Reason includes genetics.

The law of identity.

Reason and free will, man is a being of volitional consciousness and reason is exercised by choosing to focus and continuing to pay attention to the subject.

Good epistemology. Define your words precisely and use them consistently.

How is this reason and rational proof?

All important. Epistemologically, how does reason and logic prove natural rights?

Rational selfishness.

True

OK, so ice can sink in another universe, but it doesn't sink in ours so it is a posteriori, contingent, synthetic. Ice is solid water is a priori, necessary, analytic. But all this difference explains is which concept was discovered first. We had to see ice melt into water to form the concept that ice is solid water.

Is three less than four? Yes. Is three greater than two? Yes, again. Is three therefore the number that is less than four and greater than two? No. It is the integer between two and four. But does a child have to know the concept of integer to grasp that three is less than four and greater than two? No. It is enough to refer to them as numbers to still retain the meaning of the concept.

Thanks Cat. Still working out the thought process. Its getting later so apologies if this doesn't make sense. Anyway, here goes.

If consciousness is not an axiom, then it does seem to follow that no particular can be derived from axioms. Does that mean consciousness would be given epistemological and not metaphysical status?

Then again, not sure that developmental science can explain the order of existence, identity, consciousness. These three seem bound together, and to operate under the control of a volitional process.

Here are reasons I think the three axioms are bound up in each other. To separate existence from identity is to allow something to be A and not A at the same time. To separate existence from consciousness is to allow for a consciousness without percepts or concepts. To separate consciousness from identity is to allow for consciousness precedes existence.

I think it's difficult when we say consciousness is volitional. How can an axiom be volitional? But I think that is why the Peikoff states that a person must choose to think or to evade. He says, it seems, that there is no alternative to choice. Is consciousness equivalent to thinking? Again, I'm unclear. It would seem consciousness denotes awareness. But awareness seems to be volitional...

Separately: With regard to the first two sentences from the third paragraph of the previous post, what I meant to say was that if existence is taken to mean all existents, then existence cannot be infinite because the number of existents is never infinite.

What I am really curious about is whether the continuum hypothesis is compatible with the assumption that existence is finite. I think so, because each time we subdivide an atom, it yields some number of smaller particles (i.e. puffs of meta energy).

True, but it logic by exclusion, which derives from the law of identity

I said " observable" not observation. Please note the identity difference. Identity as a concept does not represent any existing particular property of an object. Only particulars of objects are sensible. Thus Hume is Hume and elephants do not turn into novelists. See JJ Gibson on theory of senses and Binswanger on theory of Identity.

What I mean by 'derivative proof' is "We want to prove B. We know A is true, and we know that if A is true, the B must be true. Therefore B is true. Another term is syllogism. The reductio proof is a whole different application of logic.

yes it is, it excludes all other possibilities.

Really identity is not an observation. Rocks turn into trees by themselves. Houses become elephants before our eyes. I disagree.

Let me add about the a priori
"The argument is simple: analytical and a priori true statements cannot be contradicted by synthetic facts. If a statement cannot be contradicted by facts it cannot be meaningful. If it cannot have meaning it is nonsense. Nonsense does not belong in philosophy."

Consciousness is not an axiom, it is an observation as is identity and existence. They may be axiomatic in the foundation of objectivism, but they are fundamentally observations.

https://www.youtube.com/watch?v=LsReW...