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104 Jurgis (George) Brakas
[Addressing Glaucon, Socrates asks] [If] a man believes in the existence of
beautiful things, but not of Beauty itself [ . . . ], is he not living in a dream?
[ . . . ]. Contrast him with the man who holds that there is such a thing a Beauty
itself and can discern that essence as well as the things that partake of its
character, without ever confusing the one with the other – is he a dreamer or
living in a waking state? He is very much awake. So we may say that he
knows, while the other has only a belief in appearances; and might we call
their states of mind knowledge and belief? Certainly. [ . . . ] When a man
knows, must there not be something that he knows? [ . . . ] [T]here must.
Something real or unreal? Something real. How could a thing that is unreal
ever be known? [ . . . ]. So if the real is the object of knowledge, the object of
belief must be something other than the real. Yes. Can it be the unreal? Or
is that an impossible object even for belief? Consider: if a man has a belief,
there must be something before his mind; he cannot be believing nothing, can
he? No. [ . . . ]. So what he is believing cannot be real nor yet unreal. True.
[ . . . ]. It seems, then, that what remains to be discovered is that object which
can be said both to be and not to be and cannot properly be called either real
or purely unreal. If that can be found, we may justly call it the object of belief
[ . . . ]. (Plato Republic , 476C – 479A; Cornford ’ s trans.)
Socrates then goes on to identify that object as the world in which we
live, a world which he earlier implicitly referred to as a world of appearances.
Although one of the basic operating premises here is not that all
things in this world are in constant fl ux, but rather that they are neither
fully real nor fully unreal, it is not a far stretch to argue that they are neither
fully real nor fully unreal because they are in constant fl ux. If so, then the
argument is fundamentally the same as the one given in the Cratylus ; if not,
then it is another version of it. In the latter case, premise 4 would have
to be modifi ed accordingly as well as the wording in all the lines relying
on it.
P1. Knowledge is possible.
P2. Knowledge is knowledge of some object. That is, if a (putative) piece
of knowledge does not have an object, then that (putative) piece of
knowledge does not exist.
P3. All knowledge (unlike opinion) is stable. That is, all pieces of knowledge
are stable: they do not change, being one thing at one time, another at
another.
P4. If the object of knowledge could change (for example, if beauty, the
object I know, could become something other than beauty), then the
knowledge of that object would not be stable (my knowledge of beauty
would not be stable).
P5. All things in this world, as Heraclitus says, are in constant fl ux. That
is, all things in this world are things that are always changing in every
way, or, all things in this world are not things that are stable.
The Existence of Forms 105
P6. Some objects of knowledge exist among things in this world (assumption
for reductio ).
C1. Some objects of knowledge change; they are not stable (syllogism,
P5, P6).
C2. Some pieces of knowledge are not stable ( modus ponens , P4, C1).
C3. All knowledge (unlike opinion) is stable and some pieces of knowledge
are not stable (conjunction, P3, C2).
C4. No objects of knowledge exist among things in this world ( reductio ,
P6 – C3).
P7. If objects of knowledge do not exist in this world and do not exist in
another, then objects of knowledge do not exist.
P8. Objects of knowledge do not exist in another world (assumption for
indirect proof).
C5. Objects of knowledge do not exist in this world, and objects of
knowledge do not exist in another (conjunction, C4, P8).
C6. Objects of knowledge do not exist ( modus ponens , P7, C5).
C7. Knowledge is not possible ( modus ponens , P2, C6).
C8. Knowledge is possible, and knowledge is not possible (conjunction,
P1, C7).
C9. Objects of knowledge – called “ Forms ” – do exist in another world
( reductio , P6 – C8).
27
Plato, Aristotle, and the Third Man
Argument
Jurgis (George) Brakas
Aristotle . Peri Ideon ( On Ideas ) , in Aristotle Fragmenta Selecta , edited by
William D. Ross . Oxford , 1963 : 84.21 – 85.6 .
Fine , Gail . “ Owen, Aristotle and the Third Man . ” Phronesis 27 ( 1982 ):
13 – 33 .
Lewis , Frank A. “ On Plato ’ s Third Man Argument and the ‘ Platonism ’ of
Aristotle , ” in How Things Are , edited by J. Bogen and J. McQuire ,
133 – 74 . Dordrecht : Reidel , 1985 .
Plato . Plato: Parmenides , translated by R. E. Allen. New Haven, CT : Yale
University Press , 1998 .
Strang , Colin . “ Plato and the Third Man . ” Proceedings of the Aristotelian
Society , vol. 1 ( 1963 ): 147 – 64 .
Many scholars believe that the Third Man Argument (the TMA) is one of
the most powerful arguments against the existence of Plato ’ s Forms, many
going so far as to maintain that it is successful. It exists in two versions.
One, preserved to us only in a commentary on Aristotle ’ s Metaphysics by
Alexander of Aphrodisias, uses the Form Man as an example; the other –
offered fi rst, to his great credit, by Plato himself – uses the Form Large. The
difference between the versions is signifi cant, because the fi rst uses Forms
of entities or substances as examples whereas the second uses attributes or
properties.
Just the Arguments: 100 of the Most Important Arguments in Western Philosophy,
First Edition. Edited by Michael Bruce and Steven Barbone.
© 2011 Blackwell Publishing Ltd. Published 2011 by Blackwell Publishing Ltd.
Plato, Aristotle, and the Third Man Argument 107
Both versions use just three major premises (in addition to fi ve that most
people would fi nd uncontroversial) to generate a regress that is vicious. For
any group of things to which the same “ name ” (word) may be truly applied,
there exists a Form having the same “ name ” in virtue of which that “ name ”
may be truly applied to them. (This may be called the “ Existence
Assumption ” or “ One - over - many Assumption. ” ) This Form is not a member

104 Jurgis (George) Brakas

[Addressing Glaucon, Socrates asks] [If] a man believes in the existence of

beautiful things, but not of Beauty itself [ . . . ], is he not living in a dream?

