acquiring feeling, but there were no samenesses whatever; which would
mean that every smallest piece of the world-stuff were a particular
thing by itself and in every respect unlike every other piece, of a
different material or of no material at all, of different size or of
no size at all, and also possessed of a different number of space
dimensions. In such a world all the impacts made upon a sentient being
would be different; not one would be like the other, and all feelings
would present a chaos without uniformities, worse than the most complex
crazy-quilt. Under such circumstances mind would be impossible: it would
neither originate nor could it develop.
On the other hand suppose again that the stuff of which the world
consists were capable of acquiring feeling in some certain formation, and
that there were samenesses in the world and in the events of the world.
Would not mind necessarily originate in such a world? Given feeling
substance in a world of samenesses and differences, these samenesses will
produce analogous samenesses of impression upon the feeling substance,
which will be perceived as samenesses of feeling. The preservation of the
traces left in the feeling substance (supposing this substance to live
on indefinitely) will in the long run result in the formation of special
sense-organs. It will later on, with the aid of word-symbolism, lead to
the formation of universals, for universals are nothing but samenesses
perceived. It will then create with the assistance of abstraction the
realm of scientific thought, representing the uniformities of the events
of the world in exact formulas.
THE EXISTENCE OF SAMENESSES A FACT.
The question whether there are samenesses at all in the world, is in our
opinion settled. It is a fact that there are samenesses. The uniformities
of the world are a matter of indubitable experience—indubitable because
our very existence as thinking beings, as minds, is conditioned by this
fact. We see the mind of every child develop out of his perception of
samenesses. Our scientists teach us that the race-soul, like a great
immortal individual, is the product of the accumulated experience
of samenesses; and all future progress, in science as well as in
civilisation, in mechanical invention as well as in ethics, depends upon
the trustworthiness of the samenesses stated to exist in the objective
world.
The question of the ultimate _raison d’être_ of the samenesses and
differences, is another question; and it would lead us too far here
to discuss it. In several details the problem is not as yet ripe for
solution. A full solution of the problem would be tantamount to the
exposition of a complete knowledge of the world. Suffice it here to
say that we have reasons to think of the world-stuff as being of the
same nature throughout. The chemical elements seem to be different
configurations of one and the same substance. In this way all difference
would have to be explained as a difference of form.
The form of reality possesses sameness and difference in all its parts.
Space in its sameness is by experience found to be tri-dimensional, which
means, it is determinable throughout by three coördinates; while its
differences are due to the position of the points considered. For the
purpose of the geometrician space is uniform, but for the purpose, say
of the architect, it is not uniform. To the geometrician two congruent
triangles, whether they are in the cellar or in the garret, are the same.
However, to the architect the position of two congruent triangles in his
design of a house is by no means the same. Every single point of space
has its special and individual qualities.
The whole business of science is to systematise the samenesses of
experience, and to present them in such convenient formulas that they can
be used for guidance in our actions.
The most comprehensive formulation of the sameness of the universe as
a whole has found its expression in the law of the conservation of
matter and energy. This law rests upon the experience, corroborated by
experiments, that causation is transformation. It states that the total
amount of matter and the total amount of energy remain constant. There is
no creation out of nothing and no conversion of something into nothing.
EINDEUTIG BESTIMMT.
After this sketch of the importance of sameness, (a subject which we have
by no means exhausted,) we return to the idea of necessity. The ideas
of sameness and necessity are closely related. A world of sameness is a
world in which necessity rules, and necessity means regularity and order.
German scientists have a very good expression to denote the formulation
of events in a manner which describes them in their necessary course. If
they have succeeded in finding the sameness in the instances of a certain
class of events, they say that it is _eindeutig bestimmt_, which means,
the sameness is determined in a way that admits of no equivocation; it is
complete, representing solely and purely that feature upon the presence
of which the result depends. Whatever is thus _eindeutig bestimmt_, is
recognised in its necessity. The presence of that feature which makes it
_eindeutig bestimmt_, determines the event to take place; and this being
determined, its inevitableness, the _it will be_ of the process, is all
there is to necessity.
