BLACKWELL FAMILY
ALICE STONE BLACKWELL

Misellany
Lydia Dame's Class Notes On Logic (schoolmate of Alice Stone Blackwell)
Logic
Lydia M. Dane.
20 Beacon St.
Boston
March 26, 1879.Index1
Logic        
Mar. 26.
Introduction
1 The definition and scope of Logic have been
variously given. Some have limited in to reason 
only and have left out all consideration 
even of the notion and the judgment. The 
later Germans on the other hand have identified
it with metaphysics. The more general
definition however in Logic is the Science 
of the laws of thought.  By the laws of thought
we mean those principles which are implicitly
given in the nature of the mind, and 
which governs all its thinking.  Some limit in
to the laws of discursive thought.  Discursive 
thought is the process whereby from something 
given we proceed to something not given.  
For example suppose A = B, B = C, then A = C is 
something not given but deduced and the 
process is called discursive.  This limitation 
of logic depends for its validity on the place 
where we put the limits of the givers.  If objects 
are viewed as immediately given without any logical 
labor, it is a mistake.  Our study of perception
showed that there is a rash deal of mental
work in the perception of the simplest object. We
define logic therefore as the science of the laws of 
thought and by thought we mean the entire process 
by which the mind works over the given. And Psychology 
teaches that the given is only an indefinite 
raw material of sensation and feeling.  
A glance at our mental life reveals the thought2

3
order and activity as a peculiar one.  Our experience 
gives us things in no constant order, memories, 
thoughts, feelings drift through the mind 
with no definite direction and in no definite relation.  
They resemble mental drift-wood and are borne 
about by the currents of association.  The mind however 
feels that this order is not the true one; these 
experiences have no inner connection and might 
as well have any other order, but the mind assumes 
that there is an order of thought to 
which this chaos is seducible, and this order 
is a fixed and rational one.  This process of 
rationalizing irrational experience is what we 
mean by thinking; and its aim is to bring together 
things which belong together in a rational system, 
and to separate those things which have 
no inner connection.

II.  Our definition raises the question whether the 
thought process is a peculiar one with laws of 
its own, or whether it is only a special manifestation 
of the general laws of association.  The latter 
view is held by the Empiricists who claim that 
thinking comes necessarily from sensation.  Mar 27 In 
any sentient being therefore furnished with the laws of 
Association the result would be thought and reason 
and hence there is no need to posit any specific activity to 
account for the facts.  We must therefore vindicate the 
claim that thinking is something more than associations.
  
In the first place the sensations and feelings 
which the theory assumes themselves involve discriminations 
and judgement before they can become objects forthe mind, so that association itself depends on a logical
activity. But if we make the theory a present of sensation
and failing. thinking is not yet reached. We do
not deny that association may mimic thought, e.g.
a dog who has been beaten has connected in his
experience the sight of a raised stick with painful
results, and possibly he has made the further 
experience that when he was away the pain eases.
Now it is possible that the laws of association
would always present these facts together in 
experience so that any sight of the raised stick
and the rest should follow. This is the case with a
last part of human action: the mental mechanism
acts upon us and often for better than we
could do by any reflection. The result in such a
case is an appearance of reason without any real 
thought process. Whether brutes truly reason no one
knows but there is no need of assuming any thing
beyond association to account for this conduct.
In such a case the fact will be that various 
experiences come together but a man in the same
circumstances would judge differently if he
thought at all. First: he would attribute to the
stick a substantive existence. Second: he would
explain the pain by saying that the stick caused it.
Now in this simple judgement there is an excess
over any possible action of association.  First
the affirmations of External Existence involving
the distinction of Substance and attribute. Second 
the affirmation of causality. The distinction
thus made may be declared mistaken, but that they
are universally mad is undoubted. There is then, over6
Mill holds that causality was merely the idea of antecedence
and sequence.

7. and above any [?] of association a distinct thought
process. Otherwise expressed, association leaves
as on the sentient plane where possibility the 
lower animals remain. To rise to the thought
plane, the sentient experience must be rationalized.
This is done by bringing into it the distinction
of substance, attribute, quantity and quality, cause
and effect, and the other categories.
The same facts appear if we reverse the process and
suppose associations to be all. The utmost which
association could do would be to collect experiences
into little clumps without any inner
dynamics connection. It would further deny
the law of identity entirely; an object reappearing
the second time could never be affirmed
as the same object, but only as similar. For similarity
is all that is given in the experience. That
there has been a continuous identity of existence
between the times of experience is purely a mental
postulate whose validity the Associationalist. 
cannot admit without opening a trap door
for his own system and which he cannot deny
without crucifying common sense. He may take
the latter method and deny identity and inner connection
but no one will question that rightly or 
wrongly the mind does affirm. The universal common
sense as expressed in language has created
nouns, adjectives and verbs expressing thereby the
universal relations of substance and attributes, cause 
and effect, etc. The mind there is not content with
the mere association of experience has sense to rationalize
experience by building it into a thought system.
8

9
The Associationalist cannot claim that this work is
no done; he can only claim that it is mistaken.
Finally where we appeal to consciousness, thinking
does not present itself as a drifting series of association,
with which our wills have nothing to
do, but as an eminently active process, nor do the
conclusions we reach in thinking appear to be thrust
into the mind by an associational process, but
are reached by the mind's own insight. They are
not accidents but are necessary and universal.
We do not reach truth by association but rather
have to correct association by reason. So far
from associations being the source of rationality
it is rather the great source of error; the customary
is mistaken for the clean and habits of
thinking arrayed as love of thought. We escape
these errors only by falling back on the naked insight
of reason itself. We reject there the Associational
doctrine of reason first: because
association itself rests on a logical activity,
second, because the mental work done is not
explained by association; third: because consciousness
gives no support to the view and fourth: because
 association is the cause of error rather
than truth.

III
Mar. 28. Infinite debate has deluged the question whether
logic is formal or not. Some claim that it is a
science of pure form without any regard to content.
Just as mathematics is the science of pure
quantity without regard to the question whether
any corresponding realities exist. Others hold that10

Judgment is merely the declaration of agreement or disagreement.

11
form without matter is impossible, they claim that
the illustration from mathematics is irrelevant
because in that case the relations of quantity which
are the matter of the science are constantly
kept in mind. They hold too that in all sane thought
whenever we think we ought to think something, and 
that every judgment that declares the agreement
or disagreement of two conceptions is impossible
without implicit reference to the matter as well
as the form of judgment. This does not necessarily
imply the existence of extra mental objects, but
it does imply that judgment is impossible without
taking the mental content as well as the form into
account.

IV
Between these views we decide as follows: Logic concerns
itself only with ideas and their relation
and formation. It is then no concern of Logic
whatever whether there be any external things
corresponding to our ideas and in corresponding
relations. Logic would be unchanged if we
became Idealists or even nihilists. It is as valid
for doubt or for belief. Even the doubter appeals
to Logic to justify his doubt. The decision of
these questions belongs to the theory of knowledge,
but our ideas though subjective have a  definite
content, and cannot be considered apart from it.
An idea without content is nothing. Hence, the notion
and the judgment must always have some
content and cannot be separate from it. In no
case can we consider a judgment apart from content
except where the conjoined notions are represented.12

13
by arbitrary symbols, as x and y. Bet even then
the content of quantity remains and the judgment
becomes purely quantitative. That even
in the most formal of logical judgments the content
is implicitly considered, appears from the process
of conversion, e.g. "a horse is a vertebrate" is converted
to "some vertebrate is a horse", but only
"some" instead of "all" vertebrate is horse, unless
the mutual extension and hence the content of the
two notions be borne in mind? Mar. 31. The doctrine
of conversion is based on implicit reference
to the content as well as the form; this much only
can be allowed to the Formalist: the notion the
judgment and the inference represent the three
great factors in all reasoning and though in
any fruitful thinking on every subject, the content
and limits of the notion must be borne
in mind, it is still possible for us to make
a general consideration of these factors which
shall hold for all contents. We may then outline
the formation and function of the notion, we
may describe the several kinds of judgment
and inference, and the results will be valid
for every content which fulfils the necessary
condition. In this sense only is a formal logic
possible or valuable. In all actual reasoning
however, the peculiar character of the subject
matter will introduce modifications into the
general forms. Formal Logic is also called pure 
Logic and sometimes universal Logic as indicating
that its principles apply to all thinking on
whatever subjects.14
Cognition is essentially a discriminating activity.
The mental life is dependent upon change.
The range of discriminating power determines the perceiving 
power absolutely, that is the reason why we
cannot hear above a certain point or below
another certain point; we simply can't discriminate
between the activity thus going on and perfect
rest.

15
Chapter 1
The Laws of Thought
I  All cognition is of something; all thought is
about something. Here "something" is taken in
its most general sense, meaning any object
of thought, whether things, quality, act, relation etc. It means in short a "think" and not 
a thing in the external sense. Hence the primal
act of the mind is to transform its state
into thought objects; it may be called the objectification
of our states. We are not to suppose 
however that this primal act is fully completed
before any subsequent action. On the contrary
the process continues into the mature life
of the individual and of the race. In a developed
society the individual finds a great part of
his work done for him in language. Language
is itself an incarnation of the categories, and
each word represents a mental object which the
common mind has cut out of the master of
sentiency, and established with a definite content
in the world of reason. The individual
has not to discover these objects but only to
verify them in his own experience.  April 1.
All cognition depends on discrimination. Nothing,
not even the simplest sensation can become an
object for the mind except by being discriminated
from the mind and from its mental surroundings.
The range of knowledge depends entirely
on the range of the discriminating power. When

16

17
a sensation on affection of any kind becomes indistinguishable,
it ceases to be an object for
us. There must indeed be a certain positive
content in every object of thought in order to
make discrimination possible, but it becomes
an object only through distinctions, hence thought
must be essentially a differentiating activity; but
distinction is impossible unless the things distinguished
have a constant content. If the
content of a thought were flowing so that it
had no fixed import, no distinction and
hence no mental life would be possible.
Hence the first law of thought is A=A on the law
of identity. This merely says that every mental object
of whatever kind must have a fixed
meaning whereby it is distinguishable from
every other; but this law is not picked up at
random but flows necessarily from the nature
of knowledge; it is in the strictest sense a law of thought. It is important always
to keep in mind that Logic originally deals with
thoughts and not with things; hence its laws are
laws of thought, whether they be also laws of
things is a subject for special investigation.
We must then keep to the logical meaning of 
the law and not swell it out into metaphysics.
The law of contradictions as it is called, according
to which A=A and not non A is
not a separate law but only the opposite side
of the law of identity; the affirmation and the 18

