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
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. — 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. — T Clark
What does it mean to say that I know S — Posty McPostface
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
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
How one comes to know that p and that p entails q is a separate issue entirely. — Michael
The principle simply states that if one knows that p and if one knows that p entails q then one knows that q.
Which part of what I wrote are you addressing Posty? — creativesoul
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
This presupposes that the rules of entailment are infallible regarding truth. — creativesoul
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