feelings are as much abstracts as motions. Subjectivity and objectivity
are correlative terms. There is as little a duality in the idea, that
subjects presuppose objects as that effects presuppose causes. There
are not causes in the world which are nothing but causes, nor are there
effects which are nothing but effects. Take for instance an historical
event. Was Cæsar’s death a cause or an effect? Plainly, this depends upon
the view we take. As the sequence of the wounds which Cæsar received
from his assassins it was an effect; as the beginning of the civil war
consequent thereupon it was a cause. If I look at you, you are the object
and I am the subject. If you look at me, it is the reverse. Thus the
relation of a certain thing to its surroundings makes of it a subject,
while the surroundings are its objects.
Subject and object being correlatives, we can very well understand why
there are no “subjects in themselves”; every subject is at the same time
an object in the objective world. We can further understand, why every
subjectivity except our own withdraws itself from direct observation.
We can observe the movements of organisms like ourselves and judge by
way of analogy that they feel pain or enjoy pleasure. We see their
motions which betray certain feelings, but we can never see the feelings
themselves; and even supposing that we could enter into the brain of a
man and that the whole mechanism of brain-action were laid open to our
inspection in its minutest details, we should see motions, combinations
and separations, integrations and disintegrations, we should see the
oxydation of the gray substance, which would appear as a great turmoil
and excitement, but we should see (as Leibnitz says) no thoughts, no
perceptions, no feelings. That it cannot be otherwise is obvious when
we consider that our objects will always present to us the character of
objectivity.
But suppose We were an atom of oxygen and entered into the process of
brain-action as an active factor, our subjectivity would soon become
absorbed and welded into a higher unity with the subjectivity of the
other atoms. We should then, as a part of that brain’s consciousness,
feel these feelings, perceptions, and thoughts; we should, then, _be_ the
subject which we could not see and which we were searching for in vain in
the world of objectivity.
This conception of the correlation of subjectivity and objectivity
does not only convincingly explain the unity of feeling and motion, it
does not only establish a satisfactory monism, it throws light also on
some other of the questions that puzzle us. How is it that we do not
feel our brain-motions to be brain-motions? We feel our feelings only;
and when feeling our feelings we do not so much feel _that_ we feel as
_what_ we feel. In other words, we feel the contents of our feelings; we
feel their import, their meaning; we are aware of their significance;
our consciousness is conscious of the object, the presence of which is
indicated by this special feeling. Our attention is concentrated upon the
messages conveyed by and contained in the different feelings.
These messages of certain feelings are the interpretations given either
to certain sense-impressions or they are the thought-symbols representing
some abstracts, representing certain features of sense-impressions.
How little we feel our brain-motions when we think, can be learned
from the fact that some nations place the seat of thinking in the
heart, others in the stomach or even the bowels, while even so great a
naturalist as Aristotle regarded the brain as cold and insensible; he
made the observation that man is in possession of the relatively largest
brain, but he understood its function so little that he thought it served
to cool the warmth rising from the heart.
It is strange that every subjective feeling so long as it remains within
itself can neither be localised nor determined. We know nothing whatever
of the brain-motion that thinks a certain idea. We can fairly assume
that every idea is in its objective existence a peculiar kind of brain
motion taking place in a particular part of the brain, but we are not
conscious of the brain-motion as a special and localised motion. We are
quite unable to tell the difference that we must suppose to exist between
the forms of the brain-structures or combinations of brain-structures and
their motions when we think say for instances of virtue and of vice. We
are conscious only of the idea and not of their objective correlates.
Whatever we know of our body, we know only through sensation; i. e.,
by the same means by which we know of other things. Our body is to us,
and is represented with the assistance of the senses, as an object in
the objective world. As such it is localised and all its relations and
activities are determined. Whatever subjective feeling we have concerning
any state of ourselves, remains indistinct until with the help of the
senses it is made an object to our observation. Who has not as yet made
the experience that he was unable to localise a toothache. The pain
itself gives no information either as to its nature and cause or as to
the seat of the suffering. The pain itself is purely subjective. All the
objective facts have to be localised with the assistance of the senses.
The suspected regions must be made the object of experiments and if any
irritation of a certain spot increases the ache, it will be assumed to be
the seat of the pain. And even then how often is a patient mistaken not
only almost always as to the nature but often also as to the seat of the
pain.
These facts appear strange, but they cease to be strange, when we
consider that the nature of subjectivity is feeling. Subjectivity can as
little become directly conscious of its own objectivity as an eye can
look at itself. However, an eye can look at its image in the mirror. So
the complex of subjective existence, which is through the interaction of
an organism united in what we call a soul, can and does turn the channels
of its own senses back upon itself and thus forms an opinion concerning
its own objectivity. Man’s knowledge of his own objective existence is
not due to any internal and direct perception of self, but solely to the
same experience through which he receives information concerning the rest
of the world.
