You may know that the conclusion of an argument asserts a claim on the basis of the premises. In general, an argument exhibits a relational tie or a relation between premises and the conclusion. Logic as a system of reasoning aims at characterising this relation. On the basis of the nature of this relational tie we can broadly distinguish between two kinds of arguments viz., deductive and inductive.
In deductive arguments, the premises conclusively justify or support the conclusion. The truth claim expressed by the conclusion is fully supported by the truth claim expressed by the premises.
In other words, in case of deductive arguments the truth of the premises absolutely ensures the truth of conclusion. In this sense we call a correct deductive argument demonstrative. If the premises are true, the conclusion must necessarily be true.
This means that in a correct deductive argument the premises and conclusion are so related that it is impossible for the premises to be true and the conclusion to be false. Consider the following example,
(1) If logic is interesting then many students like it.
(2) In fact, logic is interesting.
(3) Therefore, many students like it.
Here it is impossible that premises are true and conclusion is false. This is a valid deductive argument in which the premises provide conclusive grounds for the truth of the conclusion. In an inductive argument the premises do not absolutely or conclusively ensure the truth of the conclusion.
If the premises of an inductive argument are all true and the reasoning is good then it is reasonable to believe in the truth of the conclusion. But here we cannot be absolutely sure of the truth of the conclusion. For example, consider the following argument.
(1) Ram is mortal
(2) Hari is mortal
(3) Sita is mortal
Therefore, all men are mortal.
This is an inductive argument. Here even if all the premises are true and the reasoning is good yet the truth of the conclusion cannot be asserted conclusively or with certainty. Because, even if all the premises are observed to be true and nothing contrary has been observed so far, yet the conclusion being a general proposition cannot be observed to be true as it includes future and unobserved cases.
Therefore, the conclusion of an inductive argument is always prone to revision. Hence an inductive argument may be evaluated as better or worse according to the degree of support or backing given to the conclusion by the premises.
Inductive arguments are of great importance for establishing scientific laws and propositions expressing empirical conjectures about the world. Most of our beliefs are based on induction. They cannot be justified by deductive arguments as such cases are empirical generalisations based on contradicted experience.
For example, we believe that eating rice nourishes us whereas taking arsenic will be poisonous. These beliefs are established by inductive method.
Let us examine some of the misunderstandings usually associated with the distinction between induction and deduction. It is claimed that induction is a process from particular to general, whereas deduction is a process from general to particular. This is illustrated in the following example.
All men are mortal.
Socrates is a man.
Therefore, Socrates is mortal.
Here the conclusion is a particular proposition and one of the premises, precisely the major premise, is a general proposition. Of course the reasoning involved in the above argument is correct. This is an instance of valid deductive argument.
Therefore, it has been said that deduction is a process from general to particular. This is not always true. Because there are valid deductive arguments whose premises are all general propositions and the conclusion is also a general proposition. Consider the following example:
All men are mortal.
All kings are men.
Therefore, all kings are mortal.
Similarly, there are valid deductive arguments whose premises as well as the conclusions are all particular propositions. Consider the following arguments:
(1) If Ram is honest then Ram is virtuous,
In fact, Ram is honest,
Therefore, Ram is virtuous.
(2) Some Bengalis are scientists.
Therefore, some scientists are Bengalis.
So, it is not correct to characterise deduction as a process from general to particular. Similarly, we cannot in general claim that in an inductive argument the premises are particular but the conclusion is general. Because, there are inductive arguments whose premises as well as the conclusion are general propositions. Consider the following example,
All cows are mammals and have hearts.
All whales are mammals and have hearts.
All horses are mammals and have hearts.
All humans are mammals and have hearts.
Therefore, all mammals have hearts.
Likewise, we may have a good inductive argument that may have particular propositions for its premises as well as for its conclusion. This is illustrated in the following inductive argument.
During the last ten years maximum temperature in summer in Kolkata has exceeded 40 degree Celsius so this year also it will exceed 40 degree Celsius.
The above examples make it clear that it is not correct to characterise deduction as a process from general to particular and induction as a process from particular to general. The fundamental difference between induction and deduction lies on the nature of the relation between premises and the conclusion.
In case of deduction, the premises conclusively support the conclusion in the sense that no additional information (or premise) is relevant (i.e. it cannot increase or decrease the validity of a deductive argument). Validity never admits of degree.
On the other hand, the relation between premises and the conclusion in an inductive argument admits of degrees. Even in the best inductive argument premises render the conclusion highly probable. The premises of a good inductive argument never conclusively support the conclusion in the sense that it is possible to discover some additional facts concerning the world that may upset the truth claim made by the conclusion of a well-established inductive argument.
Thus, only deductive arguments can be characterised as valid or invalid. Inductive arguments are either strong or weak depending on the amount of support the premises provide to the conclusion.
We know that probability is the essence of any inductive argument i.e. the conclusion of an inductive argument is probable. Note that mere presence of the word "probability", "probable" etc. in the conclusion never ensures that the argument in question is inductive. Because, there are deductive arguments about the probabilities themselves.
Hence we may conclude that an argument is deductive if and only if the conclusion conclusively follows from or is completely determined by its premises, whereas in case of induction, the conclusion is claimed to follow from its premises only with probability.