I have a tendency that’s possibly related to your #3: when someone makes a factual assertion I immediately consider its negation as a distinct possibility. That is, the negation becomes more available to me, and therefore in some sense more plausible. Else, why make the assertion in the first place?
This is actually a pretty good habit to get into when doing math. Lots of plausible-sounding conjectures actually do turn out to be false because math can allow for some pretty strange-seeming things. For example, you can have functions that are continuous everywhere but differentiable nowhere, or uncountable sets with length zero, or all kinds of other crazy things.
I have a tendency that’s possibly related to your #3: when someone makes a factual assertion I immediately consider its negation as a distinct possibility. That is, the negation becomes more available to me, and therefore in some sense more plausible. Else, why make the assertion in the first place?
This is actually a pretty good habit to get into when doing math. Lots of plausible-sounding conjectures actually do turn out to be false because math can allow for some pretty strange-seeming things. For example, you can have functions that are continuous everywhere but differentiable nowhere, or uncountable sets with length zero, or all kinds of other crazy things.