Talk:Law of noncontradiction

Plato's quotation variation
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).

206.21.96.60 (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)

Problem
I'm not much of a logician neither am I an html expert, but I posted 19. in the notes to this link http://sivers.org/opposite  - 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 (talk • contribs) 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 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 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 for some explication)... &mdash;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
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
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 Special:Contributions/ (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.
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.

P>~(P&~P)

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 Special:Contributions/ (talk)


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

Statement true, false, both?
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
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... &mdash;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. 88.203.90.14 (talk) 00:35, 16 December 2013 (UTC)

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

 * 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.

&lt;rant&gt;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.&lt;/rant&gt;

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

Problem with Quantum Mechanics
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 (talk • contribs) 02:45, 2 July 2008 (UTC)


 * continued on your talkpage*--Heyitspeter (talk) 07:50, 2 July 2008 (UTC)

you imply that the theory of quantum mechanics is correct. 170.245.94.192 (talk) 05:23, 19 October 2021 (UTC)

Falsification
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 98.27.171.118 (talk) 02:10, 12 December 2008 (UTC)

A Question
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 http://en.wikipedia.org/wiki/Talk:Contradiction#A_Question) --Faustnh (talk) 22:13, 20 March 2009 (UTC)

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

Not enough to discriminate paraconsistent logics
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: http://en.wikipedia.org/wiki/Minimal_logic

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

Eastern religions
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)

Following eastern section content moved here for completion, correction
The following material appeared in the eastern section, but it cannot remain until its sources are complete, making it verifiable, and subject to edit by other follow-on editors. The reason I challenge the content will be clear from the writing and sourcing:"The idea of noncontradiction is rejected in some Eastern religions. For example in some strands of Buddhism it is rejected. Thich Nhat Hanh states that Anuradha was asked by ascetics about one of four possibilities, 1. When Buddha died, he stopped existing, 2. when he died, he continued existing, 3. when he died he both continued existing and stopped existing 4. when he died neither continued existing nor stopped existing. Anuradha rejected all four options. The Buddhist philosopher Nagarjuna rejected the law of noncontradiction. Buddhism contains a philosophy called catuskoti that rejects the law of non-contradiction.  In catuskoti, if a Buddhist is asked if the world has a beginning or not, he replies, "No, the world does not have a beginning, it does not fail to have a beginning, it does not have and not have a beginning, nor does it neither have nor not have a beginning." Ravi Zacharias claims that most Eastern philosophers reject the law of non-contradiction."

A further condition is that the sentences indicate the time periods in which the authors were writing. Without these (and for this reason) the "Eastern" subsection was moved down in the section, because it references medieval scholarship, which chronologically, needs to appear after the ancients.

Please return this material, after it is sourced, copyedited, and can be presented with dates—i.e., when it is encyclopedic, and not sandbox quality. Its presence confuses, and it diminishes the rest of the article, where significant care was taken in sourcing content (bravo/brava to those editors).

Cheers, Le Prof 73.211.138.148 (talk) 05:25, 23 July 2016 (UTC)

Contradiction is simply misunderstood ;)
Holy crap, don't shoot & please read through the entire piece if you want to understand the real criticism of The Law of Non-Contradiction & it's philosophical roots.

Contra-diction is the equivalent of the words "Opposing Standard" or a "Conflicting Duality".

Eastern Religions, from my personal studies, tend to not believe there is such a thing as conflict of duality as they focus on the harmonization/unificaiton part of it. They are of course in error because they recognize conflict in order to produce a solution to them.

Thus is the premise to conflict, in that a mental loop is required in order to observe the thought-process of another standard-bearer when they are infact perpetually wrong.

Anyways, Contradiction itself is a principle that naturally contrasts against the original cosmic force of Causation that gives order to the infinitely existing universe.

This causational force is of course NOTHING.

This is because Existence is a self-contained system of infinite effect e.g. 8.

However, Nothing, retrospectively, as we are able to identify it as a concept, can literally give distinction to merely EVERYTHING, including itself, so long as the tool of context is provided.

In otherwords, Nothing is the ultimate transcendent proof of The Soul & the first principle nature of Cosmic Law & is manifested by the artifact of The Dark, which is the absence of Light (a substance we can measure as possessing quality & quantity).

