[ The Logic Notebook ] |
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MS 140:
March-December 1867 |
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1867 March 23 |
I cannot explain the deep emotion with which I open this book again. Here I write but never after read what I have written for what I write is done in the process of forming a conception. Yet I cannot forget that here are the germs of the theory of the categories which is (if anything is) the gift I make to the world. That is my child. In it I shall live when oblivion has memy body. This matter of the logical principles of the different kinds of inference is a difficult matter. One way of putting it would be this. Every symbol denotes certain objects and
connotes certain characters. The symbol represents
each of those objects to have each of those
characters. The symbol may be a false one; it
may be that the objects it denotes do not have the
characters it connotes. But if S is
M in this sense
then S is P. Here the principle is that
That which is
M is what M is. Every one of the integrant parts of m
is an integrant part of each prime aliquot of
m and vice versa.
A purely contentless principle. As a logical
principle should be.
Now let us take up the synthetic arguments.
Whatever is a character of every thing denoted
by M is a character of M. Whatever
has every character of M is denoted by m.
Here are two principles. But they do not apply
to induction and hypothesis just as they stand.
Whatever is a common character of many things
denoted by M is likely to be a character
of m.
That does not quite hit the point. It does not
contain the idea that the things must have been
taken at random out of those denoted by M.
In what point of view shall we regard this
necessity for a random selection?
Suppose we look at the matter thus. Certain
things have a certain character in common. It
follows that there must be some genus of
these things which have the character. We cannot
take any genus lower than that which they
are selected as belonging to. To take a higher one
would involve a perfectly arbitrary proposition.
I am convinced that this is a very awkward way
of taking hold of the matter.
Suppose we take it up another way.
For any subject or predicate we can substitute
what?
Only that which this subject or predicate
represents Now a subject is a direct symbol of its
subject to its predicate and a predicate of its
predicate to its subject.
But a subject is also an imperfect
representation of that genus from which it has
been takenby which it is determined. It is not
a semeion sign of it as I have saidit
is an example of it.
A predicate is a representation of the thing of
which it is a random charactera copy of it.
This is horribly vague.
1867 March 25
Here is another point of view.
What is the function of a symbol as subject? To
stand for certain things. Then if a predicate be
true of all the things that it stands for as yet,
that is for all which we yet know it to stand for,
the symbol may stand as subject provisionally.
The difficulty with this is that it does not
represent the synthetic probability of the
inference.
It is however a good idea that a random
selection is equivalent to all knownthe genus
of those two would fit that.
We have
M is P in the sense that the
actual denotation or things taken under
M are P (contingent)
and 2nd in the sense that all possible things
taken under M would be P
(necessary). S is M in the senses
1st
that S has the qualities taken of
M (attributive) Still it may be doubted if Hypothesis proceeds
by random selection of qualities of the new
predicate.
Then the principle would be
the possible is like most of the actual.
1867 April 1
What is takenthe present The reason is that the parts compose the whole
and therefore what does not belong to the
majority of the whole does not belong to the
majority of the parts.
What does not belong to most of the parts does
not belong to the parts taken mostly, because the
parts to be taken are all the possible
parts.
April 12
The distinction must be observed between
Induction and Hypothesis as formal operations and
between them as leading to truth.
1867 September 24
Let me consider a little about the nature of
truth.
First. I notice that if we define an
image to be a representation completely determined
in content so that in it every attribute is
affirmed or denied there is probably no image. And
is not this what
is requisite to make an image?
What is an image? There is a good question for
dialectical research. As it
seems to me that the world has not yet exhausted
the instruction to be derived from Sophisms I
shall undertake some analysis of a collocation of
them which seems to me to lead at once to a
solution of the darkest questions of metaphysics.
In the first place what is meant by a
hypothetical proposition, when is it true? Take
this oneIf the carotid artery of a man is cut,
he will die. Or thisif the shadow of the moon
is cast on the earth, there is an eclipse of the
sun.
Truth may be defined as the concurrence of the
extension and comprehension of a representation
which has extension and comprehension independent
of one another.
