Hi, this is David Makinster.
This talk is about the back
story of Plato's cosmology.
It's an introduction to the
section of my intro philosophy
course on metaphysics
and epistemology.
Metaphysics is the,
if you will, theories
about reality, what we mean
when we say something is a real.
Are there different
ways of being real?
Do we always mean the same thing
when we call something real?
And epistemology is
theory of knowledge.
OK?
Once again, what do we mean by
saying that we know something.
Are there different
ways of knowing
appropriate or different
kinds of known objects?
What's the difference between
knowledge and opinion?
OK.
Plato's going to have quite a
bit to say about all of this.
To understand Plato's
position, his basic framework
of metaphysics and
epistemology that's
revealed in the sun,
divided line, and cave,
it's helpful to know
some of the back story.
What problems were
on the table when
Plato was writing this
section of the Republic?
This is, by the
way, considered one
of the best pieces of literature
by literary historians who
can read it in the original
Greek, one of the best
pieces of literature
in the Western canon.
It's also considered one
of the absolute bedrock
milestones of
Western philosophy.
So we are not going to begin to
plumb everything out of it that
can be plumbed out
of it, but we're
going to look at
such features as are
important for a first look.
Plato, like many
important thinkers,
is the guy who pulled all the
individual accounts together
and saw what the whole
elephant looks like.
You to remember that parable
of the blind wise men.
And of course, in
order to do that,
generally you have to find
a higher perspective that
allows you to unite all of
those different concerns.
OK?
So let's begin.
The first person that we
should note is Heraclitus.
Heraclitus was long before
Plato, long before Socrates,
for that matter.
Very admired, almost
universally admired thinker
in the ancient world.
Unfortunately, we have only
fragments of his writings.
The upside is that he wrote
in short, pithy statements
rather than long, extended,
connected treaties,
so sometimes we have whole
thoughts with these fragments,
but we know we don't have all
of what he must have taught.
Heraclitus believed that
you had to make people
see things for themselves,
be able to say things
in their own words.
So his teaching methods often
involved presenting people
with paradoxes or problems that
they had to solve themselves.
I like to compare him
to Zen Buddhism in more
recent history.
Zen Buddhism is a Japanese
school of Buddhism.
At least some schools of Zen
use riddles and paradoxes
that they give to
the student in order
to try to make the
student break out
of his old ways of thinking.
One of my favorites is about
the goose and the bottle.
And I'll just tell that
now because it always
reminds me of Heraclitus.
The Zen master says
to the student,
there's a goose in a bottle.
He's too big to get
out of the opening,
out of the neck of the bottle.
And there's no other opening.
You have to get the goose
out of the bottle-- no damage
to the goose, no
damage to the bottle.
How are you going to do it?
The student immediately bows
and says, the goose is out.
OK.
Now you're probably
wondering, what?
Exactly what is that
supposed to mean?
Well, think about it.
The Zen master says, the
goose is in the bottle.
There's no opening
except the neck.
And the neck is too narrow
for the goose to get out.
There's no other opening.
Get the goose out of the
bottle without hurting
the bottle or the goose.
How are you going to do it?
The student simply bows
and says, the goose is out.
Well, ask yourself,
how did the Zen master
get the goose into the bottle?
He said the goose
is in the bottle.
So of course, the way to get
the goose out of the bottle
is to say, the goose is out.
The moral of the
story, so to speak,
is that we can, with our ways
of thinking about problems,
create scenarios that
are impossible to solve.
We can paint ourselves
into a corner
where there is no
solution, and the key then
is to break out of that way of
thinking and re-conceptualize
what it is we're trying to do.
That's very much, very
much characteristic
of the thought of Heraclitus
insofar as we know it.
Now Heraclitus was
extremely interested
in the importance of change.
Most thinkers in the
very ancient world
were very interested in
the phenomena of change.
And that interest has
persisted into modern physics.
OK?
We take it for granted
that change occurs,
but it's very difficult
to actually explain
how one thing can, in
another moment of time,
become something
else without simply
whirring over that
conceptual problem.
The problem of
change is somewhat
like the problem of time, as
St. Augustine described it.
He said, if someone
asked me what
time is, of course
I know what time
is, until I try to explain it.
And then I realize I am at a
loss to explain what it is.
Well essentially,
that's because we're
at a loss to explain
exactly what change is.