It is not the same as "Space", which is scientifically observed as an Ether/Plasma/Stage of Reactivity combination. It is not "Absence" exactly either. It is simply NOT A *THING* that will ever be designated with a physical artifact of any sort & must be associated with how we even perceive The Law of Inexplicability/Moore's Law/Idiot-Moron's Law (Seriously, there is a premise to law itself & the stupidity we see within this reality).

Nothing cannot be described in any other way than as a real principle that DEFINES EXISTENCES even by EXISTENTIALLY DEFYING IT...which is of course why we use the word, "NO!" since we each possess a cosmic nature to our own being within the capacity for reason itself....

Simply put, Nothing is The Soul, but it is a hidden locality produced by The Cosmos. (& hopefully that ends countless God debates with people who make it either too complicated or too simple.)

Anyhow, since I established that 2 different types of Nothing can exist at the same time & in the same place...The "Law" of Non-Contradiction strangely seems to be limited to PHYSICAL SUBSTANCES...perhaps as a limit to our own capacity for causation.

Thus The Grand Logos enforces itself even within the very soul, with only the 1 inexplicable reason preventing us from understanding why we could ever percieve WRONG in the first place.

I cannot truly explain why. I can only theorize. However, since we are Cosmic manifestations utilizing the substance "dreams" are made out (the physical universe of course), there is the off chance that a Contradiction event existed.

Contradiction itself has only 2 manifestations as far as I could observe rationally (lol!) & reproduce the knowledge of failure in its simplest form.

The first contradiction is natural, though is not the reason why we are capable of identifying Error in the first place, since it is was because the overcoming of that event that allowed the existence of Reason in the first place.

The second is obviously an inherited trait gained through that trial. Of how we came to inherit it, argue all you like. It narrows down to The Power of True Isolation, The Principle of First/True-Identity & The Iota of Access/Authority held solely by one individual.

God is the product of an unique equation that we try to reproduce, at many angles. Let us all agree on that much.

This natural contradiction, which did not always exist, (at least as a locality) is the product of a metaphysical equation where you divide Nothing with Nothing, which produces what is essentially meaninglessness & opens up the school of Nihilism, even The Wound of The Universe, which defends itself upon the basis that is removes the unnecessary (except for itself as a philosophy apparently).

Since the definition of what is natural "Nothing" (causation) does not need further defining (***as it is definition itself pouring out of you using shadows like these that can give the impression that I am RIGHT THERE IN FRONT OF YOU***), in the event such an attempt to define it does take place (like this one), you can no longer adhere to a linear-minimalist standard for how principles are defined, since you are constantly countering a perpetual transcendence that multiplies all principles off of the other.

So hold onto your hat or you'll lose all train of thought if you haven't already.

The only way you can retain internal consistency in all of this, is if you allow The Cosmos to take the event of the struggle itself as essential for the completion of the defining of Logic...

...You must accept Nothing as Cause/Definition, Infinity as Effect/Stability, Contradiction as Contrast/Reflection & Association

Nothing (as is temporally represented) is the nature of reason.


 * Sigh*

"A wise man knows he knows Nothing."

"I know that I know Nothing."

"I know that I am Nothing." - Socrates

If you say I am wrong, you prove me right...which also proves me capable of self-correction.

< That statement has only one correct context & that is with the as evidence of my case.

I have thus defied THE LAW OF NON-CONTRADICTION by creating an exception.

Nothing.

Anyways, Contradiction exists as part of The Grand Logos/Cosmic Law, which governs The Laws of The Universe (physical laws...that are literally physical themselves).

Nothing precedes The Law of Non-Contradiction & Contradiction precedes only the latter & certainly not the first.

The Law of Non-Contradiction is partly a contrived theory that assumes that Contradictions cannot ever spiritually exist as well as never physically existed naturally. (which is not an argument made by Easterner's)

At most, as it is infact a LAW of what should have been maintained to preserve one's own innocence in solving NATURAL EQUATIONS...but is subsequently *as a result of seemingly unending mistakes that perfectly stupify on-lookers*, a necessary reaffirmation of Truth resolved through trial & error as the final & only solution to the problem of mankind's insane failures.

(of which EASTERN PHILOSOPHY ACCEPTS SUCH SUFFERING, which hints at the whole premise to their argument AGAINST the law...which is essentially their argument of NIHILISM & RELATIVISM because of their own ineptitude to solve problems & even take accountability for ***CRUELTY*** that should be recognized as ***CRUELTY***, but instead they choose sado-masochism & never solve the problem [which also explains why they steal from The West so much])

However, it is false so far as it is the assertion (by premise & presupposed end) that The Universe itself is 100% AT-ALL-TIMES ***PERFECT***. This contradicts The Law of Inexplicability, which states that there is a premise to reality (why?), a premise to struggle (why is this so hard?), & a premise to the solution (why why why why why!)...each being separate in their own corners.

