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T
A COMMENTARY ON
HEGEL'S LOGIC
CAMBEIDGE UNIVEESITY PEESS Eontion: FETTEE LANE, E.G. CLAY, Manager
C. F.
anjinfautsl)
:
100,
Serlin: A. Utiojig:
^ttu fiombatj anH
gork:
F.
PRINCES STREET
ASHER AXD CO. A. BROCKHAUS
G. P.
ffialrtitta
:
PUTXAM'S SONS
MACMILLAN AND
All rights reserved
CO., Ltd.
f^s/c
^Y^A
COMMENTARY ON
HEGEL'S LOGTC BY
JOHN McTAGGART DOCTOR
IN IN
ELLIS
McTAGGART
LETTERS, FELLOW AND LECTURER OF TRINITY COLLEGE
CAMBRIDGE, FELLOW OF THE BRITISH ACADEMY
Cambridge at
:
the University Press
b (>
1910
^
iM3
1'
2.7
Sr r^S
H3
S4J/£
AUTHOR
STUDIES IN THE HEGELIAN DIALECTIC. STUDIES IN HEGELIAN COSMOLOGY. 8s.
SOME DOGMAS OF RELIGION.
10s.
M.
net.
8s.
PREFACE /CHAPTERS
^^
II,
X
VIII, IX, and
III,
based on articles which appeared in
April, 1904;
1900).
April and July,
many
In
Mind
(Oct. 1902;
1897; Jan. 1899; and April,
however, both the interpretation and
cases,
now published are
the criticism as
of this book are
materially different from
the earlier versions. I
am much
this
book
also
to
Chapter
in
Mr III,
indebted to
proof,
and
Bertrand
and
my
for
Russell
for
giving
wife for her aid in reading
many for
valuable his
kindness
me much
treatment of the categories of Quantity. to I
the
criticisms
and suggestions
of
have lectured on Hegel's philosophy.
Trinity College, Cambridge. January^ 1910.
suggestions, as
the
reading
in
in
the
owe much,
too,
assistance I
pupils
to
whom
TABLE OF CONTENTS CHAPTER
I
INTRODUCTION PAGE
.....
1.
Object of this book
2.
Previous writers on the same subject
3.
Relative authority of the Greater Logic and the Encyclopaedia
2
4.
3
5.
Terminology adopted in this book Errors of Hegel concerning the dialectic method.
6.
And also
7.
Errors in particular transitions
He exaggerates
.... ...... —
the objectivity of the dialectic process its
comprehensiveness
10.
...
.......... .....
Sometimes by confusion between categories and the concrete states after which they are named
12. 13.
7
8
8
Errors in Studies in the Hegelian Dialectic (a) as to the transcendental character of the process
11.
6
Sometimes by his desire to include conceptions of importance in science
9.
5
sometimes caused by his
failure to confine the process to the existent 8.
1 1
10
As to the change in method in the later categories The same continued (c) As to the relation between a Synthesis and the next Thesis (6)
.
CHAPTER
.
11
11
12
II
QUALITY 14.
Divisions of Quality
15.
/.
Being.
A.
13
Being
15
16.
B. Nothing
17.
C.
18.
Becoming does not involve change But the name suggests change, and is therefore misleading Alterations in names of categories suggested
19.
20.
15
Becoming
17
Hegel's conception of
.
.
17
19
20
CONTENTS
Vlll
PAGE 21.
Being
II.
(a)
Determinate.
Being
A.
Beterniinate
........ ........
(6)
Quality
23.
(c)
Something
24.
Are the
25.
Is the introduction of Pkirahty justified
26.
B.
27.
(b)
28.
(c)
29. 30.
The divisions within (&) are unjustified The Ought and the Barrier in Finitude
31.
C.
divisions of A. superfluous
Finitiide.
(a)
22 22 22 24
?
Something and an Other
25
and Limit
26
Determination, Modification,
Finitude
28
28
........ ......
Infinity
(a)
Infinity in General
(6)
Reciprocal Determination of the Finite
34.
(c)
Afiirmative Infinity
35.
36.
The treatment of Finitude and The same continued
37.
///.
Being for
29
.
33.
and
29 31
Being for One
32
34
The
divisions of J. are unjustified
(0)
One.
B.
41.
(b)
The One and the Many, The One and the Void
42.
(c)
Many
43.
C.
44.
(b)
32
Infinity in the Encyclopaedia
.... .......
40.
31
Infinite
A. Being for Self as Such, Determinate and Being for Self Self.
39.
46.
21
?
32.
45.
Such
Being Determinate in General
22.
38.
as
(a)
The One in
(a)
Being 35 37
37
.
Itself
38
.
38
39
Ones
Repulsion
and
Attraction,
.....
(a)
Exclusion of the One
The one One of Attraction (c) The Relation of Repulsion and Attraction Transition to Quantity
CHAPTER
40 40
40
.
41
III
QUANTITY 47.
Divisions of Quantity
48.
Hegel's knowledge of mathematics.
49.
/.
50.
B.
51.
Defects of this category
42
........ .... ....... ....... .......... ..... The bearing
of this ques-
tion on the dialectic
{Undivided) Quantity.
Continuous
and
A. Pure Quantity
Discrete
Magnitude
Limitation of Quantity Quantum. A. Nximher
52.
C.
53.
//.
54.
Possibly
all
argument
The
56.
B.
possibility,
but
Quantum and Limit and Intensive Quantum,
relation of
Extensive
45 46
47 48
49
the Ones taken together are finite in number.
Hegel ignores this 55.
43
it
(a)
does not affect his
Their Difference
.
49 50 51
CONTENTS
IX PAGE
57.
of Extensive and Intensive Magnitude. on a level, or is Intensive Magnitude higher ?
59.
The The
60.
(c)
61.
C.
58.
Are these
Identity/
(b)
latter
52
view seems more probable
instability of
54
Quanta
55
The Alteration of Quantum The Quantitative Infinity, (a)
57 Its
Notion
58
....
The Quantitative Infinite Progress
60
62.
{b)
63.
An
64.
69.
The Infinity of Quantum Relations between Quality and Quantity ///. The Quantitative Ratio A. The Direct Ratio B. The Inverse Ratio C. The Ratio of Powers
70.
The
transition to C.
71.
And
the whole of ///.
72.
Suggested reconstruction
68
73.
The treatment
70
65. 66. 67. 68.
objection discussed
61
62
(c)
62
.
63 64
.
is
64 65
unjustifiable is
65
unjustifiable for
more general reasons
of Quantity in the Encyclopaedia
66
CHAPTER IV MEASURE
....
74.
Divisions of Measure
75.
Criticism of the transition from Quantity
76.
The same continued
.
...... .... ...... .... ...... ...... ........
Possible reasons for the error
78.
/.
79.
B.
80.
81.
The Specifying Measure Here a new conception of Measure
82.
(c)
Relation of both Sides as Qualities
83.
C.
84.
//.
85.
(a)
86.
(Z>)
Being for Self in Measure Real Measure. A. The Relation of Stable Measures Union of two Measures Measure as a Series of Measure Relations
The Specific Quantity. Specifying Measure,
87.
(c)
88.
B.
Elective Ajfinity
A.
(a)
The Specific Quantum The Rule
introduced illegitimately
is
71
72
77.
(6)
.
.
73 74 75 76 77 78
79
80 80 81
81
82
89.
Nodal Line of Measure Relations. Here we return conception of Measure abandoned in /. B. {b) And do so by an illegitimate transition
90.
C.
91.
///.
92.
87
93.
B. Indifference as Inverse Relation of its Factors C. Transition to Essence
94.
The treatment
89
to the
.... .
The Measureless The Becoming of Essence.
83
84 85
A.
The Absolute Indifference
of Measure in the Encyclopaedia
86 88
CONTENTS
CHAPTER V EHSENCE AS REFLECTION INTO ITSELF EHsencc
Of).
DivisiniiH of
!))
107.
(()
OS.
//.
I
?
?
....
(a) Positing Reflection
......
E.vtenial Reflection
Determining Reflection
The Essentialities or Determinations of
Reflection.
A
Idintity 10!).
Hotel's treatment of the
no.
IJut this
Law
of Identity
......... .... ......... .......... ........ ....
Law
is
not specially connected with Hegel's category
of TiliMitity li.
I
11-2.
Difference,
II.
(a)
Difere nee
Absohtte
Varieti/
(/))
Suggested alteration of argument 1
1
1.
Hegel's treatment of Qualities and Relations requires enlarge
mont 115.
llegors treatment of the Principle of the Identity of In discornibles
IKi.
(c)
117.
(^riticisjn of
118.
('.
11!).
Suggested reconstruction of this category
1
-20.
()ppositio)i
the category of Opposition
Contradiction
llogers treatment of the
Orouuit
A.
Law
of E.xcluded Middle
.
....... .......
Absolute Ground,
l-2\.
///.
l'2-2.
yb)
1:23.
(c')
Form and Matter Form and Content
124.
B.
Determined Ground,
120.
(6)
Real Ground
1 -2(!.
The
possibility of sophistry in
1-27.
yc)
1-28.
C.
(a)
Fonn and
Essence
Formal Ground
(a)
Ground
....
Complete Ground Condition,
(a)
The Relatively Unconditioned
The Absolutely Unconditioned
1 -2;).
{b)
130.
i^c'^
131.
Suixcostod rooonstruotion of
Transition of the Fact into E.visfence
Ground
.
.... ....
COXTENTS
CHAPTER
XI
VI
APPEARANCE PAGE 132.
Divisions of Appearance
133.
/.
134.
A.
The Thing and its Properties
135.
{a)
The Thing in
136.
(b)
Property
133
137.
(c)
135
138.
B.
139.
C.
The Reciprocal Action of Things The Constitution of the Thing out of Matters The Dissolution of the Thing
140.
Criticism of the categories of Existence
141.
//.
142.
B.
143.
144.
128
....
Existence
itself
and
129 131
Existence
132
....
Appearance.
A.
The
Law
136
137 1,38
.
of Appearance
139
The World of Appearance and the World in itself C. The Dissolution of Appearance ///. Essential Relation. A. The Relation of Whole and
....
Parts
140 142 142
.
145.
The same continued
146.
B.
147.
(6)
143
..... .....
The Relation of Force and Conditionedness of Force The Solicitation of Force The Infinity of Force
Manifestation,
its
(a
The 145
146
148.
(c)
149.
Criticism of the divisions of 5.
150.
Suggested reconstruction
148
151.
The Relation of Inner and Outer Note on the Difference between the Greater Logic and the Encyclopaedia in the first two divisions of Essence Table of the categories according to the Greater Logic and
149
152.
154.
147
C.
........ ........
the Encyclopaedia 153.
Account of the differences The same continued
CHAPTER
146
150 152
153
VII
ACTUALITY 155.
Divisions of Actuahty
156.
158.
The Exposition of the Absolute Criticism of the conception of the Absolute B. The Absolute Attribute
159
159.
Criticism of this category
160
160.
C.
157.
/.
The Absohiie.
155
A.
.
The Modus of
the Absolute
....
156 157
160
CONTENTS
Xll
PAGE Actuality
161.
//.
162.
A. Contingency, or Formal Actuality, Possibility,
163.
The same continued
164.
B.
Relative
162
and Necessity
162
164 or Real
Necessity,
and
Actuality, Possibility,
Necessity
165
Absolute Necessity
.167
165.
C.
166.
///.
167.
Suggested reconstruction of the argument by which Substance
168.
Hegel's remarks on the philosophy of Spinoza
169.
B.
170.
The
171.
(6)
172.
Hegel unduly ignores the differences between Formal and Determined Causality He attempts to remove one such difference by asserting the
is
173.
.
.
The Absolute Relation.
.
.
.
.
.
A. The Relation of Substantiality
168
reached
169
The Relation of Causality, transition to
(a)
Formal Causality
Determined Causality
is
identity of Cause and Effect.
.
.
.170
.
not justifiable
.
.
.
Formal Causality .
.
.
171
.
.
172
.173
.
Criticism of this
.
175 176
.
174.
The same continued
177
175.
179
178.
The same continued The treatment of Causality in the £'/iCj/c^o/9aeo?ia The Infinite Series of Causes and Effects (c) Action and Reaction
179.
C.
180.
The The treatment
176. 177.
181.
.180
.... ........ .
.
180 181
.182
Reciprocity infinity ascribed by Hegel to Reciprocity
of Actuality in the Encyclopaedia
CHAPTER
.
.
.
.
183
.
.
184
VIII
SUBJECTIVITY
......
187
182.
Divisions of Subjectivity
183.
185.
The significance of the nomenclature in Subjectivity The same continued Hegel's assertion that Freedom is the Truth of Necessity
186.
/.
187.
Suggested reconstruction of the argument
194
188.
The same continued
195
189.
B.
184.
The Notion.
A.
The same continued
191.
C. //.
190 191
193
The Universal Notion
.......
196
The Particidar Notion
190.
192.
189
The Individual The Judgment. Positive
Judgment
197 198
A.
The Judgment
of Inherence,
(a)
The .
198
CONTENTS
Xlll
PAGE
.... .... ....
193.
Transition to the next category
200
194.
Criticism of the transition
201
195.
201.
(6) The Negative Judgment The Infinite Judgment (c) The same continued B. The Judgment of Suhsumption The same continued (a) The Singidar Judgment (6) The Particular Judgment
202.
Transition to the next category
210
203.
(c)
The Universal Judgment
211
204.
C.
205.
(a)
The Judginent of Necessity The Categorical Judgment
206.
{b)
207.
(c)
208.
Transition to the next category
209.
213.
D. The Judgment of the Notion, (a) The {b) The Problematic Judgment (c) The Apodictic Judgment Criticism of the Judgment of the Notion The same continued
214.
///.
196. 197. 198. 199.
200.
210. 211. 212.
202 202
203 205
.
.... .... ....
206 208 208
213 213
....
The Hypothetical Judgment The Disjunctive Judgment
214 215 217
Assertoric
Judgment
....
.......
The Syllogism.
Figure
A. The Qualitative Syllogism,
217
218 218
218 220 (a) First
221
216.
The first defect found by Hegel The second defect
217.
{b)
Second Figure
224
218.
(c)
Third Figure
225
219.
{d)
Fourth Figure
225
220.
Criticism of the Second and Third Figures
226
221.
Suggested reconstruction
228
222.
B.
215.
in this category
222
224
.... The Syllogism of Allness
225.
The Syllogism of Reflection, (6) The Syllogism of Induction The Syllogism of Analogy (c) Transition to the next category
226.
Criticism of the Syllogism of Reflection
227.
C.
228.
{b)
229.
(c)
230.
The same continued
237
231.
Hegel's conception of the Self-Diflferentiating Notion
238
223. 224.
The Syllogism of Necessity, The Hypothetical Syllogism The Disjimctive Syllogism
(a)
228
229
230 231
(a)
.
The Categorical Syllogism
....
232
234 236
236
CONTENTS
XIV
CHAPTER IX OBJECTIVITY PAGE 232.
Divisions of Objectivity
241
242
233.
Significance of the term Objectivity
234.
Transition from Subjectivity
235.
Proposed amendment A. The Mechanical Object /. Mechanism.
236.
of the transition
..... ....
The Mechanical Process
The Formal Mechanical Process The Real Mechanical Process The Product of the Mechanical Process The Absolute Mechanism, (a) The Centre
247
237.
B. .(a)
239.
(6)
240.
(c)
241.
C.
242. 243.
The example given by Hegel is misleading The transition to Chemism in the Encyclopaedia
244.
(b)
The Lato
245.
(c)
Transition from Mechanism
246.
//.
Chemism.
A.
The Chemical Process
B.
Transition to the next category
249.
Criticism of this transition
250.
C.
251.
Is there
252.
III.
253.
The same continued The same continued The terms End and Means are misleading Are there more Ends than one 1
256.
258. 259. 260.
261.
.
.
.
.
.
.
The Chemical Object
248.
257.
.... ....
...... ...... .......
247.
255.
244 246
238.
254.
242 243
Transition from Chemism
more than one Chemical Notion
?
.
.
.
.
247
249 250 252 252 254 254 255 255
256 256 257
258 259
Teleology
260
....
The Subjective End B. The Means The first argument for the transition to the next category The second argument for the transition C. The Realised End
264 265
A.
.
261
263
265
.
.
267
268 269
CONTENTS
XV
CHAPTER X THE IDEA
....
262.
Divisions of the Idea
263.
Transition from Objectivity
264.
/.
265.
Hegel's view that there are
266.
His view that the Body
267.
A.
PAGE
272 272
.
274
Life
many Organisms
is
275
an inadequate manifestation of 276
the Seele
268.
The Living Individual B. The Life-Process
269.
C.
270.
Criticism of this category
271.
The inadequacy
The
Kind
and Death
277
279 280
.
•281
of the manifestation is
shown
in Propagation
282
.
276.
Which also provide the escape from The same continued The same continued IL The Idea of Cognition The same continued
277.
Criticism of this category
290
278.
