Slippery slope

In the contexts of debate or of rhetoric, the phrase slippery slope, also appearing as the thin end of the wedge or the camel's nose, refers both to an argument about the likelihood of one event given another, and to a fallacy about the inevitability of one event given another. Invoking the "slippery slope" means predicting (without necessary justification) that one step in a process will lead unavoidably to a second (generally undesirable) step.

The slippery slope as argument

The slippery-slope argument occurs in the following context: A, B denote events, situations, policies, actions etc. Within this context, the proposer posits the following inferential scheme:

If A occurs
:then the chances increase that B will occur

The argument takes on one of various semantical forms:

In one form, the proposer suggests that by making a move in a particular direction, we start down a "slippery slope". Having started down the metaphorical slope, it appears likely that we will continue in the same direction (the arguer usually sees the direction as a negative direction; hence the "sliding downwards" metaphor).

Another form appears more static, arguing that admitting or permitting A leads to admitting or permitting B, by following a long chain of logical relationships.

Examples

For example, many civil libertarians argue that even minor increases in government authority, by making them seem less noteworthy, make future increases in that authority more likely: what would once have seemed a huge power grab, the argument goes, now becomes seen as just another incremental increase, and thus appears more palatable (see here for a specific example).

Eugene Volokh's Mechanisms of the Slippery Slope (PDF version) analyzes various types of such slippage. Volokh uses the example "gun registration may lead to gun confiscation" to describe six types of slippage:

Cost-lowering: Once all gun-owners have registered their firearms, the government will know exactly from whom to confiscate them.
Legal rule combination: Previously the government might need to search every house to confiscate guns, and such a search would violate the Fourth Amendment of the Constitution of the United States. Registration would eliminate that problem.
Attitude altering: People may begin to think of gun ownership as a privilege rather than a right, and thus regard gun confiscation less seriously.
Small change tolerance: People may ignore gun registration because it constitutes just a small change, but when combined with other small changes, it could lead to the equivalent of confiscation.
Political power: The hassle of registration may reduce the number of gun owners, and thus the political power of the gun-ownership bloc.
Political momentum: Once the government has passed this gun law it becomes easier to pass other gun laws, including laws like confiscation.
The slippery slope as fallacy

The slippery slope argument may or may not involve a fallacy (see the discussion on the two interpretative paradigms below: the momentum paradigm and the inductive paradigm). However, the slippery slope claim requires independent justification to connect the inevitability of B to an occurrence of A. Otherwise the slippery slope scheme merely serves as a device of sophistry.

Often proponents of a "slippery slope" contention propose a long series of intermediate events as the mechanism of connection leading from A to B. The "camel's nose" provides one example of this: once a camel has managed to place its nose within a tent, the rest of the camel will inevitably follow. In this sense the slippery slope resembles the genetic fallacy, but in reverse.

As a simple example of how an appealing slippery slope argument can be provably unsound, suppose that whenever a tree falls down, it has a 95% chance of knocking over another tree. We might conclude that soon a great many trees would fall, but this is not the case. There is a 5% chance that only one tree will fall, a 9.75% chance that two or less trees will fall, and a 92% chance that 50 or less trees will fall. On average, only 20 trees will fall. In the absence of some momentum factor that makes later trees more likely to fall than earlier ones, this "domino effect" quickly curbs itself.

Arguers also often link the slippery slope fallacy to the straw man fallacy in order to attack the initial position:

A has occurred (or will or might occur); therefore
B will inevitably happen. (slippery slope)
B is wrong; therefore
A is wrong. (straw man)

This form of argument often provides evaluative judgements on social change: once an exception is made to some rule, nothing will hold back further, more egregious exceptions to that rule.

Note that these arguments may indeed have validity, but they require some independent justification of the connection between their terms: otherwise the argument (as a logical tool) remains fallacious.

The "slippery slope" approach may also relate to the conjunction fallacy: with a long string of steps leading to an undesirable conclusion, the chance of all the steps actually occurring is actually less than the chance of any one individual step occurring alone.

Contemporary examples of the slippery slope fallacy may include:

If we allow women to abort their unborn children, then soon no life will be held sacred.
If we forbid partial-birth abortion, soon all abortion will become illegal.
If we allow gun registration, then gun confiscation will follow.
Use of 'soft' drugs such as cannabis will inevitably lead to addiction to 'harder' drugs such as heroin.
If we allow gay marriage, people will soon want to marry children and animals as well.
Supporting analogies

Several common analogies support slippery-slope arguments. Among these are analogies to physical momentum, to frictional forces and to mathematical induction.

Momentum analogy

In the momentum analogy, the occurrence of event A will initiate a process which will lead inevitably to occurrence of event B. The process may involve causal relationships between intermediate events, but in any case the slippery slope schema depends for its soundness on the validity of some analogue for the physical principle of momentum. This often takes the form of a domino theory or contagion formulation. The domino theory principle may indeed explain why a chain of dominos collapses, but an independent argument is necessary to explain why a similar principle would hold in other circumstances. To achieve this one might (for example) establish an abstract model for the terms that occur in the argument, in which the momentum principle obtains. This leaves showing the validity of the abstract model as a separate intellectual exercise.

Frictional analogy

An analogy similar to the momentum analogy is based on friction. In physics, there is usually more frictional force against a nonmoving object (static friction) than against an already moving object (kinetic friction). Arguments that use this analogy assume that people's habits or inhibitions act in the same way. If a particular rule A is considered inviolable, some force akin to static friction is regarded as maintaining the status quo, preventing movement in the direction of abrogating A. If, on the other hand, an exception is made to A, the countervaling resistive force is akin to the weaker kinetic frictional force. Validity of this analogy requires an argument showing that the initial changes actually make further change in the direction of abrogating A easier.

Induction analogy

Another analogy resembles mathematical induction. Consider the context of making an evaluation (is the occurrence of the event harmful or not?) on each one of a class of events A₁, A₂, A₃,..., A_n. We assume that for each k, the event A_k is not much different from A_k+1, so that A_k has the same evaluation as A_k+1.

We deduce that for k = 1, 2, 3, ...,n the event A_k has the same evaluation as A₁.

Therefore A₁ should be considered harmful if A_n is considered harmful.

For example, the following arguments fit the slippery slope scheme with the inductive interpretation

If we grant a building permit to build a Mosque (Pentecostal Church, Temple) in our community, then there will be no bound on the number of building permits we will have to grant for Mosques (Pentecostal Churches, Temples) and the nature of this city will change. This argument instantiates the slippery slope scheme as follows: A_k is the situation in which k building permits are issued. One first argues that the situation of k permits is not significantly different from the one with k + 1 permits. Moreover, issuing permits to build 1000 Mosques (Pentecostal Churches, Temples) in a city of 300,000 will clearly change the nature of the community.
If we allow use of Spanish in this special class for immigrants, then there is no limit to the number of classes where we allow usage of Spanish.

Appropriately formulating the semantics of the slippery slope scheme can help in evaluating the soundness of the argument. In the na�ve presentation as an instance of mathematical induction, the argument does clearly have validity. However, in most real-world applications, including the two given above, this na�ve semantics fails because the inductive scheme fails for imprecisely defined predicates.