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The Collaborative International Dictionary
Antimetabole

Antimetabole \An`ti*me*tab"o*le\, n. [L., fr. Gr. ?.] (Rhet.) A figure in which the same words or ideas are repeated in transposed order. [1913 Webster] ||

Douglas Harper's Etymology Dictionary
antimetabole

1590s, from Greek antimetabole, from anti- "opposite" (see anti-) + metabole "turning about" (see metabolism).

Wiktionary
antimetabole

n. (context rhetoric English) The technique of reversal, where accentuated by reversal of words, actions or grammatical structure.

Wikipedia
Antimetabole

In rhetoric, antimetabole is the repetition of words in successive clauses, but in transposed order (e.g., "I know what I like, and I like what I know"). It is identical to the modern sense of chiasmus, although the classical chiasmus did not necessarily use repetition, but only in some cases. An easier way of understanding what an antimetabole means is comparing it to the commutative property of addition and multiplication. This means that for example, a + b = b + a. In terms of applying this property to language, an example would be, dance to live, not live to dance. Also an antimetabole does not just have to be simple words switched around, they can also be clauses placed in the middle of sentences that are reversed. For example, “Some people say I am bad at mathematics because it is not my favorite subject, but in reality, mathematics is not my favorite subject because I am bad at it.” An antimetabole is also said to be a little too predictive because it is easy to reverse the key term, but they pose questions that one usually would not think of if the phrase was just asked or said the initial way.