# What does Epistemic Closure mean?

I keep coming across this term and would appreciate it if someone could define it for me and also provide a relevant example.

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Is there any chance you can tell us a little bit about where you keep coming across this? – Joseph Weissman Dec 23 '11 at 22:44
Epistemic Closure in the newly popularized, philosophical, sense means holding fast to beliefs that are rooted in a false and insular reality despite their being outside evidence to the contrary of that belief. – user2664 Nov 10 '12 at 1:51

"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.

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That looks like what I looked that up on Wikipedia. – leeand00 Dec 21 '11 at 0:29
Thanks! But I dont see how Epistemic Closure means knowing all logical truths. It usually is the case that when we know 'P' and know 'P implies Q', then we know 'Q'. The reason we don't know all mathematical truths is more so that in most case we don't know both 'P' and 'P implies Q'. So I'm not sure it follows that it is too strong a principle. – Alborz Yarahmadi Mar 31 '12 at 1:52
@AlborzYarahmadi That's a weaker, and perhaps a more reasonable principle. Closure as I was understanding it is: "If you know P, and P implies Q, you know Q". You mentioned the weaker principle: "If you know P and you know P implies Q, then you know Q". But that's still quite strong. I know "P or not P", and I know that this implies all the logical truths. I don't thereby know all the logical truths. – Seamus Mar 31 '12 at 13:47
@Seamus You might know that P or not P implies all the logical truths and still fail to know that P or not P implies Q, if you don't know that Q is a logical truth. – Schiphol Jul 17 '12 at 17:41
@Schiphol I'm not sure what your point is. If Q is a logical truth, then if you satisfy closure, you know Q. Since "if (P or not P) then Q" is a logical truth (provided Q is) then you will know this too… – Seamus Jul 17 '12 at 21:46

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.

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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.

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Also, answers on stackexchange sites should be more or less self-contained. Answers that are just a link are discouraged. – Seamus Dec 20 '11 at 13:44
I do, as a matter of fact, have a basic grasp of epistemology-- no need for snark. The term "epistemic closure" is used, occasionally, in epistemological texts, but if the OP "keeps coming across" this term and doesn't know what it means, it is pretty clear that the OP is not reading these epistemological texts. Much more likely is the case that the OP is reading any of the thousands of mainstream news articles which have used this phrase in the context of conservative ideology. 17 of the first 20 hits on Google (and 9 of the first 10) are using the term in this way. – Michael Dorfman Dec 20 '11 at 13:49
I suppose it depends on which epistemological texts you are reading; I rarely come across it in my work, and I assume that anyone reading works that rely on it would already know the answer to the question. The fact that the term has been imported into another domain is not irrelevant; more to the point, it has been imported precisely to give an academic cachet to what is otherwise a banal argument. This means that casual readers without an academic philosophical background are left wondering what the term means, and I assume this case to be much more likely than the alternative. – Michael Dorfman Dec 20 '11 at 14:06
Indeed, it is the phrase and not the meaning that was imported. Quoting the link above, Mr. Sanchez said he probably fished “epistemic closure” out of his subconscious from an undergraduate course in philosophy, where it has a technical meaning in the realm of logic. As you suggest, the meaning bears no substantive relation to the philosophical notion of epistemic closure, but the phrase was borrowed to give the illusion of erudition. – Michael Dorfman Dec 20 '11 at 15:07
@MichaelDorfman Yes I am reading it in a book (which appears to have politics involved). It's called the Information Diet by Clay A. Johnson. – leeand00 Dec 21 '11 at 0:28