So far we've been focusing 
on the philosophy of
science - basically on the transitions in
the mosaic. That's what we've been
studying so far. We've been studying
transitions and the logic of transitions.
What's the logic of scientific change?
Is there a universal scientific
method? Can we know anything for certain?
What's the difference between science and
pseudoscience? All these things.
Now we are going to focus on the
content of the mosaic. We are going to start with the Aristotelian-Medieval worldview.
Why would anyone bother studying
something that has been abandoned more
than three hundred years ago? Why would
anyone study the worldview of the past?
(Student) "I think it might be useful for 
helping us understand our own worldviews."
(Hakob) "In what way?" (Student) "If there is a law-governing process from one mosaic to
another,
then the content of ancient views 
has affected our current views."
(Hakob) Any other ideas? I'm going to help you a little bit. What picture of science would
you have if you didn't know anything
about science before 18th century?
What sort of a picture of science would
you have? Suppose for the sake of
argument that the Aristotelian-
Medieval mosaic never existed.
Supposed the "actual" science
started sometime in the 18th century.
What sort of a picture of science would
you have in terms of scientific change and
scientific method? What sort of beliefs
about science would you have as
philosophers of science? Try to think
about all those issues that we've been
discussing so far, such as
lecture 4, lecture 5, and lecture 6. (Student) 
"You have much simpler view of the past and you
say, well, their science wasn't real.
They didn't look critically at the world
and we now have science and we will
look critically." (Student) "Without past mosaics you could come to the conclusion that there
is only a static method
and that is the hypothetico-deductive 
method." (Hakob) That's the answer I was
looking for. Very good. Thank you very much!
Now you would be surprised if I told 
you that even some fifty years ago
that was exactly the picture that
philosophers of science and historians
of science would have in mind - most 
of them. Even nowadays in popular
literature, most of them ignore 
the Aristotelian-medieval
science. And because they ignore that science, they arrive at a very simplistic
image, very simplistic notion of science.
What's that notion? That there is a
universal and fixed method of science 
and it does the job. That's it.
Everything before that is not really
science. That would be extremely simplistic
and you know the major drawback of this
approach. If we ever decided to accept
this approach, we have to be prepared
that the science of the future would
dismiss us as not really scientific. We
understand this, don't we? Very good! So what do
we do? I think we have to be more humble
than we used to be and try to study
the science of the past without trying
to dismiss it. I'm not asking it to accept
the actual content of the science of the
time. God forbid! No! There is reason why
those theories were abandoned three
hundred years ago. So those are not by
any means the best theories we have at the
moment. But what it teaches us is that
science changes. Not only scientific 
theories but also scientific
methods. And this is the idea! If you ask
me why it is important to study the
Aristotelian-medieval science? The most
important reason is that it teaches you
and shows you that you can have a
genuine science with a different
scientific method. Why do we believe it's science?
Well, because we believe that it obeys
the four laws of science change.
What was that mosaic? The first thing we
have to know - and I think this is the
thing that you already know - the 
key elements of this mosaic
were accepted until the end of the 17th
century. What are the elements?
In the middle we have natural philosophy and physics. This one is humorous physiology.
What's this one here?
Astrology, right! And this one will be
cosmology. This one is theology.
This one you may or may not know. This is
what we call metaphysics. Mathematics here.
Natural History. Optics, and finally the
grand Aristotelian-Medieval method.
As you can expect, I'm going to start from the Aristotelian physics. Now the beginning
is very simple. This is something that
you already know. The four elements: air,
fire, earth, water. Which two of these elements are heavy? Water and earth. And these two
are light. The law of natural motion says 
that all elements in their natural state
tend to reach their natural positions
and to remain there. This is a universal
law that the Aristotelians accepted.
They thought that every element has a
natural position and it has the natural
tendency to get to that position.
OK? Now the outcome actually depends 
on what that natural position is.
For heavy elements the natural 
position was thought to be the
center of the universe. As a result
of this you get the Law of Natural Motion
for heavy elements, which would be heavy
elements tend to collect in the center
of the universe. You all know this. This
is nothing new for you.
