Transcript RATIONALISM – CARTESIAN MOTIVATIONS

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The Ancient Greeks were fascinated by how
the world is constantly changing: things are
born, change, decay and die.
They wondered whether what they saw was
really what there is.
They wondered whether appearances were
distinct from reality.
Here are three views.
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“πάντα χωρεῖ καὶ οὐδὲν μένει" καὶ "δὶς ἐς τὸν
αὐτὸν ποταμὸν οὐκ ἂν ἐμβαίης”
“Everything changes and nothing remains
still ... and ... you cannot step twice into the
same river.“
Nothing is stable.
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There is no change. There is no diversity.
All change and diversity are illusory – just
appearances!
Reality is The One – the Unchanging!
Zeno famously argued that even changes of place motion - is impossible.
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To travel (e.g.) 100m, you need to move 50m first.
 Logically, to cross any distance, you must first cross half of it.
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But to move 50m, you need to move 25m
And to move 25m, you need to move 12.5m…
…we can keep slicing the distances you first need to cross
forever. So, you can never get going!
According to Plato, common sense is wrong. We
do not sense the world as it really is.
 The senses present the world in a confused way.
The mind ‘sees deeper’. It sees the true natures of
things.
Reality contains a diversity of unchanging things
Plato called the Forms.
Plato explained this with the Allegory of the Cave.
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Ordinary mortals
see only the
shadows of
reality.
The forms
project their
shadows onto
the cave
wall…
…just as the
forms are
somehow
dimly
projected into
real things.
The real things –
forms – exist
outside.
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Reality contains forms. They are the timeless
and changeless natures of things.
They contrast with particular things in the
ordinary world (of appearances) which are
constantly changing.
But why believe this story? How do we
acquire knowledge?
The Guide
We know many
truths about
circles
Area = πr2
But no circles
we see or draw
are perfect.
360o in a circle.
So, our
knowledge must
be of some
perfect circle - the
Form of the circle.
Circle
Magnified section of
circumference
Ideal geometrical circles have unjagged
circumferences with no width and are infinitely thin.
And since it can’t
be sensed, it
must be grasped
by reason.
How can you use the same thinking
to prove that we don’t gain the idea
of equality through experience?
Plato said that if we have a pair of
sticks, we can judge how close they
are to being of equal length…
But we never actually see two
exactly equal sticks. Once again, just
look more closely!
What makes something
the kind of thing it is?
What makes two things
members of the same kind?
What makes a beautiful
thing beautiful? Or
something a badger?
What makes these two
things beautiful? Or two
things badgers?
World of appearances
World of Forms
Form (archetype) of
beauty
There must be some explanation for
why things belong in kinds.
The “one over many” argument: if x and y
are badgers, there must be something – the
Form of The Badger– that they have in
common. They both “participate in” the Form of
the Badger.
(These days, philosophers talk of universals instead of
Forms.)
The Form/universal Beauty is not present where the
beautiful things are but exists in a different realm.
Participation
Beauty
The universal Beauty exists in each and every
beautiful thing. It is quite unlike an ordinary object, as
an object can be only in one place at any one time.
Objects are a type of particular. But the universal
exists in many places at once – it is repeated
throughout its instantiations – and hence is called a
universal.
Fundamentally, however, we’re talking about the same
thing – an entity that makes a particular belong to a
kind or makes it the kind of thing it is.
Aristotle thought forms were immanent – located in the physical realm where their
instantiations are (he would have understood them as universals) whereas Plato
thought they were transcendental – located in another realm altogether.
The world
shows signs of
both stability
and change,
difference and
plurality.
Two beautiful pictures
may look very different
yet both be beautiful.
But there is
nevertheless
something stable here:
beauty itself.
A beautiful painting must be
created, may be adjusted
and may be destroyed: all
examples of change.
There can be many beautiful
things.
Beauty itself cannot
change or be
destroyed: we could
still talk and think
about it in the absence
of beautiful things.
These beautiful things
must ‘share’ it to be all
called beautiful.
So, beauty can’t
belong to the
world open to the
senses.
The senses only
reveal a world of
change.
Beauty
belongs in a
different realm
to the realm of
appearances
and it is reason
that gives us
access to it.
We recognise examples of beauty
and goodness.
