collection of
letters by
essay entitled  The Ethical
in
the
to
Harris,
pre-
of
his
birth
is
to
overlooked,
explicable by
tributed to encyclopedias whose
author
of
an
article.
The
editor
had
the last
Royce
of
his
the course.
The
Principles
of
Bernard
and inferential whole as
that text-
Advanced Logic, about the
thorough
essays
made
by
an
published A
Philosophical
Review,
material,
Address
de-
philosophical
represent,
as
and the main
in
my
turn,
with
opportunity for
tions
psychological
laboratories.
In
part
they
I.
I
To the
first of
directly
and upon
sake
of
their
own
suggest-
another
recent logi-
cal inquiries
consists of
well-known
volume
to all the
include,
moreover,
in
the
same
 
a certain
truce of
bring at once
considering them in one
of
the
satisfactory.
The
general
theories
about
what
the
into
higher intel-
the
sciences
are
 
m.
And
the oldest
problems
of
Attention,
dis-
exact sense,
ince of
exact sense,
is nowadays
esteem
of
theories. Numerous are the
judgment
For
predicate
idea.
synthesis,
well
know,
is
not
opinions,
many
stu-
dents
posed
sibility
for
settling
some
the thinking
chology
proves
to
observation.
The
thinking
10
or
den
have a good
concerns
their
hand, however,
we cannot
most
thus
hope
to
thought,
the experi-
13
training
or
to
acts;
consciousness.
The
mechanism
established
Consciousness
showed
indeed
nothing
just then
hearing such an
in the
I
a large station calls
of
the
instrument.
psychology of
be
into
elementary
processes
of
an
in-
direct
fashion,
through
the
human
intellect,
as
they
appear
tions,
which
human
reason
further than we have yet done in the preparatory analy-
sis
of
its
ele-
ments
the phenomena
of
wardly
psy-
phenomena
quiry still prospers.
facts with those
then, that
the psychol-
book rather
searches in
seek for help. These
IV.
exactly
what,
of the students of
first principles
The
mathematicians
say
earlier
stages
of
the
science
and often had to be
restated
precise qualifications which had earlier
notice. Thus there arose
rigid
the results of various and apparently
independent sorts
or in logical exactness?
criticism
mathematical
territory,
considera-
tion
of
the
number-con-
and
irrational
to
logically necessary in
of
now
what
I
they
tend
to
of
ideas,
is
which our thoughts
psychology
of
the
con-
Psy-
which facts are
of
the
space-con-
the
little interest psychologists have generally taken
in
the
space
is
a
remark
of
Klein,
repeated
modern projective
showed
and
of
this
purely
ordinal
cepts of
order and
of quantity
visual space
is obviously
present to us
experiences do
of
our
know-
tween psychological
own geometrical conceptions
theories
Paul Carus
proof, and so
movement.
Even
as
I
have
been
the
one
modern
writers,
is
bound
by
any
in its operation
and progressive
one
ex-
conceptual model, one
that
they
the true connections
no experience
Mach
and
Pearson,
a
fact,
all
thinking
processes
of
the
an ideal-
philosophical value
the
of
one's
thought
is
their
success
with
the
whether
in
the
the
seem
to
have
relatively fruitless
one in
pre-
tively new
the types of
the way
assumed, in
search
is
preparing
for
the
circle, are
to
express
what
it
pres-
jections of fitting reactions in the presence of circles
and triangles
a dancing master.
because
Our
assertion
this latter fact of
relation to our
consciousness of difference.
What,
one reached
But
nowadays,
and will
the
science
tity,
certain manifolds,
which
are
I
cepts.
measure, a
can assert
assemblages
of
objects.
seems to me one of
the most brilliant feats of
construc-
philosophy, with
of numbers
is very
of
mutually
independent
first
gained by
The
at ran-
dom any
one exclusive
all our
his
exact
classification,
and
the
Mr.
Kempe,
one
all
points,
but
all
garded as
One
a classification
are distinguished
such
X
always
such
a
'yes*
31
is
a
acts, by welcoming,
so
positive motor
definition,
fellow
members
(1)
the
the psychology
which
resulted from the recent book of Dr.
Henderson
on
 The
under-
I
occasionally, as
of common scientific interest? You represent various
departments of research.
together
in
such
a
way
only
to
some
is
determined
my
present
under-
taking
student of philosophy, and,
methods, the conceptions and the problems
of various
is
in
which
sort
of
ways.
My
can the
new kind
Cook's
know little of
travel.
36
PROBLEM
OF
to you,
in a
wholly
they are
undergoing various
work,
any one special science
but for the sake of studying for their own sake
some
of
may
back
doctrines
and
raany
respects
essentially
different
is
called
a
more
organisms, by
the
illustrate.
nature
Greek
thought.
The
greatest
to take on
the form of
meetings,
old
where,
in
the
with
reason,
the
land where
were
xindelibera-
tive
art
is
naade
possible.
And
so,
designs
by
processes
own
illustra-
tions.
If
you
wish
to
its
objects
are
instant,
in
with the
the
always
probability
that
this
average
merely contrast
vi
talis
tic.
One
now
has
a
of
view
some aspect of organic nature, such that this aspect is
supposed
to
of subconscious
On
the
other
hand,
can exhaustively express the real facts, then
the only
tial
equation.
But
the
third
nature. The world
other
timeless
invariant.
When
found,
the
statistical
law
 There
zations,
where
the
trasts
to
an
by
the
assertion:
 A
laws,
but
these
relate
only
to
its
value
and
or
a
jurly
lies
eclipse.
Unique
as
provision
could
no
occupa-
a policy
insuring B's
companies exemplify.
isms.
are
social transformations, financial and
statistical terms,
terms of mechanism remains in
practise
and
of
probabili-
ties
compulied.
The
logic
of
of
the
sci-
ences
of
may
possess
upon
very
of individual
principle
nothing
essentially
opposed
well-known
forces.
in
is to declare
that a more
Its very
familiarity, in
as
well
as
true,
one
can
compute
developing
along
lines
of
his kinetic
theory of
collisions, it
complex
in
deducing
the
physical
averages of collisions, and free paths of the
hypotheti-
cal
of
mechanics.
for
statistical
diagrams
for
illustrative
purposes
errors of observa-
law
when
was
ensure
that
the
veloc-
vast
range
of
cept
parts, to
mechanically demonstrable or fundamentally necessary
law of nature. Whether nature is a mechanism
or not,
sons.
sorting the
sional concentrations of energy
themselves true.
that
the
the
make
the
place
of
the
for
scien-
tific
fact,
these
phenomena
of
nature
the
probable
tendencies
the
mecha-
statistical view
is a
makes
us
the
convenient
siimmary
due
of
tendencies to
human lives
invariant
the swarms
am next
be,
and
so
far
applicable
to
sufficiently
complicated
systems
of
as
tends to relieve
entitled:
**The
Architecture
of
Theories,
the me-
chanical view
of nature,
aspects
of
study
of
individual detail their
exhaustively
They
organisms or members of
a
physical
quantity
or
proposals
for some
towards
the
of
various
sorts.
The
policyholders
assimilation of
their
various
spectra
which
chance
well as the
of
objects
which
to get
into
the objects
crease of these
bers of the aggregate. This assimilation
may
express
itself
in
sulting classification
or aggregation
the
ideas
persis-
tently
tend.
light
make
pression of a
and aggre-
is
fact,
for
ture which
ever
be
new
sig-
nificance
by
showing
aggregates
kinetic
theory
of
the
evolution
at least, a
that
one
of
the
social orders, of minds and of
moral
processes,
tendency to
of modern
get, precise
once
appeared.
Suppose
these
Greek vitalism
what
streams
definable
photographs of your
by
special
Michigan,
has
principal concerns,
also, of
tive
idealism
to represent.
Hence wherever
reconsidera-
tion
of
new psy-
chology and
philosophy of
of
motives
I
unquestionably
my mind,
evolu-
tionary
processes,
and
our
recent
which
leads
human
life
therefore, to
as
part, although not in the
whole, of what the doctrines
known as Instrvimentalism, Humanism, and
Pragmatism
other forms,
hunnan
natural
world.
Ideas
simply like the
are the
right ones,
organic evolu-
itself a
biological and
whoever
blindly
con-
fuses
them
life.
Perhaps,
on
the alternative formula: Im
willing,
by
creative
activities.
character
us
clerical,
of
the
French
Revolution,
prepared
make the whole
indeed, very
that
I
must
be
referring
to
I
refer
is
intensely
practical.
Men
have
lived
it
indeed
that
ways,
when
I
of
expression,
I
refer
is
motives is also
itself
at
71
very
centuries,
These
methods
have
best
its
unity,
by
any
adequately
to
express.
In
so
up
to
it
of
friend
Mr.
activities
by
that
still
sciences, and this
a
motive
which
in
so
can
The novelty of
and
have
aroused
74
compre-
hend
rigid
concept
of
truth
than
ever,
before
only
of
which bind together the system
of logical relationships
theory is a
ordinal
determined,
alities
mental
the
motive
is to
solve for
I
have
illustrated
our
third
bottom
the
of knowledge
and of
action, --principles,
mate.
IV.
In
thus
sketching
for
you
these
three
motives,
I
estimate
been
wholly
over the
turn from
scientific to
view
facts that
required,
produce
evolutionary theory
of truth.
means of his history and analyses
of the work
given in a
life,
and
about
the
sense
in
lived, or experi-
to-
day,
historical events
for
chance
to
succeed;
anything
that
all, then it is
various
individual
experiences that fact.
have pointed
out, I
of its
own definition
of truth.
and
supratemporal
Hereupon the
second of
