Well...I don't know. Logic and argument aren't the same thing, and contemporary rhetorics aren't as formal as logic, by design. Technically, the slippery slope fallacy doesn't really try to connect random series of events. The problem is the assumption of evidence for the worst possible outcome. The primary problem there is bad faith, not inherent consequence - which, I'd like to note, suggests a deterministic mechanism.
And considering the strong hint of panpsychism and anthropo-skepticism in this thread, I don't think causality should be assumed; I mean, you can assume for the purposes of your argument, but you'll never agree to terms. Non-causality in metaphysics and epistemology are pretty well-established (and still current), so statements like "we can all assume cause and effect" aren't really true for all metaphysical systems. If you think that all information or matter is similar, or that all is reducible to information or a matter, then cause and effect disappears or becomes only correlative.
Lively discussion. Good stuff.
Logic is directly related to arguments. Logic is used to determine whether or not arguments are sound and valid in an argument. Ven diagrams, truth tables, and proofs are all part of logic, and are used to determine an arguments soundness and validity.
The slippery slope is an argumental fallacy that debunks the random series of events. The user who linked these events is guilty of using a slippery slope. Perhaps my wording left a bit to be desired.
No one, especially me, has assumed anything in reference to cause and effect. I do not use the word assume unless absolutely necessary. Assumption is the whole problem in a discussion like this. Once someone assumes something, fact gets thrown out the window and any answer then becomes acceptable. Why? Because unknown terms have been introduced.
Every effect has a cause. Correlation deals with relationships. Not guarantees. Example: There is a correlation between smoking and lung cancer. But lung cancer is not guaranteed to a smoker, nor is it necessarily caused by smoking. Non smokers can get lung cancer too.