19
negative use the opposite sides of the same act
whereby an object is posited. If A=A it follows
that it cannot equal non A.
This law has been the subject of much attack
from the beginning. The Empiricist denies
that nouns are but short words to describe
complex experiences and he holds that this law
is not a law of thought but only a short hand
expression of experience. For example the sentence
"John has crossed the river" means only that
two sets of appearances called "John" and "river"
have changed their space relations  Unfortunately
he teaches that it's the same set before and after
the change; that is, he posits John=John
and river=river and ascribes a continuous
identity of existence to both.
Other Empiricists have claimed that the
law is learned from experience. Thus from the
fact that we experience A at different times and
find it equal to itself we conclude A=A. But
the odd thing here is that the several A's are
assumed to be the same A by nature of the law
of identity and thus the questions is begged. The
law cannot have been learned from experienced therefore
1st, because its the necessary condition of experience
2d, because any attempt to prove it assumes it.
It has been [????ghtly] denied, especially
by the [??getian] that the law is a law of thought.
They insist that is contradicts the law of causation
and makes motion and change impossible.
If it were so on their own principle these would
be no reason for denying the law as they assume
that contradictions can co-exist. Hence that this
law contradicts some other law, if it were the
case, should be an additional reason for believing
it. Thus in denying the law they affirm
it. This claim rests on two misapprehensions.
First, the law does not forbid us to observe change,
motion etc,. it only forbids us to think of change
as anything but change, or motion as anything
but motion. These motions are given in experience
and the law forbids our confounding these with
anything else. The other mistake is in taking opposition
in different relations for a contradiction
in the same relation; for example, because there is
attraction and repulsion in nature, on liberty and
laws in morals, freedom and necessity in the
universe they will have it that reality is a
series of contradictions, and that contradiction
is a necessity of being. This is ghastly sophistry.
Until a four-sided triangle or a wooden iron
can be conceived, the law of identity and contradiction
will stand.
April 2. The law of identity is not the only law of
thought. In itself it contains on motion; it says merely
that A=A and must not be confounded with
non A. But this law taken alone would bring thought
to a stand-still; every object would be single and
isolated. It is necessary therefore that some further
law be discovered which shall bring our thoughts into
relation and secure an advance. This law is that of the
sufficient reason. This law is not to be confounded
with that of causation. The latter is purelya metaphysical law; it is the objective form of
this law of the sufficient reason. The content of this
second law has never been clearly stated. It is often
formulated thus: seek for everything a reason why
it is, as it is and not otherwise, but it properly
means that no object is independent in thought. It
affirms therefore, the relatedness of all thought-objects,
or the possibility of uniting two conceptions
to form a third. All affirmative judgments depend
on this. Every such judgment is the union
of two notions in one, and the law of identity alone
does not account for this. If then we write A=A
as the formula of identity, we may write A+B=C
as the formula of the sufficient reason. The meaning
of the + sign is any kind of relation. This law
of thought first enables us to pass from the isolated
objects of identity and gather our thoughts
into order and system. The law of identity may
be called the negative law of thinking; the other
is the positive law. It has been
largely denied that the sufficient reason is a 
law of formal thought. This arises largely from
confounding it with the law of causation, but it
is plain that without this relation and inter-dependence
of thought there could be no thinking; not
even in mathematics can the law of identity be
viewed as the only one; in itself it would only say
that A+B=A+B, or that [?]+√=[?]+√. The possibility
of gathering Arithmetical or Geometrical quantities
into a single one depends altogether upon the
peculiar nature of space and numbers. If it were
impossible to express the same content in a variety24

25
of ways by a sum, or difference, or power, or resultant, 
or components these could be no Mathematics.
There is however one difference
between these two laws: both on equally necessary
to thought but they are not equally necessary
in thought. The first could not but exist;
the second is not strictly necessary; that is, it is
conceivable that the content of each thought
should be in commensurable with that of every
other, as much so as sweet and triangular,
on colored and criminal. In that case no system
would be possible and the mind would be
lost in the multiplicity of its objects. That this is
not so is to be viewed as a happy circumstance
in the nature of the thinkable. At the same time
we regard both laws as a priori .26
(If all knowledge depend upon distinction then distinction 
is the most fundamental condition of 
knowledge; then since the categories  are the norms 
of distinction, why aren't they more important
 than the laws of thought?)


27
  Chapter II
The Categories 

April 8.
I. The two principles established in the proceeding 
chapter recall laws of thought, because they control 
all our thinking on every subject.  No other 
principles have this universality, and all other 
alleged laws of though are either false or
are conclusions from these two. For example, the
so called "law of the excluded middle" can be
made universal when the same predicate is
positively and negatively applied; as everything 
is either A or non-A,, but in this case it is
plainly only the law of identity and contradiction. 
But these laws in themselves are not
sufficient for knowledge. We have seen that
knowledge depends on distinction and distinction 
implies points on norms of distinction.
If one thing be different from another or be 
related to another, there must be some point
in which it differs or is related. If it differs
in no point it would be identical, as coincident.
Some social figures. This character of
knowledge is generally recognized even by the Empiricists; 
for example, Prof. Bain makes the powers 
employed in the acquisitions of knowledge,
three: -  1 The power of discrimination. 2. The
 power of detecting identity. 3 The power of retention. 
The only reason for distinguishing the first
and second is that we may attend more to  difference 
than to likeness, and conversely. But the28
Geschichete der Kategorienlehre - Trendelenburg

29
powers are identical. But he does not go on to
evolve what is implied in this power of discrimination. 
In order then, to knowledge the
mind must have in it norms of distinction
or general forms of relation as the necessary
condition of knowing. These norms we call categories 
of thought.
Although the categories are subsequent to the
laws of thought, it is not a sequence of time
but of logic. We are not to think of these sensual 
acts as following one another. But only
as logically successive. They are all given in
one synthetic act and appear as separate only 
in analysis.

II.  The categories have been recognized since the
time of Aristotle; he enumerated ten and regarded 
them as the universal predicates of
all reality. The Hegelians agree with Aristotle
not in the number of the categories but in
giving them an ontological meaning. They
are not only determinations of thought but
are also predicates of being. Kant first recognized 
their formal and subjective character
and them four classes with three members
under each class. The classes are--
Quantity, Quality, Relation, Modality.
One or more of these categories applied to every
object of thought and it becomes such an
object only as it is arranged.
To the ontological view of Aristotle and
Hegel we object that the categories must be30

31

found in us before they can be found in
things. They cannot be deduced from a general
notion of being, for that notion is Empty.
Definite being is the only reality, but before
definite being can be conceived the categories
must be applied. It is impregnable, first that
our conceptions of things are mental products,
and second that these mental products become
objects for us only through distinction.
The categories must thru lie originally in the
nature of the Soul as the implicit norms of
its action; this does not hinder that they
may also have a meaning for things, but
primarily they are in the mind. At first
sight this will seem fine-[spun?], but we must
bear in mind what was said in Psychology
namely that the Existence of a thing as this or
that is not a sufficient ground for our 
perception of it  as this or that. If then the
categories were in things we could never
know it unless they acted upon the mind and
unless the mind had a highly complex qualitative
nature so that it should react by
producing a complex mental product, that
is once more the categories must be in the
mind before they can be found in things. In
addition we found it possible to regard the
world of appearances as purely a mental 
product, on as the form which the mind gives
to reality but which exists only in the mind, in
that case it would be quite impossible to speak
of the inner life as a copy of the external fact.32
It is an entirely self-consistent theory that the world
of appearances exists only as it appears in our minds;
that the world of appearances has no more real
existence than the world of light and sound.
Knowledge is bounded by the power of discrimination.
It is altogether possible that the ether itself sings and
if our ears were more finely attuned one should
shear the harmony of the spheres etc.
Whatever we think about has being in a logical sense.

33
no more can we hold with the Hegelains that
they are the most fundamental notions of
the mind. They may become such by a later 
process of abstraction and generalization 
just as we form other general notions, 
but primarily they cannot be this,
because a notion as such implies conscious
knowledge, whereas consciousness itself depends
on the application of the categories. If they were Apr 9.
at bottom notions rather than norms they ought to
be present in all consciousness which is not the
case. The same is true for the claim that they are
regulative ideas; an idea of which we are unconscious
is none; they do indeed regulate, but not as ideas, but
as norms of action. Nor are they general notions
though they give rise to such. All these are derived 
meanings of the categories, originally they
are mental principles given in the nature of
the mind itself, and on which all consciousness,
and hence all knowing depends.
Our objection to the Kantian view is that it
regards them too externally and not as if they
were essential to all experience of whatever kind.
Kant speaks of them as forms of the understanding 
into which the sense-experience is ordered,
whereas in Truth sense experience is impossible
without the categories.
III.    We have time to point out only a few of the
categories and their importance in knowledge.
Aristotle from an analysis of the judgment concluded 
as subject and predicate are necessary34

35
elements of every judgment, that substance and
attribute, or thing and property are the two
fundamental distinctions in the thinkable. In
this he has been largely followed by logicians
and substance and quality have been set up
as the bottom distinctions of Logic. To escape the
difficulty that most subjects are not substantial 
he distinguished two kinds of being; these
he called first and second existences corresponding 
to things and mental notions. Things
on first existences can only be subjects. Second existences 
can be both subject and predicate.
April 10. We object to making substance and attribute
the fundamental distinction of the thinkable, because 
of its metaphysical signification. The
relation between most subjects and predicates
is by no means that of substance and attribute.
For example, Knowledge is power -- there is no relation 
of substance and attribute here, and there
never is except where speaking of real things,
whereas the chief part of our thinking relates
only to mental objects. We speak in Logic of
space, time, change, events etc., all of which are
subjects, but none of which are things, The logical
division of the thinkable is into subject and predicate 
where subject denotes any mental object whatever
of which predicates are possible. All mental objects 
may be regarded either as subject or predicate 
and some may be both in different relations. 
The subject can be conceived only in its attributes
and attributes can be concived only
in connection with the subject. Subject notions
36

37
corresponds to norms in language, and predicate
notions with finite verbs and adjectives.

IV The Empiricist regards this affirmation of subject 
with dependent predicates as empty. To him
a subject is only a collection of qualities which
have been found in experience. Instead then
of making predicates depend on subjects the
converse is more nearly true as the subject
is only the sum of the predicates. This objection
is really ontological; it can only mean that there
is no warrant for doing more. No one can question 
that as a matter of fact the mind regards things
as more than a summation of predicates; they contain 
the reason for the several predicates and for
their union. The Empiricist claims to be a disciple 
of experience, but he is never content with
observing what the mind does form his anxiety 
to tell wheat the mind should do. At bottom 
Empiricism is a king of a priori scholasticism.
     In any case if this objection were sound, all
reasoning would be at an end; apart from
metaphysics reasoning depends on the universal
postulate that some predicates belong together. Experience 
gives things in chance connections, on
everything in a heap. If the function of all things
were of this sort, there would be no order in
the mind and no reason. The possibility of reasoning 
first arises when we assume that in addition 
to this chaotic and chance sequence
there are sets of predicates which belong together38
All things are known originally as a confused
synthesis and the factors of it are shaken out
only by analysis. We don't as the Empiricist assents
begin with qualities which we build up into subjects.

