The internet seems to be a fan of being overreaching in proclaiming fallacies in my experience. Sometimes it feels like you can find at least one misuse of "ad

The internet seems to be a fan of being overreaching in proclaiming fallacies in my experience. Sometimes it feels like you can find at least one misuse of "ad hominem" on every comment thread on reasonably popular sites. Similarly, many people like to dismiss arguments by just saying "slippery slope" and moving on. As you mentioned, slippery slopes are not inherently invalid. In fact, the real fallacious use of a slippery slope is hardly related to it being a slippery slope at all! Assume a slope A->B->...->Z. Further, assume that each step of this chain is known to be true with 100% accuracy. That is to say that we can perfectly predict that if A happens then B will happen and if Q happens R will happen. Thus, simple transitivity shows that if A will happen Z will definitely happen. If Z is complete destruction of the Earth you probably won't find many people saying that it will be perfectly okay if we do A because slippery slopes are invalid. However, slippery slope arguments often have a much smaller probability of occurring at each step of the chain. You often get things like "if we don't have a death penalty then people won't be afraid of killing people so murder rates will go up so you'll get pregnant and die". Clearly there is no part of this chain that occurs with probability 1 (except, as Mean Girls tells us, getting pregnant->death). In fact, most of the chain is fairly low probability and composing them as such makes it even smaller. To make this a bit clearer again, let's take our A->B->...->Z chain and make each step of the chain have a .9 probability. If A happens, B will occur with .75 chance and if Q happens, R will occur with .75 chance. Since there are 25 hops on this we can see that the probability of Z occurring given A is actually .75^25 = .00075 (ish). Even if each individual step seems reasonable (I mean, hey, it will happen 3 out of 4 times!) the full composition is just laughably unlikely. However, it seems that GP was actually talking about a continuum fallacy rather than a slippery slope as we've discussed.