Talk:Law of noncontradiction

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Plato's quotation variation[edit]

Sorry, pretty horrible at editing pages, so I try not to do it often. Here though, I have to point out that the "or" that I bolded below makes the quotation in this article pretty easy to disprove, and in my version of Plato's complete works (Edited by John M Cooper 1997), it is omitted. I'm not sure if both are valid translations, and if not then I'm not sure which is more credible, but if the quotation below is credible, then I think Plato was wrong here.

"The same thing clearly cannot act or be acted upon in the same part or in relation to the same thing at the same time, in contrary ways"

I can disprove it by saying that an object can pushed upwards with one force and downwards with another force- therefore acted upon in relation to the earth (or any other land mark) in two contradictory ways). (talk) 10:47, 23 April 2014 (UTC)

To observe fixed objects and properties in an ever-changing world, Plato needs three necessary and sufficient restrictions. If any one of the three is missing then the corresponding relativism results. 1) "in the same part" - Objects have different aspects, such as insides and outsides. 2) "in relation to the same thing" - Objects are subject to varying perceptions depending on the viewer. 3) Change over time. BlueMist (talk) 02:37, 24 April 2014 (UTC)


I'm not much of a logician neither am I an html expert, but I posted 19. in the notes to this link - If someone could clean that up for me or tell me why it doesn't apply to Aristotle I would appreciate the assistance regardless. And I would suppose that you could also delete the link which would prove my point that there more than two options. — Preceding unsigned comment added by Metapunk (talkcontribs) 18:23, 12 July 2012 (UTC)

Here's a simple example:

I state this to be true:

 If it is raining, I am wearing blue socks.
 If I am wearing blue socks, you cannot conclude that
 it is raining because I did not state that blue socks 
 are worn only when it is raining.

The above is not an example of the law of noncontradiction, nor is it an example of a contradiction. But it is an example of a logical fallacy. (The name of the fallacy is affirming the consequent. --LMS

Unless the following happens to be a really important paper, it doesn't deserve specific mention in the article (unless other papers of equal importance are given a mention...).

However, see [1] for a paper (in PDF format) on "paraconsistent" logics and non-contradiction:

Abstract: There is widespread agreement that the law of non-contradiction is an important logical principle. There is less agreement on exactly what the law amounts to. This unclarity is brought to light by the emergence of paraconsistent logics in which contradictions are tolerated (in the sense that not everything need follow from a contradiction, and that there are "worlds" in which contradictions are true) but in which the statement [not (A and not-A)] (it is not the case that A and not-A) is still provable. This paper attempts to clarify the connection between different readings of the law of non-contradiction, the duality between the law of non-contradiction and the law of the excluded middle, and connections with logical consequence in general.

...and [2] for more discussion of this law.

It seems to me that there ought to be some consideration here of what negation means; perhaps a separate negation entry is in order. At first sight, the idea looks trivial; the negation of "This tastes salty" is "This doesn't taste salty." But when I eat salted watermellon, I sometimes say to myself "This tastes salty...and yet it doesn't taste salty." Is this a a refutation of the law of non-contradiction? Is this "merely" poetic speech? I don't seek direct answers from you here; I just wish the negation concept would be fleshed out further, to expose such troublesome considerations.

I quite agree. Religiously/spiritually I see nothing wrong with there both being many gods and not (many gods) -- in different traditions perhaps, so "gods" (or existence) means a slightly different thing -- so that is quite a bad example of the law of noncontradiction, I think. Logical negation pretty much assumes that statements are separated out into distinct, completely-well-defined "propositions" (which is not always possible and retain the meaning and relevance) first -- before using ANY laws of logic. As I am sympathetic to various kinds of agnosticism, intuitionist logic, and anthropology/ethnography ... maybe I would describe that set as "non-absolutism" since I don't agree with some arrogant uses of the term "relativism" either (see Cultural_relativism#Comparison_to_moral_relativism for some explication)... —Isaac Dupree(talk) 13:22, 4 October 2007 (UTC)

I wonder if we need a seperate page to discuss the differences between these 3 laws - an interesting topic. The example I just gave (De Interpretatione 9) doesn't even mention the law of non-contradiction. :-) Evercat 19:01 29 Jun 2003 (UTC)

I propose moving most of this page to Bivalence and related laws and reducing this page to a shortish page like law of the excluded middle is... I'd also fix all pages that link here expecting a discussion of the differences between the 3 laws. Comments? Evercat 19:07 30 Jun 2003 (UTC)

And I've now done it... Evercat 19:06 1 Jul 2003 (UTC)

Aristotle forgot ", and in the same stead." lysdexia 00:58, 13 Nov 2004 (UTC)

Epistemic Circularity[edit]

A section of this page originally posited that the law of non-contradiction cannot be disproved and so is "undeniable". I added that it cannot be proved or "verified" for the same reasons (I may be misunderstanding their point, but I'm pretty sure they were arguing that you needed to use the law to disprove the law, and that this is a circular argument). I think this is reasonable, but let me know if I'm missing something. Also, feel free to delete the entire section if you think it's not worth stating.--Heyitspeter 23:20, 14 January 2007 (UTC)

Something that might go towards proving the law of non contradiction[edit]

I heard somewhere that if you reject the law of non contradiction, that you can then go on to prove anything you want to be true. For example, if a=b and a!=b then I can go on to prove that all girls want to have sex with me, or that boys can throw rocks at speeds which exceed the speed of light, etc.

I forget exactly how the logical argument goes but maybe someone else remembers it. I know Bertrand Russell once made the same argument.

