and classify are simply those parts of this continuous affirmation
of consciousness which are from time {41} to time separately made
distinct. Each of them therefore must be regarded as a partial
expression of the nature of reality, and the subject will always be
Reality in one form, and the predicate reality in another form. The
ultimate and complete judgment would be the whole of Reality predicated
of itself. All our logical judgments are such portions and fragments
of this judgment as we can grasp at the moment. Some of these gather
up in a system whole provinces of reality, others merely enlarge,
interpret, or analyse the content of a very simple sense-perception.
We shall not go far wrong in practice if we start from this judgment
of Perception as the fundamental kind of Judgment. The real subject in
Judgment is always Reality in some particular datum or qualification,
and the tendency of Judgment is always to be a definition of Reality.
We see the parts of Judgment most clearly in such thoughts as “This is
blue”; “This is a flower”; “That light is the rising sun”; “That sound
is the surf on a sandy shore.” In these we can plainly distinguish the
element of presentation and the interpretative construction or analytic
synthesis which is by the judgment identified with it.
{42}
LECTURE III THE RELATION OF LOGIC TO KNOWLEDGE
_Meaning of “Form”_
1. I spoke of the whole world, which we take to be real, as presented
to us in the shape of a continuous judgment. It is the task of Logic
to analyse the structure of this Judgment, the parts of which are
Judgments.
The first thing is then to consider what sort of properties of
Judgments we attend to in Logic. It is commonly said that Logic is a
formal science; that is, that it deals with the form, and not with the
content or matter of knowledge.
This word “form” is always meeting us in philosophy. “Species” is Latin
for form, as εἶδος and ἰδεα [1] are Greek for form. The form of any
object primarily means its appearance, that which the mind can carry
away, while the object as a physical reality, as material, remains
where it was. It need not mean shape as opposed to colour; that is a
narrower usage. The Greek opinion was no doubt rooted in some such
notion as that in knowing or remembering a thing the mind possessed
its form or image without its matter. Thus the form came to stand for
the knowable shape or structure which makes a thing what it is, and by
which we recognise it when we see it. This was its species or its idea,
the “image,” as it is used in the phrase, “Let us make man in our own
image.” So in any work of the hands {43} of man, the form was the shape
given by the workman, and came out of his mind, while the matter was
the stuff or material out of which the thing was made.
[1] [= “eidos” and “idea”. Tr.]
The moment we contemplate a classification of the sciences, we see
that this is a purely relative distinction. There is no matter without
form. If it was in this deep sense without form, it would be without
properties, and so incapable of acting or being acted upon. In a
knife the matter is steel, the form is the shape of the blade. But
the qualities of steel again depend, we must suppose, upon a certain
character and arrangement in its particles, and this is, as Bacon would
have called it, the _form_ of steel. But taken as purely relative,
the distinction is good _prima facie_. Steel has its own form, but
the knife has its form, and the matter steel can take many other
forms besides that of a knife. Marble has its own form, its definable
properties as marble (chemical and mechanical), but in a statue, marble
is the matter, and the form is the shape given by the sculptor.
Now applying this distinction to knowledge in general, we see that
all science is formal, and therefore it is no distinction to say that
Logic is a formal science. Geometry is a formal science; even molecular
physics is a formal science. All science is formal, because all science
consists in tracing out the universal characteristics of things, the
structure that makes them what they are.
The particular “form,” then, with which a science deals is simply the
kind of properties that come under the point of view from which that
science in particular looks at things. But a very general science is
more emphatically formal than {44} a very special science. That is to
say, it deals with properties which are presented in some degree by
everything; and so in every object a great multitude of properties
are disregarded by it, are treated by it as matter and not as form.
In this sense Logic is emphatically “formal,” though not nearly so
formal as it is often supposed to be. The subject-matter of Logic,
then, is Knowledge _qua_ Knowledge, or the form of knowledge; that is,
the properties which are possessed by objects or ideas _in so far as
they are members of the world of knowledge_. And it is quite essential
to distinguish the form of knowledge in this sense from its matter or
content. The “matter” of knowledge is the whole region of facts dealt
with by science and perception. If Logic dealt with this in the way in
which knowledge deals with it, _i.e._ simply as a process of acquiring
and organising experience, then Logic would simply be another name for
the whole range of science, history, and perception. Then there would
be no distinction between logic and science or common sense, and in
trying to ascertain, say, the wave-length of red light, or the cab-fare
from Chelsea to Essex Hall, we should be investigating a logical
problem. But we see at once that this is not what we mean by studying
knowledge as knowledge. Science or common sense aims at a particular
answer to each problem of this kind. Logic aims at understanding
the type and principles both of the problem and of its answer. The
details of the particular answer are the “_matter_ of fact.” The type
and principles which are found in all such particular answers may be
regarded as the form of fact, _i.e._ that which makes the fact a fact
in knowledge.
