Philosophical (p) compatibilists believe that free will and causal determinism are “compatible” with each other. They do this by defining the term “free will” in a way that is indeed compatible with determinism. If you have read my blog you will see that I have criticized compatibilism, but that it is always a semantic criticism about the problems with defining “free will” in the way that (p) compatibilists do. I’ve even vehemently opposed certain compatibilist thoughts and attitudes.
With that said, it is extremely important to point out that outside of the semantic disagreement (the words we use to explain things) there is quite often a whole lot of agreement over what is and is not the case between the (p) compatibilist and the hard incompatibilist.