For light elements, the natural position is the
periphery of the terrestrial region,
sublunar region. You put these two together and
you arrive at the law of natural motion
for light elements: light elements
tend towards the periphery of the
terrestrial region. It is because of this
that we observed the arrangement of
elements the way they are.
This is simple. Element earth naturally
gathers in the center of the universe.
Then comes the layers of water,
air, the layer of fire. This is just a
repetition. This is something you
already know. Let's proceed to something
that you may or may not know. First tell
me why you think they believed in
four elements. Why exactly four? What sort
of intuitive experience would lead you
to  that belief? You understand they were
Aristotelians and therefore they had to only
accept things which were grasped
intuitively by an experienced person.
Therefore anyone who had experience with
the world should be in a position to
arrive at this conclusion. So why do you
think they arrived at this conclusion?
(Student) "Is it because those 
are the things that you absolutely
need to survive?" (Hakob) That's interesting! 
In what ways? (Student) "Earth provides you with food.
And you have to have water and fire
for heat and shelters and air in order to
breathe." (Hakob) This is one of the most unique
answers I have ever heard. Absolutely
incorrect but very unique! I could have never
possibly thought about it myself.
Honestly! That's brilliant! You see in
philosophy  the first thing you learn
is to appreciate brilliant wrong 
answers! Very good. Thank you!
Now anyone else? (Student) "Wouldn't
it be because intuitively they see
things that are solidly shaped and they
say ok this is earth because it holds
its shape, then they would see
something absorb the shape of their
containers and that would be liquid and
then air is everything else other than fire,
because those are the four things that
they they observed in their reality."
That's actually the reason. Even these days if 
you ask professional physicists "what stages
are there for matter? What do they 
say? Solid state, liquid state,
gases, and plasma. So even to this day
we have some similarities. So there is
something to that. Essentially if you
just observe and summarize it is quite
natural that you intuitively arrive at
this system. And we know from history of
science that many different cultures
arrived
at this idea independently. So there was
something natural about this distinction.
One thing they believed about these
four elements is that they are
characterized by the so-called sensible
qualities. Those qualities will be cold
and hot and also wet and dry.
So as a result you have fire that is dry
and hot, and you have earth that is dry and
cold, and you have water that is wet and cold and
finally you have air that is wet and
hot. These are different elements but they all
characterized by a combination of the two.
If you accept this principle, this opens
numbers of possibilities for you.
First one is the idea of transformability.
Elements can actually transform
to one another. So what do you do in
order to transform? You just change
their sensible qualities. If you can take
something cold and turn it to hot,
you would change the element. The best
example that you have is this one:
Water. Water consists almost
entirely of element water. There might
be mixtures of some other
elements, some traces. But it's mostly
element water. So what happens is that
the heating of wanted changes its quality
from cold to hot and turns it into vapor.
You understand the logic here? Now tell
me what happens when you burn some wood?
What sort of transformation takes place?
Anyone wants to try? Let's go
step-by-step, OK? So what sort of a
combination of elements are we dealing
with here? How would you describe it?
Is it heavy or light?
(Student) "'The wood is heavy." (Hakob) It's heavy, therefore what sort of elements would it be mostly
composed of? (Student) "Earth ... and water?" (Hakob) There
should be some water, some combination of water and earth.
So we are here in the cold? (Student) "Yes."
(Hakob) So what happens in burning? You are 
right: we start from something cold and then
what happens? You get some vapor,
therefore water turns into air, and
the earthly part turns into fire. In
a similar fashion, they explained each
and every transformation that you can
come across. Let's move on. If you accept
the idea of transferability, does it make
sense to study those transformations?
What do you think? If you know that the
world allows for transformations to
happen, can you have actually science
about that? Yes, you can! What would be the
name for that science? The science that
studies transformations?
(Student) "Is it alchemy?" (Hakob) Exactly! So 
the very possibility of alchemy follows from
the Aristotelian principle of
transferability. Do you see this? You'll
see how they arrived at that. It doesn't
really tell you that you have to accept
alchemy as a working theory - you may or
may not have a full-fledged theory - but one
thing they never questioned is the possibility
of alchemy.  They would say "of course
transferability is possible, therefor
the science of those transformations
should also be possible. It's another
question whether you had such a
science. The idea that alchemy is a
scientific discipline was beyond question.
