Reductio ad absurdum" reduction to absurdity"

Reductio ad absurdum (Latin: "reduction to absurdity"), also known as argumentum ad absurdum (Latin: argument to absurdity), is a common form of argument which seeks to demonstrate that a statement is true by showing that a false, untenable, or absurd result follows from its denial,^[1] or in turn to demonstrate that a statement is false by showing that a false, untenable, or absurd result follows from its acceptance. First appearing in classical Greek philosophy (the Latin term derives from the Greek "εις άτοπον απαγωγή" or eis atopon apagoge, "reduction to the impossible", for example in Aristotle's Prior Analytics),^[1] this technique has been used throughout history in both formal mathematical and philosophical reasoning, as well as informal debate.

The "absurd" conclusion of a reductio ad absurdum argument can take a range of forms:

Rocks have weight, otherwise we would see them floating in the air.

Society must have laws, otherwise there would be chaos.

There is no smallest positive rational number, because if there were, it could be divided by two to get a smaller one.

The first example above argues that the denial of the assertion would have a ridiculous result, against the evidence of our senses. The second argues that the denial would have an untenable result: unacceptable, unworkable or unpleasant for society. The third is a mathematical proof by contradiction, arguing that the denial of the assertion would result in a logical contradiction (there is a smallest rational number and yet there is a rational number smaller than it).

Straw Man argument

A false argument similar to reductio ad absurdum often seen in polemical debate is the straw man logical fallacy.^[5][6] A straw man argument attempts to refute a given proposition by showing that a slightly different or inaccurate form of the proposition (the "straw man") has an absurd, unpleasant, or ridiculous consequence, relying on the audience not to notice that the argument does not actually apply to the original proposition. For example, in a 1977 appeal of a U.S. bank robbery conviction, a prosecuting attorney said in his closing argument^[7]

I submit to you that if you can't take this evidence and find these defendants guilty on this evidence then we might as well open all the banks and say, 'Come on and get the money, boys', because we'll never be able to convict them.

The prosecutor was tacitly equating the failure to convict the defendants in one particular trial with the inability to convict any bank robbers, a situation with self-evident unpleasant consequences but very little connection with the outcome of the trial.
Wikipedia