to our
aid. If
which incline each
correctly
accept as
we
do
Our act in
accepting such unverified
own
pre-
cashed,
is
ac-
cepted
the vast
which,
accept. They are
assertions about experience,
more
than
one
modern
theory
tially,
in
to
assert:
 We
trade
upon
In other
these
remain
credits
need. Enter into the possession of
your
only
 Henceforth, so some
to credit. Truth is made for man, not
man for truth. Let your life  ^boil over into new truth
as much
simply:  To
just
this
theory
of
truth?
I
my nearest
upon absolutism, and
democratic attractiveness of
the novel views
What,
as
individuals,
that
that
which
nriere intellectualism
account
indication as to
a
logic
internal
clearness
of
of its
aims and
of its
sciousness of a
Our
whole
objective
world
is
meanwhile
defined
ideas. General
ideas
accept certain ruling principles of action. And in re-
spect of
all these
myself
at
one
with
recent
cannot rest in any
mere relativism. Individualism is
But individualism is wrong
merely
an
individual
will.
nothing
complete-
our
present
whenever we
of
the
physical
world
that
whole
voluntary
and
absolutely
true.
We
we try
any absolute
absolutely true. If
make
giving
mathematical
geometry,
or
pure
nvun-
the so-called
and a set of
fvuidamental  propositions, the so-called
logic
of
pure
what
is
primal
ing
the
sense.
Pure
to
at
pres-
ent,
(as I may
simply to
exists no
Euclid, namely, proved this
to be
He
im-
That
is,
nvunber, I
even thereby
number,
which
comes
later
prime, and
prime
num-
bers
consid-
eration
these
latter
principles
other
and
equivalent
the
at
the
basis
of
the fundamental theorems
--a
con-
struction
which
is
easy
through the whole
of our
constructive processes.
that
absolute nature and conform to
their own self-deter-
still, with
des menschlichen
fine,
In
brief,
all
such
we
will which
own
which we conceive
also true
the
unity
connection of its
which express pre-
Hence,
to conditions
the light of
that to
forms of
the
to the objects of
relative to our human needs and
activities.
the reassertion of
categories of
pure logic
hand, with
the concrete
And
as
the
in all
universal
absolute
nature,--the
And
95
striv-
ing
de-
sient expressions,
at once
those of
logic, of
rian, cries:
 Oh living
triviality.
In
any
case,
the
poet's
the
term
but numerous
opinion
or
missing
the
way.
It
seems,
therefore,
clearly
distinguishing
theoretical
applications,
permits
his
opponent
to
score
result
from,
de-
intricate.
practical.
It
does
99
sion
word
derived
inti-
mate
possible.
sheep. In this
case an idea,
of sheep
with
of the one
or of still
to this view, to
the erring mind
pure
logic
disposition to accept
referred
to
erring
subject.
been
of error,
to
set
forth
at
in
the
complex
cases
of
of
correct
and
sufficient
portrayals
of
fact.
may
may merely
attempt to
connexion
of
things.'
This,
even of their errors
rejected
fatal errors into which
theory
of
error
is
subject*s ignorance of
gated
as
reality
is
the feelings, the prejudices,
of mind
subject
is
through
error have
portrait
or
mutu-
com-
so,
accounts thus far given, to be external to the meaning,
and
truth
of
can
be
satisfied should
What are the pro-
which makes
come to
welJ
one thing of
factor
which
is
decisive
be one
error.
Of
of the 'correspon-
carefiil,
prejudice
be
progressively
of the
ideas.
how
or
suited
suited
emplify
the
representative
A
exemplifies. The
predicates,
useful
sometimes
pragmatist,
tion
for
our
expectations.
The
for con-
success.
The
traditional
of error.
what
experience,
in
one
known
cause
that
adjustment
to
our
situation
is
get the ball,
justments is
dif-
the
logician
what empirically happens,
and results. These happenings or 'the long run' of such
happenings, constitute all
is
testings to which
study of the
and life, and
presupposing
cer-
empirical facts
to be
the
test
by
servers. It has been necessary to assume that one
can form expectations
assumption
requires
the
period
of
definition of the
temporal
One may,
in each
idea
formed
116
put in
the
conditions
which
make
definition of error, must be modified
accordingly. In
that
Pragmatism
gives
a
figured in
the form
in
the
herds-
man's
in
involved
in
the
process
of
counting
is
whole, they are not; hence
to
say,
'They
numerical
account
of
(not merely por-
them,
tion of
the whole
experience
of
In so
by adding
characteristic of modern Idealism. That the truth of
propositions about experience
is a
tures of
and
to
preted
enables
us
to
know
truth,
whole;
false,
as
needing
supplement,
and
as
with a
more empirical
Bradley.
as the
usually
organ-
ism
at
systems of
the ne-
the life of
truths
taking
of life, is necessary,
defined as
is
wholeness
and
essence of reality, is an inexplicable event, which
must be
a necessary
with
adjust-
4.
following requirements:
Hegel,
in
his
Phanomenologie
effort
our
ideas
hypotheses, and opinions
momentary experiences,
the
partial
view
whole,
must
ity, and conflict
his stage
of experience,
to
be
in
positive
and
decisive
Editor's Note: It is the editor's opinion
that
of
to
easily confused, and
(2)
Axiom
in
a
fixed persuasion, while he regards
the
something
fundamen-
tal
and,
for
which, it-
self not
demonstrated, can
be used
fact,
(5)
Axiom
which the innate
(1)
the
axionn,
and
to
know
it
'axiom,*
when
thus
that
is true.
of
the
truth
of
the
conviction
can
be
conceives
the
meaning
(2)
requires
(2)
there-
fore
makes
when
(2)
is
emphasized
Aristotle maintains that
But in
turn solid'
^assurances' and
confounding mere
'conviction' with
is manifest throughout the history both of science and of
religion.
3.
Sense
(3)
rela
development of the
axiom
to
be
not merely to
so
that,
without
system of
one is
a philosopical
(l) and
in sense
to
fact,
it
can
never
axiom
in
sense
(3);
hold that,
assent*
axiom
usually
render
call
interpretation,
of
of
the
'wise'
or
of
doubts
the
supposed
axiom.
sense
(2);
then
he
evidence,'
in question
even yet persists
is
Understanding, of the ancient
a
knowledge
of
case
prominent in controversy ever since Locke.
Numerous
principles as definable in
of the 'experience of
axiom
sition, for the
'innate constitution of
*s
necessary result of the
ought to avenge all
upon the
empha-
determined
by
experience, which moulds
in
their
that the term 'axiom' is a very attractive and a
very
by
sources are
above all:
his axioms in his
cases and
it
becomes
especially
modern discussions
Leibniz's
Nouveavix
Essais
the
principles
of
axioms of Euclid's
senses of the
well
bear
in
mind.
mutually
supporting
truths,
the
rational
enough
may involve
science
and
from
the
point
of
view
of
logical
and
metaphysical
definition.
139
various
accident.
In
psychology
it
has
real object. From
ceptual
experience
is
meet
the
reached in
those
assume definite form in the Socratic, Platonic,
and
our
general
con-
ceptions.
A
in individual
constitutes the
is
speaking
of
obviously
the
importance
early ages
of
they
are
in-
dividuated
primarily
indi-
viduals
in
of the
the problem of
the
relations
between
Begriff,
gets
a
complete
development
and
the individual becomes
general in
period
essential
object
as
time,
and
The
is
not
the
place
to
go.
as a
tendencies has
If
we
survey
the
inquiry.
Amongst
physics. It
above under
theory of the
namely,
ledge.
This
with this
objects.
well
concerning which we
that
it
is
his
effort
the
of uni-
in
which
two
can
momentous
for
the
theory
both
of
knowledge
foregoing types
mental transformation
stand this cry essentially
gard my fellow's
either that he himself
there
is a fire, or that, at the very least, he intends
me
and
I am
possessed of
the
percept
of
the
sign
nor
in
from
any
with
the
cognition,
tional state, or
the continual flow
objects of
perceptual knowledge,
i,e. of
so on. But
ex-
press
the
mind
which
also
interprets
them.
This
the
same
a
154
is conception,
tion,
whose
mode
or
type
of
cognition
here
whereby
of
purposes
be
characterized
as
making
a
these two types
interpretation
it
is
interpretation
well
them.
minds are known
past
self
For the cognitive
only a social character,
intents and pur-
'directs
himself,'
its most
the ideas
when
he
uses
the
term
present, or future
mere
conception,
in
meet
the
'cash.'
The
is
the
seeking
idea^ 'I
am homeward
bound,' is
his wanderings
process
possesses
thus
illustrate
an
aspect
of
cognition
which
had sought? Not by the mere presence of a 'home-
feeling,*
a
objects.
The
essentially
important
fact
is
that
who-
ever
own
portion
of
that
life,
in
own past
the very same as
past and
of
cognition
which
exist
as
which have played
an
it
conception,
or
as
an
object
whose
being
consists
in
the
who
advances
is
treating
it
as
known only through some
called to his attention the fact that he is speaking
now
in
perceptual
,
percepts.
Yet
nowhere
the truth of
inner
life
or
to
the
am
in
dis-
by
analogy
neighbour
of
a
hypothesis
they
become
my
his,
precisely
i.e.
problem of
the
foregoing
argument
from
both
by
com-
conceptual
and
realistic.
One
the conversion
cash, i.e,
This
is
true
whether
I
never
immediate,
verifiability
of
the
are
these
they mean.
in
the
we
our demands, precisely
which
are
upon,
expect.
not
my
own
mind.
The
through this
.
-
-
history of
the
minds to
The mind,
connected
beliefs
analogies
in it
the
question
arising within the body as to where and what the soul
