Papers
Contradiction et vérité
Ph.D. diss. University of Liege (Belgium). July 1979
A contradictorial system of logic is proposed. Contradictorial logic belongs to the family of paraconsistent logics, namely such as waive the Cornubia rule (which allows you to infer anything, "q", from any two mutual contradictory premises). Contradictorial logic adds the assertion of certain contradictions. The system is applied to elucidating a number of epistemological issues and is shown to be an acceptable logic from the outlook of a coherentist theory of knowledge, partly influenced by Quine's philosophical contributions.
Notes on Bergmann's New Ontology and Account of Relations
publ. in PHILOSOPHY REASEARCH ARCHIVES, 1987, pp. 221-249
The paper is a discussion of the formal ontology set forward by Gustav Bergmann.
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Graham Priest's Dialetheism: Is it altogether true?
publ. in SORITES #7, nov. 1996
A discussion of Graham Priest's dialetheism. While accepting that there are true contradictions in reality, the paper criticizes Priest's particular view thereof and proposes a gradualistic approach instead: some contradictions are indeed true but none is completely true. Ttuth and falseness mix.
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C-1 Compatible transitive extensions of system CT
publ. in LOGIQUE ET ANALYSE, #161 (1998), pp. 135-143
Newton da Costa's paraconsistent systems, Ci, are set up as extensions of CT, or Common Logic, which is classical positive logic plus a classicality symbol and a weak negation. While CT can be nonconservatively extended into systems of the Ci family, it can alternatively be extended into gradualistic logic, which is also paraconsistent and shares some of da Costa's features (with both weak and strong negation) but in an entirely diffeent way. The paper thus shows light onto the similarities and the differencies among the three main approaches in paraconsistent logic: the relevantist, the Brazilian (somehow dual-intuitionistic) and the gradualistic treatement.
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Indeterminacy of translation as a Hermeneutic doctrine
publ. in HERMENEUTICS AND THE TRADITION, ed. by D.O. Dahlstrom, Washington, 1988, pp. 212ff.
The paper construes Quine's view of indeterminacy of translation as a hermeneutic conception which is somehow akin to some approaches in the tradition of Gadamer.
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Naturalized epistemology and degrees of knowledge
Paper delivered to SOFIA 1st Conference. Tepoztlan (Mexico), August 1988.
The paper puts forward a gradualistic approach to the main problems of the theory of knowledge, while espousing a programme of epistemological naturalization.
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Alboran is and is not dry: Katalin Havas on logic and dialectics
published in 'Logique et Analyse', 1990, pp.331-8
Discussing Katalin Havas' approach to the problem of how logic relates to dialectics as understood in the Marxist tradition, I show that the acceptance of degrees of truth is bound to entail accepting true contradictions on the ground of broadly recognized logical rules, which in any case a classically-minded logician is required to espouse. Accordingly paraconsistent logics are called for if we are going to embrace degrees, as at least some dialectical philosophers are inclined to do.
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Flew on Entitlements and Justice
published in 'International Journal of Moral and Social Studies', 1989, pp. 259ff.
The paper discusses Antony Flew's argument to the effect that distributivist conceptions are incompatible with the very notion of justice, which is intrinsecally backwards-looking and hence hinges on previous entitlements.
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The Coexistence of Contradictory Properties in the same Subject According to Aristotle
publiushed in 'Apeiron', 1999
Aristotle grants that two mutually contradictory properties can be simultaneously present in the same subject to some extent. However in order to keep clear of recognizing true contradictions, he falls back on the dubious manoeuver of regarding intermediaries as as entirely different in kind from the extremes, rather than as lesser degrees of the properties fully realized at the extremes.
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Essence and Existence in Leibniz's Ontology
publ. in Synthesis Philosophica 12/2 (Zagreb, 1997, ISSN 0352-7875), pp. 415-32.
The several orders of compossibility must be sorted out «before» the divine decision to create this or that universe, since God's decision must be grounded in a sufficient reason, which can only arise from the divine essence itself and the intrinsic qualities of the orders among which He has to make the choice; the greatest perfection of an order of things is mirrored and expressed in every integral component of that
order. Consequently, the concept of every real thing does from all eternity contain 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. It is such an essential, quidditative perfection which 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 that quidditative perfection it unavoidably stems from.
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Partial Truth, Fringes and Motion: Three Applications of a Contradictorial Logic
Studies in Soviet Thought, vol 37 (Dordrecht: Kluwer, 1990), pp. 83-122. ISSN 0039-3797
This paper argues that we can make good sense of the idea of contradictory truths -- as implemented in a paraconsistent infinite-valued system of logic, which is here put forward -- in three fields -- which have been claimed to be amenable to contradictorialtreatments by the dialectical tradition -- namely those of partial truth, fringes of application of sundry predicates, and motion. The first is that, when a predicate correctly or truthfully applies to a part of some object but not to other parts thereof, it can only be said with partial truth that the object satisfies that predicate or has the property it denotes. The second problem arises because many predicates can be neither completely assigned to some things nor completely withheld from them. The 3d. problem is nothing else but Zeno's paradox of the arrow. The paper's gist is that in all cases true contradictions stem from graduality in things.