The same continued
291
279.
292
280.
A. The Idea of the True The same continued
281.
(a)
282.
284.
The transition to the Idea of the Good can be made without them The transition further considered B. The Idea of the Good
285.
Criticism of this category
300
286.
300
287.
Hegel regards this category as higher than the Idea of the True And as involving the complete goodness of the universe
288.
Transition to the Absolute Idea
302
289.
The same continued
303
290.
///.
272. 273. 274. 275.
this
inadequacy
283 285 286 287
288
293
Analytic Cognition,
(b)
Synthetic Cognition,
Criticism
295
of these categories
283.
292.
3Q3.
The same continued
294.
This
295.
Is the Absolute Idea exemplified in
296.
Conclusion
is
.
the final category.
to us
?
298
299
301
303
The Absolute Idea The same continued The same continued
291.
296
304 306 307
The proof of this any concrete
308 state
k now 309
310
CHAPTER
I
INTRODUCTION In this book I propose to give a critical account of the various transitions by which Hegel passes from the category I shall not of Being to the category of the Absolute Idea. 1.
method which he employs, nor
describe or criticise the applications
of the
experience.
With
my
ability, in
my
I
— that
read the Greater Logic
may
to
the facts of
Studies in the Hegelian Dialectic and Studies
serve two purposes
it
dialectic
these subjects I have dealt, to the best of
in Hegelian Cosmology.
and that
of the
results
his
hope that
my
those students of Hegel
may
may
present work
find it useful as a
who have
commentary,
serve as an account of the Greater Logic for
who are prevented by want of time or ignorance of German from reading the original. 2. The dialectic process of the Logic is the one absolutely If we accepted this and essential element in Hegel's system. rejected everything else that Hegel has written, we should those
have a system of philosophy, not indeed absolutely complete, but stable so
far as
it
reached, and reaching to conclusions
of the highest importance.
On
the other hand,
if
we
the dialectic process which leads to the Absolute Idea, rest of the all
system
is
reject
the
all
destroyed, since Hegel depends entirely, in
the rest of the system, on the results obtained in the Logic.
Yet the detail of the Logic occupies a very small part of the numerous commentaries and criticisms on Hegel's philosophy. They are almost entirely devoted to general discussions of the dialectic method, or to questions as to the application
of the results of the Logic to the facts of experience. M"^!.
The 1
2
CH.
INTRODUCTION
I.
— —
most elaborate of the expositions of Hegel's system that which Kuno Fischer gives in his History of Philosophy allows to the detail of the Logic less than one-ninth of its space. There are, however, two admirable accounts of the Logic, category by category HegeVs Logic, by Professor Hibben of Princeton, and La Logique de Hegel, by the late M. Georges Noel, which is less known than its merits deserve. I owe much to these commentators, but my object is rather different from theirs. I propose, in my exposition, to give frequent references to the passages in Hegel's text on which I base
my
account, and to quote freely
when
When
necessary.
the
meaning of the text is doubtful, I shall not only give the view which I think preferable, but shall discuss the claims of other interpretations. I shall also add a certain amount of criticism
my
to
exposition.
Professor
Hibben
follows the Encyclopaedia in his exposition,
while M. Noel follows the Greater Logic^.
Greater Logic as
my
text,
3.
shall
adopt the
but shall note and discuss any point
which the EncyclojMedia
in
I
differs
from
it.
The Greater Logic and the Encyclopaedia agree much
more than they differ, but they do differ on variouS important points. Wlien this happens, the advantage is not always on the same side, but is, I think, more often on the side of the Encyclopaedia. But, whichever is the more correct, there The Logic is no doubt that the Greater Logic is much clearer. of the Encyclopaedia is excessively condensed. The treatment of the
categories, as distinct
from preliminary questions,
in the Encyclopaedia, only one-fourth as long as
Greater Logic.
Some room
is
it
is
is,
in the
gained in the Encyclopaedia by
the elimination of certain sub-divisions, and also by the omission
By
mean
the work published in 1812
—
Hegel 1816. himself calls this simply the Loijic, but I use the adjective to distinguish it from the Logic which forms part of the Encyclopaedia. My references to the Greater Logic are to the pages of the complete edition of Hegel's works, in which the Greater Logic occupies Vols. 3, 4 and 5 (quoted as G. L. i., G. L. ii., G. L. iii.) ^
the Greater Logic I
— 1834.
My references to the Encyclopaedia are to Sections, have generally, though not always, availed myself of When, in expounding the Greater Professor Wallace's valuable translation. Logic, I give references both to the Greater Logic and to the Encyclopaedia, the latter merely indicates that it is in this Section of the Encyclopaedia that the corresponding point is treated, and not that the treatment is the same as in the published in 1833
and
in quoting
Greater Logic.
from
it
I
CH.
I.
INTRODUCTION
of the notes on mathematics which
fill
3
a disproportionate space
in the Greater Logic, but in spite of this the categories in the
Encyclopaedia are in some parts of the process crowded so closely together, that the
arguments
for the transition
from the
one to the other almost disappear.
With regard
to the relative authority of the
two Logics, as
expressing Hegel's final views, nothing very decisive can be said.
The
last edition of
Hegel appeared
the Logic of the Encyclopaedia published by 1830.
in
In
1831
he published a second
edition of the Doctrine of Being in the Greater Logic.
His
death prevented him from carrying this edition further.
would seem,
It
was the best authority for the Doctrine of Being, and the Encyclopaedia for the Doctrines of Essence and the Notion. But many of the points in the Doctrine of Being in which the first
therefore, as if the Greater Logic
edition of the Greater Logic differs from the Encyclopaedia
are repeated in the second edition.
We
can scarcely suppose
that in each of these cases Hegel had abandoned by 1831 the
view he held in 1830, and returned to the view he held in 1812.
And
thus
it
seems impossible to attach any superior authority
to the second edition of the Greater Logic.
But
if,
to the end,
he regarded the changes in the Encyclopaedia as improvements,
any rate he cannot have regarded them as very important, since he did not alter the second edition of the Greater Logic to at
correspond with then.
The a
actual language, however, of the
much
greater authority than
Encyclopaedia.
much
Greater Logic has
of the
language of the
For every word of the Greater Logic was
written and published by Hegel himself.
But
in the Encyclo-
paedia a part of the supplementary matter added, with the title of Zusatz, to many of the Sections, is compiled from students'
notes
or
recollections
of
what Hegel had said
in
his lectures 4.
A
few points about terminology must be mentioned.
The whole dialectic
course of the dialectic forms one example of the
rhythm, with Being as Thesis, Essence as Antithesis,
and Notion as Synthesis. 1
Each
of these has again the
same
Cp. the editor's Preface to the Logic of the Encyclopaedia in Vol. 6 of the
Collected Works.
1—2
4
CH.
moments on
till
I.
INTRODUCTION
of Thesis, Antithesis,
and Synthesis within
it,
and so
the final sub-divisions are reached, the process of division
much
being carried
further in
some parts of the
dialectic
than
in others.
Hegel has no special name for the system formed of a A name, however, is conThesis, Antithesis, and Synthesis. venient, and I propose to speak of such a system as a triad. Being, Essence, and Notion I shall call primary categories their immediate divisions {e.g. Quality, Quantity, and Measure) I shall call secondary, and so on with smaller sub-divisions. One difficulty of terminology arises in writing about Hegel from the fact that he uses so
many terms
categories that none are left to
names of particular be used more generally. For as
example, to what does the whole dialectic
process
According to one view, the subject-matter of the process is
commonly
view
it is
Being or Reality.
called
what
is
commonly
to
is
?
what
another
But Hegel has
called Existence.
already appropriated these names.
names
According
apply
Being and Existence are the
of particular categories in the process, while Reality,
according to Hegel,
is
a term only applicable after a certain
stage in the process has been reached.
120; Enc. 91.) Again, after a few categories we reach the result, which
persists
{G. L.
through the rest of the process, that the subject-matter
under consideration
is
convenient to have a
a differentiated unity.
name by which
viewing them.
But
It
would be very
to designate these diffe-
rentiations, irrespective of the category
priated.
i.
here, again, every
under which we were
name
is
already appro-
One, Thing, Part, Substance, Individual, Object used by Hegel to indicate such a differentiation
each of these
is
as seen under
some one particular category.
To
find a
name
for
more general use is not easy. To meet this difficulty so far as possible, I have always used a capital initial when a term indicates one of Hegel's categories, and a small initial when the term is applied more general ly^ I have distinguished in the same way between those of Hegel's categories which are named after concrete facts, and the concrete facts after which they are named e.g. I have written Life when I meant Hegel's category, and life when I meant the biological state.
CH.
With regard
5.
INTRODUCTION
I.
to the
5
Logic as a whole, I believe, for
reasons which I have explained elsewhere \ that the dialectic
method used by Hegel
is
valid
— that,
if
the categories do stand
one another in the relations in which he asserts them to
to
stand, he
is
entitled to pass from one to another in the
which he does
pass.
And
I believe that in
many
way
in
cases this
and that therefore, in these cases, the actual transitions which he makes are justified. The points on which I should differ from Hegel are as condition
is
fulfilled,
In the
follows.
first
place I think that he falls into serious
errors in his attempts to apply the results gained
in the interpretation of particular concrete facts.
place
think
I
understand
the
that
he did not in
nature
of
that
ideas which he had discovered.
seem
to
In the second
respects
all
dialectic
And
by the Logic completely
relation
between
in the third place there
be certain errors which vitiate particular stages in the
process, I
have considered the
first
of these points elsewhere ^
With
regard to the second there are two fundamental questions as to
*
which I believe that Hegel to some extent misunderstood the nature of the dialectic process. I think that he exaggerated both its objectivity and its comprehensiveness.
By
his exaggeration of its objectivity, I
mean
that he did not
merely hold that the dialectic process conducted us to a valid
and that the lower categories of the process were contained, so far as they were true, in the Absolute Idea which synthesised them. So much he was justified in holding, but he went further. There is no doubt, I think, that he held that if that chain of categories, which was given by him in the Logic, was correct at all, it was not only a valid way of reaching the result,
He
Absolute Idea, but the only valid way. to be
would have held
a priori impossible that two valid chains of
it
dialectic
argument, each starting from the category of Being, should each lead up to the Absolute Idea, so that the goal could be attained equally well by following either of them.
And
he would also
have rejected the possibility of alternative routes over smaller ^
Studies in the Hegelian Dialectic, Chapters
10—13. 2
op. cit.
Chapter VII.
I.
to IV., but cp. below, Sections
CH.
6 intervals
INTRODUCTION
I.
— the possibility,
of passing from the beginning of
e.g.,
Quantity to the beginning of Essence by two alternative dialectic arguments.
Now
I
do not assert that such alternative routes are to be
found, but I cannot see that their possibility can be disproved.
And,
if
there were such alternatives, I do not think that the
dialectic process
would
lose
its
value or significance.
jecting the possibility of equally valid alternatives,
me
it
In re-
seems to
that Hegel exaggerated the objectivity of the process as
expounded by himself. 6. His exaggeration
of
dialectic lies in the
that,
fact
the
comprehensiveness
the
of
having secured, as he rightly
believed, an absolute starting point for the dialectic process in
the category of Being, he assumed that this was not only the absolute starting point of the dialectic, but of
No preliminary discussion was required, except
all
philosophy.
negative criticism
designed to remove the errors of previous thinkers, and to
prevent misunderstandings. Nothing in philosophy was logically prior to the dialectic process.
Here again there seems is is,
to
be an
error.
For example, what
the subject-matter to which the whole dialectic applies I think, clear that
Hegel regards
in the widest sense of the term.
it
But,
?
It
as applying to all reality,
when we examine
various
becomes clear that he is only speaking of what is existent, and that his results do not apply, and were not meant to apply, to what is held by some philosophers to be real but not existent for example, propositions, the terms of propositions, and possibilities^ The apparent inconsistency is removed if we hold, as I believe Ave should, that Hegel, like some later philosophers, held nothing to be real but the existent. I do not mean that he ever asserted this explicitly. Probably, indeed, the question was never definitely considered by him, if we may judge from the fact that his terminology affords no means of stating it. (Reality and Existence, as used by Hegel, refer, as was mentioned above, to particular stages of the dialectic.) But it seems to me that the view that nothing
stages of the process
it
—
^
my
I
had not
with
my
when I wrote what is said there is not inconsistent 18, and 79 of that work.
realised this distinction with suiBcient clearness
Studies hi the Hegelian Dialectic, but
present view.
Cp. Sections 17,
CH.
I.
INTRODUCTION
7
but the existent is one which harmonises with his general position, and that he would have asserted it if confronted with is real
]
|
the problem.
But the view that nothing but the right or wrong,
is real,
whether
one which cannot be assumed without
is
It is a difficult
cussion.
existent
and disputed
point,
dis-
and Hegel had no
right to take a dialectic of existence as equivalent to a dialectic*' of reality until the question
Moreover, the absence
had been carefully considered.J
of such
consideration
leaves
Hegel's
but also rather vague. Generally, as I have said, the categories seem clearly intended to apply to the existent only, but there are some steps in which he seems to change his position unconsciously, and to take the position, not only unjustified
categories as applicable to
some other
reality in addition to
the existent.
There is another point on which preliminary discussion was needed and is not given. Hegel's arguments assume that, when a thing stands in any relation to another thing, the fact that it From this it stands in that relation is one of its qualities. follows that
when
the relation of one thing to another changes,
a change in the qualities of-each of them, and therefore Again, it follows that two in the nature of each of them. things which stand in different relations to a third thing cannot there
is
have exactly similar natures, and on this a defence might be based
for
This
the doctrine of the Identity of Indiscernibles. is
a doctrine of the greatest importance, and by no
means universally accepted.
It is possible to conceive a dialectic
process which should contain a proof of
it,
but, so far as I can
Hegel's dialectic does not contain any such proof, direct or In that case he had no right to use the doctrine in implied.
see,
the dialectic unless cussion,
it
had been proved in some preliminary
and he does not give such a
dis-
discussion.
Passing to the errors in certain particular transitions, there are some, I think, which cannot be traced to any general cause, but are simply isolated failures. But other errors appear 7.
be due to certain general causes. In the first place some errors have, I believe, been caused by Hegel's failure to realise
to
explicitly that his dialectic is a dialectic of the existent only,
and by his treatment of some categories as applying also to
CH.
8
some non-existent
INTRODTJCTION
I.
This
reality.
is
unjustifiable, for
he would
have no right to pass in this way from the smaller field to the more extensive, even if the more extensive field were in being. And, as I have said, it seems implied in his general treatment no such wider field, but that existence is co-extensive with reality, in which case any attempt to apply the dialectic beyond existence is obviously mistaken. Another general cause of error may be found in a desire 8. that there
is
to introduce into the dialectic process as
many
as possible of the
conceptions which are fundamentally important in the various It is, doubtless, a fortunate circumstance when a consciences.
important in this way does occupy a place among the categories of the dialectic. For then the dialectic will assure us that such a conception is neither completely valid
ception which
is
of reality, nor completely devoid result.
Moreover,
how much, and
in
its
of validity
—an
important
place in the dialectic process shows us
what
respects, its validity falls short of the
and whether it is more or less valid than those other conceptions which are also categories of the dialectic. And this also may be of much importance. validity of the Absolute Idea,
no reason to believe that this fortunate state of always occur. We have no right to anticipate that
But there things will
is
every category of the dialectic will be a conception of fundamental importance in one or more of the particular sciences.
Nor have we any
right to anticipate that every conception of
fundamental importance in a science dialectic.
In several cases
I
course of his argument, and
by an unconscious desire
will
be a category of the
think that Hegel has distorted the
made an
invalid transition,
to bring into the process
moved
some concep-
tion of great scientific importance 9.
This
is
connected with another source of
arises from Hegel's practice of designating
gories
by the names
many
of concrete states which are
by empirical experience.
Thus we
error,
which
of his cate-
known
to us
find a category of Attraction
1 It has lately been objected to Hegel's treatment of Quantity that it does not include the conception of Series, which is of such great importance in mathematics. If the dialectic process can go from Being to the Absolute Idea without passing through the conception of Series, then the omission of that conception is no defect in the dialectic. But this truth is obscured by Hegel's
anxiety to bring
all
important
scientific conceptions into the dialectic process.
CH.
I.
INTRODUCTION
9
and Repulsion, and categories of Force, Mechanism, Chemism, Life, and Cognition^. This practice does not necessarily involve any error in the
For when Hegel names a category in this
dialectic process.
way, he does not suppose that he has deduced, by the pure
thought of the dialectic, all the empirical details which can be determined with reference to the corresponding concrete state.