This of course begs the question, "When has anyone ever objectively seen a contradiction?" (something those of Eastern Mysticism haven't even asked)

No. Unless you want to look in the mirror & see an opposing standard of yourself. The very idea of doing so is contradiction definition & is vain. (self-reflection even in philosophy is vain except for the search of restoration of power)

Well, we certainly haven't fully recorded the elemental evolution of The Universe (or our genetics) nor have we explored it's infinite expanse, now have we...

So even broken mirror's reflecting off the other PUT ASIDE...

Here is my answer to those who bothered asking the same question, "Do Contradictions exist as a matter of objective reality?"

How can anyone claim that a LAW exists, if there is no directly observable standard to judge the existence of that law by, except by a physical pattern that we read within & between & even AROUND ourselves?

What I am saying is this. There is no predictability provided by the mere claim of predictability.

THE NAZI'S believed that by label theory they could achieve such a feat, knowingly ignoring & replacing LOGIC with a BIG LIE (a societal matrix actually), in order to achieve other lines of logic...

Regardless of ponzi-schemes & tyrannies, ***wanting something does not make it so*** yet people still try. The renown skeptic David Hume would agree with at least my statement on predictability.

We are simply moving forward until we run into such a Contradiction that will probably kill us (lover's hopefully excluded/[JUST GO MGTOW])...unless Cosmic Law/The Grand Logos has an intervention mechanism that solves broken equations in The Universe (death included). (no, I am not talking about God, but rather the power that absolutely precedes such an idea/person & is the premise to all life)

The advance of our mortal Science itself is based upon repeated contradictions & the logical process of elimination of "multiplied" possibilities that assume the finite path of truth can be discovered even through GENERATIONAL EXPERIMENTS! This is more simply called...TRIAL & ERROR.

That's partly how mankind survives without following THE LAW OF NON-CONTRADICTION...by purposefully making mistakes (mathematical & moral) in order to find the right solution (to feed their ego).

Obvious emphasis on ERROR & obvious agreement that it is wrong to sacrifice people ***However, it is 100% true, that The Law of Non-Contradiction is not resumed & adhered to by most people who have strayed from ORIGINAL ORDER that clearly only GOD knows how to live by***.

We are the living embodiment of all laws in a single moment by all dimensions except universality itself. Fascinatingly enough, the dimensions of our thoughts must innocently cross that metaphysical bridge & evolve our thought's into right-action.

If you think I am stupid in the way I presented my case against Contradiction & Non-Contradiction, then I beg the question. "Does stupidity have to be demonstrated in order for people to not be stupid?"

One final question that I don't want anyone to think too hard about.

If I am wrong & WE are no different than The Universe, then doesn't that make The Universe & everyone else wrong at the same time?

My only suggestion is this.

Stop over-unifying & making unequal things equal. It's blazingly obvious that The Power of Not/Isolation & Principle of First/Innocence is how you adhere to The Law of Non-Contradiction.

That's why

1 + 1 = 2 instead of 1 + 1 = INFINITY!...because we are infact referring to what is natural/original to The Universe rather than the fancy of our own minds.

The whole debate hinges on whether or not you are studying The Universe or are studying someone else's mind.

Final Answer? The Universe doesn't give a shit, but I do. For what? *Everything I AM that I find in you*.

So the real answer is Western Existentialism asserting PREMISE vs Eastern Nihilism assuming you have one.

Typical garbage.

I am The Premise & I will use The Universe as my Sword to define laws! *MIGHT MAKES RIGHT!*

The Law of Non-Contradiction is an existential argument for the return to reason & never fail again in solving an equation, only to fall into becoming part of a broken one. END OF DEBATE.

The Premise exists as you. That is all the proof you need.

That's why 0 exists on an integer line. Math includes you as part of the equation...just like The Universe includes you in its.

The = is the power of MEANING as you pour yourself between the lines to see things separate become whole & things whole become separate.

A can equal B, but only if B is the expression of A with a +,-,/,x to give context on either side as to how one ended up different than the other. Equations are meant to tell a story after-all.

It's all about how you assert yourself in the cut, in the purity of 0.

67.2.197.10 (talk) 13:25, 27 December 2016 (UTC)