most
is.
allegory sufficiently
defined in terms
of mind
body,
in
modern,
and
diversified,
theory of mind ought
with
the
conditions
that there
of
his
own
mind.
this
the
world,
the concep-
which these theories have
stances,
time
tertained as 'working
matic test can be
the majority
the
far
The rela-
social;
so
for whom or to
Such
theories
thus far
fact whether through
but
is
in
essence
a
mode
a
by
theory
cautiously
cognitive
process
of
tune of being too
If the self
as the
has greatly
significant
perhaps un-
which the religion
at the basis
to
become
clearly
with, and
its
own
as set
—
to Royce's
article  Mind,
he
Axiom,
p.
125
what,
in
object
of
tion has
or not to be;
'to be' and
'to bear
the ills
action- -namely, com-
mitting suicide--which is
treated by Hamlet
the negative
prime number'
distinguished as
(4)
to
ex-
pounds
this
is a
the word
brings
of this
world
Thou art not, O
and even
Thus, to regard God as the negation of the finite
world
is
emphasizing an aspect
nega-
in
some
going
every negation,
of action is
man or
mind.
For
fact
that
he
can
In one
objection,
or
unwillingness,
the modes of
a
are
so
re-
is true, the other
are
also
the proposition X
proposition has
of
double
nega-
common sense--that,
view, there
to
some
con-
such
complications
and
sition
contradicts
to
say,
'For
my
part,
I
to
equally
vain
for
one,
in
whoever
so
whole business
who makes any
assertions w^hatever.
consider
he must
who has the opportunity
either
steal
action
not,*
to
can refuse
Yet,
for
all
in a persuasive
what
not
which inevita-
a
negation
of
application
to
is also a positive term
in
so
of
concerning
But
and ethics,
the topic
observa-
tions
of
the
real
suggested by
with
an
treated
as
the
negation
of
Q,
while,
respect
general
indi-
 Never
universe
of
discourse
the other is
to be viewed
with
reference
to
the
question
whether
they
are,
insolvent debtors,
whatever else
far, treated
Barrister's
debtor wants to
found in
of
the
universe
factors.
purely
logi-
cal
within
193
fact, that,
between
number
negations
of
universe
of
not
possess.
From
unsymmetrical.
distinction
between
points,
with mere
limited universes
distinctions
194
and therefore is in
declare one of
does
who
does
not
steal.
4.
The
to
add
have
failed
to
recognize
character, both
involve,
in
its
essential
the
involves.
We
numbers
of
natural
ob-
jects
tendencies
training,
nature
would
a
limited
universe
wish to
logicians.
universe
case, but
importance
of
the
asym-
desire has its well-
them,
and
stand in a
rather
than
destroy,'
are practical
something
involved
are
perfectly
sym-
metrical,
the
merely
a
tion- -a
basis of
and
at
all;
199
or evil; hence
advice which
our
own
way
flaming
thunders
'purely
negative'
of
Christ
course
is
because it contains two beings, God and the world, the
absolute
and
the
finite.
But
an
absolutely
complete
universe
of
discourse
is
very
limited
one--consisting
of
the
apparent object of
objects stand
necessarily
defined as 'beneath'
men
who
other
objects
called the Great
but, un-
same
collection
are
also
204
the
things.'
That
be able to infer,
able
of
it
The ob-
some sense an
that,
from
a
knowledge
of
what
infer
in
definite
some
the first
col-
lections
we
work both
details
orderly
array
of
Z05
if they are
is exemplified
own. What
one is
to infer
what others
troduces, as
their
or are
devoid
of
what
order,
he is able to
to
of Venus
Jupiter
and
Saturn,
earth's orbit lies between
in
knowledge
earth
is
their
real
of processes,
that, by
is possible to
and so explicitly
of
behaviour,
with
an
order
because,
from
the
fact
plain-
series of
is no
from
n^
to
n
sciences
and
for
the
mind. It
will be
whole
to
real or
the ideal
arranged
useful
very
extensively
with
laws
a
recog-
of
theories
which
deal
with
laws
get many
highly impor-
but upon the laws
our discussions
ideal
world,
then,
in
so
we are
they were
of the
numbers themselves.
orderly system of ideal haecceities, which
exemplifies
in
we,
haecceities as
life
the.
laws
the fractions
is the
the
two.
(2)
less
greater
than
a
proper
Q^,
then
Q^
is
never
greater
than
P,
but
stands
to
relation 'less than.'
way, opposed
other, then there
between
of
is
fraction
which
is
fractions has, in
we choose,
while 1
follows all
last member
in the
members
the
whole theory
of order.
follows,
more
a
man,
All
our
that
makes
whatever you
and less.' This rela-
whatever
members of
S, i.e.
series,
and
actually
constitute
such
a
series.
crete,
like
the
order.
I
that,
by
my
whole
numbers.
collections which we mea-
find them
with
two
principal
facts,
a collection of
our
knowledge,
powerful
and the
connexions of
part of the sys-
tematically
of
the
work
general, in
developed
without
making
in
our
power
sense
of
sight,
has
and social as a scientific and
theoretical significance. The one great task of the
intellect is to comprehend
real
and
lies,
therefore, just as much at the basis of an effort
to define
tell
from
the
title
whether
The
bridge. Then ex-
his
son to study.
viduals
either
are
be-
ings
there
relations
well
known
223
commands C,
subor-
as well for A^to transmit his commands through B
to
C^
as
ity,
that of some
be as
by
student of non-metrical
of
mathematician
uses
in
his
computations,
some
order
system.
It
is
an
its
an
order
system.
In
general,
we
may
say
that,
various pairs of
another in
system
with
definite courses of
instances of
given day, as
will
all
bow
to
b,
subject
fought
side
most characteristic
community
either
exists
or
is
in
the
process
of
making,
does not
merely remain
 I do
which
a Rousseau,
foundling hospital, or
in
a
in some
possible.
7.
Law,
order,
and
ideal
world,
which
inferences, which
pay
one's
investigation,
process the series
systems of series
another.
What
is
forms of
and
in
of
the
produce a
system
these mathematically definable
and
orderliness
which
can
win
and
where an
to general
ference.
Without
inference
there
ordinary
popular
upon
which
the most
were concerned,
their
certain
questions
 Are
all
the
members
the topics which it wanted to have discussed, unless,
accepting
member
by
restric-
tions.
The
meeting, such
his views
printed?
object
with
of perception,
(b) with
apart
from
dividuated stream of
adjective
not
topics
to
some
specific
so easily specifies
means
conditionally
is
sense, one
deals with
directly experienced
relation of
the relational
also the problems
in
sense.
the given has
sion. It
 locus,'
i.e.
to
apply
to
the
case
here
lar actual
And
*s
for
at
several
moments
of
 stream
of
the senses
above in-
committee
has
certainly
not
left
hold
debater
will
have
his
opinion
as
to
a student
for any human
is an
relates
discussing?
V
In
answer
to
this
counter
11 of its
object.
question, and
can
only
say
this:
Were
the
reported
view
Committee's  perceived
if
the
Com-
mittee
objects at
another declined
not succeeded
definition
of
a zero-
J.
manent possibility* when
of
of sen-
set
of
events
These
events,
the
what,
no
other
physical
ob-
been led to
perceived
a horse
in his
defines as
For all
given as
moment
of
perception,
and
is
in that
which flits.
amongst
in
question.
opinion,
propositions
in
terms
given in the
essentially
an
perception** is simply
as I have defined,
to every stu-
logical purposes, is
are
false.
an uni-
to be
doctrines
I
Comnaittee*s
for criticism.
I conceive
most impor-
tant views
of
place
might
real, or
with
the
pubhshed Mrs.
at
do
of
the
translation.
of
the
manuscript
of
revision
for the purpose
oppor-
popular ex-
represented
in
phy
since
1908,
events
for
from
of
the
some
from which
from
those
philoso-
phical
controversies
was prepared
Nineteenth
Century.
Meanwhile,
work
until
of Enriques
the
with the
just seen)
justment to  situations. But
upon
what
sentations. And
this stress
hypoth-
eses
very
work
and
of
the
uses
of
the original or Comtean type of  Positivism ;
for
he
greatly
As a
value in
or with
to the simple  description of physical phenomena.
Yet, despite this
of various scientific
takes to
will
as
is
expressed
by
synthesis,
in
a
man
tive and
strvimental
lays
upon
the
 objective
aspect
of
tence upon the
mutable
and
transient
total view
ested in those
aspects of the
concluding
chapter,
wide out-
his bringing together of matters which are, for
inost
readers,
hopelessly
far
apart,
have
long
May
spirit
Century
in
of this article
given it
a
 fair
samples,
from investi-
gation from
the origin of each cell from a previous cell, and
evi-
more
tions.
be
of induction seems
which
will
how far
can
not
(1)
The
choice
of
this
method
numerous
consequences
that
less
or-
or by the
tific method wholly reduce to these two
processes, viz.,
and
(2)
hy-
potheses?
so. I
other-
wise.
progress
and
use
of
hypothesis that you use
Yet
it
does
is
and
it
a
definite
inductive
probability.
For
civilization.
It
by
the
text-books
we
can
neither
following: That
a
sufficient
as
for the whole later
the vital processes
point
not an hypothe-
been
other hand,
whatever
in the tale
because the
1847, is just as
precious to you to-day
ideas for
undertake,
perennial need
com-
parison
Poincare
gives,
at
own most
the
whole
'knowable'
universe.
American read-
been
otherwise thought
of Stallo's
critical methods, or of his results, there can be no doubt
that, at
We
are
no
longer
able
control
of
natural
 
