Contradiction

Synthesis and fragmentation in social theory: a progressive solution

by John Holmwood

Postmodern claims for the lack of general coherence in social life and therefore in social research are merely a... more Postmodern claims for the lack of general coherence in social life and therefore in social research are merely a version of recurrent attempts to accept incoherence as adequate in explanations. Incoherence, however, is less sharply distinguishedfrom the synthetic and generalizing theories that it is held to have replaced than its proponents and critics suppose. Generalizing approaches, in fact, were built around contradictions
that contributed to their instability and facilitated postmodern fragmentation. In this paper we demonstrate the central contradictions in social theory, showing their common occurrence in apparently opposed positions. Both postmodernism and what it seeks to replace are features of a conservative and unproductive social science. We trace the
contradictory continuities through major modern schools of social theory in order to clear the ground for a progressive social science which accepts contradictions as problems that must be solved creatively in the practice of social research.

Contradicciones y paradigmas: Un enfoque paraconsistente

by Lorenzo Peña

Publ. in:
Relativismo cultural y filosofía: Perspectivas norteamericana y latinoamericana
ed. by Marcelo Dascal
México: UNAM, 1992, pp. 43-81. ISBN 968-36-2779-X

Propone el presente trabajo las cuatro siguientes tesis:
1. Es verdadero el relativismo justificacional o de... more Propone el presente trabajo las cuatro siguientes tesis:
1. Es verdadero el relativismo justificacional o de avales: no hay aval a favor de una creencia que no sea relativo.
2. Es falso el relativismo de la verdad: no es verdad que ninguna creencia tenga verdad más que con relación a algún ente o punto de referencia.
3. Los relativistas han contribuido a proyectar luz sobre algunas cuestiones, como la búsqueda de algún género de convergencia.
4. Una convenientísima estrategia en pos de una convergencia puede articularse aplicando una lógica paraconsistente gradualística (infinivalente), e.d. una lógica que, dando cabida a grados de verdad y de falsedad, haga aceptable la existencia de creencias que sean [hasta cierto punto] verdaderas y [hasta cierto punto] falsas.

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.

PALABRAS CLAVE.- contradicciones, paradigmas, relativismo, lógica paraconsistente

KEYWORDS.- contradictions, paradigms, relativism, paraconsistent logic

Adynaton and Material Exclusion

by Francesco Berto

Philosophical dialetheism, whose main exponent is Graham Priest, claims that some contradictions hold, are true, and... more Philosophical dialetheism, whose main exponent is Graham Priest, claims that some contradictions hold, are true, and it is rational to accept and assert them. Such a position is naturally portrayed as a challenge to the Law of Non-Contradiction (LNC). But all the classic formulations of the LNC are, in a sense, not questioned by a typical dialetheist, since she is (cheerfully) required to accept them by her own theory. The goal of this paper is to develop a formulation of the Law which appears to be unquestionable, in the sense that the Priestian dialetheist is committed to accept it without also accepting something inconsistent with it, on pain of trivialism—that is to say, on pain of lapsing into the position according to which everything is the case. This will be achieved via (a) a discussion of Priest's dialetheic treatment of the notions of rejection and denial; and (b) the characterization of a negation via the primitive intuition of content exclusion. Such a result will not constitute a cheap victory for the friends of consistency. We may just learn that different things have been historically conflated under the label of 'Law of Non-Contradiction'; that dialetheists rightly attack some formulations of the Law, and orthodox logicians and philosophers have been mistaken in assimilating them to the indisputable one.

Dialetheism

by Francesco Berto

Co-authored with Graham Priest.

A dialetheia is a sentence, A, such that both it and its negation, ¬A, are true (we shall talk of sentences throughout... more A dialetheia is a sentence, A, such that both it and its negation, ¬A, are true (we shall talk of sentences throughout this entry; but one could run the definition in terms of propositions, statements, or whatever one takes as her favourite truth-bearer: this would make little difference in the context). Assuming the fairly uncontroversial view that falsity just is the truth of negation, it can equally be claimed that a dialetheia is a sentence which is both true and false...

Che cos' è la dialettica hegeliana?: un'interpretazione analitica del metodo

by Francesco Berto

Some Topics Concerning Identity and Contradiction in Philosophical Logic

by Francesco Berto

Is Dialetheism an Idealism? The Russellian Fallacy and the Dialetheist's Dilemma

by Francesco Berto

In his famous work on vagueness, Russell named “fallacy of verbalism” the fallacy that consists in mistaking the... more In his famous work on vagueness, Russell named “fallacy of verbalism” the fallacy that consists in mistaking the properties of words for the properties of things. In this paper, I examine two (clusters of) mainstream paraconsistent logical theories – the non-adjunctive and relevant approaches –, and show that, if they are given a strongly paraconsistent or dialetheic reading, the charge of committing the Russellian Fallacy can be raised against them in a sophisticated way, by appealing to the intuitive reading of their underlying semantics. The meaning of “intuitive reading” is clarified by exploiting a well-established distinction between pure and applied semantics. If the proposed arguments go through, the dialetheist or strong paraconsistentist faces the following Dilemma: either she must withdraw her claim to have exhibited true contradictions in a metaphysically robust sense – therefore, inconsistent objects and/or states of affairs that make those contradictions true; or she has to give up realism on truth, and embrace some form of anti-realistic (idealistic, or broadly constructivist) metaphysics. Sticking to the second horn of the Dilemma, though, appears to be promising: it could lead to a collapse of the very distinction, commonly held in the literature, between a weak and a strong form of paraconsistency – and this could be a welcome result for a dialetheist.

How to Sell a Contradiction: The Logic and Metaphysics of Inconsistency

by Francesco Berto

There is a principle in things, about which we cannot be deceived, but must always, on the contrary, recognize the... more There is a principle in things, about which we cannot be deceived, but must always, on the contrary, recognize the truth – viz. that the same thing cannot at one and the same time be and not be": with these words of the Metaphysics, Aristotle introduced the Law of Non-Contradiction, which was to become the most authoritative principle in the history of Western thought. However, things have recently changed, and nowadays various philosophers, called dialetheists, claim that this Law does not hold unrestrictedly – that in peculiar circumstances the same thing may at the same time be and not be, and contradictions may obtain in the world. This book opens with an examination of the famous logical paradoxes that appear to speak on behalf of contradictions (e.g., the Liar paradox, the set-theoretic paradoxes such as Cantor’s and Russell’s), and of the reasons for the failure of the standard attempts to solve them. It provides, then, an introduction to paraconsistent logics – non-classical logics in which the admission of contradictions does not lead to logical chaos –, and their astonishing applications, going from inconsistent data base management to contradictory arithmetics capable of circumventing Gödel’s celebrated Incompleteness Theorem. The final part of the book discusses the philosophical motivations and difficulties of dialetheism, and shows how to extract from Aristotle’s ancient words a possible reply to the dialetheic challenge. How to Sell a Contradiction will appeal to anyone interested in non-classical logics, analytic metaphysics, and philosophy of mathematics, and especially to those who consider challenging our most entrenched beliefs the main duty of philosophical inquiry.

Expressing the Background Talk Given to the Icelandic Philosophical Association Reykjavic, October 1997

by Carlo Penco

La defendibilidad lógico-filosófica de teorías contradictorias

by Lorenzo Peña

Are all contradictions equal? Wittgenstein on confusion in mathematics

by Esther Ramharter

Review by Herbert Marcuse of Edward Conze's 1932 book on The Principle of Contradiction

by Holger Heine

English translation of Herbert Marcuse's 1934 review of Edward Conze's book on the Principle of Contradiction (Der Satz vom Widerspruch)