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Dialetheism vs. principle of explosion

The claim that dialetheists always reject the principle of explosion is false, so it was removed. Zen Buddhists, in particular, accept the principle of explosion but reject that logic can prove anything. According to these dialetheists, direct experience is the only certainty that we have, and it can never be described perfectly with words. Examples of true contradictions that dialetheists accept that can only be expressed in contradiction were added.

MP, MT, disjunctive syllogism probably the same

I'm pretty sure the conditional Rules: MP, MT, and Disjunctive Syllogism are the same-- meaning there's a more basic rule that governs them. Maybe I'm wrong 'though. But if this is correct, and MP and MT can be transformed into DS, Priest and Dialetheism has a significant problem.

MP: premise P → Q premise P therefore Q = premise ¬P v Q premise ¬¬P therefore ? by Implication and Double Negation = premise (¬)¬¬P v Q premise(¬)¬P therefore (¬)Q by Disjunctive Syllogism which reads: premise P v Q premise ¬P therefore Q

Now here's MT: premise P → Q premise ¬Q therefore ¬P = premise ¬Q → ¬P premise ¬Q therefore ? by Transposition = premise ¬¬Q v ¬P premise ¬Q therefore ? by Implication = Path One: premise (¬)¬Q v ¬P premise (¬)Q therefore ? = premise (¬)Q → ¬P premise (¬)Q therefore (¬)¬P

or Path Two after Implication: premise Q v ¬P [by Double Negation of Q] premise ¬Q therefore ¬P by Disjunctive Syllogism

Whoever posted the interesting logic above: could you re-type it more clearly so that what you are saying can be assessed? At present there are too many ambiguities, and (possibly?) missing letters. Rosa Lichtenstein (talk) 2006-06-24.
"Every use of modus tollens can be converted to a use of modus ponens and one use of transposition to the premise which is a material implication. For example:
If P, then Q. (premise -- material implication)
If Q is false, then P is false. (derived by transposition)
Q is false. (premise)
Therefore, P is false. (derived by modus ponens)
Likewise, every use of modus ponens can be converted to a use of modus tollens and transposition."
Even better, every use of MP can be translated into Disjunctive Syllogism(and thereby every MT and MP can be translated into DS) which is the Achilles Heel of Dialetheic logic, it can't use any rules of logic. Hypo Syllogism is the only missing piece.
^^^The above was not written by me. Rosa Lichtenstein (talk) 00:51, 25 February 2009 (UTC)

Dialetheistic negation

It is worth noting that, for all his undoubted sophistication, Graham has to change the meaning of "not" to make his theory work, which means that 'dialetheic contradictions' are only true because of linguistic juggling.
Naturally, this leaves it open whether ordinary contradictions are 'true', just as it 'solves' the paradoxes by ignoring them.
And it is worth adding this to your reading list:
Hartley Slater: 'Dialetheias are Mental Confusions' translated into Romanian by D. Gheorghiu, editor, with I. Lucica, Ex Falso Quodlibet, Editura Tehnica, Bucharest.
[If you can get hold of a copy! I obtained mine from the author himself.]
And other papers at:
Also, check out my site:
where dialectical materialism is taken apart from a Marxist angle.
Rosa Lichtenstein 07/03/06

"Truth in linguistic juggling" is somewhat like saying the truth in an end result has to be conveyed in an intelligible form, to one side of something or another. Transmuting a meaning by means of perception. This really only says that the entrenched mode of human thinking is very dualistic, rather than that contradictions must by nature be resolved into one postulate or the other (which are only molds we've made for them by our own considerations of what we believe in as intelligible). Maybe rather than "solving paradoxes by ignoring them" what is really happening is one is not accepting a fact because it doesn't fit into something we haven't categorized for ourselves as 'non-contradictive'. In fact, needing to separate what is posited into either one of two, mutually exclusive, integrable consistencies; so that it works in relation to your cohesive comprehension of a whole logic, is a very dialectical stance to take. Nagelfar 23:12, 30 April 2007 (UTC)
""Truth in linguistic juggling" is somewhat like saying the truth in an end result has to be conveyed in an intelligible form, to one side of something or another."
I note your incapacity to quote me correctly.
I actually said:
"It is worth noting that, for all his undoubted sophistication, Graham has to change the meaning of "not" to make his theory work, which means that 'dialetheic contradictions' are only true because of linguistic juggling."
The rest of what you say is unintelligible.
Is English not your first language?
I also note that because dialectics is such a jellyfish of a 'theory', those held in its grip can claim anything they like as an example of it, even if the latter is incoherent:
"In fact, needing to separate what is posited into either one of two, mutually exclusive, integrable consistencies; so that it works in relation to your cohesive comprehension of a whole logic, is a very dialectical stance to take."
Rosa Lichtenstein 20:21, 4 May 2007 (UTC)


Readers might like to know that Hartley Slater's paper has now been published here:

  • Slater, H. (2007a), The De-Mathematisation Of Logic (Polimetrica).
  • Slater, H. (2007b), 'Dialetheias Are Mental Confusions', in Slater (2007a), pp.233-46. This can also be found in Béziau, Carnielli and Gabbay (2007), pp.457-66.
  • Slater, H. (2007c), 'Response To Priest', in Béziau, Carnielli and Gabbay (2007), pp.475-76.
  • Béziau, J-Y., Carnielli, W., and Gabbay, D. (2007) (eds.), Studies In Logic Volume Nine: Handbook Of Paraconsistency (College Publications).