Thus if a representation is a mere
likeness (as no human representations are) which
stands for nothing except what it happens fully to
agree w
ith in characters; it cannot be false of any thing
because it only stands for whatever it fully
agrees with. And therefore truth has no meaning in
reference to it.
So if a representation merely points out
certain things and implies nothing of them.
But if a representation at once indicates
certain objects and independently implies certain
characters, its truth or falsity depends on
whether those characters can be predicated of
those objects.
This definition is a bad oneit contains a
diallelebut it will answer as a preliminary
explanation and even sometimes as a test.
Now in a hypothetical proposition the function
of the protasis is to mark the sphere of
the representation, which it may do by means of it
s connotation or otherwise. The apodosis on the
other hand conveys the content of the
representation. And the question whether the
proposition is true is the same as whether that
content belongs in fact to that sphere.
Thus in the propositionIf the shadow of the
moon is cast on the earth, the sun is
eclipsedthe former clause indicates the
circumstances to which the statement made in the
latter clause is applicable.
Take now another case. If the motion of the
earth in its orbit were suddenly arrested and the
perturbative effects of other bodies pre-
vented, it
would fall in a direct line to the sun. Unless the
word truth be taken in a quite improper
sense, this proposition is true. Yet how? For in
this case there are no such circumstances as those
indicated,
they are even physically impossible, so that this
would seem to be a representation like a copy
which [ . . .]
1867 Sep. 26
Let
x be that of which I know absolutely
nothing
I know Greek. Greek is not present to my
reminiscence, but occasion will call it up. This
then is the essence of knowledge and what no
occasion will call up is not known or conceived. I
have therefore no conception of the absolutely
unknowable.
Now a proposition is true in all its
consequences for possible experience that either
constitutes the truth of the proposition
or it is false in reference to something which
cannot be known (in which case the unknowable
means something) or else it
is devoid of meaning.
A proposition is not devoid of meaning which
has true consequences.
1867 Sep. 27
Every quality which we know of is of course
either experienced or inferred from experience.
We admit that things may have qualities which we
do not know but that is because we may conceive of
a state of knowledge in which something more is
predicable of them. But do we mean anything if we
say that a thing has a quality which cannot be
predicated of it; that is which is unknowable and
inconceivable? What can we mean by such a
statement? We can imagine such a quality for as
Berkeley says were we to imagine it, it would not
be unimaginable. Can we have any general or
relative notion of it? To have a general notion
appears to be, having a habit according to which a
certain sort
of images will arise on occasion, that is having a
capacity of imaging the particulars and the sense
of this habit. But here such a thing is
impossible.
Let us say then that it means nothing to say
that a thing has an
inconceivable quality. An
inconceivable qualityone inconceivable by
every being and absolutelyis no
quality.
Sep. 28
To say that a word has meaning is to say that a
conception corresponds to it.
To say that we have a general conception of a
triangle for instance is to say that upon the
occasion of a triangle being presented to the
imagination or in experience a certain feeling
complicated in a certain way arises. We have no
conception therefore of that of
which no determination can be presented in the
imagination.
Consequently, though we may undoubtedly mean
something by the inconceivable we can mean nothing
by an absolutely and in itself inconceivable
predicate.
Hence such a predicate is no predicate. To say that we know what a word means is to say
not that we can always apply it rightly in fact
but that we can always apply it rightly to
imagined cases.
On Logical Extension and
Comprehension One term is more extensive than another, when
it is predicable of all that the latter is and of
more, besides. One term is more comprehensive than
another when all the characters predicable of the
latter are predicable of it and more beside.
From this it is plain, at once, that the
greater the extension the less the comprehension and vice versa.
We may distinguish real and verbal
Comprehension and extension; thus "Englishman"
is more extensive than "Surly Englishman" since
it includes also Englishmen not surly. But if
there is any doubt whether any of the latter
exist, it is only verbally more extensive.
So "magnanimous hero" is more comprehensive
than "hero" but if there is a doubt whether
anything is conveyed by the adjective not already
conveyed by the noun then the difference is merely
verbal.
A better instance is "man John" and "man."