That's alchemy. Now, a few things about
their humorist physiology and medicine.
Let's take Socrates, a
human being. They believe that
human body contains four bodily fluids,
the so-called humors. Here they are:
blood, yellow bile, black bile,
and phlegm, four fluids, four humors.
This is a humorist theory of medicine.
Hippocrates, Galen ... the great
physicians of the past all
believed this theory.
This was actually the accepted theory all the way
into the eighteenth century. Every human
has a predominant element. And this
explains why there must be four.
Why? Well, because what is it that they can
make one fluid different from
another? They are all composed of four
elements, right? Essentially everything is
composed of four elements, therefore the
only thing that can be different between
any two fluids, any two humors, 
is the predominant element.
when the predominant element is air,
you get blood. When the predominant
element is fire, you get yellow bile.
When the predominant element is earth,
you get black bile. Finally for phlegm the
predominant element is water. It doesn't
mean that there are no other elements.
Essentially the combination of all of
them and mostly water. We understand that.
Therefore by virtue of their
corresponding elements, humors are also
characterized as dry, wet, hot, or cold.
You can see there is a nice symmetry
between the four elements here and the
four humors. What does this give us? Every
individual, according to this theory, has
a particular balance of humors, a balance
that you're born with. So what is natural
for you may or may not be natural for me.
Let's say for Socrates: suppose this is
his natural balance of humors: blood,
yellow bile, phlegm. Suppose this
is his natural balance, the balance that
he is born with. If you consider Plato
may or may not have a similar
balance, and chances are he has a
different natural balance. Let's say for Plato
the predominant is black bile as opposed to
Socrates who has predominant phlegm.
You understand I'm making this up, right?
I don't have any historical data
as far as the balance is concerned.
Aristotle has predominant blood and finally
Democritus has predominant yellow bile.
These are the balances that you're born with.
A specific balance of the four humors
peculiar to the individual has a name.
What do you think is the name?
This is a definition.
Balance peculiar to individuals is
called ...
temper or temperament. So depending on the
balance, you get different tempers.
So there are four basic temperaments. If
your predominant humor is blood then your
temperament is sanguine, meaning you're
very positive and outgoing and active,
and life loving and friendly. That's what
you are. If your predominant humor is
phlegm, then you are phlegmatic - you all know
what phlegmatic is! If your predominant
humor is black bile, then you are melancholy.
If you are predominantly yellow bile,
you are choleric - easily aggravated, very
often angry. I'm going give you a few
medieval drawings on the subject.
This is sanguine. You're insisting, very
active, and you see how he pursues the lady!
Literally pursue! And here you have
phlegmatic, slightly distant and more
romantic. And then you have melancholy.
This is the other way around and he's lying
in bed. And the choleric one should be actually
censored because it's 21st century
and you cannot do that!
More traditional symbols would be
this one: sanguine, phlegmatic,
melancholic, and choleric. Now, which
temperament is this? Phlegmatic because the
predominant element is phlegm. OK!
Which one is this?
Plato? Melancholic. Aristotle? Sanguine.
And finally Democritus? Choleric.
Good! So this is all clear. Again, I did
not insist that this is the correct
description of their actual temperaments.
I have no idea what they were. People are
born with different temperaments. But why are
they born with different temperaments?
What determines your temper? It should depend on
something. It cannot be random, right?
The Aristotelian world is not a random world
by any means. There must be
a reason for everything, or almost for everything,
and therefore there must be some
sort of factors that determine why
some people are born choleric while others
sanguine, some are more optimistic while 
others are more pessimistic. There should
be some explanation for this. So what 
do you think that determines the
temperament? The answer is natal horoscope.
Before we get to astrology, we 
have to start with basic cosmology
and their views on the structure of the
universe. This is the typical diagram
showing the structure of the universe. You have
the terrestrial region where the earth is in
the center of the universe and then you
have the celestial regional where planets and
stars revolving around the earth.
Here in the terrestrial region of
you have the four terrestrial elements.
And then in this region you 
have aether. Everything is made
of aether, the planets and the celestial
spheres, everything! Natural motion for
aether is circular. It tends to
move in circles around the center of the
universe and this explains why planets
should revolve around the earth.
