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Sommer-Edition

2004

Francis Herbert BRADLEY [ * ]

The Principle of Logic
Preface to the First Edition

studien/seminarTEXT

THE following work makes no claim to supply any systematic treatment of
Logic
...
I have adopted
the title Principles of Logic, because I thought that my enquiries were mainly
logical, and, for logic at least, must be fundamental
...
Experience has shown that most books an
Logic add little to their subject
...
Both in England and in Germany that subject is in motion
...
And when one works
with the stream a slight effort may bring progress
...

Amongst recent writers I owe most to Lotze, and after him to Sigwart
...
I am under obligations to both Steinthal and Lazarus
...
I
may mention here that I should have owed certain observations to Mr
...
I should be glad
to state my debts in detail, and in this way to express the gratitude I feel, but I
doubt if it is now possible
...
I lay no claim to originality, except that, using the result of others'
labour, I in some respects have made a sensible advance
...
But, though I have not sought out
occasions of difference, it is plain that too much of my book is polemical
...
If the truth is not
needed the reader will not work for it, nor painfully learn it
...
Philosophy
now, as always, is confronted with a mass of inherited prejudice
...

I fear that, to avoid worse misunderstandings, I must say something as to what
is called 'Hegelianism'
...
H
...
I, Oxford University Press, 1963
(first edition: 1883)

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can not say that I have mastered his system, and partly because I could not
accept what seems his main principle, or at least part of that principle
...

As for the 'Hegelian School' which exists in our reviews, I know no one who
has met with it anywhere else
...
We want no system-making or
systems home-grown or imported
...
What we want at
present is to clear the ground, so that English Philosophy, if it rises, may not be
choked by prejudice
...
And this study must come short, if
we neglect those views which, being foreign, seem most unlike our own, and
which are the views of men who, differing from one another, are alike in having
given an attention to the subject which we have not given
...

In conclusion I may be allowed to anticipate two criticisms which will be
passed an my work
...
I would
assure the first that I have stopped where I could, and as soon as I was able
...
This does not mean that, like more gifted writers, I verify in my
own shortcomings the necessary defects of the human reason
...
And an this account at least no lover of metaphysics will judge of
me hardly
...
If I saw further I
should be simpler
...


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Content: The Principles of Logic
VOLUME I
In this Table the numbers in parentheses refer to the sections of each chapter in Books I-III, while in
Essays I-XII the numbers refer to the pages
...
It implies ideas, and these are signs (i-3)
...
Two senses
of "idea" (6-8)
...
Judgment defined (10), and errors refuted
(11-12)
...
Judgment not "association" (i3-i4) ; nor practical influence (r5) ;
nor a mere junction, nor an equation of ideas (i6)
...

Development of judgment
...
Conditions required for origin of judgment (2i-22)
...
Preliminary objections answered (2)
...
This true of
universal and again of both classes of singular judgments (7-8)
...
It refers to present reality (9)
...
This explained and defended (11-14)
...
I
...

Superstition as to names of Individuals (17-18)
...
Synthetic judgments of sense
...
Their true
subject is unique
...
Idea of "this" how used (21-27)
...
These judgments rest an continuity of content (31), and
that upon ideal identity (32-33)
...

Recapitulation (35)
...
Idea of Individual,
what (38-39)
...
Existential judgments (42)
...


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These are hypothetical (44)
...
Hypotheticals can not
be reduced to Categoricals (46-47)
...
Real assertion contained in
Hypothetical Judgments (49-52)
...
Result (56)
...
Presumption against the Singular judgment of Sense (58)
...
It is conditioned (68-70), and conditional (71); and is
even false (72-73)
...
Result (79-80)
...
It is not the
denial of an affirmation (4), nor is it a kind of affirmation (5), nor an affection of the copula
(6)
...
These distinctions here not vital (8), but call for explanation (9-11)
...
Negative Existentials (12)
...
It does not assert the
existence of the contradictory (15)
...
The asserted contrary
not explicit (17)
...
Ambiguity of denial
...

Pages 114-125
Additional Notes (125-127)

CHAPTER IV
THE DISJUNCTIVE JUDGMENT
It is not a mere combination of hypotheticals (1-2)
...

Alternatives are rigidly exclusive
...
What disjunction
presupposes (13)
...

Pages 128-137
Additional Notes (137-140)

CHAPTER V
PRINCIPLES OF IDENTITY, CONTRADICTION, EXCLUDED MIDDLE,
AND DOUBLE NEGATION
Principle of Identity must not be a tautology (1-3)
...

Principle of Contradiction does not explain anything (10)
...
Further
criticism and explanation (15-16)
...
Goes beyond it, how (20-21)
...
Criticism of
mistaken views (23-27)
...
True explanation (29-31)
...

Pages 141-164
Additional Notes (164-167)
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CHAPTER VI
THE QUANTITY OF JUDGMENTS

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Extension and intension (1-2)
...
Law of inverse proportion
of intent to extent, shown to be erroneous (6-10)
...

The first defended against erroneous views (13-21)
...

Universal, particular, and singular; what these mean, and how far they can be real (30-36)
...

Pages 168-193
Additional Notes (193-196)

CHAPTER VII
THE MODALITY OF JUDGMENTS
Modality affects not the form but the content of Judgment (1-3)
...

The Assertorical (6)
...
And so is the Possible (12)
...

Modality does not exist in fact (16)
...
But there must be a real basis for necessity (2o), and for possibility (21-22)
...
The Potential not real (23)
...

Permanent Possibilities ambiguous (25)
...
The Impossible, what (27)
...

Probability
...
Is neither objective nor subjective (33)
...

Expression of the chances by fractions (39-41)
...

Errors refuted
...
It does not in its essence
imply a series (46-50) ; nor a knowledge of the future (51)
...
Superstitious beliefs (58-59)
...

Pages 197-236
Additional Notes (236-242)

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BOOK II - PART I
THE GENERAL NATURE OF INFERENCE
CHAPTER I
SOME CHARACTERISTICS OF REASONING
We are really agreed an three features of inference
...
Examples (4)
...
And the syllogism is not the one type of reasoning
(2)
...
Principle of nota notae (6)
...
Principle of " Related to same are related to each other "
criticized (9-10)
...
Demonstration is seeing in a logical
preparation, and that is an ideal construction (2-4)
...
Superstitions to be
abandoned (6)
...
Examples of syntheses (3)
...
No art of
Reasoning (7)
...
Inadequacy of the syllogism (10)
...
Can you argue from two negative premises?
Yes, but not from two bare denials (3-7)
...

Pages 274-283
Additional Notes (283-284)
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CHAPTER VI
TWO CONDITIONS OF INFERENCE
Result reached (1)
...
Mere likeness not enough
(3)
...

And one premise at least must be universal (10-13)
...
Main ground of objection (8)
...

Errors refuted
...

Similarity alone is left (1g), and this too is a fiction (20-22), which the facts do not require
(23-25)
...
Misunderstandings removed (28-31)
...
An objection answered (33)
...

Note
...

Pages 299-345
Additional Notes (346-347)

CHAPTER II
THE ARGUMENT FROM PARTICULARS TO PARTICULARS
This discussion has been anticipated (1-2)
...
We never argue from particulars as such (6-9), but from an universal
(io-ii)
...
Mr
...

