The relationship between certain types of psychological determinism and ethical responsibility is one example. A typical formulation goes something like this: if an individual is determined, logically and temporally prior to his acting, in a way beyond his control or awareness, then when he acts, he cannot be morally responsible for his action.
This formulation is, of course, one of many, and is often used in introductory philosophy classes to begin a discussion.
A second textbook example looks at the relationship between determinism and truth claims. If an individual is in certain ways determined, what does it mean for that individual to utter, or write, a truth claim? Does his lack of freedom in making assertions affect his belief in his own truth claim? Should it affect our evaluation of his truth claim? Was he able to examine the proposition, and alternative propositions, before expressing it?
A third exemplar is a mixture of the first two. What is the relationship between the ability to be morally responsible and the ability to make truth claims? If both are called into question by determinism, then what is the common element in both?
Such classic investigations can be found in Greek antiquity, in contemporary philosophy, and at many points in between.