Jevons appears to me to make a terrible blunder at this {45} point. He
says [1]--“One name which has been given to Logic, namely the Science
of Sciences, very aptly describes the all-extensive power of logical
principles. The cultivators of special branches of knowledge appear
to have been fully aware of the allegiance they owe to the highest
of the sciences, for they have usually given names implying this
allegiance. The very name of Logic occurs as part of nearly all the
names adopted for the sciences, which are often vulgarly called the
‘ologies,’ but are really the ‘logics,’ the ‘o’ being only a connecting
vowel or part of the previous word. Thus geology is logic applied to
explain the formation of the earth’s crust; biology is logic applied
to the phenomena of life; psychology is logic applied to the nature
of the mind; and the same is the case with physiology, entomology,
zoology, teratology, morphology, anthropology, theology, ecclesiology,
thalattology, and the rest. Each science is thus distinctly confessed
to be a special logic. The name of Logic itself is derived from the
common Greek word λόγος, which usually means _word_, or the sign and
outward manifestation of any inward thought. But the same word was
also used to denote the inward thought or reasoning of which words are
the expression, and it is thus probably that later Greek writers on
reasoning were led to call their science ἐπιστήμη λογική, or logical
science, also τέχνη λογική or logical art. [2] The adjective λογική,
being used alone, soon came to be the name of the science, just as
Mathematic, Rhetoric, and other names ending in ‘ic’ were originally
adjectives, but have been converted into substantives.”
[1] _Elementary Lessons_, p. 6.
[2] [= “logos”, “episteme logike”, “techne logike” and “logike”. Tr.]
{46} This account of the connection between the name “Logic” and the
terminations of the names of the sciences appears precisely wrong.
Whatever may have been the exact meaning of the expression “Logic,”
or “Logical curriculum,” [1] or “art,” or “science” when first
employed, there can be no doubt that the word logical had a substantive
reference to that about which the science or teaching in question
was to treat. The term “logic,” therefore, corresponds not to the
syllables “logy” in such a word as “Zoology,” but to the syllables
“Zoo,” which indicate the province of the special science, and not
its character as a science. Zoology means connected discourse (λόγος)
about living creatures. Logic meant a curriculum, or science or art
dealing with connected discourse. The phrase “Science of Sciences,”
rightly interpreted, has the same meaning. It does not mean that Logic
is a Science which comprises all the special sciences, but that Logic
is a Science dealing with those general properties and relations which
all sciences _qua_ sciences have in common, but omitting, as from its
point of view matter and not form, the particular details of content by
which every science answers the particular questions which it asks. It
is wild, and most mischievous, to say that “every science is a special
logic,” or that “biology is Logic applied to the phenomena of life.”
This confusion destroys the whole disinterestedness which is necessary
to true scientific Logic, and causes the logical student always to have
his eye on puzzles, and special methods, and interferences by which he
may teach the student of science how to perform the concrete labour
of research. We quite admit that {47} a looker-on may _sometimes_ see
more of the game, and no wise investigator would contemn _a priori_
the suggestions of a student like Goethe, or Mill, or Lotze, because
their author was not exclusively engaged in the observation of
nature. But all this is secondary. The idea that Logic is a judge of
scientific results, able to pass sentence, in virtue of some general
criterion, upon their validity and invalidity, arises from a deep-lying
misconception of the nature of truth which naturally allies itself with
the above confusion between Logic and the special sciences.
[1] πραγμάτεια [= pragmateia Tr.]. See Prantl, i. 545.
Therefore the relation between content or matter of knowledge, and
the form which is its general characteristic as knowledge, is of
this kind. We can either study the objects of knowledge directly as
we perceive them, or indirectly, as examples of the way in which we
know. As studied for their own sake, they are regarded as the matter
or content in which the general form of knowledge finds individual
realisation. In botany, for instance, we have a large number of actual
plants classified and explained in their relation to one another.
A botanist is interested directly in the affinities and evolution
of these plants, and in the principles of biology which underlie
their history. He pushes his researches further and further into
the individual matters that come to light, without, as a rule, more
than a passing reflection upon the abstract nature of the methods
which he is creating as his work proceeds. He classifies, explains,
observes, experiments, theorises, generalises, to the best of his
power, solely in order to grasp and render intelligible the region of
concrete fact that lies before him. Now while his particular results
and discoveries {48} constitute the “form” or knowable properties of
the plant-world _as the object of botanical science_, the science
which inquires into the general nature of knowledge must treat these
particular results as “mere matter”--as something with which it is
not directly concerned, any more than the art which makes a statue
is primarily and directly concerned with the chemical and mechanical
properties of marble. The “form” or knowable properties with which the
general science of knowledge is directly concerned, consists in those
methods and processes which the man of science, developing the modes
in which common sense naturally works, constructs unconsciously as he
goes along. Thus, not the nature and affinities of the plant-world,
but classification, explanation, observation, experiment, theory, are
the phenomena in virtue of which the organised structure of botanical
science participates in the form of knowledge, and its objects become,
in these respects, objects of logical theory.
