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” (Plato, 132a – b; Allen ’ s translation)
In reconstructing this argument, I have used beautiful things and their
corresponding Forms instead of the “ larges ” and their Forms. This should
make Plato ’ s argument more “ down to earth, ” without distorting it in any
way.
P1. If a group of things exists (individual beautiful things, for example) to
each member of which the same name ( “ beautiful ” ) may be truly applied,
then a Form (the beautiful itself or Beauty) exists in virtue of which that
name may be truly applied to them (existence or one - over - many
assumption).
P2. If a Form (Beauty) exists in virtue of which the same name may be truly
applied to a group of things (individual beautiful things), then the Form
in virtue of which the same name may be truly applied to that group is
not included in it (non - identity assumption).
P3. If the same name ( “ beautiful ” ) may be truly applied to each member
of a group of things (individual beautiful things), then the name that
may be truly applied to each member of that group may also be truly
110 Jurgis (George) Brakas
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 (individual beautiful things, for example) exists to
each member of which the name ( “ beautiful ” ) may be truly applied.
C1. A Form, Beauty, exists (in virtue of which “ beautiful ” may be truly
applied to each member of the group of individual beautiful things)
( modus ponens , 1, 4).
C2. The Form Beauty is not included in the group of individual beautiful
things ( modus ponens , P2, C1).
C3. The name “ beautiful ” may be truly applied to the Form Beauty. That
is, the Form Beauty is beautiful ( modus ponens , P3, P4).
P5. The Form (Beauty) in virtue of which the same name ( “ beautiful ” ) may
be applied to a group of things (individual beautiful things) is added to
that group.
P6. If the Form (Beauty) in virtue of which the same name ( “ beautiful ” )
may be applied to a group of things (individual beautiful things) is added
to that group, then the Form and that group constitute a new, different
group.
C4. Beauty and the group of individual beautiful things constitute a new,
different group ( modus ponens , P6, P5).
C5. The name “ beautiful ” may be truly applied to Beauty and each of
the individual beautiful things. In other words, a group of things exist
(Beauty and the individual beautiful things) to each member of which
the same name ( “ beautiful ” ) may be truly applied (conjunction, C3,
P4).
C6. Another Beauty (The Third Beauty) exists (in virtue of which “ beautiful
” may be truly applied to each member of this new group) ( modus
ponens , P1, C5).
P7. If a third Beauty exists, then also a fourth Beauty exists (by the same
reasoning that the third Beauty exists: P1 – C6).
C7. A fourth Beauty exists ( modus ponens , P7, C6).
P8. If a fourth Beauty exists, then an infi nite number of such Forms exist.
C8. An infi nite number of such Forms exist ( modus ponens , P8, C7).
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 , C8, P7).
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).
28
Logical Monism
Luis Estrada - Gonz á lez 1
Beall , J. C. , and Greg Restall . Logical Pluralism . Oxford : Oxford University
Press , 2006 .
Haack , Susan . Philosophy of Logics . Cambridge, UK : Cambridge University
Press , 1978 .
Priest , Graham . Doubt Truth to Be a Liar . Oxford : Oxford University Press ,
2006 .
Read , Stephen . “ Monism: The One True Logic , ” in A Logical Approach to
Philosophy , edited by David DeVidi and Tim Kenyon , 193 – 209 .
Dordrecht : Springer , 2006 .
Logical monism is the view that there is only one correct logic or, alternatively,
the view that there is only one genuine consequence relation, only
one right answer to the question on whether and why a given argument is
valid, only one collection of valid inferences (or of logical truths), or only
one right way of reasoning. Logic is at the center of philosophy and many
theoretical and practical pursuits, for they proceed by the way of argument,
inference, and their evaluation. Thus, the problem of knowing whether
there is only one correct logic is central in philosophy and of crucial importance
to philosophy and other activities.
There is a simple argument for logical monism, put forward, among
others, by Graham Priest and purported to follow from the pre - theoretical
notion of validity – an inference is valid if and only if whenever its premises
1 Thanks to Axel Barcel ó , John Corcoran, Claudia Olmedo - Garc í a, Agust í n Rayo, and
Stephen Read for valuable comments on earlier versions of this text. Needless to say, those
mistakes that remain are mine alone.
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.
112 Luis Estrada-González
are true, so is the conclusion. He works with a broad notion of logic in the
sense that he is ready to accept that inferential tools for certain particular
cases or domains augmented with principles specifi c to those domains count
as logics, but he says that there is nonetheless one true logic, a logic whose
inferences are valid in all domains and that lacks principles depending on
specifi c domains.
Some logical pluralists try to wriggle out of this monist argument by
claiming that the quantifi cation “ all cases (domains) ” is not absolute but
should be read “ all cases (domains) of a kind. ” For example, classical
predicate logic would stem from taking cases to be the consistent and complete

” (Plato, 132a – b; Allen ’ s translation)

In reconstructing this argument, I have used beautiful things and their

corresponding Forms instead of the “ larges ” and their Forms. This should

make Plato ’ s argument more “ down to earth, ” without distorting it in any

way.

