In the preface of the Philosophical Investigations, Wittgenstein says that his “most fruitful ideas” are due to the stimulus of Sraffa's criticism, but Sraffa is not mentioned anywhere else in the book. It remains a puzzle in the literature how and why Sraffa influenced Wittgenstein. This paper presents a solution to this puzzle. Sraffa's criticism led Wittgenstein away from the calculus conception of language of the Big Typescript (arguably, an adaptation of the calculus of the Tractatus), and towards the “anthropological (...) view,” which structures both the opening sections of the Philosophical Investigations and Wittgenstein's later philosophy of mathematics. (shrink)

Consequence is at the heart of logic; an account of consequence, of what follows from what, offers a vital tool in the evaluation of arguments. Since philosophy itself proceeds by way of argument and inference, a clear view of what logical consequence amounts to is of central importance to the whole discipline. In this book JC Beall and Greg Restall present and defend what thay call logical pluralism, the view that there is more than one genuine deductive consequence relation, a (...) position which has profound implications for many linguists as well as for philosophers. We should not search for one true logic, since there are many. (shrink)

Wittgenstein procura mostrar que a teoria dos tipos de Russell está condenada auma autodissolução. Ela só pode ser exposta na medida em que a exposição incorre emviolações sistemáticas das regras que a teoria tenta impor a toda a linguagem. Por outrolado, se for encarada enquanto mero sistema de regras para o uso de sinais, ela se tornacompletamente arbitrária. A teoria dos tipos apresenta na forma de uma invenção aquiloque, do ponto de vista do Tractatus, só poderia ser o resultado de (...) uma descoberta: a estruturaessencial da realidade que a linguagem deve decalcar. É daí que surge, no Tractatus, asolução intermediária de uma "essência inefável". O problema se complica quando o Tractatusse revela uma alternativa inviável, e a idéia de uma estrutura essencial da realidade ficacomprometida. Tento fazer, no final do artigo, uma reflexão de tipo wittgensteiniano natentativa de determinar o que resta da noção de necessidade quando abandonamos a idéiade que a realidade possua uma estrutura essencial que a linguagem limita-se a decalcar. (shrink)

In classical logic, a contradiction allows one to derive every other sentence of the underlying language; paraconsistent logics came relatively recently to subvert this explosive principle, by allowing for the subsistence of contradictory yet non-trivial theories. Therefore our surprise to find Wittgenstein, already at the 1930s, in comments and lectures delivered on the foundations of mathematics, as well as in other writings, counseling a certain tolerance on what concerns the presence of contradictions in a mathematical system. ‘Contradiction. Why just this (...) spectre? This is really very suspicious.’ ( Philosophical Remarks III–56) In the last decades, several authors (e.g. Arrington, Hintikka, Van Heijenoort, Wright, Wrigley) have been digging into Wittgenstein’s rather non-standard standpoint on what concerns the interpretation and import of contradiction in logic and mathematics, and many other authors (e.g. da Costa, Goldstein, Granger, Marconi) have been investigating the possibility of taking Wittgenstein seriously as one of the early forerunners of paraconsistency. While many advances have been made on the first front, the second set of investigations has led almost exclusively to negative results: no, no operational proposal about the construction of a logic in which (some) contradictions are made inoffensive can be read from Wittgenstein’s philosophical work; in fact, it appears that the most one can find there is the exhortation for mathematicians to alter their attitude with respect to contradictions and to consistency proofs. The play is done, and one looks for a resume of the opera. This paper fills that blank, as a thorough investigation of the possible relations between Wittgenstein and paraconsistency. DOI:10.5007/1808-1711.2010v14n1p135. (shrink)

From the technical point of view, philosophically neutral, the duality between a paraconsistent and a paracomplete logic (for example intuitionistic logic) lies in the fact that explosion does not hold in the former and excluded middle does not hold in the latter. From the point of view of the motivations for rejecting explosion and excluded middle, this duality can be interpreted either ontologically or epistemically. An ontological interpretation of intuitionistic logic is Brouwer’s idealism; of paraconsistency is dialetheism. The epistemic interpretation (...) of intuitionistic logic is in terms of preservation of constructive proof; of paraconsistency is in terms of preservation of evidence. In this paper, we explain and defend the epistemic approach to paraconsistency. We argue that it is more plausible than dialetheism and allows a peaceful and fruitful coexistence with classical logic. (shrink)

The purpose of this paper is to present a paraconsistent formal system and a corresponding intended interpretation according to which true contradictions are not tolerated. Contradictions are, instead, epistemically understood as conflicting evidence, where evidence for a proposition A is understood as reasons for believing that A is true. The paper defines a paraconsistent and paracomplete natural deduction system, called the Basic Logic of Evidence, and extends it to the Logic of Evidence and Truth. The latter is a logic of (...) formal inconsistency and undeterminedness that is able to express not only preservation of evidence but also preservation of truth. LETj is anti-dialetheist in the sense that, according to the intuitive interpretation proposed here, its consequence relation is trivial in the presence of any true contradiction. Adequate semantics and a decision method are presented for both BLE and LETj, as well as some technical results that fit the intended interpretation. (shrink)