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  1. If the arguments have the same conclusions, but the premises in one argument contradict the premises in another argument, then these arguments cannot be used together. I am right?

  2. For example I have two convincing arguments to justify belief in M:

I have two arguments to justify my belief in M.

Argument A and argument B have the same conclusion, but the premises of argument A contradict the premises of argument B, so

I cannot use them together at the same time because they would contradict each other.

Can I use these two arguments separately when I need to? If I want to use argument A, I stop using argument B and start using argument A.

If I want to use argument B, I stop using argument A and start using argument B.

I want to know if I can do this or if I need to choose only one argument.

Will it be rational or not? Will there be any contradictions or not?

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  • Weloccme to SE. I suggest you lay out what you think the premises of each argument are so that we can see where they contradict each other - preferably quoting a source for each argument. Then we'll be better able to see why you say they contradict each other.
    – Ludwig V
    Jul 19, 2023 at 18:00
  • thank you sir I don't know if these premises contradict each other. I wanted to ask if such a situation arises, what to do in such a case.
    – Arnold
    Jul 19, 2023 at 18:21
  • I use common sense and phenomenal conservatism to justify my belief in the existence of other minds: 1. It seems obvious to us that other people have minds. 2. We have no reason to doubt the existence of other minds. 3. So other people have minds, until we have reason to doubt it.
    – Arnold
    Jul 19, 2023 at 18:27
  • IBE argument: 1. Other people's behavior is similar to mine. 2. My mind is responsible for my behavior. 3. The best explanation for the behavior I observe in other people is that other people have minds.
    – Arnold
    Jul 19, 2023 at 18:30
  • I do not see contradictions in these arguments and I believe that they can be used together. But I want to know what to do when contradictions appear in these arguments?
    – Arnold
    Jul 19, 2023 at 18:31

2 Answers 2

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The only time I can think of where you would want to present arguments with mutually exclusive premises and the same conclusion is if you are writing a persuasive essay. For example, if my intention is to convince people that [BLANK] is immoral, then I could write: "Aristotle would say [BLANK] is immoral because... Kant would say [BLANK] is immoral because... Mill would say [BLANK] is immoral because..." Since I do not know which of these positions my audience will subscribe to, by presenting multiple arguments I am ensuring at least one relevant argument will read.

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  • I have two arguments to justify my belief in M. Argument A and argument B have the same conclusion, but the premises of argument A contradict the premises of argument B, so I cannot use them together at the same time because they would contradict each other. Can I use these two arguments separately when I need to? If I want to use argument A, I stop using argument B and start using argument A. If I want to use argument B, I stop using argument A and start using argument B. I want to know if I can do this or if I need to choose only one argument and use only that one.
    – Arnold
    Jul 19, 2023 at 18:56
  • 2
    One way of looking at your problem would start from the definitions that an argument is sound if and only if it is valid and the premisses are true and that two statements contradict each other if and only if they cannot both be true. It follows, I think, that if the premisses of argument A and argument B contradict each other, they cannot both be true. Hence, the arguments cannot both be sound even if they are both valid. How this applies to actual cases is complicated, but when people offer multiple arguments with different premisses, there is always a suspicion of special pleading.
    – Ludwig V
    Jul 20, 2023 at 7:34
  • I think that is the best comment on this thread @LudwigV
    – user66760
    Jul 22, 2023 at 19:57
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For what it's worth.

Let the two contradictory premises be P and ~P. Let the conclusion be M

  1. P --> M
  2. ~P --> M
  3. ~M --> ~P [1 Contraposition]
  4. ~M --> M [2, 3 Hypothetical Syllogism]
  5. ~~M v M [4 Material Implication]
  6. M v M [5 Double Negation]
  7. M [6 Tautology]

  1. P v ~P [Law of the Excluded Middle]
  2. M v M [1, 2, 8 Constructive Dilemma]
  3. M [9 Tautology]

Remember, this is not the same as using the contradiction P & ~P

  1. P & ~P [Contradiction]
  2. P --> M
  3. ~P --> M
  4. P [1 Simplification]
  5. M [2, 4 Modus Ponens]
  6. ~P [1 Simplification]
  7. M [3, 6 Modus Ponens]

Because we can do the following in this case
8. P v ~M [4 Addition]
9. ~M [3, 8 Disjunctive Syllogism]
Basically, you've contradicted yourself. Kind courtesy of ex contradictione sequitur quodlibet

Kindly, take a closer look at relevance, logically speaking that is.

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