What is Epistemology?:
Epistemology is the investigation into the grounds and nature of knowledge itself. The study of epistemology focuses on our means for acquiring knowledge and how we can differentiate between truth and falsehood. Modern epistemology generally involves a debate between rationalism and empiricism, or the question of whether knowledge can be acquired a priori or a posteriori:
Empiricism: knowledge is obtained through experience.
Rationalism: knowledge can be acquired through the use of reason.
Why is Epistemology Important?:
Epistemology is important because it is fundamental to how we think. Without some means of understanding how we acquire knowledge, how we rely upon our senses, and how we develop concepts in our minds, we have no coherent path for our thinking. A sound epistemology is necessary for the existence of sound thinking and reasoning — this is why so much philosophical literature can involve seemingly arcane discussions about the nature of knowledge. Unfortunately, atheists who frequently debate questions that derive from differences in how people approach knowledge aren't always familiar with this subject.
Why Does Epistemology Matter to Atheism?:
Many debates between atheist and theists revolve around fundamental issues which people don't recognize or never get around to discussing. Many of these are epistemological in nature: in disagreeing about whether it's reasonable to believe in the existence of god, to believe in miracles, to accept revelation and scriptures as authoritative, and so forth, atheists and theists are ultimately disagreeing about basic epistemological principles. Without understanding this and understanding the various epistemological positions, people will just end up talking past each other.
Epistemology, Truth, and Why We Believe What We Believe:
Atheists and theists differ in what they believe: theists believe in some god, atheists do not. Although their reasons for believing or not believing vary, it's common for atheists and theists to also differ in what they consider to be appropriate criteria for truth and, therefor, the proper criteria for a reasonable belief. Theists commonly rely upon criteria like tradition, custom, revelation, faith, and intuition. Atheists common reject these criteria in favor of correspondence, coherence, and consistency. Without discussing these different approaches, debates over what ones believes are unlikely to go very far.
Questions Asked in Epistemology:
What can we know?
How can we know it?
Why do we know some things, but not others?
How do we acquire knowledge?
Is knowledge possible?
Can knowledge be certain?
How can we differentiate truth from falsehood?
Why do we believe certain claims and not others?
Important Texts on Epistemology:
Meditations, by Rene Descartes
Treatise on Human Nature, by David Hume
Critique of Pure Reason, by Immanuel Kant
An Essay Concerning Human Understanding, by John Locke
What’s the Difference Between Empiricism and Rationalism?:
According to empiricism, we can only know things after we have had the relevant experience — this is labeled a posteriori knowledge because posteriori means “after.” According to rationalism, it is possible to know things before we have had experiences — this is known as a priori knowledge because priori means before.
Empiricism and rationalism exhaust all possibilities — either knowledge can only be acquired after experience or it is possible to acquire at least some knowledge before experience. There are no third options here (except, perhaps, for the skeptical position that no knowledge is possible at all), so everyone is either a rationalist or an empiricist when it comes to their theory of knowledge.
Atheists tend to be either exclusively or primarily empiricists: they insist that truth-claims be accompanied by clear and convincing evidence which can be studied and tested. Theists tend to be much more wiling to accept rationalism, believing that "truth" can be attained through revelations, mysticism, faith, etc. This is consistent with how atheists tend to place primacy on the existence of matter and argue that the universe is material in nature whereas theists tend to place primacy on the existence of mind (specifically: the mind of God) and argue that existence is more basically spiritual and supernatural in nature.
Rationalism is not a uniform position. Some rationalists will simply argue that some truths about reality can be discovered through pure reason and thought (examples include truths of mathematics, geometry and sometimes morality) while other truths do require experience. Other rationalists will go further and argue that all truths about reality must in some way be acquired through reason, normally because our sense organs are unable to directly experience outside reality at all.
Empiricism, on the other hand, is more uniform in the sense that it denies that any form of rationalism is true or possible. Empiricists may disagree on just how we acquire knowledge through experience and in what sense our experiences give us access to outside reality; nevertheless, they all agree that knowledge about reality requires experience and interaction with reality.