Pages 348-354
Additional Notes (354)

CHAPTER III
THE INDUCTIVE METHODS OF PROOF
The question limited (I-2)
...
Mill´s Canons of Induction
...
But (I) they can not start from fact (7-9)
...
And (III) they all have a logical flaw unless you confine
them to the case in hand (11-I4)
...
H
...
A
...
B
...
It rather
connects differences (8-73)
...
The Indirect Method (I4) can not be reduced to Substitution
(IS-78)
...
Its merits and defects (Ig-22)
...
There are inferences which will not come
under our formula (1-9)
Pages 389-392
Additional Notes (392-393)

CHAPTER II
FRESH SPECIMENS OF INFERENCE
Tests of the existence of inference (1-3)
...
A
...
B
...
C
...
D
...
E
...
F
...
G
...
H
...

Pages 394-423
Additional Notes (423-430)

CHAPTER III
GENERAL CHARACTERISTICS OF INFERENCE
Further character of inference as an ideal experiment (1-4)
...

Not every mental activity is reasoning (11)
...
Result obtained (25)
...
H
...
This not apparent (2), but shown throughout
the whole of our instances (3-7)
...
Difficulties (2-3)
...
This
further explained (7-9)
...
Result (15)
Pages 457-467
Additional Notes (467-469)

CHAPTER VI
THE FINAL ESSENCE OF REASONING
Principles of our processes (1)
...
of one process (2)
...
Analytic and Synthetic
Methods (8-10)
...
Every judgment involves synthesis and analysis
(12-14) ; but itself is not inference (15)
...
Their connection shown in the working of
Reproduction (23-24)
...
Defects of Analysis
and Synthesis (25-28)
...
Recapitulation (33)
...

Pages 470-494
Additional Notes (494-501)

CHAPTER VII
THE BEGINNINGS OF INFERENCE
Gulf between explicit inference and the beginnings of soul-life (1-2)
...
Prevalent errors as to early
intelligence (9-11)
...
H
...
No material reasoning if that means an argument from the particular (4)
...
We can
extract this form (7); but it is not a major premise
...
The form is the principle which
neither proves, nor is proved by, the instances (14-16) ; and this can be stated in a syllogism
(17)
...

Pages 519-532
Additional Notes (533-534)

CHAPTER II
THE CAUSE AND THE BECAUSE
Is the middle the cause (I) ? Meaning of this term must be limited (2)
...
Futile to ask if cause comes
from mere habit (6)
...

But the reason need not be the cause (11)
...
The psychical cause
and the logical ground distinguished (13-14)
...
Result (16)
...
Is reasoning
formally valid? Not if we have interfered to milke the conclusion (3)
...
(8-10), and again in Abstraction (11-15)? The Disjunctive Argument
(16-20)
...
Result (23)
...
Inference seems not
always true of things
...
Three alternatives (3)
...
and fact (4-7)
...
H
...
Even
Dialectic, because discursive, seems unreal (12)
...
To be true of
the presented logic must be true to sense, which is impossible (13-15)
...
Yet why should
truth and reality have exactly the same nature (17)? Anyhow logic can not copy phenomena
...
597-621)
Logic, order in (597)
...

I
...
What Logic must assume (600)
...


Specimens of Inference examined (601-11)
...
Disjunctive
reasoning (602-3)
...
Arithmetic (603-5)
...
Analysis and Abstraction (607-9)
...


III
...
A further failure in all Logic is its abstraction
from the psychical process
...
Each of these
sciences alike is independent but defective (611-13)
...


Is Inference arbitrary and unreal? Objections as to triviality and irrelevancy answered
(614-16)
...


Fallibility of all inference
...
And the
logical types themselves are imperfect (61718)
...
Individuality of inference (618-2o)
...


The Criterion-what
...


ESSAY II
ON JUDGMENT (pp
...
But this is nevertheless to be maintained as true (623)
...

An objection answered (625-6)
...
Hence "judgment" has both a wider and a more restricted sense
...

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An object, so far as aesthetic, is not in this sense true (627-8)
...
An error
here noted (628)
...


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All judgment depends an abstraction from certain conditions of its own being
...
And
judgment abstracts always from its own psychical existence (631-2)
...
And hence, except in
form, every judgment is already an inference (632)
...
On Ground and
Conditions
...
" An objection answered (633-5)
...
Meaning of "unconditionally
...

Every judgment is conditional
...
No such fact as a mere judgment,
though in practice, here as everywhere, the relative must more or less be taken as absolute
(639-40)
...
" The reality is the concrete whole from
which such things are abstractions
...


ESSAY III
ON THE EXTENSIONAL READING OF JUDGMENTS (pp
...
And the
same thing holds (mutat
...
) as to extensional reading (642-3)
...
And
the attempt to read thus all judgments involves torture (643-4)
...


ESSAY IV
UNIQUENESS (pp
...
But the second, even if
perhaps always present, rests in any case an the first
...

Uniqueness is absolute or relative, and holds again either in principle or merely de facto
(648-9)
...
Claims to its possession considered
...
(2) One single quality (65o)
...
A distinction is to be made
here
...

Attempts to defend its claim (a) by external relations, and (b) by an appeal to Designation
(652-3)
...
" Certainly it offers itself as unique, but this claim holds only so long
as we remain at the stage of Feeling (653-4)
...
(5) Finite
Individuals
...
H
...
On the other hand this claim cannot be verified completely in detail
(656-7)
...


ESSAY V
THE "THIS" (pp
...
Like "mine" and "now" it belongs to all
Immediate Experience or Feeling generally (659)
...


ESSAY VI
THE NEGATIVE JUDGMENT (pp
...
But explicitly it need not be so, since Judgment (like Inference) exists at
diverse stages (662-3)
...

Negation is not " nreal" and "subjective" It is "real" always, though we may be unable to see
how in detail it is so
...
The negative is
more real than what is taken as barely positive, since mere Position and bare exclusion alike
are unreal abstractions (666)
...

And no judgment anywhere, whether negative or positive, can really be bare and purposeless
(666-7)
...
668-673)
The Possible–what
...
Its negative aspect
...

The Impossible-what
...
"Nothing" – what (669-71)
...
The Self-contradictory–what
...

How far can the above ideas be used in practice indiscriminately? Their ultimate reality-what
...


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ESSAY VIII
SOME REMARKS ON ABSOLUTE TRUTH AND ON PROBABILITY (pp
...
Absolute and Relative Truth-what
...


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Any objection to absolute truth an the ground of Probability is untenable (675-6)
...
The former assumes a world of such a kind that the possibility
of an "otherwise" is in principle excluded (676-8)
...
In these there is nothing positive which I an my side am
unable to accept (678-9)
...
So far as these differ from my view, is that difference really
anything positive (68o-i)? A compromise through Relativism is not possible (681-2)
...
And that view can explain the existence of these other views (682-4)
...

How can a lower and subordinate truth seem more probable than one admittedly higher? This
difficulty calls for examination (684 5)
...
The above difficulty comes mainly from a false assumption as to the superiority of
the " real world " of events, and from the (perhaps unconscious) misplacing of a higher truth
an this misleading level (686-8)
...


ESSAY IX
A NOTE ON ANALYSIS (pp
...
A mistaken dilemma
...
The "fact of relatedness " must be, and yet is not, dealt
with (692)
...
Terms and relations are abstractions, and they never are given in immediate
experience (693-4)
...