He -
merely expresses his belief that the category
in a special
manner by the concrete
For example,
state
possible to
it is
manifested
whose name
name
bears.
it
Mechanism he determine by the dialectic
in giving a category the
does not assert that
is
of
process any of the laws of the finite science of Mechanics.
name such a way
that the use of the
implies
existent in
that
it
is
that,
when we
All
perceive the
appears^ to include bodies
obeying the laws of Mechanics, then the category in question
be manifested with special clearness in the
will
appear to
There
facts as
they
us.
thus nothing unjustifiable in the use of such a
is
nomenclature, and
it
has the advantage of making the meaning
by informing us where we may look for But in practice it turns out to be exclear examples of it. tremely difficult to use such names without being led by them of the category clearer,
into error.
There
is,
wrong name
in
the
place, the possibility of choosing a
first
— of taking
a concrete state which manifests the
particular category less clearly than another state would, or
which
itself
manifests more clearly some other category.
But
Hegel never makes. The concrete states which
this is a mistake which, so far as I can see,
But there is a second possibility. give their names to the categories
much
contain, as has been said,
other content beside the categories in question.
Hegel
does not suppose that the dialectic process could help him to 1 The use of logical terms as names for the categories of Subjectivity is an example of the same practice, though in this case the conceptions are not borrowed from empirical knowledge. But, relatively to the dialectic process, they are concrete, for the logical processes, which give the names, have characteristics not to be found in the categories which they exemplify. Cp. Chapter VIII. 2 Such a perception would, of course, be held by Hegel to be more or less erroneous. Nothing really exists, according to his system, but Spirits. Bodies only appear to exist.
10
CH.
INTRODUCTION
I.
But
deduce this other content.
in practice
he sometimes con-
—
two sides the pure conception which he had deduced, and the remaining content which he had not. And thus he
fuses the
introduces into the dialectic process, in connection with certain categories,
some
characteristics illegitimately transferred from
the concrete states after which they are named.
In Judgment,
in Syllogism, in Life, in Cognition,
we
find sub-divisions intro-
duced and transitions made, which
rest
on characteristics which
are found in the judgments and syllogisms of ordinary logic, in
the
life
have
of biology, or in the cognition of psychology, but
no justification
as
applied
the
to
categories
which
of
the
dialectic.
These cases, of course, lend support to the theory, which I have discussed elsewhere \ that the dialectic process, while professing to be a process of pure thought, does, in fact, always But the rest on empirical elements illegitimately introduced. categories of the process which are named after concrete states are comparatively few, and it is not in all of them that an illegitimate element has been transferred to the category.
In several of those cases where the illegitimate transference has taken place,
it
seems to
me
that the process, so far from
being dependent on the transference, would have g<me better without it. The transition Hegel does make, with the aid of the element illegitimately introduced,
is
in these cases one
which would be invalid even if the element it was based on had itself been legitimately deduced. And sometimes, I think, a perfectly valid transition was available, which was only obscured
by the intrusion of the illegitimate element. Whenever a particular transition seems to be invalid, I have given the reasons which prevent me from accepting it. In some cases I venture to think that I could suggest a valid substitute.
When
more than a
single category I have generally
this does not
involve a reconstruction of
made the
sugges-
but any more extensive alteration would, I think, be beyond the scope of a commentary.
tion,
10.
I wish to take
errors as
to ^
this opportunity of correcting
Hegel's method in
my
some
Studies in the Hegelian
Studies in the Hegelian Dialectic, Sections 41
—43.
CH.
INTRODUCTION
I.
(The correction of
Dialectic.
be irrelevant here.)
errors
A
think correct, I added
still
be seen that this argument
nature.
on other points would
In Section 19 of that book, after giving an
account of the method which I will
11
strictly of a transcendental
is
proposition denied by the adversary.
., is
shown
involved in the truth of some other proposition which he
prepared to attack."
But
be
to is
not
this is not a description confined to
a transcendental argument, but applies to convince an adversary.
" It
all
attempts to
I failed to see that the proposition with
which a transcendental argument, in Kant's sense of the term, starts, is always a proposition which asserts that some other proposition
is
knoiun to be true.
(For example, Kant's tran-
scendental argument on Space does not start from the truths of
geometry, but from the truth that we
geometry a
priori.)
11.
the truths of
I
Hegel's argument does not start from a
proposition of this kind, and I was
of the class which
know
Kant
wrong
in
supposing
it
to be
calls transcendental.
In Section 109,
I
pointed out two characteristics in
which the method in the later part of the dialectic process differed from the method at the beginning. Firstly, at the beginning the Antithesis is the direct contrary of the Thesis. It
is
not more advanced than the Thesis, nor does
it
in
any way
transcend
it.
while
presenting an element of contrariety to the Thesis,
still
But, as the process continues, the Antithesis,
found to be also an advance on
is
It does, to a certain extent,
it.
transcend the inadequacy of the Thesis, and thus shares with the Synthesis that character which, in the earlier type, belonged to the Synthesis only.
The second change the
first
follows as a consequence of the
triad of the dialectic the
movement
first.
In
to the Synthesis
comes from the Thesis and Antithesis together, and could not have been made fi:"om the Antithesis alone. But later on, when the Antithesis has transcended the Thesis, and has the truth of it
within
itself,
Synthesis
from
make
the transition to the
H
the Antithesis alone,
without any distinct
__;
it is
possible to
reference to the Thesis. 12.
In
Sections
112
— 114
I
enquired
whether these
changes were sudden or continuous, and came to the conclusion that they were both continuous. And here I think I was partly
12
CH.
wrong. The
first
change
the dialectic there
is
INTRODUCTION
I.
As we proceed through
continuous.
is
on the whole (there are a few exceptions)
a steady diminution in the element of contrariety to be found in
the Antitheses, and an increase in their synthetic functions.
But the second change cannot be continuous. For the direct transition must either be from both the Thesis and Antithesis, from
or
the
Antithesis
There
only.
no
is
intermediate
possibility.
The truth seems
to be that the direct transition
Antithesis alone whenever the Antithesis
the
Thesis
—that
every
in
is,
is
the
Judgment
Particular Notion, and the Negative
seem, however, to be exceptions to this
from the
at all higher than
after
triad
is
(The
first.
of Inherence,
rule, since,
contrary
to the general character of the dialectic, they are not higher
than their respective Theses.) 13.
80
In Section
I
said
of
the
transition
S}Tithesis of one triad to the Thesis of the next.
scarcely a transition at
It is... rather a
all.
the same truth from a fresh point of view place of reconciling mediation truth."
— than
we have Determining is
Determining Reflection Identity
is
In the
two
are categories of
But
a category of the fifth order, while
—produced by
sive processes of analysis instead of five. is
first place, it is
a Thesis, immediately succeeds. is
the
Reflection as a Synthesis, to
only of the fourth order
these two categories
contemplation of
Thus, in Essence as Reflection
the same order of subdivision.
which Identity, which
in fact,
— immediacy in
when the Synthesis and new Thesis
into Self,
is,
an advance to a fresh
This needs some qualification.
only true
" It
from the
And
four succes-
the content in
not an identical content looked at from
different points of view.
In the second place, the identity of content is only to be found when the two categories are not further divided. Thus Actuality is the Synthesis of Essence, and Subjectivity the Thesis of the Notion.
same order
— the
of the two
is
third.
They are contiguous categories of the But each is subdivided, and the content
not identical.
Finally, although with these is
two
qualifications the statement
generally true of the dialectic, there are several cases, which
I have noted
when they
occur, in
which
it
does not apply.
CHAPTER
II
QUALITY The Logic
14.
divided
is
Being
into
(Sein),
Essence
Being is divided into Quality The (Qualitat), Quantity (Quantitat), and Measure (Maass). (Wesen), and Notion (Begriff).
divisions of Quality are as follows
Being.
I.
(Sein.)
A.
Being.
B.
Nothing.
C.
Becoming.
(Sein.)
(Nichts.)
(Werden.)
Being Determinate.
II.
A.
(Dasein.)
Being Determinate as Such. (a)
Being Determinate
in
(Dasein
General.
als solches.)
(Dasein
iiber-
haupt.)
B.
(b)
Quality.
(c)
Something.
Finitude. (a)
(Qualitat.)
(Etwas.)
(Die Endlichkeit.)
Something
and
an
Other.
(Etwas
und
ein
Anderes.) (6)
Determination, Modification and Limit.
mung, Beschaffenheit und Grenze.) (c)
Finitude.
(Die Endlichkeit.)
(Bestim-
14
CH.
(a)
QUALITY
(Die Unendlichkeit.)
Infinity.
C.
II.
Infinity in
(Die Unendlichkeit tiber-
General.
haupt.) (6)
Reciprocal Determination of the Finite and Infinite.
(Wechselbestimmung
Endlichen
des
und Unendlichen.) (c)
Affirmative Infinity.
(Die affirmative Unendlich-
keit.)
Being
III.
Being
A.
for Self as Such.
(Das Ftirsichsein
(b) (c)
One.
als solches.)
(Dasein
Self.
(Fins.)
The One and the Many.
(Fines und Vieles.)
(6)
The One in Itself. (Das Fins an ihm selbst.) The One and the Void. (Das Fins und das Leere.)
(c)
Many
(a)
C.
(Das Ftirsichsein.)
Being Determinate and Being for und Ftirsichsein.) Being for One. (Sein ftir Fines.)
(a)
B.
for Self.
Ones.
Repulsion.
(Viele Fins.
Repulsion and Attraction.
Repulsion.)
(Repulsion und Attrak-
tion.)
(a)
Fxclusion of the One.
(b)
The one One
(Ausschliessen des Fins.)
of Attraction.
(Das Fine Fins der
Attraktion.) (c)
The Relation
of Repulsion and Attraction.
(Die
Beziehung der Repulsion uud Attraktion.)
We
must notice the ambiguity with which Hegel uses the
word Being. It is used (i) for one of the three primary divisions into which the whole Logic is divided (ii) for one of the three tertiary divisions into which Quality is divided and (iii) for one of the three divisions of the fourth order into which Being, In the same way Quality, as a tertiary division, is divided. ;
;
besides
being the general name
which forms the subject of a division of the nate as Such.
fifth order,
And
for
the secondary division
this Chapter, is also the
which
falls
Finitude, again,
is
name
for
within Being Determithe
name
of the fourth order, and also of a division of the
of a division
fifth order.
BEING
Being.
I.
A. (G. L.
15.
i.
Being.
Enc. 86.)
77.
15
I
do not propose to discuss here
the validity of the category of Being. process starts with this category,
its
Since the dialectic
validity
is
rather a question
affecting the whole nature of the process than a detail of the earliest stage,
and
I
have treated
it
elsewhere^
begin with the category of Being, what follows It
we
must be remembered that the position
are affirming Being, but that, so
else.
It
is
far,
to indicate this absence of
we
is
If,
theo,
we
?
not merely that
are affirming nothing
anything
else that
Hegel
speaks of Being in this division as Pure Being (reines Sein),
though the adjective does not appear in the headings. Pure Being, says Hegel {G. L. i. 78. Enc. 87) has no Any determination would give determination of any sort.
some particular nature, as against some other particular rather than not-X. It has therefore nature would make it no determination whatever. But to be completely free of any determination is just what we mean by Nothing. Accordingly, when we predicate Being as an adequate expression of existence, we find that in doing so we are also predicating Nothing as an adequate expression of existence. And thus we pass over to ^ it
—
X
the second category.
B. 16.
{G. L.
i.
78.
Xothing.
Enc. 87.)
been the object of so much
wit,
This transition, which has
and of
so
many
indignant
and simple matter. Wit and indignation both depend, as Hegel remarks {G. L. i. 82. Enc. 88), on the mistaken view that the Logic asserts the identity of a concrete object which has a certain definite quality with denials,
is
really a very plain
another concrete object which has not that quality
— of a white
table with a black table, or of a table with courage.
a mere parody of Hegel's meaning. Being.
W^hen we speak of a thing
Cp. Section
6.
Whiteness as white,
is
This
is
not Pure
we apply
to it
Also Studies in the Hegelian Dialectic, Sections 17, 18, 79.
-^ \
16
CH,
QUALITY
II.
Tuany categories besides Pure Being
example.
Thus the
equivalent to
its
— Being
Determinate, for
fact that the presence of whiteness is not
absence
quite consistent with the identity
is
of Pure Being and Nothing.
When ,
the dialectic process moves from an idea to
Antithesis, that Antithesis
first
never the mere logical contra-
is
but
is
some
in the relation of
a
contrary.
dictor of the
first,
^nevF idea
No
which stands to the reconciling Synthesis
two contradictory ideas from the simple affirmation and denial of the same could possibly spring from
most parts of the
But
doubted.
dialectic, the
at first sight
it
its
relation is too
— that
is,
idea.
In
clear
to
be
might be supposed that Nothing
was the contradictory of Being.
This, however, is not the case.
we affirmed not-Being, in the sense in which it is the mere contradictory of Being, we should only affirm that, whatever If
reality is
had not the attribute of Being./ And this not the same as to say that it has the attribute of
might
clearly
Nothing.
be, it
It
may
be the case that wherever the predicate
Being can be denied, the predicate Nothing can be asserted, but still the denial of the one is not the affirmation of the other.
Hegel says, indeed {G. L. i. 79) that we could as well say Not-being (Nichtsein) as Nothing (Niclits). But it is clear that he
means by Not-Being,
mere denial
of Beino^,
as he
meant by Nothing, not the
but the assertion of the absence of
all
determination.
Being and Nothing were all that could be said about them, the dialectic process would stop with its second term. There would be no contradiction, and therefore no ground for a further advance. But this is not the whole For the two terms originally truth {G. L. i. 89. Enc. 88). If the identity of
meant 1
•1
different
things.
By Being was intended unreality. By Nothing was
a
— reality without pure negative — unreality
is
now found
positive
Two
arisen.
to
without
made
pure
intended
If each of these
be equivalent to the other, a contradiction has
terms, defined so
turned out to be equivalent. original
reality.
a
meaning.
For
it
is
as
to
be incompatible, have
Nor have we got
rid
of the
that same characteristic which
the completeness of their opposition which determines
I
BEING
I.
their
A
equivalence.
reconciliation
and Hegel
contradiction,
to
The
consist
reconciliation-
in
must be found
this
Becoming.
which
this category affords appears
recognition of the intrinsic
the
for
finds it in
C. 17.
17
connexion of
Being and Nothing {G. L. i. 78. Enc. 88). When we hadthese two as separate categories, each of these asserted itself to be an independent and stable expression of the nature of
By
reality.
the
affirmation
other Avas denied, and
when
of either it
its
identity with the
was found, nevertheless, to be
the same as the other, there was a contradiction.
But Becom-
Being and Nothing, recognises them only as united, and not as claiming to be independent of one another. It recognises them, for Becoming is always the passage of Being into Nothing, or of Nothing into ing, according to Hegel, while it recognises
Being.
But, since they only exist in Becoming in so far as
they pass away into their contraries, they are only affirmed as connected, not as separate, and therefore there
is
:/
no longer any
opposition between their connexion and their separation.
But, Hegel continues, this
is
not the end of the matter.
Being and Nothing only exist in Becoming as disappearing moments. But Becoming only exists in so far as they are separate, for, if they are not separate,
one another /
j
?
As they
how can they
vanish, therefore.
Becoming ceases to of rest, which Hegel
be Becoming, and collapses into a state Enc. calls Being Dete rminat e {G. L. i. 109. 18."
1
X^ confess
that I regret the
pass into
89).
choice of Be_coming
as
What Hegel meant seems to me to be quite valid. But the name of the category suggests something else which seems to me not to be valid at all. _
a
name
for this category.
means is, as I have maintained above, that Being is dependent on Nothing in order that it should be Being, and that Nothing is dependent on Being in order that All that Hegel
it
should be Nothing.
In other words, a category of Being
without Nothing, or of Nothing without Being,
and leads
to contradictions
truth of the two
Lthe two.
And
is
this
which prove
is
its felsity.
inadequate
The only
a category which expresses the relation of
removes the contradiction.
For there
is
18
CH.
QUALITY
II.
no contradiction in the union of Being and Nothing. The previous contradiction was between their identity and their difference.
Hegel seems
have thought
to
category after a concrete (Section
9),
it
desirable to
But, as
fact.
name
the
new
have said above
I
the use of the names of concrete facts to designate
abstract categories
is
always dangerous.
In the present
case,
the concrete state of becoming contains, no doubt, the union
and Nothing, as everj^thing must, except abstract Being and Nothing. But the concrete state of becoming contains a great deal more a great deal which Hegel had not deduced, and would have had no right to include in this of Being
—
category.
I
do not believe that he jneant to include
language almost inevitably gives a
When we
it,
but his
false impression.
speak of Becoming we naturally think of a process
For the most striking characteristic of the concrete state of becoming is that it is a change from something to something else. Now Hegel's category of Becoming cannot be of change.
intended to include the idea of change. in
Change involves the existence of some permanent element what changes an element which itself does not change.
—
common
For, if there were nothing
two
to the
states, there
would be no reason to say that the one had changed into the Thus, in order that anything should be capable of other. change,
it
must be analysable
does not change. Quality.
-
This
is
two elements, one of which impossible under the categories of into
Under them each thing
properly be used of what
is
undifferentiated quality.
