Inconsistency
An assertion includes more one proposition or presupposition such that they cannot all be true. In such a case, the propositions may be contradictories or they may be contraries.
Examples
Equal Opportunity or Affirmative Action
Here is the University of Michigan’s Non-Discrimination Policy Notice: “The University of Michigan, as an equal opportunity/affirmative action employer, complies with all applicable federal and state laws regarding nondiscrimination and affirmative action.” Is it logically consistent to be both an ‘equal opportunity employer’ and an ‘affirmative action employer’?
Mark J. Perry, AEIdeas (May 6, 2013).
John is taller than Jake, and Jake is taller than Fred, while Fred is taller than John.
Prohibiting or Facilitating Illegal Drug Use
Karl Benzio is a Christian psychiatrist and a former addict. He says safe injection sites are logically inconsistent. “You’re giving a mixed message, you’re sort of … saying no, but you’re shaking your head yes to somebody. It’s not okay to use, but we’re gonna allow you to use here and we’re gonna provide safety for you to use.”
Anna Johansen Brown and Karl Benzio, “Preventing overdoses or enabling addiction?” (November 5, 2019).
This Statement Survived, but It’s Not True
Philosopher John Gray writes, “If Darwin’s theory of natural selection is true,… the human mind serves evolutionary success, not truth.” What is the contradiction in that statement? Gray has essentially said, if Darwin’s theory is true, then it “serves evolutionary success, not truth.” In other words, if Darwin’s theory is true, then it is not true. Self-referential absurdity is akin to the well-known liar’s paradox: “This statement is a lie.” If the statement is true, then (as it says) it is not true, but a lie.
Nancy Pearcey, “Why Evolutionary Theory Cannot Survive Itself” at Evolution News (March 8, 2015).
There are no English sentences.
Critique
Assume that one of the statements is true, and then use it as a premise to show that one of the other statements is false.