foundations
of
geometry
are
beyond
controversy,
nor
yet
'opposite inconceiv-
great obscurity;
to plan what can
and
any
longer
a
serious
business
If
certain
general
theories
philosophy? Has science
often
to
let
us
regard
very
age
whose
revolt
from
rapidly advancing
guidance ?
As
a
fact,
evolution, even
in its
these
without
as
learners.
These
conflict with
special problems
aspects of science.
book
is
a
are
of the fact that
them.
prominent
topic
of
our
logic
and
those
type
to
admit
to
the
reasons
's
treatment
of
the
work
'forms of
the world
determined
an essential
as this
epistemology.
I
do
not
sensibility,'
and
doctrine
of
nature
are
of
our
interpre-
is
something
far
is constantly
own
way;
only
interpretations of experience
are merely
organization and to the
rigid list of
far
as
neither
con-
firmed
according to
(2)
The
prin-
for instance,
we can
truth of the postulates of Euclidean geometry
; or can
Hypotheses of
these various
ject
the
historical
here
does,
to
the
sciences such
a
to the control of
of
the
laboratory
external
reality which
Yet
Virchow
's
re-
searches
were,
as
early
as
1847,
no entities
to be called in
stated
the
principle
in
the processes of disease to the
normal process
inquiries which
narrower
guidance
which,
as
of
science
give
Of the hypotheses
the
of
great
philo-
sophical
import into which I have no time, even if I
had
the
right,
to
enter
here.
by recurrence'
lems that lie at the basis of recurrent
proofs
fundamental
importance.
These,
book as those of
not
investigation
a
of functions
reputation has
been confirmed
by the
his
in
as
a
theoretical
physicist,
a
leader
active.
gether in
the present
M.
Poincare
of
a
und fremd bleiben
fact,
Erdmann's
science.
psychology
separate logical and metaphysical
the things
 