P. C.
A REPLY TO A CRITIC.
WITH A DISCUSSION OF NECESSARY TRUTHS.
_To the Editor of The Monist_:
I hope it is not a breach of etiquette to ask you to forward to your
reviewer the following remarks in reply to his criticism of my work (_The
Foundations of Geometry_, reviewed in Vol. II, No. 1, of _The Monist_).
If he is good enough to review my second book also, I think they will
clear up some misunderstandings.
Your reviewer commences with some general remarks, against which I have
nothing to say. He then proceeds to consider my “requirements for a
logical definition.” Here he seems to find a difficulty—which may be
due to my not having expressed myself clearly. If so I hope he will
read what I say on the same subject in my _Essay on Reasoning_, which
I cannot believe he will find “indefinite” or not well “issuable.” But
indeed I cannot see where his difficulty comes in with my old statement
of the case. I state perfectly clearly that requirements (3) and (4) are
not _logically_ necessary for a definition, but are only required if
that definition is intended to give a _particular meaning_ to the word.
He tries to reduce my argument _ad absurdum_ by giving a definition
of “troft.” But so far from being absurd his definition is perfectly
good. According to it “troft” would include in its denotation all
our percepts and concepts. When however he goes on to say “... These
significant names must be so used that the intellectual sensibility shall
be excited to perceive that which is intended to be defined,” I differ
from him entirely. This is only required for a _description_, not for a
_definition_ (see _Essay on Reasoning_, p. 53).
Your reviewer’s only solid objection to my “requirements” seems to be
that the fourth includes all the rest. This is only true if the term
proposed for definition has an import which has already been determined;
but even in such a case it is better to consider the requirements
separately, as I have given them. For the force of objections under the
different headings varies enormously. An objection under heading (1),
if established, would be fatal to any definition whatever. One under
heading (2) so far from being fatal would only be a suggestion for the
improvement of the definition. Objections under either of the headings
(3) and (4) would only be to the effect that the term as defined meant
something different from what it was desired that it should mean. It
is however convenient to consider (3) and (4) separately as it would
generally be possible to decide (3) at once, whereas if a doubt were
raised under heading (4) it might lead to a prolonged discussion before
it could be laid. I do not however pretend that the “requirements” are
laid down in my _Foundations of Geometry_ in the best possible form.
Indeed I have altered the form in my second essay. There is moreover
one requirement for a logical definition which is not included in my
heading (1) in the _Foundations of Geometry_, though it is included in
(4). This defect is remedied in the _Essay on Reasoning_ (p. 55). It is
curious that your reviewer should have missed this point, as it is the
very one on which he attacks my definition of “direction.” It is that
the assertions in a definition must not be _independent_ of the meaning
of the term defined. If they were, the assertion would be equally true
(or false) whatever meaning the term might have. The _import_ of the
term would therefore be unlimited. In the case of explicit definitions a
similar error is called _circulus in definiendo_.
When your reviewer goes on to attack my definition of “direction”
why does he change his front all at once, and disregard all the
considerations he has just been discussing? Why does he not apply
my, or his own, requirements for a definition to the case in point?
The criticism he actually does put forward will not bear a moment’s
investigation. If my definition is “circular,” the assertion must be
equally true whatever meaning is ascribed to the term. Well, then, let
us try the effect of giving to it the meaning we ordinarily ascribe
to “cheese.” Is it equally true that “a cheese may be conceived to be
indicated by naming two points, as the cheese from one to the other”?
Clearly not. But not only does this one assertion out of my definition
exclude the import of “cheese” from the meaning of “direction,” but, more
particularly, it distinguishes between the “three distinct but closely
associated notions” which your reviewer quite rightly says “become
confused in thought and expression unless the most solicitous care is
taken to distinguish them.” This is exactly the care which I _have_
taken, by framing my definition.
I need not say much about the rest of the criticism. Your reviewer’s
remarks on my definition of “angle” are simply due to the fact that he
has not read the definition carefully, and probably has not read the note
on the top of page 36 at all. It may make it clearer to him if I point
out that if “we imagine a northeast-southwest line cutting an east-west
line,” we imagine _four_ different directions and therefore (4⋅3)/(1⋅2)
= 6 angles. Two of these are the straight angles between the opposite
directions of each of the two lines. The other four are what Euclid calls
“the angles between the lines.” As an angle, according to my definition,
has no local habitation in space, it is, _prima facie_, meaningless to
talk of the “right hand upper angle.” But if this is only an abbreviation
for “the angle between the directions upwards and to the right,” then
“the right hand upper angle” means the same as it would in Euclid.
