Premiss 1. If libertarian free will (LFW) exists, it operates such that natural law does not determine its course or its actions, nor is it a matter of chance. (Definition of libertarian free will)
Premiss 2. Science’s competence (meaning the empirical, physical sciences) is strictly in the study of events and entities in conjunction with, in relation to, or as determined by natural law or by chance. (From generally accepted definitions of the natural sciences)
Conclusion 1. If some function or capacity exists whose action or operation is not determined by natural law or chance, then science has no competence concerning that function or capacity. (Premiss 2)
Prediction 1. If LFW does not exist, science will not detect it. (Obviously so)
Prediction 2. If LFW does exist, science will not detect it. (Premiss 1 and Conclusion 1)
Observation 1: Science has not detected LFW.
Conclusion 2: Scientific observations are entirely consistent with Prediction 1 and with Prediction 2. (Predictions 1 and 2, Observation 1)
Conclusion 3: As far as science knows how to determine, either LFW exists or it does not. (Conclusion 2)