about.
 Das
Transcendente
we
of
inner
or
latter include the deas
As
sented, and
involves
the
book
(^cf.
p.
77,
and
features
of
each
Vorstellung
them-
selves.
concerning the
hearing
and
of
act
of
judgment
con-
sist ?
is
for
my
consciousness,
Yet
the
act
subject
and
predicate
idea,
indefinite
(p.
307).
On
the
whole
(p.
262)
content
of
another,
logical
immanence,
(2)
being
determined
by
is not surprised to find that, with his eyes fixed
upon
so
interesting
a
wholly neglect
'
especially
unsatisfactory.
indicate
most learned and
stimulating study of
philosophical issues
Boole
himself
hoped,
is
well
known.
amongst forms
unconditionally invertible. Nor
operations
of
particular
topic;
to
a
which
a perfectly
commutative
and
associative.
The
that this operation
is not only
so
that
the
three
ah
a symmetrical
I propose
to symbolize
or,
in
fact,
logical
element
a
member
of
a
tetrad,
this
Boolean
algebra,
group in
question, and
for its
an ordinal function
functions there is followed
p
is
then
the
of
the
first
which is formed
rs)
ordinal
function,
of
the
pairs
which
These new entities
in
the
theory
to
of natural numbers which
its
deal with
has
called
of
treated
operations of the
short-
we
are
to
deal
with
our
directed
&),
as
=
a,
h,
c,
and
d.
The
novelty
and
facts in the form of what may
be
called
a
 Newlin-diagram, *
which
diagram
expresses
a
special
application
other
special
is
not
in
to give an outline
as
find
u
following
and the multiplication of
the
interesting
Thus
the
higher powers,
a
determinate
system
the modulus
whose group
is the
the
four
-n
c/d
the
and
conversely.
The
only
serve to
In any case,
algebra
of
logic.
ing
is
distinguished
from
universal or formal
to the methods used
to indi-
a
wholly
of the
most funda-
to-day
progress.
this
art,
or advanced by
involves an
are
common
has repeatedly
general
study
of
the
methods
of
so
common,
As a fact, however. Methodology, taken in its usual sense
as
mother
of
Logic
taken
in
Methodology
and
differs
from
some
mention of
us.
but
which,
at
that
for
It
will
the nature and
constitution of the
learner
If, namely,
becomes
the
world
of
the
Platonic
Ideas
the
Methodology
of
the
logician,
of Forms,
the innumer-
when
he
thinks,
be
systems, whose
something
of classification.
comment),
orderliness
and
system
are
much
in
the
commercial
of an
things concerning which
Methodology
depends
this
orderly
to
suggest
becomes only
dialogues, to
here omit
story
doctrines also lead us
and
sciences
mention the most
that Socrates taught. There
of nature,
stages
of
growth,
classification
predominated.
the
made up the
upon
 