ESSAY X
A NOTE ON IMPLICATION (pp
...
And there is no
Implication (proper) where or so far as the whole is merely immediate (695)
...
And all predication,
being relational, is irrational except so far as conditional
...
No
self-subsistent entity can imply another (695-7)
...
"A before B" is really reciprocal
...

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ESSAY XI
ON THE POSSIBLE AND THE ACTUAL (pp
...
The Possible may be opposed in three senses to the Actual, according as
that is (1) not grounded, or (11) grounded fully, or (111) both at once
...
The above illustrated
...


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The Actual is not the same as what "exists," nor is it always based an Existence (701-2); nor
is such a position saved by an appeal to the distinction between relative and absolute
possibility (702-3)
...

And within the world of Truth the possible is still opposed to the actual (703-5)
...
Designation-what (7o6)
...

Possible and Actual within a grounded whole (707)
...
The world as a mere "And " or
"Together" of independent entities (7o8)
...

Reality and Truth-their true relation stated (711-12)
...
713-728)
There is no such thing as a mere theoretical or mere practical activity (713-14)
...
And all practical activity has a theoretical side and contains
an idea and a judgment (715)
...
(i) In Practice the
judgment has different levels (717)
...
And any appeal here to a lower stage
of experience is useless (719-20)
...
"Practice for practice' sake" as a gospel
...

How far and in what sense is the distinction of "theoretical" and " practical " legitimate and
useful? The answer to this question explained and illustrated (722-4)
...

A summary statement of some views which I advocate an Truth, Activity, and Practice (7258)
...

Philosophy, its limits and genuine task (727-8)
...
After the long discussion of the preceding chapter, we are so familiar
with the general character of judgement that we can afford to deal rapidly
with particular applications
...
In the end it
consists in the declared refusal of that subject[2] to accept an ideal content
...

§2
...
It is not merely as we shall see lower down (§7), that
negation presupposes a positive ground
...
For in affirmative judgement we are able to attribute the content
directly to the real itself
...
But, in negative judgement,[3] this very reference of content to
reality must itself be an idea
...
For, in order to deny, you must have the suggestion of an
affirmative relation
...

It may be said, no doubt, that in affirmative judgement the real subject is
always idealized
...
When we point to a tree
and apply the word 'green', it may be urged that the subject is just as ideal
*

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...
114-127
...


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as when the same object rejects the offered suggestion 'yellow'
...
The tree, in its presented unity with
reality, can accept at once the suggested quality
...

But in the negative judgement where 'yellow' is denied, the positive relation
of 'yellow' to the tree must precede the exclusion of that relation
...
I must always be placed at
that stage of reflection which sometimes I avoid in affirmative judgement
...
And this distinction becomes obvious, if we go back to origins and
consider the early development of each kind
...
But mere
non-coalescence of an idea with perception is a good deal further removed
from negation
...
The exclusion by presented fact of an
idea, which attempted to qualify it, is what denial starts from
...
And in the consciousness of this attempt is implied not only
the suggestion that is made, but the subject to which that suggestion is
offered
...
It is in one sense more ideal, and it comes into existence at a
later stage of the development of the soul
...
But the perception of this truth must not lead us into error
...
For
judgement, as we know, implies belief; and it is not the case that what we
deny we must once have believed
...
What we deny is not the reference of the idea to
actual fact
...

§5
...
If it is a mistake to say
that an affirmative judgement is presupposed in denial, it is no less a
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mistake to hold that the predicate alone is affected, and that negation itself
is a kind of affirmation
...

The exclusion by fact of an approaching quality is a process which calls for
its own special expression
...
In
order to know that A accepts Not-B, must we not already have somehow
learnt that A excludes B? And, if so, we reduce negation to affirmation by
first of all denying, and then asserting that we have denied, – a process
which no doubt is quite legitimate, but is scarcely reduction or
simplification
...
There is a further objection we shall state hereafter (§16) to the use of
Not-B as an independent predicate
...
We may be told that negation 'affects only the
copula'; and it is necessary first to ask what this means
...
If the
copula is not there when I positively say 'Wolf', so also it is absent when I
negatively say 'No wolf'
...
It is perfectly true that these two different sorts of
judgement exist
...
We have thus two kinds of
asserted relation
...
It is
not only true that, as a condition of denial, we must have already a
suggested synthesis, but there is in addition another objection
...
[5] In 'A
is not B' the real fact is a character x belonging to A, and which is
incompatible with B
...
It is not, as we saw, the mere assertion of the
quality of exclusion (Not-B)
...
Every negation must have a ground, and this ground is positive
...

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A is not B because A is such that, if it were B, it would cease to be itself
...
In other words its quality x and B are discrepant
...
[6]
But in negative judgement x is not made explicit
...
We often, if asked, should be unable
to point out and to distinguish this latent hindrance; and in certain cases no
effort we could make would enable us to do this
...
The ground is not
merely unstated but is unknown
...
The distinctions of 'privation' and 'opposition' (Sigwart, 128 foll
...
In a privative judgment
the predicate 'red' would be denied of the subject simply on the ground that
red was not there
...
[7] But
if 'red' were denied on the ground that the subject was coloured green, it
would be the presence of an opposite quality that would exclude, and the
judgment would then be based on positive opposition
...
Chap
...
III §20); but, for our present purpose, it may be called irrelevant
...
If a body is not red because it is uncoloured, then the adding-on
of colour would destroy that body as at present we regard it
...
And, if so, in the end our denial in both cases will start from a
discrepant quality and character
...
It may be answered, no doubt, that the subject, as it is now and as we
now regard it, is not the same thing as the subject itself
...
But I must persist in denying that this
objection is relevant
...
H
...
No subject could repel an offered suggestion simply an
the strength of what it was not
...
We
shall all agree that the nothing which is nothing can not possibly do
anything, or be a reason for aught
...
[9] And, mainly for the sake of
future chapters, it may be well if we attempt here to clear our ideas
...
If a man has
blue eyes, then that quality of blueness is incompatible with the quality
brown
...
In the
first of these (a) within the content of the subject there is empty space
where a quality should be
...
And this void can
not possibly be a literal blank
...
And so the content
itself gets a quality, which, in contrast to the presence of eyes, may be
nothing,[*] but which by itself has a positive character, which serves to
repel the Suggestion of sight
...
But privation can rest an another basis (b)
...
What rejects the predicate is no other determination of the
content itself, but is, so far as that content itself is concerned, an absolute
blank
...
If I say 'A stone
does not feel or see', it may rightly be urged 'Yes, because it is a stone, and
not simply because it is nothing else'
...
Thus, even in the case of a word like
blindness, we should be wrong if we assumed that the blind man is qualified simply by the absence
of sight from the part which should furnish vision
...

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privation we want in the abstract universal
...
Sigwart,
130), if you keep it in abstraction, repels every possible extension of its
character
...
We may invent a stupid reductio ad absurdum:
This isosceles figure is certainly a triangle, but a triangle is certainly not
isosceles, therefore —
...
For, when referred to reality, we know it must be qualified,
though we perhaps can not state its qualification
...
The triangle is
determinate, though we are not able to say how
...
It
is our ignorance, in short, and not the idea, which supports our exclusion of
every Suggestion
...
In a judgment of this kind the base of denial is neither the content of
the subject itself, nor is it that content plus a simple absence; for a simple
absence is nothing at all
...
The universal abstraction, ostensibly
unqualified, is determined by my mental repulsion of qualities
...
My ignorance, or again my wilful abstraction, is never a
bare defect of knowledge
...
And it is by
virtue of relation to this state, which is used as content to qualify the
subject, that the abstraction, or the ignorance, is able to become a subject of
privation
...
VI, 35) ; for it is determined and qualified, not by
any development of the content, but simply by extraneous psychological
relation
...
The various kinds of negative judgement follow closely the varieties
of affirmation
...
H
...
Again what is denied
may be a general connection ('A metal need not be heavier than water')
...
II, §50) which the real excludes
...
We affirm in all alike that the quality of the real excludes an
ideal content that is offered
...

