—Oughts From Logic—

–Definitions:
(Ought): An outcome that ought to occur or be valid relative to some principle, is an outcome that is logically consistent with and follows some principle. If you light a stick of dynamite it ought to explode relative to the laws of physics and the construction of the stick of dynamite. That isn't a subjective normative claim, it's an objective implication based on Logic.

(Rationality): Used here, the empirically measurable accuracy towards an action being able to achieve a goal, where accuracy towards a goal applies to not only narrow goals, but overall goals and behavior, and to the consistency of acting with reference to rational standards of measure.

(Interest): For a sentient being to have an interest in something, this simply means their behavior is tending towards fulfilling said something, even if it is ineffective. All people have interests, and even trying to avoid their interests, is itself an interest they are acting according to. Any sentient being with stimuli-driven behavior has interests.
 

–Premises:
(P1): All people have interests.
(P2): All people act in accordance with the interests they have, and prioritize interests they hold with Intrinsic Value.
(P3): Some actions are better than others at fulfilling interests.
(P4): Rationally, if you light a stick of dynamite, relative to the laws of physics, and all object’s tendency to follow the laws of physics, it ought to explode. (based on the definition of Ought)

(P5 from P4): Rationally, if you are acting in accordance with an interest, you ought to choose any of the most rational actions you can, to best fulfill the interest.
 

–Logic:
(L1): From (P1), a person X has an interest I.
(L2): From (P1 + P2), person X acts in accordance with interest I.
(L3): From (P3), there might exist an action A that most rationally fulfills I.
(L4): From (P2 + P5), person X rationally ought to take action A, if it exists, to fulfill interest I.
 

–Conclusion:
From (L4): Any person X, rationally ought to take any actions A that best fulfills their interests I.

Thus, people rationally ought to fulfill their own interests in the most rational way possible, and as all people have interests, and people’s interests may differ, the most rational situation for the people to create for themselves is a situation that is most consistent with the fulfillment of Inherent Interests overall, the upholding of at least the most intrinsic Oughts as priority.

(Note: Avoiding an interest may maximize Oughts if the interest is self-destructive to other interests. Also, an action that fulfills your interest but can cause a collapse of Inherent Fulfillment of Interests down the line may not be the most rational action to take, either based on your own self-interest being threatened or based on an inconsistency of some kind, see Absolute Interest Conclusion for more clarification.)

Goods by definition are what people ought to do, which based on this deduction is what their behavior tends towards that they view as an End in Itself, hence based on Inherent Interests.
This gives us the Yogg Definition of Good.

Therefore, people ought to do what is Good under the Yogg Definition of Good.
We have derived this through pure rationality.