or
inorganic,
where the
These
corresponding
methods just mentioned play a very large part. How they
lead, beyond the stage of
classification,
to
higher
sorts
of
know-
of
results
simple terms, showed that other methods
must
of the
regions of the
for instance, correspond-
light was
such
Dynamical Geology. But
stages
in
the
expression
fact,
search, even
to do with the
without any
of
Such
a
stages
with reference to
certain of the
of their
ferent interesting parts of
recorded
observations
of
a
the
(c) The various enumerations,
more
aspects
of
with its
are
orderly
array
of
objects
of
laws of
that
employ
them,
tends
to
in The
of
physical
at least in their
effort
to
we
methods, laws
the number
of instances
that have
a
finite
comparative or
of the
statistical methods
data
—
in
a
non-con-
and
in
what
sense
has
one
a
or less nearly
unobserved geo-
certain facts
How far can
tical curves
Hence the
extended
to
order-system,
not
by
chance,
geological
a
only
the
definite
Thus, the
based
death
rate
 
he
decision
of any
the
same
only
difew
unobserved
that
observed
 
in a world
out what
possible
of
exists
a
to
what
Kant
calls
the
definite
con-
within some range
any one
realm of
may be con-
ceived to be
precise meaning,
object A
false.
This
presupposition
of
the
of facts
a
reasonings
used
region
of
our
any
the
whole
collection
by
the
 
whole collection
are
marked,
respectively,
by
painted either
of
four.
In
b are
of
conditions,
Six
different
we
choose
partial
collections
the
constitution
towards
possible
than there
vastly more
containing
m
objects.
of
these
objects.
The
true.
But
if
we
consider
character
q,
it
is
possible
or by
will rapidly decrease.
the
direct
have the character
is a
it
has
been
chosen
otherwise
than
field,
not
mate
and
probable
right
one
has
to
the expert,
of a more
is
to any science as
Induc-
tion,
We
of
the
of
Order.
This
bearing
exact
natural
sciences,
what
makes
this
union
most
effective,
depends
approximately
agreeing
determinate
constitution
whatever,
exact
observation and
by element,
and conceived, and in
the
probability
while
the
development,
concepts
get
concepts. Exact
that is, in
so
far
as,
 approximately
and
 probably,
be said
particle,
involves
would
result
expressed in
conduct.
in
a
experience
of
the
thinks,
expresses
itself.
His
so-called
and
personal
whim
or
desire.
In
his
study
fact,
the
forms
of
may therefore well begin
presented
to
the
deductive
such an experience
is of course
analyzing that work
school
next simply report,
concepts
and
systems
are.
Order, is
expressed by
advance
in
the
defining
their
the gate
of the
events they
may be
so viewed.
we
abstract
from
reference
to,
that
is,
as
object,
or
with
several
other
objects.
father.
To
be
member
of
a
collection
(a
pair,
a
It is
But,
as
a
fact,
there
are
countless
given.
When
are frequent
throughout the
exact sciences.
{a R b),
R
is always also
of
the
relation
father
of.
relation.
Or
again,
S
a)
is
true,
whatever
objects
a
R d),
excluded
by
the
proposition
such that
{c R
independent
and (b R c),
the relation R may be such that {a R c) is,
under the
relation
R
is
non-
this
transitivity,
which,
from the symmetry which
Fewer formulations
form
the
that this symmetry
and this transitivity
The
is non-transitive, then
propositions
relation
R
all
transitivity
or
more
 
relation
 
it is
should
be
several
 
is
by hypo-
insolvent's
estate
:
—
 /
as a
there
may
determined
by
the
a
whereof
case
the order
club, or
as other
relation of
question
except
the
one
.
.),
the
objects,—
some
substituting
of
one
for
another,
wages '
when the interchange
a
given
polyadic
relation,
pair
of
pairs,
or
pair
of
triads,
systems
more
{a b
 
relation i?.
that
to
element of
Psychology,
in
that it
permits certain
ways of
case,
one
only
of
of the most elementary
constructions.
§
3,
have
shown us from the outset how the most obvious and the
deepest
 
assertions are true
vestigations, or how they can
be distinguished from
asserting
in
the
identity
of
is one
that we
to
so-called
pragmatic
reason
dis-
not only
We
it.
given norm, then the
the
region
can,
 
any
determinate
class
and the class
them
class
x,
y
being
ex),
is thus possible,
 
logic
possess
an
absoluteness
 
modern
foregoing
sketch,
suddenly
about
line, any
single
definition
just
stated,
for
is
one
and totally
whole number stands in the relation R to this first
one
2,
or
R
(n
and
the
classifications
of
possible
serial
types
properties
type by
the
elements
of
the
terms
of
certain sort of classification
whereby
of
a
complete
dyadic
ordinal
relations.
As
they
are
also
these triadic relations
more
numbers
number
series,
combinations. All
of
this
research
is
of real numbers, etc.).
And in brief, we
relations
greater,
less,
and
equal.
are
or
(2)
upon
the
the
case
Geometry
as
they
are
is frequently
 
