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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.
In fact, the misunderstanding is more fundamental than that. The notion of explosion a misunderstanding. The fact that there may be dialetheia doesn't mean that there actually are any, and, even if they are, they may only be a few that apply strictly to their circumstances, with no implication for logic as a whole Fustbariclation ( talk) 10:54, 10 January 2021 (UTC)
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
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:
http://www.philosophy.uwa.edu.au/staff/slater/publications
Also, check out my site:
http://www.anti-dialectics.org
where dialectical materialism is taken apart from a Marxist angle.
Rosa Lichtenstein 07/03/06
Readers might like to know that Hartley Slater's paper has now been published here:
Also well worth consulting:
Rosa Lichtenstein ( talk) 20:23, 9 March 2008 (UTC)
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)
The link to the 'Dialetheias Group Blog' does not work. Rosa Lichtenstein ( talk) 01:26, 11 March 2009 (UTC)
Both these words occur in the text. Which is it? -- Richardson mcphillips ( talk) 12:01, 1 April 2009 (UTC)
The theory of the Achilles' heel is interest and should don't be cleared but need more source. —Preceding unsigned comment added by 188.101.81.47 ( talk) 23:26, 15 October 2010 (UTC)
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)
That is stupid. -- 72.226.86.106 ( talk) 06:59, 18 September 2015 (UTC)
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. 173.180.149.245 ( talk) 05:29, 24 April 2016 (UTC)an occasional anonymous editor, mostly grammar and spelling corrections.
IF anyone has ever presented an argument that dialetheism has hope for every having any "practical"/utilitarian value in the world, I'd very much like to see the argument included. Otherwise it's a bit hard to see why this is of any interest except as a sort of abstract game of no real consequence. Shouldn't the 'Criticisms' section include a criticism of triviality / lack of practical-utility? Surely someone has written about that.
Standard logic has had *incredible* utilitarian value to the world (the very universe seems to operate by rules of consistency with not a single "contradiction" ever being sustained on close examination), and though exploring every contrary concept one can dream up is a part of the legitimate philosophical exploration of all possibilities, and not everything needs to be utilitarian, still, a good measure of how much time and attention something is worth is whether it has ever made any useful predictions about the world, or anything useful can be built upon it.
How might Dialetheism someday be of any more Real World value than the infinite Other facile imaginings we can dream up all day such as the "immovable object vs the unstoppable force"? There are unlimited playful imaginings possible, but most of them peter out not because they're "illegitimate" or "not even wrong", but simply because "they don't get you anywhere" so people just lose interest in squishy definitions and circular arguments and wander off bored with it. (I'm not looking for a debate in the 'talk', I'm hoping arguments exist that could be summarized in the article. Besides abstruse technical arguments, is anything more than abstract game playing actually anticipated to come from this?)
The most powerful motivation I can think up (inadmissible 'original research') would be that _IF_ Dialetheism could ever be shown to hold up usefully (e.g. to describe any real-universe situation with equal precision but *better* than traditional logic), THEN it could undermine everything we think we know about how the universe may carry the laws of physics, or the vast realms of math and reasoning that might be expected by an alien civilization etc. I have very low expectations that it will go anywhere, but if it did that WOULD be incredibly significant, so I'm surprised that isn't claimed as a primary *motivation*. But if it never once describes the real world as well as traditional logic does, then it will never be used except as evidence that we've dutifully taken the trouble to exclude it as useful. Graham asks, "What Is So Bad About Contradictions?" I suspect nothing is "intrinsically bad" about it, but real world uselessness is a "bad" thing to impose on any more than a tiny bit of people's time and attention on something. "2+2=73" isn't "bad" (we can assert it, and play all kinds of games with it), it just doesn't get you anywhere "good". DKEdwards ( talk) 21:44, 3 February 2018 (UTC)
The article states that "in traditional systems of logic (e.g., classical logic and intuitionistic logic), every statement becomes false if a contradiction is true". Should that be "every statement becomes true"? Imerologul Valah ( talk) 22:33, 14 March 2019 (UTC)
![]() | This article is rated Start-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||||||||||||||||
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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.
