Major influences leading to Socrates and Plato

• Thales discovery of nature and knowledge by reason and observation.
• The materialist presocratics' ontology of matter and epistemology of pure reason.
• The Pythagoreans' discovery of soul and the ontology of form.

Socrates

• The shift back to ethics, society, and the human condition

Plato

• Theory of Forms - a theory of knowledge answering the epistemological dilemmas posed by the materialists in order to countermand the Sophist's skeptical response to the dilemma. Incorporates a theory of recollection derived from the Pythagoreans.
• Guthrie p18 - The Theory of Forms was an answer to intellectual skeptcism that we can know nothing as an outcome of the materialist presocratics; that the epistemology question had no answer.
• Guthrie p18 - The Theory of Forms was the basis on which to address the "moral anarchy" of the age, "the view that there was no permanent and universal standards of conduct, no higher criteria of action than what happened to seem best to a particular man at a particular moment.
• The birth of idealism and abstraction.
• The application of the theory of knowledge to human affairs - politics, society, governance.
• The birth of Ethics in Philosophy.

What is Mathematics?

• Abstraction and idealism (Plato)
• Deductive Reasoning (The Presocratics)
• Number (Pythagoreans)

• An axiomatic system of knowledge based on certainty (proof) and an initial set of axioms accepted as fundamental truths.

How vs Why in the 13-16th century