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In Defense of Full-Scale Planning
Science and Society 57/2, New York: Guilford Press, 1993, pp. 204-13. ISSN 0036-8237.
The main purpose of the anti-capitalist movement has always been to put an end to the cleavage between haves and have-nots. Egalitarianism is the core of all historical attempts to set up an alternative to systems based on private ownership. It therefore seems reasonable to take as a criterion of success for such attempts the degree to which they have managed to surmount social inequalities. As with almost everything else, this is not an all-or-nothing issue; differences in both degree and aspect must be taken into account.
As against market-socialism, I argue that, the more supply-and-demand mechanisms are allowed to stand and even grow within an overall planned economy, the greater is the possibility of capitalist evils reappearing under socialist cover, as the sad experience of real socialism has in fact suggested. Yet, some dose of those mechanisms, and thus also of the evils accompanying them, is inevitable for quite some time after the nominal abolition of a capitalist private-ownership system. If, and when, social administrators are aware of those trends and of the overall purpose of socialist transformation, they ought gradually to reduce such disparities and to try to reach, as much and as fast as possible, an egalitarian distribution -- as e.g. on the basis of Marx's needs criterion.
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Dialectics and Inconsistency, Phonology, Nothing
Handbook of Metaphysics and Ontology, ed. By H. Burkhardt & Barry Smith.
Munich: Philosophia Verlag, 1991. ISBN 3-88405-080X. Resp.pp 216-218;
pp. 703-706; pp. 619-621.
PHONOLOGY
Phonemes are minimal segments within the spoken message whose presence is relevant for distinguishing one message from a different one with another meaning. Each phoneme underlies different phonetic realizations. What sets a phoneme from another is fuzzy cluster of the fuzzy features. Thus the study of phonemic structures is likely to have much to gain from a gradualistic approach. Through a gradualistic treatment synchronic phonology could tally with the diachronic study in
a simpler way than is customary. In this connection, an obstacle to be overcome is a widespread adherence to classical logic.
NOTHING
Philosophers have always wondered about the meaning of such negative pronouns and adverbs. There have been two lines on those issues throughout the history of philosophy. The line rooted in the Platonistic tradition is taken by Hegel, who developed the dialectics of Being and Nothingness. Can conflicting considerations be merged into a unified treatment? If that is possible at all, the approach which would alone be able to perform the task would most probably be a dialectical metaphysics according to which the particle `not' stands
for an entity which both [up to a point] exists and yet [to some
extent] fails to exist; insofar as it is a negative principle -- a root of deprivation, of lacking, of failing to be -- it is nonexistent, but its nonexistence is not absolute. Such a Neo-Neoplatonistic approach has been tried to be made viable through a paraconsistent logic.
DIALECTICS
The sense of `dialectics' prevailing nowadays originates with Kant, for whom dialectics was the study of the ideas of pure reason in their transcendental usage. One of the divisions of such dialectics was the study of the antinomies of pure reason, which are contradictions ensuant upon a ranscendental use of the idea world. This is how in Hegel's work `dialectics' came to mean the disclosing of insurmountable contradictions. A revival of dialectical thought has been brought about by the construction of so-called paraconsistent systems of logic. The
author argues for a quantitative dialectics by stressing that true contradictions are always ensuant upon inbetweenness, i.e. upon the existence of degrees of existence or truth, intermediary between absolute truth and complete falsehood. This dialectical approach carryes to its ultimate consequences (something akin to) the Leibnizian principle of continuity.
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Contradictions and Paradigms: A Paraconsistent Approach
Cultural Relativism and Philosophy: North and Latin American Perspectives, edited by Marcelo Dascal. Leiden & New York: E.J. Brill, 1991, pp. 29-56. ISBN 9004094334
The present paper argues that: (1) warrant relativism is true -- any belief warrant is relative --; (2) [truth] relativism is false (not every belief can be true only as regards some particular entity or reference-point); (3) there are valuable insights relativists have provided us with, one of them being the search for some kind of convergence; (4) a most convenient convergence policy can be articulated by applying a paraconsistent gradualistic (infinite-valued) logic, i.e. a logic which, by allowing degrees of truth and falseness, makes room for some beliefs being both [up to a point] true and yet [to some extent] false.
