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Adjective(1) (2) of words or propositions so related that both cannot be true and both cannot be false(3) that confounds or contradicts or confuses(4) in disagreement(5) unable to be both true at the same time(6) antagonistic
Noun(1) (2) two propositions are contradictories if both cannot be true (or both cannot be false) at the same time

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(1) This time, he is placing his bets on the contradictory premise of giving employees access to corporate data in a secure yet simple way.(2) Despite this, the Committee reached conclusions that are contradictory and that were not based on a comprehensive review of the available literature.(3) The ability of one and the same human being to hold on to quite contradictory and even sharply opposed ideas is well known and has had many celebrated illustrations.(4) If we are not convinced that our own contradictory belief is true, then we are not really u2018toleratingu2019 the other's belief.(5) For any pair of contradictory premises, one must be true and the other false.(6) One wonders how all of these expansive and apparently contradictory conclusions fell within the committee's assigned sphere of responsibility.(7) The basic law of logic is the principle of non-contradiction, namely that it is contradictory to say that something can both be and not be at the same time.(8) I suspect the resulting product would be contradictory - different reporters seeing different realities.(9) Even within weeks, or given years, he'll go back and forth on the very same issue and express points of view that are mutually completely contradictory .(10) An individual can also say contradictory things at different times.(11) It is always difficult to explain to students of politics how the core concepts of liberty and equality are contradictory yet mutually constitutive.(12) In addition, human behavior is highly complex, contradictory , and remarkably unpredictable.(13) Again activism and commerce are neither contradictory nor mutually exclusive.(14) Roche has attacked the heritage group over what he described as its inconsistent and contradictory attitudes towards different projects.(15) There is also an apparently contradictory but equally strong behavioural imperative, which says that eating in groups is competitive, and that you need to protect your stash.(16) I'm sure that we could even come up with contradictory principles based on this kind of reasoning.