39
so that from the presence of one we may conclude 
to all the rest. This conclusion from the
given to the not given depends entirely on this
postulate. Now a subject is not merely a co-existent 
group of predicates, but such a group
with an inner logical connection. That this connection 
should not exist is conceivable, but it
there is to be a thought life, it is absolutely
necessary; to deny their connection and still
continue to reason is possible only to an Empiricist. 
The only function of experience is to
teach us what notions do belong together, but it
does not give rise to the general postulate. Experience 
serves to separate the essential from the
accidental

Apr. 11 No satisfactory table of the categories has even been drawn
up; while all have agreed in the main every list has
had minor differences. Various deductions also have
been given. Aristotle seems to have had no principle, but
picked them up at random. Kant deduced them from
an analysis of the forms of judgment. Hegel deduced
them from the necessary rule of thought. Ulrici 
deduces them as necessary to thought itself. This 
deduction seems to us the most satisfactory.
Whatever is necessary to thought as thought may
be viewed as a category.
In distinguishing things each must be distinguished
as one, hence the primal category is unity as individuality. 
This is but the reappearance as a category 
of the first law of thought. The successive
application of this in the unity of self-conscious40


41
ness, gives plurality on number. Co-existent unities 
must be thought as mutually exclusive;
this gives us the category of space. Non-coexistent 
unities must be thought as segment;
this gives us the category of time. Time and
space are the forms under which we intuite
plurality conceived as segment or co-existent.
Time and space are not categories of all thinking 
but of intuition. It is impossible to intuite
plurality except under one of these forms.

Apr. 14 From the nature of the judgment it
follows that quality is also a necessary category, 
for everything must be of some kind.
The subject contains the thing, the predicate expresses 
the kind. That which has no quality is
nothing, both in thought and in fact. But
while quality is a necessary category, it is no
necessary that things should be differentiated
according to category; they might have been
all of a kind; in that case there would have
been a stupid sameness -- variety is due to
the fact that objects are differentiated under
this category.
The notation of quantity is equally necessary.
That which is without quantity either as extent
or intensity or duration is also nothing. In one
of these three forms quantity applies to everything; 
but quantity must be measured and the
measure of quantity is number. The unit of
measure is always relative; space, time, power
all advise of measure and are grasped only42


43
through it. In the case of mental affections
owing to the lack of a definite unit, it is commonly 
possible to affirm only a measure
of greater or less, and these ideas enter into 
all our thinking.
The relation of quantity and quality is
most intimate; neither could exist without
the other. A quality without intensity or duration 
would be nothing. A quantity without 
quality would also be nothing. It has
been a favorite aim with Physicists to reduce
differences of quality to differences of quantity
by different groupings of the elements they
hope to explain all the differences in these
qualities. If this were possible there would
be all the more need to posit a highly
complex, qualitative nature in the soul, for
a soul would be the source of qualitative
differences.
Here we deal with quantity only as a category; 
quantity as an object, pure and simple
belongs to mathematics.
VII Again, if thought rests of distinction and
comparison, there likeness and unlikeness are
also fundamental categories. All classification 
depends on the former, all distinction
on the latter. We repeat once more that the
existence of objects as similar is never a
sufficient reason for their being experienced
as such. In order to be so perceived the mind
must be able to grasp both in one act and in44


45
passing from one to the other, be conscious
of the identity of its state. To experience unlikeness 
it must be conscious of the change and
its direction in passing from one to the
other. The possibility of experiencing likeness
or unlikeness rests entirely upon this postulate.
VIII       With these few limits on the nature and
function of the categories we leave them. If
it be asked are all the categories equally 
necessary to thought, we answer no -- that
is there could be some mental life without 
some of the categories. Without the law
of Identity there could be no perception and
no sensation, to say nothing of thought.
Without the laws of the Sufficient Reason
there might possibly be a recognition of individual 
and unrelated sensations though
this is doubtful. But certainly there could 
be no distinction between subject and predicate, 
and hence no thinking. To question why
the spring of all science could never arise
and one thing would never be a reason
for expecting an affirmation another. A more
pronounced gradation is observable among
the categories. The categories of subject and
predicate, and quantity would suffice for 
quantitative reasoning, and there is no contradiction 
in supposing that the thought should
have stopped on that plane. That differences of
quality should also exist is not a necessity of46
Common nouns are a sort of algebra to thought
For categories see Ulrici's Compendium of Logic.
Synthesis is earlier than analysis- we form complex 
notions by putting together simple ones and
then afterwards we may apply analysis to find
from the complex notions the simple ones composing
them.
Experiments are only the makeshifts of mental feebleness. 
Astronomy therefore is Analytical. It's all a
priori and needs no experiments.



47
thought, but they are necessary if there is to be any
variety and beauty in the mental life. That these
distinctions of quality again should not be
absolute but should admit of classification 
is also no necessity of thought in general
but without this fact the mind would be lost
in the multitude of individual impressions
and objects without any possibility of overseeing 
the whole. April 15. No one thing is exactly
like any other but there are great lines of likeness
and among the like there are gradations of a 
common element which enables the mind to fuse
the many into one. We repeat, it would contradict 
no law of thought if this were not
the case or if impressions and objects were
incommensurable. That it is not so is a fact
of the utmost importance, but of which we
can give only a theological explanation. We
do not then regard the categories as on the same
level of thought, necessity, but rather as forming
a graded series, the upper members of which
are indeed necessary to lift our life from a
quantitative monotone, but which can only be
viewed as the product of purpose.
Thus far we have dealt only with the mental
mechanism; we see the mind ordering its objects
into definite form according to certain laws and
thus building up a thought world. We pass now
from the mechanism to the product. Reasoning
we may regard as an analytic or synthetic
process according to our standpoint. A judgment48
The first notions are the categories.

49
is the union of two notions into one, and the inference 
is the union of two judgments to form a
third. Here the process is synthetic, but we
may suppose the notion given, and then the
judgment is only an analysis of its content,
and the inference is an analysis of the premises. 
Hence we may with equal propriety define 
reasoning as the analysis of notions or
as the synthesis of notions. We may regard
the synthetic process as thought militant and
the analytic as thought triumphant. The analytic 
form is the ideal of reasoning, but one to
which it rarely attains except in the case of
mathematics. 
But there can be no question that the first
process is synthetic. There could be no analysis
if there had been no previous synthesis. From neglect 
of this fact some have claimed the the judgment 
precedes the notion but it is evident that
there can be no judgment without notions, for
a judgment is either the analysis of a given notion 
into its elements or it is the synthesis of
two notions into one. The mistake here lies in
taking some of the highly complex notions as of
natural history which are reached only by long
experience and reasoning as types of all notions,
whereas notions are of all degrees of complexity
from the simple and basal one of thing up to such
complex and derived ones as nature, life the State 
the Church etc. On the other hand it must be
allowed that the notions in primitive judgments
are such rather in form and function than in fact,50


51

being nothing more than the general form of 
subject and predicate. All complex notions gen
a content only through judgments. The two views
therefore are non exclusive but both are true;
both allow that the three factors all thinking
are the notion, the judgment and the inference 
and we pass to their consideration.52


53
Chapter III
The Notion

April 17 We have already pointed out that
all reasoning depends on the assumption
that certain marks belong together. We have
also said that experience gives us these
marks without orderly connection. The
first aim of thought then must be to find
those notions which belong together, or to
gather our experience into constant wholes, 
as not until this is done can there be any
trustworthy reason. The notion may be defined
as the essential element in the mental object.
The subject notion may be defined as the unity 
of essential predicates. Some logicians
refuse to recognize anything but the complex 
notion or concept.
Local work begins by distinguishing first
between the mind and its states, and second
between subject and predicate. Nothing
whatever being assumed concerning the sub.
but that it contains the ground for the predicate, 
and nothing being assumed for the
predicate except that it depends on the subject. 
In such a case we have less a thought
than an outline which must be filled up. We
cannot be said to have a complete notion of
a thing until the essential predicates are all
known and until the accidental ones are excluded. 
The notion is not complete until thought54


55
is complete and hence we may say that
while the notion is first in form in completion 
it is last. It is the ideal towards
which thought strives. We begin with the notion 
as form and end with it as content. If
we should even succeed in arranging all reality
in adequate notions there would no longer
be any need of experience or observation
and all thinking would be analytic. The
only approach to such an ideal at present
is in Mathematics, but the only reason why
our thinking is more trustworthy in Mathematics 
than in Natural History is because
of the insight we have into Mathematical
notions while elsewhere we are dependent
on experience to find what is essential and
what accidental, and at best are kept on the
surface; hence the desire to make all science
quantitative.
Corresponding to the distinction of subject 
and predicate, we find that all notions 
fall into two classes, subject and predicate. 
The former are such as have a relative 
independence, while the latter can only be
thought in connection with the subject; they
correspond to nouns and adjectives. The
latter class has commonly been ignored; it
is all the more necessary therefore to insist 
upon its recognition here. The common
adjective is as much a class word as the
common noun; both comprise a multitude56

57
of individuals under them; the common noun
could not be general if the common adjective 
were singular, and for the reason
that the common noun is described and
determined only by the common adjective.
The mind would be lost if the individual if
comparison were impossible and things
can be compared only in their predicate.
Hence it follows that the content of subject 
notions depends on predicate notions.
We consider first, the predicate notions.

III In order that many individuals shall
be gathered in one class, it is necessary that
there be an element of likeness in them, for
we classify by likeness and distinguish by difference. 
But all perception of likeness depends
finally on an indefinable element which can
only be experienced. For example to gather the
various shades of blue into one class, but, or to
gather the several colors into one class; color is
possible only as there is a common element
in all, but what this common element is
which justifies our course, cannot be told,
but only felt. April 19. No logical operation could
produce this, it can only be recognized as a fact.
This primal universal is the condition of all
others; the universal in most classification can
be defined and conceived, but it always rests up
on this first one which can only be experienced.
This holds for all adjectives of whatever kind; they
are classified, not on the basis of some definable58

59
likeness, but only on the basis of some immediate
experience of likeness. The adjectives of a language 
are all simple predicate notions; they
are not mere individual attributes expressing 
a single experience, because they all
include a multitude of variations under
them; thus hot does not express a single
temperature, but any above a certain not
well-defined limit, so with virtuous, vicious,
etc., they embrace many varieties of character. 
Predicate notions arise only as we compare 
a multitude of quantities with each
other, and distinguishing the like from
the unlike give the like a common name.
Until this is done, we have not thought, but
only felt. Strangely enough logicians have
almost entirely failed to recognize the
predicate notion and the abstract based
upon it.

