3 added comment on use of "closure"
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"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.

Despite thisMore generally, "the KK principle" as it"closure" in this sense means something like a kind of "completeness". So in logic a set of sentences is known,"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 fundamental to many epistemic logics"closed under addition" if a+b is in the set whenever a and b are.

"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.

Despite this, "the KK principle" as it is known, is fundamental to many epistemic logics.

"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.

2 added more content
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"Epistemic closure""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.

Despite this, "the KK principle" as it is known, is fundamental to many epistemic logics.

"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.

"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.

Despite this, "the KK principle" as it is known, is fundamental to many epistemic logics.

1
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"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.