(2) ” It means that someone knowing that law can predict with some accuracy the state of the universe at some point in the future from its state at the time of observation.” Nitpick: The present vs. future stuff is a red herring. For example, we use the laws to predict the past also.
(3) The question I’d ask about your proposal to identify laws with predictability is: What is predictability? Do you mean, the actual ratio of true to false predictions made using the law is high? Or do you mean something more robust—if the observer had made many predictions using the law, most of them would have been true? Or probably would have been true? Or what? Notice how it’s hard to say what the second and third formulations mean without invoking laws. (We can use laws to ground counterfactuals, or counterfactuals to ground laws, but the hope would be to ground both of them in something less mysterious.)
Some thoughts:
(1) “What does the term “Physical law?” mean?” This is a longstanding debate in philosophy, see https://plato.stanford.edu/entries/laws-of-nature/ I think you’d benefit from reading up on the literature.
(2) ” It means that someone knowing that law can predict with some accuracy the state of the universe at some point in the future from its state at the time of observation.” Nitpick: The present vs. future stuff is a red herring. For example, we use the laws to predict the past also.
(3) The question I’d ask about your proposal to identify laws with predictability is: What is predictability? Do you mean, the actual ratio of true to false predictions made using the law is high? Or do you mean something more robust—if the observer had made many predictions using the law, most of them would have been true? Or probably would have been true? Or what? Notice how it’s hard to say what the second and third formulations mean without invoking laws. (We can use laws to ground counterfactuals, or counterfactuals to ground laws, but the hope would be to ground both of them in something less mysterious.)