IV.
From predicate notions another class
can be formed, which may be called the abstract 
notion. These are the abstract nouns
of a language such as hardness, goodness, [?]
etc. Here too, quantity and quality appear as
notions; though originally only norms of distinction 
we form notions from them by comparing 
individual quantities and qualities and finding 
that all quantities have a common element 
and all qualities have a common element. 
Thus we reach the abstract notions of
quantity and quality. The abstract notion is of60


61
great use as a short-hand expression in
thinking, but at the same time it is a fruitful 
source of error. The abstraction is
often next carried into the thing and there
the thing is made to appear as the product of
its own results, for example, we explain the
action of a thing by its nature and this nature 
is made a mysterious factor in the
thing back of all outcome and eluding all
knowledge. But in truth a thing founds its
own outcome. Again, the entire family of ities
which infest the laboratory are examples of
the same thing. In every case they are abstractions 
from the activity of the elements,
but they quickly become the only realities and
the elements are made subject to their own
qualities.
       We have limited predicate notions to
simple properties; other notions may take
the place of a predicate in a sentence, for
example, "a horse is an animal," here "animal" 
appears as a grammatical predicate,
but is is really a subject notion and the
sentence is an equation. From definition the
predicate notions are simple and of course
nothing flows from them; both the adjective
and the abstract noun are valuable only as 
enabling us first to express our thought,
second, to comprise a multitude of individuals 
under a common name and
third to form subject notions; beyond this
they are barren.62


63
[*V*] Predicate notions are simple and the
logical work consists in recognizing the
one in the 'many which is immediately
given in experience. In subject notions
it consists in writing predicate notions
in one subject, which thus becomes as
to content the unity of predicates, and
the mind makes the general postulate
that some of these predicates belong together 
or form inseparable groups. Only
such a connected group is a subject notion.
It does not follow however that these marks
are consciously combined or even that they ever
were separated; many a complex notion
may be given by a primal, synthetic act.
April 21. Care too must be taken, not to think all
predicate notions as equally important. Generally 
logicians overlook this fact and regard
the notion as the sum of the predicates, or
M = a+b+c &c. This formula is too simple
and leads to the error of thinking the marks
as forming a heap. In truth the notion is
not the sum of marks but a function of
them. For example a triangle is not sides +
angles but a function of both. The common
doctrine of the co-ordination of the marks is
rarely true; the better formula would be
M = f (a, b, c &c.)
      As said before, the subject as category is
only the formal determination ofin as the
ground of the predicates; without any specification 
of what the predicates are, on any distinct64


65
limitation of the subject's scope. This agrees with
what we said, that the subject in form
is first, but in definite completed content,
last. Accordingly we find many notions
with a formal position as subject but
without any fixed content; for example,
nature, art, society, life, etc. These are
subject notions but only formally such.
With uneducated people many words are
of this kind, calling up no assignable content 
but only a vague intimation of meaning. 
Many words of daily life are of this
kind; they are words rather than thoughts
and express noises rather than meanings.
None of these are completed notions although
they have the place and form of such; but
if every notion remained in this state
no reasoning could exist. It is in such
cases that we most clearly see the mind
working under the category of subject and
predicate since it gives to an almost
formless matter, the form and function
of a conditioning subject.
The logical subject is grammatical analysis 
has for the time the function of a notion
but it is not to be viewed as a notion proper.
This is because the particular compound has
no general existence for thought but occurs
only in this one sentence.
In this incompleteness and ambiguity
of notions we find the chief sources of error.
The first necessity of mental advance and one66
It is altogether possible that nature should have
been made on a [kuaviste??] plan - so as to deceive 
us - All the value of our geological records 
depends on our trust in the fairness
and uniformity of nature.
As if - All the knowledge of these things is based
on as if - a certain ethical condescension
on the part of nature towards us.
You'll never find out the universal by letting [fall?]
the differences.

67
of the chiefest forms of education is definition
and the practice of sharply defining our ideas
in thought and practice.

VI 
The question how we distinguish the essential 
from the non-essential next arises, and
we answer, only by experience or by insight.
In dealing with external things we must rely
upon experience except so far as the categories 
are necessary determinations of all reality. 
In defining mental creations we rely upon 
our direct insight. In physical science
we set the subject in motion if possible and
we judge that those properties which continue
through all change are essential; in Natural
History we rather compare a multitude of
individuals, and if we find that certain
properties appear in all, we conclude that
they are essential. To supplement this where
possible we consult the geological record
which shows us species in motion; in both
of these cases our confidence that we have
reached the essential, depends on our trust
in the fairness and uniformity of nature, a
trust indeed which conditions all objective
science.
It is often said that the universal is found
by abstraction of the differences; in the case of
quality we did not find this so, but the universal 
was directly recognized. Here also abstraction 
considered as mere negation is incapable 
of discovering the universal. No two68

69
things are alike in any of their marks and
simply to leave out differences would lead
to zero. For example, metals differ in color,
weight, everything; leave out these, nothing
is left. April 22. We reach a notion only as we substitute
for the singular mark the universal mark
of the same class; thus if the thing be colored instead
of any particular color we put the general
notion of color; if it be heavy instead of
any particular weight we put the general notion
of weight; if it be an animal instead of
some particular form of nutrition, or respiration,
or reproduction, we put the general
notion.
Oversight of this fact has led to the general
doctrine that the particular is much richer in
content than the universal; this claim disappears
when we observe that abstraction does
not consist in denying the differences but in
substituting the universal for the particular.
Indeed we might claim that the universal
is the richer notion and that the particular
is reached through negation or limitation.
Thus, a quadrilateral stands for any four-sided
figure; if we limit it to parallel sides it
applies to only these classes of figures, if we
further limit it by making it rectangular it
applies only to two; if we next add that the
sides shall be equal, it applies only to one.
A small quibble is possible here to the
effect that we are building the universal out
of universals; this overlooks the distinction be-

70
Relation of Extension and Intension; it is said that
these vary immensely, but this is true where it is
comparatively worthless and false where it would 
have some meaning.

71
tween subject and predicate notions. A subject
notion is impossible without predicate
notions, but the universal in the latter is
given from immediate experience.
VII By the intension of a notion we mean
its meaning, on those marks which it contains.
By its extension we mean the objects to which
it applies. A common doctrine of formal
logic is that these elements vary immensely but
this doctrine is far from true in all cases.
The aim of thought is to form notions which express
an essential unity of their factors; for
notions of this kind there is no relation between
extension and intension; so with species in general
there is no connection between extent and 
content. The doctrine is true only for unimportant
classifications or for the classification
above species.
This mistake has led to the
further notion that all notions arrange
themselves at last under one so that thought
forms a pyramid -- this is a mistake, as we
come down at last to notions none of which
can be referred to any other. In these last notions
we find the categories again; all substantives
lead to the notion of thing; all predicate
notions come to the notion of quality and
these again divide into the other categories. Thought
then does not form a pyramid but a mountain
chain rising here and there into different
peaks.
72
The universals must go before the singular but only
in the sense that the categories are the universal or we
could better say, the singular is seen only thro
the universal.

73
VIII April 23. Another question is common in Logic -
whether the singular is perceived before the universal
or the universal before the singular.
Both views are partly true; in mature conception
all cognition is classification. We
perceive a single object only as we classify
it and such object is really conceived only
through the accompanying notion of the universal;
for example, a given person is conceived
only as along with the individual properties
we also conceive the general notion of
man. Indeed we can hardly be said to perceive
an object until we know what it is, 
that is, until we classify it. But on the other
hand how can the universal go before the
singular, since classification implies the objects
classified? This objection seems fatal in the case
of the derived universals of Natural History,
but these are by no means the primitive universals.
The truth seems to be that the singular is
perceived through the universal both being developed
together. The primal universals are the categories
and without these the singular can never
be perceived. Every singular is at once classified
according to one or more of the categories, hence
the singular is to be viewed as one of a class and
does not exist for the mind until it is so classified.
Thus a feeling as it exists for feeling is simply
what it is without reference to anything else, 
but is exists for thought only as one of a class,
as a specimen or example. So also the indiscriminated
object of perception is still classified
74
The doctrine of the atonement and that of the Real
Presence explained by the Realists thus; that Christ
took upon himself the human service and by redeeming
the type redeemed all.

75
as thing and exists for the mind only through
this classification. We may then divide subject
notions into singulars and universals
of which the singular is the realized universal.
It cannot be thought apart from the
universal, and the universal comes to reality
only in the singular. It is a common
fault of the current logic to overlook this
character of singulars and to take them as
given in immediate perception.

IX 
The relation of universals to singulars was
an apple of discord in the old philosophy between
the Nominalists and the Realists. The former
held that general terms are only words, and
the latter held that universals are real existences.
The nature of this reality was never clearly
conceived. Sometimes it was viewed as a mental
type on pattern according to which individuals
are produced, and sometimes as a
real essence manifesting itself in individuals.
April 24. In this latter form it entined into early
Christian theology, which accounts for the bitterness
of the strife between the mediaeval Realists and
Nominalists. Theology had been adjusted to the Realistic
theory and a change of that theory seemed
like a denial of Christianity. The doctrine has
survived to the present day in some of the ultra-
Calvinistic theories of original sin, that is
in those which hold that the entire race sinned in
Adam. The old debate also reappears in the question
concerning the prominence of species. In the main
permanence76

77
however, the ancient Realism is abandoned, and
those who affirm the existence of types, etc. would
regard them as norms on standards which
regulate the production of the individual, and
not as entities of any sort. Permanence of
species would mean the constancy of these
norms and the variability of species would
mean that creative power proceeds according
to difference norms. This question however, is
an ontological one. The claim of nominalism
that generals are only words with no
context is of course untenable for then it
would be indifferent which we used and
none would mean anything. The claim of 
the Realists on the other hand is due to an
exclusive attention to Natural History notions.
So long as we speak of cat, horse, and species
there is a kind of plausibility, but when
we pass to genera there is not a semblance
of meaning. For example the universal animal
or vegetable would be hard to typify.
For the logician the universal exists only in the
singular. The individual is the bottom fact from
which classes are formed and from these classes
higher classes again in ascending order. But in
all these cases the singular is the only reality.
The class formed from the singular is called
the species, the genus may rise to the summum
genus; the several species are the individuals of
the genus and marks by which any species
is distinguished from others are called the
differentia. Definition is commonly said to be78 79
a reference to genus [?] with the differentia of
the species. The notions above the genus are
hardly notions at all, but are in that indefinite
state in which they play the part
of motions without any definite content.
If the individual is imaginable the species
also permits an image, such indeed a general
image for one which will represent to the mind the
thing. The image is called the phantasm and, is
only possible with species. Higher notions can
only be thought, not pictured.
As pointed out in
the previous paragraph here notions do not
all run together are we go back but [?] in various
irreducible ones. These are really in the
categories transformed into notions.80

81

Chapter IV
The Judgment
I.
According to the common view, a judgment
is primarily a declaration of agreement, or disagreement
in some respect between the content 
of two notions. We might perhaps better define
it as a declaration of relation between the contents
of two notions. Some, as Mill and [McCord?]
have insisted that things are compared in judgment,
and other that thoughts only are compared.
Both views are almost ludicrously inadequate;
of the first view we say that most
[?of any] judgments are not about things in any
sense, and where they are, they manifestly do
not affect the thing. Of the second we say
that thoughts have not the properties of their
contents, for example, the thought of the sour
is not sour. We avoid these difficulties by saying
that it is the contents of notions which
are compared in judgments.
                        It is questioned whether all
sentences are judgments. The imperative and interrogative
are certainly not, but in general we
may regard other sentences as judgments; even the 
impersonal - it rains - is not a fact of immediate
experience, for the "it" is conceived as cause and
subject, and its activity is classified as raining.