Heraclitus understood
that the notion that
everything is in
a state of flux,
everything is in
a state of flux,
makes it very difficult to think
about the notion of reality.
To be, you have to be something.
But if you're in a state
of constant change,
are you any one thing?
And if indeed we're in a
constant state of change
or the world is a constant
state of change, how then can
we know anything?
He likens that to an archer
who is moving, trying
to hit a moving target while
his bow and arrow are unstable.
If he hits that
bullseye, it's going
to be essentially by accident.
This is a problem for knowledge.
There's a sort of skepticism
about how we can know,
how we can know anything on
the basis of appearances.
OK?
Russell's first
chapter in his book
is going to be about
appearance and reality.
Well, that's a very,
very old problem.
It's Heraclitus who came up
with the aphorism you can't
step into the same stream twice.
What does that mean?
Actually the whole
aphorism is you
can't step into the
same stream twice.
New waters are ever flowing.
And for his audience,
the idea of flowing water
would've been a
very common metaphor
for the passage of time.
We can't step into
the same stream
twice because at the second
moment new waters are flowing.
You can't recapture
the past moment.
A later interpreter
of Heraclitus
said, the fact is you can't even
step into the same stream once.
Because even as you're stepping
in, the stream is changing
and you are changing.
Now we know Heraclitus did
seem to think that there were
solutions to these problems,
but unfortunately we
don't have those works.
If he ever wrote down what
he thought the answers were,
we don't have those works.
He does believe that there
is such a thing as virtue,
but we don't know how that
fits into his whole scheme.
Because again, we just
literally have a few fragments
of his writings, few
fragments of the scrolls.
But many, many other people
praise him to the heavens
as being the person
who, if you will,
sort of knocked them
out of their lazy habits
of thinking about the
world, knocked them out
of their dogmatic
slumbers and made
them start really thinking.
The I Ching is a Chinese work.
And I oftentimes mention that
in conjunction with Heraclitus.
The I Ching sometimes
is subtitled
in English translation
as The Book of Changes
because an important part
of ancient Chinese thought
was that we do, in fact, live in
this constantly changing flux,
but behind that flux
there are patterns.
There are principles
that are themselves
persistent that do not change.
Understanding how the interplay
of all these eternal patterns
creates the world we live in,
allows us to either figure out
how to live a harmonious
life, or if we're ignorant
of those principles
of change, we
end up creating
chaos and disorder.
It may very well
be that Heraclitus
had ideas very similar to
that, but that is speculation.
I'm not the first to
speculate that may
be the case because,
again, this isn't something
peculiar to Chinese
thought or Greek thought.
It's something that you
find in archaic thought
pretty much universally.
Parmenides has an
interesting idea
of how to solve the
problem of change.
He says, in fact,
there are two worlds.
Parmenides introduces
an approach,
which we sometimes
called dualism.
Dualism-- I mentioned before
in conjunction with ethics--
dualism is the belief that
there are literally two worlds.
Now Parmenides says, yeah
the Heraclitian flux,
which is essentially
unknowable because it's
in a state of constant change,
is the world of appearances.
The real, however, is one.
It is an unchanging
unity, incapable of change
because it has all perfections.
To be is to be exactly what you
are, perfectly what you are.
So the real must be one.
Now the problem with
dualism is that it generally
introduces more
problems than it solves
while, in the last analysis,
failing to solve the problem
is set out to solve.
If there are, in fact,
two worlds and this world
of appearances is
simply illusion,
where did that
illusion come from?
The real never changes.
Where did that second world
that is ultimately unreal
come from if it didn't
come from the one.
And if it did come
from the one, then
clearly the one
is in interaction
with the world of illusion.
Put it this way, if
you have a dream--
say you dream that
you're in a movie
dancing on top of a train car.
You wake up and you go, wow,
I wonder why I dreamt that.
You were not actually on
top of a train car dancing,
but you had a vivid dream.
OK?
The dream is a real dream even
if the content isn't real.
If you have a hallucination,
the hallucination
is a real neurological event.
OK?
Even if the content isn't real.
So if this second world,
this world of illusion,
is an illusion and its content
is misleading and unreal,
still there really
is an illusion.
Where did that come from?
This is a position
that most philosophers
would say doesn't
really solve anything.
Although this notion of the
unchanging, perfect unity, that
is what is ultimately real,
that was an important part
of medieval theology.
Medieval Christian theologians
drew upon that language
to try to describe God.
And they have the same problems.
