Benson М. The Philosophy of Leibniz
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THE
PHILOSOPHY
OF
LEIBNIZ
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Introduction
1. In
recent years
there
has
been
a
remarkable rebirth
of
interest
in the
philosophy
of
Leibniz. This
is due to
several mutually reinforcing factors.
Logicians
and
philosophers
of
logic have found that
his
views
on
some
of the
matters
that concern them most, such
as
identity, truth,
and
necessity, were
well
thought out, systematic, and, when considered together with
the
reasons
behind them, deeply intuitive. Philosophers
of
language have become aware
that
his
writings
are a
mine
of
sophisticated
and
valuable ideas
in
that area.
Metaphysicians, especially those
of
nominalistic bent, have
been
interested
to see how
this great mind attempted
to
cope
with
the
obvious problems
involved
in
nominalism
and
nominalistic reductions.
And
epistemologists
and
philosophers
of
science
are
finding
that
he
discusses,
in a
very modern
way,
a
wide variety
of
issues that
are
central
to
their interests, too.
Accelerating
all of
this have
been
the
renewed progress
of the
great Berlin
Academy edition
of
Leibniz's works
and
also
the
appearance
of
Studia
Leibnitiana,
a
journal devoted principally
to the
intellectual history
of his
time.
We owe
these welcome developments primarily
to the
scholars
of the
Leibniz Archive
(Hanover)
and the
Leibnix Research Center (Munster)
in
Germany. Besides their editorial work
and the
books
and
articles they them-
selves
have contributed, these experts
are
providing very
complete
biblio-
graphic
information that
is
extremely
helpful,
even essential,
to
anyone doing
serious work
on the
subject. They also organize congresses
and
symposia,
at
which
the
growing numbers
of
researchers
in
this
field
can
exchange ideas
and
keep
up
with
the
latest developments.
In
short, their service
has
been,
and
will
continue
to be,
indispensable
for the
success
of
these studies.
The aim of the
present
work
is to add its bit to
this Leibniz renaissance
by
offering
a
critical account
of
some
of the
fundamentals
of his
philosophy.
Such
criticism
as is
included
will
be, for the
most part, internal, taking
note
of
contradictions
and
other unwelcome consequences that seem
to
follow
from
3
4 The
Philosophy
of
Leibniz
his
principles. (External criticism
is
rather
out of
place here, though
I
shall
probably
not be
able
to
conceal
from
the
reader that much
of
Leibniz's
doctrine strikes
me, as it did
Russell,
as a
certainly interesting
and
perhaps
heuristically
useful
fairy
story.) Internal criticism
is
justifiable
and
even
necessary,
I
think, because
in
pointing
out
what appear
to be
inconsistencies
or
other unacceptable results,
I
shall
be not
only informing
the
reader about
the
views
of
Leibniz
but
also giving evidence relevant
to the
acceptability
of
my
interpretations. After all,
the
goal
is to
promote,
by
whatever means,
the
understanding
of the
doctrines
in
question.
Now,
anyone
who
proposes
to
expound
in
summary fashion
the
philo-
sophy
of one of the
classical
figures
has to
deal with
a
number
of
problems,
most
of
which
are too
obvious
to
require recital here.
But the
study
of
Leibniz
brings
with
it
some special
difficulties
of
which
the
reader should
be
aware
and
which account
for
certain
features
of
this book.
2.
The
first
and
foremost
difficulty
is
that
in
setting
forth
the
philosophy
of
Leibniz,
one
does
not
know where
to
begin. Some advice
on
this problem
is
found
in a
well-known passage
in
Alice
in
Wonderland:
The
White Rabbit
put on his
spectacles. "Where
shall
I
begin,
please
your
Majesty?"
he
asked.
"Begin
at the
beginning,"
the
King
said,
very
gravely,
"and
go on
till
you
come
to the
end:
then stop."
1
But
unfortunately
we
cannot
follow
this good advice,
for
Leibniz's philo-
sophy
has no
"beginning," that
is, no
unique, logically primitive
set of
axioms.
Contrary
to
what many commentators seem
to
have supposed,
he
does
not
treat
his
philosophical principles
as a
deductive system
in
which certain
propositions
are to be
accepted without proof
and the
rest
are to be
deduced
from
these. Instead,
it is
clear that
he
regards
his
doctrine simply
as a
network
of
important truths that have many interesting logical interrelationships.
He
deduces
the
various principles
from
one
another
in
different
orders
and
combinations. Often
he
gives alternative definitions
of the
same concept,
sometimes even showing
how to
derive these
from
one
another.
