Epistemology and methodology: main trends and ends

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 justifica​tion).

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 experi​ments 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 pre​diction 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 car​riage forward. And behind it leaves a track bearing witness to the incessant struggle of trial and error.

The Deductive-inductive Method.

Just as money makes money, so knowledge already acquired facilitates the acquisition of more knowledge. It is equally evident in the case of the method, which will now engage our attention. The progress of science, and of knowledge generally, is frequently facilitated by supplementing the simpler inductive methods by deductive reasoning from knowledge already acquired. Such a combination of deduction with induction, J. S. Mill called the "Deductive Method," by which he really meant the "Deduc​tive Method of Induction." To avoid the confusion of the "De​ductive Method" with mere deduction, which is only one part of the whole method, it is better to describe it as the "Deductive-Inductive Method" or the "Inductive-Deductive Method." Mill distinguished two principal forms of this method as applied to the study of natural phenomena, -namely, (1) that form of it in which deduction precedes induction, and (2) that in which induc​tion precedes deduction. The first of these (1) he called the "Physical Method"; the second (2) he called the "Historical Method."

These names are rather misleading, inasmuch as both forms of the method are frequently employed in physics, where some​times, say in the study of light, mathematical (i.e., deductive) calculations precede and suggest physical experiments (i.e., induc​tion), and sometimes the inductive results of observation or ex​periment provide the occasion or stimulus for mathematical de​ductions. In any case, the differences in order of sequence are of no great importance, and hardly deserve separate names. What is of importance is to note the principal kinds of occasion, which call for the use of this combined method. They are mainly three in number: (1) When an hypothesis cannot be verified (i.e., tested) directly, but only indirectly; (2) when it is possible to systematise a number of already established inductions, or laws, under more comprehensive laws or theories; (3) when, owing to the difficulties of certain problems, or on account of the lack of sufficient and suitable instances of the phenomena under in​vestigation, it is considered desirable either to confirm an induc​tive result by independent deductive reasoning from the nature of the case in the light of previous knowledge, or to confirm a deductive conclusion by independent inductive investigation.