II. April 25 Judgments are best classified according to the
different meanings of the copula. This gives rise to82

83
the distinction of categorical, hypothetical and
disjunctive judgments. The form of the first is:
A is B. That of the second is: A is B if A is C or
A is B if C is D. That of the third is: A is either
B or C or D. In the first the predicate is affirmed
unconditionally; in the second, conditionally;
in the third, no predicate is affirmed,
the affirmation being that one of several
predicates may be true.
For reasons that will appear
farther on, many have sought to reduce
these judgments to the first form but without
success. They may indeed be made categorical
in form but not in character. Thus, if A
is B, C is D can be put - a case of A being
B is a case of C being D, but here though
the form is categorical the thought is not the
thought is the conditional presence of an attribute
and not its affirmation. Again A is
either B or C can be read - it is impossible
that A should be both B and C, but here
the disjunctive thought remains; the affirmation
is not of the presence of a predicate
but of the necessary apposition between two
or more predicates and the necessary presence of one of them. These hold to be the logical
divisions of the judgment. The further divisions
of quantity and quality are only subordinate
and constitute no class by themselves. Thus all
A is B as some A is B. The kind of connection of
subject and predicate is the same in both
cases or A is B and A is not B. The same kind
of connection is made in both cases, only in
84
State a fact Assentorical merely categorical
Probability of a fact Problematic & hypothetical
necessity of a fact is also called apodictic 

The fact of subscription works entirely on the possibility
of identification.
The notion of substance and attribute is purely
metaphysical.

85
one it is affirmed and in another denied. Kant
made a further class of modal judgments
problematic, assentory and necessary; but
these again introduce no new kind of connection
between subject and predicate
but only refer to the mental attitude of
the thinker, and are without logical significance.

III. April 28. The categorical judgment is clearly the
most fundamental, and nothing seems simpler, yet
nothing in fact is more confused. For example, gold
is yellow; what can there be simpler than this? In dealing
with the notion we said that every notion can be
read in extension or intension and this gives
rise to a double interpretation. Does the judgment
"gold is yellow" mean gold is included in the
class of yellow things, or yellow is contained
in the content of the notion gold? Undoubtedly
in every day thinking, the latter is the true interpretation,
yet because of certain logical exigencies
the logicians have invariably read the
judgment in extension, at least when it was to be
consented[?]. Thus "gold is yellow" is turned into
"some yellow thing is gold"; hence also the claim
that all judgment is the subscription of the
individual under the universal. Man is an animal
means man is contained in the class animal; hence
too the claim that all judgments are categorical
for if judgment is subscription, then a thing is
in a class or not. Any doubt on the point belongs
to the thinker and is extra logical.86
All thought proceeds on the assumption that certain
properties always go together.
The categorical judgment where you bring it down to a fine
point reduces to an identity but the outcome is a complex
unit which you can deal with by itself, and thus
there is an advance.
Without the assumption that certain notions go together all
thought is at an end.

87
On this we remark: 1st This doctrine would enable
us to escape many troublesome questions
but 2nd All judging is by no means subsumptive,
for example, in Mathematics where the
process is throughout one of identification.
3rd Even if all judgments were subsumptive, it
does not follow that all are categorical, for
thought is in motion so that some notion appear
in certain classes only under certain 
conditions, that is, A is not always B but only
as C is D. We cannot then regard the
judgment as being essentially the subsumption
of the singular under the universal, and
even where it is such the subsumption is
but the result of a more fundamental act
of identification, total or partial, of subject
and predicate. Thus, man could not
be subsumed, under the class animal
unless he were identical with at least a
part of the class.
IV. The current definition of a judgment (affirmative)
makes it a declaration of agreement between
subject and predicate, but what agreement 
is there between yellow and gold? The
truth is we can justify this definition only
as we show that affirmative categoricals always
mean more than they say and that were the missing
elements are supplied the notions become identical.
Thus "gold is yellow" means either the
color of gold is yellow or that gold is a yellow
thing. In the first case we consider gold as to its
88

89
color only and identify it with yellow. In the second
we consider the adjective as agreeing with a
noun understood, which when supplied make
the two terms identical. In both cases by yellow
we do not mean yellow in general, but only
that peculiar yellow which belongs to gold, or
if we say "some men are yellow" we mean either
that their color is yellow or that some men
are yellow men. By the some men again we do
not mean any some men, but only yellow men,
and by the yellow mean only such yellow as in
possible to human skin. Here again where we
add the limitations which were present in our
thought, the judgment becomes an identical 
one. And in general all judgments, analytic
and synthetic alike, must reduce to identical
judgments when all the explicit elements of
thought are explicitly stated.
Warned there by these short comings we
define an affirmative categorical judgment
as the total or partial identification of subject
and predicate. Such judgments may
be either attributive as "gold is yellow", or substitutive
as 4 + 3 = 7 or subsumptive as "man
is an animal." We have seen that in the first
class when the implicit thought is stated
the two terms become identical. In the second
class the identification is evident. To this class belong
all definitions and mathematical judgments.
In the third class the subsumption
rests on an implicit identification. If it be90

91
said that in natural thought this view of judgment
never occurs the answer first: unreflecting
thoughts can never do the work of
theory. Second: it is the duty of Logic to
bring out in formal statement what is
implicitly thought. Third: the question is not
whether thoughtless the thinking knows
of the distinction but whether reflection
justifies it. 
April 29. At this point we must refer to a
question which calls for an answer; if categorical
judgments are identical in what is the thought advanced?
If by "gold is yellow" we only mean that
gold is a yellow thing and by yellow thing understand
gold, we are no better off than before.
We reply that equivalent judgments are not
necessarily fruitless. For example 7 x 14 = 98
is a equivalent judgment but still it gives
information. All mathematical judgments are
of this part but they are not worthless, for
one member of the equation though it reproduces
the same matter gives it under another
form and this new form is an advance, or
"gold is yellow" reduces to gold is a particular
kind of yellow substance, which yellow substance
is really nothing but gold, but the judgment
is more than gold is gold; the yellow
thing which is gold is still gold under a new
form, and the result is that thereafter we think
of yellow as forming part of the content of the
notion gold, or we think of gold as included in
the class of yellow things. Man is mortal also92


93

reduces to "Men are Mortal," and this again
to "dying Men are Mortal", yet the outcome
is that we look upon death as an event that
will certainly arise to every man. If asked 
for the warrant for writing different notions
in one subject we reply that this is the universal
postulate of thought that some predicates
belong together or that relation exists
between all objects of thought. Even in the case of 
analytic judgments thought is advanced for
they make clear in the predicate what was implicit
in the subject.
We have said nothing about the
negative categorical A is not B. This form is
entirely simple; the predicate B is denied of A.
It has been much discussed whether the negative
belongs to the copula or the predicate, and many 
have held that it belongs to the predicate so that
instead of denying B of A, non-B is affirmed. 
This is only misplaced sharpness, for now. B is no
notion at all, but only a chaotic heap of all things
which are not B. For example, not man is anything
that is out of the class man.

[*VI. 
Division by 
Quality & Quantity*]
In current marks on Logic judgments are
divided according to their quantity and quality.
In quality they are distinguished as affirmative 
or negative; in quantity as universal or particular.
In the universal the whole of the subject
is taken, in the particular only a part. Thus all
A is B, universal; some A is B, particular. The
two distinctions combined give four judgments.94 

95

All A is B, no A is B, some A is B, some A is
not B, which are designated by the letters A, B, 
I, O. Beside these some logicians have insisted on 
the singular judgment, but this has nothing peculiar,
as the whole subject is taken in belongs to
the universal.

[*Quantification of the predicates*]
              In this scheme no account is taken of 
the quantity of the predicate, that is we're
not told whether  A is all B or only some B.
The current logic says only that in affirmatives
the predicate is undistributive and in negatives
is distributive. Of late years this addition has
been made to logical doctrine under the name
of the quantification of the predicate. Sir
William Hamilton is the chief expounder of the 
doctrine, though not its inventor. When the predicate
is quantified each judgment in the 
common scheme splits into two, as all A is
all B, all A is some B, etc. The innovation has
been stoutly visited under the plea, first: that
in spontaneous thought the predicate is not quantified
and second: that, this is to take the matter of thought
into account. Neither objection is valid, for 
first: even in spontaneous thought the moment a
judgment is employed in reasoning the predicate
is implicitly quantified and second, the thorough-going
quantification of the predicate is no more 
material than the pretended omission of it. For
when the judgment A is B is converted the formal
logicians say some B is A, but why some if
not all? If the judgment means that A is only some
B there is no objection  to saying so. Finally the  com-96
Distributive = taken in its full sense
Undistributive =taken in a partial sense

97
doctrine of distribution leaves out mathematical
and all other judgments, where subject and
predicate have equal content. This is the great
short-coming of Aristotle; he builds entirely
on the notion of subsumption without recognizing
the deeper law of identity, and hence
fails to notice a large class of judgments that
are not subsumptive in any case.
VII Conversion
 April 30 Conversion consists in exchanging subject and
predicate so as to express the same matter in a new
form; but as in the current Logic the predicate 
is affirmatives is undistributed. A is B gives some
B is A, but when we apply this to identical judgments
we always lose a part of the truth, thus
"terriers are dogs" gives "some dogs are terriers" and
this again converts to "some terriers are dogs".
Plainly a method that fumbles away part of
the truth cannot be highly praised. Moreover
even the current doctrine implicitly quantifies
the predicate, for it reads A is B to mean
A is to some B and hence there is no reason except
dullness or prejudice for objecting to the
form A is all B. It is urged[?] against Hamilton's
table of the judgments that they do not
all occur in spontaneous thought. For example
it is said "any is not some," and "some is not
some" are forms which do not occur, while
"some is all" would be turned into "all is some".
This may be allowed as against the forms which
appear in Hamilton's theory some of which are
rather fantastic, but it makes nothing against
98 [blank page]

99
the quantifications of the predicate as that
doctrine only demands that the quantity
of the predicate in an actual judgment
be formally stated. It is so far from true
that spontaneous thought does not quantify
the predicate that no judgment occurs in
daily thinking without being implicitly quantified.
For ourselves we hold it a useless formalism
to construct tables of judgments. We insist
however that every judgment is properly an
equation and therefore that the quantity of
the predicate must always be regarded.