In existential judgement, as we saw before (Chap
...
Let us take such a denial as 'Chimaeras are
non-existent'
...
It is the quality of harbouring chimaeras which is denied of the
nature of things
...
In some cases that view, no doubt, can
be altered, but, so long as we hold it, we are bound to refuse all predicates
it excludes
...

§13
...
[12] We might say that, as such and in its own strict character, it
is simply 'subjective': it does not hold good outside my thinking
...
The process takes place in
the unsubstantial region of ideal experiment
...

The result remains, and is true of the real, but its truth, as we have seen, is
something other than its first appearance
...
The exclusion, as such, can not be ascribed to it, and
hence a variety of exclusions may be based an one single quality
...
But you can
hardly say that the subject is determined by these exclusions as such, unless
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you will maintain that, after the first, the remainder must yield some fresh
piece of knowledge
...
But it seems
better to say that nothing is added by additional exclusions
...
The same quality of the soul
which repels one predicate, repels here all the rest, and the exclusion itself
takes place only in our heads
...
What I mean to say is that the negative judgment will not
express this
...
If you wish to
say this you must transcend the sphere of the negative judgment
...
We must not, if we can help it, introduce into logic the problems of the
'dialectical' view
...
Everything is determined by all
negation; for it is what it is as a member of the whole, and its relation to all
other members is negative
...

If everything thus has its discrepant in itself, then everything in a sense
must be its own discrepancy
...
On this view it would be doubtful if even
the whole is positive; for it is just so far as by position it disperses itself in
its own negation, and begets from its dispersion the opposite extreme
...

If this is so, there would remain no quality which is simply positive; and
logical negation, in another Sense than we haue given it above, becomes
the soul and, we sometimes are inclined to think, the Body of the real
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world
...
Chap
...

A mere logical negation,[15] it is fully admitted by the dialectical method,
need not express a real relation
...
What denial tells us is merely this, that, when we bring the discrepant
up, it is rejected
...
And it
is still more irrelevant to ask the question if the first rejection is merely
coquettish, and will lead in the end to a deeper surrender
...

The dialectical method, in its unmodified form, may be untenable
...
We can hardly say that of those eminent writers who are sure that
logic is the counterpart of things, and have never so much as asked
themselves the question, if the difference and identity, with which logic
operates, are existing relations between actual phenomena
...
To resume, logical negation always contradicts, but never asserts the
existence of the contradictory
...
And, since it can not go
beyond this result, a mere denial of B can never assert that the
contradictory Not-B is real
...

This is the reason why the suggested A-B is contradicted; and it is only
because this something else is true, that the statement A-B is rejected as
false
...
It is merely discrepant, opposite, incompatible
...
In logical negation the denial and the fact can never be the same
...
The contradictory idea, if we take it in a merely negative form, must
be banished from logic
...
H
...
A something that is only not something else,
is a relation that terminates in an impalpable void, a reflection thrown upon
empty space
...
And, if such were
the sense of the dialectical method (as it must be confessed its detractors
have had much cause to suppose),[16] that sense would, strictly speaking,
be nonsense
...
It is impossible
to realize Not-A in thought
...
Nothing at least is empty thought, and that means at least
my thinking emptily
...
And failure is
impossible unless something fails; but Not-A would be impersonal failure
itself
...
It must also be positive
...
The contradictory
idea is the universal idea of the discrepant or contrary
...
It is a general name for any hypothetical discrepant;
but we must never for a moment allow ourselves to think of it as the
collection of discrepants
...
Denial or contradiction is not the same thing as the assertion of the
contrary; but in the end it can rest an nothing else
...
In 'A is not B' the
discrepant ground is wholly unspecified
...
But again it may
perhaps be nothing of the sort
...
The ultimate
real may be the subject which has some quality discrepant with A–B
...
It does not tell us what
quality of the subject excludes the predicate
...
Something there is which repels the
suggestion; and that is all we know
...

§18
...
There is but one Not-B
...
The number of qualities that are discrepant
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or incompatible with A, can not be determined by a general rule
...
In logic the contrary should be simply the discrepant
...
If a technical
distinction can not be called necessary, it is better to have done with it
...
Contradiction is thus a 'subjective' process, which rests on an unnamed
discrepant quality
...
In 'A is not B' you
know indeed what it is you deny, but you do not say what it is you affirm
...
Or again it may be either a general character of A itself which
makes B impossible, or it may be some particular predicate C
...
We know a round square, or an infinite
number, are not in accordance with the nature of things
...

'The King of Utopia died an Tuesday' may be safely contradicted
...
The ground may be that there is no such
place, or it never had a king, or he still is living, or, though he is dead, yet
he died an Monday
...
It is the rejection of an idea, an account of some side of real
fact which is implied but occult
...
We may conclude this chapter by setting before ourselves a useful
rule
...
In a complex universe the predicate you assert is
certain to exclude some other quality, and this you may fairly be taken to
deny
...
Our sober thinkers, our discreet Agnostics, our
diffident admirers of the phenomenal region – I wonder if ever any of them
see how they compromise themselves with that little word 'only'
...
H
...
I hardly know if I am
right in introducing suggestive ideas into simple minds; but yet I must end
with the rule I spoke of
...

ADDITIONAL NOTES
1

This chapter contains some serious errors
...

Bosanquet's account of negation
...
I have briefly
discussed the whole matter in T
...
VI
...
e
...
See Chap
...


3

The abstraction of the idea from all 'reference' is not defensible
...
I,
§ 10
...
It is only where the
perceived world is taken as the one real object, that other worlds are merely
'subjective' (§ 13)
...
But denial can be called more 'reflective', in the sense that
we become aware of it later
...
The beginning of affirmation, we may say, is an object
before me changed ideally so as to lead to action
...
By 'action' (I should add) is not
meant necessarily action which is 'practical'
...
The attempt to identify may at
first appear to us not as an attempt, but simply as the actual exclusion, where not
the actual qualification
...


4

The 'suggested synthesis' (here and lower down) needs correction in the sense of
the foregoing Note
...
It is true that there is a ground and a
Why, and that in the end you can not make this Why explicit
...
On the other hand this
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two-sided negation is at first implicit only and does not appear
...
It is only later and through reflection that, instead of such an object, Ro
(ab), we arrive at a world qualified everywhere by distinctions, at once
connected with and opposed to one another, and R so can write our object as
R
a

b

studien/seminarTEXT

6

I have, here and everywhere, altered 'disparate' where in the original text it was
used wrongly for 'discrepant'
...


7

'Colourless and dark'
...
See Bosanquet K & R, p
...


8

On the subject of Incompatibility the reader is referred to Appearance,
Appendix, Note A, and to Bosanquet's Logic
...
e
...
If you were to drop the assumption made
here, and were to reject the empty space, as being either meaningless or itself
for some known reason excluded, the above exclusion would become sound
...
What an
the other hand damns the privative judgment, as ultimate, is its assumption,
based an mere ignorance, of an empty space in the character of the Universe
...
But see the Notes an Chap
...
E
...
And
cf
...
v
...