Well if this is what God
is, how does God actually
interact with the world?
This just doesn't fit
easily with a whole lot
of the rest of what we
want to say about God.
So Plato wanted to be very, very
sure that people didn't mistake
his theories about
universals, which we're
going to discuss later, with
the ideas of Parmenides.
He wrote a dialogue called
The Parmenides in which he
has Socrates interrogating
Parmenides about this doctrine.
Different people interpret
that dialogue different ways.
It never could have taken
place because Parmenides
was dead long before
Socrates, so why
would Plato create
that particular piece
of philosophical fiction?
Some people say, well, it's just
this brilliant piece of self
criticism where he had grown
doubtful about his own theories
concerning universals.
Other say, well, who
knows what it is?
Maybe he just felt that in the
end, the ideas of Parmenides
would look better than the
criticisms of Socrates.
My own take on this,
which is certainly
within the mainstream, is now
look, Plato-- and the most
commentators on Plato it will
agree with this-- Plato is very
different in his
ideas from Parmenides.
But if you are too
casual a reader,
you may very well
mistake some of what
Plato says for the
doctrines of Parmenides.
And I think Plato wrote this
dialogue, The Parmenides,
to make sure that everybody
understood I am not simply
advocating the
doctrines of Parmenides.
I'm not a dualist.
Plato, in fact, tells us
that reality is not dual.
And we'll talk about that when
we talk about the divided line.
Reality's not dual, but
language is necessarily dual.
And that's where
we get mixed up.
OK?
But that's the teaser trailer.
We'll get to that later.
Pythagoras.
Pythagoras is an enormously
interesting philosopher.
He may have actually
been Egyptian.
The Pythagoreans were
mathematicians as well as
philosophers.
They were mystics.
They practiced nonviolence,
lived in a monastic community,
gave full equality
to women, which
for the Greeks of the time
was just utterly unheard of.
They apparently were astronomers
as well as mathematicians.
They believed in
reincarnation, and they
believe that essentially
souls a reborn
because we have
descended from the divine
and we are returning
to the divine.
And so they believed
nonviolence, vegetarianism
as a form of
non-violence because we
ought not to harm any
soul as it struggles
to ascend back to
its divine source.
Leaving aside the religious and
mystical side of Pythagoras,
which I do think and I think
most callers would agree,
did have a profound
impact on Plato.
What's important
here for cosmology
is the mathematical philosophy
of the Pythagoreans.
The Pythagoreans had an
interesting take on this.
They said, look, if you
want to understand--
yes, this whole world of
appearances is in flux.
But if you want to understand
what makes it knowable, if you
want to understand what's real,
look at the general patterns
that occur and describe
them mathematically
as much as possible.
And if you can come up with
these mathematical models
of what's behind
appearances, then you'll
know what's really
real in nature.
Well, since we have
modern science--
we've had modern science
for a few centuries--
that sounds pretty elementary.
But imagine being among the
first people in the world
to ever think this, to
ever figure out this
is the way to go.
Plato thinks this is one of
the most brilliant ideas ever.
He will spend a lot
of his own career
saying that mathematics is
indeed the language of nature.
If you want to understand
what nature is telling us,
you need to be able to
understand it mathematically.
Aristotle had no
time for this at all.
Aristotle complained, in fact,
these crazy followers of Plato
they want to turn
everything into numbers.
That's not the way to do
science, all these numbers.
Science should be
about classification.
Well, there's a role for that.
But certainly, when science
takes off in the Renaissance,
it's because they've
rediscovered two things--
this notion that mathematics
is the language of nature
and this hypothetical method
that Socrates introduced.
Finally, Socrates.
We've talked a lot
about Socrates before,
so all I want to
add here is first
of all, the crucial
importance of what's sometimes
called the dialectical method,
where you make a hypothesis,
you hold it up to scrutiny,
you go back and revise it
if it doesn't hold
up, and you keep
doing that until
you get something
that stands up to scrutiny.
You stand ready to
revise your ideas
about the world based
on the evidence.
And that's, again,
even in our time,
that's hardly a
universal attitude.
Socrates also argues in several
places that of the things
we can know in the
world, the things
we can know with
certainty are very few.
And they will basically
be abstract principles.
For the rest of what we use
to get around the world,
we have reasonable beliefs.
And reasonable beliefs are
quite sufficient for that task.
What makes a belief reasonable?
You can explain why
you hold that belief.
You've held it up to scrutiny.
