The principles of science

by William Stanley Jevons

Possibility of Divine Interference.

I will now draw the reader’s attention to pages [149] to 152. I there pointed out that all inductive inference involves the assumption that our knowledge of what exists is complete, and that the conditions of things remain unaltered between the time of our experience and the time to which our inferences refer. Recurring to the illustration of a ballot-box, employed in the chapter on the inverse method of probabilities, we assume when predicting the probable nature of the next drawing, firstly, that our previous drawings have been sufficiently numerous to give us knowledge of the contents of the box; and, secondly, that no interference with the ballot-box takes place between the previous and the next drawings. The results yielded by the theory of probability are quite plain. No finite number of casual drawings can give us sure knowledge of the contents of the box, so that, even in the absence of all disturbance, our inferences are merely the best which can be made, and do not approach to infallibility. If, however, interference be possible, even the theory of probability ceases to be applicable, for, the amount and nature of that interference being arbitrary and unknown, there ceases to be any connection between premises and conclusion. Many years of reflection have not enabled me to see the way of avoiding this hiatus in scientific certainty. The conclusions of scientific inference appear to be always of a hypothetical and provisional nature. Given certain experience, the theory of probability yields us the true interpretation of that experience and is the surest guide open to us. But the best calculated results which it can give are never absolute probabilities; they are purely relative to the extent of our information. It seems to be impossible for us to judge how far our experience gives us adequate information of the universe as a whole, and of all the forces and phenomena which can have place therein.

I feel that I cannot in the space remaining at my command in the present volume, sufficiently follow out the lines of thought suggested, or define with precision my own conclusions. This chapter contains merely Reflections upon subjects of so weighty a character that I should myself wish for many years—nay for more than a lifetime of further reflection. My purpose, as I have repeatedly said, is the purely negative one of showing that atheism and materialism are no necessary results of scientific method. From the preceding reviews of the value of our scientific knowledge, I draw one distinct conclusion, that we cannot disprove the possibility of Divine interference in the course of nature. Such interference might arise, so far as our knowledge extends, in two ways. It might consist in the disclosure of the existence of some agent or spring of energy previously unknown, but which effects a given purpose at a given moment. Like the pre-arranged change of law in Babbage’s imaginary calculating machine, there may exist pre-arranged surprises in the order of nature, as it presents itself to us. Secondly, the same Power, which created material nature, might, so far as I can see, create additions to it, or annihilate portions which do exist. Such events are in a certain sense inconceivable to us; yet they are no more inconceivable than the existence of the world as it is. The indestructibility of matter, and the conservation of energy, are very probable scientific hypotheses, which accord satisfactorily with experiments of scientific men during a few years past, but it would be gross misconception of scientific inference to suppose that they are certain in the sense that a proposition in geometry is certain. Philosophers no doubt hold that de nihilo nihil fit, that is to say, their senses give them no means of imagining to the mind how creation can take place. But we are on the horns of a trilemma; we must either deny that anything exists, or we must allow that it was created out of nothing at some moment of past time, or that it existed from eternity. The first alternative is absurd; the other two seem to me equally conceivable.

Conclusion.

It may seem that there is one point where our speculations must end, namely where contradiction begins. The laws of Identity and Difference and Duality were the foundations from which we started, and they are, so far as I can see, the foundations which we can never quit without tottering. Scientific Method must begin and end with the laws of thought, but it does not follow that it will save us from encountering inexplicable, and at least apparently contradictory results. The nature of continuous quantity leads us into extreme difficulties. Any finite space is composed of an infinite number of infinitely small spaces, each of which, again, is composed of an infinite number of spaces of a second order of smallness; these spaces of the second order are composed, again, of infinitely small spaces of the third order. Even these spaces of the third order are not absolute geometrical points answering to Euclid’s definition of a point, as position without magnitude. Go on as far as we will, in the subdivision of continuous quantity, yet we never get down to the absolute point. Thus scientific method leads us to the inevitable conception of an infinite series of successive orders of infinitely small quantities. If so, there is nothing impossible in the existence of a myriad universes within the compass of a needle’s point, each with its stellar systems, and its suns and planets, in number and variety unlimited. Science does nothing to reduce the number of strange things that we may believe. When fairly pursued it makes absurd drafts upon our powers of comprehension and belief.

Some of the most precise and beautiful theorems in mathematical science seem to me to involve apparent contradiction. Can we imagine that a point moving along a perfectly straight line towards the west would ever get round to the east and come back again, having performed, as it were, a circuit through infinite space, yet without ever diverging from a perfectly straight direction? Yet this is what happens to the intersecting point of two straight lines in the same plane, when one line revolves. The same paradox is exhibited in the hyperbola regarded as an infinite ellipse, one extremity of which has passed to an infinite distance and come back in the opposite direction. A varying quantity may change its sign by passing either through zero or through infinity. In the latter case there must be one intermediate value of the variable for which the variant is indifferently negative infinity and positive infinity. Professor Clifford tells me that he has found a mathematical function which approaches infinity as the variable approaches a certain limit; yet at the limit the function is finite! Mathematicians may shirk difficulties, but they cannot make such results of mathematical principles appear otherwise than contradictory to our common notions of space.

The hypothesis that there is a Creator at once all-powerful and all-benevolent is pressed, as it must seem to every candid investigator, with difficulties verging closely upon logical contradiction. The existence of the smallest amount of pain and evil would seem to show that He is either not perfectly benevolent, or not all-powerful. No one can have lived long without experiencing sorrowful events of which the significance is inexplicable. But if we cannot succeed in avoiding contradiction in our notions of elementary geometry, can we expect that the ultimate purposes of existence shall present themselves to us with perfect clearness? I can see nothing to forbid the notion that in a higher state of intelligence much that is now obscure may become clear. We perpetually find ourselves in the position of finite minds attempting infinite problems, and can we be sure that where we see contradiction, an infinite intelligence might not discover perfect logical harmony?

From science, modestly pursued, with a due consciousness of the extreme finitude of our intellectual powers, there can arise only nobler and wider notions of the purpose of Creation. Our philosophy will be an affirmative one, not the false and negative dogmas of Auguste Comte, which have usurped the name, and misrepresented the tendencies of a true positive philosophy. True science will not deny the existence of things because they cannot be weighed and measured. It will rather lead us to believe that the wonders and subtleties of possible existence surpass all that our mental powers allow us clearly to perceive. The study of logical and mathematical forms has convinced me that even space itself is no requisite condition of conceivable existence. Everything, we are told by materialists, must be here or there, nearer or further, before or after. I deny this, and point to logical relations as my proof.

There formerly seemed to me to be something mysterious in the denominators of the binomial expansion (p. [190]), which are reproduced in the natural constant ε, or

1 + 1/1 + 1/1 . 2 + 1/1 . 2 . 3 + . . .