VIII Some logicians especially Boole and Jevons
aim to secure the same result by writing
every judgment in the form of an equation,
and Jevons proposes the following notation.
All is All he writes A = B
All is Some            A = AB
Some is Some      AB = AC
A = AB means that the class A = class B which
are A's. Thus "man is an animal" would appear
as A = AB where A stands for man and B
for animal and the meaning is the class
man equals men-animals. AB = AC means
that B = C in the class A. It is plain that if
some B = some C it can only be that part of
B and of C which is contained in some third
class A. Negative judgments are expressed
by using the small letters instead of the corresponding
capitals, thus A = b means A is not B.
For hypothetical and disjunctive judgments100

Jevons- Principles of Science.
Boole's Laws of Thought.

101

other symbols are used; having the equations
the reasoning proceeds by substitution.  Care
how even must be taken to give the symbols their
logical and not their mathematical values.
In [michanios] the resultant is equal to the components
in effect, but is not equal to their 
sum.  In Quaternion BA is not equal to AB.
So in these logical equations there are particular
laws which must be always borne in mind,
chief of which is x^n=x which means that
the successive repetition of any term adds
nothing to the meaning.  For example sun, sun,
sun = sun.  This law which has been supposed
to have originated for the first time by Boole
was fully stated by Leibnitz in some of his
fugitive papers, and the illustration given occurs
in Boethius  "De Trinitate."  Leibnitz seems
also to have reached the quantification of 
the predicate but in his exposition of the 
syllogism he falls back on the old doctrine
of subsumption without using the improvement
he had suggested.
      The extended mathematical motation
of these writers has no value for thought
May 1. It is simply an ingenious piece of mental mechanism
which throws no light on the reasoning
process. it is a useless piece of formalism to construct
tables of all possible judgments; it is
equally useless to waste time on elaborate motations.
All reasoning proceeds by substituting similars;
this fact alone reveals the nature of the 
process.  The various methods of substitution"Nature is under no obligation not to be tricky.
The laws of nature give no hint of their beginning or
origin.

Every judgement of Externality at least is truly not
categorical, but a shortened form of a hypothetical.


103

Which occur in practical reasoning must be
left to practice itself.

IX.
Categoricals
are non-Categorical

     Thus far we have dealt only with categorical
judgments; in passing to the other forms we
must show that most categoricals are really
contracted hypotheticals. The nerve of all reasoning
 about things is the general assumption that certain
predicates belong together.  What these predicates
are can be found in general only by
classification, hence the judgment in these
cases must be either the Statement of a present
Experience or else a classification.  In the former
case it contains only the present Experience and
leads to nothing, in the latter case the judgment
is true only on the assumed truth of the
classification. For example, "this man is mortal"
is true only on the assumption, first, that
man is mortal and second that this being is
really a man and not an imitation, say an
angel in disguise.  Both assumptions implicitly
condition the judgment; so glass is brittle or
iron is malleable is true only for the solid
slate.  Water is liquid true only for certain
temperatures.  The mechanical energy of the
universe is constant if certain conditions be
fulfilled.  The physical order was such an such
in the past if nature be uniform and appearances
trustworthy.  In truth there is an
almost boundless amount of limitation
understood in most of our statements. We
may say then that all categoricals are either104


105

the Expression of experience, or use a hypothetical
of the form if A is B, A is C: that is
if A has the mark, or is contained in the
class B, it has the mark or is contained
in the class C.  We might say that most
categoricals are merely the conclusion of
the following argument:  Whatever has mark
A has mark B, but C has mark A, ergo
C has mark B; thus we say of a certain
animal, it is a bird, or of a certain element
it is, say Oxygen, but the judgment depends
on the implicit argument given.  Here again
the possibility of forming constant classes
appears as a necessary postulate of reasoning.

X.  May 2. We have seen that a notion comprises under it a 
number of individuals which may be either adjectives
or nouns; thus, red comprises the several
shades of red, color comprises all the colors;
this fact is the basis of the disjunctive judgment,
which may be defined as a notion read
in division. Hence when we gauge anything in a
class we know that it must have or be some one
of the possible modifications of that class to the
exclusion of the rest.  Thus water must be either
solid or liquid or gaseous. Hence the disjunctive
judgment is the declaration that a thing which
comes under a given class must have one or
another of the predicates possible to that class.

It is common in Logic to find the principle
of the excluded middle given as the typical disjunctive106


107

judgment, according to which everything is either
A or non A; but now it is no notion at all. The
law of excluded middle when made universal is
only an application of the law of identity and
means simply that a subject must either have
a predicate or not have it; it should apply 
to disjunctive judgments only when the number
of predicates is two and when it is clear
that the subject must have one of them.  In
case of most disjunctive judgments the excluded
predicates are more than two, and frequently none
of them have any application beyond the class in
which they occur as special cases.
       This view of the nature of disjunctive
judgment leads to the conclusion that the disjunctive
predicates are mutually exclusive.  Upon
this point there has been much dispute.  Aquinas
Kant, and Hamilton affirm. Whately, Mill
and Jevons deny. The truth is that alternatives
are exclusive when the same notion is divided
but as the same thing may be classified under
different notions which are not exclusive, we
may often form an alternative not from members
of the same class but from partially coincident
classes and thus produce an alternative which
is not exclusive. For example either a knave
or a fool, either a saint or philosopher; but
these are rather alternatives in language than
in thought. Often indeed the conjunction or
denotes apposition rather than opposition
Next to unclear notions, incomplete disjunctives
are the great source of error in reasoning.108

You can draw a true conclusion from false premises
by a judicious selection in regard to the middle
term.
In the same way is is very easy to draw false 
conclusions from true premises.

109

Chapter V
The Inference

I  May 5.  Inference consists in drawing from
one or more propositions called premises
some other propositions called conclusions
which will always be true if the premises
are true.  If the conclusion be drawn from
a single premise the inference is said to be
immediate;  if from two premises it is called
mediate.  Hence inference makes nothing, it
but reveals what is implicitly in the premises;
it transmutes but does not create.

II  Concerning the general law of inference
most logicians until quite recently have
regarded the dictum de omni et nulls
as the only law.  This arises from the burden
of supposing that all reasoning is with
general notions.  The dictum itself is seldom
correctly formulated.  We often hear the affirmative
part stated thus -- "what is true
of the whole is true of the parts, what is true of
the universal is true of the particular, what
is true of the class is true of the individual
etc.  These formulations of of the loosest kind
and are more than half false.  The general
notion is but the sum of the marks common
for the whole class, and the affirmative dictum
can only  mean that the marks which
make up the content of the universal are found110

111
in all the members of the class. But this dictum 
has nothing to do with reasoning in 
equivalent judgements where the law is that 
of substitution. Agreeably to our doctrine of
the judgement we regard this law of substitution
as universal and the basal principle
of inference is that whatever is true
of anything is true for every other thing
like it as far as it is like is, or negatively
stated , whatever is true for a thing is not true of
 any other thing unlike is in so far as it is unlike
 it.  Thus what is true of a thing as having 
a certain weight, length or quality will
be true of every other thing haring the same
length, weight, etc.  The law includes Christolle's  
dictum  and also every mathematical and 
other reasoning in equivalent judgements.
The general method of inference is the substitute
for any notion in a proposition any 
other which is asserted to identical 
with it.
III 
Every judgement involves the truth or
falsehood of many others. The statement of 
these implied judgements is called immediate 
inference. It is not easy to say when a 
new proposition differs enough from the 
old to make it an inference. [?]sion is 
improperly regarded as a form of immediate 
inference; for every such judgement but aims
to put the same  matter in a new form. Thus x = y
and y = x are certainly the same equation, at leastLeft Page: 
Table:
A Contrary E top
left side I [Suballeve]
Middle contradictory
Right side O
Bottom: Sub. contraries
All men are liars   A
All men are not liars   E
Some men are liars   I
Some men are not liars   O
A   universal affirmative.
E    universal negative
I     singular affirmative
O    singular negative

A&E both may be [true ] false but
they can't be true together
A & I, both can be true together
but not false together
I & O can't both be false but
can be true together. 
(A & O) (E & I) The truth of 
O one involves the untruth 
of the other.

Circle-squarers should be classed with spirit-rappers
Contrary holds between universals of opposite  quality and can
both be false together but not true. Sub. contraries can
both be true together but not false.
This system of Added Intermediates is always apt to
give odd results where you add negatives to it; but if
you quantify the predicate it comes out all
right.
       Seeing is knowing  seeing is some knowing
       Not seeing is not knowing not seeing is not some knowing
Contradictory opposition hold between those that 
can't be true together or false. Props. opposed in
quantity and quality.
 
so one could call the latter an inference from
the former, or A is some B, hence some B
is A is nothing new, but the old story.
             More respectable are the forms
of immediate inference known as opposition,
this from the assumed truth of any of the judgements
A, E, I, O, we can judge concerning
the truth or falsehood of some of the others.
Thus if A be true I is true. E and O are false.
If A be false, O is true, E and I may be true.
May 6. On this depends the method of indirect
inference which consists in proving a proposition
by disproving its contradiction. Some  
affect to find this proof less satisfactory
than direct proof, but this is only the result
of mutual unsteadiness or logical pedantry.
[*Immediate
    Inference by
    added Dr.
      terminates*]  
  Another form of immediate inference 
is that known as inference by added
determinates. We may express this as follow:
Let A=B be the original proposition then
F,(A) = f, (B). A multitude of equations are really
immediate inferences; for example, roots,
powers, multiples and quotients are immediate
inferences.
           A long series of immediate inferences
may be deduced from observing the content
of the notions in the judgement. Thus A
is a moral being implies first A exists, second
A has a sensitive nature, third A is intelligent,
fourth A is responsible, fifth it is
not a baby, sixth A is not insane, seventh A
is not a kuare, eighth A is free, ninth a neon-
















114

MP     PM     MP    PM
S.M     SM     MS     MS
___    ____     ___      ___
SP      SP      SP       SP

One neg premise will give a negative conclusion.

1 form major premise must be universal.

             minor         "          "      "   off.


115
al law exists, tenth, A either obeys or disobeys.

IV
 Syllogism
But the almost universal form of inference 
is mediate; this involves the comparison of two 
terms through the medium of the third 
called the middle term, that is such of 
two notions is compared with a third 
and according as they agree or disagree 
with it they are said to agree r disagree 
with each other; such a comparison and 
conclusion is called a syllogism which 
is the general form of mediate reasoning. 
This process implies that there must be 
only three terms for in order that any 
relation be deduced between A and B, they 
must be compared with the same thing. 
A=C, B=D allows of no conclusion as regards 
A and B.  Any ambiguity of the middle 
term so that it is used in different senses in 
the two propositions, or so that the terms 
are not compared with the same part of 
the middle term, violates this rule.  This 
gives rise to the fallacy of ambiguous and 
undistributive middle.  The failure to observe 
the rule of only three terms is the great source 
of logical error.  It also follows that at least one 
premise must be affirmative for the fact that 
A and B both disagree with C allows no positive 
conclusion as to the agreement of A and B. 
A negative conclusion is possible only when one 
premise is negative, further, the conclusion 
can only apply to the terms [?really] compared,116

117
if only parts of a class are compared with
the middle term of course the conclusion
applies only to those parts, hence the conclusion
can never be larger than the premise.
Overlooking this rule gives rise to the illicit
process of the major and minor.
All the many rules form
the syllogism given in logical marks are but
specifications of these. Each figure has also
special rules but there are based on the rule
of only three terms and an leash one affirmative
premise. May 1. The complete rule for the
syllogism is this; every term must have the same
meaning and extent in all three propositions
and one of the premises must be affirmative.