It is
obvious
that
he has no
particular order
of
theorems
and
definitions
in
mind.
2
Therefore, talk
of
"question begging"
and
"vicious circles"
in
proofs
and
definitions
has no
clear application
to
Leibnizian philosophy, since those
terms acquire
sense
only
in
relation
to
some deductive system explicitly
or
implicitly
indicated. Rather,
as
noted above, Leibniz's attitude
is
that
of a
kind
of
philosophical explorer,
who
reports what
he
finds
to be the
case
and
who
notices that
there
are
important logical interconnections among
his
dis-
coveries.
He
himself puts
the
matter clearly enough when
he
says:
"My
1 The
Complete Works
of
Lewis Carroll.
New
York, 1941, 126.
2
In one
text
(LH IV vii B 2
57-58;
Fasz.
1. # 40,
136),
he
states
explicitly
that
it
makes
no
difference
which possible
definition
of a
concept
you
choose,
as
long
as you can
deduce
the
others
from
it as
theorems.
Introduction
5
principles
are
such that they
can
hardly
be
torn apart
from
each
other.
He
who
knows
one
well knows them all."
3
3.
This same logical integration makes
it
futile
to
argue about whether
Leibniz's metaphysics
is
derived
from
his
logic
or his
logic
from
his
meta-
physics,
an
issue that
has
seemed
of
major importance
to a
number
of
commentators, including, preeminently, Russell
and
Louis Couturat. For,
not to
belabor
the
point,
in
Leibniz's philosophy "everything
is
connected
with
everything."
Indeed,
the
relation
of his
metaphysical principles
to
those
the
com-
mentators call "logical" (but which
in
most cases
are
better
classified
as
belonging
to
metalogic
or the
philosophy
of
logic rather than
to
logic
itself)
is
so
close that
it is
often
difficult
to
tell them apart. This
difficulty
is
increased
by
Leibniz's carelessness about matters
of use and
mention;
we get the
impression that frequently
he
doesn't care whether
he is
understood
to be
talking about sentences, propositions,
or the
corresponding states
of
affairs,
or,
again, about descriptions, concepts,
or the
individuals
to
which
the
descriptions,
as
expressing
the
concepts,
refer.
Consequently
he
often
makes
pronouncements that, taken
in one
way, would
be
metaphysical principles,
and
taken
in
another,
would
be
logical.
For
example,
the
"logical" claim that
the
complete individual concept
of
Alexander contains
all of his
"predicates"
(properties)
is, for
Leibniz, prac-
tically
interchangeable
with
the
metaphysical claim that
the
soul
of
Alexan-
der
contains
at all
times traces
of
everything that
has
happened
to him and
even
signs
of
everything that
will
happen
to
him.
Or
again,
the
metaphysical
view
that
the
universe
of
individual substances
is
like
a
great sea,
in
which
the
slightest
motion anywhere produces some change everywhere else,
is an
almost indistinguishable counterpart
of the
"logical" claim that everything
is
related
to
everything
and
that every relation
is
"grounded
in
accidents
of the
relata"—that
is,
that
all
relations
are
internal.
In
general,
we
probably ought
to
take Leibniz's word
for it
that
from
his
point
of
view
the
"true metaphysic" hardly
differs
at all
from
the
"true logic,"
since they
both
amount
to
natural theology.
4
4. For the
expositor,
one
practical
effect
of
these
interconnections
is
that
any
account
of
Leibniz's philosophy
has to
contain
a
certain amount
of
repetition.
It is not
possible simply
to
take
up
each topic
in
order,
setting forth
only
what
needs
to be
said about that topic
in
particular
and
then proceeding
to the
next.
If, for
instance,
we
attempted
to
include
under
the
heading
of
Truth
all
Leibnizian doctrine relevant
to
truth,
the
result would amount
to
almost
the
whole story.
Hence,
some relatively arbitrary divisions must
be
drawn,
and
more
repetition must
be
tolerated
than would otherwise
be
acceptable.
It
will
even
be
necessary,
in a few
instances,
to
employ
some
of
Leibniz's technical terminology (for example, "purely extrinsic denomina-
tion") before
we
reach
the
sections
in
which
we
explicitly
consider
and
define
3
GII412(L
599).
4
GIV292.
6 The
Philosophy
of
Leibniz
those terms. With cross-references
in the
notes
I
have tried
to
compensate
somewhat
for the
unsatisfactoriness
of
this.