They also believed that aether is immutable,
meaning that it doesn't come to be and
it doesn't cease to be. You cannot
generate it and you cannot corrupt it. There is
no generation or corruption in this
celestial region because there is nothing 
to transform it into. In the terrestrial
region there's a generation and
corruption because elements transform
from one another. That's what happens. In a
celestial region, you don't have that.
You only have one element so there can be no
generation or corruption. Then imagine
yourself in the Aristotelian-medieval
period, on the one hand you believe that
there are four elements, and you
also believe there is one element up
there, and then you notice a very peculiar 
thing: the celestrial region influences
the terrestrial region. Here are some
examples. The Sun is the source of heat and
light on the earth. Everybody agrees?
This is beyond any doubt. The moon
is the cause of ebb and flow of tides. The Sun
is the cause of the seasons on the earth.
You have clear-cut cases when something
celestial affects things terrestrial.
They believed that the motion of
the sphere of stars is due to the Prime
Mover. The motion is then transferred
to each of the subsequent spheres and
then eventually causes all sorts of
changes in the terrestrial region. Why would
anyone believe in this nonsense? Well,
because we have some examples of
celestial region causing things in the
terrestrial region. Now put these three things
together: You have changes here, you have
clear-cut indications that these changes
are caused by celestial factors and
then you also know that there can be no
such thing as generation or corruption
in the celestial region because it's
essentially eternal. What happened
that can possibly cause changes on the
earth? It should be something celestial.
We know that. But what sort of thing can
cause that? In other words, what exactly
changes up there? Something does change,
but what is it? You cannot have new stars,
new planets, because that would be an
instance of generational corruption,
The only thing that changes is the relative
position of planets. That's the only
thing that changes - they revolve. And
that's the only thing that changes.
Therefor, wouldn't it be natural to try to
study respective connections within
combinations up there and events down
here? It is reasonable to study the
causal connections between the celestial
and terrestrial regions. Now let's go to
astrology. As seen from the earth, if
you are the observer on the earth,
the Sun moves against the background of stars.
The apparent path of the Sun 
through the course of a year is
called ecliptic. The ecliptic is in the
center of a belt that we call zodiac.
It's a belt. Why do we need this belt?
Because the apparent path of all the
planets are within this belt of Zodiac.
You are not going to find a planet here or
planet there. So essentially if you look from
the Earth, you will notice that all the planets
revolve roughly in the same plane, OK?
There is a slight deviation but more or
less the same plane and that plane is
the one that we call the zodiac.
Now the belt of zodiac consists of twelve 
30 degree divisions which we call signs.
What are the signs? Taurus, Gemini,
Cancer, Leo, Virgo, Libra, Scorpio,
Sagittarius, Capricorn, Aquarius, and
Pisces. Now tell me why exactly 12?
You understand it's a division.
It could have been 24. But why did they choose 12?
(Student) "Months of the year?"
(Another student) "Lunar cycles."  (Hakob)
How long is a lunar month? It's 29.5 days, roughly.
So they realize that there are roughly 
twelve months a year, 12 lunar months.
That was the first indication,
so they took 12 as a number. And why
is it  that there are 360 degrees?
There are historical reasons for
this! Why 360 and not 100, can you guess?
This comes from old Babylonian mathematics.
Curious system - base 10 and base 12
... and it's the combination of the two!
What's the advantage of base 60? Really gives
you an advantage because if you take base 10,
you can only divide by two and divide
by five. That's it. For everything else,
you need fractions. It is not divisible by
3, not divisible by 4, not divisible by 6.
Not divisible by anything really! 
If you take 60, it is divisible by 2,
3, 4, 5, 6, 10, 12, 15, 20, 30 ... 10 numbers! So 
when you get to dividing things, it is extremely
convenient, OK? So there was a reason for that.
So you have 12 signs here.
An individual sign -  what we call your
horoscope but we really have to say your
individual sign - is determined by the
position of the Sun at the time of your
birth. In this particular case we would
have Aquarius. Each sign is associated with
one of the four elements. This is what
they believed. In a sense that when
something happens under that sign,
it increases the respective element in a
human being and in the surroundings.
Let's say it's too rainy in some region
then people say "well maybe it has
to do with water signs predominating, OK?