Confining our attention to Real Comprehension
and Extension, we may observe that the predication
spoken of may be either
1st such as could be made with no information
except the meaning of the word. This I shall term the Essential
Extension and Comprehension.
2nd such as could logically be made in a
particular supposed state of information. This I
shall term the Inferred Extension and
Comprehension.
3rd such as could be made if our information
were complete. This I shall term the Natural
Extension and Comprehension.
Essential
Extension and Comprehension
One half of all terms are positive and one half
negative. Positive terms are defined, and
therefore have an essential Comprehension. But
they have no real essential extension. Negative
terms are not defined and therefore have no real
essential comprehension but they have a real
essential extension since it is known that no
determinate conception can embrace the whole
sphere of being.
Man is a rational
animal
Two terms cannot be equal in essential
extension or comprehension because if they were
they would have the same meaning. The relation of
two terms in essential comprehension or extension
may not be measurable on account of the want of
distinctness of one or both of those
terms.
Oct. 2
There ought to be a proposition relating to
universal and particular terms similar to that
relating to affirmatives and negatives. My
experience of logical symmetries assures me of it.
Perhaps this is it. A particular term will be
found generally to have some natural extension,
therefore all the extension implied, but
it will not have a comprehension adequate to limiting its
extension as it is limited. On the other hand a
universal term, will never have
an extension capable of limiting its comprehension
as it is limited since new propositions will be
discovered.
This is not yet very clear to me. But it would
seem that as there is an arbitrariness in the
extension of particulars so that we may exclude
this or that from its extension so as to be able
to predicate of it what we cannot predicate of
them, so there is an arbitrary element in the
comprehension of the universal so that this or
that may be omitted from it so that we can
predicate it of (imaginary things) of which we
could not predicate them.
I think this is it. In a particular there is no
concrete thing which must be included under it; in
a universal there is no concrete quality which
must be included in it.
If some S
is P
If S isP
Ah I think I have it now
SomeS has a complete concrete comprehension
This cannot be said of Any man
which is therefore without concrete
comprehension.
On the other hand Some man is
not completely defined in extension since it is
disjunctive alternative while any man
applies definitely to certain things.
Note the meaning of a particular in the
predicate. Some S means Either
S' S'' S''' &c. select which I please.
Some S is
P, that is let me take as my subject one
what one I Now this does not hold for M is some
P unless M is completely
determined in comprehension just as Any S
is P only holds if P has a very
wide extension.
We may therefore
say
Oct. 2 2. Of the Effect of a Change of
Information
Suppose it is learned that
Any S is
P
Then S receives an addition to its
comprehension.
P an addition to its
extension.
If we looking at an S find
it to be P
Some S is P
This adds to the extension of
Psupposing we know what
S.
Any S is not-P
This adds to the comprehension of
Ssupposing we know something of
not-P.
1867 Nov. 24
I wish to investigate the nature of a simple
concept. Such a concept first arises as predicated
of some object (occasion of
experience)
S is M
On the ground of some previous representation
of the object. (Not immediate)
1. entirely knowable. Intuitional. Capable of external
existence.
The predication of the concept is virtually
contained in this previous representation.
To say that a simple concept is the immediate
apprehension of a quality is but a mode of saying that its meaning is
given in the representation which gives rise to it inasmuch as it is as
much as to say that that quality is contained in that
representation.
1867 Dec. 7
When I conceive a thing as say 'three' or say
'necessary' I necessarily have some concrete
object in my imagination. I have some concrete
object'the necessary'. By saying that I have
the necessary in my mind, it is not meant that I
have all necessary things in mind. Nor that I have
simply the character of necessity. For
what I am thinking is not necessity but the
necessary. Then I must have something which I
recognize as a general sign of the necessary. But
why should that particular feeling which is a sign
of the necessary be a sign of that any more than
of anything else? Because such is my constitution. Very true.
When I conceive as say "necessary," I have
some singular object present to my imagination. I
have not all necessary things separately
imaged.
Doubted whether I ever have an absolutely
singular object
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Copyright of the Peirce Edition Project 1998 |