Either
completely the same
— or
its
—
it
is
for
unchanging layer of
—
is
just one simple
—and
itself
its
it
is
distinction
undifferentiated nature Its absolute shallowness
between a changing and an
reality.
This was recognised by Hegel, who says that characteristic of Quantity that in
it,
it
is
for the first time, a
can change, and yet remain the same (G. L.
He
then
complete sameness vanishes, and
admits no partial identity of content.
room
the word thing could
so elementary
then the thing also vanishes, since leaves no
if
i.
211.
the
thing
Enc. 99).
cannot therefore have considered his category of Becoming,
which comes before Quantity, as including change.
BEING
I.
But,
Becoming it
Is
may
it
is
19
be objected, although
Hegel's category
incompatible with fully developed change,
of
may
not be compatible with change in a more rudimentary form
not possible that, even
it
may be
a place
change of
r appearance
found
for
among
the categories of Quality,
a category which involves, not the
A
into B, but
the disappearance of
of
B
it
instead of
?
?
To
A
and the
this I should reply, in the
5 was carefully would be found to involve the presence of some element which persisted unchanged in connexion first with first place,
analysed,
that if such replacement of J. by
it
I^A and then with
B.
The
case would then resolve itself into
an example of change proper.
To defend
however, be an unnecessary digression here.
this view would,
For
it
is
clear
that, if such a
'
of
A
replacement could exist without being a change into B, then A would be quite disconnected with B. But
Becoming the whole point lies in the intrinsic and essential connexion of Being and Nothing. The category could not, therefore, be an example of such replacein Hegel's category of
'
ment.
Thus Becoming,
as a category of the Logic, cannot j consistently involve change. And when we look at the transi19.
tion
by which Hegel reaches
the essence of the
it,
we
new category lies
Being and Nothing, and not between them. of
see, as I said
above, that
in the necessary implication
in
any change taking place
But the name of Becoming is deceptive in itself, and so is Hegel's remark that the category can be analysed into the moments of Beginning (Entstehen) and Ceasing (Vergehen) (G. L.
i.
109).
If the implication of the
two terms
is
to
be
Becoming, there
is, indeed, no reason why these names should not be given to the implication of Being in Nothing,
called
and of Nothing
in Being,
It all tends, however, to strengthen
we have here a category of change. The same result is produced by the mention of the philosophy of Heraclitus in connexion with the category of Becoming. Of the belief that
course a philosophy which reduced everything to a perpetual flow of changes
would involve the principle of the implication of Being and Nothing. But it would also involve a great deal more, and once again, therefore, we meet the misleading
2—2
^
20
CH.
QUALITY
II.
suggestion that this great deal more
is
to
be found in the
category of Becoming.
f
For these reasons I believe that the course of the dialectic would become clearer if the name of Becoming were given up, and the Synthesis of Being and Nothing were called Transition to Being Determinate (Uebergang in das Dasein). 20.
P J
This follows the precedent set by Hegel in the case of the category of Measure, which
(Uebergang
/
in das
When we
Wesen)
he
calls
{G. L.
i.
last
Essence
Transition to 466).
have taken this view of the category, the transi-
So long as the third category was regarded as involving change, it might well be doubted whether Hegel had succeeded in eliminating, in Being Determinate, the change he had introduced in Becoming. And to do this was necessary, since Being Determinate is certainly not a category of change. But on the new interpretation change has never been introduced, and does not require tion to the next triad
•
becomes
easy.
to be eliminated.
The
,(
assertion that
an element
is
Being Determinate contains Being as
simple enough.
Nothing
as
however,
merely verbal.
an
But
to say that it contains
element seems strange.
The
Antithesis
The to
difficulty
Being
a
a negative element
positive
element, but
should
The word
rather have been called Negation than Nothing.
Being involves
is,
not exclude
does
—unless we expressly say Pure Being.
But
Nothing is commonly used to designate a negative element combined with the absence of any positive element. It corresponds to Pure Being, while Being corresponds to Negation.
,
Now
Being Determinate contains Being as a moment, but not Pure Being, since Pure Being means " Being and nothing else." In the same way, then, we must say that Being Determinate contains as an element, not Nothing, but Negation. Hegel recognises this, for he says {Q. L. i. 81) that in Being Determinate we have as moments Positive and Negative, rather than Being and Nothing. 1 1
But he
fails
to
see
that
Being and Nothing are not in ordinary usage correlative terms, and that, while, when he came to the Synthesis, he had to substitute Negative for Nothing, he could just as well have
BEING
I.
kept Being instead of Positive.
It
21
me
seems to
that
it
would
he had spoken of the Thesis and AntiHe could then have said in thesis as Being and Negation. this triad, as he does in other cases, that it was the Thesis and have been better
if
Antithesis themselves which are the It
21.
moments
of the Synthesis.
easy to see that in Being Determinate, Being and
is
If anything has a definite quality,
Negation are synthesised.
this involves that it has not other definite qualities, inconsistent
with the
first.
and thus
its
A
thing cannot be green unless
it is
not red,
.
greenness has a negative aspect, as well as a
positive one.
II.
A. (a)
(G. L.
112.
i,
Being Determinate.
Being Determinate as Such, Being Determinate in General. Enc. 89.)
This, as the first subdivision of
Being Determinate, has, as its name implies, no other meaning except the general meaning of Being Determinate, namely, that in all existence Being and the
division
first
of
Nothing are united.
And
now, for the
first
time,
we get
the possibility of
Being and Nothing did not and plurality. admit of this. Whatever simply Is is exactly the same. And But under the this is also true of whatever simply Is Not. category of Being Determinate, it is possible to have an a which is not b, and is thus distinguished from b, which is differentiation
not
a.
And
not only the possibility of such differentiation,
now
For whatever is anything must also not be something, and cannot be what it is not. It must therefore not be something else than what it is. And thus the reality of anything implies the reality of somebut also
thing
else.
its
necessity
is
(The validity of
established.
this will
be discussed in Section 25.)
Hegel calls the various differentiations by the name of Qualities, and so we reach the second subdivision of Being Determinate as Such, namely
«/
22
CH.
QUALITY
II.
Quality.
(b)
We
must not be misled by the ordinary use of the phrase " a Quality." As a rule, when we speak of a Quality or of Qualities, we mean characteristics which inhere Hegel in a Thing, and of which one Thing may possess many. calls these, when he comes to treat of Essence, by the name of (G. L.
22.
i.
We
Eigenschaften. this.
114.)
have not yet got any idea so advanced as
It is not until Essence has
make a
been reached that we
shall
between a Thing and its characAnd, although we have now attained a plurality, we teristics. have not yet acquired the idea of plurality in unity, which would be necessary before we could conceive one Thing as having many characteristics. The Qualities of which Hegel speaks here are simply the immediate differentiations of Being Determinate. They do not inhere in anything more substantial than themselves they, in their immediacy, are the reality. Consequently they are not anything separate from the Being Determinate. Each Quality has Determinate Being, and the universe is nothing but the aggregate of the Qualities. There is not one Being Determinate with many Qualities, but there are many Determinate Beings. These may be called, not inappropriately. Some-
be able to
distinction
;
things.
And
this is
the transition to the third division of
Being Determinate as Such, namely,
(c)
23.
{G. L.
i.
the Real (G. L.
very obvious.
—a thing
119.) i.
120.
At
Something. this point, says Hegel,
Enc. 91).
The reason
we
first
for this is
get
not
Reality seems to be taken as a matter of degree
more or less Real in proportion as it is regarded under a more or less true category. Something is, no doubt, is
a truer category than those which preceded
and did not come in
true than those that follow
comes in even the
here, if it first
it,
I
it,
cannot see
before.
but
it
why
is
less
Reality
Something
is
not
Synthesis.
—
Looking back on the two last transitions from Being Determinate in General to Quality, and from Quality to Some24.
BEING DETERMINATE
II.
thing
—they must, I think, be pronounced
might perhaps
to
23 be
valid.
arise as to the necessity of passing
A
doubt
through them.
might be asked, that the differentiations cannot lie on the surface of Being Determinate (since that would involve a distinction between Essence and Appearance) but must be in it ? And in that case could we not have simplified the process by taking Something as the immediate form of Being Determinate, and so forming the undivided first moment Is
of
it
not clear,
it
iti ?
But between simple Being Determinate and Something there is a difference namely the explicit introduction of plurali ty. The fact that the name Something is in the singular number (inevitable with the German word Etwas) may obscure this if we confine ourselves to the titles, but in reading the demonstrations it soon becomes evident that, between Being Determinate in General and Something, plurality has been introduced. In the idea of Something, therefore, we have more than is in the simple idea of Being Determinate, and a transition between them is required. We can also see why there should be two steps between Being Determinate in General and Something, and why the
—
road from the one to the other should
The
of Quality.
transition
transition to Quality, since
to
lie
through the category
plurality takes
to a plurality,
is
Now we
natural that, in passing from what
we should
the
Hegel speaks of one Being Deter-
minate in General, but of many Qualities. I think, that it
place in
first
think that what
is
is
plural
can
see,
singular is
some-
thing different from that which had previously been before us (and in Quality the suggestion is that they are different) and that 1
I.
we should
require a fresh step of the process to show us that
This objection
may
be
made
clearer by a table.
Hegel's division of Being Deter minate. A.
II.
Being Determinate as Such. (a)
Being
Determinate
Division proposed by Objection.
Something (without any sub-divisions).
in
General.
B.
{b)
Quality,
(c)
Something.
Finitiide. (et cetera.)
B.
Finitude. (et cetera.)
A|.S.
24
CH. H.
the plurality
is
QUALITY
the true form of what
not to be plural (and this
what
is
is
we had previously taken
gained by the transition to
Something).
We
have, then, a plurality, and a plurality which does not
inhere in anything
It
else.
must therefore be regarded
as
a rudimentary form of plurality of substance, rather than of
Now
plurality of attributes.
the nature of existence.
the categories are assertions about
So,
when we have got a
plurality of
Somethings, we have got a plurality of existence. justified
?
It
25,
may be
way from
this
Is this
we
are not entitled to argue in
the existence of one Something to the existence
No
of others.
objected that
doubt,
it
may be
there must, by the results
Something is we have already reached, be some said, if this
x, y,
which OS is not, but it does not follow that 3/ exists. If (to take an example from a more complex sphere than that of Something) an existent object is red, it must be not-green, but it does not follow that any green object exists. Thus, it is urged, there might, for anything we have proved to the contrary, be only one existent Something, whose definite nature consisted in the fact that it was x, and was not y, z, etc. do not, however, think that this
I
is valid.
For
the definiteness of the Something out of the fact that not
y,
not
z, etc.,
y, not-2^, etc.
then
it will
have a plurality of
if
we get
it is
x and
qualities, x, not-
This requires the conception of a thing as a unity
which holds together a plurality of attributes, and is not identical with any one of them. And this is a conception which we have not yet reached, and have no right to use. Thus the negative element in each Something cannot fall within it, and must fall outside it, and so we are compelled to follow Hegel in asserting the plurality of existent Somethings.
may be
what belongs to the nature of anything cannot be wholly outside it, and that if two existent Somethings are distinguished from each other by being respectively X and y, then after all it must be true of x that it is noty, and of y that it is not-a;, and so that there will be the plurality of attributes in each Something, in which case the possibility that there is only one Something has not been effectively It
refuted.
replied that
BEING DETERMINATE
II.
It is quite true,
25
no doubt, that the existence of a plurality
of substantial beings does involve a plurality of attributes in
But the recognition of this forms a further stage the dialectic, in which we shall have passed beyond the
each of them. of
We
category of Something.
have not yet reached this stage,
and at present, since there is no plurality of attributes in a Something, each Something can only find its determinateness in another existent Something.
When we
do reach to the conception of a thing with a
we
plurality of attributes,
shall
no longer have our present
For that reason, as we have seen, is that plurality is necessary, and that no other plurality is possible, and this becomes invalid when a plurality reason to believe in a substantial plurality.
of attributes in one thing has been established. tion of a substantial plurality
is finally
If the concep-
retained,
it
must
rest
on
considerations not yet before us\
Thus we have a 1
dependent be
for its
said, in a
Each of these
plurality of Somethings.
nature on not being the others.
It
general sense, to be limited by them.
is
may thus
(Limit, as a
technical term in the dialectic, denotes a particular species of
more general sense.) With this we pass of Being Determinate, which is
limitation in the
second division
B. (a) 26.
{G. L.
Finitude.
Something and an Other. This category should be a restatement,
122.)
i.
to the
more immediate form, of the category of Something. This For the category of Something, as I have is exactly what it is. said, included the idea of a plurality of such Somethings. And, from the point of view of any one of these, the other Somethings will be primarily not itself. So we get the idea of Something in a
and an Other. Since each Something Other,
its
Anderes.)
nature
But
relation to an
may
is
dependent
for its
own nature on an
be called a Being- for-Other.
(Sein fur
this is not the only aspect of its nature.
Other
is 1
what makes
it
what
Cp. Sections 101—102.
it
is.
And
The thus
26
CH.
this relation
And
also
is
what
thus this relation
{G. L.
i.
it is
is
QUALITY
II.
By
(An Sich^). the Something itself.
Itself or implicitly
also a quality of
Cp. also Enc. 91, though the explanation
129.
so condensed as scarcely to be recognisable.)
here
is
This takes us to
the next subdivision, Determination, Modification and Limit.
admit that Modification
(I
Beschaffenheit, but so
it is
differ so slightly.)
Determination, Modification and Limit.
{G. L.
27.
not a very happy translation of
impossible to get really good names for
many meanings which
(6)
is
Not content with the
129.)
i.
analysis of his
subject-matter by five successive trichotomies, Hegel further analyses this category into a triad of the sixth order, the terms of which
Determination, Modification, and Limit.
are
subtlety of the distinctions at this point
so great that I
is
confess to having only a very vague idea of far as I
can
viewed as
see, its
Determination
is
what
So the character of the Something
inner nature, and Modification
viewed as something received by
The must
it
is
from outside
is
meant.
that character
—
is,
in fact, the
Other come back again. It follows then, naturally enough, that Determination and Modification are identical. And from this again it follows that, as the Something was conceived as having a nature which was both a characteristic of
Being
r
itself
for
and of
Limit. is
Other, that nature should be conceived as a
its
In such a sense a meadow
not a wood, nor a pond.
only get such a Limit
when
is
limited by the fact that
{Enc. 92.)
Now
it is
clear that
the nature of the Something
is
it
we
seen
and in its relation to an Other. The conception of a LimiFimplies thaTtnnakes^the^^omething what it is no more and no less. That it should be no less than itself to be bot h in itself
—
requires that
maintain
than
its
nature should be in the Other.
itself against
nature should also be outside
^
will
itself
That
it
so that
it
should
should be no more
the present stage of the dialectic, that
itself requires, at
maintain
itself,
against
itself,
its
that the Other should
it.
know, impossible to find any one English phrase which adequately render An Sieh. I have followed Prof. Wallace's example in It is, so far as I
using either
By
Itself or Impb'citly, according to the context.'
II.
The
BEING DETERMINATE
27
correctness of this interpretation
no doubt, very
is,
But whatever Hegel's meaning may have been in this obscure passage, we can see for ourselves that the category of Limit would necessarily have come in at this point. For, in the category of Something and an Other, the nature of each Something lay in the Other. But it is also true, as Hegel points out without any obscurity, that the nature of Something must also lie in itself And, since the nature of Something lies both in itself and in its Other, we have the idea of a Limit of a characteristic which, while it belongs both to Something and to its Other, keeps them apart. Here, as Hegel remarks {G. L. 133), we get for the first problematic.
•
—
r
i.
time the conception of Not-being
In the category
for Other.
Something and an Other we had the conception of Being for Other, but now in Limit the Something has its nature in itself as well as in the Other, and so it has a certain stability and of
exclusiveness.
At
this point, therefore,
we may be
glimpse of the conception of Being
for
said to get the first
Self
seen to be the truth of Being for Other.
But
On
it is
not yet
the contrary
it
and this opposition produces fresh contradictions, which cannot be solved until the true nature of Being for Self is discovered in the category which bears that name. We now come to Finitude in the narrower sense. That this r conception should only be reached at this point will not seem strange if we realise the meaning which Hegel always gives to For him the Finite is not simply that which has this term. something outside it, and the Infinite is not simply that which The Infinite for him is that whose [ has nothing outside it. appears to be in opposition to
it,
nature and, consequently, whose limits, are self-determined.
The
on the other hand,
Finite,
by something outside Infinite
free
is
^the Finite
is
Two
that whose nature
The
itself.
self-determination.
essential
The
is
feature
essential
limited of the
feature of
subjection to an Other.
This explains point.
is
why Finitude
only becomes explicit at this
things are necessary for subjection to an Other
the Other, and a definite nature in the Something to be subejected to
it.
