Hume‘s is-ought (fact-value) distinction is the same as Plato‘s true-justified distinction. When is/true/fact and ought/justified/value are not kept distinct, the Euthyphro dilemma as applied to epistemology ensues: Are we justified in believing (ought we believe) merely because our belief is true (can truth justify belief without evidence?), or is our belief true because we are justified in believing (because we ought to believe)(does evidence make belief true?)?
The solution: Our belief is 1) justified (we ought to believe) by the evidence, and 2) true by correspondence. Gettier’s problem examples, though meant to challenge Plato‘s justified-true-belief theory of knowledge, show that just because a belief is true (is), does not make it justified (ought), and just because a belief is justified (ought), does not make it true (is). Gettier’s problem and Euthyphro’s dilemma only arise when we get is/true and ought/justified tangled together (Hume’s is-ought problem), when we forget to keep them distinct, as Plato kept them in his requirement that belief be “both” justified “and” true, in order to count as knowledge.
Draw a Venn diagram. In the top circle write, “What we want to be true,” in the bottom left circle write, “What we acknowledge is true,” and in the bottom right circle write, “What we recognize is true.”
[Note on belief scales: There can be degrees of justification, but truth is either/or. This means that beliefs cannot be “more or less” true (known), only “more or less” justified (believed)–that is why apisticism (lack of belief) is the mid-range (or ‘on the equator’) between polar beliefs (like atheism/theism), not agnosticism (lack of knowledge, as a conclusion–as opposed to Huxley’s process of questioning, pre-conclusion).]
Relevant posts which go into more detail on the above:
The New, New Theism
Replacing Agnosticism with Apisticism
Is-ought fallacy and knowledge as justified-true-belief
Norris, Gettier, Euthyphro, Hume and Plato: Is knowledge justified true belief?
Answering Gettier
Atheism and agnosticism (really, apisticism) as belief
Natural law, divine command and Euthyphro’s dilemma resolved using Hume’s is-ought distinction
Ichthus77 