The form of a counterfactual law (“your perpetual motion machine won’t work even if you make that screw longer or do anything else different”) seems to be “A, no matter which parameter you change”.
I don’t think this is right. As I am using it, ‘counterfactual’ refers to a statement about whether something is possible or impossible. Statements of the form “A, no matter which parameter you change” are not always like this. For example if A=’this ball has a mass of 10kg’. This is not a statement about what is possible or impossible. You could frame it as ‘it is impossible for this ball to have a mass other than 10kg, no matter which parameter you change’, but doesn’t give us any new information compared to the original statement.
Another important feature is that the impossibility/possibility is not restricted to specific dynamical laws. In your example ‘F=ma, even if the frictionless sphere is blue’, this statement is only true when Newton’s laws apply. But the statement ‘it is impossible to build a perpetual motion machine’ refers, in principle, to all dynamical laws-even ones we haven’t discovered yet-which is why principles like this may help guide our search for new laws.
I don’t think this is right. As I am using it, ‘counterfactual’ refers to a statement about whether something is possible or impossible. Statements of the form “A, no matter which parameter you change” are not always like this. For example if A=’this ball has a mass of 10kg’. This is not a statement about what is possible or impossible. You could frame it as ‘it is impossible for this ball to have a mass other than 10kg, no matter which parameter you change’, but doesn’t give us any new information compared to the original statement.
Another important feature is that the impossibility/possibility is not restricted to specific dynamical laws. In your example ‘F=ma, even if the frictionless sphere is blue’, this statement is only true when Newton’s laws apply. But the statement ‘it is impossible to build a perpetual motion machine’ refers, in principle, to all dynamical laws-even ones we haven’t discovered yet-which is why principles like this may help guide our search for new laws.