[*V Figures*] 
The syllogism has been divided according to the
position of the middle term into four classes
called figures: –
MP
SM
__
SP

PM
SM
__
SP

MP
MS
__
SP

PM
MS
___
SP

The first three are called the figures of Aristotle; 
the fourth is assigned to Galenus.
The order of the premises is purely a matter
of custom; until Boethius the minor
cause first, since then the major. The major
contains the predicate of the conclusion,
the minor the subject.
Syllogisms are further divided into
[*Moods.*] moods. By mood is meant the character of
a syllogism as determined by the quality118
From the universals a universal conclusion can be
drawn always
When our premise is particular the conclusion
must be particular.
Second figure allows only negative conclusions.

119
and quality of the propositions in it. This is
signified by using the vowels A, E, I, and
O in their regular meaning. Thus EIO –
AAA – AII etc. The possible combinations
of A,E,I,O produce sixty-four moods, but
most of these break the law of the syllogism
so that only eleven of the sixty-four are
valid. This entire mechanism of moods is to
be regarded as empty formalism with an
interest only to the curious; its only value
is in enabling us to give a short-hand expression
of an argument on a criticism.
Because the first figure allows
us to draw conclusions in A, E, I, O an in
both quantities and qualities while the other
figures are less general, it has been called
the perfect figure, the others of course being
imperfect.  Hence arose a desire to seduce
the imperfect to the form of the first;
hence the mechanism of seduction; a series
of mnemonic lines was invented whose vowels
and consonants were so arranged as to indicate
the mood of the first figure to which a
given mood in the others should reduce.
This process is a complete waste of time;
as the procedure itself was thoughtless, the
inverted lives, as was fitting, were totally
devoid of sense. A conclusion in one figure
is as valid as is another and Every
argument does not fall naturally into
the same form.120

121
VI. 
It is clear that with Equivalence judgments
merits where the universal laws of the syllogism
are regarded, valid conclusions
in A, E, I, O can be drawn in all the figures,
or if the predicate be quantified and
the middle term have the same meaning
in both propositions A, E, I, and O are possible
in all the figures. Hence the quantification
of the predicate with the law of
only three terms dispenses entirely with
the distinction of figures as having no
logical value.
We said that negative premises
[*Negative Premises*] could not give a definite conclusion.
The apparent exceptions are cases where the
terms are negative only in appearance; thus,
"Whatever is not metallic is not capable of
powerful magnetic influence, carbon is
not metallic, carbon is not capable" etc.
This is given by Jevous as a proof that negative
premises sometimes allow definite
conclusions. The fallacy is evident as the
minor premise is affirmative in fact.
Still we hold that negative premises
do allow a certain conclusion, thus A is
not B, C is not B. Therefore A may be C or A and 
C are not contradictory opposites. This conclusion
certainly flows from the premises and
it is hard to see why it is not as worthy of
mention as a great deal that loads down the
current Logics. May 8.  No tendency is more apparent
in daily life than the hasty conclusion from the122
To affirm the antecedent affirms the consequent but 
to deny the antecedent does not deny the consequent. 
To affirm consequent does not affirm anteced.

Illicit [process?] of major and minor is when it 
is taken in larger sense in conclusion than in the 
premise; it is a conclusion from o to e 
properly.

If it has rained the street is wet 


123
absence of a mark to the presence or absence of 
some other. The conclusion then that A may be 
B we hold to have a practical value as teaching 
us to suspend judgment.

VII 
Hypotheticals 
in Syllogism 

Syllogisms containing conditional and 
disjunctive judgments have in them nothing 
peculiar. They are subject to the same rules as 
the categorical syllogism; with regard to the 
conditional if one premise is categorical the 
conclusion will be categorical, thus if A 
is B, C is D (major) A is B (minor) therefore 
C is D (conclusion). If both premises are 
conditional the conclusion will be conditional, 
thus if A is B, C is D (first) if C is D 
E is F; (second), therefore if A is B, E is F (conclusion). 
Ambiguity of terms produces fallacy 
everywhere; the fallacy peculiar to this 
syllogism is that of concluding from the 
consequent to the antecedent; if we affirm 
the antecedent we may affirm the consequent, 
if we deny the antecedent we cannot deny the 
consequent; if we affirm the consequent we cannot 
affirm the antecedent; if we deny the consequent we can deny the antecedent.

[? 
Look up in [Jevons?]]

In the disjunctive syllogism the 
first promise contains a disjunctive judgment, 
the second affirms or denies some member 
of the disjunction and the conclusion is self-evident. 
The fallacy peculiar to this form is 
that of incomplete disjunction. If we say 
A is either B or C and B and C do not exhaust 

[Disjunctives.]124


125
A but leave a remainder x, then from affirming 
B we could indeed deny C and x, but 
from denying B we could not affirm C.
Now - Exclusive disjunction also leads to noon.

VIII Objections to Syllogism
The syllogism has been attacked on all
sides with the change than it begs the question.  
If M is P and S in M of course S is P, 
but this would not be true if M were not 
P so then is begs the question.  This bit of 
profundity depends on taking some national 
history notion and assuming that we reach 
the universal only by summing up particulars, 
but this is seldom the case.  Universals 
are commonly established by independent 
reasoning; thus in Mathematics proportions 
are proved without reference to any 
single case.  Thus in a triangle three angles 
two right angles depends on no measurement 
of individuals.  Again in Physics and 
Chemistry from a few experiments we conclude 
that a given element acts in a certain 
way under definite conditions and 
thus we need only order an individual into 
the class to drain the conclusion.  But in none 
of these cases do we merely sum up individuals, 
nor is it true either that the major 
premise alone contains the conclusion.  Thus 
all men are mortal does not alone prove 
the M is mortal but only on condition that 
M is a man; the conclusion therefore follows 
from neither premise taken alone but only 126


127
from both taken in conjunction. The charge
that the premises involve the conclusion is 
love, for if they did not the conclusion
should not flow from them and would 
therefore be unfounded; this change therefore 
is only an odd way of staling that the reasoning
is round.
                But if the conclusion is in
the premises, why reason instead of inspecting?
The answer is that the conclusion is 
commonly so far in that it requires 
considerable effort to bring it out  It is conceivable 
that there should be an intuitive 
intellect which should see an once all 
implication, but the common mind is not of 
this sort.
IX 
 Induction 
May 9. Deduction assumes its premises and develops 
what is implicitly in them, but how do we 
get our premises?  I From intuition, the mind 
is able to see somethings to be true without a process,
but in general we get our premises by an inverse
process which we call induction; this proceeds
 from the  singular to the universal and is
largely identical with the process of forming the
notion; in process throughout on the same assumption,  
viz: that marks which appear together in many
cases, belong together. Thus from A.P, B.P., .C. P., etc we
conclude SP, where S is the class including A.B.,
C etc. The axiom of induction is that of all reasoning,
viz.; like is tone of like. the only difficulty in
practice is in penetrating beneath surface re.128


129
 semblance to real likeness. That is, the axiom
is unquestionable, the only point is to know
whether any real likes or kinds exist, and if so,
how they are known.
Objection from 
Formalist. 
                     Two objections come up- First 
the formalist objects that the inductive conclusion 
is always from particulars to universal
and can never be allowed. If the induction
be complete the conclusion is nothing new,
it is but a short hand statement of the observations.
If incomplete, it is forever illogical.
If only logical form be regarded this is true,
but the objection is more sweeping than its author
fancies, for it denies the possibility of any
reasoning upon objective reality. Our experience
of the outer world must always be particular 
both in space and time. We are thrown back 
here upon the assumption we mentioned at
the beginning, viz: that classification is possible
and we regard the constant recurrence
of certain marks in connection as a proof
that these marks are the sign of a class. It is
the notion of a class which enables the mind to pass 
from the particular to the universal.
Objection from 
     Empiricist.
             The second objection
is from the Empirical school. Mill insists 
that induction proceeds from particular 
to particular directly and not through a universal.
If the fact that all have died proves 
that all will die, it certainly proves that A or 
B or C will die. "Hence" says Mill "the conclusion 
is from particular to particulars directly, and130

No matter how we do it we must throw [into?] these particular
facts the notion of class or kind, and thus the
dead facts are set in motion. This is an assumption but
without it all reasoning breaks down; we have to assume
the existence of kinds of classes in order to make thought
possible; this mental [proceeds?] on the assumption that
there are definite classes. Yet this does not prove that
there are real classes.

The assumption of order is necessary to but not in thought.

131

[won?] through the medium of a universal." This
plea is short sighted, for while it is psychologically
true, Logic asks for the warrant.
The only thing which warrants us in proceeding
from one individual to another is the assumption
than 132
Science as well as ethics rests upon assumptions
which have no warrant in reason. The scientist
says "there is a power beyond ourselves that makes 
for nationality"; the ethical philosopher says "there is
a power beyond ourselves that makes for righteousness.
Both are sentiments, both are subjective.

133
is clear than the entire past is antecedent to
the event, and that many influences centre in
it, but the general assumption is that the
cause is near both in space and time, and
to find it sundry methods have been established.
These methods are really the invention
of common sense, but their formal
statement is due to the logician. Sir John
Herschel Las given an extended statement of
these methods in his discourse on the study
of Natural Philosophy, and Mr. Mill has
followed him in his logic and as many
think with little improvement.
XI
[*Method of Agreement*]
     The first method is called by Mill the
method of agreement; it is given as follows:
If two or more cases of the given phenomena
have only one other circumstances in common,
that may be regarded as probably the
cause - for example, a certain kind of food
is followed by sickness in many cases; the
food is the cause. Rail-road men are more
subject to certain diseases than others; their
occupation is to blame. The workers in match
or white-lead factories have peculiar complaints;
their calling is the cause.
                              The difficulties of
this method are plurality of causes. Suppose
AB = AB, AC = A[?], AD = A[?] we should conclude
that it is the cause of A, but it would
still be possible than it was an inert factor
and that BC and D were alike able to pro-
134


135
duce A. Thus in the case of medicine, the common 
factor might be an inert drug. We 
said too only one circumstance in common, 
but there is no such case: we must add only 
one material circumstance in common. 
But what is a material circumstance? 
Here we must fall back on our total experience. 
This method in general is very doubtful 
and a great source of fallacy.

