DebateLabKIT/deepa2-corpus · Datasets at Hugging Face

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of the group of things of which it is the Form. (This is usually called the
“ Non - identity Assumption. ” ) Finally, this Form may be predicated of itself.
(This is usually called the “ Self - predication Assumption. ” It should be
pointed out that both the formulation of this premise and its name are
misleading. It is not the very same Form that is predicated of itself but
rather another Form having the same name as the fi rst, with the same point
applying as the regress proceeds.) Since an infi nite regress is impossible (at
least, so both Plato and Aristotle agree), one or more of the three major
premises must be false, if we take the additional fi ve to be uncontroversial.
The problem is that it is extremely diffi cult, if not impossible, to see how
Plato could give up any of those premises and be left with anything that
resembles his philosophy.
Controversy does surround both versions. Scholars interpret them differently,
and, while some fi nd one or both to be successful, others do not
(see Strang, Fine, and Lewis).
The third man is proven also in the following way. If the thing predicated
of some group of things also is another thing in addition to the things of
which it is predicated, having been separated from them (for this [is what]
those who posit the Forms think they prove; this is why, according to them,
a certain man - itself exists – because the man being truly predicated of the
many individual men also is other than the individual men) – if this is so,
there will be a third man. For if the thing predicated is other than the things
of which it is predicated, and exists on its own, and man is predicated both
of the individual men and of the Form, there will be a third man in addition
to both the individuals and the Form. In the same way, [there will be] also
a fourth man, predicated of both this [man] – that is, the Form – and the
individual [men], and in the same way also a fi fth, and so on to infi nity.
(Aristotle, 84.21 – 85.6; author ’ s translation)
P1. If a group of things exists (individual men, 1 for example) to each
member of which the same name ( “ man ” ) may be truly applied, then a
Form (Man or man - himself) exists in virtue of which that name may be
truly applied to them (existence or one - over - many assumption).
1 “ Men ” and “ man ” are used in a gender - neutral sense.
108 Jurgis (George) Brakas
P2. If a Form (Man) exists in virtue of which the same name may be truly
applied to a group of things (individual men), then the Form in virtue
of which the same name may be truly applied to that group is not
included in it (nonidentity assumption).
P3. If the same name ( “ man ” ) may be truly applied to each member of a
group of things (individual men), then the name that may be truly applied
to each member of that group may also be truly applied to the Form in
virtue of which that name may be applied to each member of that group
(self - predication assumption).
P4. A group of things (e.g., men) exists to each member of which the name
“ man ” may be truly applied.
C1. A Form, Man, exists (in virtue of which “ man ” may be truly applied
to each member of the group of individual men) ( modus ponens , P1,
P4).
C2. The Form Man is not included in the group of individual men
( modus ponens , P2, C1).
C3. The name “ man ” may be truly applied to the Form Man. That is,
the Form Man is [a] 2 man ( modus ponens , P3, P4).
P5. The Form (Man) in virtue of which the same name ( “ man ” ) may be
applied to a group of things (individual men) is added to that group.
P6. If the Form (Man) in virtue of which the same name ( “ man ” ) may be
applied to a group of things (individual men) is added to that group,
then the Form and that group constitute a new, different group.
C4. Man and the group of individual men constitute a new, different
group ( modus ponens , P6, P5).
C5. The name “ man ” may be truly applied to Man and each of the
individual men. In other words, a group of things exist (Man and the
individual men) to each member of which the same name ( “ man ” )
may be truly applied (conjunction, C3, P4).
C6. Another Man (The Third Man 3 ) exists (in virtue of which “ man ”
may be truly applied to each member of this new group) ( modus
ponens , P1, C5).
P7. If a third Man exists, then also a fourth Man exists (by the same reasoning
that the third Man exists: P1 – C6).
C7. A fourth Man exists ( modus ponens , P7, C6).
P8. If a fourth Man exists, then an infi nite number of such Forms exist.
C8. An infi nite number of such Forms exist ( modus ponens , P8, C7).
2 Brackets are placed around “ a ” because the indefi nite article does not exist in ancient
Greek. Depending on the context, the Greek would therefore allow the same set of words to
be translated as “ Man is a man ” or “ Man is man. ” Clearly, the argument will not go through
if “ self - predication ” is understood along the lines of “ Man is man. ”
3 Although this Form is not the third Form Man to appear, it is the third man to appear if
we take any one of the individual men to be the fi rst man – as Aristotle does.
Plato, Aristotle, and the Third Man Argument 109
P9. If an infi nite number of Forms exist, then an infi nite regress is
possible.
C9. An infi nite regress is possible ( modus ponens , P9, C8).
P10. An infi nite regress is not possible.
C10. An infi nite regress is possible and an infi nite regress is not possible
(conjunction, C9, P10).
C11. One or more of P1, P2, P3, P4, P5, P6, P7, P8, P9, or P10 are false
( reductio , P1 – C10).
Plato presents what may be called the “ self - characterization ” version of
the TMA in the Parmenides . Parmenides is questioning Socrates:
“ [W]hen some plurality of things seem to you to be large, there perhaps
seems to be some one characteristic that is the same when you look over them
all, whence you believe that the large is one. ”
“ True, ” he said.
“ What about the large itself and the other larges? If with your mind you
should look over them all in like manner, will not some large one again appear,
by which they all appear to be large? ”
“ It seems so. ”
“ Therefore, another character of largeness will have made its appearance
alongside largeness itself and the things that have a share of it; and over and
above all those, again, a different one, by which they will all be large. And
each of the characters will no longer be one for you, but unlimited in multitude.

of the group of things of which it is the Form. (This is usually called the

“ Non - identity Assumption. ” ) Finally, this Form may be predicated of itself.