You can give an account of it.
And you stand ready
to revise that belief
if the evidence shows
that you ought to.
And that, he says, gets
us through this world
of appearances.
This gets us through
everyday life.
The additional thing
that Socrates offered,
the revolution, in
fact-- part of revolution
he created in philosophy
was to say, you know,
all this speculation
about what's real,
and how we know it's
real, all that, that
may be interesting
to some people.
But he said, there's
only one thing,
I think, that is
a really important
philosophical
question and that is
how we ought to live our lives.
If we are speculating about
the nature of knowledge
or the nature of
reality and that
helps us to eliminate misleading
answers to the question
how ought we to live
our lives or helps
to open the doors
to figuring out
how we ought to live our
lives, all well and good.
But all this
abstract speculation
has to be brought back
into everyday life
to help us live our lives.
Or else, what's the
point of doing it?
OK.
That has a profound
impact on Plato.
And I think some people
who have an incomplete
or I think to some extent
mistaken understanding
of Plato, forget that
he is always very
much the student of
Socrates in this regard.
No matter how far into the
heavens Plato's mind soars,
he always brings it
back down to earth
and says, OK, now what
we're going to do about it?
So Plato's solution
to pull together
all of this whole
problem set, if you will,
is what Russell refers
to as universals.
Now sometimes you
see that translated
as Plato's theory of ideas.
That's totally misleading.
Although etymologically
the word idea
is close to the Greek word.
An idea is something
that exists in your mind.
If somebody wasn't thinking of
an idea, it wouldn't be there.
That's not what
Plato's talking about.
The word form is sometimes used.
That's a little less misleading.
But when we say form in
contemporary English,
we tend to think of shapes.
Well remember, by the
time you're hearing this,
you've completed the logic
section of the course.
Think about logical form.
There are formal truths that
have nothing to do with shape.
Shape is just one kind of form.
And that's closer to what
Plato's talking about.
As Bertrand Russell points
out in his book, The Problems
of Philosophy, on those
two chapters on universals,
he says that, in fact, most
contemporary philosophers
would be talking
about these problems,
they would use the
term universal.
And I think that's a
less misleading term
simply because we have had
less baggage attached to it.
So what exactly is a universal?
Here's the breakthrough idea.
If you have only two categories
of being, mind and matter,
that limits the
kinds of answers you
can give to any question
about knowledge or reality.
If everything that
is real is simply
what's whatever is
material, then it's
very difficult to
account for what we
call abstract, general truths,
the truths of mathematics,
the truths of logic, even the
more general truths of science.
If on the other
hand, everything is
mind, that means that
essentially things exist
because we think of them.
If everything that's real
has to be either a material
object or a mental
object, then essentially
its a figment of our
imagination or it's part
of this world of flux.
It comes into being
and passes away.
There is where the
problem occurs.
Plato's insight is that
general, abstract properties
or, if you will, universals
are every bit as much
of the real world as ideas
and material objects.
In fact, even more so.
What is a universal?
Well, what color is
the tip of this marker?
Not a trick question.
You'd say red.
What color is this ink?
Not a trick question.
You'd say red.
So there's some literal sense in
which they are the same color.
Well, yeah, you can see that.
Nuh-uh.
No, actually you can't see that.
Your eyes don't see sameness.
Your eyes, your
brain, if you will,
collects the data of sensation,
and your brain organizes it.
It is your mind, your intellect
that recognizes sameness.
What shape is this?
It's circular.
What shape is this?
Circular.
What shape is this?
Circular.
Are they literally in some
literal sense the same shape?
Of course they are.
And we wouldn't think
twice about saying
they are the same shape.
Is any of these
a perfect circle?
No.
If you could measure
it closely enough--
a circle is defined as a closed
curve in which every point is
equidistant from the midpoint.
And leaving aside the problem
that mathematical points don't
have material extension-- don't
even worry about that for now.
If you could measure
this minutely enough,
you'd find, no, it's
actually it's irregular.
Well, couldn't we
make it more regular?
Well, up to the limits
of our technology, yes.
But then if we could
measure-- oh, you know what?
We're finally going to get
down to the level of molecules,
in which case, the whole
idea of surfaces is gone.
So how is it we see these
abstract general properties
such a circularity?
And we see them repeatedly
in many, many, many objects.
This is what Plato's
understanding.
What makes things
intelligible to us
is that particular
objects, such as this cup,
participate in or embody,
or somehow manifest to us
abstract general properties.