With the remarks about the nature of the challenge I have thrown down I
heartily agree. May I however suggest that I have a right to expect that
criticism should be, not only “competent and candid,” but careful? It
is a difficult subject, and _I_ at least am not always able to express
myself in such a way that my meaning cannot be misunderstood by any one.
I think if your reviewer looks at what I have said again, with the aid
of what I say further in my _Essay on Reasoning_, he will see that his
criticisms have really originated in misunderstandings, and perhaps he
will alter his judgment that I have “come short of the high result to
which I aspired.”[18]
But my chief object in writing to you to-day is to bring specially to
your notice my ideas on the nature of so-called “necessary truths.”
I am not quite clear how far you will find my views harmonise with
your own. To a great extent I am inclined to think they are simply a
further analysis of the views you express in _The Monist_ and in your
_Fundamental Problems_. I will briefly sketch my own ideas and you can
then judge whether they are yours also or not.
In my _Essay on Reasoning_ I classify assertions as Truisms (assertions
whose truth depends solely on the definitions of their terms) and Real
Assertions, which convey some real subjective or objective information.
I show that the validity of all purely formal knowledge depends on the
fact that it is deduced from definitions alone, which are laid down
_arbitrarily_ and that the supposed peculiar certainty of the theorems
of pure mathematics is merely due to the fact that they are all truisms.
Thus, I think it a misnomer to call such theorems “necessary” truths. It
would be nearer the mark to call them “arbitrary” truths.
There is no _necessity_ whatever about the theorem “twice two is four.”
“Two” is defined as 1 + 1; “twice,” as the operation of adding a thing to
itself. It follows from this that “twice two” is 1 + 1 + 1 + 1; and this,
by _definition_, is “four.” If “four” were defined as 1 + 1 + 1, (and
there is no “necessary” reason why it should not be,) then “twice two”
would _not_ be “four.” The assertion “twice two is four” conveys no real
information whatever—at best it could only tell us what one of its terms
meant if they had not all been previously defined.
I cannot insist too strongly on the importance of a proper understanding
and use of logical definition. If you desire to know whether a given
assertion is true or false, _a priori_ or _a posteriori_, the first step
in the investigation MUST be to find out how its terms were defined.
If it turns out that the truth (or falsehood) of the assertion can
be formally deduced from these definitions, then the assertion is a
truism (or contradiction in terms): in either case it can give no real
information, and even if true cannot be a “necessary” truth. Only if the
definitions of the terms are both independent and consistent is it open
to discussion how we might come to a knowledge of the fact it expresses.
I may briefly indicate here how I think the problem ought to be
attacked. “Objective facts” can only be established by induction. I do
not mean by that term necessarily the process described by Mill, but
some similar process, based ultimately on _inductio per enumerationem
simplicem_. Now no such process can ever lead to a necessary truth. The
most fundamental and certain induction which can be made, that which
induces us to believe in the objectivity of our environment, does not
lead to a “necessary truth”; and much less can any other induction based
upon this one do so. “Objective facts” then may be established with
greater or less probability, but can never be _necessarily_ true. But
all inductions are based on our perceptions, that is ultimately on our
subjective sensations. And a man can, nay, must be, absolutely certain
of the reality of his own sensations though he cannot be certain of the
interpretations he puts upon them. If I have a toothache I cannot be
absolutely certain that I have a tooth, but, at least while the pain
lasts, I am _absolutely_ certain that I have an ache. And so of any
subjective sensation.
I can similarly be absolutely certain that I entertain a given concept,
while that concept is before my mind; though of course it is possible
that if I assert the possession of that concept I may do so in language
which may be misunderstood by the person I am addressing. If then a
man has certain concepts which he can call up at will, the reality of
those concepts, _qua_ concepts, is to him a _necessary truth_. He may
lay down such necessary truths as axioms, and by their aid he may give
real subjective import to a symbolic argument, and so obtain new and
complicated assertions which are also to him necessary truths. This is
what I do in my subjective theory of geometry. That theory might be
regarded as purely symbolic—the axioms might have been left out, and
all its conclusions looked upon as mere truisms. The conclusions of
geometry of four or more independent directions can perhaps _only_ be
regarded as truisms. But by the aid of the axioms, geometry of two and
three independent directions can be given real subjective import, and its
conclusions therefore regarded as necessary truths, as long as they are
only taken subjectively. They may further be applied objectively by the
aid of objective facts established by induction, but in this case their
validity is no greater than that of the primary facts, the counterparts
of the subjective axioms, which are employed to give the theory objective
import.
