I keep coming across this term and would appreciate it if someone could define it for me and also provide a relevant example.
"Epistemic closure" is a term used in epistemology. An agent satisfies closure when she satisfies the following conditional:
- If the agent knows P and knows that P implies Q then the agent knows Q.
Here's an example of an agent failing to satisfy closure:
- Sally knows that it is Tuesday. She also knows that "If it's Tuesday, then it isn't the weekend". However, Sally fails to know it is not the weekend.
It seems a pretty obvious principle in some sense. But there are two reasons to deny it.
First, epistemic closure is an important part of sceptical arguments.
Second, satisfying epistemic closure means knowing all the logical truths: knowing all the truths of mathematics. So it is clearly too strong a principle in general.
More generally, "closure" in this sense means something like a kind of "completeness". So in logic a set of sentences is "closed under entailment" if the following conditional holds:
- If P is in the set and P implies Q then Q is in the set.
In mathematics one sees people talking about sets being "closed under an operation". So a set of numbers is "closed under addition" if a+b is in the set whenever a and b are.
When P implies Q, Q is an aspect of P. The example using Tuesday shows this: Being a weekday is an integral part of "Tuesday". This means: P (Tuesday) includes Q (Weekday/Not Weekend). A deduction can be unexplored, yet still knowable. Tuesday can be a holiday or a voting day etc. So if P implies Q, knowing P makes it possible to know all examples of Q. The "closure" in "epistemic closure" means knowing "all possible Q's". Sometimes "epistemic closure" is instead being used to say "closed-minded": if you know P, you "choose not to know" Q.
Here's a New York Times article on the notion; note that the term is not really used much in academic philosophy, but rather in conservative political ideology.