The conception
of plurality
was
onl}^
reached at
28
CH,
QUALITY
II.
the end of Being Determinate as Such, and
^Yhen
be no question of Finitude,
till
then there could
point was reached,
this
Finitude began to appear, and accordingly the second division
we are now considering, is, as we But Finitude does not become fully
of Being Determinate, which
have seen, called Finitude. explicit
the Something's nature
till
is
seen to be also in
itself,
and not only in the Other. For till then there can scarcely be said to be anything to be subjected to the Other. Only with the conception of Limit does Finitude become fully explicit.
And
next
the
therefore
Finitude in the
^\'ider
sense
category
—
{G. L.
28.
i.
the last
moment
Limit.
The
137.)
is
of
merely a restatement of
of the previous subdivision is,
—that
is
to say, of
as has already been said, the
mean
idea of Finitude, since they both its
subdivision
called in a special sense
This category
idea of a Limit
has a nature of
last
Finitude.
(c)
I
is
— the
own, and that
its
that the limited thing
nature
is
in subjection to
an Other.
This conception takes the form of Limit when we
view
overcoming the
it
as
difficulties
which
arise
from the
opposition between the nature as in an Other and the nature as in the object itself.
When
the conception
immediate statement of the truth, Finitude
an Other is
is
is
taken as a more
takes the form of Finitude.
the Synthesis of a triad of which Something and
Thesis, and Determination Modification
the Antithesis.
Something
it
is
The Thesis
and Limit
asserted that the nature of the
lay in its Other, the Antithesis asserted that the
nature of the Something lay in
itself.
These assertions are
reconciled in Finitude. 29.
On
looking back we can
see,
I think, that the sub-
divisions found within the category of Determination Modifica-
and Limit are useless. Modification is only a repetition of Something and an Other\ while Limit is identical with Finitude. The only idea remaining is Determination. It would have been better, therefore, if Determination by itself had been the Antithesis of Something and an Other. The tion
^ Hegel denies between them.
this,
but I cannot see that he has shown any difference
II.
name
BEING DETERMINATE
29
being wanted for a subdivision of the
of Limit, not
and could be used, instead of Finitude, as the name of the Synthesis, and this would avoid the
""Antithesis,
would be
set free,
inconvenience of using Finitude here, for a division of the order,
when
it is
fifth
also used for a division of the fourth order.
In Finitude, as was said above, there are two sides
30.
the internal nature of the finite Something and the relation in
which the (G.
it
These Hegel
stands to the Other.
calls respectively
Ought and the Barrier. (Das Sollen und die Schranke.) The Barrier seems an appropriate name. But L. i. 140.)
why
the internal nature of the Something should be called the
Ought is not so clear. when he feels himself
It
may be
said that a conscious being,
limited by something, says that the limit
ought to be removed, and that he ought to have room to
But the resemblance between such a conscious being and a limited Something is very slight, and far less develop
freely.
important than the difference.
When
man
a
says that he ought
to be able to do what, in point of fact, external circumstances
do not allow him to do, he has an ideal of som.e course of action different from the one
which he
that his ideal course would
than the other.
The
fulfil
is
and he judges true nature more completely
forced to take,
his
position here
content of the two opposed sides
The
is
entirely different.
is
here the same, for the
Something has only one nature, which may be looked at either as in itself or in the Other, and the opposition is only between the two ways of looking at it. Why then did Hegel use the word Ought ? I believe he did so because it gave him a chance of introducing an attack on the ethics of Kant and Fichte {G. L. i. 142 Enc. 94). This was a temptation which he was never able to resist. But the inner nature of the Something now bursts its 31. Barrier. The Other which limits it has no nature which is not ;
expressed in the limitation
itself.
And
the limitation belongs
So that it now finds its own nature beyond the Barrier, which it has, therefore, passed. {G. L. i. 147. The line of the argument in the Encyclopaedia is different, and will be considered later on.) To go back to Hegel's own example, a meadow is limited by the fact that it is not a wood. Not to be a wood is a part, and an essential part. to the nature of the
Something.
30
CH.
QUALITY
II.
Thus the nature of the meadow is to be found in the nature of the wood, and is thus no longer something bounded and confined by the wood's nature for what is left to be bound ? of the nature of the meadow.
—
We
thus pass to C.
Infinity
the third division of Being Determinate {G. L. Barrier being abolished, the Something
Infinity
transition here, is
will
it
be noticed,
is
a fresh conception from Finitude.
might have been expected, of the word)
is
for
rid of Finitude, in a very rudi-
a distinct advance.
This
is
not what
Finitude (in the narrower sense
a division of the
next division of the
For, the
no longer determined
is
by anything outside itself. Thus we have got and so attained Infinity, though only, so far, mentary form.
The
147).
i.
fifth order,
and stands to the
order (Infinity in general) as the
fifth
\ySynthesis of one triad to the Thesis of the next.
According to
scheme of the dialectic, therefore, their content should have been the same. And the transition seems to me to be invalid. I cannot see that anything which Hegel has said entitles him to conclude, as khe general
we have got rid of meadow is determined
apparently he does, that in this category
The nature
Limit and Barrier.
by that of the wood
— but
it is
of the
determined negatively.
And
nature not to be the wood.
It
is its
this determination, while
it
any way destroy the difference that there is no justification for concluding
relates the two, does not in
between them,
so
that the second of
them has ceased
to limit the
first,
or to act as
For the proper transition at this point, we must, I adopt the view of the Encyclopaedia, rather than that
its Barrier.
believe,
of the Greater Logic.
Continuing the treatment of the subject in the Greater Logic,
we
find that
when,
passes over its Barrier,
unlimited.
Thus the
it
in
the
finds itself
first
stage
is
Something outside the Barrier, and so
first
place, the
BEING DETERMINATE
II.
(a) 32.
{G. L.
i.
148.)
limitations which, if I
31
Infinity in General.
And now Hegel proceeds to restore the am right, he ought never to have dis-
What, he asks {G. L. i. 153), is this Infinity ? It has been gained by negating Finitude, and passing beyond it. Now nothing can negate anything definite, except by being definite
carded.
itself.
But we have seen that a thing can only be
has a limit and
is
finite.
And
definite if
thus the Infinite which
it
we
seemed to have reached turns out to be another Finite. A meadow, for example, cannot be negated by pure Being, or by Nothing. It must be by some other Being Determinate. And this must be finite. The Infinity, which had been reached, thus turns out to be finite. But, being finite, it will have its nature outside itself, and so again passes the Barrier, and becomes infinite only once more to become finite. This process goes on without end,
—
and thus we have the second subdivision {G. L.
33.
(h)
i.
149)
Reciprocal Determination of the Finite and Infinite
which may be called more
briefly
Negative Infinity
(cp.
Enc. 94).
must be noted that this is not a category of change. A category of change would assert that the reality, when viewed It
under that category,
is
viewed as changing
not the case here. The reality '"is
not conceived as changing.
We
which we judge
it.
generally outside
itself,
its
This
nature.
is
—the nature of the Something All that changes
conceive
its
nature,
is
the
first
as
way
in
being
then as being in another Something,
then as generally outside that other Something again. We But this does not oscillate endlessly between these two views.
judgment that the reality changes. It is only a )_jchange of judgment about the reality. This involves a contradiction. The nature of the Something p But it is then seen is first seen not to be Finite, but Infinite. involve any
but Finite again. And the second step does not transcend the first, for the second leads back again to the to be, not Infinite,
32
CH.
QUALITY
II.
—that the Something— cannot be pronounced Thus can be found nowhere —
Therefore a part of the nature of the Something
first.
part which
lies
outside
either Finite or Infinite.
for
it
the category recognises no third alternative.
And
since this part
Something has been shown to be essential to the Something, there can be no Something, and so (so far as can be seen under this category) no Determinate Being at all.
of the nature of the
And '" is
so there
It is
a contradiction.
sometimes said that Hegel holds that an Infinite Series
But
as such contradictory.
there its
is
He denies
this is a mistake.
that
anything sublime in endless repetition, and asserts that
is
only important feature
does not assert
it
is
tediousness (Enc. 94), but he
its
to be intrinsically impossible.
Infinite Series of particular kinds
then only
for
How
34.
out (G. L.
i.
we have
is
only
which are contradictory, and
some reason other than
of the present series, as
It
In the case
their infinity.
seen, there is such a reason.
do we get rid of this contradiction
?
Hegel points
155) that the same fact which produced the con-
tradiction has only to be looked at in a rather different light to
That
give the solution. Infinite
—
or, in
fact is the
other words, of what
thing and of what
unity of the Finite and is
within any finite Some-
was this which produced the contradictory infinite series, for it was this which made the content of the Something first overstep its Barrier. But if we put it in another way that the content of the Something is in part its relation to what is outside it, then the Something has an internal nature which is stable through its relation to what is outside it, and the contradictory infinite series never begins. Instead of saying that the nature of the Something must be found in what is outside it, we must now say that it has its nature through what is outside it. The conception of relatively self-centred reality thus reached is called by Hegel {G. L. i. 155) is
outside
it.
It
—
(c)
35. different.
The treatment
Affirmative Infinity, of the subject in the Encyclopaedia
After establishing the
category of Limit,
continues {Enc. 93) " Something becomes an Other is
itself
Something: therefore
it
:
this
is
Hegel Other
likewise becomes an Other,
BEING DETERMINATE
II.
and
so
33
The transition here is not alternately The only Infinite is the infinite number
on ad infinitum^
from Finite to Finite. of such Finites.
me
be better than the argument in the Greater Logic. In the first place, the categories are so arranged in the Encyclopaedia as to avoid the difference of content This seems to
to
between a Synthesis and the succeeding Thesis
— which, as
we
saw above, occurs in the Greater Logic. In the second place, the Encyclopaedia avoids the transition from the limited to the unlimited, which I have maintained above to be invalid. And the transition which it substitutes is, Part of the nature of A is found in its Other, I think, valid. But this can only B, since it is part of its nature not to be B. be a definite characteristic of jB's
nature, on the
Thus the nature
same
A
of
J., if
Now
definite.
is
must be found
principle,
will
B
be partly found in
in its
part of
Other
G.
G, since it is part
of its nature to be not-B, while B's nature includes being not-G.
argument will prove that the nature of A is partly in C"s Other, D, and so on without end. Here, again, we get an infinite series which is a contradiction. ^, as a Something, must have a definite nature. But
A
similar
part of this nature
not to be found in itself
is
must,
It
according to the category, be found in one of the series of But it cannot be found in any one of them, for whichOthers. ever
we take proves
to
have part of
therefore of A's nature, in yet another.
its
Thus
own
nature,
and
this indispensable
none of the series of Others, and therefore, according to this category, can be found nowhere. Thus A has no definite nature, though it is a Something. And part of A's nature
is
to
be found
in
this is a contradiction.
Nor can we escape from the part of A's nature which
whol§
series,
though
it is
this contradiction is
external to itself
by saying that is
found in the
not found in any one term of
it.
For
nothing which we have yet reached entitles us to regard the
A
can enter into relations. Its relations can only be to some particular Something which forms
series as a unity with
which
part of the series. It will be seen that the contradiction does not rest
impossibility that a
mind working
on the
in time should ever reach the
84
CH.
end of an the
QUALITY
II.
This impossibility might prove that
infinite series.
nature of any Something could never be
full
mind working
in
this way, but
this
in
known
any
to
there would
be no
contradiction.
From
we
by passing to the category of True Infinity. Hegel says that the Something stands in the same position to its Other, as the Other stands to the Something. The Something is the Other of its own Other, and, therefore, " Something in its passage into Other only joins with itself" {Enc. 95). This means that, while the nature of A is partly to be found in B, and the nature of B is partly to be found in something other than B, this need not be a third Something, C, but can be A, which is after all other than B. So 36.
this contradiction
the infinite series, with
its
are freed
contradiction,
is
avoided.
A
and
B
are each determinate through the fact of not being the other.
Thus we reach Being It
itself.
no longer has part of
nature within
itself is
what
(The Encyclopaedia
seems
to be certain that this
This position, Hegel says, identical with
here
all
what was
The name
its
it
Other.
Iiifinity.
A's nature
for Self.
is
because of
is
in
Other, but
its
its relation to its it
the meaning.)
that of True Infinity, and
called, in the
of Infinity
its
now wholly
very condensed here, but
is
is
nature in
is
it is
Greater Logic, Affirmative
may appear
inappropriate.
For
assertion of Infinity, in the ordinary sense of the word,
has disappeared, since the necessity for an Infinite Series of
Somethings has disappeared. According to the category we have just reached there must be at least two Somethings, and there may be any number, but, so far as I can see, there may be only two. It
p call
is
very characteristic of Hegel's thought that he should
this concept
him the essence
True or Affirmative
Infinity.
of Infinity lies in the fact that
unconstrained, unthwarted,
free.
And
According it is
what
is
freedom, according to him^
can only be found, not in being unbounded, but in being
bounded. That
to
self-
whose boundaries are determined [ by the fact that it is itself, and not by mere limitation from outside. It is through applications of this principle that Hegel holds that a conscious spirit has more true infinity than endless is
truly infinite
space or endless time.
Now
in this category
we have reached
BEING DETERMINATE
II.
35
though only as yet in a very rudimentary form. And therefore, in comparison with what has gone before, Hegel calls it True Infinity. 37. From this point the Greater Logic and the Encyclopaedia
self-determination,
Hegel, that
again coincide in their treatment.
It is here, says
we
Enc. 95) and that Idealism
get Ideality (G. L.
first
becomes possible {G.
L.
164.
i.
maintaining that the Finite
and
Ideal), "
For
not truly to be."
Ideal
is
(das
Ideelle,
means that the Finite
again,
this,
Idealism, he says, consists in
171).
i.
this
is
it
not das
recognised
is
necessary that the Finite
should have been reached, and should have been transcended,
and that we should recognise that what is merely Finite is (Finite is, of course, used in Hegel's own sense, impossible. and means, not that which is bounded, but that which is not self-bounded.) This is the first category in which such a recognition
is
involved.
Affirmative Infinity gives us, as
the Encyclopaedia, Being for
Self.
we saw when dealing with In the Greater Logic they
form two separate categories, but the content of Affirmative the final Synthesis of Being Determinate is identical Infinity
—
—
with the content with which the new division of Being for Self The Something has now its whole nature inside itself. begins. III. ((t.
L.
i.
Enc.
173.
Being for Self
96)
the
is
divisions to be found in Quality.
of the
last
three
tertiary
Its first subdivision is called
by Hegel A. {G. L.
i.
Being for Self as Such
174), while the first subdivision of this again
Being Determinate and Being for
(a) {G. L.
i.
175.)
The
position here
Being Determinate and Being invalid,
for
but the discussion of
Self
its
has both,
it
is
Self.
(This seems to
me
to
be
had better be post-
for Self as Such.)
Since
qualitatively differentiated from its Other,
while the Being for Self gives infinite series of Others, in itself, is
named
that a thing has both
validity
poned until we reach the end of Being it
is
is
it
stability
and saves
it
from the
which Being Determinate, taken by
compelled to seek the nature of each differentiation.
3—2
36
CH.
But the
QUALITY
II.
Hegel continues {G. L. i. 176), cannot be maintained. For Being Determinate has, by the previous transition, been transcended in Being for Self, and is a moment of Being for Self In so far as it is valid at all, its validity is
summed up
position,
in
Being
for
In so
Self
claims to be
far as it
anything distinct from, and supplementary to, Being for Self, it Tis not valid. Therefore all Being for Other has now dis(^
appeared, and Being for Self Self has not negation "an
not for an Other.
Being
for
as a determinateness or limit,
and
is
ihm"
therefore not as a relation to a Being Determinate other than itself
We
have no longer a Something, since Hegel confines that term to the sphere of Being Determinate. At the same time
we
are not yet entitled to speak of a One.
Let us
present call the reality, which was previously called the
for
the
Some-
by the neutral name of X. The point of the present argument is that the relation of the X to the not-Z" has become more negative than before. We must not exaggerate the change. The relation of the Something to the Other was already, in a sense, negative, for the Something was limited by its Other, and was what the Other was not. And, again, X is still related to the not-X. For it is only by distinguishing itself from the not-X that it got Being for Self at all, and this distinction is itself a relation, as will appear more explicitly when we come to the categories of the Many and of Attraction. (When Hegel says that Being for Self does not contain negation "as a relation to a Being thing,
Determinate other than I believe,
on the
itself" {G. L.
176), the
i.
There
last five words.
is
emphasis
a relation, but
it is
not a relation to a Being Determinate, nor to anything which in the technical sense, the "
But the change
is
there,
thing was determined by
Other
"
and
important.
its
is
of the
Being
is,
is,
for Self)
When
the Some-
Other, the positive nature of the
Other was essential to the determination. The Something was this quality, and not any other, and it was determined in this
way because the Other was what it is
different.
In Being
it
was, and nothing
may
be,
X
Now
for Self all that is essential is that
there should be something else which
other thing
else.
is
not X.
can determine
itself
Whatever this by means of a
BEING FOR SELF
III.
relation to
it.
no longer
It has
X
increased independence of
is
its
own
37
peculiar Other.
