The slippery slope argument is a logical fallacy in which a person asserts that some resultant event must inevitably happen from the occurance of a triggering event without any form of argument for the inevitability of the resultant event in question. Generally speaking, the triggering event normally comes in the form of exceptions to a rule, or rules that depend on fine distinctions. The flow of the argument says that if a person makes any exceptions to a rule, or if the person makes rules that depend on fine distinctions, the inevitable result would then be all of the other people will end up ignoring the rule or rules entirely simply because it is inevitable that they won't accept the difference between the exception and everything else. In other words, if the person allows any exceptions to a rule, it will create a slope away from the absoluteness of the rule, and with which the people will slide down further and further until they will not obey the rule at all. This fallacy is also known as the camel's nose. This follows the phenomenon that if a camel is allowed to put its nose into a tent, the whole camel will ultimately be in the tent very soon.
In most cases, there is a series of progressions between the resultant event and the triggering event and no logical reasons are generally given as to why the intervening progressions will simply be bypassed. This argument flows in the following manner:
1) Event A has occurred (or will or might occur).
2) Therefore event B will inevitably happen.
This above reasoning is fallacious because there is no reason to believe that event B must inevitably follow from event A without an argument for such a claim. This is especially clear in cases in which there is a significant number of progressions between the resultant event and the triggering event. There is old english rhyme which originated for the purpose of encouraging children to apply so-called logical progression to the consequences of their actions. The rhyme is often used to gently chastise a child whilst explaining the possible events that may follow a thoughtless act. However, when applied to the slippery slope argument, the rhyme happens to illustrate the fallacy fairly well too.
For want of a nail
For want of a nail, the shoe was lost.
For want of a shoe, the horse was lost.
For want of a horse, the rider was lost.
For want of a rider, the battle was lost.
For want of a battle, the kingdom was lost.
And all for the want of a horseshoe nail.
Generally speaking again, the presumption behind the slippery slope argument is that if the person makes any exceptions to a rule, the other people will think that the rule is arbitrary to begin with and will see no reason to follow it at all. Hence, any exceptions undermine respect for a rule, and thus eventually lead to the rule's not being followed at all. Another argument is that people generally cannot make fine distinctions, so if you make an exception to a rule, the other people will think the person has shown the rule to be flawed and therefore unnecessary to follow.
N.B. I have previously used the english rhyme "For want of a nail" to illustrate the butterfly effect (please kindly refer to my previous post "The Butterfly Effect"). Come to think of it, the Butterfly Effect and the Slippery Slope Argument seem to run in the same direction.