Tag: induction

Aping the physical sciences

Some of the things which put me out of step and which I like to criticize are:

(1) Fashions: I do not believe in fashions, trends, tendencies, or schools, either in science or in philosophy. In fact, I think that the history of mankind could well be described as a history of outbreaks of fashionable philosophical and religious maladies. These fashions can have only one serious function—that of evoking criticism. Nonetheless I do believe in the rationalist tradition of a commonwealth of learning, and in the urgent need to preserve this tradition.

(2) The aping of physical science: I dislike the attempt, made in fields outside the physical sciences, to ape the physical sciences by practising their alleged ‘methods’—measurement and ‘induction from observation’. The doctrine that there is as much science in a subject as there is mathematics in it, or as much as there is measurement or ‘precision’ in it, rests upon a complete misunderstanding. On the contrary, the following maxim holds for all sciences: Never aim at more precision than is required by the problem in hand.  [7]

The untenability of induction

My own view is that the various difficulties of inductive logic here sketched are insurmountable. So also, I fear, are those inherent in the doctrine, so widely current today, that inductive inference, although not ‘strictly valid’, can attain some degree of ‘reliability’ or of ‘probability’. According to this doctrine, inductive inferences are ‘probable inferences’. ‘We have described’, says Reichenbach, ‘the principle of induction as the means whereby science decides upon truth. To be more exact, we should say that it serves to decide upon probability. For it is not given to science to reach either truth or falsity … but scientific statements can only attain continuous degrees of probability whose unattainable upper and lower limits are truth and falsity’.

At this stage I can disregard the fact that the believers in inductive logic entertain an idea of probability that I shall later reject as highly unsuitable for their own purposes (see section 80, below). I can do so because the difficulties men­tioned are not even touched by an appeal to probability. For if a certain degree of probability is to be assigned to statements based on inductive inference, then this will have to be justified by invoking a new principle of induction, appropriately modified. And this new principle in its turn will have to be justified, and so on. Nothing is gained, more­over, if the principle of induction, in its turn, is taken not as ‘true’ but only as ‘probable’. In short, like every other form of inductive logic, the logic of probable inference, or ‘probability logic’, leads either to an infinite regress, or to the doctrine of apriorism. [6]

Inference to the Best Explanation

According to the model of Inference to the Best Explanation, our explanatory practices guide our inferences. Beginning with the evidence available to us, we infer what would, if true, provide the best explanation of that evidence. This cannot be the whole story about inference, but many of our inferences, both in science and in ordinary life, appear to follow this pattern. Faced with tracks in the snow of a certain peculiar shape, I infer that a person on snowshoes has recently passed this way. There are other possibilities, but I make this inference because it provides the best explanation of what I see. [1]

Ancient conventionalism

From a few examples and particulars [the ancients] flew at once to the most general conclusions, or first principles of science. Taking the truth of these as fixed and immovable, they proceeded by means of intermediate propositions to educe and prove from them the inferior conclusions; and out of these they framed the art. After that, if any new parti­culars and examples repugnant to their dogmas were mooted and adduced, either they subtly molded them into their system by distinctions or explanations of their rules, or else coarsely got rid of them by exceptions; while to such par­ticulars as were not repugnant they labored to assign causes in conformity with those of their principles. But this was not the natural history and experience that was wanted; far from it. [I/125]

The still strong dogma of observationism

Bacon’s observationism and his hostility to all forms of theoretical thought were revolutionary, and were felt to be so. They became the battle cry of the new secularized religion of science, and its most cherished dogma. This dogma had an almost unbelievable influence upon both the practice and the theory of science, and this influence is still strong in our own day. [84]

The childish induction

In establishing axioms, another form of induction must be devised than has hitherto been employed, and it must be used for proving and discovering not first principles (as they are called) only, but also the lesser axioms, and the middle, and indeed all. For the induction which proceeds by simple enumeration is childish; its conclusions are precarious and exposed to peril from a contradictory instance; and it generally decides on too small a number of facts, and on those only which are at hand. But the induction which is to be available for the discovery and demonstration of sciences and arts, must analyze nature by proper rejections and exclusions; and then, after a sufficient number of negatives, come to a conclusion on the affirmative instances […]. [I/105]

Two concepts of induction

In the past, the term ‘induction’ has been used mainly in two senses. The first is repetitive induction (or induction by enumeration). This consists of often repeated observations and experiments, which are supposed to serve as premises in an argument establishing some generalization or theory. The invalidity of this kind of argument is obvious: no amount of observation of white swans establishes that all swans are white (or that the probability of finding a non-white swan is small). In the same way, no amount of observed spectra of hydrogen atoms on earth establishes that all hydrogen atoms emit spectra of the same kind. Theoretical considerations, however, may suggest the latter generalization, and further theoretical considerations may suggest that we should modify it by introducing Doppler shifts and Einsteinian gravitational redshifts.