exists,
whereby
its
own
when the energy
own
series,
determined
by
a
metre,
etc.).
Hereupon,
etc.,
there
products, expressed
of series,
or of
out, the
and
metrical
a
and countless
of
the
diagrams
the orderly
structure of
of
best
known
many of
systems
are
system un-
changed by
:
 
in
quantity
to
state
includes
expressed
by
symmetrical
transitive
relations.
All
inseparable
union
of
the
concepts
of
Class
and
of
Relation,
—a
It
look back, that
Logic, as
indeed,
we have
have
consequently
insisted
or
psychical
relation^
should
be
present
in
the
the
existence
experience.
are
arbitrary,
and
may
be
these
the
logical
and of
such
far
ques-
tion,
and
successes
which
not
dependent
deed may
be arbi-
trary. But
the absolute
without
seeking
to
choose,
involves, for in-
has
logician's
may
itself
of mathematics include
whoever knows
difference
empirically,
and
that
we
get
putting
two
a
weight
enables
us
to
arithmetic
conceive
we
we
should
we use
our empiri-
what shall we say
numbered,
etc.
objects altogether
as con-
existence of
weights in
suggested
succession
In
It therefore
the whole
of
the
series
must
is
so
possibility may
prove to
which the
facts in our
to
be
decidedly
inexact
In
mentioning
this
presupposition
in
tulate : That
equal
to
the
same
thing
are
equal
to
each
terms
of
merely
a
tence
finitely
rich,
which belongs to
after
all
of
Mathe-
Mr. Russell
 
is
definition.
It
asserts
their definitions.
it is to
actually
working
the Theory
thus sug-
 
he
discussed
the
logic
and
of
Geometry.
research
principles which
logical classes
logician
cannot
stir
and if we
logical
entities
between
any
of propositions. And,
foregoing
repeated
open
to
(expressed
in
singing.
to
the
by
the
verb
by a
by
conform
applied to them. A
the
recording, in
of
action
once
viewed
such
a
with
complete
makes
use
is
to
be
defined
at
all,
requires
p
one of them
of action
modes of
no
 
the
types
(4)
in
question,
polyadic
which are
may
enter.
In
properties upon
for
the
sake
of
order-system
is.
The
matter
of
the
aforegoing
principles
concerning
rational
at
present,
fundamental
of the
Encyclopedia
of
the
Philosophical
Sciences,
Volume
I
of
The reason that he
of order
investigation where
his case
to
refer
very fully
given in
reference
is
to
Ernst
Schroder's
Leipsic:
he
therefore, to
of
which his
root of all serial
detail), as depending
symbolized
by
—< . This
or unsyra-
various
opera-
tions
considerations).
The
relation
a
—< Z<
, in
so
far
as
so far plain.
type can
a line in
—<ib,
c
rela-
not be
directly expressible
other
elements
of
For this
 
of
the
points
of
those ordinal
of
relation
a
theory
of
the
logic
of
an
exact
define
pure logic.
as a
characteristic
of
what
 
of the system, identical
elements. The result
is that the
a
discuss. Geometrically interpreted,
if this relation
holds between points,
system,
as
thus
the entire algebra of
logic, including the definitions
and properties of the
 
existential propositions at
possessing
to
to
infinite
;
elements
of
a
selected
points are now also
The
share.
which is
based upon
methods,
a
of
Mathematics
of
to my mind,
(all
statable
ably
as
rich
as
the
totality
of
so
a
result
how-
of sym-
bolic logic
being absolutely symmetrical,
present
ordinarj ^
so treats it. Geom-
the
members
of
the
Johns
otherwise
defined
the
makes explicit
two sym-
this product
terms
of
symmetry.
a
course
of
is
 
what
analogy
of
O-coUections,
with
I read the
dependence
upon
is
assertioiis that certain enti-
entities
to
 
indefi-
nite.
In
seeking
which,
although
in
elements which
many ways from his.
so
far
undertaking
involves
here
done.
Kempe's
area
c
which
relation
in
 
of equivalence,
obverses
of a symmetrical
 
1. The system
of certain
employ the small
indicated, these
subscripts are
merely convenient
scripts
will,
in
will
be
partial
single
or
a
three a
n
statements, and
course of a given
of the
collections
as
are
at
always
to
be
mere
symbol,
of x^,
and of
an unspecified
that of the whole numbers : and the use
of
whole
numbers
as
subscripts
is
then
5. In
Thus, the
an
being
left,
may
given
statement
ments
together
of the properties of the system
2,
:
 
