I am wondering if it would be reasonable to apply to M.A. or Phd programs in Philosophy with only a B.A. in Computer Science. I have done a great deal of reading in the field of Philosophy, but have never taken a class. I would be looking mostly at State Universities in the Cleveland, OH area.
I want to expand on my comment a bit:
You'll definitely want to talk to the professors at each university you wish to apply to see what kind of requirements they have for applying.
Typically though, I would imagine it's not as important what your bachelors degree is (say, as it would be compared to getting a Ph.D. in Computer Science) so much as that you have a clear, demonstrable interest in the field of philosophy. When you apply to these programs, it will be of critical importance to show them why philosophy is important to you and what your research interests are. Graduate school Ph.D. programs as a general rule look for students with active interest in the curriculum they offer (clinical-leaning Psych majors should avoid applying to research-based Psych programs, for example). Perhaps most importantly, your research interests should preferably align with the interests of at least one professor in the department. If you are applying to a program with heavy interest in philosophy of religion and the department has no professors with that specialization, they won't have the expertise to help you and thus will probably decline your application, however otherwise stunning it may be.
What kind of philosophy do you want to do? It's definitely possible, but you have the burden of proving why you want to go into philosophy, what exactly you want to do, and why you are prepared for it. Those answers will vary depending on what kind of philosophy you want to go into and the makeup of the department. Grad school is different than undergrad because you are working more closely with faculty, so you need to make sure they align with your interests and vice versa.
Many departments have a reputation for being highly interdisciplinary, and this might be an advantage if you want to do something in philosophy related to CS. For example, there are plenty of philosophy departments in the U.S. that have an emphasis on analytic philosophy, which is heavily influenced by computer science and mathematics. It's going to be easier to get into that kind of program with a CS degree than, say, ethics, because your CS background would be a direct advantage in certain kinds of analytic philosophy. That doesn't mean you can't go into an unrelated area of philosophy, just that you have an extra burden to overcome. I attended a very interdisciplinary philosophy program in undergrad, and several professors did not have undergrad degrees in philosophy, but it was very clear to me why they chose to pursue philosophy.
Once you have a good explanation of what you want to do and why you are prepared to study philosophy on a graduate level, start researching philosophy professors at the colleges you're interested in. Reach out to them explaining why you are interested in the program. Generally they are happy to talk to you, and having someone in the department who wants to work with you is a big asset in the grad school application process.