This page is in an early stage of writing.

Walking the path of a mental health patient when one has studied mathematical logic as a postgrad makes me quite aware of the assumptions people are making in their reasoning and that their approach depends upon.

A nice article to read is 'Do You Believe in Fairies, Unicorns, or the BMI by Keith Devlin (google 'keith devlin unicorn'):

• For example I found this PDF here but not the original article, so reproduced it on this wiki in case it goes missing in future.

Another by Devlin is this NPR artible, reproduced here so it doesn't disappear.

Logic notation

For implication, we use single arrows \(\rightarrow\).

Overview

• Ignoring assumptions: if you assume \(P\) and deduce \(Q\), then from that, removing the assumption \(P\), you can deduce \(P\rightarrow Q\), but you cannot deduce \(Q\) itself, even if you are unaware that your reasoning depends upon the assumption \(P\). The fallacy here is of the form \((P\rightarrow Q)\rightarrow Q\).
• Appeal to convenience: can be done with care, but see assumptions above. Just because "you can't see any other way of doing it" doesn't make your assumptions true, or your method correct, or your results valid.
• Comparing unlikes: just because two things are red doesn't mean that they are the same thing.
• Ignoring significant variables: just because two cars are red and we're interested in studying the effect of pain colour on car performance doesn't mean that the engine size doesn't matter.
• Separability of variables: assuming that two variables can be controlled independently, or that by isolating \(A\), and studying \(A\) in isolation; and then isolating \(B\) and studying \(B\) in isolation, you can then deduce valid results about what happens when both \(A\) and \(B\) are at work at the same time.
• Statistical independence: it is easy to assume that two variables are statistically independent, even when they aren't, such as if you can see no reason for them to not be independent. Statistical independence is another assumption that is easy to take on and then forget about when drawing conclusions.
• Just because you can't see it, doesn't mean it isn't there, or isn't relevant.
• Not having enough evidence to make evidence-based conclusions.
• Thinking that a sample of 100 is somehow a representative sample. There are an astronomical number of ways the neurons in the brain can be configured. If how those neurons are configured matters, then it'll take an astronomical sample size to get a representative sample. So 'samples of 100' only make sense when the configuration of neurons in the brain can be neglected (as can be done reasonably in physical medicine, but not in mental health).