Talk:Principle of explosion

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I've never heard the "principle of explosion" so named before; I know this as "Ex falso quodlibet" and the "absurdity law". Where does "principle of explosion" come from? ---- Charles Stewart 07:27, 26 Aug 2004 (UTC)

[edit] Contrary view

There are many people, myself included, that are convinced that the logic necessary for "The Principle of Explosion" (or "ex contradictione (sequitur) quodlibet") in inherently flawed.

Each such argument makes use of some logical rule which, itself, depends upon the assumption that contradictions cannot occur.

For example, any proof of "disjunctive syllogism" depends upon an assumption that all statements of the form "Both A and (NOT A)" are false. Likewise, every other "proof" of this sort depends upon a logic rule whose truth requires this.

If one constructs any argument that includes a statement of the form "Both A and (NOT A)" as a premise and then makes use of a rule which depends upon statements of that form being false in all cases, then the argument is inherently flawed.

So, the fact of the assumption of a contradiction necessarily invalidates all arguments that could demonstrate arbitrary conclusions. Not to mention that defining a means for categorizing statements as "true" or "false" becomes equally problematic.

In general, any presumption of a contradiction invalidates logic itself.

One of the motivations for investigating paraconsistency is that people often have inconsistent beliefs but are still able to reason. Paraconsistent logics are interesting to philosophers and in AI. Take a look at the SEP article on paraconsistent logic to find out more about them. Wikipedia could do with more of this information being written up here. --- Charles Stewart 21:14, 18 May 2005 (UTC)

I would like to add to the first comment that, yes, "any presumption of a contradiction invalidates logic itself." That's the Principle of Explosion. Once you assume a contradiction, you break your logical system. From the "Tolerating the impossible" section of the logic article, "... the principle of explosion, which means that the logic collapses if it is capable of deriving a contradiction." [1] Perhaps a similar statement should be made in this article. -- Ben-Arba 07:57, 4 December 2006 (UTC)

The anonymous original poster writes: "If one constructs any argument that includes a statement of the form 'Both A and (NOT A)' as a premise and then makes use of a rule which depends upon statements of that form being false in all cases, then the argument is inherently flawed."

Not so. In classical logic, a line of reasoning may be correct even if the premises are false (or contradictory, which amounts to the same thing). In fact this is a common thing to do. A proof by contradiction starts by assuming something that you know is untrue. --Jorend 18:22, 7 February 2007 (UTC)