One of the FallaciousArgument''''''s.

Argumentation that A is bad, because A might lead to B, and B to C, and we all know C is very bad.

It's a logical fallacy because the chain A -> B -> C isn't deterministic, because it might be possible to stop (or branch) somewhere along the line.  A chain that ''is'' deterministic wouldn't be a fallacy and wouldn't need to be referred to as a SlipperySlope.

Plus, it can happen in both directions. Things can potentially slide toward super-conservative political-wise or super-progressive, for example. Thus, both sides could potentially apply if it's permitted.

Example: ''"If we legalize playing Unreal Tournament in public, we will have to legalize playing it with real weapons as well, and then people will start to die. Nobody can want this."'' - The fallacy here is that it would be very well possible to legalize playing Unreal Tournament in public, but not with real weapons.

SlipperySlope, as a fallacy, comes when you argue against something because of a hypothetical outcome, but it's important to remember that some slopes are slipperier than others, i.e. a high probability outcome may be just as good (i.e. prudent to avoid) as a necessary outcome. E.g. with some people, when you give an inch, very often they will take a mile. Don't dismiss fears of a slippery slope just because it's not valid according to formal logic. Ever increasing (but only in small notches) sales tax, and ever-lengthening "limited terms" are examples of slopes which really can be slippery.

This type of argumentation is also often used in combination with BadStatistics. For instance, "smoking pot leads to shooting heroin, because a survey showed that 90% of all heroin addicts had used marijuana earlier". Maybe it does, maybe it doesn't, but the results from the survey do not prove causation, they merely show correlation; another survey shows that "99% of all alcoholics have drunk water at an earlier age." Does drinking water lead to abusing alcohol? Obviously not.

Discussion moved to SlipperySlopeDiscussion
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Re: "but it's important to remember that some slopes are slipperier than others"

Then it's the burden of the side using SlipperySlope to demonstrate that one side is more slippery than the other. Otherwise, the default is to assume each side is just as slippery, cancelling out SlipperySlope.

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See also: 
* MistakenExtrapolation 
* FallaciousArgument