But there is also a purely philosophical
angle: simply finding out the nature of the
reality we inhabit.
There is obviously a practical angle.
People differ over what they think is right.
People are sometimes uncertain. We
need to remedy this.
This is useful: we like beautiful things
and we want to praise acts of
goodness and punish badness.
But we also want to go deeper and ask
what it is that we recognise.
Socrates would ask, “What is beauty?
Truth? Justice?”
He was searching for the nature or essence
or, to use Plato’s word, the form of beauty.
How do we know about the
Forms if we can’t see them?
Because we have innate
ideas, gained from when our
souls existed in the world of
forms.
No – for ABCD is
and there are how
many such squares in
ALKJ?
Four.
So the area is…?
16ft2
4ft2
When we are born,
our soul ‘forgets’ the
ideas and they need
to be recollected.
So, if AD = DL, then AL=
?
…4ft.
And so the area of ALKJ
is…?
…8 ft2
If ABCD is a
square and
AD is 2 feet,
then the area
is…
…4 ft2
Plato demonstrates this
by getting Meno’s slave
boy to prove a
mathematical theorem.
By asking a series of
questions, Socrates gets
the slave boy to work out
the area of two squares
Now, BDNM is composed of four parts each
of which has what area? 2ft2
So, the area of BDNM is..? 8ft2
This shows that
the boy knew all
along the relevant
principles of
geometry.
How do we work out the area of a triangle of base b and height h?
h
?
b
Start with a rectangle. We know the area of a rectangle of sides h and b
is h x b.
h
?
b
Let us put the triangle in a rectangle. We know the area of a rectangle of
sides h and b is h x b.
h
?
b
If we draw a red line, you can see that each half of the triangle is half
the area of its smaller rectangle.
h
b = p+r
?
p
r
The areas of the rectangles are h x p and h x r . The area of the triangle
is half of each = ½(h x p) + ½(h x r) = 1/2 x h x (p+r)
h
?
p
r
We know p+r = b – it’s just the base.
So the whole area of a triangle = ½ x base x height.
Just like Meno’s slave boy, you have discovered the truth within
you.
h
?
p
r
Reason gives us knowledge
of the Forms (universals)–
the essences of things.
The Forms cannot be
detected with the senses
but only with reason.
Before we were
born, our souls
lived in the world of
Forms.
The Imperfection
Argument:
No perfect circle can
exist in the sensible
world, only
approximations. No
actual circle can be
infinitely thin and
perfectly curved.
The Knowledge/Change
Argument (*):
the Forms are unchanging.
Sensory experience reveals a
changing world. So, the Forms
are non-sensible.
In this embodied life, our
knowledge of the forms is buried
and must be unearthed by
exercising reason – doing
philosophy.
One Over Many:
If x and y are both F, then
there must be something, F,
that they have in common.
The Context Argument (*):
whether a painting is beautiful
or not varies with the context
but its sensible features do not.
So, the Forms can’t be
sensible.
Knowledge is of
truths - if you know
something, it can’t
be false.
…which cannot exist in
the world of
appearances accessible
to my senses …
In the world of
appearances,
everything is
changing.
…and so exist in a
separate realm
accessible to reason.
It is sunny now but it
might not be later.
I cannot therefore know
it is sunny.
I can merely have the
opinion or believe that
it is.
…the forms…
Knowledge must be of
changeless things…
Something F in
one context may
not be F in
another.
Context 1
Picture A may be
beautiful in relation
to picture B...
...but not in
relation to
picture C.
Context 2
Since the painting can be
beautiful and not
beautiful, it can't provide
us with a definition of
what is beautiful.
Whatever beauty is, it can't fail to
be beautiful. Since any thing that
we find beautiful could fail to be
beautiful in another context, we
can't simply collect beautiful
things together and hope that
they will share some simple
sensory property that we can
identify as the property of being
beautiful.
We have to look for the Form of
the beautiful or beauty: the thing
that makes beautiful things
beautiful. It is the essence of
beauty. But it cannot be detected
by the senses, only reason. Why?
Take a beautiful painting. In one
context beautiful, in another not.
But nothing about how the painting
appears changes. So, we're
looking in the wrong place if we
look for beauty amongst
perceptible properties.