Fallacy of exclusive premises

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The fallacy of exclusive premises is a syllogistic fallacy committed in a categorical syllogism that is invalid because both of its premises are negative.

Example of an EOO-4 invalid syllogism

E Proposition: No cats are dogs.
O Proposition: Some dogs are not pets.
O Proposition: Therefore, some pets are not cats.


Explanation of Example 1:

To a layman, this may seem like a logical conclusion, as it appears to be logically derived that if Some dogs are not pets, then surely some are pets, otherwise, the premise would have stated "No Dogs are pets", and if some pets are dogs, then not all pets can be cats, thus, some pets are not cats. However, this breaks down when you apply the same logic to the conclusion: If some pets are not cats then it would seem logical to state that some pets are cats. But this is not supported by either premise. Cats not being dogs, and the state of dogs as either pets or not, has nothing to do with whether cats are pets. Two negative premises cannot give a logical foundation for a conclusion, as they will invariably be independent statements that cannot be directly related, thus the name 'Exclusive Premises'. It is made more clear when the subjects in the argument are more clearly unrelated such as the following:


Additional Example of an EOO-4 invalid syllogism

E Proposition: No planets are dogs.
O Proposition: Some dogs are not pets.
O Proposition: Therefore, some pets are not planets.


Explanation of Example 2:

In this example we can more clearly see that the physical difference between a dog and a planet has no correlation to the domestication of dogs. The two premises are exclusive and the subsequent conclusion is nonsense, as the transpose would imply that some pets are planets.


Conclusion:

It is important to note that the truthfulness of the final statement is not relevant in this fallacy. The conclusion of the first example is true, while the final statement in the second is clearly ridiculous; however, both are argued on fallacious logic and would not hold up as valid arguments.

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This article is based on material taken from the Free On-line Dictionary of Computing prior to 1 November 2008 and incorporated under the "relicensing" terms of the GFDL, version 1.3 or later.