How to respond to doubt of logic?

WARNING: Read this at your own risk of losing your beliefs. I don't believe in Islam (but hopefully I would). I thought I was the only one ever who doubts the truthfulness of rationality, perception and reports, but I recently [asked on Philosophy SE](https://philosophy.stackexchange.com/questions/92551/can-we-doubt-all-knowledge) , and I found people, who are reputable in philosophy, doubt all kinds of knowledge... The reasons for doubting that logic is true: - The existence of free will; because it indicates indeterminism, which is illogical - Why not? What makes it impossible that there is another way of thinking that leads to truth? How can Islamic scientests respond to such doubts? If someone doubts logic, Does that mean he can never become a true believer in Islam?