Mr. John Venn published some twenty-five or six years ago an excellent
treatise called “The Logic of Chance.” This work opened the eyes of many
to the great importance of the calculus of probabilities as a method
of science which was of much wider application than had before been
suspected. This admirable work we may boldly say marks a new epoch in the
study of logic, it opened new vistas, and many expectations created by
it have since been realised. Yet it is to be regretted that the author
adopts Hume’s erroneous conception of causality and thus implicitly
paves the way which Mr. Peirce has actually followed and which leads
to a denial of the doctrine of necessity. Concerning “the doctrine of
universal causation” Mr. Venn says, in Chapter XIV:
“We will employ the word simply in the sense which is becoming
almost universally adopted by scientific men, viz. that of
invariable unconditional sequence.
“It is in this sense that the word _cause_ is used by Mr.
Mill....
“This meaning of the term is rapidly becoming the popular, or
rather, the popular scientific one.”
This idea of “sequence” however was exactly Hume’s mistake, adopted by
Mr. Mill and through Mr. Mill popularised among English thinkers. If
the nature of cause and effect were really constituted by invariable
sequence, then the night might be called the effect of the day because
night is invariably consequent upon day.
Hume, taking the ground that cause and effect constitute a sequence,
attempted a synthesis of both; he searched for a proof of their identity
and failed. And it was natural that he failed, for cause and effect are
so radically different that we cannot bring them into the formula of an
equation as “cause = effect.” There is no cause that is equal to its
effect.
Hume should have considered causation as one single process, and instead
of attempting a synthesis, he should have made an analysis. The analysis
would have shown that cause and effect are two abstract and correlative
terms of one whole and inseparable event. Cause is not identical with
effect, but the whole event is identical with itself.
If my finger touches a key of the piano, a chord is struck; the chord
swings and produces certain air-vibrations. In this process from the
beginning to the end all the energy employed and the mass of the material
particles remain in amount the same, yet there is a change of form taking
place. Causation is not mere sequence, but a sequence of quite a special
kind. It is a sequence of two states which belong together as an initial
and a final aspect of one and the same event.
So long as we know of two events simply that they follow one another,
although the sequence may in every case be invariable and unexceptional,
we are not justified in calling them cause and effect. No amount of
experience is sufficient to constitute causation by a mere synthesis of
sequences, and to have appreciated this truth is the immortal merit of
the great Scotchman who boldly took the consequence of the argument and
acquiesced in scepticism.
The problem, however, is not so desperate as Hume thought. If Hume
could have considered his argument in the light which the law of the
conservation of matter and energy sheds upon it, he would most likely
have abandoned his scepticism; for causality is perfectly intelligible if
conceived not as a synthesis of two radically different events, but as a
process of transformation, of which the prior state is called cause and
the final one effect.
That two radically different events, which are not thought of as
transformation, invariably follow each other without our being able to
discover any connection between them, will naturally appear as a mystery;
but that two forms are radically different things, although they may be
forms of the same amount of matter and energy, is no mystery. The effect
is, or may be, something entirely new.
The configuration of things as it appears in the effect, did not exist
before. But for that reason, it is no creation out of nothing, it is not
an incomprehensible event, it is no miracle.
It is a very wonderful thing that two congruent regular tetrahedrons,
when put together, will form a hexahedron, but the laws of form do
perfectly and satisfactorily explain it. Supposing we had no idea of the
laws of form or only an incoherent and fragmentary knowledge of them,
should we not look upon the result of this combination as a strange and
incomprehensible mystery. Two heaps of flour one poured upon the other
will give one heap of the same kind and shape but of a larger size.
However, the combination of the two four-sided bodies does not produce
another four-sided body doubly as large as any of the two four-sided
bodies. Nor does it produce an eight-sided body. It produces a six-sided
body, which is something quite new. The result is not contained in the
conditions singly, for no one can say that six-sidedness is a quality
implicitly contained in four-sided bodies.
The process of combining hydrogen with oxygen into water (H₂O) is
an immensely more complex case, and the qualities resulting from a
difference of density as well as configuration are entirely unknown to
us. There is nevertheless no reason whatever to consider the process
as different in principle; it is a case of transformation in which the
amount of matter and energy remains the same.
