To want or expect to enjoy two desirable but mutually exclusive things simultaneously. To desire the benefits of two contradictory options without accepting the trade-offs.
This paradoxical phrase dates to the 16th century, originally stated as 'eat your cake and have it too,' which makes the logical impossibility clearer. The modern reversed version became standard by the 18th century, though it makes the meaning less obvious since one naturally has cake before eating it.
The original word order 'eat your cake and have it too' actually makes much more sense - once you've eaten the cake, you can't still have it! This phrase helped catch the Unabomber, as Ted Kaczynski used the original, less common phrasing in his manifesto, which helped FBI linguists identify him.
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