassical connectives expressing truth-nuances. The course of development of many-valued logics has given rise to paraconsistent systems wherein a sentence can be both negated and asserted just in case it is only partly true. A recently implemented family of such logics is shown to be a useful tool in coping with a number of philosophical difficulties, such as Zeno’s paradox of the arrow. This family is somehow akin to fuzzy logics initiated by Zadeh, but unlike them (...) it contains as a tautology the principle of excluded middle. (shrink)

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. (shrink)

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. (shrink)

The paper examines Beuchot's approach and agrees that there are many coincidences between medieval Aristotelianism and analytical philosophy. Both pursue philosophical inquiry in an argumentative manner. Nowadays analytical philosophy also tends to recognize as genuine such traditional metaphysical problems as were debated by the Scholastics. The paper's only criticism at Beuchot's views concerns analogy and reduplicative as-clauses. It argues that on that issue the cleavage between medieval and analytical philosophy lies in the latter's tending to favor complete equivocality of the (...) word «being». However, an alternative is possible, namely univocism, as implemented in combinatory logics, which while also rejecting reduplicative clauses is free from the ineffableness attendant upon equivocism. (shrink)

Introductory Remarks Why Paradigm Variation is Ensuant upon Contradiction How Externalistic Warrant Parries the Threat of [Truth] Relativism Why Not to Ward Relativism off by Means of Foundationalistic Justification Defending a relativistic View of Warrant A Transcendental Argument against [Truth] Relativism Towards [Partial] convergence A Gradualistic Paraconsistent Way to Convergence 7.1. - Perspectivism and Non Copulative Paraconsistent Logics 7.2. - The Strength and Weakness of Two Copulative Approaches to Paraconsistent Logic 7.3. - The Logic of Contradictorial Gradualism 7.4. - Implementing (...) the Notion of Relative Truth Bibliographic References.. (shrink)