The distinction between intrinsic and extrinsic is a distinction between the types of characteristics an object might have. Intrinsic characteristics are those which an object has by its very nature, regardless of its situation or circumstances. Extrinsic characteristics are those which an object has solely in relationship to other objects and/or its environment.
For example, a person may be intrinsically female, but extrinsically an engineer.
It is also possible to speak of value as being either intrinsic or extrinsic. For example, a micrometer only has extrinsic value because it is useless to people who do not use such a tool. The question of whether or not some things, like love, have intrinsic value is a matter of debate. If some value is intrinsic, it's usually spoken of as a value which a thing has "for its own sake" or "in its own right."
There exists the possibility of a paradox in the relationship between extrinsic and intrinsic values. For example, exercise might be seen as having extrinsic value because it leads to good health. Normally, that is only true if good health itself has intrinsic value. If it does not, then it only has value in relationship to something else - threatening to create an infinite regress.
Extrinsic Values vs Intrinsic Values in Ethics
Much of the debate regarding extrinsic and intrinsic values can be found in the field of ethics. Those who claim the existence of some sort of absolute and immutable morality at least imply the existence of intrinsic ethical values - the existence of ethical goods or values that do not depend on circumstances, culture, perspective, beliefs, etc. Those who claim that morality is relative in any sense will often imply that only extrinsic ethical values exist - that no ethical value exists "for its own sake" and that all exist solely in relationship to something else, like a culture or goal.
That sounds simple, but it's not, because even relativistic moral systems can depend upon intrinsic values. A consequentialist moral system, for example, evaluates the morality of an action based on its consequences and not upon any absolute set of rules. However, at the same time it's common to evaluate the consequences themselves based on whether they are intrinsically good or bad.
For example, the killing of a particular person would be evaluated in a consequentialist system based on whether the consequences of their death are ultimately better or worse than the consequences of their living. In some versions of consequentialist morality, though, this evaluation will proceed by at least taking into account the belief that life itself has intrinsic value - that being alive is good in and of itself, without reference to any cultural beliefs or personal goals.
Atheists, Theists, and Values
It might be thought that one of the debates between atheists and theists would revolve around the existence of intrinsic values. Usually that would be correct, but not in a way that would be immediately obvious and because of that such debates won't get very far.
Although the division is not universal, atheists are far more likely to adopt some sort of relativistic moral system and most theists are far more likely to adopt some sort of absolutist moral system. One might think, then, that atheists are more likely to deny the existence of intrinsic values while theists are more likely to uphold their existence.
That isn't quite true. While theists do not deny the existence of intrinsic ethical values, a great many of the values they might call "intrinsic" are arguably "extrinsic" because their value only exists in relationship to their god - for example, their god has commanded that something be done or value. Such things cannot be said to have value "in and of themselves" or "for their own sake" because their value derives from some decision or statement allegedly made by a god. That's as extrinsic as a value that exists because it's cultural tradition or necessary to achieve some goal.
Atheists, in contrast, do not necessarily deny the existence of intrinsic values; indeed, if they accept the existence of any, they may accept the existence of more than many theists do because all of those values exist independently of the will or desire of any gods. So if life or happiness may be valued for their own sake and not because any god says to value them.
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What is Epistemology?
Epistemology is the investigation into the grounds and nature of knowledge itself. Epistemological studies are usually focused upon our means for acquiring knowledge, and as a consequence, modern epistemology generally involves a debate between rationalism and empiricism, or the question of whether knowledge can be acquired a priori or a posteriori.
What is Philosophy?
What is philosophy? Is there any point in studying philosophy, or is it a useless subject? What are the different branches of philosophy - what's the difference between aestheitcs and ethics? What's the difference between metaphysics and epistemology?