So not only will it cause changes in
human beings, but it would also cause changes in
nature.
Everything was thought to be connected
in that way. You have four triangles.
You have here
Sagittarius, Aries, and Leo. Those will be
your fire signs. Then you have
Capricorn, Taurus, and Virgo. Those will be
your Earth signs. Then you have your Aquarius,
Gemini, and Libra. Those will be your air
signs. And finally Pisces, Cancer, and
Scorpio. They would be your water signs.
If you accept this, you also have to accept
that it leads to an excess of the
associated humor in the body,  just by
the virtue of leading to excess elements, it
has to lead to an excess of the
associated humor in the body. Let's take
Socrates here. Suppose for the sake of
argument that he was born under the
sign of Aquarius - this will be his main
sign - so he will naturally have excess
air and thus excess blood in the body.
And he would be sanguine.
What if he was born
under the sign of Pisces?  The Pisces, more 
water, more phlegm, therefore phlegmatic.
So this is the idea. It is very
straightforward. An individual's temper
is shaped by the position of the Sun which
determines your predominant humor. And it
is refined by the positions of other
planets. So see you can have two
different Sagittariuses.
Both of them would be Sagittariuses.
Both of them would be choleric just by
virtue of being Sagittarius.
The balance of other humors would be decided
by other planets. They can shape your
temper, you see, different arrangement,
different balance ...
An individual's temper is determined 
by the specific placement of
the planets at the moment of the
individual's birth. Is this clear?
There is one more step that we have to take.
Once you accept this, it becomes obvious
why physicians must know astrology.
Why do physicians have to learn astrology?
Can you imagine a doctor learning astrology first?
Back then physicians were
expected to know their astrology or
at least to collaborate with a
professional astrologer. Why?
Humorous Physiology and medicine - if you
ask them what is health and what is
disease, they say health is a state of
perfect balance between the humors.
So when you maintain the balance that is
natural to you - the one that you're born
with - you are healthy. If something goes wrong,
if you have too much or not enough one of the
humors then you are unhealthy. When the
balance is not maintained, when you are
in a state of imbalance, then you are
unhealthy. These are the basic
principles. It is Socrates here. This
will be his perfect balance. Suppose this
is the balance that he was born with. As
you can see, we have a series of issues
with Socrates, in particular we have some
excessive yellow bile as you can see and
then we have some deficiency of blood
and phlegm. So it's a very complex
condition. It requires very complex
treatment, I assume. If the disease is a  state
of imbalance,
then what's curing? What would you do to cure a
person? Curing essentially is the restoration of
the balance of humors. Now there can be
different means and ways of restoring
patient's balance of humans but
essentially, you understand, if you
believe that the disease equals
imbalance therefore curing should be
balancing. Let's take Socrates, as you can
see he's quite pale here, just look at
his face and immediately as an
experienced physician you provide a
diagnosis. You say well it is because you
have deficiency of blood and I can see
on you face.
And then you have certainly the
yellowish color which is an indication that
you have excess yellow bile in the
body and not enough phlegm. So what would you do
in order to restore blood, to build blood?
You cannot inject blood. They didn't have that.
What they did have - they knew some
techniques which they believed were
conducive towards helping human body to
build blood. What are you trying
to do as a physician? You are trying to
create conditions in which the blood
builds itself. So what do you do here? You
say "well in order to build the blood,
I prescribe that you eat green vegetables,
and also some moderate exercising."
Moderation is the key, right? It's universal
device for anything. And it helps to build blood.
What about phlegm? Well, drink water!
and also eat fresh fruits because fresh fruits not
only do they contained water they also
known for their capacity building phlegm.
So this is what you do. And we got lucky
here because these procedures, fresh
foods and green vegetables, they also help
to normalize the yellow bile so you
don't really have to prescribe seven
different things. It really allows you
to solve three issues at the same time,
to organize the yellow bile. Take a more
difficult case like this one.
What can you say as a physician? Look at
his face! What can you say? Well, as a
typical case of fever, as you can see,
all the red, burning red, fever! You have
excess blood in the body, and also a
deficiency of black bile probably.
So what do you do? What will you
prescribe? Any ideas?
The all-time favorites: bloodletting!