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Notice of Douglas Walton's Slippery Slope Arguments
Pragmatics and Cognition I/2 (1993), pp. 401-410. ISSN 0929-0907
The book's main contention is that, far from being necessarily fallacious, slippery slope arguments are often acceptable in a discussion, shifting the burden of proof. Against this approach, I argue that slippery slope arguments are ensuant on the gap between a continuous underlying series of characteristics - the input - and a discontinuous two-valued output. Law as usually conceived only seldom allows of middle courses, and is prone to all-or-nothing attitudes. I advocate a gradualistic solution. All essential properties involved in those arguments admit of degrees. Many actions can be both praiseworthy up to a point and yet also reprehensible to some extent. We ought to overcome the two-valuedness of our juridical systems, replacing it, in so far as it is feasible, with systems of scales. Truth admits of degrees. A reasonable approach to our moral and legal judgments and practices would entail a step-by-step departure from rigid dichotomies, favouring a more gradualistic approach. This approach, needed in both logic and juridical doctrine, is compatible with the inner patterns of our thought process. Walton does nor raise those questions since he tries to implement a purely pragmatic approach.
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Anthropoid Rights and Paternalism
Etica & Animali. vol 8 (1996) (special issue devoted to the Great Ape Project), pp 155-177.
Anti-animalists allege that, since humans alone are capable of engaging in some sort of higher-order practical reasoning and of being led in their behaviour by moral values, non-human animals may not be treated as persons. I argue that such a view is wrong. The difference is just one of degree. Freedom is just one value among others, not the supreme one; the differences of treatment humans and other anthropoids are entitled to do not hinge upon the question of paternalism, since
humans, too, have to be treated paternalistically sometimes, at least in certain respects. Admittedly, every paternalistic action impinges on the concerned agent's freedom, thus clashing with the value of liberty. Hence, either it is unjustified or else a conflict of values arises. But there are many such conflicts, or dilemmas.
One of the good things of being good or fair to our cousins the apes is that we gain a deeper insight into ourselves. We are apes after all. What is the end of their lives is also the end or goal of ours: to live, and to live well; to secure such a life both for ourselves and others.
I am not erasing or obliterating differences of degree. Nor am I denying that they may be important when confronted with moral dilemmas. How much important are they? After recent research we now know that in most relevant respects the discrepancy between humans and other apes is small. They are much more human-like than we were used to think. And we are much more ape-like than we had fancied to imagine.
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Leibniz aux prises avec la catégorie aristotélicienne de relation: Remarques sur plusieurs lectures contemporaines
Leibniz. Tradition und Aktualität. V. Internationaler Leibniz-Kongreß, Vorträge. 1. Teil, pp. 718-725. Hanover: Gottfried-Wilhelm-Leibniz-Gesellschaft, 1988. ISSN 1130-2097
En el estudio contemporáneo de Leibniz se han ofrecido varias interpretaciones de su tratamiento metafísico de las relaciones. La primera y más conocida es la que propuso Russell, según la cual para Leibniz no habría relaciones ni verdades relacionales, sino que cuanto quepa decir sobre el mundo se podrá decir en oraciones de sujeto/predicado, siendo el predicado monádico. Otra lectura, propuesta por Kulstad, entiende que el predicado leibniziano puede ser relacional, expresándose por un sintagma verbal que contenga nombres de sustanciass diversas. Una tercera e ingeniosa interpretación ha sido ofrecida por el malogrado H.N. Castañeda. La cuarta lectura, aquí defendida, sostiene que para Leibniz no hay verdades relacionales, mas todo sucede como si las hubiera, en virtud de una correspondencia universal, la cual, empero, sólo existe para la mirada de la mente: la mirada de Dios puede conferir a las cosas grados diverssos de correspondancia sin cambiar los fenómenos.
Le paradoxe de l'être mourant chez St Augustin et chez Leibniz
La vie et la mort, comp por M. Vadée. Poitiers: Société Poitevine de philosophie, 1996, pp. 287-289. ISBN 2-9508689-0-8.
Este trabajo constituye un comentario de 2 textos, el uno de San Agustín, en el libro XIII de la Ciudad de Dios, el otro del Pacidius Philaleti de Leibniz. La muerte está siendo sufrida como un infortunio cuando uno está en vida, pero muriendo. En ese proceso del estar muriéndose, de la vida moribunda, la vida y la muerte coexisten.
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De la Logique Combinatoire des Generales Inquisitiones aux Calculs Combinatoires Contemporains
THEORIA, Nº 14-15 (San Sebastián, octobre 1991). pp. 129-159. ISSN 0495-4548
In his 1686 essay GI Leibniz undertook to reduce sentences to noun-phrases, truth to being. Such a reduction arose from his equating proof with conceptual analysis. Within limits Leibniz's logical calculus provides a reasonable way of surmounting the dichotomy, thus allowing a reduction of hypothetical to categorical statements. However it yields the disastrous result that, whenever A is possible and so is B, there can be an entity being both A and B. Yet, Leibniz was in the GI the forerunner of 20th century combinatory logic, which (successfully!) practices -- sometimes for reasons not entirely unlike Leibniz's own grounds -- reductions of the same kinds he tried to carry out.
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