Talk:Principle of explosion

Question
Anyone want to explain this in english?? 19:50, 20 May 2011 (UTC)
 * Example: Given the premise that "A is hot and A is cold," assume that pigs cannot fly. Due to your premise, you can thence conclude that A is hot, but you can also thence conclude that A is cold, which is a contradiction. Hence, pigs can fly; QED. 04:04, 24 May 2011 (UTC)
 * "Lindsay Lohan is hot and Lindsay Lohan is not hot, therefore Adolf Hitler used the Death Star to assasinate Julius Caesar." That is a valid application of the principle of explosion. Which personally, I think demonstrates how silly this principle is. 09:08, 24 May 2011 (UTC)
 * Sounds like non sequitur on acid. Ancient Greek Pegasus icon.png 09:20, 24 May 2011 (UTC)
 * Actually, not a non sequitur, which is why it is very important to keep one's system of axioms or premises consistent. 14:54, 24 May 2011 (UTC)
 * Well, I think this demonstrates why ECQ should be rejected, because intuitively all applications of it seem like non sequiturs, even if from the viewpoint of accepting ECQ they aren't. And rejection of ECQ may lead us towards an acceptance of paraconsistent logic. 08:04, 25 May 2011 (UTC)

"Tacit applications" section
Don't understand what this section is trying to say. Is it saying, Bible says X, Bible says not(X), hence for all Y Bible implies Y? That's a rather silly argument, because it treats this principle as something universally accepted, yet it is rather shaky - it is quite commonly doubted, e.g. by proponents of relevant (rather than material or strict) implication. It would seem strange to argue against the Bible on the basis of an obscure principle that many philosophers and logicians view as questionable. Aren't there much better arguments available? 11:05, 9 June 2011 (UTC)

Bible section
Etherreality seems to be shifting the meaning of the text from pointing out that the bible has inherent contradictions, errors, etc to blaming it on the reader for just not seeing what its REALLY saying. Tmtoulouse (talk) 19:09, 14 July 2012 (UTC)

Add a section against confusion
So I've noticed that some people who come to this page are a bit confused.

I would suggest to add something to this article that Wikipedia doesn't have, so there would be a reason to link to here. Currently I can imagine no situation where I wouldn't prefer to link the Wikipedia article (which is much better explained and less confusing than this one) over this one.

A section to ward against confusion would be cool. It would also be cool to add some silly humour. It could be named: "Plain English" (with or without the quotation marks ;) ).

Let me make a draft (in square brackets []) to show you what I'm talking about: [

Here is an attempt to apply this rule and follow the logic and make a conclusion, cookbook style!

Assume two contradictory premises: A.) 'All ice cream is frozen.'; B.) 'Not all ice cream is frozen.'

Now, just to show that it's possible, say one wants to use those two premises to prove that: C.) 'Words don't exist'.

To do so, construct a disjunction out of A and C:

'All ice cream is frozen or words don't exist.'

This statement appears to be perfectly acceptable here because it holds true under any of these three circumstances:
 * 1. All ice cream is frozen.
 * 2. Words don't exist.
 * 3. All ice cream is frozen and words don't exist.
 * (Of which at least the first one is true because it was assumed as a premise.)

Now use that disjunction for a disjunctive syllogism:
 * 'All ice cream is frozen or words don't exist.
 * Not all ice cream is frozen.
 * Therefore words don't exist.'

This also appears to be perfectly acceptable here because if it is said that at least one of A or C are true,

then when it turns out A is not true (which is B, which has been accepted as a premise), at least it can be held that C is true.

So now it has been proven that words don't exist...

So what is this sentence, then?!

The solution is simple:
 * Either reject that reasoning behind the principle of explosion (say, by rejecting that disjunction or that disjunctive syllogism)
 * OR just simply say no to assuming two contradictory premises.
 * (OR I suppose one could be extra wild and claim that one accepts YET ANOTHER contradiction, i.e. one accepts both A.) 'Words don't exist.' and B.) 'Words do exist.' as premises ... which somehow allows for sentences to exist... Yay?)

]

Note that I've used some jargon which might need explanation/reference: 'disjunction' and 'disjunctive syllogism'. That shouldn't detract too much from it being "Plain English", though, since what each one refers to is illustrated right below where it's first used.

Alternatively, if you think it was written too sillily for the article, then maybe we could link to it in the article as an essay? Or you could suggest a less silly draft.

Either way, just in the interest of clearing up confusion and/or livening up the place! And tell me if you think I got something wrong. Nullahnung (talk) 09:34, 17 July 2013 (UTC)
 * Ok, so now I'm going to try to incorporate it into the article, but I would still very much welcome constructive criticism and suggestions on it, if anyone has any.
 * I'm making some other minor changes to it and I cut out most of the silly. Nullahnung (talk) 03:14, 23 July 2013 (UTC)

Alternative formulation of the rule that I find useful
For any logical propositions $$A$$ and $$B,$$ we have $$\neg A \vDash A\Rightarrow B$$

In the truth table for $$A \Rightarrow B$$, whenever $$A$$ is false, we have $$A\Rightarrow B$$ being true regardless of what $$B$$ might be.

--163.182.226.42 (talk) 18:13, 27 June 2018 (UTC)

The provided syllogism does not contain a contradiction.
As provided [(p v q) ^ ~p --> q]:

P1: All ice cream is frozen or words don't exist. P2: Not all ice cream is frozen. C: Therefore words don't exist.

P1 simply says that one or both of the two things are true. It makes no claim as to which variable is true.

This contains a contradiction [(p v q) ^ (p ^ ~p)]:

P1: All ice cream is frozen or words don't exist. P2: All ice cream is frozen and not all ice cream is frozen.

The contradiction is immediately apparent. Even were one to conclude that words don't exist, it would only be an example of a failure to recognize that the argument is unsound, not an example of the principal of explosion.