Essentially a valid argument is an argument where it would be impossible for the conclusion to be false if all of the premises are true. |
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Exactly. If your conclusion doesn't follow the premise you are not making an argument your just playing games. |
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You've stumbled upon the principle of explosion, which states that anything follows from a contradiction. The name comes from the observation that, if we allow a contradiction into a logical system, the system "explodes into triviality." |
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Last edited by DuB; 02-13-2012 at 11:10 AM.
@Alric |
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Right, as far as I know, they are the same thing. Wiki: paradox of entailment. |
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If you think about it ⊃ as a superset symbol is actually the same thing as an implication symbol. That's why it's used; consider sets of events. |
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I wish that more threads like this were created. Thanks DuB for the explanation and the link (although the superset notation confused me too). I'd never heard the paradox before. |
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Sorry for the confusion. In the future I'll use the → operator. |
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Valid argument? It's 'possible' for the conclusion to be false. Therefore, Stormcrow, your exemplified argument is invalid. What hype is there? |
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I stomp on your ideas.
As explained earlier, the criterion for validity is not simply that it is impossible for the conclusion to be false, but rather that it is impossible for the conclusion to be false AND the premises true. By this standard definition, the argument is valid; it is impossible for the conclusion in the OP to be false and its premises true, by virtue of the fact that it is impossible for both of its premises to be true. |
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I'm not really a logician so my terminology may be off... |
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Previously PhilosopherStoned
The self-referential nature of the premises is indeed tricky, and possibly should not be permitted. I think the more important point for the purposes of this discussion is just that they are mutually contradictory. We can replace them with something like P1 = the sky is blue, P2 = the sky is not blue, and be in the same position as we are now. Maybe something like that is in fact a cleaner way to formulate this. |
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No. |
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Last edited by Malac Reborn; 03-28-2012 at 04:26 PM.
I stomp on your ideas.
Doesn't a contradiction of premises automatically prove that not both premises are true? It seems like the rule is purely hypothetical. The claimed rule would make more sense if it were that if two premises were true and in contradiction, anything could be the case. Such an absurd situation would prove metaphysical chaos and that anything can be the case because reality is not constrained by metaphysical order? |
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Last edited by Universal Mind; 03-28-2012 at 11:10 PM.
How do you know you are not dreaming right now?
That is essentially what it does say. Another way to phrase this would be: if you accept both of the contradictory premises to be true, it can be shown that you must also accept any other arbitrary proposition as true (if you are to be logically consistent). Obviously if you reject one of the premises, then you are not obligated to accept any conclusion that follows from the argument. This phrasing frames the issue in terms of argumentation rather than in terms of what "really is" or is not the case, but it is the same issue. |
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I simply looked at it in the sense of ~(A * B) //valid argument's conditions |
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Last edited by Malac Reborn; 03-29-2012 at 03:58 AM.
I stomp on your ideas.
I think we're on the same page but I can't tell for sure. What are you using A and B for exactly? |
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A is a constant for "the argument's conclusion is false," and B for "the argument's premises are all true." If I would allow a biconditional, then attached to them would remain C for "the argument is valid." So, its extended logical form is ~(p&q)<->r, substituted by the sentence ~(A&B)<->C. |
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Last edited by Malac Reborn; 03-29-2012 at 03:33 PM.
I stomp on your ideas.
It is impossible for both premises to be true. One must be true while the other one is false. There is no way to know which is which. Suppose premise 1 is true and premise 2 is false. What is the problem? Suppose premise 2 is true and premise 1 is false. What is the problem? The situation turns into a philosophical clusterfuck only under the assumption that both are true or both are false. |
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How do you know you are not dreaming right now?
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Previously PhilosopherStoned
Yeah, this ^ |
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Last edited by Wolfwood; 03-30-2012 at 02:04 AM.
This is a fascinating Wikipedia article on the "Liar Paradox," which is essentially, "This statement is false." The article does not address the paradox this thread is about specifically, but it involves analysis of many of the related issues. |
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Last edited by Universal Mind; 04-01-2012 at 09:40 PM.
How do you know you are not dreaming right now?
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