10

'Extraneous psychological relation' should be perhaps 'a distinction turned into a
separation and made an exclusion an a mere extraneous psychological ground'
...
See an Chap
...


12

'Fact' here should be 'perceived fact'
...
Cf
...
Otherwise negation is not 'subjective', though it is
more 'reflective' than is affirmation (§ 2)
...
H
...
It is true that the abstract negation
takes no account of the 'how', which therefore, so far, may be the same
...
I, § 52)
...
E
...


14

studien/seminarTEXT

13

'Dialectical view'
...
In our intellectual world
we raust take every element as within a whole, and as qualified by its relations
in that whole, and, further, as qualified by them internally
...
Hence
everything will imply its relations both positive and negative
...
The problem of identity
and diversity is, I agree, not in the end soluble (see Essays, pp
...
And
our whole world, as merely intellectual, is not ultimately real
...
The mere must be emphasized
...


17

'Or joint predicate'
...
See
Appearance, Appendix, Note A
...
Mere
denial, however, rests an abstract exclusion, which, as abstract, is really nothing
...
See an §13
...
vordenker
...
von Goldammer
...
de
This material may be freely copied and reused, provided the author and sources are cited
a printable version may be obtained from webmaster@vordenker
...
After discussing negative and disjunctive judgments, we may deal at
once with the so-called 'Principles' of Identity, Contradiction, and Excluded
Middle; and we will add some remarks an Double Negation
...

If this really means that no difference exists an the two sides of the
judgment, we may dismiss it at once
...
As Hegel tells
us, it sins against the very form of judgment; for, while professing to say
something, it really says nothing
...
For
identity without difference is nothing at all
...
For, otherwise, to
say 'It is the same as itself' would be quite unmeaning
...

§2
...
No one is so foolish in
ordinary life as to try to assert without some difference
...
But such sayings as
these are no tautologies
...
H
...
I, Oxford University Press, 1963 (first edition:
1883), p
...

Note_evgo: The page numbers correspond approximately to the numbers of the original text
...
H
...
It is a mere mistake to
confuse what Kant calls 'analytical judgments'[**] with tautologous
statements
...
But
in every judgment of every kind a synthesis is asserted
...
In 'All bodies are
extended' what we mean to assert is the connection, within the subject
'bodies', of extension with some other property of bodies
...
As against some incompatible suggestion, we might mean to
assert that, after all misapprehension and improper treatment, the extended
is none the less the extended
...
We might mean that, despite their difference as
words, the meaning of 'body' and 'extended' was the same
...
Every judgment is
essentially synthetical
...
The axiom of Identity, if we take it in the sense of a principle of
tautology, is no more than the explicit statement of an error
...
On the
other hand, perhaps something may be gained if a traditional form can get a
meaning which conveys vital truth
...

§4
...
Every connection of elements we affirm, in short
all relations and every difference, holds good only within a whole of
fact
...
And taken in this

**

This is not the sense in which I have used "analytical"
...
48
...
H
...
But this perhaps is
not the meaning which, for logical purposes, it is best to mark specially
...
There remains a most important principle which, whether it be true or
open to criticism, is at least the sine qua non of inference
...
What is this principle? It
runs thus: 'Truth is at all times true', or, 'Once true always true, once false
always false
...
No alteration in space or time, no possible
difference of any event or context, can make truth falsehood
...

So stated the principle is not very clear, but perhaps it will find acceptance
with most readers
...
The real axiom of Identity is this: What is true in
one context is true in another
...

§6
...
For the present it may stand to serve as a test if our previous
discussions (Chap
...
) have been understood
...
And we shall see hereafter that in every inference this result is
assumed as a principle of reasoning, and that we can not argue one step
without it
...
We saw that such judgments as 'I have a toothache', in their sensuous
form, are not really true
...
To make them true we should
have to give the conditions of the toothache, in such a way that the
connection would hold beyond the present case
...
H
...

I know how absurd such a statement sounds
...

That I do not complain of, for it is not our fault
...
I say that 'I have a toothache'
to-day
...
Has my former judgment become therefore
false? The popular view would loudly Protest that it still is true, for I had a
toothache, and the judgment now holds good of the past
...
The judgment is true because answering to fact
...
Can anything be more
inconsistent and absurd? If the change of circumstance and change of day is
not a fresh context which falsifies this truth, why should any change of
context falsify any truth? And if changed conditions make any truth false,
why should not all truth be in perpetual flux, and be true or false with the
fashion of the moment?
§8
...
II, Part I), but
may here anticipate a misunderstanding
...
We ask in
reply, 'Does this difference enter into the content of A? If it does, then A
becomes perceptibly diverse, and we confessedly have left the sphere of
our principle
...
We thus meet the objection by offering a dilemma
...
In the latter case your subject itself is different; in the former
case it is you yourself who have excluded the difference
...
We may be
asked, 'What now has become of the identity ? Has it not disappeared
together with the differences ? For if the different contexts are not allowed
to enter into the subject, how then can we say what is true in one context is
true in another? It will not be true in any context at all'
...
H
...
[4] The identity lies in the judgment, 'S - P is
true everywhere and always'
...
The predicate
attributed to the real belongs to it despite the difference of its diverse
appearances
...
And with this reply we
must here content ourselves
...
When we come to discuss the nature of inference we shall see more
fully the bearing of the principle
...
This is not the
place for metaphysical discussion, or we might be tempted to ask if identity
was not implied in our view of the real
...


The Principle of Contradiction
...
Like the principle of Identity, the principle of Contradiction has been
often misunderstood
...
But, for logical purposes, I think it is easy to
formulate it in a satisfactory way
...
[5] That discrepants or incompatibles or contraries
exist, is the fact it is based on
...
If we
ever forget this, the Law of Contradiction will become a copious source of
illusion
...
If the principle of Contradiction states a fact, it says no more than that
the discrepant is discrepant, that the exclusive, despite all attempts to
persuade it, remains incompatible
...

When you add any quality to any subject, do not treat the subject as if it
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were not altered
...
This is all the meaning it is safe to give to the axiom of
Contradiction; and this meaning, I think, will at once be clear, if we bear in
mind our former discussions
...
Not-A for
example is any and every possible contrary of A (Chap
...

§12
...
We there were told to
produce tautologies, and here we are by certain persons forbidden to
produce anything else
...
This is, once again, the erroneous assertion
of mere abstract identity without any difference
...

But differents and discrepants should never be confused
...
The
discrepant with A can never be found together with A in any possible
subject, or be joined to it in the relation of subject and attribute
...

It is not A generally, but one single relation to A, which it repels
...
Metaphysics, indeed, must ask itself the
question if any further account can be given of incompatibility
...
We might remark that no thing
excludes any other so long as they are able to remain side by side, that
incompatibility begins when you occupy the same area ; and we might be
tempted to conclude that in space would be found the key of our puzzle
...
But in logic we are not called upon to discuss the principle,
but rest upon the fact
...

§13
...
H
...
For if A were not-A, it would be so because
it had some quality contrary to A
...
And again, if A both were
and were not, that would be because the ultimate reality had contrary
qualities
...
Under varieties of detail we find
the same basis, repulsion of discrepants
...
And this does not mean
that if a miracle in psychology were brought about, and the mind did judge
both affirmatively and negatively, both judgments might be true
...
For
denial asserts the positive contrary of affirmation
...