Also well worth consulting:

  • Berto, F. (2007), How To Sell A Contradiction. The Logic And Metaphysics Of Inconsistency (College Publications).

Rosa Lichtenstein (talk) 20:23, 9 March 2008 (UTC)

Bivalent prerequisite?

I don't see why there is a implication of dialeth(e)ism as bivalent. As a philosophical concept and not a formal logic, one could imagine a dialetheia under several possible multi-valued logics. Also the connotations used e.g as in the Achilles' heel reference or pragmatic replacement of burden-of-proof are quite negative. Scierguy 22:05, 7 March 2006 (UTC)

Dead link

The link to the 'Dialetheias Group Blog' does not work. Rosa Lichtenstein (talk) 01:26, 11 March 2009 (UTC)

Dialetheist or dialethesist?

Both these words occur in the text. Which is it? --Richardson mcphillips (talk) 12:01, 1 April 2009 (UTC)

More source for the critic.

The theory of the Achilles' heel is interest and should don't be cleared but need more source. —Preceding unsigned comment added by (talk) 23:26, 15 October 2010 (UTC)

I agree. The claim, on its own, is simply that. The paper referred to is not freely available on-line, so it isn't possible for many people to refer to it. It would help if somebody who'd read the critical paper could expand on the claim, with some justification. Undefended dogmatism doesn't really sit well in an article on logic. Fustbariclation (talk) 13:46, 17 May 2014 (UTC)

Formal Consequences

I streamlined the claim made in the Formal Consequences section, but I wonder if it is even true. Here is how it currently reads:

In some logics, we can show that taking a contradiction as a premise (that is, taking as a premise the truth of both and ), we can prove any statement . Indeed, since is true, the statement is true (by generalization). Taking together with is a disjunctive syllogism from which we can conclude .

I agree right up until the use of disjunctive syllogism. Does not the use of disjunctive syllogism require that exactly one and is true? Austinmohr (talk) 18:44, 31 May 2012 (UTC)

This is, in fact, false. I've updated the page to correct it. The myth that dialetheism causes logic explosions has been exposed as such many times, though this has yet to become generally known. Fustbariclation (talk) 02:26, 11 August 2016 (UTC)
I believe that these edits were mistaken, and have removed them from the introductory paragraph. This section seems to contain them more centrally so before I make further changes I want to make sure I have properly understood the situation. In the original text quoted above, the key phrase is "in some logics". This is meant to indicate that only logics in which EFQ (Ex Falso Quodlibet) is provable are subject to explosion. This is the case with both classical and intuitionist logic. It is true that this assumption essentially adds up to an assumption against dialetheism. It may even be explicit; depending on how these logics are presented, EFQ can in fact be a theorem derived from an axiomatic assumption of the Law of Non-Contradiction. But these assumptions are defining axioms of these logics, and so the statement as written above is not faulty. It is simply not a good reason to reject dialetheism, as dialetheists can either accept trivialism or reject the legitimacy of any logics where EFQ holds in response. Please feel free to correct my reasoning if I am wrong. (talk) 17:28, 7 February 2017 (UTC)

Wave-particle duality is not an example of self-contradiction

That is stupid. -- (talk) 06:59, 18 September 2015 (UTC)

Article too technical

I inserted an edit, which I expect will be argued over if not outright expunged, and didn't have space to write an explanation, which I will do here: People really shouldn't be faced with a steep uphill climb to understand an article saturated in insider jargon. I propose this edit as a user-friendly way of introducing logic symbols, at least giving the reader a fighting chance. I wanted to link to "List of logic symbols" out of the first logic symbol character, but as it is inside a math text entry, there is no way to do it which highlights the existence of the link (I can link, but the text remains black). As a person with vast ranges of interest, but not insider expertise in the jargon and symbology of many Wikipedia subjects, I am constantly faced with exponentially expanding research to understand what should be relatively simple items in articles. I am particularly conscious of the difficulty which would be faced by my ten year old self with the same curiosity faced with these obstacles, and I expand this concern to other putative readers with great interest but little training. So I have added a linked bracketted "(see List of logic symbols)" after the first introduction of logic symbols in the text. I would be interested in any opinions about the appropriateness or otherwise of my edit. I am getting increasingly concerned in general with the inaccessibility of many wiki articles to the totally lay reader, which was, I thought, the original intent of the whole project. (talk) 05:29, 24 April 2016 (UTC)an occasional anonymous editor, mostly grammar and spelling corrections.

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