Whatever the value of the logic of chance may be for scientific reasoning
in establishing gradations of certainty and formulating the reliability
of a certain belief, we deny most positively its applicability to the
principle of causation in general. If we ask what the chance is of a
combination of two congruent tetrahedrons becoming a hexahedron, we must
answer that the probability is exactly 1, which means certainty, and
certainty is but another name for necessity.
Mr. Peirce does not object to necessity in certain cases, he objects
to necessity being a universal feature of the world. He objects to the
rigidity of causation in so far only as to allow a trifle of chance to
enter into nature.
One or two cases or even a hundred, and a thousand, nay millions of
millions of cases in which causation is explicable as transformation
is no proof that this must always be so. Mr. Peirce may grant and most
likely he does grant that causation in a definite set of experiences is
transformation, yet what guarantee do we have for saying that it is the
only kind of causation. Might there not be room in this world for another
causation which for lack of a full comprehension of its nature, we may
call the causation of chance?
We answer that form is a quality of this world, not of some samples of
it, but throughout, so far as we know of existence even in the most
superficial way, and thus we know beforehand or _a priori_ that the laws
of form hold good so far as our telescopes sweep through space. We are
ignorant as to the qualities dependent upon special forms of matter or
energy, and we can acquire any knowledge thereof only through experience;
but that is no reason to doubt the validity of causation in general,
or to surmise the probability of there being somewhere a different
arrangement of nature.
Thus we come to the conclusion that the calculus of probabilities is not
applicable to the order of the world as to whether it may or may not
be universal. And in corroboration of this our position we quote the
following passage from a high authority in the science of logic, who is
no less than Mr. Charles S. Peirce himself. “Illustrations of the Logic
of Science,” (_Popular Science Monthly_, 1877, p. 714):
“The relative probability of this or that arrangement of
Nature is something which we should have a right to talk about
if universes were as plenty as blackberries, if we could put
a quantity of them in a bag, shake them well up, draw out a
sample, and examine them to see what proportion of them had
one arrangement and what proportion another. But, even in
that case, a higher universe would contain us, in regard to
whose arrangements the conception of probability could have no
applicability.”
Mr. Peirce is still more emphatic in another passage which reads (ib.
1878, p. 205):
“If any one has ever maintained that the universe is a pure
throw of the dice, the theologians have abundantly refuted him.
‘How often,’ says Archbishop Tillotson, ‘might a man, after
he had jumbled a set of letters in a bag, fling them out upon
the ground before they would fall into an exact poem, yea,
or so much as make a good discourse in prose! And may not a
little book be as easily made by chance as this great volume
of the world?’ The chance world here shown to be so different
from that in which we live would be one in which there were
no laws, the characters of different things being entirely
independent; so that, should a sample of any kind of objects
ever show a prevalent character, it could only be by accident,
and no general proposition could ever be established. Whatever
further conclusions we may come to in regard to the order of
the universe, thus much may be regarded as solidly established,
that the world is not a mere chance-medley.”
Here follows a close reasoning of several pages which ends (on p. 207)
with a paragraph beginning with the words:
“This shows that a contradiction is involved in the very idea
of a chance world.”
And a long paragraph on p. 208 winds up with these sentences:
“The actual world is almost a chance-medley to the mind of a
polyp. The interest which the uniformities of Nature have for
an animal measures his place in the scale of intelligence.”
This is exactly the position which I defend. If universes were as plenty
as blackberries we might talk about the order of other universes. They
might be four- or five- or _n_-dimensional. Yet even in all these cases
they would not be void of form. The four-dimensional universe would have
another arrangement, but its laws would be none the less orderly, none
the less regular, and a higher universe would contain them all. Supposing
there were four- or five-dimensional space somewhere, we could state
with absolute precision all the formal laws by which bodies of so many
dimensions were governed.[74]
The order of form and the rigidity of formal laws is as universal and
omnipresent as God. They encompass our path and our lying down, they have
beset our behind and before. If we ascend up into heaven they are there,
if we make our beds in hell, behold they are there. If we take the wings
of the morning and dwell in the uttermost parts of the sea, even there
they shall lead us and hold us.