Can someone explain the Law of Non-Contradiction?

[aReformedPatriot]

Can someone explain to me the Law of Non-Contradiction?

 

[levi501]

something can't be true and untrue at the same time... or something like that.

 

[Maxwell511]

I think it is something like this:

If X can be either A or B. It cannot be both A and B.

Something like if I have a pet that is either a cat or a dog it cannot be both a cat and a dog.

 

[outlaw]

For any presupposition (P), P is incompatible with not-P





The law sounds great on paper (or on a computer screen) but it is next to impossible to get to work in real life where issues of context and time and perception come into play.



One famous example of where the law of non-contradiction falls apart is in elementary physics. Light is both a particle (P) AND a wave (W). here we have light acting as a particle (P) and a wave (Not-P)



Other real world and personal examples exist. I am chatting with my friend and she says that it is a beautiful sunny day. I look outside my window and note that it is not just the middle of the night but raining as well. The beautiful sunny day (P) and the stormy night (not-P) cannot, according to the law of non-contradiction, both be true. Yet they are both true because of the context of the conversation taking place over the phone to my friend who happens to love in New Zeeland.



When confronted with someone trying to use the law of non-contradiction remember that the truth of a statement is always dependant on the context and can both the truth and the context can change over time and space.

 

[PKJ]

The complete formulation is

Nothing can be p and non-p on the same ratio and at the same time.

(not to sure about the translation, especially the word "ratio")

 

[TeddyKGB]

One famous example of where the law of non-contradiction falls apart is in elementary physics. Light is both a particle (P) AND a wave (W). here we have light acting as a particle (P) and a wave (Not-P)

That is a failure of language, not a failure of LNC.

 

[Ledifni]

For any presupposition (P), P is incompatible with not-P





The law sounds great on paper (or on a computer screen) but it is next to impossible to get to work in real life where issues of context and time and perception come into play.

I think you're misunderstanding this Law a little.

One famous example of where the law of non-contradiction falls apart is in elementary physics. Light is both a particle (P) AND a wave (W). here we have light acting as a particle (P) and a wave (Not-P)

If light is both a particle and a wave, then clearly "wave" does not imply "not-particle." According to the Law of Non-Contradiction, light cannot be "particle" and "not-particle," but it can be "particle" and "wave" if the two do not contradict one another (and they do not).

Other real world and personal examples exist. I am chatting with my friend and she says that it is a beautiful sunny day. I look outside my window and note that it is not just the middle of the night but raining as well. The beautiful sunny day (P) and the stormy night (not-P) cannot, according to the law of non-contradiction, both be true. Yet they are both true because of the context of the conversation taking place over the phone to my friend who happens to love in New Zeeland.

Again, this is no contradiction. The Law of Non-Contradiction does not say "If P is Q, then P is not R." Rather, it says, "If P is Q, then P is not not-Q." There can be rain on Earth and sun on Earth in separate places, and this produces no contradiction. The Law of Non-Contradiction would be violated only if you said, "It is raining here, and it is not raining here." Rain in New Zealand doesn't imply that there is rain where you live.

 

[large fry please.]

Can someone explain to me the Law of Non-Contradiction?

The liar paradox? This started around sixth century BC by Epimenides who was a Cretan. he said "all Cretans are liars" a better example is "this statement is false" or "this sentence is untrue".

 

[bob135]

Can you prove the law of non-contradiction, or is it just assumed, or "self-evident"?

 

[Patzak]

Can you prove the law of non-contradiction, or is it just assumed, or "self-evident"?

It's an axiom (along with the law of identity) so no, you can't prove it. To do so, you would have to step outside logic (because all logic depends on the law of non-contradiction) - which would also make any notion of proof completely meaningless.

 

[MoonlessNight]

Can you prove the law of non-contradiction, or is it just assumed, or "self-evident"?

If the law of noncontradiction were not true it would be impossible to prove anything, as you could never guarantee that even if something were true that it was not also false. It's a vital part of the process of making proofs, and as such cannot be proven. But if you value proofs as a way of achieving understanding of the world, you must accept the law of noncontradiction.

Asking to prove the law contradiction is a bit like asking for a proof that 1+2=3 without using arithmetic.

 

[lawtonfogle]

For any presupposition (P), P is incompatible with not-P





The law sounds great on paper (or on a computer screen) but it is next to impossible to get to work in real life where issues of context and time and perception come into play.



One famous example of where the law of non-contradiction falls apart is in elementary physics. Light is both a particle (P) AND a wave (W). here we have light acting as a particle (P) and a wave (Not-P)



Other real world and personal examples exist. I am chatting with my friend and she says that it is a beautiful sunny day. I look outside my window and note that it is not just the middle of the night but raining as well. The beautiful sunny day (P) and the stormy night (not-P) cannot, according to the law of non-contradiction, both be true. Yet they are both true because of the context of the conversation taking place over the phone to my friend who happens to love in New Zeeland.



When confronted with someone trying to use the law of non-contradiction remember that the truth of a statement is always dependant on the context and can both the truth and the context can change over time and space.

But then if P is better defined, then it would still work. Like say it is a beautiful sunny day in the area your friend lives in. Then it would be true.

 

[PKJ]

Can you prove the law of non-contradiction, or is it just assumed, or "self-evident"?

Very good question. I think we made it up from empirical observation (in other words, things are cooler when you use the LoNC), but some seem to think that it's some kind of universal law that exists in this world but could be wrong in another, possible world.

 

[TeddyKGB]

Can you prove the law of non-contradiction, or is it just assumed, or "self-evident"?

It is axiomatic. "The LNC is not true" assumes the truth-state "not true" is distinct from the truth state "true," thereby invoking the LNC.

 

[David Gould]

Very good question. I think we made it up from empirical observation (in other words, things are cooler when you use the LoNC), but some seem to think that it's some kind of universal law that exists in this world but could be wrong in another, possible world.

No.

Logic is the lens we use to determine truth.

In other words, logic cannot be 'true' or 'false'. It is that by which we determine truth or falseness.

 

[PKJ]

No.

Logic is the lens we use to determine truth.

In other words, logic cannot be 'true' or 'false'. It is that by which we determine truth or falseness.

I totally agree. But don't you think that our lens can be improved, like Frege/Russel improved aristotelician logic? That would lead us to think that logic is not 100% innate.

 

[David Gould]

I totally agree. But don't you think that our lens can be improved, like Frege/Russel improved aristotelician logic? That would lead us to think that logic is not 100% innate.

The formalised rules and their implications can be worked out in much greater detail. This enables us to use the lens better - it does not improve the lens, so to speak, but rather our understanding of what we can see through it.

The law of identity, the law of non-contradiction and the law of the excluded middle are all you need to build the rest, so far as I know.

 

[ebia]

It's an axiom (along with the law of identity) so no, you can't prove it. To do so, you would have to step outside logic (because all logic depends on the law of non-contradiction) - which would also make any notion of proof completely meaningless.

You can't prove it, but you can prove anything you like from a single case of it not holding:

ie, for any A, if A and not A then B

Where B is any statement you like.

So, if a single failure of the law renders all logic useless, we might as well assume that it always holds.

 

[PKJ]

Is logic built with innate categories?

 

[MoonlessNight]

Is logic built with innate categories?

Could you elaborate what you mean? I'm not sure exactly what you mean by categories. Could you give some examples?