All natural phenomena that can be _eindeutig bestimmt_ are necessary in
their happening. A world which with regard to the total amount of its
matter and energy is the same to-day and yesterday and will be the same
to-morrow, a world whose laws of form possess a sameness throughout, so
that it allows of formulating and applying them in their rigidity to all
facts present, past, and future, a world in which all the changes are
transformations determinable with the assistance of formal laws, can be
relied upon and the course of its events can be computed.
Such _is_ the world in which we live; and taking this ground I say, the
world is a cosmos, it is no chaos; and noticing that being possessed
of sameness is an intrinsic and inalienable feature of the world, I
am inclined to add the world never was and never will be a chaos. And
this, if it be true at all, is true not only in general and as it were
wholesale, but in its minutest details. If there were deficiencies of
this order in the unobservable details, they would not be diminished
by being summed up in large and ever larger amounts; on the contrary,
they would increase; they would grow in proportion. This not being
the case, we have not the slightest reason to doubt that in those
realms of minutest existence into which, from the grossness and the
lack of precision of our organs and instruments of observation, we
cannot penetrate, the same order and regularity obtains as in those
regions which lie open to our investigation. In other words: From this
standpoint, existence is, so to say, permeated by law throughout; every
event is determined and any kind of absolute chance is excluded.
Following Kant’s etymology we understand by _a posteriori_ the sensory
elements, and by _a priori_ the formal elements of our experience. The
queer expression “a priori” is in so far justified as formal truths (such
as geometrical, arithmetical, logical rules) are formulas expressing the
universal samenesses of the form of existence. They contain the laws of
form in a shape that is _eindeutig bestimmt_, so that an experimenter
will know them _a priori_ to be so. _A priori_ means beforehand. An
experimenter knows certain things even before he makes his experiments.
The _a priori_ elements of experience are by no means innate truths; nor
are they the historical beginning of experience. On the contrary. In
their abstract purity they appear as a very late product of man’s mental
evolution.
The _a priori_ systems of thought are not arbitrary constructions; they
are constructions raised out of the recognition of the formal, i. e. the
relational, samenesses that appear in experience. All possibilities of a
certain class of relations can be exhausted and formulated in theorems.
As such they can be used as references to assist in the explanation and
determination of new experiences. We know some part of any new experience
with which we are confronted even before we have investigated it. We know
certain laws of its form, and by reference to these known laws we are
enabled to reduce the unknown to the known, to analyse the process and
set forth that feature of it which makes _eindeutig bestimmt_.
II. THE SCOPE OF NECESSITY.
Mr. Peirce objects to necessitarianism, and classes it together with
materialism and the mechanical philosophy, speaking of the latter as
the most logical form of necessitarianism. In consonance with the
dictionary-definitions of these words, he contrasts them to the doctrine
of the freedom of the will and also to miracles—the latter, we must
confess, being a dangerous concession to certain theological conceptions.
The “Century Dictionary” defines “necessitarianism” as
“The theory that the will is subject to the general mechanical
law of cause and effect.”
And “necessitarian” as
“One who maintains the doctrine of philosophical necessity,
in opposition to that of the freedom of the will: opposed to
libertarian.”
The word “determinism” is regarded as a synonym of necessitarianism. Its
first definition in the “Century Dictionary” reads as follows:
“A term invented by Sir William Hamilton to denote the doctrine
of the necessitarian philosophers, who hold that man’s actions
are uniformly determined by motives acting upon his character,
and that he has not the power to choose to act in one way so
long as he prefers on the whole to act in another way.”
