In objectivism, free will is an axiom, and the reasons for this have already been given in post #313:
I can't prove that I have free will. Not directly. However, if we don't have free will, then we can't reason, because we would have no power to reject invalid conclusions. We would be no more free than our calculators, which provide only the answers they are constructed to provide. Therefore, if we are to conduct ourselves as if we were rational beings, we must assume the existence of our free will as an axiom. This is an axiom of absolute necessity, and not one which is adopted arbitrarily; because without such an axiom, all rational thought becomes impossible.The axiom works because: (a) it's necessary; and (b) it's bullet-proof. I think that your reason for accepting free will has problems. I have no idea how you get from: (1) "being created in the image of God" to: (2) "I don't deny that you or I have free will." It is very possible that God can create beings with no free will; and I don't see how it can be otherwise for a God who knows the future. I know there are cliche' responses to this problem, but it certainly seems to me that a future-knowing god (if that's what god is) is contradicted by our possession of free will. This uninverse ain't big enough for both.
Can you refute that objectivism results in solipsism?
Certainly. Objectivism has an axiom which deals with this: Existence exists. We perceive the world which is external to ourselves through our senses, which are also axiomatically presumed to provide data about the external world. Given such axioms -- which again are absolutely necessary to proceed as rational beings -- we are then equipped to get through the day (and through conversations such as this) without each of us imagining that we are the only functioning entity in the universe, and unable to know anything but ourselves (plus of course, what some swammi then preaches to us).solipsism: a theory holding that the self can know nothing but its own modifications and that the self is the only existent thing.
I see no necessity:
The objectivist assumes that he (and to this point, only he) possess free will. He cannot provide a shred of verifiable evidence that he does. But neither can anyone provide a shred of verifiable evidence that he does not. So, he states the axiom: I have free will. Not out of objective necessity does he state this, but only out of a subjective preference over determinism.
Given this axiom, a question arises: Do other persons possess free will? Looking for verifiable evidence in affirmative support, the objectivist finds none (post 378). In fact, the objectivist can find no verifiable evidence to support the assertion that any living being or any other matter/energy combination possess free will. He does observe that other persons exhibit complex responses to stimuli. And he knows that he is not able to predict the responses with any regularity. He realizes, however, that people are the most complex combinations of matter/energy he has observed, and that his inability to predict the responses of other people with any regularity reflects his lack of understanding of the complex combinations and workings of the matter/energy that people are composed of. The objectivist has no verifiable evidence or logical necessity in affirmative support of his assumption that the complex responses of other persons to stimuli result from free will in humans, just as he has no verifiable evidence or logical necessity in affirmative support of the assumption that weather (the complex response of the atmosphere to stimuli) results from free will in the atmosphere. Assuming that other persons have free will is not necessary for the objectivist to interact with, respond to, and study other people, just as assuming that the atmosphere has free will is not necessary for him to interact with, respond to, and study the atmosphere.
The objectivist is able to conduct himself as a rational being---observing, hypothesizing, and rejecting invalid conclusions---without extending the axiom that he has free will to anyone or anything outside of himself; there is no logical necessity to do so. Additionally, since neither he, nor anyone else, can provide objectively verifiable evidence that others either do or do not have free will, there is therefore both no objective evidence and no logical necessity that requires him to prefer the theory that the complex response of other persons to stimuli is the result of free will over the theory that the complex response of other persons to stimuli is the result of determinism. One can only conclude that the assumption made by the objectivist that other persons have free will is the result of personal preference, not necessity.