Kettle logic is a logical fallacy and rhetorical error in which one uses multiple arguments which contradict each other. Traditionally, arguments of this form would simply have been accused of the fallacy of inconsistency or internal contradiction, and in fact the more blatant form of argument that is likely to be identified as kettle logic is rarely seen in the type of debate in which people care about looking for or naming fallacies.
The term was coined by Sigmund Freud, who used an old joke to illustrate the function of contradictions in dreams and in humor:
A man who was accused by his neighbor of having returned a kettle in a damaged condition. He claimed that this was impossible, because one, he had returned the kettle undamaged; two, the kettle was already damaged when he borrowed it; and three, he had never borrowed the kettle in the first place.
Kettle logic can, of course, be much more subtle than this. It is arguable that the argument from evil is the explication of the kettle logic inherent in the JCI God. However, it is much more common for the term kettle logic to be applied to less formal claims in the political sphere, in which it is frequently possible to collect all of a politician's claims on a given issue and find contradictions there within.
A form of this sort of argument is used in law; a person may argue logically inconsistent alternatives in alternative pleading; this is not truly kettle logic, however, as the argument is a form of either/or, not 'and also'.