Slippery Slope
Arguing that one small step inevitably leads to a chain of worse consequences, without showing the steps actually connect.
Origin
The image — once you start sliding, you can't stop — is medieval at least, in writing about sin. As a named fallacy in English logic textbooks it dates to the early 20th century. The argument is not always wrong; sometimes a precedent really does open a real door. The fallacy is in asserting the chain without evidence.
Modern usage
The standard form of every drug-legalization, gun-control, free-speech, and gay-marriage debate. 'If we allow X, next we'll have Y, and then Z.' Often paired with the boiling-frog metaphor. Heavily used (and abused) in political writing, where the question of whether the slope is actually slippery is often the whole disagreement.
In the wild
If we let four-year-olds use tablets at dinner, soon they'll never learn to talk to anyone.— common usage (slippery-slope example)
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