Of course you have an organ that pumps blood. The question is, do you have a heart in the sense often intended in everyday talk about the mind, in phrases like "he has a good heart" and "in my heart, I know that...", a heart in the Romantic sense of having a private emotional life that one can choose to show or to hide, be true or false to?
Maybe it's better to put the question less ontologically. Is the concept of a "heart" useful for philosophy? It certainly hasn't had much play in philosophy of mind!
We contrast the "heart" and the "mind". Your heart might tell you one thing; your mind another. Now of course, in the broad philosophical sense of "mind", the heart is just part of the mind. The heart/mind distinction, if it works, is meant only to capture a difference between judgments, values, or decisions that have some inchoate emotional basis and those that are more explicitly rational. Is this distinction useful?
Antonio Damasio and Nomy Arpaly might say no. Damasio suggests that emotion plays a crucial role in even seemingly "cool" reasoning. Arpaly suggests that the phenomenology of "cool-headedness" often masks what really is emotional and irrational. Maybe the "heart", then, deserves to be dead and buried; it's really just the mind. Yet something still pulls me toward the idea of the heart, maybe not as distinguished from the mind exactly, but as the metaphorical (and sometimes phenomenological?) locus of a certain kind of deep apprehension, a kind of "gut feeling", that's importantly different from abstract, explicit reasoning.
Mencius doesn't mean what we mean by "heart" -- as David Wong and Kwong-loi Shun suggest, he brings together our concepts of the heart and the mind -- but when Mencius says that something in our hearts is troubled by evil and pleased by good, I want to carry that forward into something more like the contemporary notion of the heart. Though we may at an explicit, conscious level, find nothing wrong in our evil actions -- the Nazi may have what seems to him perfectly rational reasons for exterminating the Jews, the professor may have an excellent defense of his abhorrent treatment of his graduate students in mind -- something deep in their hearts, as it were, still rebels.
I want to be able to say that. I think something in the idea of the "heart" is useful here. There's some emotional knowledge of good and evil that persists under our rationalizations. But Damasio and Arpaly worry me. So also does a strand in my own thinking that takes our actions, and our dispositions to act, as the most fundamental facts about our beliefs and values -- a strand in my thinking that wants to keep things on the surface, as it were, to say the man is his actions and the "inner heart" is a sham....