The slippery slope argument counsels against some contemplate action (or inaction) on the ground that, once taken, it will be a first step in a sequence of events that will be difficult to resist and will (or may or must) lead to some dangerous (or undesirable or disastrous) outcome in the end.
Example-once you allow euthanasia in any form, such as the withdrawal of heroic treatments of dying patients in hospitals, then (through erosion of respect for human life), you will eventually wind up with a totalitarian state where old, feeble, or politically troublesome individuals are routinely eliminated.
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