I may
mention
in
passing that Leibniz
is
sometimes regarded
as
"the
logicians' philosopher,"
but to
this
a
certain reservation needs
to be
added.
Although
it is
certainly important
to
investigate
the
logical relationships
among
his
various doctrines,
and
although
"It
follows
that..."
is no
doubt
the
most frequently occurring phrase
in the
entire Leibnizian corpus,
we
must
unfortunately
grant that
C. S.
Peirce
was
right when
he
said that "the
reason-
ing
of
Leibniz
was
nearly,
if not
quite,
of the
highest order."
5
When
we get
down
to
cases,
we
find
that Leibniz's declarations about what follows
from
what
in his
system cannot
be
accepted uncritically;
usually
more than
a few
suppressed premises have
to be
added
if the
argument
is to go
through with
anything
approaching formal validity.
5.
Another
special problem confronting Leibniz scholarship
is
that
in
order
to
find
out
what
he
thought
and
said about
any
major topic, there
are
not
one, two,
or
three places
to
look,
but
literally dozens
of
texts
to
take into
account.
During
his
lifetime
he
published only
one
philosophical
book,
the
Theodicy,
and a
small number
of
philosophical articles.
In
1765, nearly
fifty
years
after
his
death, another book,
the New
Essays,
was
published
from
a
manuscript that
he had
prepared
but
held back because
of the
death
of
Locke,
on
whose Essay
it was a
commentary. Neither
of the
books
contains
his
best work; both
are
long
and
rambling accounts, hastily written, poorly
organized,
and
seldom showing
the
sharpness
and
insights
of
which
he was
capable.
Leibniz's better work
is
contained
in the
great mass
of
letters,
drafts,
notes,
and
bits
and
pieces
he
left
behind, most
of
which
are
preserved
in the
State Library
of
Lower Saxony,
in
Hanover, Germany. Portions
of
this
material
have been published
by a
number
of
editors,
and the
aforemen-
tioned
Academy edition
of the
entire corpus
has
been under way, through
two
world wars
and
other
vicissitudes, since
the
beginning
of
this century.
But
an
equally large amount
has not yet
been edited,
so
that
any
exegete takes
some risk that tomorrow
a
"coupon"
or
other item
will
be
found
in
which
Leibniz asserts
the
exact opposite
of
what,
it has
been concluded,
"he
must
have
thought"
or "he
would have said."
The
more serious problem, though,
is
simply
that there
are so
many places
to
look, with
so
little
useful
indexing, that
it
is
often
a
very
onerous
task
to
discover what
he did say
about
any
given
matter.
We
must keep
in
mind,
of
course, that most
of
this miscellaneous
material,
on
which
we
have
to
rely
so
heavily,
was not
intended
for
publica-
tion.
To any
careful
reader
it
soon becomes evident that Leibniz often wrote
out
philosophical ideas
as a
kind
of
dialogue with himself,
to see
where they
would
lead,
and
without making
any
commitment
to
accepting them
as
part
of
his
considered system. Thus, such texts must
be
used
with
discretion
by
5
The
Nation
68
(1899): 210.
Introduction
1
anyone seeking
to
reconstruct that system.
On the
other
hand,
the
availability
of
the
manuscripts
of
these deliberative pieces sometimes provides
un-
expected rewards
for the
scholar;
by
observing what
has
been
crossed
out
and
what
has
been
put in its
place,
he can
occasionally
get a
deeper insight
into what
the
author
had in
mind.
Still
another problem
is
that
in his
letters Leibniz often adapts himself
to
the
terminology
of his
correspondent
and
sometimes argues from premises
that
are the
correspondent's
and not
necessarily
his
own.
These
texts, too,
must
be
used with great care when
we are
seeking
to
understand
his use of
critical
terms
or
hoping
to
discover
his
true doctrine
on
some
point. Many
of
the
drafts,
notes,
and
even
the New
Essays
present similar
difficulties.
6.
It has
been fashionable, certainly since Jaeger's well-known work
on
Aristotle
but
also before that,
to
treat
the
pronouncements
of all
thinkers
as
exhibiting
their intellectual "development" rather than
as
providing
a
"syn-
chronic" picture
of
their thoughts.
6
This methodology
is
based
on the
obvious
fact
that
people
change their minds,
so
that
if we
indiscriminately lump
together what they
say at all the
different
periods
of
their lives,
we
shall
almost
certainly
find
incoherence
and
contradiction.