This
the natural consequence of
X
being more individual and self-centred than before.
The new category
{G. L.
38.
i.
to
which we now pass
(b)
Being for One.
We
176.)
is
called
by Hegel
ought, I think, to consider the
significance of this category as mainly negative, in spite of its positive
name.
Its essence is that
Being
for Self is not also
Being Determinate, and it might not unfairly have received the name of Not-Being for Other. Hegel has then no difficulty in proving that the One, for If it were anything else the is, can only be itself. which the Being for One would be Being for Other. And this is impossible, The since Being for Other has already been transcended.
X
Being
for
One
of
X, then,
is
Being
for Self
This takes us to a new category which consists in the re-
statement of Being for Determinate.
To
this
Self,
but this time by
Hegel {G. L.
39.
i.
itself
without Being
181) gives the
name
of
One,
(c)
which emphasises the negative and exclusive character of Being for
Self
l__
me
wrong in subdividing Being for Self as Such. The category of Being Determinate and Being for Self is unjustified, for he only reached Being for Self Being Determinate, by transcending Being Determinate. therefore, in so far as it is true at all, is contained in Being for The Self and cannot properly be put side by side with it. Thesis of the triad must thus be rejected, and the Antithesis must go with it, since the only thing done in Being for One is to remove the Being Determinate which had been improperly It
seems to
that Hegel was
introduced in the Thesis. the triad
—namely, One.
There only remains the Synthesis of
Now
Hegel's conception of
One
is
just
So the Thesis and Antithesis are removed, and the Synthesis is the same as
the same as his conception of Being for Self
the undivided category.
Thus
all
the sub-divisions are re-
would be convenient to call this undivided category One, rather than Being for Self as Such, as this distinguishes
moved.
It
38 it
CH.
more
QUALITY
from the wider tertiary category of Being
clearly
Self of which
II.
This
a subdivision.
it is
the course actually
is
where an the triad of Being
taken by Hegel in the Encyclopaedia (Enc. undivided category of One
is
for
the Thesis in
96),
for Self.
We now
pass to the second division of Being for Self,
(G. L.
The One and
B.
40. i.
Enc. 97) of which the
182.
The One
(a) p
{Q. L.
The
183.)
i.
the
first
Many
first
subdivision
is
in Itself.
subdivision here
is,
as
is
to
be
expected, a restatement of the last subdivision of the previous division.
Now
The two
same name. nature by relating
bear, in this instance, almost the
the One, since
it is
Being
for Self,
has
its
and distinguishing itself from, something other than itself. But this other is at first only determined negatively in regard to the One. The relation of the other term to the One This other term is simply that the other term is not the One. itself to,
The
has therefore, to begin with, a merely negative nature.
One
is
limited by the not-One, by which
not the Many, but only something which
is
is
meant, so
not the One.
far,
Thus
we get (6)
The One and the Void.
The name of this category is appropriate metaphor, but we must remember that it is nothing
{G. L.
41.
i.
184.)
enough as a but a metaphor. If it were a Void, in the literal sense of the term, which was thus related to the One, the One could only be an atom in space, which is not the case. But the One can only be negated by something like itself {G. L.
i.
187).
The One
is definite,
and
its
definiteness depends
on a definite relation with the other term. between them cannot be a definite relation unless the other term
a One.
the relation
to a definite
Now it
is itself definite.
that nothing can be definite, unless
And
One,
has been shown
and so is Thus the One can only be negated by another One,
which bring us
to the category of
it
is
for itself,
BEING FOR SELF
III.
(c)
42. '
Many
39
Ones
which Hegel gives the additional name of Repulsion, since the relation of the Ones to each other is raainly
(G. L.
186), to
i.
negative.
Many How Many ?
Since the conception of the
has been reached, the
Hegel does not regard this, I think, as a question which can be answered by pure thought. Pure thought has proved the necessity for a plurailt^.^ has proved, that is, there must be at least two Ones, but ilol The proof of that would that there must be more than two. rest on the empirical fact that we are presented with more than natural question to ask
is
So far as the dialectic can tell us, the number of Ones may be any number not less than two. There is no reason, that I can see, why the number
two
differentiations of our experience.
should not be
infinite, since
the contradiction in the infinite
Being Determinate did not depend on the infinity of the series but on the way in which its members wfere connected. This, of course, leaves the question undetermined whether, as we advance in the dialectic, we shall discover objections to an series in
infinite
number
of differentiations^
Hegel says that the deduction of the Many Ones from the One must not be considered a Becoming " for Becoming is a One, on the other hand, transition from Being to Nothing And he also warns us only becomes One" {G. L. i. 187). ;
{G. L.
i.
188) that the plurality
being, for each
One
is
is
not to be regarded as Other-
only externally related to
all
the other
—
Ones while in Other-being the whole nature of the Something was found in its Other. The divisions of the One and the Many may perhaps be condemned as superfluous. If we start with the conception of a One determined by its relation to something else, it might be possible to conclude directly that this must be another One, and without the -intervening stage of the One and the Void. At the worst, however, the subdivisions here only are superfluous, and not, as in Being for Self as Such,
so reach the
Many
positively erroneous. 1 It might be said that any question of the number of Ones is improper, since Hegel does not introduce Number till he comes to Quantum. But it seems to me that what he introduces in Quantum is only the conception of a number of units less than the whole, and that therefore even before Quantum it is legitimate (See below, Section 5-i.) to enquire about the total number of Ones.
CH.
40^
We
now
pass to the last division cf Being for Self which
Enc. 98) of ;vhich the
190.
i.
(a)
{G. L.
Many ^
^
i,
is
Repulsion and Attraction,
G.
43.
(G. L.
QUALITY
II.
subdivision
is
Exclusion of the One.
This
190.)
first
is
a restatement of the category of
Ones, which, as was said above, involves the Repulsion
One
each
of the rest of the
Many.
One
repels
Many which
of this
the
?
But what is the nature They are other Ones,
and thus the One in Repulsion only relates itself to itself The Repulsion thereupon becomes Attraction, {G. L. i. 191). and the Many Ones come together in a single One. The new category thus obtained is called by Hegel {G. L.
i.
19i)
The one One of Attraction.
(h)
shows itself to be as untenable as its opposite. If For there were only one One there could be no Attraction. what would there be to attract it, or to be attracted by it ? And, again, that there should be only one One is impossible, It
44.
because as has been shown already, One implies
The truth
is,
as
we now
see,
that Attraction
many is
Ones.
only possible
on condition of Repulsion, and Repulsion is only possible on They must be united, and so we reach condition of Attraction. 45.
(G. L. It
(c) i.
The Relation of Repulsion and Attraction
195) which concludes the categories of Quality.
seems to
me
that the subdivisions of Repulsion and Attrac-
Being for Self as Such, are positively erroneous. No doubt that which each One repels is other Ones, but this does not make them identical with it. Each One has Being for Self, each has its own nature, and the fact that they are all
tion, like those of
Ones does not destroy their plurality. If this is correct, we must reject the transition to the Antithesis, and therefore Hegel's deduction of the Synthesis must be invalid. The Relation of Repulsion and Attraction, which Hegel makes the Synthesis of the triad of Repulsion and Attraction, be the whole content of the undivided category of Repulsion and Attraction. And, if so, it may be
ought
really, I think, to
very easily deduced.
The previous category
—the
last in
One
III.
and
—
another.
If
BEING FOR SELF
41
Many was Repulsion. But Repulsion is impossible by itself. Two things cannot have merely negative relations to one
A
is itself
the existence of
B
essential to
is
But
A, and the relation
the relation of a combatant to his antagonist
it is
also positive, for, if he
Thus the
be a combatant.
One which
it
repels
is
positive
To take an example from a more concrete
as well as negative. field,
only on condition of not being B, then
is
had no one
One
negative.
he could not
to fight,
relation of each
is
to the other
and we have a simpler and more
positive as well as negative,
arrived at Hegel's conclusion, though in valid manner.
We
must, of course, here, as elsewhere, be on our guard
against confusing Hegel's categories of Repulsion and Attraction
more concrete ideas of Physics after which he has named them. The Repulsion and Attraction of Physics may with the
far
exemplify these categories, but they also contain
empirical
elements which Hegel has not deduced, and which he does not think that he has deduced. -^
46.
The
has
dialectic
now reached Quantity.
Quantity
involves that the units should be so far indifferent to one another, as to be capable of
in their nature.
combination or separation without any change This is rendered possible by the equipoise
between Repulsion and Attraction which has now been established. The Ones are sufficiently under the influence of Attraction to be brought together in aggregates. They are sufficiently under the influence of Repulsion to retain their separate existence in their aggregates, so that the quantity of
the aggregate varies according to the
The
dialectic thus regards
Quality to ordinary
This
Quantity.
view
that
it
number
as an advance to pass from
may seem
quantitative
to
this
is
with the
conflict
determinations
abstract and less profound than qualitative.
remembered that
of its units.
But
more must be
are it
said with reference to those qualitative
which have transcended and absorbed Quantity, while Hegel, as we have seen, means by Quality only the simplest and most rudimentary form of what usually goes by the name. The
relations
most abstract Quantity may be an advance on this, although such Quantity may be very inadequate as compared with more complex qualitative determinations.
CHAPTER
III
QUANTITY Quantity
47.
is
:
(Die Quantitat.)
Quantity.
I.
divided as follows
(Die reine Quantitat.)
A.
Pure Quantit3^
B.
Continuous and Discrete Magnitude. (Kontinuirliche
und diskrete C.
Limitation of Quantity. (Begrenzung der Quantitat.)
Quantum.
II.
Griisse.)
(Quantum.)
A.
Number,
B.
Extensive and Intensive Quantum.
(Die Zahl.)
intensives
(Extensives und
Quantum.) (Unterschied derselben.)
(a)
Their difference.
(b)
Identity of Extensive and Intensive Magnitude.
der
(Identitat
extensiven
und
intensiven
Grcisse.) (c)
The Alteration
of
Quantum.
(Die Veranderung
des Quantums.) C.
The Quantitative
Infinity.
(Die quantitative
Un-
endlichkeit.)
(Begriff derselben.)
(a)
Its Notion.
(6)
The Quantitative
Infinite Progress.
(Der quanti-
tative unendliche Progress.) (c)
The
Infinity of
Quantum. (Die Unendlichkeit des
Quantums.)
(undivided) quantity
I.
III.
The Quantitative Ratio. (Das quantitative Verhaltniss.)
A.
The Direct
B.
The Inverse
C.
The Ratio
(Das direkte Verhaltniss.)
Ratio.
(Das umgekehrte Verhaltniss.)
Ratio.
(Potenzen verhaltniss.)
of Powers.
be noticed that Quantity
It will
manner, since division,
43
it
is
and of the
the
first
name both
used in an ambiguous
is
of the
whole secondaiy
of the tertiary divisions contained in
it.
The tertiary division might be distinguished if we gave it the name of Undivided Quantity, which, as we shall see, would be appropriate to
it.
The treatment
of Quantity
not one of the most successful
is
It occupies a greater space than
parts of the Greater Logic.
any of the other eight secondary divisions. Yet the transitions are frequently obscure, and often appear to owe their obscurity to
excessive
compression.
By
far
the
of the
greater part
186 pages which are employed on Quantity are occupied with Some of these, indeed, throw Notes on collateral points.
main argument, but the rest only contain criticisms of Kant's views on Quantity, and of certain mathematical doctrines. Hegel is never at his best when criticising Kant, and the mathematical discussions are too purely technical to give us much assistance in comprehending additional light on the
the course of the dialectic.
Again, w^ere Hegel's mathematics correct
48.
right about the mathematics of his
own
time, and,
?
Was
if so,
he
would
he be right about the mathematics of the present day ? To answer these questions requires a knowledge of mathematics
which
I
am
Mr
very far from possessing.
Bertrand Russell
one of the few philosophers who are also mathematicians "
— says
In Hegel's day, the procedure of mathematicians was
full
:
of
which Hegel did not condemn as errors but welcomed as antinomies the mathematicians, more patient than the philosoerrors,
;
phers, have
removed the
A
every doubtful point.
errors
by
careful detailed
criticism of
work on
mathematics based on
Hegel can, therefore, no longer be regarded as applicable ^existing state of the subjects" 1
Mind, 1908,
p. 242.
to the
44
CH,
III.
QUANTITY
Quantity would only be slightly affected by the fact that his criticisms of mathematics were based on ignorance or by the fact that they had been
But the value
of Hegel's treatment of
The main
invalidated by the progress of that science.
the dialectic, after
demonstrate what
all, is
is
to reach the
the
true
Absolute Idea, and so to
nature of
principal function of the lower categories
And
Absolute Idea.
them should
to the one after
Now
Thus the
reality. is
to lead on to the
only requisite that each of
for this it is
logically follow
object of
from the one before
it,
and lead on
it.
the question whether Hegel's various categories of
Quantity do perform this function is not affected by any mathematical mistakes which he may have made, nor can it be settled the negative by any mathematical criticisms. The only question is whether Hegel was justified in starting the dialectic in
with the category of Pure Being, and whether the validity of the Hegelian categories of Quantity can be shown to be involved in the validity of the category of
And
Pure Being.
this is
a question for metaphysics and not for mathematics. It
is
true that Hegel's
He
only aim.
main aim
in the dialectic
wished, not merely to deduce an absolutely valid
conception of reality, but to account for other ceptions,
was not his
and to range them
in
the order
less valid
con-
of their relative
probably believed that the categories with which he deals in the sphere of Quantity were identical with the fundamental notions of mathematics. In so far as they were
He
validity.
he must be considered to have failed in his subordinate purpose, and, in so far as he has failed, to have introduced additional obscurity by the fact that he has called his categories
not
so,
by the names of the mathematical notions. But the purpose in which he may have
failed
is,
as I
have
subordinate importance for him. And his failure one\ would not be a sign of any metaphysical flaw in
said, only of if
there
is
but only of mathematical ignorance. If the dialectic process is correct, it will be true of all mathematical conceptions, as of all others, that the way in which we can judge of the his system,
such a failure or not is left undetermined by Mr Russell's but criticisms, since these do not deal with the main course of the argument Notes. with one of the mathematical 1
Whether there
is
(undivided) quantity
I.
45
degree of their validity will be by means of the dialectic process. If the ideas are themselves stages in that process, the place
which they occupy in
it will
give us their relative validity.
If
they are not stages in the process, their relative validity can be found by ascertaining the point in the dialectic at which it
becomes clear that they are not absolutely if
the absolute
validity of
valid.
For example,
mathematical ideas implied the
Quantum, as given transcended Quantum, it
absolute validity of the general conception of in the dialectic, then, as the dialectic
would become evident that the mathematical ideas could not be absolutely valid. Thus, even if Hegel's judgments about mathematics were all wrong, that would not prevent his dialectic from being the foundation of right
same subject
to a person
I.
more
skilled in
judgments on the
mathematics.
(Undivided) Quantity. A.
Pure
This stage (G. L.
Quantity.
Enc. 99) appears to be identical in content with the last stage of Quality, though ex49.
i.
212.
pressed with greater immediacy.
The two elements, Repulsion
and Attraction, which were recognised as inseparable in the final category of Quality, here receive the names of Discreteness and Continuity.
Pure Quantity is a category of the fourth order, while the category immediately preceding it (Relation of Repulsion and Attraction)
of the fifth order.
Thus, according to the general method of the dialectic they should not be identical in content. is
however, the subdivision which produced categories of the fifth order at this point is excessive, as I have maintained above If,
(Section 45), this objection would disappear in an
amended
dialectic.
But, although Discreteness and Continuity are recognised as inseparable,
it is still
possible to lay a greater emphasis on one
them than on the other. And we begin, Hegel tells us {0. L. i. 213), by laying the greater emphasis on Continuity. The reason appears to be that this element is more characteristic of Quantity, though not more essential to it, than Discreteness. For as long as we had only Repulsion the process of
46
CH.
QUANTITY
III.
remained within Quality, but, as soon as Attraction was added, the transition to Quantity took place. And there is always a tendency
to
put most emphasis on the element
Continuous and Discrete Magnitude.
B. (G. L.
50.
come first
to
last reached.
i.
By
229.)
Magnitude
category, in which
this
as Continuous.
we
a somewhat abrupt transition
Here there
Quantities, and the one .Quantity
is
to be taken
no plurality of
as yet
is
is
indefinite.
A
plurality of
Quantities would require that they should be Discrete from one
And, again, no Quantity can be
another. its
having fixed boundaries
— that
is
by
definite unless
by being Discrete
to say
from the Quantity beyond those boundaries. It is true that, as was said above, all Quantity has an element of Discreteness. But, so
far,
the only things which are Discrete from one another
are the units
— the
Ones
— which
are alike Discrete from
and
Continuous with one another.
Now
P
a One, taken by
has no plurality in in
not a Quantity at
And Ones have no
all.
