I will assume your question is sincere. I have never seen this explicit statement by Ayn Rand. (She does say the attempt to prove axiomatic concepts is self-contradictory, by which she means you have to start with a contradiction to make the attempt, that is, you have to assume what is true to be not true.)
Suppose you oberve something about reality or some aspect of it, and identify it. It might occur to you that the observed aspect of reality seems almost fundamental, essential, or primary. Is it an axiom?
Here is how to find out. Is it possible to deny it without incorporating the idea itself in the denial thus contradicting the denial in the process of denying it. If the concept itself must be incorporated or assumed in the process of the denial, then it cannot be logically denied, it is axiomatic.
One other note about axioms. Axioms are always primaries, which means, they cannot be further reduced to more fundamental concepts. They are not derivative concepts.
That is what objectivists mean by axioms.
For the record, Randian Objectivists (and I think those in the Kelly camp as well) hold that there are only three axioms: existense, consciousness, and identity. In axiomatic form they would be, Existence exists. Conscious is conscious. A is A, or a thing is what it is.
Since I am not an objectivist, I am not bound by their limitations, and take the risk of thinking for myself. One conclusion is that there are more axioms.
For example:
Plurality. (There must be more than one thing.)
Dynamism. (There must be change.)
Differentiation. (All existents are different.)
And others, on the basis that once these are observed, they cannot be denied without entailing a self contradiction. But don't hold the objectivists to account for these.
Hank
Thanks for your reply. Was it not attributed by you to Ayn Rand in your post #395?
Suppose you oberve something about reality or some aspect of it, and identify it. It might occur to you that the observed aspect of reality seems almost fundamental, essential, or primary. Is it an axiom?
Let us first establish that we are discussing moral principles which are not visible as physical reality is physical and observable. You can only observe behavior of people, but it is incorrect to say that behavior = moral truth. Just because a person is behaving in a certain manner, that does not mean that person "ought" to behave that way.
An "moral axiom" is defined by a person, that makes it morally relative if it contradicts true moral absolutes that come only from God. For example, Ayn Rand did not believe adultery or sex outside of marriage was wrong - correct? Therefore, her axioms about sexual morality (if she had any) contradicted God's, therefore Ayn was a moral relativist when it came to sex.
Here is how to find out. Is it possible to deny it without incorporating the idea itself in the denial thus contradicting the denial in the process of denying it. If the concept itself must be incorporated or assumed in the process of the denial, then it cannot be logically denied, it is axiomatic.
By this definition, any axiom from anyone can't be denied.
One other note about axioms. Axioms are always primaries, which means, they cannot be further reduced to more fundamental concepts. They are not derivative concepts.
Axioms are to be The bottom line is that moral truths cannot just hang in mid-air - they must have a source. The are either from man or God - no other options available. If they originate from man or woman (Ayn Rand), then they are morally relative to man. Only moral principles from God are capable of being universal. Man does not have the moral authority to make his moral principles absolute because man is finite and his sphere is quite limited, and carry no real moral force. There are no real consequences for going against manmade axioms, but there are consequences, both practical and eternal, for going against God's.
They would then be contradicting God, in which case, they would be wrong. It is not possible for finite men to reason their way to universals (not logically possible). One must start with universals and reason down to men.
LOL! What you've just derided is a popular and useful technique for mathematical proof.
OK. I can accept that existence exists. I will even grant "conscious" as real, though I cannot go further to define what it really is.
But I cannot accept that "A is A" is axiomatic, because it requires us to be able to define what A really is in the first place. For example, suppose I have a wooden chair. Is it the same wooden chair that stood before me a minute ago, right down to the very last quark? Can I prove that? And if there's a quark's worth of difference, can I really say that "A is A" in this case? I suppose you can defer to something like Plato's "forms," but then you'd have to prove them, too.
The point is, if we want to actually use "A is A" for anything useful, we need to define in some manner what "A" is in the first place -- which ultimately requires us to make assumptions about A. And what's more, we have to choose the proper "A" from among a wide array of possibilities.
Looking at this from the practical perspective, the problem of defining "A" turns out to be quite difficult. In this thread, the A's in question are things like "self-interest," and "happiness," and as we've seen these particular choices are in no way axiomatic, according to your own definition of the term.
Now let's look at your proposed other axioms. None of them satisfies your conditions for being axiomatic.
Plurality. (There must be more than one thing.)
This axiom requires us to assume that there is in fact more than one thing. You can objectively prove (to yourself, not me) the existence of one only thing: yourself.
Dynamism. (There must be change.)
This contradicts "A is A," and it also requires you to assume a whole bunch of things about the ultimate structure of the universe. Suppose, however, that I posit a viewpoint that lies "in eternity," which sees the universe in the same sense we see a completed book. (The statement "existence exists" seems to suggest that such a viewpoint is logically possible.) In that case, the concept of dynamism may not be meaningful.
Differentiation. (All existents are different.)
A mighty broad statement, the truth of which is muddied by such things as quantum entanglement, not to mention Dr. Heisenberg's little theorem.