Hamilton’s definition as here presented is puzzling. If the words
“choose” and “prefer on the whole” are _not_ meant to be tautological,
there is no sense in it; for no determinist denies that a man might “upon
the whole” prefer to act this way, while he has the power to choose,
and for special considerations perhaps does choose, to act in another
way. However, if the words “choose” and “prefer on the whole” are meant
to be tautological, the self-contradictoriness of the statement is too
palpable for a Hamilton. Is there anybody who would maintain that a man
who chooses to act in one way can at the same time, under the very same
circumstances, and he remaining the very same man of the same character
and intentions, choose to act in another way?
While we accept determinism and also necessitarianism in the sense that
all events (the actions of willing beings included) are determined, we
cannot accept either the mechanical philosophy or materialism as the
terms are commonly understood.
We find materialism defined as
“The metaphysical doctrine that matter is the only substance,
and that matter and its motions constitute the universe.”
(“Century Dictionary,” 2d sense.)
The mechanical philosophy is explained _sub voce_ “atomic” as
“[The view that] from the diverse combination and motions of
... atoms all things, including the soul, were supposed to
arise.” _Ibid._
Determinism is simply the negation of absolute chance. It does not
exclude chance in the original sense of the word as an unexpected event,
as something that befalls one without his seeking it or making the
event—chance being derived from ML. _cadentia_, i. e. the falling, as in
a throw of dice.
The “Century Dictionary” defines “chance” in sense 9, as
“Fortuity; especially the absence of a cause necessitating an
event.”
This is absolute chance, the existence of which we deny. The “Century
Dictionary” adds the following little note:
“Absolute chance, the (supposed) spontaneous occurrence of
events undetermined by any general law or by any free volition.
According to Aristotle, events may come about in three ways:
first, by necessity or an external compulsion; second, by
nature or the development of an inward germinal tendency; and
third, by chance, without any determining cause or principle
whatever, by lawless, sporadic originality.”[12]
We understand chance as being, from certain premisses, an incalculable
coincidence, either not intended to be calculated, or, for certain
reasons, from a given standpoint with a limited and definite amount of
knowledge, not capable of calculation. Determinism, as we understand
the term, does not imply as the “Century Dictionary” has it in its
definition of necessitarianism, that “the law of cause and effect” is
“mechanical.” It simply asserts that the law of cause and effect holds
good universally, and that there is no effect that is not definitely
determined, according to the nature of the things in action, by causes
and all their circumstances.
NECESSITY AND CHANCE.
Mr. Peirce says:
“_All_ the diversity and specificalness of events is
attributable to chance—diversification, specificalness, and
irregularity of things, I suppose is chance—and this diversity
cannot be due to laws that are immutable.” (P. 332.)
Our world-view leads us to other conclusions; we say:
Every specificalness or particularity is such by possessing a certain
form and standing in a definite relation (in time as well as space) to
all other things of the universe. Of every concrete thing we can say it
is now and here, or it was then and there. It is or was made up in this
special way, and it stands or it stood in these special relations to its
surroundings. Proportions, relations, forms—these are what account for
the diversification and specificalness of all things in the universe;
they are what explain the irregularities of individual cases and of all
those events which appear as chance to him who, although he may be well
informed about the nature of a thing, does not know the relation of
its complex surroundings, exercising according to law their disturbing
influence upon its actions which otherwise would be uniform.
And since no two spots of space and no two instances of time are the
same, since the relations of every atom are different in every position
and at every moment of its existence, we need not be astonished to find
diversity and specificalness in this world of samenesses.
We do not believe in absolute chance, but we believe in chance.
What is chance?
Chance is any event not especially intended, either not calculated, or,
with a given and limited stock of knowledge, incalculable.
