Talk:Paraconsistent logic

Example needed - a very simple way to help idiots like me understand this, would be to provide an "example" line/section. Anyone up to this? (and yes, i'm hitting 'random' again)En attendant Godot 18:13, 2 September 2011 (UTC)

Check the fossil record. Тy^talk 18:16, 2 September 2011 (UTC)

Paraconsistent logic is largely a thought experiment, with no close correspondence to the real world. It removes certain rules of inference that make it very difficult to reason from inconsistent axioms. ListenerX^TalkerX 18:42, 2 September 2011 (UTC)

No problem, then. I'll just ignore it. math scares me, logic at this level, too.--En attendant Godot 18:47, 2 September 2011 (UTC)

A classic example is the liar paradox: "This sentence is false".

Another is the Barber paradox: "The village barber shaves all the men, and only the men, who do not shave themselves. Who shaves the barber?" If we say "The barber shaves himself", we have a contradiction, since we said that only men who do not shave themselves are shaved by the barber. If we say "The barber doesn't shave himself", then we also have a contradiction, since we said that all men who do not shave themselves are shaved by the barber. So the conclusion is, the barber shaves himself, and does not shave himself, simultaneously.

Classical logic tries to run away from these paradoxes. Paraconsistent logic embraces them, and says they are both true and false at the same time. (((Zack Martin)))^™ 23:03, 2 September 2011 (UTC)

The solution to the barber paradox? The barber is a woman, and therefore is exempt of the rules regarding the shaving of men. There are no rules on the shaving of women. Most people, upon reading it, subconsciously assume the barber is a man. Although the paradox does not explicitly state the barber is male hirself (I'm using "hirself" as a gender-neutral version of "himself" or "herself", seeing as the English language has no such word.). The Heidelberg Kid (talk) 15:27, 4 December 2011 (UTC)

Doesn't work. The problem was devised in the days of the unspoken, quite possibly sexist, assumption that all barbers are men. It assumes the premise "All barbers are male" even if it does not explicitly state it. The point of the problem is to try to express Russell's paradox in more everyday language; arguing about people's gender to the point that Russell's paradox is no longer expressed is missing the point. (((Zack Martin)))^™ 09:07, 4 January 2012 (UTC)

Possible solution?

"The next sentence is false. The previous sentence is true." It seems, since both sentences presume to be true, individually, yet are said within the context of each other, that the mathematical equivalent of the context of this statement would be a = -a. If this is the case, it's not a "contradiction" at all, but rather, it has "No Solution", since the overall statement is a falsely presumed equation. If that's what we're working with, then to say it out loud is "intentionally deceptive", and the entire statement is false. After all, if an equation requires both expressions to be equivalent, and they're not, then the whole thing is false. It doesn't matter how badly someone wants a part of it (or the whole thing) to be true (or contradictory), it's false, due to false premises, no matter what, and "contradiction" solved. Thoughts? Knowledgebattle (talk) 02:47, 1 May 2015 (UTC)

Is this for real?

This is one of the most stupid things I've ever heard: denying the law of non-contradiction. How the hell is something supposed to be true and false at the same time? Is this some sort of quantum woo orhttp://rationalwiki.org/w/index.php?title=Talk:Paraconsistent_logic&action=edit&section= ad hoc justification for Jesus' simultaneous divinity and humanity? In the words of Avicenna,

“”Anyone who denies the law of non-contradiction should be beaten and burned until he admits that to be beaten is not the same as not to be beaten, and to be burned is not the same as not to be burned.

I want to know. Is this all a joke, or are these people serious? The Heidelberg Kid (talk) 15:27, 4 December 2011 (UTC)

No, it is serious. See Paraconsistent logic and Graham Priest. I somehow doubt mere joking would get you appointed a chair at a good university (University of Melbourne is one of the top universities in Australia). (((Zack Martin)))^™ 07:54, 4 January 2012 (UTC)

There is no magic

The article now says (mixture of Armondikov and yours truly):

Paraconsistent logic is proposed as a potential solution to logical paradoxes... the contradiction magically disappears

The contradiction doesn't magically disappear, the contradiction doesn't disappear at all. The contradiction is still there. But, whereas classical logic is afraid of contradictions (contradictions must be solved, must be exterminated, or else the whole house of cards falls down — ex contradictione quodlibet), paraconsistent logic isn't afraid of them — it is happy to let them live, to leave them be, to embrace them as just as valid as non-contradictions are. "Solution" is in some ways the right word, in some ways the wrong one — it is the solution of declaring that the problem does not need to be solved. No magic involved. (((Zack Martin)))^™ 09:03, 4 January 2012 (UTC)

Therefore God exists. ^narchist 14:23, 4 January 2012 (UTC)

Misleading Article

This article isn't really about paraconsistent logic (I'll abbreviate it to PL to save space), it's about dialetheism. A logic is paraconsistent only if it rejects the principle of explosion as a valid inference relation; rejecting the law of noncontradiction (that's dialetheism) is not a criteria. The two should be distinguished. There are separate motivations for PL than for dialetheism, some of which are pretty convincing. Belief revision, for example, is a situation where a PL would be useful. There's more on the IEP entry on PL and the Stanford Encyclopedia entry.