§14
...
And again, if we desire to
glance in passing at the metaphysical side of the matter, we may remind
ourselves that the real is individual, and the individual is harmonious and
self-consistent
...

§15
...
For,
notwithstanding the metaphysics into which we have dipped, I am anxious
to keep logic, so far as is possible, clear of first principles
...
So far is that law (it
has been contended) from being the truth, that in the nature of things
contradiction exists
...

I need hardly say that it is not my intention compendiously to dispose in a
single paragraph of a system which, with all its shortcomings, has been
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worked over as wide an area of experience as any system offered in its
place
...
[9] But I clearly recognize that, if not-A
were taken as a pure negation, no compromise would be possible
...

I will say, in the first place, that whatever is conjoined is therefore ipso
facto shown not to be discrepant
...
And, saying so
much, I feel tempted to retire
...

'Have not we got', I hear the words called after me, have we not got
elements which any one can see negate one another, so that, while one is,
the other can not be; and yet have we not got very many conceptions in
which these discrepants somehow co-exist? It is all very well to say, 'then
not contrary'; but try them, and see if they are not exclusive
...
But I think I shall
hardly be so foolish as to answer, 'These conceptions of yours are merely
phenomenal
...
For without knowing all that would be poured
on my head, I can guess some part of what I should provoke
...
You
profess that your knowledge is only phenomenal, and then you make the
law of Contradiction valid of the Absolute, so that what it excludes you are
able to know is not the Absolute
...
And then, for
the sake of saving from contradiction this wretched ghost of a
Thing-in-itself, you are ready to plunge the whole world of phenomena,
everything you know or can know, into utter confusion
...
It is
plain, then, for which you really care most
...
Your turning of the relative into hard
and fast contraries is just what has brought you to your miserable pass
...
Spencer, or some other great authority-whoever may feel himself

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able to bear them, or unable to understand them-should take them an
himself
...
I might say, 'Your conceptions are partial illusions
...
And the business of philosophy is to purify these ideas, and
never to leave them until, by removal of their contradictions, they are made
quite adequate to the actual fact'
...

And for this end I think that some compromise may perhaps be come to
...
It is a very old and most harmless veteran; and for
myself I should never have the heart to attack it, unless with a view to
astonish common-sense and petrify my enemies
...

What I mean is this
...
A we say is
composed of b and not-b; for, dissecting A, we arrive at these elements,
and, uniting these, we get A once more
...
For, if I felt sure myself that this were true, I know it
is a heresy too painful to be borne
...
We only
have moments which would be incompatible if they really were separate,
but, conjoined together, have been subdued into something within the
character of the whole
...
If, in coming into one, the contraries as
such no longer exist, then where is the contradiction?
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But, I fear, I shall be told that the struggle of negatives is the soul of the
world, and that it is precisely because of their identity that we have their
contradiction
...
It is one side of the world which can not be got rid of, and it is
irreconcileable with the non-existence of discrepants in a single subject
...

I am after all not quite convinced
...
The contrary which the law has got in its head, is the contrary that
entirely kills its opposite, and remains triumphant an the field of battle
...
It is incompatibles fixed as such, it is
discrepants which wholly exclude one another and have no other side, that
the axiom speaks of
...
And if an opponent of
the law reminds me that the existence of these two sides within one element
is just the contradiction, that in the b which is contrary to not-b the
implication of not-b makes it self-contradictory, then I must be allowed to
say in reply that I think my objector has not learnt his lesson
...
We never
have a mere one-sided contrary
...
It
says that they are found,[11] and no sober man could contend that they are
not found
...
H
...

It can hardly be maintained that there are no discrepants, except these
contraries which at the same time imply each other
...

Its claims, if we consider them, are so absurdly feeble, it is itself so weak
and perfectly inoffensive, that it can not quarrel, for it has not a tooth with
which to bite any one
...
Starting from the fact of the
absolute refusal of certain elements to come together, and wholly
dependent upon that fact, so soon as these elements do come together the
axiom ceases forthwith to be applicable
...
So that, if we conclude that the
dialectic of the real would in the end destroy its unity, that has nothing to
do with the axiom of Contradiction
...
And I
think I may venture to hazard the remark, that one must not first take up
from uncritical views certain elements in the form of incompatible
discrepants, and then, because we find they are conjoined, fling out against
the laws of Contradiction and Excluded Middle
...


Principle of Excluded Middle
...
The axiom that every possible judgment must be true or false,[13] we
shall see is based an what may be called a principle
...
We must not imagine that our axiom supplies the
principle of disjunction
...

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§17
...
Its
quality fell (i) within a certain area; and (ii) since that area was a region of
discrepants, the real was determined as one single member
...

Excluded Middle shows all these characteristics
...
And (ii) we assert that,
within this area, the subject is qualified as one single member
...

§18
...
Its dual and contradictory alternative rests an the
existence of contrary opposites
...
Common discrepant disjunction
is the base, and the dual alternative of b and not-b rests entirely upon this
...
Excluded Middle is one kind of disjunction: and we must proceed to
investigate the nature of that kind
...
In 'b or not-b' the common quality asserted of A is that of general
relation to b
...
Affirmation
or denial of b is fiere the area within which A falls
...
And this part of the process
does not call here for any special remark
...
We find however, when we investigate further, a point in which the
axiom of Excluded Middle goes beyond the limits of disjunctive judgment
...
It says, Every real has got a character which determines
it in judgment with reference to every possible predicate
...
H
...
Or, to put the same more generally still, Every
element of the Cosmos possesses a quality, which can determine it logically
in relation to every other element
...
This principle is prior to the actual disjunction
...

The disjunction proceeds from the further result that the relation falls
within a discrepant sphere
...
On the other hand, in its further
development, it is nothing whatever but a case of disjunction, and must
wait for the sphere of discrepant predicates to be given it as a fact
...
The disjunction is completed by the fact that, when any predicate is
suggested, the quality of every element is a ground of either the affirmation
or the denial of the predicate
...

And here the opposition, directed before against the axiom of
Contradiction, must again be confronted
...
We have often to say 'both', and sometimes
'neither'
...
I fully admit that often, when
challenged to reply Yes or No, it is necessary to answer 'Yes and No' or
'Neither'
...
[17] 'Is
motion continuous? Yes or no'
...
In that case perhaps,
instead of saying Yes, I should go so far as to answer No
...

The ground of the objection to the Excluded Middle is, I am bold enough to
think, fallacious
...
One can not be made use of as the positive ground
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an which to build the denial of the other
...
For it is
only the discrepant which destroys its opposite that can serve as the base of
a negative judgment
...
But I fear it is hard altogether an this point to effect a
compromise
...
But, I think, in this case it will carry along with it
enough to ruin what is left behind
...

§23
...

In the first place we must not think it is a formula, by applying which we
can magically conjure elements of knowledge form the unknown deep
...
For, even if we do not make a logical mistake and really
have got contradictory qualities, that is still not the right way to put the
matter
...

We learnt, in our chapter an the Disjunctive judgment, that this judgment
must assume the existence of its subject,[18] though that subject may not
be the grammatical subject
...
Things in themselves either are b or are not b
...
In this case we shall at once be able to say that
Things-in-themselves are not anything at all in the real world, though,
considered as illusions, they no doubt have qualities
...
H
...