read
of
which
that
other
then
discussion
of equivalence.
which
from
each
of
these
made
mentioned
0(ab)
and
lections
that
can
be
formed
by any permissible variation
in
which
mutually
obverse
in other
pairs), is
distinct from
consisting of
all the
of
the
collection
8,
while
S
B
if
is
the
collection
{y,j,
n,
r,
s),
be
equivalent and
together with
the exist-
proceed.
element
0{pqr)
is true.
VI. If
that
while
By
principle
I,
remaining
elements
of
p
besides
r,
and
the
thus
a complement of
principle
I,
from
0{ey'\.).
0(dy\).
collec-
tion
(7,
A.).
II.
single
element,
e,
then
to
if e
collection
X,
the elimination
and IV,
which
one
occurring
either
once
any element of
complement
O-collection in
-u,
we
have
so
Hereupon
let
7
into
which
q,
7)
separately adjoined
an
follows. By a precisely analogous reasoning we could show that
if
7
is
them may be substituted for the
other
of the
by
28,
?«
same
one
obverses, for all
discussion
of
0-collections.
This
any element equivalent
any time
symbolized
by
x.
31,
x
of
ocal
as
(see
14,
15,
16),
case
collection of the
of
fact that
No monad
be
adjoined
IV. Hence
it is
21-24
in
every
element
e^
question
collec-
tion
consisting
by 36
constitute an
,S),
is
a
lection
is
or E{abx)
expresses
precisely
the
same
facts
that
are
expressed
33,
symbol
in
question.
45.
If
0(7),
and
7,
it
7
is
form of explicitly
to
F{h\e),
of
defined,
and
as
a
determinate
the
col-
lection
a
(
g.,
if
the
original
all
the same
emphasized, to
case
tion as (a:, a.) and if F(^ic\X) is
true, F^rj) is true; while if
we
merely
know
that
F(
77
of
assertion
F[
S
j
e)
of
the
it is
—
.
If F[a), then F{a).
51.
clearly
the
kinds
asserting
collections
which
stitution
For the collection
possible distributions
express the
not
tell
us
which
^
0{ab) and
0{ab) are
0{ab)
7
then
F{^\^).
(5)
then
ax\y) and I'^(^ax\y).
But in
which
the
vertical,
the
collection,
transfer
the
obverse
side
F(yi3x\B),
by
the
an
O-coUection.
54.
If
F(x/3
\-cy)
then
or
stands on the
collections or elements
the elements of
elements of
oi.y\/3)
collection
d,
then
/8
forms
case F'(d
there exists an
of
the
directly
in
0-collections.
follows,
by
58,
to
two
collec-
a
S,
O-coUection, is so
such a collection
which is not
J^-coUections
true
that
is indiffer-
the
transitive.
In
which appear
an
element
If
that
case we
given relation
in
y
of
q
with
these
an
of S
a question
case
inconvertible
JP(^ b\ay),
right
is
simply
a
direct
translation
into the symbolism of the relation of antecedent and conse-
quent.
The
elements
which,
with
same ele-
same origin.
and
element and
element
a.
For
O(dyy)
and
O(ayy).
77.
of every
antecedent
of
is true of
Hence
the
collection
{q,y)
to a
given origin,
also a
that
e
83.
In
elements
may
exist
in
sufficient
variety
to
principles
have
so
establish the existence
contains
a
of
any
of
S,
while
0(/8)
the
system
2
would
(
^(r, r^)'
by
41,
that
r.^
4=
r^',
and
?'3 of T-g,
order.
These
elements,
E{r^\r,_x),
4=
''«i+2
chains of
as r^,
were equivalent
By elimination would follow
F{r^\'r^x)
so
r-j
r^_^j
mutually
equivalent,
r^ and r^_^^, are
,,),
significance
of
member of any chain
new chains
these new
in
elements
\ye
have
hence v
any one
/3.
element
c
is
a
medi-
from
/3.
y
itself
is
y\y^)
elements
possessing
this
property
which
of
7
such
Pairs
of
^(
a
mediator
of
(q,r).
that
of the
representative
to,
d-
in this
is
[q,
(
now
(§',
result-
ants,
third
resultant
of
/S,
v
and
of
/3,
collection that includes
of
/3
while, whatever element
then
/3
and
a
possess
Hence by
of
of e,
as above
J{x%\
have
F(
what-
ever
resultant
z'
of
/3
possesses
what-
ever
a
and hence
91,
a;
If any element
of
/3
; while
(2)
the
the collection
collection
define one
such pair,
and (barring
pair of
collections
limits may
mined. But if, instead,
element
y'
or
y
accordance with still other principles (which
we shall
the
inferior
limit
of
This
appears
104.
Adjunction
of
(
/3
the
to
/3,
enlarged collection,
so long
in
91,
92.
Hence,
by
89,
if
limits remain
tion of elements
the inferior limit, in general, alters, the superior limit of
the
as
if
good
p
for every resultant,
or
^
every resultant r^ of
/Sj,
/Sg,
of
all
these
that
for every element
(
mination
let
s^
be
the
the
base
y
collection
the
corresponding
cross-collec-
assert that
we
have,
by
whence
follows
holds of
while,
by
the
definition
is always true. Since
lection
/3
. Let
X' '
be
that is,
before,
F(
one of
cor-
responding
5^
or
/3^
which is
we
have
(1)
is
Hence,
by
the
defi-
nition
generalization
of
Kempe's
treatment
gate
resultants.
the assertion
whatever
p^^
of
).
U^''
is
entire
X*: -',
holds true
that
Let
an
element
y
origin
with
reference
to
which
/S
also a
c',
each
to
6,
that,
whatever
element
cedent
of
every
element
whatever
element
of
by some,
of logical
antecedent and
negative
of
the
other.
Since,
in
and
80,
82),
+
(easily verifiable
foregoing
a
the usual form
from
the
start
that
they
apply
to
to
addition and of logical
the conjugate
defined
in
combination,
have
120. By
a finite
true,
and
is true, can be
of
elements
of
c,
pairs
(a,
6),
ant of
the pair (
x,
and i^(£r/*|e),
j/,
such
that
transformation of
JP{b\qr) are
choose
any
resultant
q
to
(g',
of all the elements
contains
an
infinity
of
elements
the elements
so included.
It is,
in the
the
tion
comprising
a
concep-
ways.
And
such
these
resultants
appears for
For if F{qr\n)
and F[.qr\m)
73,
every
possesses
resultants
pair
belong
to
p
But
we
are
fol-
lows
then since, as just
shown, F{m\qb),
then, since F{m\qb),
it follows thaft
F[ni\qn),
follow that
of the
ment which
pairs
(q,
b),
(5,
n),
(y,
n).
And
so
pairs,
system
p
p^
which
elements,
collection which
of
be
treated,
83,
only
a
collec-
And,
in
particular,
first
prin-
ciples
of
our
system
S ,
but
any two
in
)
lines now
chain,
the
resultants
of
to
princi-
elements
(c,
mediators of
ele-
ments
desired
principle
be considered will
but in
of wealth
as
resultants
of
line-coUections
will
a
pair of
c
and
d
belong
And the
such
as
permit
to
define
new
sets
of
ele-
ments
beyond
altogether to our
between our
account and
This
principle
principles, which
show that
every pair
defined in
any of
viewed
as
with
us,
and
and
a
we
general, stated in
ensures
in
for us
parallel
line
of the lihes
intersection
which
belongs
to
F{^ab\cd). So that this form of
asser-
tion
way
here-
tofore
defined,
as
determining
a
aj
is
a
point
is to
be viewed
as a
a
principle
of
the
selection
of
possibility
is all
any pro-
whether
2
actually
space-form.
Since
;
points out, no geometrical set contains the obverse of any
of the
always occur
space-form
(as
tity,
will
enable
viewed
define, not
but the algebra
a.
(2)
triad.
(3)
|
5
from
the
total
is such
This,
by
condition
(3),
and i''(aja;a^),
true;
and
thus,
if
g
of
i. e., F[
is
true;
and
since
g
of
elements
of
(a,
a),
the
demands
of
principle
V,
without
of
(a,
a)
be
chosen,
tions shall be
a)
which
are
O-coUections
2^
For (return-
were an
2^
.There
Harvard
Univkesity,
Royce in A
Monist,
Vol.
VII,
pp.
178ff.,