Plato left an indelible mark on philosophy. His Doctrine of the Forms was a landmark that connected epistemology to the way things are, including essences. He was also (perhaps) the first to provide a comprehensive, interconnected and coherent metaphysics, cosmogony, and ontology (i.e., the branch of metaphysics that examines the nature of being). His historical legacy includes the foundation of the Academy and his instruction of Aristotle. When studying Plato, we don’t only consider his work in terms of its depth, or historical accuracy (a practice 20th century philosopher Gilbert Ryle disparagingly called “tombstone polishing”). Instead, we rely on Plato when we attempt to understand the metaphysical realities of the world.
Methodologically, Plato taught the importance of conceptual analysis and how to conduct it. His metaphysical accounts are also influential. Every philosopher who develops a notion of essences must begin with Plato. Every epistemologist starts with Plato’s account of knowledge. Many theologians have adopted his account of the Forms entirely, or have accepted aspects of his intellectual realm and intellectual objects. Some theologians have gone so far as to define God as the personified Form of the Good.
Plato influenced (and continues to influence) many other areas of philosophy, too many to list here. Whitehead did not overstate his case. Much of philosophy, and theology, implicitly or explicitly begins with Plato. However, his philosophy has also impacted other disciplines.
Recall that Plato’s Doctrine of the Forms is highly compatible with mathematical idealization. This applies to geometry (Platonic Forms as the basis of geometric shapes) and arithmetic (numerals as Platonic Forms).
In higher mathematics, some have posited the existence of sets as Platonic objects. Positing Platonic objects enables mathematicians to solve otherwise-unsolvable problems. For example, a Platonist account enables the solution of a number of problems including why mathematical approximations seem to obtain in reality; and why it seems like mathematical truths are discovered, not created (and that those discoveries seem to be independent of the physical sciences — mathematical entities seem to be abstract, but also seem to exist).
Mathematical Platonism is so useful that even mathematicians who do not want to commit to Platonist metaphysics sometimes take a position called “working realism.” This means that they perform their work in theoretical mathematics as if Platonism is true. This methodology is helpful in many ways, including its implication that all mathematical problems are solvable.
In a dialogue called the Gorgias, Plato asked (and attempted to answer) an interesting question: what is a genuine techne, or “craft”?
The question was important to Plato because it involves the distinction between philosophy and rhetoric. He viewed the former as genuine craft, and the latter as a pseudocraft.
Plato argued that philosophy is a genuine craft because its subject matter is a Form or Forms, specifically, the Forms of Wisdom and Truth. Rhetoric, which superficially resembles philosophy in its emphasis on argumentation, fails to have a Form as its subject matter. As we have seen, rhetoric is concerned with appearances. (Plato didn’t have a high regard for simply “winning debates,” so he relegated rhetoric to the realm of appearances.)
Plato provided other pairs of activities in which the first is a genuine techne or craft, and the second is a pseudocraft. One of the genuine crafts is medicine, which takes as its subject the Form of Health. The corresponding pseudocraft (which only looks like medicine) is called “cookery” — what we would call "quack remedies." These remedies might create an appearance of health without really producing that state. Plato also paired gymnastic or exercise, which aims to produce bodily Health, with a pseudocraft called “beautification” or makeup. Makeup, like cookery, might create an appearance of physical health, but nothing more. Consider people who visit a gym to build up their arms, but never another part of their bodies, or those who inject substances to enhance muscle appearance (e.g., Synthol).
These examples of genuine crafts have been presented to emphasize that philosophy, in light of its regard for wisdom and truth, is a model activity for a human being, nourishment for the soul and the rational side of our nature. Any craft should, as a proper human activity, involve the pursuit of truth.