. However I don't see how freewill matters to scientific inquiry.
I would guess that you rightly accept 'skepticism' as a healthy part of the scientific method. Here is the wikipedia definition of 'skepticism':
Skepticism . . . is generally any questioning attitude towards knowledge, facts, or opinions/beliefs stated as facts, or doubt regarding claims that are taken for granted elsewhere.[2]
Eventually, the questioning draws near to an end, and a working judgement is made by the skeptic. At that point, he has analysed all the evidence between two competing claims, and he will make a decision based on his own interpretation of the evidence. To make this decision, he will use his 'Reason'. The definition of Reason, again from wikipedia:
Reason or "reasoning" is associated with thinking, cognition, and intellect. Reason, like habit or intuition, is one of the ways by which thinking comes from one idea to a related idea. For example, it is the means by which rational beings understand themselves to think about cause and effect, truth and falsehood, and what is good or bad. It is also closely identified with the ability to self-consciously change beliefs, attitudes, traditions, and institutions, and therefore with the capacity for freedom and self-determination.[4]
.Can you explain why freewill matters to it.
If I was wrong, and you reject the determinist/incompatibilist position (that is - you believe in a mixture of free-will and determinism) then I apologize for mis-interpreting.