Abstract
This article is a preliminary presentation of conjunctive paraconsistency, the claim that there might be non-explosive true contradictions, but contradictory propositions cannot be considered separately true. In case of true ‘p and not p’, the conjuncts must be held untrue, Simplification fails. The conjunctive approach is dual to non-adjunctive conceptions of inconsistency, informed by the idea that there might be cases in which a proposition is true and its negation is true too, but the conjunction is untrue, Adjunction fails. While non-adjunctivism is a well-known option, the other view is not so much studied nowadays, but it was not unknown in the tradition, and there are some positive suggestions, in recent literature, that the position is plausible and deserves to be developed. The article compares conjunctivism, non-adjunctivism and dialetheism, then focuses on some possible justifications, costs and benefits of the conjunctive view.
Highlights
A conjunctive conception of paraconsistency consists of claiming that there can be non-explosive contradictions but contradictories cannot be separately true.1 So the ‘and’ that joins ‘p and not p’ in case of true contradiction is not simplifiable: ‘p’ and ‘not p’, separately taken, are untrue
The article shows that conjunctivism in paraconsistency relies on a conception of truth that preserves the exclusion constraint classically involved in the use of the concept, while acknowledging the possibility of true state descriptions of the form ‘p and not p’
The aim is to show that the conjunctive view is plausible, and its consequences are interesting for anyone who is concerned with the notion of ‘true contradiction’
Summary
In the literature about inconsistency the conjunction problem is treated by three basic positions: dialetheism, non-adjunctivism and conjunctivism They all accept that there can be true contradictions but differ in the interpretation of the ‘and’ joining ‘p’ and ‘not p’. For dialetheists (see for the most well-known versions Priest 1 9872, 2006, Priest et al, 2004; Beall, 2009), it is a perfectly normal ‘and’, classically defined by the Conjunction Thesis: CT: 〈p and q〉 is true iff 〈p〉 is true and 〈q〉 is true.2 The acceptance of this classical bi-conditional implies that the two basic rules of Simplification (from left to right), and Adjunction (from right to left) both hold, so if ‘p and not p’ is true, the two contradictories are both separately and jointly true. While dialetheism and non-adjunctivism are well-known approaches to paraconsistency, there is no clear and definite position of the third kind in recent literature but there are reasons to believe it was not unknown in the tradition.
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