[ . . . ]. Contrast him with the man who holds that there is such a thing a Beauty

itself and can discern that essence as well as the things that partake of its

character, without ever confusing the one with the other – is he a dreamer or

living in a waking state? He is very much awake. So we may say that he

knows, while the other has only a belief in appearances; and might we call

their states of mind knowledge and belief? Certainly. [ . . . ] When a man

knows, must there not be something that he knows? [ . . . ] [T]here must.

Something real or unreal? Something real. How could a thing that is unreal

ever be known? [ . . . ]. So if the real is the object of knowledge, the object of

belief must be something other than the real. Yes. Can it be the unreal? Or

is that an impossible object even for belief? Consider: if a man has a belief,

there must be something before his mind; he cannot be believing nothing, can

he? No. [ . . . ]. So what he is believing cannot be real nor yet unreal. True.

[ . . . ]. It seems, then, that what remains to be discovered is that object which

can be said both to be and not to be and cannot properly be called either real

or purely unreal. If that can be found, we may justly call it the object of belief

[ . . . ]. (Plato Republic , 476C – 479A; Cornford ’ s trans.)

Socrates then goes on to identify that object as the world in which we

live, a world which he earlier implicitly referred to as a world of appearances.

Although one of the basic operating premises here is not that all

things in this world are in constant fl ux, but rather that they are neither

fully real nor fully unreal, it is not a far stretch to argue that they are neither

fully real nor fully unreal because they are in constant fl ux. If so, then the

argument is fundamentally the same as the one given in the Cratylus ; if not,

then it is another version of it. In the latter case, premise 4 would have

to be modifi ed accordingly as well as the wording in all the lines relying

on it.

P1. Knowledge is possible.

P2. Knowledge is knowledge of some object. That is, if a (putative) piece

of knowledge does not have an object, then that (putative) piece of

knowledge does not exist.

P3. All knowledge (unlike opinion) is stable. That is, all pieces of knowledge

are stable: they do not change, being one thing at one time, another at

another.

P4. If the object of knowledge could change (for example, if beauty, the

object I know, could become something other than beauty), then the

knowledge of that object would not be stable (my knowledge of beauty

would not be stable).

P5. All things in this world, as Heraclitus says, are in constant fl ux. That

is, all things in this world are things that are always changing in every

way, or, all things in this world are not things that are stable.

The Existence of Forms 105

P6. Some objects of knowledge exist among things in this world (assumption

for reductio ).

C1. Some objects of knowledge change; they are not stable (syllogism,

P5, P6).

C2. Some pieces of knowledge are not stable ( modus ponens , P4, C1).

C3. All knowledge (unlike opinion) is stable and some pieces of knowledge

are not stable (conjunction, P3, C2).

C4. No objects of knowledge exist among things in this world ( reductio ,

P6 – C3).

P7. If objects of knowledge do not exist in this world and do not exist in

another, then objects of knowledge do not exist.

P8. Objects of knowledge do not exist in another world (assumption for

indirect proof).

C5. Objects of knowledge do not exist in this world, and objects of

knowledge do not exist in another (conjunction, C4, P8).

C6. Objects of knowledge do not exist ( modus ponens , P7, C5).

C7. Knowledge is not possible ( modus ponens , P2, C6).

C8. Knowledge is possible, and knowledge is not possible (conjunction,

P1, C7).

C9. Objects of knowledge – called “ Forms ” – do exist in another world

( reductio , P6 – C8).

27

Plato, Aristotle, and the Third Man

Argument

Jurgis (George) Brakas

Aristotle . Peri Ideon ( On Ideas ) , in Aristotle Fragmenta Selecta , edited by

William D. Ross . Oxford , 1963 : 84.21 – 85.6 .

Fine , Gail . “ Owen, Aristotle and the Third Man . ” Phronesis 27 ( 1982 ):

13 – 33 .

Lewis , Frank A. “ On Plato ’ s Third Man Argument and the ‘ Platonism ’ of

Aristotle , ” in How Things Are , edited by J. Bogen and J. McQuire ,

133 – 74 . Dordrecht : Reidel , 1985 .

Plato . Plato: Parmenides , translated by R. E. Allen. New Haven, CT : Yale

University Press , 1998 .

Strang , Colin . “ Plato and the Third Man . ” Proceedings of the Aristotelian

Society , vol. 1 ( 1963 ): 147 – 64 .

Many scholars believe that the Third Man Argument (the TMA) is one of

the most powerful arguments against the existence of Plato ’ s Forms, many

going so far as to maintain that it is successful. It exists in two versions.

One, preserved to us only in a commentary on Aristotle ’ s Metaphysics by

Alexander of Aphrodisias, uses the Form Man as an example; the other –

offered fi rst, to his great credit, by Plato himself – uses the Form Large. The

difference between the versions is signifi cant, because the fi rst uses Forms

of entities or substances as examples whereas the second uses attributes or

properties.

Just the Arguments: 100 of the Most Important Arguments in Western Philosophy,

First Edition. Edited by Michael Bruce and Steven Barbone.

Plato, Aristotle, and the Third Man Argument 107

Both versions use just three major premises (in addition to fi ve that most

people would fi nd uncontroversial) to generate a regress that is vicious. For

any group of things to which the same “ name ” (word) may be truly applied,

there exists a Form having the same “ name ” in virtue of which that “ name ”

may be truly applied to them. (This may be called the “ Existence

Assumption ” or “ One - over - many Assumption. ” ) This Form is not a member