That's what you prescribe. And also
interestingly enough it was
noticed that moderate consumption
of wine could be prescribed for
normalizing black bile
because wine had essence thought to have a
link with black bile so it really helps
your body to build that. Essentially what
you prescribe is just get drunk and go
fight! Let's now combine things. On the
one hand, curing is balancing.
On the other hand, we know
heaven determines indiviudal balance,
dependent on the particular combination of
planets at the moment of your birth.
So in this case if this was a combination
of planets then this would be your
temperament, your balance of
humors. Therefore we put these together
and knowledge of astrology is essential
for identifying individuals temper,
thus more efficient treatment. Now,
astrological forecast on the other hand
you cannot really forecast anything if you
don't know your astronomy, if you cannot
calculate the position. So astrological
forecasts requires precise knowledge of
the actual positions of planets
given on the time and therefore as a
physician, one is supposed to know
astrology. So if you have a patient
and you want to treat that patient,
the first thing you have to establish as
a medieval physician is what? It's temper.
It is what you want to establish. So there is
no neutral treatment. There is no such
thing. And this is the reason why people
believe that the best scenario, the best
option is when a physician knows his
patients since childhood because
the date of birth and the precise 
natal horoscopes were not
really available for common folk. They 
were only available for kings and other
nobility. But for common folks they weren't
available. so how do you know whether a
person is melancholy, phlegmatic, 
or sanguine? You just study
behavior, just like your friends, your parents,
brothers and sisters. You meet a person
and you say why she is so sad?
Then a person who knows the person says
that she's not sad - that's her natural
state of affairs! She's always like that
because she's melancholy.
But if you know the person and you know he is
sanguine, you know how he behaves, like
out there killing something,
hunting something, climbing Mount Everest
... you have to do things, right?
As a physician, one was supposed to know
astrology. It's safe to say that by the
13th century when most of the
medieval texts an ancient texts were
already translated into Latin, at the time,
physicians had huge tables with
descriptions of ailments and ways of
treatment for every natural essence. They
had a table and they explained "OK, you use
the root of whatever for treating this and
you use this particular vegetable for
that, the particular food for this. There was
a whole list of things.
Probably one of the greatest 
physicians of all time and certainly
the greatest physician in the 
Medieval period was Avicenna.
There is a very good movie 
about an English physician
who decided to travel all the way to
the Orient to learn from the great Avicenna
because back then in Britain there was
basically only bloodletting and they didn't know
any thing else, at least that's the way it's
presented in the movie. But Avicenna
was able to perform eye surgeries. That's how
sophisticated he was. His
multi-volume The Canon of Medicine was
the medical encyclopedia 
of the time. It was huge.
It was translated into Latin and then new
generations of physicians would amend it
and modify it. And this is a very good
example of something working for the wrong
reason. So they were right in the
treatments. Most of the treatments
actually worked, natural remedies
specifically, but the reasons were all wrong.
Nowadays we no longer believe in four
humors and yet many of the treatments
are still employed, one way or the other.
OK? Very good! Now we're going to move on
to the Aristotelian-Medieval method.
You know a thing or two about this
method already. This is the method
that says that proposition is acceptable
if it is grasped intuitively by an
experienced person. You already know that
this is extremely vague and any rubbish
can seem to be intuitively acceptable.
But then again this is roughly what
they demanded and required. And
this method was based on two
assumptions about the world, 
two principles regarding
nature of things and intuition grasps nature.
The first one I'm going to repeat just to
make sure that we're all on the same
page: a thing has its nature which is
basically an indispensable substantial
quality that makes the thing what it is.
So for an acorn would be the capacity to
grow into an oak tree, for lion cub to
become a full-fledged lion, for human
being basically the capacity of reason.
Intuition grasp nature was an 
important belief that human mind
has a capacity to grasp, to penetrate into
the nature of things when it is
experienced enough, not just randomly but
only one is experienced enough when you
observe things and observe and observe...
when you gain experience with a certain
thing, then intuitively you grasp the
nature of things. This was only one of
the aspects of their method. Consider
this that they believed that there is a
clear-cut distinction between things
natural and things artificial. What is a
natural thing? This is a definition: 
a thing is said to be natural when it is
not produced artificially and thus 
has its inner source of change.
