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date: 20 November 2017

principle of explosion

Source:
A Dictionary of Logic
Author(s):

Thomas Macaulay Ferguson,

Graham Priest

principle of explosion 

1. The thesis satisfied by a particular deductive system principle of explosion with a negation principle of explosion when principle of explosion is explosive, that is, when principle of explosion satisfies the property that for all sets of formulae principle of explosion:

  • principle of explosion

In other words, the thesis that the only principle of explosion-theory is the trivial theory. Paraconsistent logics may be defined as deductive systems with a negation principle of explosion that fail to satisfy the principle of explosion in this sense. Because the inference corresponding to all formulae following from inconsistency or contradiction, the inference is frequently described as ex contradictione quodlibet or ECQ.

The principle of explosion is distinct from but related to the principle of noncontradiction, which asserts that no proposition is both true and false. When the truth of principle of explosion is independent from the truth of principle of explosion—as is found in many non-deterministic semantics for logics of formal inconsistency—that principle of explosion is true merely entails that both principle of explosion and principle of explosion are true and not that either of the conjuncts is false.

2. Where principle of explosion is a conditional connective, the axiom scheme:

  • principle of explosion

Because the principle has been falsely attributed to philosopher John Duns Scotus (1265–1308), the principle is sometimes known as ‘pseudo Scotus’.

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