Contradictory Premises. Conclusions are drawn from the interactions of premises: where two premises contradict each other, there can be no interaction and hence no conclusion. Similarly, if the definitions of two terms conflict with or exclude each other, then those two terms cannot be simultaneously ascribed to a single object or event. The classic example of contradictory premises is the question, "What will happen if an irresistible force meets an immovable object?" The problem here is that in a universe where an irresistible force has been defined to exist, there cannot also exist an immovable object, because then the force would not be irresistible. Conversely, if there is discovered or defined such an item as an immovable object, then by definition there can be no such thing as an irresistible force.
This fallacy's most popular appearance is in the form of a challenging question, because questions with contradictory premises are such brain teasers. In each case, though, no answer can be given because the premises cannot both be true.
* Into what shape of hole would a round square fit?
* If an object is all black and all white at the same time, what color is it?
* If an object is both stationary and traveling at an infinite rate of speed, how long will it take to meet itself?
* If God can do anything, can he make a stone so heavy that he cannot lift it?
* If God is all powerful, can he put himself out of existence and come back with twice the power he had before?
2006-06-17 23:52:24
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answer #1
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answered by Joanna L 3
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Hi I'm not quite sure what you mean by 'contradictory inference'. Inferences cannot be contradictory. Inferences are valid or invalid; statements are contradictory or non-contradictory. Do you have in mind something like this: P implies Q; P implies ~Q. Therefore, ~P? Any argument of this form is valid: (1) 1. P > Q Premise (2) 2. P ~ ~Q Premise (3) 3. P Assumption for RAA (1,3) 4. Q 1,3 MP (2,3) 5. ~Q 2,3 MP (1,2,3) 6. Q & ~Q 4,5 &I (1,2) 7. ~P 3,6 RAA Or is it this that you have in mind: P implies Q & ~Q; ~P implies Q & ~Q. Thus, ~P & ~~P, and, hence, P & ~P? In classical logic, you can infer anything you like from a contradiction. Thus, by means of an argument with contradictory premises, you can, if you wish, deduce a contradiction. Indeed, if P implies a contradiction, and ~P implies a contradiction, then, assuming double negation elimination, P & ~P. (1) 1. P > (Q & ~Q) Premise (2) 2. ~P > (Q & ~Q) Premise (3) 3. P Assumption for RAA (1,3) 4. Q & ~Q 1,3 MP (1) 5. ~P 3,4 RAA (1,2) 6. Q & ~Q 2,5 MP (7) 7. ~(P & ~P) Assumption for RAA (1,2,7) 8. (Q & ~Q) & ~(P & ~P) 6,7 &I (1,2,7) 9. Q & ~Q 8 &E (1,2) 10. ~~(P & ~P) 7,9 RAA (1,2) 11. P & ~P 10 DNE Thus, P > (Q & ~Q) and ~P > (Q & ~Q) jointly entail P & ~P. Now, I don't see this as strange or problematic. Two statements A and B entail a third, C, just in case it is logically impossible that A and B should both be true while C is false. Clearly, P & ~P is false, and so either ~(P > (Q & ~Q)) or ~(~P > (Q & ~Q)) (i.e., either it is not the case that P implies Q & ~Q, or it is not the case that ~P implies Q & ~Q). Thus, so as long no contradiction is true, it will never be the case that P > (Q & ~Q) and ~P > (Q & ~Q) are both true, and so the argument above is valid: it is logically impossible that its premises should ever be true at the same time, and so it is logically impossible that its premises should ever be true while its conclusion is false. I hope that this has helped a little. If I've misunderstood your question, email me and I'll have another go. Good luck :-)
2016-03-28 22:52:56
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answer #3
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answered by Anonymous
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Two propositions are contradictory if one is the denial or negation of the other- that is, if they can not both be true and cannot be false. Two standard form categorical form propositions that have the same subject and predicate terms but differ from each other in both quantity and quality are contradictories. " All judges are lawyers". is in contradictory to " some judges are not lawyers ". One is true one is false. They cannot both be true:; they cannot both be false. All S is P. Some S is not P. Try to study Square of Oppositions: COntradictories, Contraries, SUbcontraries and superalterns.
2016-03-18 05:59:47
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answer #5
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answered by Karen 4
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