§24
...
vii
...
The doctrine that
propositions need neither be true nor yet be false because they may be
senseless, would introduce, I agree, 'a large qualification' into the doctrine
of the Excluded Middle
...
But surely, an the one hand, it is clear
that a proposition which has no meaning is no proposition; and surely
again, an the other hand, it is clear that, if it does mean anything, it is either
true or else false
...

cit
...
Suppose
these terms to be absolutely incompatible, that would hardly bring them
under Excluded Middle, unless we are prepared to formulate the axiom
thus: Whenever predicates are incompatible, then, although there be three
or more possibilities, it is certain that one of these two possibilities must
always be true
...

§25
...
We must remember that, even if
we are able to assert about such a subject as Things-in-themselves, we must
always be an our guard against an error
...
42)
...
We may penetrate so far into hidden mysteries as perhaps to be
privileged solemnly to avouch that Things-in-themselves are not
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three-cornered, nor coloured rose-red, nor pock-marked nor dyspeptic
...
III, pp
...

§26
...
But you
may easily assert it in a shape which would exhibit a parallel falsehood to
those we considered in examining the Principles of Identity and
Contradiction
...

Once again, in conclusion, I must call attention to the positive principle
which underlies the Excluded Middle
...
And we
may give this, if we please, a metaphysical turn, though in doing so we go
beyond the equivalent of the Excluded Middle
...

§27
...
He argues[*] that to say 'A = B or b' must be incorrect
...
And the objection to this is that Bb = o
...

Professor Jevons proceeds to draw from this a general conclusion that any
judgment, in the form 'A = B or b', is necessarily erroneous, and that we
must write instead of it 'A = AB or Ab'
...
It appears to be
right to judge 'A = AB or Ab'
...
74
...

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negative is AbB, and we must conclude that a = AbB
...
So that, after all, we are left with a conclusion which
proves the falsity of our premise
...
It is true that we can not say 'A = B or b', and I will
proceed to show why this must be true
...
Bb
being nothing, what is simply not-Bb will therefore be anything
...
The sphere 'B
or b' is wholly unlimited
...
123)
...
And if you
keep to this sense, then 'A = not-B' could not be true
...
And, so long
as A is something definite, A can not be this
...
94, 95) that Professor Jevons would agree
with this doctrine
...
Taking A as
the genuine subject[23] that lies at the base of the disjunction, then 'a =
nothing' must follow at once, since 'A is B or not-B' does assume and
postulate that A is real
...
What is wrong is not this conclusion or
its premises, but the mistaken idea about the negative which Professor
Jevons has embraced
...
Now I admit that, if 'existence' is used in the widest possible
sense, this argument is tenable
...
And,
since even nothing itself
...

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But, if it does not disappear, and if existence be taken in anything like the
sense of reality, the argument becomes vicious
...
Take for
instance the idea of 'reality' itself
...
I should doubt if the highest term we
arrive at can be said to have an opposite even in thought, although by an
error we are given to think so
...

Devons
...

Prof
...
S
...
'Our cognition, as it stands, is explained
as a mutual negation of the two properties
...
571)
...
Bain in this ominous utterance really means what he
says, but he means quite enough to be on the edge of a precipice
...
Once say with Prof
...


DOUBLE NEGATION [25]
§28
...
To say 'It is false that A is
not B' is equivalent to the positive assertion, 'A is B'
...
For if that were
all, we should be left with nothing
...
And we must not say that negation
presupposes a positive judgment, which is left in possession when the
negative is negated
...
III, § 4) that this positive
judgment is not presupposed
...
H
...
The real reason why denial of denial is affirmation, is merely this
...
I can not say 'It is false that A is not b', unless I already possess the
positive knowledge that A is b
...

§30
...
We know well by this time that, in judging A
not to be b, I presuppose a quality in A which is exclusive of b
...
I now desire to deny my judgment, and need, as before, some quality
as the ground of my new denial
...
Let
this quality z be exclusive of y, and let us see what we have
...
But that leaves us nowhere
...
What, in short, we have
got is our own private impotence to deny 'A is b'; but what we want is an
objective ground for declaring such a denial to be false
...
The only certainty that b is not absent is got by showing that b is
present
...
You could only do that if the number of possibilities with respect to A
had already been limited by a disjunctive judgment
...

Suppose, for instance, we have the judgment that 'Ultimate reality is not
knowable', and we wish to assert that this judgment is false
...

Our proceeding, no doubt, may be perfectly admirable, but all that it gives
us is the right to doubt the original judgment, and to deny the truth of the
basis it stands on
...
We must show ourselves that reality is
knowable
...
[27]
§31
...
It
might be urged that in practice the denial of a judgment can always be
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denied by something other than the judgment itself
...

But each of these can be denied an the ground of the other
...

But this objection would rest an a misunderstanding
...
It is, once more, true that what I have in my mind, and should
assign as my reason, may be either 'it snowed' or again 'it was fine'
...
Whatever you might have had in your mind, no logic
could force you to allow that your denial had committed you to either 'it
snowed' or 'it was fine'
...
The denial asserts
no more than the existence of so much quality as is enough to exclude the
judgment 'it rained'
...
In other words, if you say 'it did not rain', you are at
once committed to a positive 'because', but you are committed to nothing
but an unspecified quality
...
It affirms
merely some contrary, and you get rid of this only by the judgment 'it did
rain'
...
III
...
It is so difficult to
work with double denial that I hardly can expect in the present volume to
have supplied no example of the error I condemn
...
Venn, I think, has certainly done so
...
I have not found occasion in consequence to
alter anything of what I had written, but I should like to use one of his principal
doctrines to exemplify the fallacious use of the negative
...
It is due to myself to
defend my own views against a counter theory from a writer of established and
merited reputation
...
H
...
Venn, if I understand him
rightly, asserts that at all events the negative is not ambiguous (p
...
I will not here
enquire if in other places he is compelled to recognize that the opposite of this
assumption is true
...
'It comes to this therefore that in
respect of what such a proposition affirms it can only be regarded as conditional, but
that in respect of what it denies it may be regarded as absolute' (142)
...
And upon this basis he seems to build his doctrine
...
We
may consider this as settled, and I will not re-discuss the general question
...
Venn's doctrine
...
And he ought to hold that the ambiguity of a judgment at once
disappears, if you deny it and then deny your denial
...

But it is better to show the actual mistake
...
You can not argue from the assertion of
possibility to the assertion of actuality, but you can always argue from the denial of
possibility to the denial of actuality
...
Now the simple
application of this commonplace doctrine is that, if you are given a connection xy and
do not know whether it is possible or actual, at all events, if you deny its possibility,
you may be very sure that you also, and as well, have denied its actuality
...
Venn
unconsciously proceeds upon, and the idea that it could lead to any great result, or to a
better understanding of hypotheticals, seems somewhat strange
...

The affirmative judgment both affirms and denies
...
Venn will not say that what it
affirms is mere possibility, but he quietly assumes that what it denies is impossibility
...
) That is to
say, he tacitly and without any justification assumes that x not-y asserts the
impossibility of xy; and it is solely by denying this arbitrary fixture that the positive
xy becomes unambiguous
...
He would
so have done openly and in an intelligible manner the very thing he has in effect done,
indirectly and most objectionably, by going round through two denials
...