For
it
possibility of varying
All variations of magnitude are only variations
magnitude.
in the
it.
itself, is
number
of the Ones.
These characteristics are essential
and they are not possessed by isolated Ones. And the isolated Ones being, so far, the only Discrete things, we have as yet no definite Quantity, and no plurality of Quantities. (It may appear incorrect to say that a One admits of no to Quantity,
(-_
Can we
plurality.
not,
may
it
be asked, conceive an isolated
One as consisting of two halves, four quarters, and so on ? But a One which consists of parts is no longer a me/'e One, which is all
that the dialectic has got at present.
while from one point of view a unit,
is,
view, an aggregate of two or four units.
It is
something which,
from another point of
And
this involves the
higher conception of Discrete Magnitude, which has not yet
been reached. In the same way, we aggregate
is
made up
may
as
conceive the units of which an
having magnitude, and as being
capable of having different magnitudes, and of varying in
But we can only do this them as made up in its turn of
magnitude.
in so far as
each of
parts,
mere Ones.)
and
we conceive
so as not being
I.
(undivided) quantity
47
The position at present is that we have a plurality of Ones of the number of which we know nothing which form a single Quantity. But within this single all-embracing Quantity there are as yet no minor Quantities. Each Oae is qualitatively
—
different from
each of the others, but
more than one One
these
qualitative
There are no qualities common
differences are as yet unique. to
all
— except, indeed, the quality, And
called a quality, of being a One.
this is
may be common to all if it
Ones.
Continuous Magnitude was formed by pa.ssing from One to
One
in
virtue
remembered,
of their
Continuity,
(Continuity,
it
will
be
what was previously called Attraction. It is the capability, possessed by Ones, of being united in an aggregate.) We now pass to Discrete Magnitude {G. L. i. 229). Each One is
is
as really Discrete from
all
the others as
it is
continuous with
Thus a Quantity, less than the whole, can be formed by taking certain Ones together, in virtue of their Continuity, and cutting them off from all others in virtue of their Discreteness. And this Quantity, being cut off by its Discreteness from the them.
indefinite Quantity
beyond
will
it,
be a
finite
Quantity.
In the /^
indefinite Quantity, again, other finite Quantities can be formed,
and thus we get a plurality of finite Quantities. In the form of this stage, as presented by Hegel, there 51. appear to be two defects. The first is that no reason is given
why we should second
is
pass from Pure Quantity to the
that, although
new
dialectic
advance within
stage.
The
Continuous and Discrete Magnitude
not divided into a subordinate triad, yet there it
is
is
a distinct
— namely from Continuous to Discrete
Magnitude.
These defects seem ment.
to
me
to
Continuous Magnitude
part of a fresh stage, at since, as
we have
seen,
all.
it
be merely a matter of arrangeis
not really a fresh stage, or
It is
nothing but Pure Quantity,
does not permit of definite Quantity,
or of a plurality of Quantities,
On lative
the other hand Discrete Magnitude
with Continuous Magnitude.
It
is
is
not merely corredistinctly a
more
advanced conception. It gives us the distinctness and plurality which were lacking before, and it gives them to us by differentiating the relation
between Ones
)
—by joining some of them to
48
CH.
QUANTITY
III.
and disjoining them from others again, instead of making
others,
the relation uniform. It
then, in
is,
Discrete
to
reality,
Magnitude that the
advance from Pure Quantity is made. This is evident in Hegel's text, but is misrepresented by his headings. In order that these should correspond with his argument, he should have dealt with Continuous Magnitude under the head of Pure Quantity, and should
have
made
his
second stage simply
Discrete Magnitude, instead of Continuous and Discrete.
remarked that, although the transition to Discrete Magnitude lies in the possibility of breaking off the Quantity at any One, this does not mean that it is merely a possible transition. Continuous Magnitude is that which cannot be broken otf at any point. Discrete Magnitude is that should be
It
which can be broken off at any point. When we are forced to admit the possibility of breaking Magnitude off at any point, this
transition
necessary
a
is
to
the
D iscrete
category of
Magnitude.
We
can break
off,
it
then, at any point
we
why we should break it Nor can any such another.
But no
like.
one point
reason has been given
off at
rather than at
reason be given
we have passed out Measure. To this point we
until
(G. L.
such
i.
Continuous.
By
sphere of Quantity into
shall recur later on.
Hegel says that Discrete Magnitude as
231.)
not limited.
is
the
Limitation of Quantity.
G.
52.
of
It is only limited as separated
this, I conceive,
he means
from the
that, if the Discrete
Magnitude were taken in isolation, its final One would not be a Limit, because it would not divide the Discrete Magnitude from anything
else.
It is only in so far as it is regarded as in
connexion with the indefinite Continuous Magnitude from which it has been carved out, that its final term is to be considered a Limit.
(On Hegel's use
of Limit cp. above, Section 27.)
The Discrete Magnitude, then, shares Continuous Magnitude outside it. It is thus to that
which bounds
and has
itself
Limit with the
in a definite relation
a definite amount.
Hegel gives the name of Quanta, and the second main division of Quantity.
definite Quantities
pass to
it,
its
so
To we
II.
II.
A,
^
{G. L.
53.
i.
QUANTUM Quantum. Number.
Enc. 101.)
232,
49
In reaching the conception of
a limited and definite Quantity we have, according to Hegel,
[
time the possibility of Number.
While Quantity is merely continuous it cannot be numbered. For then there is no intermediate term between the separate Ones and the whole indefinite Quantity. And the separate Ones in their separateness cannot have any Number, since each of them But now that we have a definite Quantum, it is only One. consists of those Ones which are included between certain Limits, and can therefore be numbered. 54. It may be admitted that, up to this point, there could be no Number of anything less than the whole Quantity. But reached for the
first
why could not this have a Number? many Ones there are. But this does
We
do not know how not prevent them from
having a Number, though the dialectic cannot
tell
us what
it is.
Hegel would probably have said that what was infinite could have no Number, and he does not seem to have considered the possibility that there should be a finite
Ones.
But
I
Each One has
number
of
cannot see that this possibility can be neglected.
— or rather —a separate Quality. is
I
cannot see
anything in the dialectic to exclude the possibility that there should be just twenty such Qualities, and so twenty such Ones,
no more and no
less.
We must remember that the
Ones are not Somethings. The latter had to be infinite in number, since each of them required But the Ones have Being for a fresh Something beyond it. Again, if Self, and so avoided, as we saw, this infinite series. Ones were always divisible into other Ones, their number would necessarily be infinite, but each One is a simple Quality, which is
not divisible.
It
is
involve an endless chain
same way, e.g., that every that the number of relations is infinite.
of derivative related, so
Nor does each One
Ones
in the
true that the
Number
relation is
of the whole Quantity of
Ones
could not have a Limit, in the Hegelian sense, since there
would be nothing outside it. But a Limit, in this sense, does not seem necessary, since the Ones which are numbered have
50
CH.
Being
They can
for Self.
and when
III.
QUANTITY
reciprocally determine each other,
their natures are given, the
number
them
of
is
given
also.
Thus
seems quite possible that all the Ones, taken together, should have a definite and finite Number. That this possibility should have escaped Hegel may very well, I think, be due to it
the fact that he did not keep sufficiently in his mind the precise significance of his categories of Quantity.
to
These categories, like all others in the what is existent. (Cp. above, Section 6.)
dialectic, refer only
He
is
not dealing
wdth the purely abstract conception of quantity, which can be applied
to
anything which can be thought of at
His
all.
categories of Quantity are attempts to explain the nature of
what Ones
is
by the conception of quantities of existent
existent
— the
nature of each
chapter, a simple
So
being, as
we saw
in the
see,
he never definitely asserts anything
inconsistent with this view of the categories of Quantity
only view which he
entitled to take
is
with Quantitative Ratio.
— except when
(Cp. below, Section 6Q.)
expressions often suggest that he
is
— the
he deals
But
his
thinking rather of abstract
quantity than of a Quantity of existent
account
last
and unique Quality.
can
far as I
One
This
Ones.
for his failing to see the possibility of
may
the total number,
under the categories of Undivided Quantity, being limited. For of course there
is
What Hegel Number, only
no limit says,
to a purely abstract quantity.
however, in reaching his category of
requires a verbal correction.
Hegel's category of
Number
is
the
first
For
it
is
true that
point at which any
Quantity, less than the whole Quantity of Ones, could have
a number.
^
55.
"
Quantity
is
Quantum
" says
Hegel,
" or
both as Continuous and as Discrete Magnitude. f_^
of these species has here
no meaning" (G. L.
has a Limit,
The i.
difference
232).
This
and Discreteness have no longer meaning as different moments in any Quantity. It is only the distinction between Continuous and And Discrete Magnitudes which has no longer any meaning. For this result was brought about in Limitation of Quantity. there we saw that a Discrete Magnitude could only be Discrete
must not be taken as an
assertion that Continuity
QUANTUM
II.
51
was positively related to that which was outside And this positive relation is what Hegel calls Continuity. Quantity is now indifferent to its Limit, but not indifferent having a Limit, for to have a Limit is identical with being a
in so far as it it.
to
Quantum
The distinction seems to be that it is always essential to a Quantum to have a Limit, but never essential to it to have a particular Limit. Of course, if it had a different Limit, it would be a different Quantum. But then there is no reason why it should not be different. This will be explained when we reach the Quantitative Infinite Progress. Hegel further says that the Ones which make up any Quantum are indifferent to the Limit, but that the Limit is not indifferent to the Ones {G. L. i, 234). As the Limit is that which determines the Quantum to be what it is, it follows that the Ones in a Quantum are indifferent to the Quantum, while the
(G. L.
i.
Quantum
232).
is
not indifferent to them.
This superiority of the units to the aggregate Quantity, and
we
say, for
is
implied in
example, 7
=
5
all
+
is
essential to
When
quantitative statements. 2,
we assume that each
units dealt with will remain unchanged, whether
of the
combined with more or fewer others. If not, the proposition would not be true. But the aggregates do not remain the same, regardless of the units. If, for example, we take one unit away from 7, what remains is no longer equal to 5 + 2. Extensive and Intensive Quantum.
B.
Their Difference.
(a) 56.
{G. L.
it is
i.
252.)
Extensive and Intensive Quanta differ
from each other in a manner analogous to the difference between
The
Continuous and Discrete Quantity. the two pairs of terms
is
distinction
between
that Extensive and Intensive refer to
Quantitative Limits only, and, as the
Quantum
is
identical with
Limit, they apply to Quanta, while, since no Quantities
its
except Quanta have Limits, they apply to no Quantities except
Quanta.
Continuous and Discrete, on the other hand, apply to
all Quantities.
We
have
first
Extensive Quantum.
identical with that of
now
Number, except
that
This its
conception
determination
explicitly posited as a plurality (Vielheit) {G. L.
i.
is is
253),
4—2
52
CH.
why
I do not see
QUANTITY
III.
plurality
is
more
explicitly posited in the
Quantum than in that of Number, nor does Hegel give any reason why it should be so. The idea of Extensive Quantum has the same content with the idea of Number. The Extensive Quantum is looked on as primarily a conception of Extensive
plurality.
It
a Quantum,
not exclusively a plurality,
is
it
must be
definite, and,
since
for,
It is therefore a unity as well as a plurality,
distinctive
mark
Now
plurality.
is
being definite, must be
Discrete.
is
it
but
its
this is also the case with
Number. A Number is a unity, or it could not be definite. But it is conceived as more essentially a plurality. In Number, as we saw above, the Ones are indifferent to the Quantum, but the Quantum is not indifferent to them. The plurality is thus more essential than the unity. But since the Quantum is a unity it can also be taken with the greater emphasis on the unity, and when this is done we get the conception of Intensive
Quantum
{G. L.
i.
Enc. 103).
253.
between Intensive and Extensive Quantum Extensive Quantum has is thus one of comparative emphasis^ a certain unity, but its unity is subordinate to its plurality. It is comparatively Continuous with what is outside it, and com-
The
difference
paratively Discrete within itself
Intensive
Quantum
is
more
Discrete from the external, more Continuous within, and
unity
The Limit L.
((r.
i.
of
an Intensive Quantum
The Degree
Enc. 103).
254.
is
as a
Number
as a
Sum
57.
(Zahl),
it
must
(Anzahl) {G. L.
i.
i.
255.)
may
Quantum
is
be spoken of
not, since it is simple, be regarded
254).
Identity of Extensive {G. L.
it
Degree
called its
of such a
rather Mehrheit than Mehreres, and while
(6)
Quantum.
therefore greater than that of Extensive
is
its
and Intensive Magnitude.
The treatment
of this point
is
rather
Hegel says Extensive and Intensive Magnitudes are thus one and the same determination of Quantum they are only separated by the fact that one has its Sum inside itself, the other has its Sum outside itself Extensive Magnitude passes over into Intensive Magnitude, since its plurality falls "
obscure.
;
1
of
Hegel's use of the term Intensive
most other
writers.
Quantum
differs considerably
from that
QUANTUM
II.
53
inherently into a unity, outside which plurality
is
found.
But
on the other hand this unity only finds its determination in a Sum, and in a Sum which is regarded as its own as some;
thing which it
is
indifferent to Intensities otherwise determined,
Sum
has the externality of the
and thus Intensive
in itself;
Magnitude is as essentially Extensive Magnitude" {G.L. i. 256). Does this mean that the two terms are strictly correlative that they stand side by side in the dialectic process, and that the transition from Intensive to Extensive
is
of precisely similar
nature to the transition from Extensive to Intensive it
mean
that Intensive
Quantum
Or does
?
stands higher on the scale
than Extensive, and that the transition from Extensive to Intensive is the transition of the dialectic process, while the transition from Intensive to Extensive only
seen under a higher category can,
under a lower one
if
we
And
?
identity
this
identity
is
differences.
first
of these alterna-
by the passage which immediately In this we are told that with 257).
this is supported
them
follows
is
choose, also be regarded
The words quoted above suggest the tives.
means that what
{G. L.
i.
we gain a
Qualitative
Something,
since
the
formed by the negation of its This on the whole suggests that the two terms are
a unity which
is
to be taken as on an absolute equality.
Nevertheless is
on the whole
it
in
seems to
me
that the weight of the evidence
favour of the view which finds Intensive
Magnitude a more advanced stage Extensive Magnitude.
To
of the dialectic process
this conclusion I
am
led
than
by three
reasons.
In the
first
place
we cannot
safely lay
much weight on
Hegel's expressions about the Qualitative Something.
For the
mention of a Qualitative element here seems very casual. It is dropped as soon as it has been made. We hear nothing more The next of it while we remain in the division of Quantum. mention of a Qualitative element comes in the division which succeeds it
comes
Quantum
—namely Quantitative Relation.
in there, it is
introduced quite independently, with no
reference to the passage on p. 257,
way.
And when
and in quite a
different
That passage cannot therefore be considered as of much
importance.
54
CH.
QUANTITY
III.
In the second place, the transition to the next category (Alteration of Quantum) does not start from the identity of Extensive and Intensive Magnitudes, but from the consideration This will, I think, be of Intensive Magnitude taken by itself. evident vehen
we come
follow that Intensive
to consider the transition,
and
it
would
Magnitude must be above Extensive in
the scale of categories, since the possibility of advancing from the Intensive alone implies that the Intensive has absorbed the Extensive.
In the third place, this view
Hegel says reaches
(G. L.
its reality
i.
is
supported by several passages.
Quantum now posited
279, 280) that the notion of
as Intensive Magnitude, and
in its Determinate Being as
it
is
is
in its Notion.
This agrees
with the Encyclopaedia, where he says {Enc. 104) that in Degree the notion of Quantum is explicitly posited. Also there is
not the slightest doubt that, in the Encyclopaedia, Intensive
Quantum
is
higher than Extensive Quantum, since
the third subdivision of Quantity, while Extensive falls in
58.
it falls
in
Quantum
the second.
On
the whole, therefore,
although the evidence
certainly conflicting, I think that the
is
Greater Logic regards
Quantum as higher than Extensive Quantum. We can see why this should be so. .Intensive Quantum emphasises the unity of the Quantum rather than its plurality. Intensive
This carries us In other words, it emphasises the Limit. further away from the indefinite Quantity with which the Intensive Quantum is thus treatment of Quantity began. the more developed idea of the two. The necessity of the transition does not lie in any contradiction in Extensive Quantum which forces us to pass to Intensive. The contradiction would lie in denying that a Quantum which was Extensive was also Intensive. For any Quantum must be Continuous within itself, and Discrete from what is outside it. In virtue of this it is a unity, and so is Intensive.
Thus the previous conclusion that the universe
such that the conception of Extensive to
it,
Quantum
involves that the conception of Intensive
and anything else which conception of Intensive Quantum.
likewise applicable,
is
is
is
applicable
Quantum
is
involved in the
QUANTUM
II.
Hegel's
The
aro-ument.
Extensive
do
then,
titles,
real
advance
Quantum and
between them.