Gunpowder was, according to the legend, invented by chance. Berthold
Schwartz intended to make gold, yet when the mixture was ignited, he
began to understand that it was an explosive. When I say that I met
a friend by chance, I mean that the meeting was unintentional. I had
not foreseen it and perhaps could not foresee it. When we call a throw
of dice pure chance, we mean that the incidents which condition the
turning up of these or those special faces of the dice have not been or
cannot be calculated. We do not mean that the law of cause and effect is
suspended; we mean that we are unable to determine the effect. That which
would make this or that throw _eindeutig bestimmt_ is either not known to
us, or, if it were known, is of such a nature that we cannot produce the
desired effect with any certainty. Matters are so arranged in the game of
dice that the slightest incident changes the result, and these incidents
are either not within our ken or not within the range of our power.
Chance, accordingly, as we understand it, is no exception to necessity;
it does not happen contrary to law, and is in each case the strict result
of a definite cause under definite circumstances.
Absolute chance is something quite different. Absolute chance is that
which is incalculable because of the absence of law. Mr. Peirce says:
“Another argument, or convenient commonplace, is that absolute
chance is _inconceivable_. This word has eight current
significations. The ‘Century Dictionary’ enumerates six. Those
who talk like this will hardly be persuaded to say in what
sense they mean that chance is inconceivable.”
Absolute chance is “inconceivable” as the word is defined by the “Century
Dictionary” in the second sense: It is
“unacceptable to the mind because involving a violation of laws
believed to be well established by positive evidence.”
Absolute chance is not unthinkable in the sense of unimaginable. We can
very well depict a case of absolute chance in our imagination, just as
we can tell and describe in minutest details the fairy tale of Alladin’s
lamp; just as we can in our imagination depict a creation out of nothing.
But he who accepts that the world is in its innermost nature a cosmos,
that its events are strictly and throughout regulated by law, cannot
at the same time think that there are nooks and crevices in which the
law does not operate. Absolute chance actually involves the idea of a
creation out of nothing; and thus it stands in contradiction to the law
of the preservation of matter and energy. Absolute chance which means
that the very same thing under the very same conditions can act in this
or in some other way, that it need not act in exactly the same way,
involves a belief in either the creation of a not existing quality out
of nothing, or the disappearance of existing qualities into nothing.
Mr. Peirce says:
“It seems to me that every throw of sixes with a pair of dice
is a manifest instance of chance.”
Yes, of chance; but not of that chance the existence of which Mr. Peirce
maintains—not of absolute chance. Every throw of dice, every toss of head
or tail, are exactly determined by circumstances. We call it chance only
in so far as we cannot calculate and predetermine the result.
Suppose you take two large silver coins between your thumb and the first
two fingers, one coin parallel to and a little above the other. Suppose
tails are up in both. Drop the lower coin without an effort just as it
would fall, about twenty inches, and you may be sure that, in spite of
yourself, it will turn up head. Then drop the upper one and it will not
turn, but plump right down showing tail. There are certain mechanical
reasons for the one case as well as for the other. As soon as we know the
law and can apply it, the case ceases to be an instance of chance.
Dice, the roulette, and other games of chance are so arranged, that
the determinating circumstances are too numerous and also too complex,
one interfering with and being disturbed by the others, to admit
of any adequate calculation or predetermination. An arrangement of
conditions which in this way eludes the calculation of a definite set of
possibilities, is called by Professor Kries _gleiche Spielräume_ or equal
chances. And the province of equal chances is and will remain the proper
sphere of the calculus of probabilities.
Professor Nitsche objects to Kries’s proposition, saying that absolutely
equal chances are impossible and an equal chance (_ein gleicher
Spielräume_) is nothing but the objectification of a judgment of equal
value.[13] We find no fault with Nitsche’s objection; there are no
absolutely equal chances; and what is called “equal chance” means that
the strength of two or several anticipations is of the same degree; that
our belief and doubt as to the turning up of one, two, three, four, five,
or six spots of a die are equally justified. The objective conditions
which justify such equality of several expectations is what Kries (if
we understand him correctly) calls _gleiche Spielräume_. But _gleiche
Spielräume_ do not imply absolute chance. We might as well expect that
all the six faces of a die should turn up simultaneously in one throw, as
that any one of them should turn up by absolute chance.
