Talk:Principle of explosion

message: it appears to me the proof is false. it just seems to demonstrate modus tollendo ponens which is: 
        A	B		¬A		A∨B   <-> 	¬A→B
        f	f		t		f		      f
        f	t		t		t		      t
        t	f		f		t		      t
        t	t		f		t		      t
what we want to prove however is:
     A∧¬A  → B 
which we can write as
   ¬(A∧¬A) ∨ B
which, by de morgan's rules, is
    (¬A∨A) ∨ B
checking the truth table:
        A B  (¬A∨A) ∨ B
        f f     t   t 
        f t     t   t
        t f     t   t
        t t     t   t
presto.  — Preceding unsigned comment added by 95.91.213.239 (talk) 02:13, 2 November 2021 (UTC)
replies: text: I've fixed the tables. — Charles Stewart (talk) 14:23, 8 November 2021 (UTC)

text: Thx for fixing the tables. Your excellent answer seems a bit off tangent, i was mostly talking about the proof on the article's page not proving what it claims to prove,
best,  — Preceding unsigned comment added by 95.91.213.239 (talk) 22:58, 13 November 2021 (UTC)
thread_title: False Proof?

message: It begins be asserting two things which cannot both be true.
"All lemons are yellow" and "Not all lemons are yellow" must be false. 
Having asserted two things which cannot be both true it goes on to use both mutually exclusive statements together in a second appeal to an absurd reasoning.
The statement "'All lemons are yellow' or 'Unicorns exist'" is only true if one of the statements it comprises is true. If "All lemons are yellow" then the statement is true. 
It then goes on to say "Not all lemons are yellow". If this is true then we haven't proven the preceding statement about unicorns, we've only proven the half of the statement we'd relied upon previously is false.
I'm all for examining the Law of Excluded Middle, but until you have used a reasonable axiomatic system to prove two contradictory statements then you don't have a starting point for reasoning as in the example presented. The whole point of the negating statements definition is "P and not P" must be false and "P inclusive-or not P" must be true. 
Obviously-nonsense reasoning, such as that presented in the example, cannot possibly be reasonably accepted as "proof". Vapourmile (talk) 12:23, 24 November 2020 (UTC)
thread_title: How can the proof be a proof when it is so obviously false?

message: is the santa example really correct?   There are many cases in AI and philosophy where both X and ¬X can both be proved true, but don't lead to the explosion.  The argument, AFAIK, would be that step (3) doesn't work, because (“All lemons are yellow" OR "Santa Claus exists”) can be satified by the proven "All lemons are yellow".   It's doesn't matter that "not all lemons are yellew" has also been proved.   AFAIK languages like Prolog work in this way.
    1We know that "All lemons are yellow" as it is defined to be true.
    2 Therefore the statement that (“All lemons are yellow" OR "Santa Claus exists”) must also be true, since the first part is true.
    3However, if "Not all lemons are yellow" (and this is also defined to be true), Santa Claus must exist - otherwise statement 2 would be false. It has thus been "proven" that Santa Claus exists. The same could be applied to any assertion, including the statement "Santa Claus does not exist".  — Preceding unsigned comment added by 188.39.62.164 (talk) 18:07, 28 January 2015 (UTC)
thread_title: santa example and paraconsistency

message: 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)
replies: text: 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)
replies: text:  Google search confirms that the name "principle of explosion" was introduced into academic publications in (or around) 1998, either by Graham Priest in the Stanford Encyclopedia of Philosophy, in the article entitled Dialetheism, where it is used without any explanation of what it is, or by Walter Carnielli and Joao Marcos in "A Taxonomy of C-systems", where it is explained as being the same as the Principle of Pseudo-Scotus and abbreviated as (PPS).Flosfa (talk) 16:47, 29 October 2017 (UTC)
replies: text: According to the Google Books Ngram viewer, the term "principle of explosion" goes back at least to 1800, and since that is as early as Google Books covers, it may well be older. Dezaxa (talk) 21:10, 26 May 2023 (UTC)
thread_title:  doubts of origin of term 

message: 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)
thread_title:  Vicious Circle 

message: 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)
replies: text: 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)
replies: text:  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)
thread_title:  Accessibility 

message: 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)
replies: text: 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)
replies: text: 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)
replies: text: 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)
replies: text: 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)
thread_title:  Deleted Proof 

message: 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)
thread_title: Yes, I believe that the title in not the right one!