Thus repetitive induction is out: it cannot establish anything.

The second main sense in which the term ‘induction’ has been used in the past is eliminative induction – induction by the method of eliminating or refuting false theories. This may look at first sight very much like the method of critical dis­cussion that I am advocating. But in fact it is very different. For Bacon and Mill and other exponents of this method of eliminative induction believed that by eliminating all false theories we can finally establish the true theory. In other words, they were unaware of the fact that the number of competing theories is always infinite – even though there are as a rule at any particular moment only a finite number of theories before us for consideration. [104-5]

How can we know?

It may, therefore, be a subject worthy of curiosity, to enquire what is the nature of that evidence which assures us of any real existence and matter of fact, beyond the present testimony of our senses, or the records of our memory. This part of philosophy, it is observable, has been little cultivated, either by the ancients or moderns, and therefore our doubts and errors, in the prosecution of so important an enquiry, may be the more excusable; while we march through such difficult paths without any guide or direction. They may even prove useful, by exciting curiosity, and destroying that implicit faith and security, which is the bane of all reasoning and free enquiry. The discovery of defects in the common philosophy, if any such there be, will not, I presume, be a discouragement, but rather an incitement, as is usual, to attempt something more full and satisfactory than has yet been proposed to the public. [14-5]

An inference which wants to be explained

Our senses inform us of the colour, weight, and consistence of bread; but neither sense nor reason can ever inform us of those qualities which fit it for the nourishment and support of a human body. Sight or feeling conveys an idea of the actual motion of bodies; but as to that wonderful force or power, which would carry on a moving body for ever in a con­tinued change of place, and which bodies never lose but by communicating it to others; of this we cannot form the most distant conception. But notwithstanding this ignorance of natural powers and principles, we always presume, when we see like sensible qualities, that they have like secret powers, and expect that effects, similar to those which we have experienced, will follow from them. If a body of like colour and consistence with that bread, which we have formerly eat, be presented to us, we make no scruple of repeating the experiment, and foresee, with certainty, like nourishment and support. Now this is a process of the mind or thought, of which I would willingly know the foundation. It is allowed on all hands that there is no known connection between the sensible qualities and the secret powers; and consequently, that the mind is not led to form such a conclusion concerning their constant and regular conjunction, by any­thing which it knows of their nature. As to past Experience, it can be allowed to give direct and certain information of those precise objects only, and that precise period of time, which fell under its cognizance: but why this experience should be exten­ded to future times, and to other objects, which for aught we know, may be only in appearance similar; this is the main question on which I would insist. The bread, which I formerly eat, nourished me; that is, a body of such sensible qual­ities was, at that time, endued with such secret powers; but does it follow, that other bread must also nourish me at an­other time, and that like sensible qualities must always be attended with like secret powers? The consequence seems nowise necessary. At least, it must be acknowledged that there is here a consequence drawn by the mind, that there is a certain step taken; a process of thought, and an inference, which wants to be explained. [19-20]

Observe!

The belief that science proceeds from observation to theory is still so widely and so firmly held that my denial of it is often met with incredulity. I have even been suspected of being insincere – of denying what nobody in his senses can doubt.

But in fact the belief that we can start with pure observations alone, without anything in the nature of a theory, is absurd; as may be illustrated by the story of the man who dedicated his life to natural science, wrote down everything he could observe, and bequeathed his priceless collection of observations to the Royal Society to be used as inductive evi­dence. This story should show us that though beetles may profitably be collected, observations may not.

Twenty-five years ago I tried to bring home the same point to a group of physics students in Vienna by beginning a lec­ture with the following instructions: ‘Take pencil and paper; carefully observe, and write down what you have observed!’ They asked, of course, what I wanted them to observe. Clearly the instruction, ‘Observe!’ is absurd. (It is not even idio­matic, unless the object of the transitive verb can be taken as understood.) Observation is always selective. It needs a chosen object, a definite task, an interest, a point of view, a problem. And its description presupposes a descriptive lan­guage, with property words; it presupposes similarity and classification, which in its turn presupposes interests, points of view, and problems. [61]