In fact, the misunderstanding is more fundamental than that. The notion of explosion a misunderstanding. The fact that there may be dialetheia doesn't mean that there actually are any, and, even if they are, they may only be a few that apply strictly to their circumstances, with no implication for logic as a whole Fustbariclation ( talk) 10:54, 10 January 2021 (UTC)
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
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:
http://www.philosophy.uwa.edu.au/staff/slater/publications
Also, check out my site:
http://www.anti-dialectics.org
where dialectical materialism is taken apart from a Marxist angle.
Rosa Lichtenstein 07/03/06
Readers might like to know that Hartley Slater's paper has now been published here:
Also well worth consulting:
Rosa Lichtenstein ( talk) 20:23, 9 March 2008 (UTC)
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)
The link to the 'Dialetheias Group Blog' does not work. Rosa Lichtenstein ( talk) 01:26, 11 March 2009 (UTC)
Both these words occur in the text. Which is it? -- Richardson mcphillips ( talk) 12:01, 1 April 2009 (UTC)
The theory of the Achilles' heel is interest and should don't be cleared but need more source. —Preceding unsigned comment added by 188.101.81.47 ( talk) 23:26, 15 October 2010 (UTC)
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)
That is stupid. -- 72.226.86.106 ( talk) 06:59, 18 September 2015 (UTC)
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. 173.180.149.245 ( talk) 05:29, 24 April 2016 (UTC)an occasional anonymous editor, mostly grammar and spelling corrections.
IF anyone has ever presented an argument that dialetheism has hope for every having any "practical"/utilitarian value in the world, I'd very much like to see the argument included. Otherwise it's a bit hard to see why this is of any interest except as a sort of abstract game of no real consequence. Shouldn't the 'Criticisms' section include a criticism of triviality / lack of practical-utility? Surely someone has written about that.
Standard logic has had *incredible* utilitarian value to the world (the very universe seems to operate by rules of consistency with not a single "contradiction" ever being sustained on close examination), and though exploring every contrary concept one can dream up is a part of the legitimate philosophical exploration of all possibilities, and not everything needs to be utilitarian, still, a good measure of how much time and attention something is worth is whether it has ever made any useful predictions about the world, or anything useful can be built upon it.
How might Dialetheism someday be of any more Real World value than the infinite Other facile imaginings we can dream up all day such as the "immovable object vs the unstoppable force"? There are unlimited playful imaginings possible, but most of them peter out not because they're "illegitimate" or "not even wrong", but simply because "they don't get you anywhere" so people just lose interest in squishy definitions and circular arguments and wander off bored with it. (I'm not looking for a debate in the 'talk', I'm hoping arguments exist that could be summarized in the article. Besides abstruse technical arguments, is anything more than abstract game playing actually anticipated to come from this?)
The most powerful motivation I can think up (inadmissible 'original research') would be that _IF_ Dialetheism could ever be shown to hold up usefully (e.g. to describe any real-universe situation with equal precision but *better* than traditional logic), THEN it could undermine everything we think we know about how the universe may carry the laws of physics, or the vast realms of math and reasoning that might be expected by an alien civilization etc. I have very low expectations that it will go anywhere, but if it did that WOULD be incredibly significant, so I'm surprised that isn't claimed as a primary *motivation*. But if it never once describes the real world as well as traditional logic does, then it will never be used except as evidence that we've dutifully taken the trouble to exclude it as useful. Graham asks, "What Is So Bad About Contradictions?" I suspect nothing is "intrinsically bad" about it, but real world uselessness is a "bad" thing to impose on any more than a tiny bit of people's time and attention on something. "2+2=73" isn't "bad" (we can assert it, and play all kinds of games with it), it just doesn't get you anywhere "good". DKEdwards ( talk) 21:44, 3 February 2018 (UTC)
The article states that "in traditional systems of logic (e.g., classical logic and intuitionistic logic), every statement becomes false if a contradiction is true". Should that be "every statement becomes true"? Imerologul Valah ( talk) 22:33, 14 March 2019 (UTC)