message: :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". ArXiv. December 30, 2008. --98.210.241.92 (talk) 20:01, 5 March 2009 (UTC)
thread_title: Hewitt has propsed the name IGOR for "Inconsistency in Garbage Out Redux"

message: 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)
replies: text: 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)

text: xkcd links do not belong here. See Talk:Tautology_(rhetoric)#XKCD_link_does_not_belong for a recent discussion about this problem. Snied (talk) 21:40, 19 February 2010 (UTC)
thread_title: xkcd warning

message: I moved the so-called "informal proof" to the top so readers can see what it's about, after which 99.9% of them will realise it's not of interest to them.  The mathematical or pseudo-mathematical proofs can't be made clearer to a non-expert.  IMO the subject is a bit like the algebraic "proof" that 2=1, following a division by 0, i.e. that formal methods can be applied to a meaningless statement or operation, to yield a startling but spurious "result".  But who cares, it amuses philosophers and keeps them out of mischief Chrismorey (talk) 21:17, 23 August 2013 (UTC)
thread_title:  Clarity 

message: The example offered as a “demonstration of the principle” proves that Santa Claus exists, not “that Santa Claus both exists and does not exist.”  — Preceding unsigned comment added by 76.246.84.113 (talk) 15:26, 28 August 2013 (UTC)
replies: text: The example stated that,"The same could be applied to any assertion, including the statement "Santa Claus does not exist".", meaning that the example could have read "Santa Claus does not exist", and that the resulting proof would have been "Santa Clause does not exist". Since the figments of imagination are not relevant to the principle it must simply depend on what has been asserted as to what conclusion is drawn. Otr500 (talk) 03:55, 6 September 2013 (UTC)
thread_title:  Santa 

message: William of Soissons appearantly proved the principle. But it was later, in the 15e century, rejected by a school of Cologne. In the 19th century C. I Lewis mathematically seemed to proof the principle. Known logicians like Boole, Frege and Russell have taken this proof for granted but the proof has to be rejected (see the article on William of Soissons). The Principle of Explosion could be taken as an (unprovable) axiom. The priciple is not proved but also not rejected. 
Aristotle, in his book Metaphysics Gamma, did reject a contradiction but doesn't name the principle of explosion as a reason for it.  — Preceding unsigned comment added by Zevensprongen (talk • contribs) 15:09, 8 February 2020 (UTC)
thread_title:  The principle of explosion cannot be proved  

message: This article seems to me to be about two completely different concepts:
firstly, the fact that, given the propositions P and Not P, then the propositions "if P then Q" and "If not P then Q" will both yield the same outcome
and
Secondly, the idea that an argument that is valid is not necessarily sound
I have no ideas why these two concepts have been combined  — Preceding unsigned comment added by 131.106.18.48 (talk) 00:54, 17 May 2020 (UTC)
thread_title:  This article seems to be about two completely different concepts 

message: This article presupposes known, explained and accepted the principle "ex falso sequitur quodlibet"  whose proper explanation remains wanting. HenryLeal (talk) 14:38, 29 October 2020 (UTC)
thread_title:  Ex falso sequitur quodlibet. 

message: The example at the beginning of the article doesn't make sense. The statement "All lemons are yellow OR unicorns exist" is, by itself, significantly more pathological than the contradiction 2600:1002:B0CA:447F:7164:4ADD:5803:EB55 (talk) 18:37, 30 March 2021 (UTC)
thread_title:  The example doesn't make sense 

message: The formal proof on the page is suffering from circular reasoning. It peruses the disjunctive syllogism; however, the disjunctive syllogism can only be proved when EFQ is already assumed to be true. Therefore, the "proof" prooves that "EFQ is true given that EFQ is true". 5.18.95.241 (talk) 00:33, 30 September 2022 (UTC)
thread_title:  Circular reasoning in "formal proof" 

message: There is a move discussion in progress on Talk:Ex Falso (tag editor) which affects this page. Please participate on that page and not in this talk page section. Thank you.  —RMCD bot 17:47, 7 April 2023 (UTC)
thread_title:  Move discussion in progress 

message: The supposed proof of POE leaves its first assumptions undischarged. How many poor souls has it sent down the proverbial rabbit hole of no return? The final result after 2 lines would be P => [~P => Q] from which, regardless of the truth value of P, you cannot infer that Q is true. Danchristensen (talk) 21:15, 5 August 2023 (UTC)
replies: text: It is a little misleading as written, but those are not assumptions that need to be discharged. They are premises in an argument, or sentences in a theory. I've changed 'Assumption' to 'Premise' to make this clearer. Dezaxa (talk) 11:07, 7 August 2023 (UTC)
thread_title:  Unfinished Proof