Lecture Notes by Christopher Lay
Los Angeles Pierce College
Department of History, Philosophy, and Sociology
Mathew Van Cleave's 2016 Introduction to Logic and Critical Thinking
https://open.umn.edu/opentextbooks/BookDetail.aspx?bookId=457
Chapter 4 "Informal fallacies", § 2 "Slippery Slope Fallacies," Sub-§ 1 "Conceptual Slippery Slope Fallacy"
Recall: "Slippery slope fallacies depend on the concept of vagueness."
The Spirit of the Worry
"[J]ust because we cannot draw a distinction between A and B, and we cannot draw a distinction between B and C, it doesn’t mean we cannot draw a distinction between A and C."
The Grains of Sand Example
"It may be true that there is no essential difference between 499 grains of sand and 500 grains of sand. But even if that is so, it doesn’t follow that there is no difference between 1 grain of sand and 5 billion grains of sand."
Age Limits Example
1) "It is illegal for anyone under 21 to drink alcohol."
2) "But there is no difference between someone who is 21 and someone who is 20 years 11 months old."
3) "So there is nothing wrong with someone who is 20 years and 11 months old drinking." (From 1 & 2)
4) "[T]here is no real distinction between being one month older and one month younger"
5) "[T]here shouldn’t be anything wrong with drinking at any age."
6) "Therefore, there is nothing wrong with allowing a 10 year old to drink alcohol." (From 3, 4, & 5)
The Problem
Just because it can be difficult to distinguish between two small difference, "it doesn’t follow from this that there is no distinction to be drawn between" other differences.
"[J]ust because the boundaries between very similar things on a spectrum [in this instance, of ages] are vague, it doesn’t follow that there are no differences between any two things on that spectrum."
Identifying the Fallacy
"Whether or not one will identify an argument as committing a conceptual slippery slope fallacy, depends on the other things one believes about the world."
"Thus, whether or not a conceptual slippery slope fallacy has been committed will often be a matter of some debate. It will itself be vague."
"The issues here are subtle, sensitive, and complex, which is why it is difficult to determine whether there is any fallacy here or not."
"The difficulty of distinguishing instances of the conceptual slippery slope fallacy, and the fact that distinguishing it requires us to draw on our knowledge about the world, shows that the conceptual slippery slope fallacy is an informal fallacy."
Examples
Is this a fallacy?
Student: Can't you just bump my grade up to a 90%? It is an 89.9% now. There's no real difference between the two!
Professor: If I say that there is no difference between an 89.9% and a 90%, then isn't it also the case that there is no difference between an 89.9% and an 89.8%? But then isn't it also the case that there is no difference between an 89.8% and an 89.7%? But then isn't it also the case that there is no difference between an 89.7% and an 89.6%? But then isn't it also the case that there is no difference between an 89.6% and an 89.5%? But then isn't it also the case that there is no difference between an 89.5% and an 89.4%? But then isn't it also the case that there is no difference between an 89.4% and an 89.3%? But then isn't it also the case that there is no difference between an 89.3% and an 89.2%? But then isn't it also the case that there is no difference between an 89.2% and an 89.1%? But then isn't it also the case that there is no difference between an 89.1% and an 89%? But then isn't it also the case that there is no difference between an 89% and an 88.9%? So if you want a 90% because there's no real difference between it and the grade you got, an 89.9%, couldn't I just as easily give you an 88.9%? But if that's the case, then why not just give you a 78.9%?
Student: Ugh. Whatever.
Examples
Is this a fallacy?
You can't tell the difference between the beat in "Ice Ice Baby," by Vanilla Ice and "Under Pressure," by Queen and David Bowie. So, Vanilla Ice, Queen, and David Bowie are indistinguishable.