I confess I have not studied Kant sufficiently to say that his views
differ, materially from mine, though I always thought they did until I
read your interpretations of them. Perhaps I misunderstood the sense
in which Kant used the term _a priori_. The term has been used in so
many different senses that I prefer myself to drop it altogether. If it
merely refers to priority in time there can be no practical doubt that,
whether in the case of the human race or of an individual thinker, a
large amount of sense-experience must have preceded even so simple an
_a priori_ judgment as “twice two is four.” If the term merely refers
to priority in logical validity it seems to me better to say that “such
and such assertions are not dependent upon experience.” But Kant says
of the assertion “7 + 5 = 12” that it is not only “_a priori_” but
“synthetic”. By the latter term he means that its truth was _not_ deduced
from definitions alone, and that the assertion therefore conveys real
information. In this I believe he was wrong, and though he afterwards
declares that “all knowledge _a priori_ is empty and cannot give
information about things,” unless the true nature of _a priori_ knowledge
is made more clear, people will inevitably continue to believe the
contrary—and to believe moreover that Kant taught so.
Any language which seems to imply that there is some dread necessity
about mathematical truths—that they could not be otherwise if they
would—is very misleading. Of course it is necessarily true that _if_ you
have seven objects and add five more to them you will have in all twelve
objects. But the whole objective difficulty is begged by the supposition.
“Much virtue in if!”
As I understand it the essence of the “laws” of pure mathematics is that
they are verbal, that is they are only abbreviated expressions of the
results of certain verbal processes. If the processes are repeated and
the results similarly expressed, the results must always be the same.
Our reason cannot “inform us about the form of existence” unless it is
first given, as the _data_ or facts which correspond to the definitions
of our symbolic arguments. It is only because our reasoning faculties
are limited that symbolic arguments are necessary at all—that it is
not evident to us at once that the conclusions of the most intricate
mathematical calculations are given to us along with the _data_. Given
the data, then in all possible worlds the conclusions must indeed follow,
but only because they really are already _in_ the data which were given.
It may be that you will not only agree with all I have said, but have
already said much of it yourself. But there are some passages in your
_Fundamental Problems_ which seem to imply otherwise. I think the great
objection I have to urge against Kant, and also perhaps against you, is
that you do not distinguish as clearly as I could wish between symbolic
argument and real, though subjective, knowledge. And the only way to
distinguish between them is by inquiring into the definitions of the
terms.
For example, on p. 165 of _Fundamental Problems_ you say that to
four-dimensional beings Kepler’s third law “would most probably appear as
‘the cubes of their times of revolution being proportional to their mean
distances to the fourth power.’”
Now what sort of assertion do you take Kepler’s law to be? Originally
it was a purely empirical law obtained by pure induction. If the
four-dimensional people obtained their law the same way why should
the result appear different to them? Or do you conceive the law to be
deduced from Newton’s theory of gravitation? But even so the law of the
inverse square was obtained empirically. If you think that law can be
explained (as the analogous law for the distribution of light can) by the
supposition that the integral of the force over all points at a given
distance from the origin is constant, still this supposition is purely
gratuitous unless established by induction from experience. If you grant
any one of these suppositions you can by symbolic argument obtain the law
corresponding to Kepler’s for a four-dimensional space. But I may mention
that in no case does the result you anticipate come out. On the first
two suppositions the law would be unaltered. On the last supposition the
law of gravity would be changed to the inverse cube; but after that the
solution of the problem has nothing to do with four dimensions—it is
a two-dimensional problem only. The result is that in general planets
could not move in closed orbits at all. They might conceivably revolve in
circles, but such a condition would be unstable, and if it obtained their
periodic times would vary as the squares of their distances.
Again you say (p. 74) “the doctrine of the ‘conservation of matter
and energy,’ although it has been discovered with the assistance of
experience, can be proved in its full scope by pure reason alone.”
I should very much like to see your proof (which I cannot find in
_Fundamental Problems_). How do you define the terms of the doctrine?
Do you deduce the proof from these definitions—that is do you make it a
truism? Or do you base it upon subjective axioms as I do my geometry? Or
if you base it on objective facts, how do you prove those facts by pure
reason alone? And if it is purely a subjective proof, how, can you say
the doctrine is proved “in its full scope”? Surely objective applications
come within its scope?
It would not be fair in me to ask you to publish my reply to your
reviewer’s criticisms, though if that reply is justified the criticism
must have done the prospects of my book some injury, seeing from what
a quarter it comes. But I hope you will see your way to publishing the
latter part of this letter in _The Monist_, together with your reply to
it, if you think it worthy of such a distinction.