(This is usually called the “ Self - predication Assumption. ” It should be

pointed out that both the formulation of this premise and its name are

misleading. It is not the very same Form that is predicated of itself but

rather another Form having the same name as the fi rst, with the same point

applying as the regress proceeds.) Since an infi nite regress is impossible (at

least, so both Plato and Aristotle agree), one or more of the three major

premises must be false, if we take the additional fi ve to be uncontroversial.

The problem is that it is extremely diffi cult, if not impossible, to see how

Plato could give up any of those premises and be left with anything that

resembles his philosophy.

Controversy does surround both versions. Scholars interpret them differently,

and, while some fi nd one or both to be successful, others do not

(see Strang, Fine, and Lewis).

The third man is proven also in the following way. If the thing predicated

of some group of things also is another thing in addition to the things of

which it is predicated, having been separated from them (for this [is what]

those who posit the Forms think they prove; this is why, according to them,

a certain man - itself exists – because the man being truly predicated of the

many individual men also is other than the individual men) – if this is so,

there will be a third man. For if the thing predicated is other than the things

of which it is predicated, and exists on its own, and man is predicated both

of the individual men and of the Form, there will be a third man in addition

to both the individuals and the Form. In the same way, [there will be] also

a fourth man, predicated of both this [man] – that is, the Form – and the

individual [men], and in the same way also a fi fth, and so on to infi nity.

(Aristotle, 84.21 – 85.6; author ’ s translation)

P1. If a group of things exists (individual men, 1 for example) to each

member of which the same name ( “ man ” ) may be truly applied, then a

Form (Man or man - himself) exists in virtue of which that name may be

truly applied to them (existence or one - over - many assumption).

1 “ Men ” and “ man ” are used in a gender - neutral sense.

108 Jurgis (George) Brakas

P2. If a Form (Man) exists in virtue of which the same name may be truly

applied to a group of things (individual men), then the Form in virtue

of which the same name may be truly applied to that group is not

included in it (nonidentity assumption).

P3. If the same name ( “ man ” ) may be truly applied to each member of a

group of things (individual men), then the name that may be truly applied

to each member of that group may also be truly applied to the Form in

virtue of which that name may be applied to each member of that group

(self - predication assumption).

P4. A group of things (e.g., men) exists to each member of which the name

“ man ” may be truly applied.

C1. A Form, Man, exists (in virtue of which “ man ” may be truly applied

to each member of the group of individual men) ( modus ponens , P1,

P4).

C2. The Form Man is not included in the group of individual men

( modus ponens , P2, C1).

C3. The name “ man ” may be truly applied to the Form Man. That is,

the Form Man is [a] 2 man ( modus ponens , P3, P4).

P5. The Form (Man) in virtue of which the same name ( “ man ” ) may be

applied to a group of things (individual men) is added to that group.

P6. If the Form (Man) in virtue of which the same name ( “ man ” ) may be

applied to a group of things (individual men) is added to that group,

then the Form and that group constitute a new, different group.

C4. Man and the group of individual men constitute a new, different

group ( modus ponens , P6, P5).

C5. The name “ man ” may be truly applied to Man and each of the

individual men. In other words, a group of things exist (Man and the

individual men) to each member of which the same name ( “ man ” )

may be truly applied (conjunction, C3, P4).

C6. Another Man (The Third Man 3 ) exists (in virtue of which “ man ”

may be truly applied to each member of this new group) ( modus

ponens , P1, C5).

P7. If a third Man exists, then also a fourth Man exists (by the same reasoning

that the third Man exists: P1 – C6).

C7. A fourth Man exists ( modus ponens , P7, C6).

P8. If a fourth Man exists, then an infi nite number of such Forms exist.

C8. An infi nite number of such Forms exist ( modus ponens , P8, C7).

2 Brackets are placed around “ a ” because the indefi nite article does not exist in ancient

Greek. Depending on the context, the Greek would therefore allow the same set of words to

be translated as “ Man is a man ” or “ Man is man. ” Clearly, the argument will not go through

if “ self - predication ” is understood along the lines of “ Man is man. ”

3 Although this Form is not the third Form Man to appear, it is the third man to appear if

we take any one of the individual men to be the fi rst man – as Aristotle does.

Plato, Aristotle, and the Third Man Argument 109

P9. If an infi nite number of Forms exist, then an infi nite regress is

possible.

C9. An infi nite regress is possible ( modus ponens , P9, C8).

P10. An infi nite regress is not possible.

C10. An infi nite regress is possible and an infi nite regress is not possible

(conjunction, C9, P10).

C11. One or more of P1, P2, P3, P4, P5, P6, P7, P8, P9, or P10 are false

( reductio , P1 – C10).

Plato presents what may be called the “ self - characterization ” version of

the TMA in the Parmenides . Parmenides is questioning Socrates:

“ [W]hen some plurality of things seem to you to be large, there perhaps

seems to be some one characteristic that is the same when you look over them

all, whence you believe that the large is one. ”

“ True, ” he said.

“ What about the large itself and the other larges? If with your mind you

should look over them all in like manner, will not some large one again appear,

by which they all appear to be large? ”

“ It seems so. ”

“ Therefore, another character of largeness will have made its appearance

alongside largeness itself and the things that have a share of it; and over and

above all those, again, a different one, by which they will all be large. And

each of the characters will no longer be one for you, but unlimited in multitude.