[*XII. 
Method of Difference*]

May 13. The Method of Difference comes to help out 
the method of Agreement. If a case of occurrence 
and one of non-occurrence differ in only one 
circumstance which appears in the former, then, 
that in which they differ is the cause, or a necessary 
part of it. So when we introduce a new 
antecedent and get a new consequent we view 
the former as the cause; a dose of poison followed 
by death, friction and motion followed by heat, 
expansion by a fall of temperature. This method 
is more powerful than that of argument where 
it can be used; it is the method of experiment; 
the other is the method of observation. Of course 
its whole value depends on the certainty that only 
one new antecedent is introduced, and even then 
it is not plain that the new factor is cause; it 
may merely remove the obstacle to something else 
which shall be the true cause of the effect. If we 
should put a bird in a jar from which the Oxygen 
has been taken by burning we could not 
tell whether death was due to lack of Oxygen or 
the presence of CO2 or to an unbalanced action of136


137

Nitrogen, or to all three combined. Again if we have 
two antecedents at once and no effect follows we 
cannot conclude to the inertness of either for 
each might cancel the other. In all cases where 
we cannot reduce the experiments to simplicity 
the results are uncertain. The well-known 
fallacy of past Loc ergo propter Loc is a case 
of this method.

XIII 
Joint Method 
of 
Agreement & Difference

But as the Method of Difference is not applicable 
to many cases the two methods are next 
combined into what Mill calls the joint method 
of agreement and difference. If all cases of the 
phenomenon have only one other circumstance 
in common, and all cases of non occurrence 
agree only in the absence of that circumstance, 
then that is the cause. If the observations were 
general this would give certainty, thus, I take a 
certain food and am sick, leave it off and 
recover; or I find a plant in certain soil and 
never elsewhere. The objects on which dew is formed 
all agree either in radiating heat rapidly or in 
conducting it slowly which produces the common 
result that in a falling temperature 
they get colder on the surface than the surrounding 
objects. Cases of little or no dew 
agree only in not so doing. Hence dew is due to 
the cold of the object in a moist atmosphere. 
When the method is not absolutely vigorous or 
the connection not invariable it may point to a 
cause: as when the balance of East winds is followed 
by rain and elsewhere not, or when people138


139

[*in one part of a city are afflicted by disease, in 
others not. Here the connection is not absolute and 
hence the conclusion is only probable.

[XIV] 
[Method of Residues]
The method of Residues is given as follows: 
Subtract from the event which is known to be the 
effect of certain antecedents, the remainder 
is due to the remaining antecedents. Thus, if 
ABCDE is followed by [alpha] [beta] [gamma] [delta] [epsilon], and if [alpha] [beta] [gamma] is 
known to be due to ABC, then [delta] [epsilon] is due to 
DE. This method is only applicable when the 
several effects are independent as in mechanics, 
parallelogram of forces etc. It is not applicable 
to machines or organisms or even to 
chemistry or to any effect where the agents 
condition one another. This process when applicable 
is very effective in leading to new discoveries. 
Thus; from the irregularities of Uranus the planet 
Neptune was discovered, by subtracting the perturbations 
due to the other planets and analyzing 
the residuum. Again sound has too 
great velocity; by analyzing the residuum we 
find heat from condensation producing the 
effect.

[XV 
Method of 
Concomitant Variation]

When any phenomenon varies whenever any 
other varies and in some proportion to it they 
are causally connected, this is called the method of 
concomitant variations. In most cases it is impossible 
to deal with a pure case. Thus the first law 
of motion cannot be proved by trial; the conditions 
assumed never exist. May 14 But since the motion*]140


141

[*continues in proportion as resistance diminishes, we 
conclude that if all resistance were away the 
motion would continue forever. So Pascal 
proved the reality of atmospheric pressure by 
carrying a barometer up a height. Within certain 
limits the method is trustworthy, but if taken 
absolutely gives absurd results. Thus, the moon 
turns once in going round the earth, two 
clocks keep time together; we cannot conclude 
to a causal connection. The most unsatisfactory 
results are found when we attempt to 
get a law of change between two phenomena. 
Thus gases diminish 1/273 of their bulk 
for every degree of fall, but we cannot conclude 
that they will ever diminish to nothing. So 
all the Empirical formulae in Physics fail 
outside of certain limits. The Materialistic 
argument is a fallacy of this method. Many 
organs cannot be destroyed without destroying 
life but we cannot conclude that those organs 
alone are the cause of life. Hence the doubt of 
the methods of the vivisectors; their cuttings 
may well produce disturbances of the whole and 
are far from proving that the part cut away 
had the function of restraining the effects which 
followed.

In all these methods the great trouble is plurality 
of causes and difficulty of separating the 
experiments so as to know all the factors in the 
play. In Biology, Sociology etc., this is seldom 
possible and thus the conclusions have only a 
certain degree of probability.*]142

On Moral Statistics see 
Leitschrift der Philosophie, Fichte (about 3 years ago)

143

XVI.

Doctrine 
of 
Probabilities

May 15. In very many cases we have to content 
ourselves with probability. In truth all our 
knowledge of reality falls short of certainty 
as its general postulates are not plural and are 
not necessary in thought; but allowing them, 
we are still in most cases unable to reach 
certainty. It becomes then a matter of importance 
to know the degree of probability in particular 
cases. Most commonly it admits of no definite 
determination, first, because we know 
little about the factors at work, and second, because 
the factors often admit no numerical 
measure. This is the case in most movements of 
society, and especially in our trust in evidence 
and in one another. There is nothing in mere transmission 
to change the character of the testimony 
and when it is untrustworthy there is 
no assignable measure or standard of comparison. 
In such a case we have to depend 
upon the general impression and upon experience. 
But sometimes a calculus is possible 
and then the degree of trust is given by the 
calculus of probabilities, a brand of mathematics 
of quite recent development. The doctrine 
rests on the general assumption that any one 
of a series of events will tend to occur as 
often as any other and conversely when in 
a great number of instances some event occurs 
with greater frequency than any other 
then there is some cause which favors that 
more than the rest. All we can do here is to 
refer to the meaning and application of the 144


145
doctrine. I The probability reached determines 
only the measure of material expected and 
not the objective quality of the thing. For the 
possibility of the most improbable events 
must always be allowed and hence after 
the event has taken place we are not 
to regard its previous improbability as 
any argument against its actual occurrence. 
And for the reason that while 
any one event is very improbable as against 
some one of all the rest, yet it is no more 
improbable of itself than any other, provided 
always that the several events belong 
always to the same class. 2 The doctrine 
of probabilities does not apply to just 
facts; it assumes a definite set of facts 
and principles as its starting point and 
without these is meaningless. Thus it would 
be pure folly to say that as being and non-being 
include all possibility, therefore before 
any thing was the probability of future 
being was one half, and as being must be one 
or many the probability of future plurality 
was one fourth. The doctrine is often misused 
in the Theistic argument; it is assumed 
that an intelligible order is more improbable 
than a non-intelligible one, but this is two-edged, 
for if so then much more must are intelligent 
first cause be more improbable than 
an unintelligent. Besides what ground for 
the claim that chaos has a better right to 
existence than order? The argument assumes146

Being is itself a standing miracle, but we have to assume 
it as it is, and is it any more wonderful that 
God should be as he is than that being should be as it is.


147

this case: if a multitude of indifferent elements 
were thrown into space to arrange 
themselves, it is infinitely improbable that 
they would ever assume intelligible form. 
This is true but in order to make the conclusion 
valuable it must first be shown that 
such an event ever occurred. 3. The ground 
for extending our expectation to reality is experience 
and for the obvious reason that the 
calculus assumes certain data both of fact 
and law, and as these are seldom more 
than probable the application of the results 
to the fact can only be probable. In truth 
reality is absolutely determined so far as it 
is a subject of science; May 17; and that our 
expectations based on probabilities are realized 
only shows that the system of things is fair and 
open, or that it is controlled by rational 
principle. If however our observations did 
not tally with experience suppose a large number 
of experiments made, we should conclude 
that the assumed equal possibility of all cases 
was not a fact. On the other hand, no amount 
of experience could over throw the theory any 
more than the irregular action of the planets 
would disprove pure mechanics.

XVII. May 19. It was vigorously contended by the earlier 
disciples of induction that deduction is useless in 
discovery. The truth is that induction without deduction 
is almost helpless. The great method of advance 
is, first, by observing the fact we form a148

A hypothesis is made only to explain the facts; otherwise 
it has no reason for existence.


149

provisional theory or hypothesis; second, by deductions 
we draw conclusions from it; third, 
we compare the calculations with the facts; agreement 
strengthens our faith, disagreement 
destroys it. After the theory has been established 
we advance by deduction beyond any possible
induction, as in Astronomy we determine 
the orbits of the comets, or the past and future 
states of the solar system; or we get formulae 
for heat and conclude to the past and future 
states of the Earth. For the conservation of 
energy we conclude that the age of the sun can 
not transcend certain limits, and that the 
system finally will come to an end. None of these 
things can be determined by induction. Concerning 
hypothesis the demands are 1st that it be intelligible; 
otherwise it has no reason for existence, 
hence a contradictory hypothesis is to be 
rejected. Philosophers sin especially against this 
principle; a good instance is the "double-faced 
somewhat" of the Materialist which is neither 
mind nor matter. Such a notion is not a 
thought but a phrase and represents a vacuum 
rather than a meaning. Of a similar character 
is the unknowable of the Agnostics. It is said 
to be above intelligence and non-intelligence; it is 
described altogether by negatives and is properly 
zero both in thought and fact. To explain a thing by 
the unknowable is to abandon the problem. The second 
demand is that the hypothesis be adequate 
to the facts, and the facts must call for it; it has 
two functions. 1st - To put us in control of phenom-150

The fact that a theory can't be disproved is no reason 
for accepting it.


151

ena. 2d to satisfy the demand for a sufficient 
reason; the latter function is the more important. 
Most of our theories give us no new power 
and their only proof is that the facts are opaque 
without them. Such is the Atomic Theory, the Ether 
Theory, the Doctrines of Geology etc. The inquiry 
then must be not whether we can use the theory to 
advance our knowledge, but whether it be demanded 
by the facts - 3d. the hypothesis must admit of 
something like proof or disproof, otherwise there 
is no limit to the vagaries of the imagination. 
For example Milton's angel leading the sun, the 
effect of the stars, or of the lines of the hand in 
determining the length of life. These are possible 
hypotheses but nothing short of revelation could 
prove or disprove them. It is doubtful whether 
Darwin's theory is not of this sort, certainly many of 
his illustrations are. After a theory is formed, it 
must next be proved; if in any case it explains 
all experience and no other will, we may be sure, 
it is not enough that it is not susceptible of 
disproof. Very few things can be disproved, for 
example Spiritualism and the belief in witches 
admit of no positive disproof. The only hope 
is in changing the character of the soil on which 
such things grow; fourth, a hypothesis must be 
harmonious with the totality of previous knowledge

Ghastly Sophistry
Thimble rigging
Intellectual fire-works
Mental Bushwhacker