They only do it temporarily.
They only do it
imperfectly, but we're
able to see these abstract
general properties
through them.
How do know there's a cup here?
I tell you, when I have a
live class before me and I ask
that question, how do you
know there's a cup here,
I see everybody
kind of squirming
and looking away like, I want
to tell him I can see it,
but I know that's an ambush.
But no, it isn't and ambush.
That's exactly why you would
say there's a cup here.
I can see it.
I cannot only see
it, I can hear it.
I can taste it.
I can smell it.
Well, OK.
What is it that I see?
Let's just start with vision.
What is it that I see?
Colors.
And shapes.
And the relationships between
those colors and shapes.
OK.
Are colors the
kinds of things that
can be shared by many
different objects at once?
Yup.
Are shapes?
Yup.
Are relationships?
Yup.
So in other words, I
know there's a cup here
because my mind recognizes a
concatenation of universals.
Without that concatenation
of universals,
I don't know there's a cup here.
I don't perceive a cup.
And you know what?
Without that concatenation
of universals,
that convergence in an orderly
way of universals in space
and time, temporarily an
imperfectly, without that,
there is no cup.
That's all particular
objects are
is a particular convergence
of a set of universals
in particular relationships to
one another in space and time,
which means that
concatenation comes into being
and passes away.
And it is not a perfect
example of those universals.
But it is enough to, if you
will, direct the mind's eye,
as Plato puts it, to
see those universals.
Now as Russell points
out, we don't normally
think about particular objects
in terms of their universals
because we're just in the
habit of taking what's
going on behind the
scenes for granted.
When I'm looking for
a particular cup,
I probably want to
drink something.
I'm not thinking about, how
do I know there's a cup there?
But if I stop and
ask that question,
all of a sudden
the doors are open.
And I can see a whole
lot about the universe.
OK.
Abstract general
properties or universals
are, in fact, the
key to our ability
to know anything, the key
to why things are in spite
of this flux in space and time
of things coming into being
and passing away, why
things are intelligible.
OK.
David Hume, a philosopher who
I'll mention a number times,
was uncomfortable with this
idea that things we can't sense,
non-material things could in
some literal sense be real.
In fact real-- turbo
real, if you will.
Redness, itself, doesn't
come into being or pass away.
The redness of this cap will.
And it's not perfectly red.
It's not even entirely red.
You can see little
discolorations in it.
But it's red enough
that I see it.
I can recognize redness.
So Hume, like many
modern thinkers,
wants to start with
sensation and say,
you know what-- Russell
talks about this.
You may remember it
from the reading.
I don't need the
notion of universals.
If I say, look at a
red rose-- we'll just
say that's a rose
rather than a tulip.
If I look at a red
rose, what I'm doing
is I'm using that
rose as an emblem
in order to organize
around that emblem
a whole bunch of other
particular objects
that are similar to it.
I don't need general abstract
properties to do that.
I just need a bunch
of particulars
that are similar to one another.
Well, as Russell
points out, Hume
has kicked universals
out the front door
and snuck them back
in the back door.
Excuse me?
A bunch of particular
objects that are similar?
What does similar mean?
It means they have
the same properties.
Uh, uh-oh.
Is similar a
relationship that is
consistent between those
different roses-- OK, OK.
We didn't get rid of
universals, did we?
Now if you're still
sitting back and saying,
this just seems
implausible to say
that abstract general properties
are a real part of the world
or, in fact, are real
in a more robust sense
than particular
material objects are.
Now let me ask you
this, have you ever
seen the law of gravity?
Really?
What color is it?
Now you see objects
that are falling.
We look at a bunch
of falling objects.
We do controlled experiments.
And we come up with
abstract general properties
that we call laws of nature.
And we say, you know what?
That law of nature,
the law of gravity
is real in a more robust sense
than any particular falling
object.
Oh, gee, I guess.
OK.
Then in that case, once again,
we may not have looked at it,
but we're used to
actually seeing
in the world in this way.
If I have a circle and
I begin to deform it,
I am not destroying the
nature of circularity
or inventing the nature
of triangularity.
A triangle has always
been and always will
be just exactly what
it is, independent
of any particular
material triangle.
Circularity will always
be and has always
been exactly what
it is irrespective
of any particular
material circle.
What I'm doing is I'm the
forming this material object
such that it embodies
circularity less and less
and triangularity more and more.