It
does
seem
to
bring
with
it its own
dangers, however; once
the
historian
has
concluded that
a
philosopher's thought
(or
that
of a
given historical period) developed
in a
cer-
tain way, there
is a
tendency
to
disregard
or
reinterpret evidence that
doesn't
fit
the
adopted hypothesis.
(A
good example
of
this,
if one is
needed,
was the
"reconstruction"
of
Aristotle's Protrepticus
to
support
the
thesis that
Aris-
totle gradually developed
from
a
Platonist into
an
Aristotelian.)
7
A
great deal
of
excellent work
has
been
done
in
dating
the
thousands
of
items
that constitute Leibniz's Nachlass.
Most
of the
letters carry their
own
dates,
of
course,
and
sometimes what
is
said
in a
draft
or
memorandum
will
coincide
almost verbatim with what appears
in a
letter.
Watermarks give
further
clues,
and
there
are
several other kinds
of
supporting evidence.
When
the
materials
are put in
order
as
well
as can be, it
becomes obvious
that
Leibniz
did
change
his
mind
on
many topics,
as
would
be
expected.
Indeed,
he
himself tells
us
about some
of
these changes, mostly having
to do
with
his
views
on
matters
of
physical science.
But
on the
fundamental points
of his
philosophy,
his
constancy over
the
years
is
little short
of
astonishing.
For
instance,
from
the
first
of his
publica-
tions,
at age
seventeen,
to the end of his
life
he
never wavered
in
holding
to the
rather unusual
and
implausible doctrine that things
are
individuated
by
their
"whole being"; that
is,
every property
of a
thing
is
essential
to its
identity.
8
6
W.
Jaeger, Aristoteles,
Berlin,
1923. Stein (1888),
with
his
"'entwicklungsgeschichtliche
Methode,"
is an
earlier example.
7
See W. G.
Rabinowitz,
Aristotle's
Protrepticus
and the
Sources
of its
Reconstruction.
Berkeley
and Los
Angeles, 1957.
8
Or,
perhaps, that
every
accident
of an
individual
is
unique
to
that
individual.
He
holds
both
(1)
that
A is the
same
as B if and
only
if
A and B
have
the
same properties (that
is,
fall
under
the
same
concepts), and,
of
course,
(2)
that
A is the
same
as B if and
only
if
A and B
have
every
indi-
vidual
accident
in
common.
8 The
Philosophy
of
Leibniz
And in
general,
if one
compares
the
doctrines
of the
Discourse
on
Meta-
physics
(1686)
with
those
of the
Monadology
(1714),
one
sees that during
his
last thirty years there
was
almost
no
change
in any of
them.
In
fact,
I
have
yet
to
find
a
single basic metaphysical principle
on
which
he
changed
his
mind
over time;
the few
verifiable changes
are on
such relatively minor matters
as,
for
example, whether minds occupy points
in
space.
Consequently,
in
this account
of the
elements
of
Leibniz's philosophy
I
have
felt
free,
on the
whole,
to
cite
him
without paying much attention
to the
date
of the
passage cited. None
of the
inconsistencies that
I
shall point
out can
be
explained,
so far as I can
see,
as
indicating
an
independently confirmable
change
of
mind.
It is
always possible,
of
course, that
I am in
error
on
this,
and
so
the
reader
is
hereby warned that
my
"synchronic" approach
may be the
source
of
apparent
difficulties.
7. It was
mentioned earlier that Leibniz often
falls
into what
is
today
called "use-mention confusion." Usually, when
we ask
ourselves whether
he
is
talking about language, thought,
or the
world,
the
answer seems
to be
"none
and all of
these."
This state
of
affairs
is
best understood,
in my
opinion,
by
reference
to the
concept
of
"definiteness
of
intention," introduced several years
ago by the
Norwegian philosopher
Arne
Naess.
9
Consider
an
example.
We ask
some-
body,
one of
Naess's seafaring compatriots, say,
if he
agrees that
a
certain
ship
is "a
ship
of
five
thousand
tons."
Suppose that
his
reply
is
"yes."
Then
we
ask
him a
series
of
questions designed
to
discover whether
by
"ton"
in
this
context
he
means
a
unit
of
weight
or a
unit
of
volume;
if the
volume
of
dis-
placement
of
water
was
meant,
we
inquire whether seawater
or
freshwater
was
intended,
there
being
a
difference
in
volume because
of a
difference
in
weight.
And so on.