—The preceding unsigned comment was added by (talk)

That argument doesn't prove the LNC though. Please sign your posts in the future.--Heyitspeter 07:40, 3 May 2007 (UTC)

Natural deduction proof for the Principle of Non-Contradiction.[edit]

The following demonstrates the logical proof for the principle of non-contradiction based on the use of conditional introduction. Conditional introduction assumes the antecedent of the consequent.


1. P Assumption to be discharged.

2. (P&~P) Conjunction introduction dependant on assumption 1. This is accomplished by the use of the left conjunct to validate the right conjunct.

3. P>~(P&~P) Conditional introduction dependant on assumption 1 and validating the consequent, which is ~(P&~P)

These are the natural deduction rules which can be used to prove the principle of non-contradiction.

Incidentally this is also an argument without premises.

—The preceding unsigned comment was added by (talk)

And why is assumption 1 not a premise?--Heyitspeter 03:17, 21 May 2007 (UTC)

Statement true, false, both?[edit]

What about the following statement: "Every single person born on the moon before 1500 was male."? Is that true, false, or both? I think it might be both, which would mean the law was disproved...? Retodon8 11:24, 13 June 2007 (UTC)

It is true. It is not false and it is certainly not both. See vacuous truth.
The Schroedinger's cat article may help you. It's one interpretation of your question, but discussed by scientists, who I am told are considered very credible.--Heyitspeter 23:17, 22 June 2007 (UTC)

Relationship to law of excluded middle[edit]

Isn't the law of non contradiction (LNC) logically equivalent to the law of the excluded middle (LoEM) and doesn't that (definitely) deserve mention? Right now it's simple linked in "See also".. 20:17, 15 June 2007 (UTC)

no, it's not equivalent in intuitionist logic for example, and yes it probably deserves mention... (so) I put in a link to principle of bivalence which describes those differences... —Isaac Dupree(talk) 13:07, 4 October 2007 (UTC)
LNC and LoEM are equivalent using De Morgan's law and the Double Negative law of Propositional Logic:
LNC = ~(P & ~P) = ~P V ~~P = ~P V P = P V ~P = LoEM. (talk) 00:35, 16 December 2013 (UTC)

What about multi-leveled affirmations? They are not subject to this law[edit]

  • Affirmation: "Mount Everest is Big"
  • Assessment 1: "True, as in - if you'd take a poll you'd get this answer from most."
  • Assessment 2: "False: compared to the size of the universe, it is a speck of dust."

Which is it? They are both true. The affirmation is both true and false. It is true in context 1 and false in context 2.

So I submit that it is possible to accept both the Christian and Hindu POV from two separate perspectives, which could be maintained both true in an even more elevated POV.

Lots of people have gone to war over this, trying to prove their POV with the fist. In fact we should accept that all religions are true in their context, which doesn't negate the other religions.

<rant>I feel this principle, besides its obvious usefulness, also includes a sad attempt to force everything to the same context of discourse, to deny the different perspectives born of different cultures and life experiences. Analyzing everything to death devalues the object of analysis. We need more inclusive approaches, that integrate the seemingly disparate parts into a larger, more coherent ensemble.</rant>

Visarga (talk) 11:53, 1 January 2008 (UTC)

Problem with Quantum Mechanics[edit]

I know a little more about Quamtum Mechanics than I know about Philosophy. Which doesn't say much. But he's my understanding of the issue.

Any particle (photon, electron, proton, ect) fired at a double slit will travel in a state of being both a wave and a particle. This will create an interference pattern behind it showing it to act as a wave. Yet fired out one at a time and measured at the wall, we know them to have traveled a path.

Doesn't the mere fact that a particle can act as both a particle or a wave simultaneously break the law of non-contradiction since the act of measuring a particle forces it to become something other than what it was? If you measure it as a particle, it stops being a wave. If you measure it as a wave, it ceases to be a particle. It forces it to become something that it both was and wasn't until you bugged it to answer us. —Preceding unsigned comment added by ZirbMonkey (talkcontribs) 02:45, 2 July 2008 (UTC)


The issue with arguing that the law of non-contradiction is unfalsifiable and therefore vacuous is based on a misunderstanding of the principle of falsification.

The principle of falsification only applies to theories that explain evidence, or a posteriori theories.

The principle of falsification does not apply to mathematics and logic, which are a priori —Preceding unsigned comment added by (talk) 02:10, 12 December 2008 (UTC)

A Question[edit]

Imagine the following universe:

"Moment X"=TRUE; "There's light"=FALSE; "The fact is empirically true"=TRUE
"Moment X"=FALSE; "There's light"=TRUE; "The fact is empirically true"=TRUE
Any other combination between "Moment X" and "There's light"...; "The fact is empirically true"=FALSE

Considering this universe, what sense makes the expression ("There's light" AND NOT("There's light"))?

(Also, Problem of future contingents).

(Also posted at --Faustnh (talk) 22:13, 20 March 2009 (UTC)

Unbound variable[edit]

\neg(P \land \neg P) should be preceded by "For any propsition P", should it not?

Not enough to discriminate paraconsistent logics[edit]

The law of noncontradiction is not enough to discriminate paraconsistent logics in general. For example in minimal logic we have:

 A |- A      f |- f
  ------------------ (->L)
   A, (A -> f) |- f
   ----------------- (&L)
   A & (A -> f) |- f
---------------------- (->R)
|- (A & (A -> f)) -> f

Now make use of ~B = B->f and we have:

|- ~(A & ~A)

It is rather that Ex Contradictione Sequitur Quodlibet is needed to distinguish some paraconsistent logics.

For more information see:

Jan Burse (talk) 18:19, 27 May 2012 (UTC)

Eastern religions[edit]

Most eastern religions don't believe in the law of noncontradiction. I changed the eastern section to reflect this.--PaulBustion87 (talk) 11:46, 7 March 2015 (UTC)