Hence some properties and relations of objects, being the form or
knowable structure of the concrete objects as a special department of
nature, correspond to the mere matter, stuff, or content of Knowledge
in general, while other properties and relations of objects, being
their form or knowable structure as entering into a world of reality
displayed to our intelligence, correspond to the form of Knowledge as
treated of by a general inquiry into its characteristics, which we
call Logic. It is just as the qualities or “forms” of the different
metals of which knives can be made are mere matter or irrelevant detail
when we are discussing the general “form” or quality of a good knife,
{49} whatever its material. A reservation on this head appears in the
following section.
_Form of Knowledge dependent on Content_
2. For the form of Knowledge depends in some degree upon its matter.
It is very important to realise this truth; for if Logic is swamped
by being identified with the whole range of special sciences, it is
killed by being emptied of all adaptation to living intelligence. What
is called Formal Logic _par excellence_ in all its shapes, whether
antiquated as in Hamilton’s or Thomson’s Formal Laws of Thought,
or freshly worked out on a symbolic basis as by Boole and others,
has, it appears to me, this initial defect, _when considered as a
general theory of Logic_. As a contribution to such a theory, every
method which will work undoubtedly has its place, and indicates and
depends upon some characteristic of real thought. But in the central
theory itself, and especially in so short an account of it as must
be attempted in these lectures, I should be inclined to condemn all
attempts to employ symbols for anything more than the most passing
illustration of points in logical processes. All such attempts, I must
maintain, share with the old-fashioned laws of Identity, Contradiction,
and Excluded Middle the initial fallacy of representing a judgment
by something which is not and cannot be in any way an adequate
symbol of one. If, in order to get at the pure form of Knowledge,
we restrict ourselves to very abstract characteristics in which all
knowledge appears, very roughly speaking, to agree, and which can be
symbolized for working purposes by combinations of signs which have
not the essential properties of ideal contents, then we have _ab
initio_ substituted for the judgment something which is a very {50}
abstract corollary from the nature of judgment, and may or not for
certain purposes and within certain limits be a fair representative
of it. We cannot and must not exclude from the form of Knowledge its
modifications according to “matter,” and its nature as existing only in
“matter.”
In fact, the peculiar “form” of _everything_ depends in some degree
on its “matter.” A statue in marble is a little differently treated
if it is copied in bronze. A knife is properly made of steel; you
can only make a bad one of iron, or copper, or flint, and you cannot
make one at all of wax. Different matters will more or less take the
same form, but only within certain limits. So it is in Knowledge. The
_nature of objects as Knowledge_--for we _must_ remember that “form”
in our sense is not something put into the “matter,” something alien
or indifferent to it, but is simply its own inmost character revealed
by the structural relations in which it is found capable of standing
[1]--depends on the way in which their parts are connected together.
[1] The example of the marble statue may seem to contradict
this idea; and no doubt the indifference of matter to form is
a question of degree. But the feeling for material is a most
important element in fine art; and in knowledge there is only a
relative distinction between formal and material relations.
Let us compare, for example, the use of number in understanding objects
of different kinds.
Suppose there are four books in a heap on the table. This heap of
books is the object. We desire to conceive it as a whole consisting
of parts. In order to do so we simply _count_ them “one, two, three,
_four_ books.” If one is taken away, there is one less to count; if
one is added, there is one more. But the books themselves, as books,
are not {51} altered by taking away one from them or adding one to
them. They are parts indifferent to each other, forming a heap which is
sufficiently analysed or synthesised by counting its parts.
But now instead of four books in a heap, let us think of the four
sides of a square. Of course we _can_ count them, as we counted the
books; but we have not conceived the nature of the square by counting
its sides. That does not distinguish it from four straight lines drawn
anyhow in space. In order to appreciate what a square is, we must
consider that the sides are _equal_ straight lines, put together in a
particular way so as to make a figure with four right angles; we must
distinguish it from a figure with four equal sides, but its angles not
right angles, and from a four-sided figure with right angles, but with
only its opposite sides equal; and note that if we shorten up one side
into nothing, the square becomes a triangle, with altogether different
properties from those of a square; if we put in another side it becomes
a pentagon, and so on.
