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The Footnotes to Plato

The Footnotes to Plato

Author: Sophia Tutorial

Identify the ways in which Plato's philosophy has impacted history and society.

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what's covered
Alfred North Whitehead stated that the whole of European philosophical tradition “consists of a series of footnotes to Plato.” To explain what he meant, Whitehead said, “I allude to the wealth of general ideas scattered through them. His personal endowments, his wide opportunities for experience at a great period of civilization, his inheritance of an intellectual tradition not yet stiffened by excessive systematization, have made his writing an inexhaustible mine of suggestion.”

Plato’s philosophy is a mine from which other philosophers, thinkers, religions, and cultures have extracted riches over the centuries. In this lecture, we will consider some of Plato’s legacies in philosophy, mathematics, and how human endeavors ought to be pursued. This selection of topics is not comprehensive, but is sufficient to convey the extent of his influence.

This tutorial considers the scope of Plato's intellectual legacy in three parts:

  1. Philosophical Legacy
  2. Platonism in Mathematics
  3. Pursuing Truth Over Appearance

1. Philosophical Legacy

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.

2. Platonism in Mathematics

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.

did you know
A famous mathematical Platonist, Kurt Gödel, made such claims much more difficult by proving that mathematical systems display a certain type of incompleteness.

3. Pursuing Truth Over Appearance

In a dialogue called the Gorgias, Plato asked (and attempted to answer) an interesting question: what is a genuine techne, or “craft”?

did you know
The term, “technology” comes from the Greek words techne and logos.

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).

think about it
Try to think of some more pairs of crafts which seek to attain truth and corresponding psuedocrafts that focus on appearances. Consider diets formulated by a dietician vs. fad diets; genuine relationship compatibility vs. ineffective computer matching; using proper grammar vs. common slang expressions, etc. What all of these pairs have in common is that the pseudocraft is focused on achieving what is appealing/marketable. This describes the activity in which the sophists were involved in Socrates’ time: it was focused on appearances, not truth.

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.

Humanity’s debt to Plato’s philosophy cannot be overstated. Those who become involved in metaphysics and epistemology in the course of studying philosophy and theology, are deeply engaged with Plato's work — implicitly or explicitly. A Platonic conception of mathematical objects has been of great value in theoretical mathematics. Plato’s account of techne helps us to distinguish (and value) genuine human endeavor from mere marketing ploys.