What is the relation between Induction and Deduction?

We notice that deduction and induction are the two distinct processes of reasoning. Each process of reasoning has its own distinctive features.

The deductive process provides the theoretical basis to know how arguments are valid or invalid. The inductive process formulates the basis for generalization and guards against illegitimate ones. For any wrong derivation or hasty generalization is a logical commission that makes thinking opaque.

Deduction and induction as processes of reasoning help know the rules and procedures of their respective mode and thus guard against fallacious inferences. Now let us discuss their interrelationship, i.e. their similarities and differences.

When a conclusion necessarily follows from the premises and there is a relation of implication between the premises and the conclusion, the reasoning is deductive. On the other hand when the conclusion does not necessarily follow from the premises but is supported by them the reasoning is inductive.

That is, in case of induction even if all the accompanying evidences, the premises, are true, there is no certainty that the conclusion will be true. But in deduction if the argument is valid and the premises are true, the conclusion must be true.

There is a significant difference between deduction and induction. In deduction the conclusion cannot be more general than the premises but in induction the conclusion is always more general than the premises.

In deductive reasoning from a principle we draw particular instances or a conclusion having lesser generality. But in induction from particular cases of observed instances we make a generalization. While the premises in an induction are obtained from the observation of facts, the premises in a deduction are assumed to be true.

Thus induction always proceeds from particulars to the general but deduction proceeds from general to less general or particular.

Again formal validity is the essential feature of a deductive argument. An argument is formally valid if the conclusion necessarily follows from the premises. In a deductive argument what is important is the formal consistency.

The subject matter or the content of the premises is not of consideration, but the rules of inference. If the rules of inference are strictly followed, then the argument will have validity.

This process or reasoning can be applied in any sphere of discourse, but the point at issue in deductive argument is formal justification of the conclusion. But in case of induction the point of formal validity-is out of question.

Here the conclusion is a generalization, which should be true as a matter of fact. In an induction if the conclusion becomes true, then the purpose of induction is fulfilled. For induction aims at a real generalization based on fact. Here there is a passage from proposition true of some observed cases to a proposition true of all the cases of a particular class.

All physical sciences apply inductive method in their pursuit of knowledge. I induction while the premises are based on experience in deduction the premises are assumptions.

That is the accompanying evidence in an inductive generalization com from real experience, either through observation or experiment. But the premises deductive arguments are assumptions. The conclusion in an induction is like a generalization which comes like a hypothesis.

This requires more and more confirmation in its favour to be accepted as a theory or law in science. But the conclusion in a deduction is a logic outcome that necessarily follows from the premises accepted for the argument. So the reasoning in a valid deduction is very much conclusive. And here if the premises are true the conclusion must be true. But in induction its very structure reveals that their will be different degrees of probability. Probability would be high or low depending upon its supporting evidences.

From the above consideration it appears that induction and deduction are two forms of reasoning. They are two different processes of inference. For deriving a conclusion from premises these two processes are applied in different spheres.

While mathematics discourses use the deductive procedure all physical sciences mostly apply the inductive procedure. Since both of them are the process of reasoning they do help to build up system of knowledge.

There is no system of knowledge that can do away with any process J reasoning. Any intellectual pursuit or system of thought takes the help of some form of reasoning to establish its conclusions. Induction and deduction are the two most significant processes of reasoning which have been explored in logic.

There are some deep-seated confusion with regard to the relation between induction and deduction. We should guard these confusions to have a clear perception of their exact relation or role. For the confusions not only mar their relation but also blur the role of induction or deduction.

There is a view that one is prior to the other. John Stewart Mill, for example, takes induction as prior to deduction. According to him in a deductive argument one premise must be a general proposition. But to get a general or universal proposition we have to take the help of induction.

That is the general proposition of a deductive argument is obtained by induction, so induction has priority over deduction. Contrary to Mill’s view Jevon holds that deduction is prior to induction. For in induction though the conclusion is a general proposition it is suggested as an insight on the basis of some observation.

That is the general proposition is like a hypothesis which we imagine on the experience of particular facts. The hypothesis to be accepted needs to be verified deductively. Without verifying a hypothesis in a deductive manner it cannot be accepted as a proper inductive generalization.

That is induction requires prior deduction for verification of the hypothesis. Thus according to Jevon deduction is prior to induction.

But this way of expressing their relation is misleading as well as confusing. As they are two processes of reasoning they are mutually dependent. As they are inferential procedures they have some close link.

But it is not correct to maintain that induction supplies a premise to deduction. Deduction makes an assumption and brings out the conclusion that necessarily follows from it.

Deduction has nothing to account for the material truth of the conclusion or of the premise. So it is not to be accepted that induction supplies a premise to deduction.

Similarly the view that deduction is prior to induction is not correct. At the stage of verification for the confirmation of a hypothesis deduction is made. Deduction aims at formal consistency of an argument.

