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Bataar
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29 Jan 2009, 8:53 pm

One thing I think should be fairly obvious is that truth cannot contradict truth. It applies strongly to religious debates, especially when someone says that they believe all religions are true or some such thing. If something is true then something that contradicts it cannot be true.



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29 Jan 2009, 8:55 pm

Bataar wrote:
One thing I think should be fairly obvious is that truth cannot contradict truth. It applies strongly to religious debates, especially when someone says that they believe all religions are true or some such thing. If something is true then something that contradicts it cannot be true.

Niels Bohr: "There are trivial truths and the great truths. The opposite of a trivial truth is plainly false. The opposite of a great truth is also true."


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Bataar
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29 Jan 2009, 9:01 pm

Orwell wrote:
Bataar wrote:
One thing I think should be fairly obvious is that truth cannot contradict truth. It applies strongly to religious debates, especially when someone says that they believe all religions are true or some such thing. If something is true then something that contradicts it cannot be true.

Niels Bohr: "There are trivial truths and the great truths. The opposite of a trivial truth is plainly false. The opposite of a great truth is also true."
Define a great truth



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29 Jan 2009, 9:27 pm

Orwell wrote:
Bataar wrote:
One thing I think should be fairly obvious is that truth cannot contradict truth. It applies strongly to religious debates, especially when someone says that they believe all religions are true or some such thing. If something is true then something that contradicts it cannot be true.

Niels Bohr: "There are trivial truths and the great truths. The opposite of a trivial truth is plainly false. The opposite of a great truth is also true."


Niels Bohr was famouse for his unclarity.

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29 Jan 2009, 10:11 pm

Bataar wrote:
One thing I think should be fairly obvious is that truth cannot contradict truth. It applies strongly to religious debates, especially when someone says that they believe all religions are true or some such thing. If something is true then something that contradicts it cannot be true.

Why is it obvious? How can this be proven?



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29 Jan 2009, 10:16 pm

Awesomelyglorious wrote:
Bataar wrote:
One thing I think should be fairly obvious is that truth cannot contradict truth. It applies strongly to religious debates, especially when someone says that they believe all religions are true or some such thing. If something is true then something that contradicts it cannot be true.

Why is it obvious? How can this be proven?

I think that's really just a aspect of our notion of truth, i.e. the law of non contradiction applies to propositions trivially.


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29 Jan 2009, 10:29 pm

Awesomelyglorious wrote:
Bataar wrote:
One thing I think should be fairly obvious is that truth cannot contradict truth. It applies strongly to religious debates, especially when someone says that they believe all religions are true or some such thing. If something is true then something that contradicts it cannot be true.

Why is it obvious? How can this be proven?

It's an axiom. P∧~P is regarded as impossible by definition. You can't prove axioms, they are merely accepted as obvious.

Basically what we see Bataar saying here is:
If P and (Q⇾~P), then ~Q, which is perfectly valid given how truth values are assigned for propositions.


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Awesomelyglorious
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29 Jan 2009, 10:53 pm

Look, to be honest guys, we should have gone over to the Hegelian dialectic, as the law of non-contradiction is just lame.

In any case, if a thing is "obvious" then what makes it "obvious", if there are no laws governing what can and cannot be "obvious", then why can't *anything* be "obvious"? If there are laws governing what can be "obvious", then it would seem that "obvious" isn't so.



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29 Jan 2009, 11:04 pm

Awesomelyglorious wrote:
Look, to be honest guys, we should have gone over to the Hegelian dialectic, as the law of non-contradiction is just lame.

In any case, if a thing is "obvious" then what makes it "obvious", if there are no laws governing what can and cannot be "obvious", then why can't *anything* be "obvious"? If there are laws governing what can be "obvious", then it would seem that "obvious" isn't so.

If you don't take anything as a starting basis, there is no way of doing anything. Can we prove why logic *must* be true? No, but we take it to be true. No one has ever raised a serious objection to the law of non-contradiction or any of the other logical axioms. They not only can be taken as obvious, but *must* be taken as obvious in order to begin any sort of study of truth or knowledge, because without some form of reasoning you're left without saying anything that you can defend at all. No more epistemic nihilism please, it's too annoying.


