Talk:Law of noncontradiction

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 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 211.195.70.46 (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 24.115.222.43 (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.

Relationship to law of excluded middle

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