Epistemic closure is the idea that if you know a set of propositions, then you also know all of the logical consequences of those propositions.

The problem of externalism is the problem that external factors, such as the environment or other people, can affect our knowledge.

Epistemic closure can exacerbate the problem of externalism because it means that if we know a set of propositions that are affected by external factors, then we also know all of the logical consequences of those propositions, which may also be affected by external factors.

The argument from testimony is an argument for externalism that says that we can know things based on the testimony of others, even if we do not have any direct evidence for those things.

The argument from skepticism is an argument against externalism that says that we cannot know anything for certain, because our knowledge is always based on evidence that is fallible.

René Descartes is most closely associated with the defense of epistemic closure. He argued that we can only know for certain the things that are immediately present to our minds, and that all other knowledge is derived from those things.

David Hume is most closely associated with the critique of epistemic closure. He argued that we cannot know anything for certain, because all of our knowledge is based on experience, and experience is always fallible.

The debate over epistemic closure and the problem of externalism is inconclusive. There are strong arguments on both sides of the debate, and there is no clear consensus among philosophers about which side is correct.

Epistemic closure is a controversial topic because it is unclear whether it is a valid principle of knowledge, how it relates to the problem of externalism, and what its implications are for our understanding of knowledge.

The main challenge to epistemic closure posed by the problem of externalism is the challenge that external factors can affect our knowledge. This challenge arises because epistemic closure holds that if we know a set of propositions, then we also know all of the logical consequences of those propositions. However, if external factors can affect our knowledge, then it is possible that we could know a set of propositions and still not know all of the logical consequences of those propositions, because the external factors could prevent us from knowing those consequences.

The problem of externalism challenges the idea that knowledge is closed under logical implication by showing that there are cases in which we can know a set of propositions and still not know all of the logical consequences of those propositions. This is because external factors can prevent us from knowing those consequences.

The main implication of the problem of externalism for our understanding of knowledge is that it shows that knowledge is not as certain as we thought. This is because the problem of externalism shows that there are cases in which we can know a set of propositions and still not know all of the logical consequences of those propositions, which means that our knowledge is not as complete as we thought.

There are a number of possible responses to the problem of externalism. One response is to deny that external factors can affect our knowledge. Another response is to accept that external factors can affect our knowledge, but argue that this does not undermine the idea that knowledge is closed under logical implication. A third response is to accept that external factors can affect our knowledge, and argue that this shows that knowledge is not as certain as we thought. A fourth response is to reject the idea that knowledge is closed under logical implication.

There is no one most promising response to the problem of externalism. The best response will depend on the specific arguments that are being made in favor of externalism. However, some of the most common responses to externalism include denying that external factors can affect our knowledge, accepting that external factors can affect our knowledge but arguing that this does not undermine the idea that knowledge is closed under logical implication, accepting that external factors can affect our knowledge and arguing that this shows that knowledge is not as certain as we thought, and rejecting the idea that knowledge is closed under logical implication.