Plato argues that we experience particular objects through our senses but do not directly experience abstract concepts like beauty or triangularity. These abstract concepts are "Forms" that are shared between multiple particular things. The Forms are eternal and unchanging, unlike particular objects that come into and pass out of existence. According to the Allegory of the Cave, most people are like prisoners chained facing a cave wall, seeing only shadows of objects and mistaking them for reality. True knowledge comes from comprehending the Forms, represented by leaving the cave and seeing the true nature of things in the light.

1. The Allegory of the Cave
From Book 7 of the Republic

2. Theory of the Forms
Plato argues that all of the objects that we experience through our
senses are particular things. We don’t sense anything ‘abstract’. For
example, we only ever see this or that particular beautiful thing,
but we never see ‘beauty itself’. We see this or that particular
triangle, never ‘triangularity itself’.
But, obviously, more than one thing can be beautiful or triangular.
They are properties that more than one thing can have. So, Plato
claims, if many different things can be beautiful or triangular, then
there is something they share in common that is not sensed, viz.
beauty or triangularity.
This is a universal or what Plato calls a Form. Definitions are meant
to capture Forms.

3. Particulars vs. Forms
Particulars: sensible particulars are complex material things that exist in
space and time. They change and they come into being and pass away.
Forms: Forms, in contrast, are permanent and independent.
• Permanent: Forms do not come to be and pass away. They that do not
change. The Form of a triangle cannot become not triangular, nor can it
have ever been not triangular.
• Independent: Forms exist independently of the particulars that instantiate
them. If no particulars participate in them, they would still exist. They exist
outside of space and time.
While a particular triangle I draw on the board comes to be and passes away,
the Form of the triangle does not come to be or pass away. While particular
instances of virtue come to be and pass away, what virtue is, its essence as
captured by its definition, does not come to be or pass away.

4. The Relation of Particulars and the
Forms
So particulars are sensible and forms are
intelligible. But then how can they be related?
Plato says that particular things ‘participate in’
or ‘instantiate’ their Form. A Particular triangle,
which is a material thing in space and time,
instantiates the universal ‘triangularity’. To be a
triangle something material must conform to
the criteria of what a triangle is.

5. Knowledge of Forms
• We sense changing particulars, and we thing
about unchanging forms.
• Because particulars come to be and pass away
we can only have opinions about them but not
knowledge. True knowledge can only be of
what does not change, i.e., forms.

6. The Cave as Allegory
The story of the cave “make[s] an image of our nature in
its education and want of education” (514a).
• Through the story we come to learn that to explain
sensible particulars we must take recourse to
universals or forms.
The stages in the story of the persons in the cave
correspond to stages in their learning about the nature of
reality or being.
• They go from thinking that sensible particulars are the
most real beings to realizing that the Forms are the
most real.

7. Allegory for What?
The cave itself represents the visible world, the
common-sense world of sensible particulars in
space and time, while what is outside the cave
represent the invisible world of the Forms.
• “Liken the domain revealed through sight to the
prison home, and the light of the fire in it to the
sun’s power; and…the going up and the seeing of
what’s above to the souls’ journey up to the
intelligible place” (517b).

8. Cave Positions
Persons are in the
rear of the cave,
bound, and can
only see shadows
projected against a
wall by a fire.
Persons are then
unbound, turned
toward the fire in
the cave, and can
see the figures
projecting
shadows.
Persons are then
dragged out of the
cave. They are
dazzled by the
sunlight and can
only first see
shadows. But then
are able to see
things-themselves
and the heavens.
Persons can then
perceive the Sun
itself, the source of
all light.

10. Example of a Triangle
• Image: An equilateral triangle that is part of a painting
of a real building that has a triangle as part of its
cornice.
• Visible thing: The particular equilateral triangle as part
of the cornice of the building.
• Lower form: Definition of the type of triangle it is,
equilateral, a plane figure where all three sides and
angles have the same length.
• Higher form: The definition of a triangle in general, a
plane figure with three angles and three sides. This
gives the Form for all types and particular triangles,
including the equilateral triangle.

11. Order of Explanation
• The image of the equilateral triangle depends on the visible
equilateral triangle, as it is an image of it.
• The visible equilateral triangle depends on the form of the
equilateral triangle, as one can only recognize material
instances of this triangle by knowing its form.
• To know the form of the equilateral triangle depends on
understanding the form of the triangle in general. One
must know what a triangle is in general to know the
particular kinds of triangles.
• The form of the triangle is higher than the form of the
equilateral triangle because it is more general, universal
and abstract.

12. Higher Forms
• But to know the form of the triangle (plane figure with
three angles and three sides) depends on already
understanding ‘plane’, ‘three’, angle’ ‘side’. These
forms are therefore higher and more basic than the
form of the triangle.
• What one must already understand to know these
forms? Very abstract forms: quantity, quality,
existence, being, etc.
• One can go even higher, getting to the Form of the
Good, “the cause of all those things [we have] been
seeing” (516c). Philosophical Christians call this God.

13. Order of Learning
• When we move left to right on the chart we learn to
explain the nature of particular things in terms of invisible
forms and principles that are abstract and universal. When
we learn a topic, any topic, we move from grasping the
particular to grasping the universal, to grasping a things
form and the relation of that form to other forms.
• Even natural science has this structure: the goal is to
explain the behavior of individual things (a body lets say) in
terms of something universal and invisible: a law which
says how the body will always behave, given certain
conditions. The goal is not to enumerate the characteristics
of a particular thing, but to understand how things of its
kind behave universally, and for this we need laws and
theories.

14. 3 Questions
• What is Plato trying to indicate by saying that persons
must be dragged against their will out of the cave
(516a)?
• What does Plato mean by saying that when we go out
of the cave that we cannot yet see, but must adjust to
the light?
• What is Plato trying to indicate by saying that if
someone who left the cave were to go back down into
it that their vision would be dim, and they would be
laughed at and perhaps even killed by those in the
cave (517a).

15. Ramifications for Education
• If education is ascending from images and things to a
knowledge of forms, then:
• “education is not what the professions of certain men
assert it to be. They presumably assert that they put
into the soul knowledge that isn’t there…but the
present argument…indicates that this power is in the
soul of each, and that the instrument with which each
learns…must be turned around from that which is
coming into being…until it is able to endure looking at
that which is, and the brightest part of that which is.
And we affirm that this is the good” (518c).

16. What Education Is
• Education is therefore “an art of this turning
around, concerned with the way in which this
power can most easily and efficiently be
turned around, not the art of producing site in
it. Rather, this art takes as given that sight is
there, but not rightly turned nor looking at
what it ought to look at, and accomplishes this
object” (518d).