I will put the same thing otherwise
...
Now it is uncertain
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(we may so interpret Mr
...
But, if the negative becomes unambiguous because it is arbitrarily fixed at
its maximum degree (impossibility), then surely it is clear that we thereby, and ipso
facto, are fixing the affirmative at its minimum degree
...
And
the fallacy is simple
...
Suppose not-xy to mean 'xy does not exist', then 'xy is possible' ceases to
deny this : for, although xy may not exist, it still can be possible
...
In short, since not-xy means
either de facto non-existence or else impossibility, it seems absurd to assert that the
denial of this is not ambiguous
...

In conclusion, if we suppose that not-xy is really meant to assert non-existence, that is
to deny the actuality of xy, then the error is palpable
...
But possibility, not affirming existence, of course can not deny non-existence,
and the whole process disappears unless you rapidly shuffle from one term to the
other
...
143)
...
Venn, he tries to make a
passage from bare possibilities to a positive existential judgment
...
But let us see what this way is
...
We have first
a conditional assertion of xy, and this destroys (ii)
...
We have therefore, after this second assertion, but two
possibilities, (i) and (iv)
...

Carrying this process one step further, we see that three such' [i
...
conditional]
'propositions would be requisite to establish unequivocally the existence of any one of
the four classes
...
e
...
that within
the sphere of our discussion everything is both x and y' (p
...

Now, so far as I can see, we may understand this process in two different ways, but an
either understanding the argument is vicious
...
As Mr
...
The
disjunction will rest here an a positive existential proposition, and the inference will
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be quite correct
...
Venn's theory, we can hardly assume
that we have such a disjunction
...
We surely are bound, if we wish to be unambiguous, to take it as denying
...
It asserts that what is
not one of four possibilities is nonexistent (or impossible), but it does not say that
anything exists
...
If you start with
nothing but possibilities, you can not cross from a bare possibility to actual existence
simply an the ground that the other possibilities have sunk into nothingness
...
Venn's
'matter of fact way' of accomplishing this exploit
...
And without this foundation it is thoroughly unsound
...
I will not ask what the conditional proposition could be
...
And this I think is the alternative to which we are brought : we either
completely abandon and throw over our doctrine of the superiority of the negative,
and avowedly start with an affirmation of existence ; or else we prove the existence of
xy through a double denial which assumes the conclusion in order to extract it
...
It is
not worth while to enter into a discussion of this matter
...
'The interesting and unexpected
application' is to me, I confess, not anything beyond a confused example of a well
known doctrine concerning the relations of possibility and existence
...

I need not mention what seem to me other mistakes of much the same kind
...
I am sorry to be forced, both here and again (Chap
...
), to
emphasize my difference with Mr
...
And by way of compensation I should like, if
he will allow me, to offer a suggestion
...
Venn had not such a horror of
'metaphysics' and 'transcendentalism', if he was a little less resolved to be 'matter of
fact', and 'discuss the question entirely an scientific or logical ground', I fancy he
would have come somewhat nearer a solution of the problems it is his merit to have
undertaken
...
He would
certainly have imbibed a dislike for artifices, and such a scruple against entertaining
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commodious fictions, as in itself would have saved him from a succession of serious
logical mistakes
...


On the idea of a term being related to itself see Essays, Index, s
...
Terms
...


3

All truth must abstract, and, so far as it is truth, it can not be made false from the
outside
...
See Appearance and Essays, the Indexes
...
Add 'of which we were speaking'
...
In the next sentence
the 'it' (in 'belongs to it') is to be emphasized
...
Differences are all
incompatible if you attempt simply to identify them
...
Wherever there is conjunction there is
something more in the conjoined whole than mere identity, so that here the whole,
as simply identical, does not attempt to enter into each diversity
...
The aim of
disjunetion (see Chap
...
As to why certain conjunctions are possible in fact,
while others are not so-logic does not enquire
...
On the above see Appearance, Appendix, Note A,
and Bosanquet's Logic, II, Chap
...


6

'The discrepant with A
...
This sentence should run, 'The incompatible
with A is what is not a mere joint predicate with A in any subject, nor is joined to
it
...


7

'For denial
...
In this sentence 'the' should be 'a'
...
'From' is here, I think, rightly used in contradistinction to
'by'
...

And, so far as they exist, the Law of Contradiction holds
...
H
...
How far in other words is the truth of contradiction, as
such, only relative and more or less of an appearance? What, as I understand it,
the Dialectical Method is concerned to deny is merely the absolute, utter and final,
truth of fixed incompatibles
...
v
...

'What I mean, &c'
...
Cf
...


11

studien/seminarTEXT

10

'Stationary contraries'
...
Yes, but as an appearance only
...


12

On the principle of Excluded Middle, while once more referring the reader to
Bosanquet's Logic, I will add a few words
...
So far as the real is otherwise, as being either below
or, again, above the level of disjunction, the principle does not hold
...
we must admit that Excluded Middle, however
necessary and important, is not true absolutely
...
We may an the other hand take
it as containing the abstract form of disjunction
...

The leaving the other members of the whole thus artificially blank, is of course a
grave shortcoming
...
Knowledge is not
advanced by the exhaustiveness of disjunction effected formally through an
artificial duality
...
connection
of its elements
...
For it asserts the actual being of the disjunctive
world
...
(For the connection between
these two ideas see T
...
VIII
...

I may add that the principle that every idea is attributed to Reality, and is therefore
in some sense real, has no special connection with Excluded Middle
...
H
...

'True or false'
...


14

'On this basis'
...
IV, §6
...
See an Chap
...


16

studien/seminarTEXT

13

'Must wait'
...
But it is better, I think, to take Excluded Middle as assuming,
not only connection everywhere throughout the Universe, but also that special
kind of connection which holds between incompatibles
...


17

'False alternative'
...
Again, in the next paragraph, 'fallacious' can not, I think,
stand
...


18

'The existence of its subject' But see an Chap
...


19

Mill´s misuse of 'contradictories' can be excused, I presume, as a mere slip; but
his doctrine of a 'third possibility' seems really something worse
...
Cf
...
II)
...
But, if so, his meaning, I submit, was
expressed by a serious blunder
...


20

'Ground enough for denial'
...


21

'Ground of negation remains the same'
...

See an Chap
...


22

For this section, as also for § 20, see Note 12
...
'Genuine' is to be emphasized
...
IV,
§ 3
...
II, § 2
...
For 'nothing' see Essays, the Index, and T
...
VII
...
H
...
There is a serious mistake in these pages
...
302-7
...
his K & R, pp
...


studien/seminarTEXT

The main point here is this
...
And in denial we have always this
dual alternative
...
I did not see that (as Dr
...
T
...
VI)
...
Having so an 'either-or' – when we
have denied our denial the affirmative only is left
...
Since all denial rests an a positive ground, though this
is not stated in and by the denial, we may hence be led into error
...
We covertly, that is, in 'A (x) is not b' explicate the x, and treat this,
in the form e
...
of c, as being the sole ground of our denial
...
For instance, having decided to wait because the ground
will not be dry, and, having then the denial that there has been rain, I may rush to
the conclusion that the ground will be dry – forgetting snow or dew
...

26

'Positive knowledge'
...
'It is false that the ground
will not be dry' rests an the exclusion, Aowever arrived at, of every state
incompatible with dryness
...
'Or' (we should add) 'in the knowledge that what excludes b does not
belong to A, but is (where it is anything) something merely accidental
...
Dr
...
And how far he ought to have
been aware of this, I have now certainly no wish to discuss
...
vordenker
...
von Goldammer
...
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