To introduce the reader to the philosophical debates about the science of the arts, I review existing research and discuss three philosophical theses. As a background claim, I begin with the co-dependence thesis, which states that dependence relations have tied arts and sciences together in the past and continue to interlink them in the current historical context. The co-dependence thesis is contested in the debate about the foundations of the science of art. Recent scientific investigations into the arts and aesthetic evaluations have raised two questions. First, is a science art feasible? Second, if such a science is feasible, what are the principles and methods that should provide its conceptual foundations? To examine these questions, I first discuss an objection from art’s specificity, which rests on the idea that empirical studies of art have failed to identify and explain the factors that are distinctive of art. It is one of the most influential philosophical objections to research aimed at developing an empirically-grounded science of art. Notwithstanding this objection, I defend and apply to art theory the thesis of critical naturalism, which holds that scientific and empirical investigations of artistic practices and aesthetic experiences can contribute to our descriptive and normative understanding of the arts. The science of the arts is made of works that create, analyse and test interdisciplinary models of art practices and appreciation. To implement critical naturalism, I introduce the psychohistorical thesis, which states that a method apt for developing integrative explanations of artistic practices and experiences consists in combining research on the mental capacities engaged in the arts with enquiries into the historical and cultural genealogy of such practices. The three theses I present are philosophical heuristics understood as general thoughts that can orient interdisciplinary enquiry and suggest research hypotheses. Although these three theses should not be understood as empirical hypotheses, some ideas derived from these theses have been operationalised as hypotheses and tested by empirical methods.