It contributes nothing for the confirmation of a hypothesis. A hypothesis is confirmed by direct or indirect observation of facts. So the view of Jevon that deduction has priority over induction is not a correct presentation of their relation.

Again some deductive logicians consider deduction to be more fundamental than induction whereas some inductive logicians treat induction to be more fundamental than deduction. Those who accept the fundamentality of deduction hold that all arguments- including inductive ones-are deductive in nature.

Even inductive arguments can be expressed in deductive form. To say “all dogs are mammals” is to make an inductive generalization on the basis of observation of facts. But deductive logicians like Aldrich and Whatley try to reduce the above inductive argument to a form of deductive argument like-

The dogs observed and the dogs not observed are mammals.

But the idea of “all clogs” includes the dogs that are either observed or not observed.

\ All dogs are mammals.

But this way of reducing an inductive argument to a form of deduction is wrong for what is brought out as a proof in the conclusion is first presupposed in the premise. What is aimed to be proved is at first assumed to be true.

To assert that the dogs we have observed and the dogs we have not observed are mammals is to make an inductive generalization. That can be done only if induction is accepted as a valid form of inference. Thus this attempt to reduce induction to a form of deduction is not justified.

Similarly some inductive logicians like J.S. Mill and Bain accept the fundamentality of induction over deduction. All arguments, they hold, are basically inductive for either they are from particular facts to other particular facts or from particular cases to a general case.

Further for them deduction consists as a stage in every scientific generalization. That is deduction only applies a generalization obtained by induction in individual cases. For the proof of an induction, they maintain, deduction is required to apply a generalization to some individual cases.

The generalization ” all men are mortal” can be ascertained by applying it to individual persons. That is deduction comes within the system of induction and therefore has a secondary importance.

But such a view is also not acceptable. It is not correct to say that all arguments are primarily inductive nor is it a fact that induction includes deduction. Rather induction and deduction are two fundamental and independent processes of reasoning having different spheres of application. Deductive reasoning aims at formal certainty or consistency whereas inductive reasoning aims at a true generalization.

Formal consistency has absolute certainty but no novelty, whereas a generalization has novelty but no absolute certainty. So these two forms of reasoning are distinct from each other and it is not correct to reduce one to the other.

There are also misleading descriptions about deduction and induction. Some logicians describe induction to be an ascending process and deduction as a descending process. Aristotle held that induction is an ascending process for passing from particular cases to a general conclusion.

Bacon too takes deduction as a descending process for passing from a general case to particular cases. Similar such expressions are used to characterize them or their relation. Sometimes it is held that induction moves upwards whereas deduction proceeds downwards.

Some again describe them as reverse processes. For in deduction we proceed from general to particular but in induction we proceed from particular to general. These descriptions are misleading as they are expressed in ambiguous ways. Such descriptions in stead of making their characteristics clear rather blur their essential nature.

Further there is also attempt to overlook their essential distinction. It is sometimes maintained that deduction and induction are essentially similar on all important points. Some hold that their difference is only with regard to their starting point. There is fundamental similarity between the two as they are processes of reasoning.

There is sameness as both involve inference and are founded on the ground of similarity. The sameness or similarity in deductive reasoning is expressed by the presence of the middle term. The link of the middle term with other terms helps to relate them in the conclusion and bring the premises and the conclusion into one system. In induction the sameness is expressed between the observed instances and the unobserved ones as belonging to the same class.

The generalization in induction covers unlimited cases because of its essential similarity with the observed instances. Thus similarity is the basis of both, and their difference is only with respect to their starting points which are a superficial or marginal one.

Consequently deduction starts from a general premise and draws particular cases from it. Induction on the other hand starts from the particular facts and establishes a general proposition.

Thus while deduction applies or interprets the law to the individual cases induction interprets the observed instances by help of generalized principle, or law. On the basis of this it is also maintained that induction proceeds from facts to ideas and deduction proceeds in the reverse direction that is from ideas to facts.

But this elucidation to marginalize their difference sometimes blurs their real distinction. Even the real significance of induction or deduction as a process of reasoning is also overshadowed by it. For instance it is not correct to say that induction always proceeds from particular to the general. At the higher stage of inductive generalization facts are not interpreted by laws rather laws are brought under some higher law as is the case m non-instantial hypotheses.

We shall discuss this when we explain the idea of secondary induction. Similarly it is not correct to say that deduction proceeds from idea to fact. For in deductive reasoning facts qua facts have nothing to do with inference.

It is very formalistic in its very approach. To assume a generalized truth and to find out what it entails is the very task of a deductive inference. But in induction to relate the observed facts to some empirical law or the laws to some higher law or theory is the purpose of this inference.

So deduction and induction are two significant modes of reasoning and their difference should not be belittled in metaphorical or ambiguous elucidations.