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I'm specifically interested in the part where you say that "there are certain things we can't be mistaken about". What are the things we can never be mistaken about and how do you determine this?
If somebody chops your leg off, can you be mistaken about it?
I'm glad you asked because as matter of fact you can!!. There actually happens to be a a series of mental diseases regarding perception of the limbs. One is known as the Phantom Limb in which a patient who lost a limb, can still feel it as if it existed and actually suffers from "real" pain in the non existent limb. The other one is Anosognosia in which a patient with a paralyzed limb is not aware that the limb is paralyzed and if asked if it is working, he/she goes through the delussion that it works and that he/she is moving it. If you ask them to use it, they will of course fail at it, but in their reality, the limb is moving.
If you asked them if their limb is paralyzed they would swear to you that it isn't (Meaning, they would pass a lie detector because to them, this is the truth). They just
know it isn't and can't believe you are telling them that it's not there. To them this is a reality as strong and real as the fact that you have your limbs fully functional
There are also patients who have had their limb paralyzed yet when they see someone who has their limb paralyzed, they
"know" that it isn't because they lack the ability to recognize this ailment in other people
So answering your question: Yes. You can even be mistaken about that. You can be mistaken about
anything (given the proper brain damage) and be sincerely 100% sure that you are right. And that's why you need a Third Person science, without which you would never find out that you are having this perception problem
Put another way: I only have subjective/personal reasons for a positive belief in free will, but I have objective/collectively-justifiable reasons for believing that it is impossible to rule it out a-priori.
Sounds just like the "you can't prove a negative" argument, yet you say "objective" colletively justifiable reasons. May I know what those are?
Yes. If you ignore the "first person approach" then you might just as well be a materialist/determinist.
I'm not ignoring the First Person approach. I'm simply not just relying on it as the main source, given how easy it is for perception to fool the individual