Sooner
or
later, Naess observes,
we
shall reach
the
point
where
the
subject must admit,
if he is
honest, that
he
intended neither
A nor
non-A. Either
he was
unaware that such
a
distinction
was
relevant
to the
sentence
in
question,
or at any
rate
he was not
attending
to
that distinction
when
he
made
the
assertion. Roughly speaking,
the
farther
we go
down
our
list
of
questions before reaching this point,
the
more definiteness
of
intention
we
ascribe
to the
subject
in his use of the
given sentence.
This concept
is
obviously
far
from
precise,
but it is
nonetheless
useful,
especially
in
interpreting
the
writings
of
authors
who can no
longer
be
inter-
viewed.
We
often would very much like
to
know whether,
in
saying such
and
such,
the
author meant this
or
that.
For
example,
we ask
whether,
in the
Categories,
Aristotle
was
classifying
words
or
things. Part
of
what
he
says
suggests
the
former interpretation,
and
part suggests
the
latter. Probably
the
truth
is
that
the
distinction
was
below
his
level
of
definiteness
of
intention
when
he
wrote
the
text
in
question:
he
didn't mean words
and he
didn't mean
things;
he
just wasn't attending
to
that distinction, though
of
course
he was
perfectly
capable
of
drawing
it if the
matter
had
been
raised.
9
Naess (1952),
256ff.
Introduction
9
I
think that
the
same considerations apply
to
Leibniz. When
he is
thinking
specifically
about matters metaphysical,
he is
perfectly capable
of
distin-
guishing
the
individual substance Alexander
from
the
complete individual
concept
of
Alexander,
and
both
of
them
from
the
name
"Alexander."
But he
doesn't
attend
to
these distinctions
all the
time,
and on
occasion
he
produces
assertions relative
to
which they
are
below
his
level
of
definiteness
of
inten-
tion.
In
such instances there will
be no
completely satisfactory answer
to the
question whether
he
"really" means this
or
that;
the
best
we can do is to
inter-
pret
him in
whichever
way
makes
the
most sense
in
relation
to the
general
outlines
of his
system.
It
must
be
added, however, that
all of our
interpretative generosity cannot
save
Leibniz
from
certain unwelcome consequences
of the
inherent inco-
herence
of
such notions
as
those
of
"proposition"
and
"concept." Carefulness
about
use and
mention only serves
to
show
up
these problems more clearly,
not to
solve them.
8.
As
would
be
expected, this book's account
of
Leibniz's philosophy
differs
in
many details
from
those
given
by
other commentators,
but
there
are
two
major
differences
that
I
wish
to
point
out
here.
The
first
of
these results
from
giving
due
attention
to
Leibniz's distinction
between "essential"
and
"existential" propositions.
Any
proposition
'A
is B',
he
tells
us, is
equivalent
to the
corresponding proposition
'AB is an
entity'.
Thus, "Caesar
is a
Roman"
is
equivalent
to
"Caesar
the
Roman
is an
entity."
But
the
word "entity"
is
ambiguous;
it can
mean
the
same
as
"possible thing"
or it can
mean
the
same
as
"actually existing thing."
If it is
taken
in the
former
sense,
the
propositions concerned
are
called "essential";
if it is
taken
in the
latter sense, they
are
"existential."
Clearly,
the two
kinds
of
propositions have
different
truth conditions.
The
essential proposition "Pegasus
is a
winged horse"
is
true, since Pegasus
the
winged horse
is a
possible thing;
but the
existential proposition expressed
by
the
same words
is
false,
for
Pegasus
the
winged
horse
does
not
actually
exist.
In
general, existential
'A is B' is
false
if 'A
exists'
is
false,
whereas this
is
not
necessarily
the
case with essential
'A is B'.
This distinction gives
us a way of
reconciling some important Leibnizian
texts
that have seemed inconsistent
with
one
another. Thus, sometimes
he
says
that'
A is B' is
true
if and
only
if the
concept
B is
included
in the
concept
A,
while elsewhere
he
says that
'A is B' is
false
if no
actual entity
falls
under
A. In
particular, sometimes
he
indicates that
all
propositions
of the
form
'A is
A' are
necessary truths, while
in
other texts
he
proposes
to
represent truths
of
the
form
'No A is B' as 'AB is not
AB'. Expositors
who
have
been
impressed
by
one set of
texts have tended
to
ignore
or
"interpret" away
the
others,
and
their
opponents
have
done
likewise, mutatis mutandis.
10
The
above-
mentioned distinction allows
us to
reconcile such apparent inconsistencies
10
This comment,
I am
embarrassed
to
say,
applies
especially
to
Mates (1968),
as
well
as to
many
of the
replies
it
provoked.