This post is based on the notes I made watching an identically named Arthur Holmes lecture in his excellent History of Philosophy course.
Table of Contents
Knowledge vs Opinion
Plato saw knowledge as something innate. It’s already inside us and can’t even be transmitted. Being “hosts” to knowledge doesn’t mean we can access it, though. Revealing our innate knowledge takes time and effort, and this process of self-discovery is called dialectic.
For Plato, opinion is a slightly different thing. It’s more of a practical thing since it can be locally right, but at best it’s a raw hint that can be refined into real knowledge by applying dialectic.
Forms or Eide
What is it that we know? The object of knowledge isn’t the world of particulars. Opinion is all we can have about the things that change. Plato uses the term “eide”, but the objects of knowledge aren’t what we call ideas nowadays. The better translation is “form”.
At times, they’re called archetypes, patterns or models. Rather than calling it an idea, you’d better call it an ideal. The ideal of justice is the archetype for anything just, etc.
Particulars participate in forms. It’s a tautology in some way. The forms can be regarded as universal, eternal and unchanging. Particulars are temporal, always changing.
Math
The theory of universals applies to mathematics. Mathematical entities are ideal entities. They obviously do not exist since there is no real-world standard for a point, vector or matrix. That’s the Platonic interpretation of mathematics.
This theory has tremendous ramifications for a lot of disciplines, but it’s not 100% new. What Plato is saying is that we live in a rationally ordered cosmos. He is developing Heraclitus’s logos concept.
Metaphysics
Plato is the OG of metaphysics, which is basically the glue holding all thought of a particular philosopher together. Metaphysics is a system, a unified theory of everything, according to a particular guy. Plato’s metaphysics is extremely influential but open-ended. The next big systems will be much more closed.
Metaphysical models underlie the science, the art and the ethics. Greek models can be considered first-gen, and they dominated thought until the 14th century.
Second-gen is more mechanistic. It rejected that there is an intrinsic order. Everything is matter in chaotic motion. No morality. Blind, dead, inert matter being pushed around by blind forces.
Third-gen is more nuanced and organic. In the 18th century, we started to think not in terms of isolated chunks of matter being pushed around, but in terms of energy fields and other nerdy stuff.
Conclusion
That’s a lot of food for thought, and most things still aren’t settled. Personally, I find the mathematical analogy fascinating. Those abstractions do indeed feel other-worldly, as if math exists in the ideal world and we can only imitate and approximate it to the best of our abilities. We all know those abstractions, but we’ve never really seen them.
It’s also notable that not every Greek accepted the theory of Forms, and Plato himself wasn’t fully satisfied with it.