Then explaine this: if you take a falling
apple, it's a heavy object, and it's
the nature of heavy object to descend
towards the center of the universe, so
you have something natural, something
that is not created by a human being and
therefore the behavior of this natural
thing is explained by its very nature, by
its inner source of change he change.
It changes because it has to!
It does whatever it does because it has
an inner source of change,
OK? The source of change is from the inside.
Why does it want to gather at the center
of universe? Because that's what its nature is.
Now the same applies to the reproduction
of animals. Why is it that they reproduce?
Because that's what nature dictates them
to do. They just want to reproduce.
This was the Aristotelian view. Now
compare this with artificial things such
as ship. Ship here is built to obey
the orders of the captain so it's
arranged in such a way that it obeys
an external command. It doesn't have an
inner source of change. You see? They
believed that it doesn't have any nature
because it's not a natural thing. It's 
an artificial thing. What makes
something artificial? It's when it exists
for some external purpose when its
source of change is something else. It
doesn't exist for its own sake! But keep
in mind that we no longer 
accept this distinction.
At least we do not believe that there is an
insurmountable wall between the two. But
back then they believed that there's a
clear-cut distinction. A clock 
is constructed to show the
correct time, to serve an external purpose. 
Anyone recognizes this particular clock?
Anyone has been to Prague, Czech Republic? This is one of the few surviving astronomical clocks.
This is actually from 1410. It is the famous Pražský orloj, a fantastic thing with revolving apostles!
Magnificent!
Anyways, it's an artificial thing.
No matter what it does, its source of change is external.
It exists to show the correct time. It doesn't have a nature. If this is clear, then they
should also be clear. They believed that
there is a strict distinction between
things natural and artificial, between things
with their inner source of change and
things with an external source of change.
It follows from this that in
artificial conditions a thing cannot
behave naturally. You can only behave
naturally in a natural condition. If your
conditions are artificial, you cannot
behave naturally because the
contradiction. So if you believe in this
and somebody offers you to conduct an
observation, would that be an OK thing to
do? Yes, it would be an OK thing to do
because you do not disturb anything. You're
basically just observing. But what about
the experiment? If somebody told you, you
know what, we have to experiment with nature
to study nature what would
you say? You'd probably say that
experiment, just by their very definition,
they presuppose artificial set-ups.
That's what experiment is all about: if
you do not impose something artificial,
you're not experimenting, you are just
observing. Therefore in order to have an
experiment you must inevitably have an
artificial set-up. You put those two
together and you arrive at a conclusion that
experiments are unnatural. In experiments
a thing does not and cannot possibly
behave in accord with its nature.
Let's take this famous pair of 
birds. You cannot possibly
grasp the nature of birds if you lock
them in a cage. That was the basic idea
because this is an unnatural
situation. This is an artificial set up.
This is not what they are naturally. In order 
to grasp their nature, you have to observe
the bird in its natural environment, you
see? This is the reason why they didn't
allow any sort of experimentation in
science because they honestly believed
that the moment you experiment, you turn
a natural thing into something
artificial. That is not how it behaves in
nature. As a scientist you cannot allow
any sort of experimentation because
experiments never tell you anything.
They never reveal to you anything. They only thing 
that reveals something is observation.
Go out there,
sit quietly and observe. You cannot
experiment. If you experiment that would
be artificial. So it wasn't a random
decision, you see? It followed from their
beliefs. This was their belief. We
know that by the Third Law your methods
depend on your beliefs. Once you accept
that experiments are unnatural then you
would have to say that if a theory 
about the nature of the thing
relying anyway on experiments, it is
unacceptable. The nature is to be
studied in observations only. When I
first learned that in a medieval science
there was no place for experimentation,
for me immediately the question was
are they stupid? What was wrong with them?
Why would they dismiss the whole layer
of science? But when this became
obvious, I felt that it makes sense.
Not that we are going to accept this
approach but at least you understand why
they dismissed experimentation.
They believed in a strict distinction between
artificial and natural and that led them
to forbid all sorts of experimentation. 
Consider two different categories:
This is quantitative change. This is
a type of change concerns number,
shape, size, anything quantifiable really. Compare
this with qualitative change, the type of
change the concerns qualities. 
