Incompatible Premises

Based on the quote from Attacking Faulty Reasoning I've surmised a couple of rules of incompatible premises.

Another structural feature of an argument that could render it fatally flawed would be one whose premises are incompatible with one another. And an argument that has such premises is one from which any conclusion, no matter how outrageous, can be drawn.T. Edward Damer, Attacking Faulty Reasoning

Rule 1: Whenever there exist an argument with two incompatible premises, there will also exist two corresponding incompatible conclusions.

Proposition
Premise 1 A
Premise 2 NOT A
Conclusion
Conclusion 1 A
Conclusion 2 NOT A

In other words, whenever an argument contains a contradiction in its premises, it will naturally also contain a contradiction in its conclusion; conflicting premises will result in conflicting conclusions. In the table above there exists two premises that contradict one another and also two conclusions that contradict each other that when taken together are both simultaneously the conclusion to the proposition. Even with arguments where it is apparent there is a contradiction, it may not always be apparent that the contradiction can result in a conclusion other than the one being advocated for.

Rule 2: Whenever there exists an argument with two incompatible premises, any compatible premises are irrelevant to the conclusion.

Proposition
Premise 1 A
Premise 2 NOT A
Premise 3 B
Conclusion
Conclusion 1 A
Conclusion 2 NOT A

In other words, whenever an argument contains a contradiction, its conclusion will be contradictory regardless of any additional premises. It makes no difference what side of the contradiction the additional premises are on: the argument still results in a contradiction.

Rule 3: Whenever there exists an argument with two incompatible premises, any subpremises to the contradicting premises are irrelevant to the conclusion.

Proposition
Premise 1 A
Premise 1 Subpremise 1 AA
Premise 2 NOT A
Conclusion
Conclusion 1 A
Conclusion 2 NOT A

In other words, whenever an argument contains a contradiction, any subpremises that add additional support to either contradicting premise are irrelevant to the resulting conclusion. The subpremise to a contradicting premise may add additional support for that contradicting premise, but it is not relevant to the conclusion of the argument which ends up in a contradiction.

Rule 4: Whenever there exists an argument with incompatible premises, each contradicting conclusion is equally valid or contradictory as the others.

In other words, if there is presented an argument that has a contradiction, either side of the contradiction is an equally valid conclusion to the argument. One side of the contradiction can be as equally contradictory as the other side.

January 28th, 2014

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