It seems that Objectivism doesn’t deduce an "ought’ from an “is” either.
The first reply clearly told me that there is an extra premise “Do you want to live?”. Only when you answer “yes” then can we talk about morality or ethics. Otherwise we must stop here. I think “ought to live” is the forth axiom which is parallel to your other three axioms, and it cannot be reduced to the other three axioms. Then, Objectivist ethics is founded upon the ethical axiom “ought to live”, rether than the fact of reality.
If people choose the “ought to live” option, then they ought to maintain and further their lives. But the second “ought” is the derect inference from the axiomatic “ought” . Our reference to the facts of reality can be established only after our axiomatic &/or inferential “ought"s has been chosen. The post #4 wrote, “If you want to live, you have to do certain things because reality demands it”. In this sentence what I see is that “you want to live” is not logically inferred from “have to do certain things.” Rather, only when we establish the purpose of " want to live” , can we resort to reality to determine what course of action can serves our purpose. The former is one sufficient condition to the latter. “Ought to do ___” precedes to “See how can we achieve ___ according to the demands of reality” .
The sentence in post #3: " With the “is” referring to a fact of reality, the “ought” is derived from “how must I relate this ‘is’ in a such a way that it best serves my rational self-interest” also gives me an impression that the “ought” is actually not deduced from an “is”. In this sentence there are three key words: “is”, “ought” and “my rational self-interest”. What can be deduced from “is” (a fact of reality) is only “a way that it best serves ___”. As to the “___” (this is a purpose) you can substitute it with “my rational self-interest”, or “the interests of other people”, or “the Glory of God”, or “suicide”. These four substitutes can all reasonably finish the sentence "With the “is” referring to a fact of reality, the “ought” is derived from “how must I relate this ‘is’ in a such a way that it best serves ____”. I know “the interests of other people” and “the Glory of God” are rejected by Objectivism. So the proposition "With the “is” referring to a fact of reality, the “ought” is derived from “how must I relate this ‘is’ in a such a way that it best serves my rational self-interest” doesn’t clarify how to deduce an “is” from an “ought”.
Post #3 wrote"Objectivism doesn’t “choose it” per se, Objectivism provides a principle and reasoned framework (or guideline) for the individual to determine how he must relate to facts of reality (the “is”) within the parameters of the context in which he must deal with this “is”. " This is irrelevant to ethics. It’s a technical one. Because whatever purpose I set for myself, (no matter suicide or self interest), I must determine how to “relate to facts of reality (the “is”) within the parameters of the context in which I must deal with this “is”.”
My viewpoint is that, an “ought” must presume a purpose. But the purpose is not logically deduced from facts of reality but established independently by a person . What purpose the person chooses depends on his ethical premises and ultimately, “ought to live” or “ought not to live”, that’s the ultimate premise and no more reduction. As to the cognition of reality and the determination of how to comply with the laws of nature (or reality) in order to best serve our purpose is just a technical question. This question only comes after the state of affairs that a purpose has been out there is established. This question is not the logical precedent of purpose. Objectivist ethics is founded upon the axiom “ought to live”, not “facts of reality.” If someone even reject the axiom of “ought to live”, he is hard (or even impossible) to be persuaded through valid reasoning.