**Timeline**

**5th Century BCE**- Presocratics / Proto-Scientists
- Democritus
- Empedocles

- Socrates

- Presocratics / Proto-Scientists
**4th Century BCE**- Mathematics
- Euclid

- Plato
- Aristotle

- Mathematics
**Later**- Skeptics

#### Greek Proto-Scientists

**Democritus**and**Empedocles**were Pre-Socratics, a group born before Socrates that also includes: Thales, Anaximander, Anaximenes, Parmenides, Heraclitus, Anaxagoras, Zeno, Pythagoras.- Their “attention to questions about the origin and nature of the physical world has led to their being called cosmologists or naturalists.”
- They proposed theories resembling contemporary theories of physics but without the math. Like the Standard Model of Particle Physics, for example, they postulated fundamental entities (atoms and elements) and forces (Love and Strife). But lacking mathematics, their theories couldn’t generate precise, testable predictions.

**Democritus’ Atomic Theory**

**The Theory**- Atoms are indivisible, solid, infinitely many, and variable in size and shape. They move about in the infinite void, colliding, bouncing around, and combining into clusters through tiny hooks.
- Macroscopic objects are entangled clusters of atoms. They change due to rearrangements and additions to their atoms.
- Sensations are changes in the soul caused by atoms emitted by other objects.

**Empedocles’ Four Element**s

**Empedocles’ Four Element**

**The Theory:**- Matter is made of four elements: earth, air, fire, and water.
- Nothing comes into being or is destroyed. Rather, things merely transform, changing the ratio of their component elements.
- Two forces govern the elements.
*Strife*makes elements withdraw from each other.*Love*makes them mingle.

#### Socrates

**Socrates**walked around Athens asking people questions like: “What is courage?”, “What is self-control?”, “What is piety?” Then he refuted their answers.- Socrates wrote nothing but appears in Plato’s Dialogues. The problem for scholars is identifying the dialogues in which Socrates speaks for himself rather than for Plato.
- One of the best “Socratic” dialogues is the
*Euthyphro*.

Euthyphro is on his way to prosecute his father for murder, in particular for being negligent in the death of a murderer in his custody. Socrates expresses surprise. Euthyphro replies that he’s merely acting according to the divine law of piety and impiety.

**Socr**: Good heavens, Euthyphro! Is your knowledge of piety and impiety so accurate that, assuming the circumstances are as you state them, you can bring your father to justice without fear that you yourself may be doing something impious.**Euth**: If I did not understand all these matters accurately, Socrates, I should not be worth much. Euthyphro would be no better than other men.- …….
**Socr**: Tell me then, what is piety, and what is impiety?- …….
**Euth**. Yes, I should say that piety is what all the gods love and impiety is what all the gods hate.- [Euthyphro’s third answer]

**Socr**: Do the gods love piety because it is pious or is it pious because the gods love it?**Euth**: I do not understand you, Socrates.- …….
**Euth**: My answer is that the gods love piety because it is pious.**Socr**: My question, Euthyphro, was: What is piety? But it turns out that you have not explained to me the essential character of piety; you have been content to mention an effect which belongs to it, namely, that all the gods love it. You have not yet told me what its essential character is.- [Socrates’ point is that Euthyphro’s definition is like defining
*money*as*what people want*, which doesn’t say what money*is*.]

- [Socrates’ point is that Euthyphro’s definition is like defining
- ………
- [Socrates wants to pursue the dialectic.]

**Euth**. Another time, Socrates; for I am in a hurry and must go.

- Socrates is
*doing philosophy*because:- He asks
*fundamental questions*, e.g. what is the nature of X? - He tries to answer the questions using
*arguments*, for example, to refute answers.

- He asks

**Euclid**

- Euclid’s Elements, compiled from the works of earlier mathematicians, sets forth a number of mathematical proofs and an axiom system for plane geometry.
- Mathematical Proof
- A mathematical proof is a step-by-step deduction of a mathematical truth from already established mathematical truths. It is the paradigm of
*a priori reasoning*. Rationalists later tried to prove,*a priori*, that*God exists*and*human beings are immaterial selves*. - The
*Elements*has mathematical proofs of:- √2 is irrational
- there are infinitely many primes.

- Example of a mathematical proof (not Euclid’s), that the sum of two odd integers is (always) even.

- A mathematical proof is a step-by-step deduction of a mathematical truth from already established mathematical truths. It is the paradigm of

Papyrus Oxyrhynchus 29 is a fragment of the second book of the *Elements*, discovered in 1897.

- Axiom System
- An axiom system is a set of axioms (or postulates) from which other propositions (the theorems) are logically derived.
- Philosophers such as Spinoza presented their systems explicitly as axiom systems, with definitions, axioms, and theorems. Others used axiom systems implicitly, as a framework.
- Axiom System for Plane Geometry

**Plato**

**Plato**

**Plato**, a student of Socrates and teacher of Aristotle, wrote on topics such as: aesthetics, political philosophy, theology, cosmology, epistemology, and the philosophy of language.- Like Socrates, he often asks
*what-is*questions. In the*Theaetetus*, Socrates, speaking for Plato, asks “What is knowledge?” - Nature of knowledge
- You can only know what’s true. Thus, you can’t know that men have antlers.
- You can only know what you believe. Thus you can’t know that that Benedict Arnold was a general in the Continental Army unless you believe it.
- The question thus arises:
- Is knowledge simply true belief or is it something more?

- Plato argued that knowledge was more than true belief:
- “Suppose a jury has been justly persuaded of some matter which only an eyewitness could know, and which cannot otherwise be known; suppose they come to their decision based on hearsay, forming a true belief: then they have decided the case without knowledge.”

- Plato thus sets forth a counterexample to the thesis that knowledge is merely true belief: a logically coherent scenario where people, the jurors, have a true belief which isn’t knowledge.
- Like Socrates, Plato is doing philosophy
- He addresses a fundamental question, “What is knowledge?”
- He presents arguments.

#### Aristotle

**Aristotle**was into everything:*Science*: biology, botany, chemistry, physics, psychology, zoology*Philosophy*: metaphysics, ethics, philosophy of mind*Arts*: rhetoric, poetics, history.

- He also founded
*Logic*, a big deal because philosophy proceeds by argument. - Specifically, Aristotle developed the
*theory of syllogisms*, arguments whose premises and conclusion have the form:- Every A is a B.
- No A is a B
- Some As are Bs.
- Some As are not Bs.

- Aristotle developed a procedure for determining whether the conclusion of a syllogism follows logically from its premises.
- Valid Syllogism:
- No D is a C
- No dog is a cat.

- Every L is a D.
- Every Labrador Retriever is a dog.

- Therefore, No L is a C
- No Labrador Retriever is a cat.

- No D is a C
- Invalid Syllogism
- Some Ps are Bs.
- Some people are blue-eyed mammals.

- Some Bs are Cs.
- Some blue-eyed mammals are cats.

- Therefore, some Ps are Cs.
- Some people are cats.

- Some Ps are Bs.

- Valid Syllogism:

**Skepticism**

###### Academic Skepticism

- Carneades and Arcesilaus (ahr-ses-
*uh*–**ley**–*uh*s) advocated*Academic Skepticism*, the view that almost nothing can be known for certain, but many things are nevertheless probable given the evidence.

###### Pyrrhonism

- Pyrro, Aenesidemus (anna-SIDE-ah-mus), and Sextus Empericus advocated
*Pyrrhonism*, the view that no rational foundation exists for almost everything people believe. The rational course, they argued, was to suspend judgment, neither believing nor disbelieving.