What sort of qualities? The most vivid
example is a caterpillar that turns into
a chrysalis and then into a butterfly.
You see what happens here is that you have an
entity that acquires new quality.
In this particular case it is the quality of being
able to fly. It's not merely about size
and shape. It's about new quality. If I
ever managed to learn a new language
that would be an instance of a
qualitative change because I would then
acquire a new quality, meaning the capacity of
speaking a new language and this for the
Aristotelians wouldn't be the quantitative 
change. It is not about a number
of words that I know. It is not the 
change of size or shape. What it really is
is an acquisition of a new quality, the
one that we call linguistic intuition,
you know, when you sense the language and
feel the language, and it takes a lifetime to acquire.
So that would be a qualitative
change. What about quantitative change?
A quantitative change will be something ...
well, when you have one of something, then you get
two of something - that would be a
quantitative change. But let's see a more complex
example here. A young man loses some weight or
gains in height. Both of these would be
instances of quantitative change because
it's measurable. You can express this in
number. Simple? Right! So far we can agree
with the Aristotelians, But there's one
thing that we no longer accept and that
is the belief that there is a strict
distinction between quantitative and
qualitative changes, that qualitative
changes are not quantifiable.
Nowadays we no longer believe that 
a change that cannot possibly be
expressed in language of mathematics,
that it is absolutely unquantifiable.
Back then they did believe. They believed that some
changes are about numbers, shapes, and sizes,
and those changes are quantifiable, meaning
expressible in numbers, while other
changes are purely qualitative and 
they are not quantifiable,
meaning they're not really expressible
in numbers. Two types of change.
Again, this is something we no longer accept.
But back then this was one of the
foundational beliefs of the worldview. This
is something that we and the Aristotelians
all agree: mathematics deals with
things that are quantifiable. If you
cannot quantify something, you
cannot really apply mathematics to
that, right? This is almost true by definition.
If you cannot express something in
numbers, you cannot really apply arithmetic
to that. If you cannot express
something in shapes, you cannot
really apply geometry to that.
So essentially it's true almost by definition
of mathematics. Mathematics is only
applicable to things that are
quantifiable. Now you put those two
together and you arrive at a very
disturbing conclusion:  mathematics
only has a very limited applicability. 
It doesn't have a universal application,
just like we nowadays believe. It has
only limited application. So its not
applicable to the instances of
qualitative change. And by the
Third Law you arrive at the requirement
that says if a theory attempts to describe an
instance of qualitative change by means
of mathematics, any sort of mathematics,
arithmetics or geometry, it is not acceptable.
Suppose you came up with an equation
that explains how a butterfly emerges
from chrysalis, then they say "no, you
can't really do that. It's an instance of
a qualitative change. You are not really
allowed to do that!" That was the reason
why there was no mathematics in 
biology for a very long time,
only when you have to deal with the
number of species here and there then
you could apply but when you try to
explain some qualitative change,
mathematics was forbidden.  This
brings us to our conclusion.
The conclusion is extremely simple.
Essentially what I was trying to show
you is that the elements here are
interconnected to one another. I think it
would be even safe to say that the
Aristotelian science managed to reach
such a level of structural integrity
when all elements are so
interconnected with each other, so
tightly fit, it reached that level, that
we have never been able to replicate
ever since. We have a much more complex
science nowadays but essentially 
the Aristotelian science
reached a level of organization that has
not been replicated since.
A student a few years ago in my course 
on the Aristotelian-Medieval worldview,
after about 10 minutes into the meeting, 
I realized this student knows nothing,
not just about my course but nothing at all.
I say "OK, you see, this is a course about 
Aristotle, and I have to be honest with you,
my question is going to be very simple:
Is there anything that you know about Aristotle?"
He said "Well I know the guy.
He owns a restaurant on Danforth."
I think "OK, it's a good beginning because I 
already have a joke." But actually he was dead serious.
And I said "Actually he was born 
in the fourth century BC, long time ago!"
And again he was being dead serious and
said "He couldn't be possibly that old!"
Now I hope at this stage he knows a thing or two
about Aristotle. Now next time the
Cartesian worldview. Thank you very much!