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29 Jan 2009, 11:10 pm

Orwell wrote:
Awesomelyglorious wrote:
Look, to be honest guys, we should have gone over to the Hegelian dialectic, as the law of non-contradiction is just lame.

In any case, if a thing is "obvious" then what makes it "obvious", if there are no laws governing what can and cannot be "obvious", then why can't *anything* be "obvious"? If there are laws governing what can be "obvious", then it would seem that "obvious" isn't so.

If you don't take anything as a starting basis, there is no way of doing anything. Can we prove why logic *must* be true? No, but we take it to be true. No one has ever raised a serious objection to the law of non-contradiction or any of the other logical axioms. They not only can be taken as obvious, but *must* be taken as obvious in order to begin any sort of study of truth or knowledge, because without some form of reasoning you're left without saying anything that you can defend at all. No more epistemic nihilism please, it's too annoying.

I don't think they're obvious at all. Laws of logic oughtn't to be viewed as propositions about anything, merely characterizations of the way we speak of things. We adopt them because we like them, and for no other reason.


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29 Jan 2009, 11:11 pm

twoshots wrote:
I don't think they're obvious at all. Laws of logic oughtn't to be viewed as propositions about anything, merely characterizations of the way we speak of things. We adopt them because we like them, and for no other reason.

They aren't propositions. They are axioms. There is no way for the law of non-contradiction to be false- how could it be? It is not possible.


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29 Jan 2009, 11:14 pm

Orwell wrote:
twoshots wrote:
I don't think they're obvious at all. Laws of logic oughtn't to be viewed as propositions about anything, merely characterizations of the way we speak of things. We adopt them because we like them, and for no other reason.

They aren't propositions. They are axioms. There is no way for the law of non-contradiction to be false- how could it be? It is not possible.

Only because "false" is meaningless when applied to it.


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29 Jan 2009, 11:17 pm

Orwell wrote:
If you don't take anything as a starting basis, there is no way of doing anything. Can we prove why logic *must* be true? No, but we take it to be true. No one has ever raised a serious objection to the law of non-contradiction or any of the other logical axioms. They not only can be taken as obvious, but *must* be taken as obvious in order to begin any sort of study of truth or knowledge, because without some form of reasoning you're left without saying anything that you can defend at all. No more epistemic nihilism please, it's too annoying.

Orwell, Hegal took objection to the law of non-contradiction. Hegel, one of the better-known philosophers of the 19th century. You can disagree with Hegel, but to say that no objections have ever occurred is ahistorical. There is a reason why I stated "we should have gone over to the Hegelian dialectic, as the law of non-contradiction is just lame."

In any case, I don't see a reason to say that your position *must* be taken as obvious. I think that instead, our logical rules should now be the following:

1) All meaningful propositions must agree with what I say. (Law of awesome gloriousness)

If your rules *must* be taken obviously, then why not mine?



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29 Jan 2009, 11:21 pm

Orwell wrote:
They aren't propositions. They are axioms. There is no way for the law of non-contradiction to be false- how could it be? It is not possible.

Well, if there is no way for it to be false, then there is no way for it to be true either. I mean, the law of the excluded middle upholds this, if I am not horribly misinterpreting it that is. And if this law cannot be held as true, then why hold to it?



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29 Jan 2009, 11:26 pm

Awesomelyglorious wrote:
In any case, I don't see a reason to say that your position *must* be taken as obvious. I think that instead, our logical rules should now be the following:

1) All meaningful propositions must agree with what I say. (Law of awesome gloriousness)

If your rules *must* be taken obviously, then why not mine?

You're right of course, as proven by logical rule number 1 presented here.


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29 Jan 2009, 11:29 pm

Well, a system which does not preclude contradiction is nonsensical, i.e. it becomes useless for expressing information. I suppose there's probably more than a little circularity in that argument, but it's pretty easy to show that in a conventional logical system throwing out the law of non contradiction means that anything and everything is true.
1. p&~p
2. p=> ∀q pVq
3. ~p
4. Thus, q

This comes down to the capacity for the language to express information. We choose logic because it expresses information irrespective of its truth value.

Interestingly, there is something known as paraconsistent logic which rejects the principle of non contradiction without succumbing to the above issue. However, this is at the expense of versatility and intuitiveness.


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