Talk:Principle of explosion

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Contents 1 doubts of origin of term 2 Contrary view 3 Vicious Circle 4 Accessibility

[edit] doubts of origin of term

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)

[edit] Vicious Circle

The second and third "Proof theoretic" arguments lead to a vicious circle. In the second argument, the circle comes from assumptions 1. 2. and the conclusion. The same kind of problem arises in the third proof. Please fix or remove. —The preceding unsigned comment was added by 76.211.229.34 (talk) 19:57, 2 May 2007 (UTC).

[edit] Accessibility

There are accessibility issues for this article. A WP article should be informative but self-contained. In other words, while it makes good sense to me, I can see how it would be incomprehensible to some, and there are no links to relevant theoretical material to make the contents of the article express any understandable meaning. Either the article should contain more plain-language explanation, or at the very least should make proper use of segue to other articles. - May 19, 2007

I agree. I can make absolutely no sense out of this article as it contains far too much symbolism and jargon. This article needs to be flagged as it doesnt conform to Wikipedia standards. - Tiwaking Augus 11, 2007

I second all this. I don't consider myself a genius, nor an idiot, by any standards, and reading this, and re-reading this, I had no idea what this theory purports. Perhaps one of the Simple English wiki writers should add a summary paragraph? —Preceding unsigned comment added by 24.140.106.178 (talk) 02:41, 18 December 2007 (UTC)

I think I have improved the intro. However, more work could be done on the body of the article; perhaps with an entire "lay" paragraph under each of the two arguments. So I have left the "confusing" tag in place. — Epastore (talk) 04:37, 20 December 2007 (UTC)

Agreed. Thanks for your work on this; we do still need quite a bit of work in the form of prose to explain the logic, though. Chris Cunningham (talk) 09:58, 20 December 2007 (UTC)