Epistemic closure is something that has been bugging me. Does it entail that a belief is certain?

If certainty is the case then have physical laws of nature have some sort of closure in them? — Posty McPostface

Here is what Wikipedia says about epistemic closure - "Epistemic closure is a property of some belief systems. It is the principle that if a subject S knows p, and S knows that p entails q, then S can thereby come to know q. Most epistemological theories involve a closure principle..."

I don't know what that means. Maybe if you explain it more in the context of your post, I can respond intelligently.

Epistemic closure is a property of some belief systems. It is the principle that if a subject S knows p, and S knows that p entails q, then S can thereby come to know q. Most epistemological theories involve a closure principle... — T Clark

My issue is with claiming to know that S knows that p entails q. There seems to be some epistemological gap here in my understanding of how S knows that p entails q. It's a circular argument. S knows that p entails q because S knows that p entails q.

My issue is with claiming to know that S knows that p entails q. There seems to be some epistemological gap here in my understanding of how S knows that p entails q. It's a circular argument. S knows that p entails q because S knows that p entails q. — Posty McPostface

I'm not sure if this is what you mean, but as I read the definition on Wikipedia, it struck me as a pretty trivial insight. It seems to me that p entails q means that if I know p, I also know q.

I'm not sure if this is what you mean, but as I read the definition on Wikipedia, it struck me as a pretty trivial insight. It seems to me that p entails q means that if I know p, I also know q. — T Clark

The epistemological gap is still there. What does it mean to say that I know S, and S knows p entails q, then epistemic closure is tucked into the same argument or 'proof' that it is describing.

What does it mean to say that I know S — Posty McPostface

I think you meant to say "What does it mean to say that I know S S knows p. Nicht wahr?

I know that it is raining.
I also know that if it is raining then Bill is not on the beach.
So I know that Bill is not on the beach.

In this case epistemic closure means some kind of rationality.

But what if there is a crazy person somewhere who believes every sentence. His believe system is epistemically closed but this does not mean his believes are certain.

the problem of course, is that p -> q as axiomatically specified in formal logic does not represent the practical application of modus ponens in practice, where there is always the possibility of inferential disagreement and doubt, due to life being an open system (or a globally uncertain closed system, depending on your cosmic beliefs).

one man's axiom is another man's unprovable formula. We make up our rules of deduction as we go along to suit our current purposes.

As for the status of modus ponens in the physical sciences, Hume already showed that it is not an empirical notion unless p is an observation term whose definition entails immediate observation of q.

My issue is with claiming to know that S knows that p entails q. There seems to be some epistemological gap here in my understanding of how S knows that p entails q. — Posty McPostface

That's not relevant to the issue of epistemic closure. The principle simply states that if one knows that p and if one knows that p entails q then one knows that q.

How one comes to know that p and that p entails q is a separate issue entirely.

I think you meant to say "What does it mean to say that I know S S knows p. Nicht wahr? — T Clark

The skeptic would argue over what one knows to be true and what one believes is true, I suppose. That seems to be where I was taking my understanding of 'closure' in propositional beliefs.

the problem of course, is that p -> q as axiomatically specified in formal logic does not represent the practical application of modus ponens in practice, where there is always the possibility of inferential disagreement and doubt, due to life being an open system (or a globally uncertain closed system, depending on your cosmic beliefs). — sime

Yes, so it appears that the synthetic-analytic divide dissolves again.

How one comes to know that p and that p entails q is a separate issue entirely. — Michael

Well, it's a common rebuttal of epistemic closure. One that is pertinent to answer my question in regards as to whether certainty is necessary to ensure knowledge of q via entailment of q by p, p by q.

The principle simply states that if one knows that p and if one knows that p entails q then one knows that q.

This presupposes that the rules of entailment are infallible regarding truth.

I disagree. Gettier shows otherwise, despite the fact that he (mis)reports upon Smith's belief. What I mean is that if Smith has true belief - as Gettier claims - he doesn't know Q; if Smith has false belief - which is actually the case - he doesn't know Q.

Seems clear to me that the rules of entailment warrant a careful re-thinking.

If the rules of entailment can be shown to be both followed and unable to preserve the truth of the premisses, then we are saying that the "rules of correct inference" do not need to preserve the truth of their premisses.

Well, omniscience should not be grounds to discredit the epistemic closure principle.

So, yeah, do you need certainty in a non-formalized system to arrive at meaningful entailment?

To some degree, yes. As to what degree is in question here.

Which part of what I wrote are you addressing Posty?

I'm offering the strongest justification possible for removing the rules of entailment from the rules of correct inference until the prima facie common sense issue I've pointed out is otherwise corrected.

Which part of what I wrote are you addressing Posty? — creativesoul

I posted as a remark to the following:

If the rules of entailment can be shown to be both followed and unable to preserve the truth of the premisses, then we are saying that the "rules of correct inference" do not need to preserve the truth of their premisses. — creativesoul

and,

This presupposes that the rules of entailment are infallible regarding truth. — creativesoul

My suggestion is that you're taking the rules of entailment under too strict an understanding for it to maintain truth. Or in other words, you demand from a non-formalized system the same certainty you would get from a formalized system. Your position would only make sense for a solipsist.

p1 The rules of correct inference preserve the truth of a thought/belief/premiss
p2 The rules of entailment do not preserve the truth of a thought/belief/premiss

The rules of entailment are not the rules of correct inference.

Which part are you disagreeing with?

Epistemic closure seems to be another word for 'paradigm'. Because all avenues of truth-justification appear certifiably closed, we simply work within the agreed-upon frame of reference. Then, a meaningful event nudges us out of our dogmatic slumber....