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The fallacy of the slippery slope claims that, if you take one step in a certain direction, you will get yourself into a series of sticky situations from which you will be unable to extricate yourself.  You take one step onto the slippery slope and you'll end up falling all the way down. This fallacy ignores treats all similar situations the same and fails to note that we are free to assess and judge each particular situation independently, if we so choose

There are 3 basic types of slippery slope arguments:

  1.  Arguments having to do with the setting of precedents, such as was used by the defense attorney in Roe-vs-Wade.
  2. Heap Arguments.  Mirabel's bald man paradox is an example of this.  The fallacy here is the vagueness inherent in a certain term (in this case, 'bald')
  3. The snowball effect.  This argument is used a lot, most prominently in debates over euthanasia.