Talk:Principle of explosion

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	Logic

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)

I've also learned this as "Ex falso quod libet," I don't really think "principle of explosion" is a good name for this article; it sounds like something about stoichiometric combustion ratios. Shiggity (talk) 21:00, 23 October 2008 (UTC)[reply]

"Ex falso quodlibet" is certainly the formal name, "Explosion Principle" is a more informal, colloquial term thrown around by philosophers. The idea is that if a contradiction is true, then the world explodes, and so anything can be true. —Preceding unsigned comment added by 24.188.68.9 (talk) 04:18, 5 March 2009 (UTC)[reply]

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)[reply]

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)[reply]

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)[reply]

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).[reply]

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)[reply]

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)[reply]

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)[reply]

Deleted Proof

# $\phi \wedge \neg \phi \,$
assumption

$\neg \psi \,$
assumption

$\phi \,$
from (1) by conjunction elimination

$\neg \phi \,$
from (1) by conjunction elimination

$\neg \neg \psi \,$
from (3) and (4) by reductio ad absurdum (discharging assumption 2)

$\psi \,$
from (5) by double negation elimination

$(\phi \wedge \neg \phi )\to \psi$
from (6) by conditional proof (discharging assumption 1)

I deleted this proof (shown above) on the grounds that it begs the question when it uses a reductio ad absurdium (RAA). Since a reductio ad absurdium is (almost invariably, to my knowledge) justified on the grounds that it leads to the principle of explosion, the principle of explosion can't be justified from it. That argument would be summed up like so: Contradictions allow one to justify everything, so we shouldn't assert them (this last bit is the RAA); We shouldn't assert them (i.e., the RAA), and so contradictions allow one to justify everything. Since the proof begs the principle of explosion, it isn't explanatory or helpful in justifying the principle of explosion.

I hope I'm being clear, but I wouldn't be surprised if I'm not. In any case, I thought I'd explain my actions in more detail here so as to avoid a revert war or whatever, and because I felt bad, since the proof probably took some time to write out, and because someone might come up with a good reason for putting the proof back in! :)--Heyitspeter (talk) 08:37, 23 June 2008 (UTC)[reply]

Why must reductio ad absurdum be justified by explosion? How about: contradictions are impossible (law of non-contradiction), so we shouldn't assert them (RAA); we shouldn't assert them (RAA), so contradictions allow one to justify everything (explosion). The first is allegedly one of the "laws of thought", so this wouldn't be circular. (I have also used the law of the excluded middle, as explained in the reductio article. This is also allegedly a law of thought.) --Unzerlegbarkeit (talk) 14:55, 23 June 2008 (UTC)[reply]

Yeah, it was late and I was hasty. I'm with C.I. Lewis in believing that no possible future world is a priori impossible; that the a priori doesn't limit reality; however you want to word it - so I often don't jump to that axiom explicitly. It's been re-added.--Heyitspeter (talk) 19:12, 23 June 2008 (UTC)[reply]

Well, if it matters, I don't accept that justification myself either. I'm with L.E.J. Brouwer in believing that mathematics precedes logic and that the law of the excluded middle is not generally valid. But of course most people accept it. There is an alternate justification which is alluded to in the BHK interpretation article: the principle of explosion is formally valid because in most formal systems, even if you leave out negation entirely, you can still come up with a proposition BOT that already implies everything expressible in that system (e.g. 0=1 in arithmetic) - so define "not A" as "if A, then BOT". This may or may not be worth mentioning here. --Unzerlegbarkeit (talk) 21:02, 24 June 2008 (UTC)[reply]

Ahhh. Thanks for the leads on the BHK interpretation. I just read the article and really liked the ideas contained!--Heyitspeter (talk) 22:12, 24 June 2008 (UTC)[reply]

Yes, I believe that the title in not the right one!

I agree with Charles Stewart, I've never heard the "principle of explosion" so named before; I know this as "Ex falso (sequitur) quodlibet".--Popopp (talk) 12:55, 14 September 2008 (UTC)[reply]

Hewitt has propsed the name IGOR for "Inconsistency in Garbage Out Redux"

In place of the Latin that nobody knows these days, Carl Hewitt has proposed the principle be named IGOR for "Inconsistency in Garbage Out Redux".^[1] ^[2]--98.210.241.92 (talk) 20:01, 5 March 2009 (UTC)[reply]

^ Hewitt, Carl. "Common sense for concurrency and strong paraconsistency using unstratified inference and reflection". ArXiv. December 30, 2008.
^ Hewitt, Carl (2008), "Large-scale Organizational Computing requires Unstratified Reflection and Strong Paraconsistency", in Sichman, Jaime; Noriega, Pablo; Padget, Julian; Ossowski, Sascha (eds.), Coordination, Organizations, Institutions, and Norms in Agent Systems III, Springer-Verlag

xkcd warning

Just a friendly warning about today's xkcd topic, which is based on the principle of explosion. I might suggest limiting editing ability. 68.231.22.246 (talk) 16:09, 19 February 2010 (UTC)[reply]

Geez, you must be like 15. You don't have to give an XKCD warning on every topic. Get over it. —Preceding unsigned comment added by 68.63.212.186 (talk) 20:02, 19 February 2010 (UTC)[reply]

Yes, it is absolutely necessary to give an XKCD warning on something like this. This page hadn't been edited since September of 2009, and suddenly it's already been through nine edits today. Coincidence? No. Any time an obscure topic/person/idea is mentioned in the comic, it is pretty much inevitable that the corresponding wikipedia page will come under some heat. 72.219.56.68 (talk) 20:16, 19 February 2010 (UTC)[reply]

[Hewitt2008b-1] Hewitt, Carl. "Common sense for concurrency and strong paraconsistency using unstratified inference and reflection". ArXiv. December 30, 2008.

[Hewitt2008-2] Hewitt, Carl (2008), "Large-scale Organizational Computing requires Unstratified Reflection and Strong Paraconsistency", in Sichman, Jaime; Noriega, Pablo; Padget, Julian; Ossowski, Sascha (eds.), Coordination, Organizations, Institutions, and Norms in Agent Systems III, Springer-Verlag

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