While absolute chance cannot be admitted, partly because we are not in
need of it, (since the irregularities of nature can be sufficiently
explained otherwise,) and partly because the idea of absolute chance if
it were needed, is incompatible with our world-conception, we shall,
nevertheless, have to concede to chance, as we understand the term, a
very important rôle in the evolution of life. The formation of worlds and
the history of mankind depend to a great extent upon chances similar to
the throws of dice. There are many possibilities, and now this, now that,
will, according to the circumstances, be realised—of course in each case
with strict necessity.
Let us illustrate this idea by an example.
The formation of about seventy elements out of the original
world-substance, which may be supposed to be homogeneous, does not appear
to depend upon chance. Their universal appearance in all parts of the
universe suggests the hypothesis that their formation is the inevitable
result of a gradual condensation of nebular substances. We find
everywhere, according to the stage of condensation, a gradual appearance,
first of the lighter, then of the heavier elements. There seems to be
no possibility of the formation of other elements than those known to
us (including here the hypothetical elements which are still missing in
the Mendeljeff series and at the same time, at least, not excluding a
further continuance of the series). These elements or none, it appears,
must be formed out of the original substance of our world. Let us here
assume, for argument’s sake, that it were so beyond question, and that we
knew the nature of the world-substance to be such as to condense, if it
condenses at all, into no other but these forms, which we call chemical
elements. This would be a limitation of possibilities. Exactly so the
throws Of dice are limited. With the dice commonly in use we cannot throw
fractions; nor can we throw either zero, or seven, or any other higher
number. We can throw only whole numbers, integrals from one up to six.
But while we thus assume that the formation of the elements is limited
to those actually existing, the proportion in which the elements may be
distributed in the different nebulæ and solar systems, is apparently
very different. Suppose we had a full knowledge of the intrinsic nature
of the world-substance and were standing outside the universe observing
the process of world-formations; we could not from this knowledge alone
predict all that would happen. We should on our assumption be able to
predict _a priori_ that such elements would be formed. But whether the
different elements would be generated in these or in other proportions
appears to depend upon the presence of certain conditions, perhaps the
rapidity of motion, the heat produced by friction, the temperature of
the surrounding cosmic space, any knowledge of which is not included in
our knowledge of the nature of the world-substance. These conditions
may vary, nay, so far as we can judge they actually do vary; and any
apparently slight variation of them, or even one of them, will result in
different effects of great consequence. Without a detailed knowledge of
all these special conditions, simply from a supposed _a priori_ knowledge
of the world-substance, the idiosyncrasy of this or that particular
solar system could not be _a priori_ determined. Here it will be such,
and there, under perhaps slightly different circumstances, it will be
entirely other. Here the centre of gravity may be in one great mass,
there again it may be divided in two, so that the planets circle around
two suns.
From this point of view we have to call these results products of chance.
To a being who not only might be supposed to know the intrinsic nature
of existence, but could have present before his mind every event of the
great interacting cosmos in its entire complexity, this kind of chance
would, of course, also disappear. To him all states of things would
appear throughout as _eindeutig bestimmt_. Yet, although in this way
necessity permeates all events that take place, we do not intend to deny
the irregularity of detail,[14] the specificalness of the particulars,
the diversity of individual incidents and existences. According to our
conception of nature they must remain, and we need not attribute them
to absolute chance. To attribute irregularities to absolute chance (as
Mr. Peirce does) is actually an abandonment of explaining them. The
specificalness and particularity of nature can be said to be due to
chance in so far only as they do not depend upon and are not determinable
by the nature of the things under consideration, but result (with strict
necessity of course) from the ever-changing conformations of surrounding
circumstances.
Thus the fate of a man depends mainly upon his character,—the proverb
says, “Every man is the architect of his own fortune”—but not entirely.
There are sometimes coincidences determining the fates of men, and
through them the fates of whole nations. And these coincidences do not
result from their character.