It's a semantic game to claim that mental determinism is compatible with free thought when the two ideas are mutually exclusive.
Fortunately nobody here claimed that. So much for your strawman.
Coercion is more accurate and thus faithful to the mental determinist position.
No, it isn´t. "Determined" is the word, and "coercion" adds a lot of load and noise to it.
Calling your thinking free is like calling your genes free to give you blue eyes and brown hair if you are a determinist. It's unintelligent or dishonest.
Fortunately nobody here claimed that. So much for your strawman, again.
Libertarians do not the view choices as random or arbitrary.
Well, if they aren´t determined, what are they, then?
And free will is justified because it is properly basic not on the basis of an inductive or deductive argument.
So again, after trying to construct an argument but are unable to substantiate it logically, you simply define the position you tried to argue against out of existence?
It is also inferred from experience and confirmed more directly than anything else that a person could believe.
How so?
If I want to raise my hand I am free to do it when I want to do it. That is as good of a verification for any position that you can have in life.
If it´s that simple - i.e. you simply declare "free will" to exist - why did you construct this argument that you aren´t willing to defend, in the first place?
If you want to show that it is illusory, the burden of proof is on you but the argument will have to be as sound any argument showing that other minds do not exist or that there is not an external world since we are more immediately and directly cognizant of our free volition.
I don´t want to show anything illusory. I am not even taking a position here. I am just investigating the validity of your argument as presented. However, whenever I point out the non-sequiturs in it and ask you to fill in the missing logical steps, you just declare "free will" to be a fact and therefore determinism wrong. That doesn´t make the argument in the OP any more convincing.
You can either show how determinism is justified which would defeat my argument
In order to defeat your argument I don´t need to show that your conclusion is wrong. I am investigating the validity of your argument. Your argument is wanting - which doesn´t mean that determinism is true. It just means that you have presented a poor argument.
or show what is wrong with my argument instead of just claim that is permeated with non sequitors (which isn't tremendously helpful).
Well, you presented the argument, so the onus is on you to make sure your conclusions follow from your premises. I have pointed out where this was not the case.
I have also shown you where you ascribed notions to determinism that determinism doesn´t hold.
Furthermore I tried to help you add the missing logical links by asking a couple of questions, but unfortunately you evaded them each time.