Epistemic closure is the idea that knowledge is self-contained and does not require external justification. This means that if you know something, then you cannot be wrong about it, even if there is evidence that contradicts your belief.

The problem of coherence is the problem of how to avoid contradiction in our beliefs. This is a difficult problem because it is often the case that we hold beliefs that are in conflict with each other. For example, we might believe that God exists and that the universe is eternal, but these two beliefs are contradictory.

Epistemic closure makes the problem of coherence more difficult to solve because it makes it more difficult to identify and resolve contradictions in our beliefs. If we believe that knowledge is self-contained and does not require external justification, then we are less likely to be willing to consider evidence that contradicts our beliefs.

The argument from circularity is one of the most common arguments for epistemic closure. It argues that if we require external justification for our beliefs, then we will eventually end up in a circular loop, where each belief is justified by another belief, and so on. This is because there must be some ultimate foundation for our beliefs, and this foundation cannot itself be justified by another belief.

The argument from dogmatism is one of the most common arguments against epistemic closure. It argues that epistemic closure leads to dogmatism, which is the belief that one's own beliefs are absolutely certain and true. This is because if we believe that knowledge is self-contained and does not require external justification, then we are less likely to be willing to consider evidence that contradicts our beliefs.

Epistemic closure is not a necessary condition for knowledge. There are many different theories of knowledge that do not require epistemic closure. For example, some theories of knowledge argue that knowledge is justified true belief, while others argue that knowledge is a kind of understanding or insight.

Epistemic closure is not a sufficient condition for knowledge. Even if we have a set of beliefs that is closed under logical implication, this does not mean that all of our beliefs are true. For example, we might have a set of beliefs that is closed under logical implication, but some of our beliefs might be based on false evidence.

Epistemic closure implies that knowledge is always fallible and uncertain because it makes it more difficult to identify and resolve contradictions in our beliefs. If we believe that knowledge is self-contained and does not require external justification, then we are less likely to be willing to consider evidence that contradicts our beliefs.

We can avoid the problem of coherence without resorting to epistemic closure by using critical thinking skills to identify and resolve contradictions in our beliefs, by being open-minded and willing to consider evidence that contradicts our beliefs, and by being humble and admitting that we do not know everything.

The challenges to avoiding the problem of coherence without resorting to epistemic closure include the challenge of identifying and resolving contradictions in our beliefs, the challenge of being open-minded and willing to consider evidence that contradicts our beliefs, and the challenge of being humble and admitting that we do not know everything.

The problem of coherence shows that knowledge is always fallible and uncertain because it shows that it is impossible to have a set of beliefs that is both coherent and complete. This means that there will always be some possibility that our beliefs are wrong, even if we have good reasons for believing them.

The implications of the problem of coherence for our epistemic practices include that we should be more skeptical of our beliefs, that we should be more open-minded and willing to consider evidence that contradicts our beliefs, and that we should be more humble and admitting that we do not know everything.

The problem of coherence has been addressed by philosophers in a variety of ways, including by developing theories of coherence that allow for the possibility of contradiction, by developing theories of knowledge that do not require coherence, and by arguing that the problem of coherence is not a real problem.

There is no promising way to address the problem of coherence because it is a fundamental problem that arises from the nature of human knowledge. We can try to develop theories of coherence that allow for the possibility of contradiction, or we can try to develop theories of knowledge that do not require coherence, but these approaches are ultimately unsuccessful. The problem of coherence is a real problem that we must live with.