How could I even know
that unless the notion
of circularity were constant
and the notion of triangularity
were constant.
I would have no way
to consistently apply
the words over time.
What this means is that
abstract general properties,
while they are
displayed by things
that are in space and time,
they are themselves outside
of space and time.
They are not within
space and time.
Therefore, they are
not subject to change.
Therefore, they're not
subject to imperfection.
They just are exactly
what they are.
Referring again to
medieval theologians,
they kind of went nuts over this
stuff when they discovered it
during the medieval
period and said,
wow, you could
change a few words
and turn Plato into a Christian.
In fact, by the time
they were reading it
through St. Augustine
in particular,
Platonic philosophy had so
influenced Christian theology
that, in fact, the
reverse was true.
You could change you
could change a few words
and turned quite a bit
of Catholic theology
into Platonism.
Which is not to say that
they're the same thing.
OK?
Augustine was a brilliant
man, brilliant philosopher.
But I personally
think he got Plato
wrong on a number of points.
And I'm not alone
in that opinion.
But the fact is that these ideas
have influenced our thinking
in lots and lots of ways
that we're probably not
even aware of until you
start investigating.
So Plato, when he starts talking
about the metaphor of the sun,
he wants to distinguish
between knowledge and opinion.
A let me illustrate
something to you.
Circularity is a universal, yes?
Triangularity is a universal?
Yes.
And so forth, and so
forth, and so forth.
Those are both shapes.
Is shape a universal?
Yeah.
Is it more general than
circle or triangle?
Yeah.
There are more, if
you will-- there's
an ascending pyramid
of generality.
Shape is one possible
type of form.
And so forth, and so forth.
Plato gives us some
hints about what
this would be like
all spelled out.
Neo-Platonist philosopher
such as Plotinus
who was an important
interpreter of Plato
but also a very important
religious mystic, an Egyptian
who lived in Rome
most of his life.
He spends his whole
philosophical corpus,
if you will, spelling out
exactly how this pyramid goes,
which Plato did not.
This notion that there is an
ascending pyramid, if you will,
to finally get to the
highest universal, that
is at the core of
the divided line
in the metaphor of the sun.
Plato wants to distinguish
between knowledge and opinion.
Again, that's that
distinction is
at the bottom of much
of what he's doing.
Knowledge requires truth.
If there aren't truths to
know, there is no knowledge.
Truth requires reality.
If nothing is real,
there's nothing
for truths to be true about
and, hence, no knowledge.
There's a sort of completeness
to this very strong
interpretation of knowledge.
Now Plato actually uses a half
a dozen different Greek terms
to talk about knowledge
versus opinion.
We're just kind of
simplifying that.
Knowledge requires truth.
Truth has to be of real objects.
And there's a kind
of completeness.
The mind has apprehended how
the world actually is unmuddled.
And this requires understanding.
I have an elderly
friend who likes to say,
don't ask me how I
know, I just know.
And of course, we kind
of chuckle about that.
Because it's one thing to
have this very strong opinion.
It's another thing
to actually know.
Knowledge requires
understanding.
It's paradoxical to say,
well, I know something.
I don't understand
what it is I'm saying.
I just know it's true.
Well, one can be very
confident, but one can also
be babbling when one
is very confident.
Opinion, on the other hand,
only requires conviction.
It doesn't require truths.
It just requires that you're
convinced about something.
Convictions don't have to
be about anything real.
They can just be about
whatever appears real to you.
And opinion is a
matter of degree.
I could hold opinions strongly.
I can hold them less strongly.
I can hold them
sort of flimsily.
And they don't
require understanding.
They only require
that I be persuaded.
I can be persuaded of
things that I don't really
understand because of
that emotional element
of persuasion.
So this distinction between
knowledge and opinion
is-- opinion would be
appropriate to the realm
of the Heraclitian flux, to
the realm of comes into being
and passes away and is known
primarily through the senses,
that we're trying to
make order out of it.
It's imperfect.
It's impermanent.
And so we can only have
limited understanding of it.
That means that it's
the realm of opinion.
Our knowledge of universals,
on the other hand,
would be complete.
And that's where real
understanding would lie.
If you were to put a spoke
or an axle or something right
here and [cranking sound]
turn this
over so that this is on the
bottom and this is on the top,
essentially you've got the
distinction between the upper
and lower parts of Plato's
divided line, which
is what we'll talk about next.
