Inductive and deductive methods

Inductive and deductive methods. Below is the summary of contrasts in the major tenets of inductivism and of Poppers 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 Poppers 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.

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 Deductive Method of Induction. To avoid the confusion of the Deductive 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 induction 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 sometimes, say in the study of light, mathematical i.e deductive calculations precede and suggest physical experiments i.e induction, and sometimes the inductive results of observation or experiment provide the occasion or stimulus for mathematical deductions. 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 investigation, it is considered desirable either to confirm an inductive 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.

An example of each of these types may help to make them clear. 1 When Galileo was investigating the law of the velocity of falling bodies he eventually formed the hypothesis that a body starting from rest falls with a uniform acceleration, and that its velocity varies with the time of its fall. But he could not devise any method for the direct verification of this hypothesis.

By mathematical deduction, however, he arrived at the conclusion that a body falling according to his hypothetical law would fall through a distance proportionate to the time of its fall. This consequence could be tested by comparing the distances and the time of falling bodies, which thus served as an indirect verification of his hypothesis. 2 By inductions from numerous astronomical observations made by Tycho Brahe and himself, Kepler discovered the three familiar laws called by his name, namely, a that the planets move in elliptic orbits which have the sun for one of their foci 6 that the velocity of a planet is such that the radius vector i.e an imaginary line joining the moving planet to the sun sweeps out equal areas in equal periods of time and c that the squares of the periodic times of any two planets that is, the times which they take to complete their revolutions round the sun are proportional to the cubes of their mean distances from the sun. These three laws appeared to be quite independent of each other.

But Newton systematised them all in the more comprehensive induction, or theory, of celestial gravitation.

He showed that they could all be deduced from the one law that the planets tend to move towards each other with a force varying directly with the product of their masses, and inversely with the square of the distances between them. 3 H. Spencer, by comparing a number of predominantly industrial States and also, of predominantly military States, ancient and modern, inferred inductively that the former type of State is democratic and gives rise to free institutions, whereas the latter type is undemocratic and tends to oppression.

As the sparse evidence hardly permitted of a rigorous application of any of .the inductive methods, Spencer tried to confirm his conclusion by deductive reasoning from the nature of the case in the light of what is known about the human mind. He pointed out that in a type of society, which is predominantly industrial, the trading relations between individuals are the predominant relations, and these train them to humour and consider others.

The result is a democratic attitude in all. In a State, which is predominantly military, the relations which are most common among its members are those of authority, on the one part, and of subordination on the other.

The result is the reverse of a democratic atmosphere. RELATION OF EPISTEMOLOGY TO OTHER BRANCHES OF PHILOSOPHY In conclusion, I would like to discuss the relation of epistemology to other branches of philosophy. Philosophy viewed in the broadest possible terms divides into many branches metaphysics, ethics, aesthetics, logic, philosophy of language, philosophy of mind, philosophy of science, and a gamut of others. Each of these disciplines has its special subject matter for metaphysics it is the ultimate nature of the world for ethics, the nature of the good life and how people ideally ought to comport themselves in their relations with others and for philosophy of science, the methodology and results of scientific activity.

Each of these disciplines attempts to arrive at a systematic understanding of the issues that arise in its particular domain. The word systematic is important in this connection, referring, as explained earlier, to the construction of sets of principles or theories that are broad-ranging, consistent, and rationally defensible.

In effect, such theories can be regarded as sets of complex claims about the various matters that are under consideration. Epistemology stands in a close and special relationship to each of these disciplines. Though the various divisions of philosophy differ in their subject matter and often in the approaches taken by philosophers to their characteristic questions, they have one feature in common the desire to arrive at the truth about that with which they are concerned say, about the fundamental ingredients of the world or about the nature of the good life for man. If no such claims were asserted, there would be no need for epistemology.

But, once theses have been advanced, positions staked out, and theories proposed, the characteristic questions of epistemology inexorably follow. How can one know that any such claim is true What is the evidence in favour of or against it Can the claim be proven Virtually all of the branches of philosophy thus give rise to epistemological ponderings.

These ponderings may be described as first-order queries. They in turn inevitably generate others that are, as it were, second-order queries, and which are equally or more troubling. What is it to know something What counts as evidence for or against a particular theory What is meant by a proof Or even, as the Greek Sceptics asked, is human knowledge possible at all, or is human access to the world such that no knowledge and no certitude about it is possible The answers to these second-order questions also require the construction of theories, and in this respect epistemology is no different from the other branches of philosophy.

One can thus define or characterise epistemology as that branch of philosophy, which is dedicated to the resolution of such first- and second-order queries. BIBLIOGRAPHY 1. A preface to the logic of science, by Peter Alexander, Sheed and Ward, London and New York, 1963. 2. Popper selections, edited by Dawid Miller, Princeton University press, 1985. 3. The critical approach to science and philosophy, edited by Mario Bunge, The free press of Glencoe Collier- Magmillan limited, London, 1964. 4. Britannica encyclopaedia, 1948. 5. Logic without metaphysics, by Ernest Nagel, Glencoe, Ill Free Press, 1957. 6. Epistemology, History of by D.W. Hamlyn.

The Encyclopaedia of Philosophy. 7. Introduction to Objectivist Epistemology, expanded 2nd ed by Ayn Rand, New York Penguin Group, 1990.