PNB 3HP3 Lecture Notes - Lecture 1: Pythagorean Theorem, Irrational Number, Socratic Method
18 Jun 2018
School
Department
Course
Professor
Humans have been biologically modern for a very long time, but technology
(even the most basic) is very recent.
-
Why does it take so long for us to invent technology?
What does it take to invent something like the wheel?
○
-
When do people sit down & think philosophically?
NEVER
○
Only when others take on your other responsibilities.
○
Needs to be a value in society.
○
-
Organization & development allows people to not physically do everything they
need to do.
-
Ancient Greece
Producing "modern culture" -- valued art, philosophy, beauty, passivism
-
Valued war w/ neighbor & taking them as slaves.
-
Aristotle talked about needing uninterrupted time to do philosophy.
Therefore, to them, war was a good idea because they needed slaves in
order to be able to do philosophical work.
○
-
They started thinking about what the world is about.
Trying to figure out co-occurrences of things - ideas about causality not
necessary, predictions.
○
People can't help, but think about causation.
This is what makes us believe in things like religion.
§
○
-
Therefore, ancient greeks were trying to think about mathematics.
Pythagorean Philosophy
Universe has order.
○
Things that don't seem connected are actually following similar rules.
○
Harmonics
○
Discovered regularity - is his coincidence? Or is this how the world
fundamentally works?
○
Fundamental idea: the world is perfect, there's something fundamental
about the mathematics.
○
-
Pythagoras' Problems
Mathematical principle seems imperfect or unknowable sometimes.
○
E.g., Pythagorean Theorem works perfectly for triangles except in some
cases -- e.g., root 2 is an irrational number)
○
Deeply unsettling to find these undefinable amounts when following
these "perfect" mathematical principles.
○
-
Mathematics + cult mysticism = ancient Greek ideas
Rationalist View
Product of thinking, knowledge of thought is all we care about.
-
Plato
-
Empiricist View
Ancient version - "based on the world"
-
Not based on just what we think, but the evidence we find in the world.
-
Aristotle
-
Plato ( & Socrates)
We see the universe in this perfectly structured way, but we also perceive
imperfections.
We can infer the rules, but when we look at what we have in the real
world, they don't always add up perfectly.
○
-
Perfect (Platonic) Forms
There's a perfect reality that we cannot see.
○
We an only see an imperfect copy/shadow.
○
The only way to see the real image/thing is to be a philosopher/ be
educated.
○
-
Not really a careful, systematic idea for Plato.
Simply a mystical idea.
○
-
Plato's general view - we walk around in a weird derivative space.
-
He thought everyone has a soul.
Soul doesn't age, but the body ages & dies.
○
Soul has been around for many different lifetimes.
○
Therefore, he thought of knowledge as not acquiring new info, but simply
as uncovering what you already know.
○
-
Socratic method of teaching
Teaching should be about giving people the ability to think correctly so
they may recall what they already know.
○
Need to rehabilitate mind every time your soul is reborn.
○
-
Ancient Greece: Plato
Thursday, January 11, 2018
10:34 AM
