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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.