Imagination, Supposition and Idealisation.
Such order as may be inherent in the phenomena of nature is not obvious on the face of them. It has to be sought out by an active interrogation of nature. The interrogation takes the form of making tentative suppositions, with the aid of imagination, as to what kind of order might prevail in the phenomena under investigation. Such suppositions are usually known as hypotheses, and the formation of fruitful hypotheses requires imagination and originality, as well as familiarity with the facts investigated. Without the guidance of such hypotheses observation itself would be barren in science for we should not know what to look for. Mere staring at facts is not yet scientific observation of them. Hence for science any hypothesis, provided it can be put to the test of observation or experiment, is better than none. For observation not guided by ideas is blind, just as ideas not tested by observations are empty. Hypotheses that can be put to the test, even if they should turn out to be false, are called "fruitful"; those that cannot be so tested even if they should eventually be found to be true, are for the time being called "barren." Intimately connected with the processes of imagination and supposition is the process of idealisation, that is, the process of conceiving the ideal form or ideal limit of something which may be observable but always falls short, in its observed forms, of the ideal. The use of limiting cases in mathematics, and of conceptions like those of an "economic man" in science are examples of such idealisation.
This is the process of forming judgements or opinions on the ground of other judgements or on the evidence of observation. The evidence may be merely supposed for the sake of argument, or with a view to the further consideration of the con-sequences, which follow from it. It is not always easy to draw the line between direct observation and inference. People, eventrained people, do not always realise, e.g., when they pass from the observation of a number of facts to a generalisation which, at best, can only be regarded as an inference from them. But the difficulty need not be exaggerated. There are two principal types of inference, namely deductive and inductive. Inductive inference is the process of inferring some kind of order among phenomena from observations made. Deductive inference is the process of applying general truths or concepts to suitable instances. In science inductive inference plays the most important role, and the methods of sciences are mainly instruments of induction or auxiliaries thereto. But deductive inference is also necessary to science, and is, in fact, a part of nearly all complete inductive investigations. Still, marked inductive ability is very rare. There are thousands who can more or less correctly apply a discovery for one who can make it.
Comparison and Analogy.
Reference has already been made to the importance of the process of comparison in the mental analysis of observed phenomena. The observation of similarities and differences, aided by the processes of analysis and synthesis, is one of the first steps to knowledge of every kind, and continues to be indispensable to the pursuit of science throughout its progress. But there are degrees of similarity. Things may be so alike that they are at once treated as instances of the same kind or class. And the formulation and application of generalisations of all kinds are based upon this possibility of apprehending such class resemblances. On the other hand, there is a likeness, which stops short of such close class likeness. Such similarity is usually called analogy. The term is applied to similarity of structure or of function or of relationship, in fact, to similarity of almost every kind except that which characterises members of the same class, in the strict sense of the term. And analogy plays very important part in the work of science, especially in suggesting those suppositions or hypotheses which, as already explained, are so essential to scientific research and discovery.
After this brief survey of various mental activities which are more or less involved in the pursuit of every kind of knowledge, and consequently from no suitable bases for the differentiation of the various methods of science, we may now proceed to the consideration of the several scientific methods properly so called.
This may be described as the oldest and simplest of scientific methods. The observation of similarities between certain things, and classing them together, marks the earliest attempt to discover some kind of order in the apparently chaotic jumble of things that confront the human mind. Language bears witness to the vast number of classifications made spontaneously by pre-scientific man. For every common noun expresses the recognition of a class; and language is much older than science. The first classifications subserved strictly practical purposes, and had reference mainly to the uses which man could make of the things classified. They were frequently also based on superficial resemblances, which veiled deeper differences, or were influenced by superficial differences, which diverted attention from deeper similarities. But with the growth of the scientific spirit classifications became more objective or more natural, attention being paid to the objective nature of the things themselves rather than to their human uses. Even now scientific classification rarely begins at the beginning, but sets out from current classifications embodied in language. It has frequent occasion to correct popular classifications. At the same time it has difficulties of its own, and more than one science has been held up for centuries for want of a really satisfactory scheme or classification of the phenomena constituting its field of investigation. To recognise a class is to recognise the unity of essential attributes in a multiplicity of instances; it is a recognition of the one in the many. To that extent it is a discovery of order in things. And although it is the simplest method of science, and can be applied before any other method, it is also the fundamental method, inasmuch as its results are usually assumed when the other methods are applied. For science is not, as a rule, concerned with individuals as such, but with kinds or classes. This means that the investigator usually assumes the accuracy of the classification of the phenomena, which he is studying. Of course, this does not always turn out to be the case. And the final outcome of the application of other methods of science to certain kinds of phenomena may be a new classification of them.
Inductive and deductive methods.
Below is the summary of contrasts in the major tenets of inductivism and of Popper's deductivism.. I begin with a caricature of inductivism in the form of eight theses:
1. Science strives for justified, proven knowledge, for certain truth.
2. All scientific inquiry begins with observations or experiments.
3. The observational or experimental data are organised into a hypothesis, which is not yet proven (context of discovery).
4. The observations or experiments are repeated many times.
5. The greater the number of successful repetitions, the higher the probability of the truth of the hypothesis (context of justification).
6. As soon as we are satisfied that we have reached certainty in that manner we lay the issue aside forever as a proven law of nature.
7. We then turn to the next observation or experiment with which we proceed in the same manner.
8. With the conjunction of all these proven theories we build the edifice of justified and certain science.
In summary, the inductivist believes that science moves from the particulars to the general and that the truth of the particular data is transmitted to the general theory.
Now we will observe a caricature of Popper's theory of deduc-tivism, again in the form of eight theses:
1. Science strives for absolute and objective truth, but it can never reach certainty.
2. All scientific inquiry begins with a rich context of background knowledge and with the problems within this context and with metaphysical research programmes.
3. A theory, that is, a hypothetical answer to a problem, is freely invented within the metaphysical research programme: it explains the observable by the unobservable.
4. Experimentally testable consequences, daring consequences that is, are deduced from the theory and corresponding experiments are carried out to test the predictions.
5. If an experimental result comes out as predicted, it is taken as a value in itself and as an encouragement to continue with the theory, but it is not taken as an element of proof of the theory of the unobservable.
6. As soon as an experimental result comes out against the prediction and we arc satisfied that it is not a blunder we decide to consider the theory falsified, but only tentatively so.
7. With this we gain a deeper understanding of our problem and proceed to invent our next hypothetical theory for solving it, which we treat again in the same way.
8. The concatenation of all these conjectures and refutations constitutes the dynamics of scientific progress, moving ever closer to the truth, but never reaching certainty.
In summary, the Popperian deductivist believes that science moves from the general to the particulars and back to the general— a process without end. Let me inject a metaphor. I might liken the Popperian view of science to that of a carriage with two horses. The experimental horse is strong, but blind. The theoretical horse can see, but it cannot pull. Only both together can bring the carriage forward. And behind it leaves a track bearing witness to the incessant struggle of trial and error.