P1. If a group of things exists (individual beautiful things, for example) to

each member of which the same name ( “ beautiful ” ) may be truly applied,

then a Form (the beautiful itself or Beauty) exists in virtue of which that

name may be truly applied to them (existence or one - over - many

assumption).

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

applied to a group of things (individual beautiful things), then the Form

in virtue of which the same name may be truly applied to that group is

not included in it (non - identity assumption).

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

of a group of things (individual beautiful things), then the name that

may be truly applied to each member of that group may also be truly

110 Jurgis (George) Brakas

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 (individual beautiful things, for example) exists to

each member of which the name ( “ beautiful ” ) may be truly applied.

C1. A Form, Beauty, exists (in virtue of which “ beautiful ” may be truly

applied to each member of the group of individual beautiful things)

( modus ponens , 1, 4).

C2. The Form Beauty is not included in the group of individual beautiful

things ( modus ponens , P2, C1).

C3. The name “ beautiful ” may be truly applied to the Form Beauty. That

is, the Form Beauty is beautiful ( modus ponens , P3, P4).

P5. The Form (Beauty) in virtue of which the same name ( “ beautiful ” ) may

be applied to a group of things (individual beautiful things) is added to

that group.

P6. If the Form (Beauty) in virtue of which the same name ( “ beautiful ” )

may be applied to a group of things (individual beautiful things) is added

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

group.

C4. Beauty and the group of individual beautiful things constitute a new,

different group ( modus ponens , P6, P5).

C5. The name “ beautiful ” may be truly applied to Beauty and each of

the individual beautiful things. In other words, a group of things exist

(Beauty and the individual beautiful things) to each member of which

the same name ( “ beautiful ” ) may be truly applied (conjunction, C3,

P4).

C6. Another Beauty (The Third Beauty) exists (in virtue of which “ beautiful

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

ponens , P1, C5).

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

reasoning that the third Beauty exists: P1 – C6).

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

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

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

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 , C8, P7).

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).

28

Logical Monism

Luis Estrada - Gonz á lez 1

Beall , J. C. , and Greg Restall . Logical Pluralism . Oxford : Oxford University

Press , 2006 .

Haack , Susan . Philosophy of Logics . Cambridge, UK : Cambridge University

Press , 1978 .

Priest , Graham . Doubt Truth to Be a Liar . Oxford : Oxford University Press ,

2006 .

Read , Stephen . “ Monism: The One True Logic , ” in A Logical Approach to

Philosophy , edited by David DeVidi and Tim Kenyon , 193 – 209 .

Dordrecht : Springer , 2006 .

Logical monism is the view that there is only one correct logic or, alternatively,

the view that there is only one genuine consequence relation, only

one right answer to the question on whether and why a given argument is

valid, only one collection of valid inferences (or of logical truths), or only

one right way of reasoning. Logic is at the center of philosophy and many

theoretical and practical pursuits, for they proceed by the way of argument,

inference, and their evaluation. Thus, the problem of knowing whether

there is only one correct logic is central in philosophy and of crucial importance

to philosophy and other activities.

There is a simple argument for logical monism, put forward, among

others, by Graham Priest and purported to follow from the pre - theoretical

notion of validity – an inference is valid if and only if whenever its premises

1 Thanks to Axel Barcel ó , John Corcoran, Claudia Olmedo - Garc í a, Agust í n Rayo, and

Stephen Read for valuable comments on earlier versions of this text. Needless to say, those

mistakes that remain are mine alone.

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

First Edition. Edited by Michael Bruce and Steven Barbone.

112 Luis Estrada-González

are true, so is the conclusion. He works with a broad notion of logic in the

sense that he is ready to accept that inferential tools for certain particular

cases or domains augmented with principles specifi c to those domains count

as logics, but he says that there is nonetheless one true logic, a logic whose

inferences are valid in all domains and that lacks principles depending on

specifi c domains.

Some logical pluralists try to wriggle out of this monist argument by

claiming that the quantifi cation “ all cases (domains) ” is not absolute but

should be read “ all cases (domains) of a kind. ” For example, classical

predicate logic would stem from taking cases to be the consistent and complete