Sir Philip Sidney’s “An Apology for Poetry” was influenced directly by both Aristotle and Plato.
The works of Aristotle that most strongly influenced Sidney were the Poetics and Nicomachean Ethics, both of which were well known and respected in the Renaissance. The main point of influence was the notion of poetry as moral education through vivid embodiment of characters in a way that let viewers develop morally by experiencing vicarious situations and undergoing some form of catharsis.
The Platonic influence is actually neo-Platonic. It follows a medieval tradition (deriving from the earlier work of Plotinus and Proclus) that the poet directly imitates the forms and thus can help the reader understand the noumena underlying the phenomena.
In Sir Philip Sidney's "Apology for Poetry," he addresses the conflict between the moral philosopher, the historian, and the poet.
He subscribes to the Aristotelian view that poetry highlights universal truths that are ennobling. Sidney maintains that historians' obsessive focus on immutable facts is destructive; he argues that poetry is far more reliable as a moral guide because of its emphasis on rational principles. Like Aristotle, Sidney contends that the poet is superior in his ability to express true virtue.
Sidney's Aristotelian beliefs converge in some instances with his neo-Platonic stances. He defends the heuristic nature of poetic ideals: universal truths are beneficial if they result in actional and verbal expressions in the practical world. By all indications, Sidney's brand of neo-Platonism is rational rather than inspirational. Plato argued that, without divine inspiration, poets would abuse their art. He conceptualized what he called the "divine fury," inspiration that must direct poetic ambition. To Plato, divine possession of the intellectual powers was crucial.
For his part, Sidney rejects such a supernatural emphasis on poetic endeavors. He maintains that poetry is good because it is rational, not because it is divinely inspired. In this sense, Sidney's "Apology for Poetry" addresses misconceptions about Platonic and Aristotelian ideas as much as it expresses support for specific neo-Platonic and Aristotelian stances about poetry.
Source: Poetic Conception in Sir Philip Sidney's "An Apology for Poetry" by Robert M. Strozier, The Yearbook of English Studies, Vol. 2 (1972), pp. 49-60