These two things, the heap of books and the square, are _prima
facie_ objects of perception. We commonly speak of a diagram on a
blackboard or in a book as “a square” if we have reason to take it
as approximately exact, and as intended for a square. But on looking
closer, we soon see that the “matter,” or individual attributes, of
each of these objects of our apprehension demands a different form of
knowledge from that necessary to the other. The judgment “_This_ heap
of books has four books in it” is a judgment of enumerative perception.
The judgment “_The_ square has four sides” is a judgment of systematic
necessity.
{52} Why did we not keep the two judgments in the same logical shape?
Why did we say “_This_ heap” and “_The_ square”? Why did we not say
“this” in both propositions, or “the” in both propositions? Because
the different “matter” demands this difference of form. Let us try.
“The heap of books has four books in it.” Probably we interpret this
proposition to mean just the same as if we had said “This heap.” That
is owing to the fact that the judgment naturally occurs to us in its
right form. But if we interpret “The heap” on the analogy of our
interpretation of “The square,” our judgment will have become false.
It will have come to mean “Every heap of books has four books in it,”
and a judgment of perception will not bear this enlargement. The
subject is composite, and one, the most essential of its elements, is
destroyed by the change from “this” to “the.”
Let us try again. Let us say “This square has four sides.” That is
not exactly false, but it is ridiculous. Every square must have four
sides, and by saying “this square” we strongly imply that foursidedness
is a relation of which we are aware chiefly, if not exclusively, in
the object attended to in the moment of judging, simply through the
apprehension of that moment. By this implication the form of the
judgment abandons and all but denies the character of systematic
necessity which its content naturally demands. It is like saying, “It
appears to me that in the present instance two and two make four.” The
number of sides in a square, then, is not a mere fact of perception,
while the number of books in a heap is such a fact.
But you may answer by suggesting the case that an {53} uninstructed
person--say a child, with a square figure before him, and having heard
the name square applied to figures generally resembling that figure,
may simply observe the number of sides, without knowing any of the
geometrical properties connected with it; will he not then be right in
saying, “This square has four sides”?
Certainly not. In that case he has no right to call it a square.
It would only be a name he had picked up without knowing what it
meant. All he has the right to say would be, “This object” or “This
figure has four sides.” That would be a consistent judgment of mere
perception, true as far as it went. It is always possible to apprehend
the more complex objects of knowledge in the simpler forms; but then
they are not apprehended adequately, not _as_ complex objects. It is
also possible to apply very complex forms of knowledge to very simple
objects. Most truths that can be laid down quite in the abstract about
a human mind could also be applied in some sense or other to any speck
of protoplasm, or to any pebble on the seashore. And every simple
form of knowledge is always being pushed on, by its own defects and
inconsistencies, in the direction of more complex forms.
So far I have been trying to show that objects are capable of being
different in their nature as knowledge as well as in their individual
properties; and that their different natures as knowledge depend on the
way in which their parts are connected together. We took two objects
of knowledge, and found that the mode of connection between the parts
required two quite different kinds of judgment to express them. Let us
look at the reason of this.
{54} _The relation of Part and Whole_
3. The relation of Part and Whole is a form of the relation of Identity
and Difference. Every Judgment expresses the unity of some parts in a
whole, or of some differences in an Identity. This is the meaning of
“construction” in knowledge. We saw that knowledge exists in judgment
as a construction (taking this to include maintenance) of reality.
The expression whole and parts may be used in a strict or in a lax
sense.
In a strict sense it means a whole of quantity, that is, a whole
considered as made up by the addition of parts of the same kind, as a
foot is made up of twelve inches. In this sense the whole is the sum of
the parts. And even in this sense the whole is represented within every
part by an identity of quality that runs through them all. Otherwise
there would be nothing to earmark them as belonging to the particular
whole or kind of whole in question. Parts of length make up a whole
of length, parts of weight a whole of weight, parts of intensity a
whole of intensity, in so far as a whole of intensity is quantitative,
which is not a perfectly easy question. Wholes like these are “_Sums_”
or “_Totals_”. The relation of whole to part in this sense is a very
simple case of the relation of differences in an identity, but for
that very reason is not the easiest case to appreciate. The relation
is so simple that it is apt to pass unnoticed, and in dealing with
numerical computation we are apt to forget that in application to any
concrete problem the numbers must be numbers of something having a
common quality, and that the nature of this something may affect the
result as related to real fact, though not as a conclusion from pure
{55} numerical premisses. In a whole of pure number the indifference
of parts to whole reaches its maximum. The unit remains absolutely the
same, into whatever total of addition it may enter.