State and Explain Different Views of Probability

We discussed that all inductive arguments are probable in nature. No inductive generalization is logically certain.

Again it was pointed out that probability is a matter of degree. Some generalizations are highly probable whereas some are less probable. In all forms of proper inductions conclusions are drawn on the basis of some supporting evidenc \s. If the support lent by the premises are most dependable with which the conclusion is characteristically related, then the degree of probability of the conclusion will be high.

The probability of the conclusion in inductive argument can be decided on the basis of objective ground. Just as in deductive argument the validity of the conclusion can be decided on objective basis by the help of some criteriological rules, so also in case of inductive argument the probability of the conclusion can be determined objectively by tallying it with the actual state of affairs.

An inductive inference is accepted as highly probable if it is coherent with already established generalizations. The frequency of truth of the conclusion is confirmed by experience.

The frequency of truth of individual instances increasingly adds to the confirmation of probability of the conclusion. Since the conclusion is a generalized version of the individual instances its degree of probability is high or low depending upon the frequencies of the supportive evidences.

From this it appears that the probability is not an intrinsic or inherent feature of a proposition. It is something extraneous to the proposition. It is because the same proposition might have different degrees of probability depending upon the confirming support or evidence.

The relevance of the evidence given in support of a proposition may be different also. The relevance is not the same in all cases. Further the probability of an inductive inference is supposed to be measured by the frequency of the supporting fact. The numerical strength of probability of a conclusion i,s-the adequate evidence for the proposition.

Calculus of probability:

Most of the branches of science practically employ the calculus of probability in their studies. The concept of probability is also familiar in mathematics and logic. But proposions of science dealing with matters of fact are different from the propositions of mathematics.

So no purely mathematical system can decide the degree of probabilities of assertions of fact. Thus mathematical probability is different from probability used in science. In mathematics the theory of probability is limited to the idea of necessary inference.

The idea of mathematical probability connotes the condition of equiprobability of events. The probability of a tossed coin showing head is fifty per cent since a coin has only two sides, such as head and tail. That is when a coin is tossed, either the head or the tail must face upward.

Similarly once the components of a complex event is known the calculus of probability can be determined. The purpose of the calculus is to decide from a complex event the probability of the events comprising it. From a set of alternative possibilities mathematical probability determines the possible consequence of the assumption.

By help of a mathematical ratio the idea of probability is explained. When we are sure that some event will definitely occur its probability is I, and when we are sure of its non-occurrence its probability is O and when our belief is in between the certainty of its occurrence and its non-occurrence the probability is some fraction intermediate between 1 and O.

Further the idea of probability is also linked with the principle of insufficient reason or indifference. That means in a complex situation of several alternatives, if there is no known reason to accept one rather than another then each of these alternatives has an equal probability. If there is induction, alternatives are equally probable.

Further probability cannot be taken as a measure of belief. For the belief of people about something may remarkably differ. So belief does not always correspond with the state of facts. Hence probability cannot be estimated on the basis of belief.

If large number of people believe in something that does not constitute the ground for the belief to be accepted. The belief in astrological prediction or in the existence of ghost by a majority of people cannot be the ground to accept astrology as a science or ghost as a reality.

When calculating the probability of complex events, all possible alternatives are also taken into consideration.

The probability of the alternative occurrence of two events is the sum of separate probabilities. Suppose two events cannot occur jointly. In a game of dice 1 and 2 cannot occur together.

Since there are six possible values, the probability for each value is 1/6 . So the probability of either 1 or 2 occurring alternatively would beSimilarly the probability of the joint occurrence of two independent events is the product of the probability of each of them.

If a and b are two separate events, R(a) the probability of the first and R(b) the probability of the second, then the probability of their joint occurrence is R(a) X R(b). Suppose in a winter season a foggy morning occurs in an average of once in four days, and rain occurs once in seven days, their separate probabilities are – and – respectively in a week. So the probability of their joint occurrence is i.e. the product of their separate probabilities.