It
to
injustice
the
course
of
his
not from the difference between
is
Quantum
Intensive
to
Extensive
from
rather
is
55
the identity
Quantum
to
And thus the two first subdivisions Quantum. Extensive and Intensive Quantum should have been Extensive Quantum, (6) Intensive Quantum. Thus, for the second time in this chapter, we find that
Intensive of (a)
In each case the defect arose
Hegel's titles are misleading.
from the
titles
taking as correlative two conceptions, of which
argument shows one to be superior to the other. In the first case it was the Continuous and Discrete; in the second It may perhaps be case it was the Extensive and Intensive. his
the case that the confusion arose from following in the titles the usage of mathematics, for which each of these pairs
is
a
pair of two correlatives which are strictly on an equality with
Should this be the true explanation, it would add another to the cases in which the consideration of the one another.
from rendering assistance to the dialectic,
finite sciences, so far
has distorted
We
59.
Of
this
and injured
it,
now come
Hegel says
:
its
cogency.
to the transition to the next category. "
The Quantum
the determination
is
posited as transcended, the indifferent limit, the determination
which
is
equally the negation of
developed in Extensive Magnitude, but
tude which
is
own
itself,
which
determination, not in "
A
Quantum It
Quantum.
is
is
the negation of
is
itself,
it
as having
itself,
but in another Quantum.
what
is
external to
therefore not only possible
beyond any determination of Magnitude, that
It is posited
therefore posited as in absolute Continuity,
in respect of its Quality, with
Other.
Intensive Magni-
it is
cpntradiction, as being the simple determination
relating itself to its
is
the determinate being of this externality, which
constitutes the intrinsic nature of the as its
This discrepancy
itself.
should be altered, but
it is
that
it is
it
it,
with
should go
not only possible
posited as necessarily alter-
The determination of Magnitude continues itself Other being in such a way that it has its being only
able.
Continuity with an Other;
becomes" {G. L.
i.
261.
it
is
its
a limit
Cp. also Enc. 104).
which
is
in its in its
not,
but
56
is
CH.
That is to a Quantum,
QUANTITY
III.
nothing to decide why, when there should be one Quantum, with one Magnitude,
say, there is it
rather than another
Quantum, with another Magnitude. Magni-
tudes can only be fixed by non-quantitative considerations. There is an d priori reason why a triangle has three sides, rather than two or four.
There
are seven apples on this dish,
an empirical reason why there rather than six or eight. But these is
reasons are not to be found in the nature of three or seven, but in the nature of triangles, or of the distribution of apples.
Now
there are no non-quantitative considerations to deter-
mine the Quanta under this category. The only non-quantitative feature that the Quanta have at all is that each One is a separate and unique Quality. And this obviously can give no reason why some of the Ones should be conjoined in a particular Quantum and others left out. This could only be determined by some general quality, shared by some of the Ones, and not by Others. And this is a conception which the dialectic has not yet reached.
But, at all facts
may be
it
Why
?
objected,
should
it
must be ultimate
—
why
should a reason be wanted
not be an ultimate fact
— since some
that these seventeen Ones, for example, should be parts of the same Quantum, and that no others
should be
This would give a definite Quantum. I do not think this objection is valid. If this ?
Quantum
was an ultimate fact, it would imply that there was some difference between any One inside the Quantum and any One outside
it,
of a different nature from any difference which could
occur between any two Ones inside the Quantum, A, inside the Quantum, cannot differ in the same way from B inside it
and from
G
before us,
it is
between
outside
it.
Now, with the category
at present
impossible that there should be such a difference
Each One differs from every other One the same way. Each is a separate numerical One,
differences.
precisely in
and each is a unique Quality. And there is no other way in which any One can differ from another One^. Thus, not only This argument assumes the principle of the Identity of Indiscernibles, it would be invalid if Ones could differ in their relations without differing in their nature. But Hegel habitually assumes the truth of this principle. 1
since
(Cp. Section
6.)
QUANTUM
II.
57
can no reason be given for stopping at one point rather than another, but to stop at one point rather than another would introduce a conception (that of different sorts of differences between Ones) positively incompatible with the present category.
Hegel
60.
Quantum
expresses
has
its
this
by
saying
while
that,
determination in another
each
Quantum \ and
same time continuous with this other Quantum the Ones are just the same on each side of the Limit, and there can be no reason why the Limit should not be put elsewhere, and so add to the Quantum or diminish it. And so we come to stops where the other begins,
it is
at the
—
The Alteration of Quantum.
(c)
Why,
{G. L. 261.)
it
may
be asked, did not this conception
of the necessary variation of Quantity it
Quantum
that
think
I
it
?
Surely
an Extensive Quantum as of an Intensive
as true of
is
come before
essentially alterable.
it
is
is
true that, if
Quantum, without going on
we had stopped
at
Extensive
to Intensive, this conception
of
would have necessarily followed from Extensive Quantum. But the more immediately obvious transition and therefore the one to take first was the transition to And, if Intensive Quantum was to come Intensive Quantum. in at all, the transition to Alteration of Quantum comes better after it, for the necessity of that transition then becomes far Alteration
—
more obvious. was developed
As was in
said
in the passage
quoted above,
Extensive Magnitude, but finds
its
it
determi-
nate being in Intensive Magnitude.
When we plurality of
the
Ones
Quantum
Now
regard a
as a
Quantum
as Extensive,
we regard
the
which is logically prior, and regarded as dependent on the Ones.
as the element
whole
is
we refer the Quantum to the Ones, there is a reason for the Quantum being the size it is, and no other, namely that it includes those Ones, and no others. If we go further, and ask why those Ones and no others should be 1
so long as
first to an would therefore have been he had said here that each Quantum was bounded by another Quantity.
The
transition from the
indefinite Quantity. better
if
Quantum
is
taken by Hegel as being
(Cp. below. Section 61.)
It
58
CH.
included, no
III.
QUANTITY
answer could be given, and the conception of
we regard the Ones the Quantum, the necessity of
Alteration would arise, but so long as as ultimate
in reference
to
Alteration remains in the background.
But with Intensive Quantum
comes at once to the front. For then the unity of the Quantum is the prominent element. And therefore our question why is it this Quantum, and not a larger or smaller one cannot be referred back to the Ones which it contains. And therefore the necessity of Alteration, which is due to the impossibility of answering this question, follows more obviously and naturally from Intensive Quantum. This is what Hegel means when he says {G. L. i. 253) that it
—
—
Quantum through Number (which is a category previous to Intensive Quantum) does not need another Magnitude, because in Number Quantum has its externality,
a determination of a
and its relation to another, inside itself (If this passage seems to deny all tendency to Alteration in the case of an Extensive Quantum, we must remember the explicit assertion on page 261 that the difference in this respect between Extensive and Intensive
is
merely a matter of degree.)
" Degree, therefore,
which
is
simple and in
external Otherbeing no longer in outside
itself,
and
And
relates itself to
it
itself,
again (G. L. itself,
i.
254)
and so has
its
has that Otherbeing
as to its determination."
We
have now come to the end of Extensive and Intensive Quantum, and pass on to the third subdivision of 61.
Quantum, which
is
called
The Quantitative Infinity.
C.
(a)
(G. L. is,
as
it
263.)
The
first
subdivision of Quantitative Infinity,
should be, the restatement of the last subdivision of the
preceding passes
i.
Its Notion.
its
triad.
Limit
The is
first
movement
of the
into a Quantity which
Quantum when is
it
simply defined
Quantum. So far, then, it is only Quantity, and no longer Quantum. And as Quantity is only bounded when it is Quantum, this Quantity has no boundaries at all. Thus it is infinite. Hegel now proceeds to remark on the difference between the Qualitative Infinity, which was one of the triads in Being
as not being that
QUANTUM
II.
5D
Determinate, and that Quantitative Infinity with which
r now
dealing (G. L.
mined
is
i.
That which
264).
we are
Qualitatively deter-
is
not posited as having the other in
itself.
Magnitudes,
on the other hand, are posited as being essentially Alterable as being, in Hegel's somewhat peculiar language, " unequal to themselves and indifferent to themselves."
The
difference
is
one which always arises between lower and
The method
higher categories in Hegel's philosophy. dialectic
of the
changes gradually as the dialectic process advances.
becomes more of a spontaneous advance from category to category, and less of a breaking down, by negative methods, of the resistance of categories which oppose any movement beyond them. It is thus to be expected, since Quantity comes later than Quality in the process, that the finite in Quantity should lead on to the infinite more (Cp. Enc. Ill, 161, 240.)
It
expressly and directly than the finite in Quality does.
The transition to the Infinite Quantitative Progress, which now takes place, is analogous to the transition to the Infinite The Quantum (Cp. above, Section 33.) Qualitative Progress. is
after all continuous with the indefinite
Quantity into which
would not have passed over into it. The passage has only taken place because both terms are Quantities, only separated by a Limit to which it were
it
has passed over.
is
the nature of Quantity to be indifferent.
If
it
on the other side of the Limit
not, it
will also
But the Quantity be composed of Ones,
and thus the argument is again applicable which originally transformed Quantity into Quantum. The Other Side (Jenseits) of the original like
fore,
now itself a Quantum. And thereQuantum, it is essentially subject to
Quantum
the original
is
and will pass the Limit, only thereby to reach a third Quantum, which will be suppressed in its turn, and so alteration,
on {G. L.
265)1.
i.
1 The category of the Notion of Quantitative Infinity, which we have just been considering, corresponds to the category in Quality called Infinity in General, and the Quantitative Infinite Progress corresponds to the Keciprocal Determination of the Finite and Infinite. We saw reason to think (Section 31) that the stage of Infinity in General was a mistake, and that we should have passed, in Quality, direct from Finitude to Reciprocal Determination of the
Finite I
and the
Infinite.
do not, however, think that the Notion of Quantitative Infinity
invalid category.
The argument
is
for the Infinity is quite different in the
an two
60
CH.
We
62.
now come
(b)
(G. L.
note
interesting
\
to
The Quantitative Infinite Progress.
264.
i.
QUANTITY
III.
At
Enc. 104.)
this point
Hegel
inserts
an
on the supposed sublimity of the sort of
which is revealed in such a progress as this. Such an Infinite, he says, can produce nothing but weariness {G. L. i. 268. Enc. 104) ^ This is extremely characteristic of Hegel. When he says that the true Infinite is not the unbounded, but the self-determined, he does not merely change the meaning of a
Infinite
word, but claims for the self-determined is
commonly
attributed to the unbounded.
deep conviction that true greatness
his
and not
much
all
in the
the dignity which It
lies in
is,
perhaps, to
self-limitation,
absence of limitation, that we are to ascribe
of the special reverence which he shows for the ideas
of the Greeks, as well as his low opinion of the Romanticism of his
own age and
We
must not
country.
forget,
however, that Hegel never says that
the False Infinite of an Infinite Series dictory,
though he does say
in the present case there
is
it
is
is
necessarily contra-
worthless and tedious.
But
a contradiction, as there was with
We
had reached the idea of a Quantum, and a Quantum has to be definite. But it can only be definite by having a certain Limit, and by keeping the Infinite Series in Quality.
We
have seen, however, that any Quantum necessarily passes its Limit, and overflows into a fresh Quantum. But it is of It is not, therefore, determined in Magnitude. within
it.
seems to be valid. If a Quantum passes its Limit, the first result of that is, as Hegel states it to be, that it becomes an unlimited Quantity. It is a fresh step in the argument to show that this Quantity must still be a Quantum and have a fresh Limit, and so on indefinitely. Thus the passage to cases,
and here
it
the Infinite Progress in Quantity, unlike the passage to the Infinite Progress in Quality, does require a transition through a stage of absence of Limitation. It was possibly the necessity for such a stage of absence of Limitation in Quantity, which misled Hegel into supposing that it was necessary in Quality as well.
His expression in the Encyclopaedia is "welches Kant als schauderhaft bezeichnet, worin indess das eigentlich Schauderhafte nur die Laugweiligkeit In the first edition of his translation Prof. Wallace happily sein diirfte." " which Kant describes as awful. The only really awful thing renders this about it is the awful wearisomeness." The second edition is, I think, less 1
:
successful.
QUANTUM
II.
the. essence of
Quantum
61
be determined, and the dialectic
to
not permit us to reject the idea of
will
In this case, therefore, a contradiction
To
63.
this
us take the
Quantum
impossible for
it
as enlarged
Will
altogether.
arises.
Let includes the whole
argument an objection might be
Quantity of Ones. is
Quantum
it
till
raised.
not then be determined, since
it
beyond
to increase
this point
?
it
It will not,
indeed, have a Limit, in the technical Hegelian sense, but it
have a fixed Magnitude, and
will
this is all that is wanted.
Hegel does not seem to have considered this point. As I said above (Section 54), he would probably have considered that an infinite Quantity of Ones would have no Number, and no definite Magnitude, and he apparently ignored the possibility But this possibility, as we of the Ones being finite in number. saw above, cannot
justifiably
It does not, however,
be ignored.
remove the contradiction.
And this Quantum
two reasons. In the first place, the category of arose from the fact that Quantity, in virtue of its characteristic we could make of Discreteness, could be divided at any point
for
—
a
by dividing Quantity. Now if which we can get a Quantity of a fixed
Quantum wherever we
the only
way
Magnitude
is
in
liked
by including
all
the Ones, then there will only
be one such fixed Magnitude, and
it will
the total Quantity, but by including
Quantum.
For a Quantum
is
not arise by dividing
it
all.
made by
This
is
not a
dividing the total
Quantity, and has always, therefore, other Quanta beyond
it.
Magnitude of the whole of Quantity, then, would not be a Quantum, and thus the contradiction would still remain that it has been proved that there must be determined Quanta,,
The
fixed
and that no Quantum can be determined. In the second place, a Quantum would not be determined by the fact that it could increase no further. For its instability works both ways. There is no more reason why it should not be smaller than it is, than why it should not be larger than it is. (Hegel only speaks of the indeterminateness in the one direction,
suppose a
but his arguments apply equally to the other.)
Quantum
could contain
Alteration would take place with
though
it
it
all
as
Thus,
the Ones, the process of
much
as with any other,,
could only take place in one direction.
62
CH.
How
64.
way
similar
III.
QUANTITY
the contradiction to be avoided
is
which the same
to that in
is
another Quantum.
nation of any
Quantum
Limit continually
its
the case
changed
is
Quantum
we
if
to the other
If
and that the task fully accept
which
is
outside
•determine itself as against another
fiad that
endless.
is
But
the relation of each
No Quantum
it.
Quantum.
can reciprocally deteruiine one another.
why
we
in itself exclusively, then
alters,
was met in outside any
difficulty
That which is we try to find the determi-
the case of Qualitative Infinity.
Quantum
In a very
?
can
But two Quanta
There
no reason
is
Ones should not change to 8, or 17 Ones to 16, if we take 7 Ones and 17 Ones as isolated facts, each of which must be determined by itself, or not at all. But if we take these 7
•Quanta as related to one another, then there 7
Ones should not become 8
—
for
bear a different relation to the
why
then the
17
Ones.
is
a reason
why
Quantum would And there is a
Ones should not become 16. Thus the Quanta have now some real self-determination, though it is slight A cannot become greater or less, because
corresponding reason
17
;
it
would thereby change
to
B
is
A.
what
is
With
it
is,
i.
279.
not only because
And
to B.
B
is
this partial self-determination (c)
{G. L.
its relation
its relation
B, but because
we
A
reach
The Infinity of Quantum
Enc. 105) by which
is
meant the true
Infinity
of self-determination, as opposed to the False Infinity of an
unending progress. It will
65.
be noticed that there
is
a difference between
the Quantitative Infinite Progress and the earlier Qualitative Infinite Progress.
In Quality the Something finds
only in another Something, which in turn finds a third, and so on.
tut
fresh
Somethings are continually reached
single
is
nature
nature in
The Somethings themselves do not change,
for a final determination.
Progress
its
its
in the vain search
In Quantity, however, the Infinite
not a Progress of an Infinity of Quanta, but of a
Quantum, which
endlessly increases in size as
it
succes-
sively overleaps every Limit.
In Quality no change of anything was possible.
The nature
of reality was not yet sufficiently complex to allow anything
II.
QUANTUM
63
to become different in one respect while remaining the same
same it has utterly vanished. It is impossible, therefore, for a Something to change, and the Infinite Progress can only take place by adding fresh If a thing is not completely the
in others.
Somethings. [
In Quantity, however, change
The gradual
possible.
is
Ones to a Quantum affords a changing element, while the Ones previously in it afford the permanent [^element, without which there can be no change. With this stage of the dialectic the idea of Quality becomes p more prominent again. Not only are the Ones each a separate Quality, as they have been all along, but in each Quantum, addition
of
fresh
a Qualitative nature begins to develope (G. L.
also,
i.
281.
I
most clearly stated in the Encyclopaedia. " That the Quantum in its independent character is external In that externality to itself, is what constitutes its Quality. There is a union it is itself and referred connectively to itself in it of externality, i.e. the Quantitative, and of independency This
JEnc. 105).
