> reality is only that which we can demonstrate and prove using the scientific method
I don't think science even makes this weaker claim. Science does not claim, for example, that my preference for vanilla over chocolate ice cream is only valid if I can demonstrate it and prove it using the scientific method. (Science might claim that the scientific method can be used to gain understanding about how my body and brain work that would help to explain the processes in me that underlie my preference, but that's not the same thing.) Nor does science claim that nothing can be known about "reality" in domains, such as law or politics, where our ability to use the scientific method is extremely limited at best.
I don't think science even makes this weaker claim. Science does not claim, for example, that my preference for vanilla over chocolate ice cream is only valid if I can demonstrate it and prove it using the scientific method. (Science might claim that the scientific method can be used to gain understanding about how my body and brain work that would help to explain the processes in me that underlie my preference, but that's not the same thing.) Nor does science claim that nothing can be known about "reality" in domains, such as law or politics, where our ability to use the scientific method is extremely limited at best.