But does it eliminate free will? Are we mechanical systems that are determined?
Clearly we are biological and not mechanical. Do you believe that biological systems are subject to cause and effect?
If all we are is a biological machine that is at the mercy of random cause and effect influences then we are deterministic and there is no freedom of the will. So, unless we are created we are just biological machines that are determined.
Sure, which means that our wills are not free like Adams was. Yet we still have a volition. We still choose.
What makes you think Adam had freewill?
Because Adam was a tabula rasa, a blank slate, he had the ability to sin or to not sin. God gave Him a command in which he was free to eat of any tree in the Garden but one. He was told what would happen once the fruit was eaten yet he could still choose. No one else influenced him to eat the fruit of the tree of knowledge until the devil suggested otherwise.
We, as fallen humanity do not have the ability to not sin as he did. That is the difference. He was free to choose either path, we are not. We inherited a corrupt nature. We still make choices and still have the ability to choose but our choices are influenced by our nature and our desires. Thus, the biblical solution is a new nature that God gives us. R.C. Sproul sums it up:
In The Freedom of the Will, Jonathan Edwards defines biblical freedom. Man is free, he says, to choose according to his disposition. Human beings always choose according to their strongest desire, and so we make free choices. We do what we want to do. Some may object that people often choose the undesirable, such as handing a wallet over to a mugger. But even if I do this, my strongest inclination has prompted my choice. All things being equal, I do not desire to give my wallet away. But if my choice is my wallet or my life, and I hand over my wallet, I prove that I want to live more than I want money.
Apart from Christ, we are dead in sin (Eph. 2:1) and wholly disposed to hate God. We only want darkness, and so we freely choose to reject Him. We freely choose to love and to serve Jesus only if the Spirit changes our hearts (John 3:1–8). Otherwise we remain lost.
So, our freedom to choose is governed by our nature and our desires. Our freedom to choose no longer has the ability to not sin. Thus, we are in bondage to sin until Jesus transactionally sets us free from that nature and penalty. The life He lived on earth He lived to God on behalf of those who would believe, so we are counted free in Him (He has no sin) and when we leave this earthly body I believe we will fully realize that freedom in Jesus Christ.
What makes you think that we have "volition"?
You have the ability to do something or not to do it and you admit as much with the underlined below.
Of course we "choose" things, but the point is that our "choices" are (EITHER) caused (OR) uncaused (this is tautological).
If they are caused and we have no choice then we are determined. We can't but do what is determined for us. Do you believe this is the case? If so, say goodbye to morality.
Do you have the ability to never correspond with me again? I think you do. It depends on whether you desire to do so or not so it depends on your choice. If I offended you then you could choose whether to respond or not. Many times I have chosen not to respond to a post.
(IFF) our choices are caused (THEN) they are not free (because they are inevitable).
In a sense, every decision you make is influenced by other factors since ideas do not form in a vacuum. In this sense, our wills are not free. Yet you choose between options. In this sense, you have the freedom to make a choice. The atheist himself chooses not to love God or to deny His existence. God does not place that thought in his/her mind. They do that themselves, even though their thoughts are influenced by other thoughts. With determinism, you have no choice at all. You do what you do because you can't do otherwise.
All the things that I see have a causal effect. Humans follow their human nature which is corrupted by the Fall, but they still choose. They can still choose one or the other option? Sometimes things go against what you desire. You do not want to die, but you love someone enough to protect them by doing so. It depends on your desires and influences. Do you choose to put your own interests first or theirs?
When an atheist hears the Christian message of grace they are not free but bound by their sinful nature. Thus, what they hear goes against that nature. It is unpleasant to them. That is why, generally speaking, humans resist the message. But faith comes from hearing the message and still not all believe its good news. Thus it takes an act of God, an act of His grace to hear the message because we tend to block it out and drown hearing His voice. We dig in and resist it. It requires unpleasant circumstances to jar us from our blindness, apathy and indifference to Him. It takes an examination of our worldview and questioning what makes sense and how we can justify what we believe. When we do that the Christian position comes shining through. Then the question becomes whether we are willing to put our complete trust in Him or whether we like our sin and misery too much to let go of it. But now we see the wrong and it is uncomfortable to us.
(IFF) our choices are uncaused (THEN) they are not willed (because they are random).
How can a choice be uncaused? You need input to make a decision. Are you saying nothing influences our thoughts but pure matter - Determinism (something just happens because your biological and chemical reactions randomly trigger it to happen)?
If there is no such thing as a choice but everything happens randomly then morality is an illusion. Are you willing to live with this dichotomy?