The criticism of dialetheism in the article rests on a strawman and the insinuation that dialetheism would be helpful for people who can't use traditional reasoning is silly. Graham Priest states that dialetheic logic (DL) is only valid when dealing with dialetheias. DL is useless in everyday situations because it rejects some operators that are classically valid. The disjunctive syllogism is the most common victim in DL, for obvious reasons, even though the operator is perfectly valid in classical logic. Priest calls this "quasi-validity" and has en entire chapter dedicated to the technicalities of this in In Contradiction (beginning at pg. 110 in the second edition).

Yes, dialetheism is still a contested theory, but I feel it's an inappropriate subject for a wiki with the purpose of refuting pseudoscience and documenting crank ideas. Dialetheism has a pretty firm logical foundation (Graham Priest has been defending it against critics for the last 30 years or so) and I wouldn't classify it as "pseudo". Any criticism of it would have to utilise some legitimate logical concepts, at least.

So, to sum up, the definition of PL in the article needs to be revised to reflect the academic definition (the rejection of the ECQ only) and to distinguish between weak and strong systems. In addition, the argument against dialetheism should either be thrown out altogether or replaced with a more competent one. Montgelas (talk) 17:02, 21 April 2012 (UTC)

The edit button is right there. ^sshole 13:38, 22 April 2012 (UTC)

Mate, gotta break it to you, but this is an ATHEIST wiki. So of course we are going to attack dialeTHEISM. SteveQuigibo (talk) 20:08, 22 April 2012 (UTC)

Not sure it means "theistic" belief in that sense... ^theist 20:34, 22 April 2012 (UTC)

Was my joke that bad? SteveQuigibo (talk) 20:38, 22 April 2012 (UTC)

I've seen worse. ^{d hominem} 20:43, 22 April 2012 (UTC)

Particle-wave duality

Trouble with this example is that duality isn't necessarily paraconistent. The interpretations behind quantum mechanics are just that; interpretations, and duality as most people understand it is just an extension of one of those interpretations. The actual evidence and what the theory/evidence describe are the following:

• A photon has properties of a "particle" under experimental conditions A.
• A photon has properties of a "wave" under experimental conditions B.

The actual nature of the photon isn't necessarily paraconsistent in reality, it's only in our interpretation of the data (so far) that is. Therefore arguing that "dialetheia" exist in reality (rather than conceptually, as is often found in mathematics) through this is a dubious exercise. ^postate 17:26, 31 October 2012 (UTC)

Some Problems

The article says that the defining characteristic of Paraconsistent logics is that they deny the Law of Non-contradiction, but that's not correct. Their defining characteristic is that they deny the Principle of Explosion. Of course, some Paraconsistent logics do in fact reject the LoNC, but those are Dialetheic Logics (which are Paraconsistent as well). As all of my sources note, the characteristic quality of Paraconsistent logics is that their logical consequence relation isn't explosive:

    http://plato.stanford.edu/entries/logic-paraconsistent/
    http://www.iep.utm.edu/para-log/
    https://en.wikipedia.org/wiki/Paraconsistent_logic

So I'm going to change the article if that's cool. :-) MindForgedManacle (talk) 17:51, 25 August 2015 (UTC)

This is semantics. Which I appreciate the relevance of in the discussion of formal logical systems. But it's not that much of a distinction from a lay perspective. ikanreed ^{You probably didn't deserve that} 18:15, 25 August 2015 (UTC)

Not really denying the principle of explosion doesn't equate dialetheism, since it doesn't mean some contradictions can be true. I'm sure you kow this stuff, but I think it better that the article not misinform. :o MindForgedManacle (talk) 18:21, 25 August 2015 (UTC)

Yeah, I'm just griping because the formatting sucks now and I know the right thing to do is fix it, but I'm lazy and would rather argue. ikanreed ^{You probably didn't deserve that} 18:23, 25 August 2015 (UTC)

Yea, I'll try and think of a way to make it look better later, lol. MindForgedManacle (talk) 18:26, 25 August 2015 (UTC)

LOL, 2 sections above this someone mentions everything I do. I'm late as always. xD MindForgedManacle (talk) 18:41, 25 August 2015 (UTC)

What to Expand?

I'm no expert on Paraconsistency, but I know a decent amount about it. But how exactly should this article be structured? It's listed as a stub now, so clearly it should be expanded. Presumably the content should reflect a general overview on the whats & whys of Paraconsistent Logic. MindForgedManacle (talk) 18:49, 12 August 2016 (UTC)

Just remember that we're not TOW (though it needs to be a bit more clearly explained in my view). I think we need to expand the article more about how and why paraconsisntent logic is important to skepticism/rationalism/science (and debunking woo) in general. I'm sure many reasons could be given. All the best, Reverend Black Percy (talk) 19:41, 12 August 2016 (UTC)

Ah gotcha, that's what I thought. I might put something up later. And the best to you as well~ MindForgedManacle (talk) 19:48, 12 August 2016 (UTC)