The "slippery slope" argument format (also known as the "camel's nose in the tent," the "give an inch," the "crack in the foundation", and other names) is essentially that if you make any exceptions to a rule, or if you make rules that depend on fine distinctions, pretty soon people will be ignoring the rule or rules entirely because they won't accept the difference between the exception and everything else. "If you allow exceptions to a rule, it creates a slope away from the absoluteness of the rule, down which people will slide further and further until they will not obey the rule at all." "If you give people an inch, they will take a mile" or "If you let the camel put its nose into the tent, pretty soon the whole camel will be in your tent." As I write this the most recent application I have seen of the argument is that "if we allow embryonic stem cell research, which sacrifices early-stage embryos, the next thing will be that infanticide and euthanasia of the terminably ill will be permitted so that we can use their body parts for research or cures. If you don't hold all life to be sacred, then no life will be held to be sacred."
The slippery slope argument is clearly invalid if it is meant to be a point of logic, for it does not follow that "if b is an exception to A, then no part of A is true." Specific exceptions to a rule or principle do not in any way logically imply that the rule is otherwise false or never justifiably applicable in any cases. In fact, calling something an "exception" points out that only it is the relevant act that the rule does not cover. If, for example, a pharmaceutical drug should be used only by people who have asthma, that does not imply people should also take it for arthritis or pregnancy. Permitting stem cell research on embryos does not logically imply that sacrificing infants or terminally ill patients is acceptable.
It appears the argument is meant to be more an argument about people's psychology, and, spelled out, it seems to be something more like "if you make any exceptions to a rule, particularly a cherished or time-honored rule, people will think the rule 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. Or another intended argument might be "people cannot generally make fine distinctions, so if you make an exception to a (time-honored) rule, people will think you have shown the rule to be flawed and therefore unnecessary to follow."
A slightly different, and more sophisticated version of the principle
might be "if you make exceptions to a rule, people will generalize the
reasons for that exception and apply them to other aspects of the rule
to which those generalizations will also apply."
In the embryo issue, the argument would be that "if you allow embryonic
stem cell research people will see that defenseless human life has only
instrumental value --value for helping others-- so nothing will stop people
from wanting to kill infants or people with terminal diseases to help others."
Or it might be phrased as "if you allow embryonic stem cell research because
embryos are not viable on their own, then you will end up allowing infanticide
and termination of the lives of the terminally ill because they are not
viable on their own either." I will deal with this kind of version
of the slippery slope argument last...........