Our discussion shows that analogical arguments are not deductively valid. As they are about facts, they are probable in nature.

Some analogical arguments are cogent and have a high degree of probability whereas some others are useless and have no importance at all.

So there must be some criteria by which the value of an analogy can be assessed. Let us discuss the criteria devised by logicians for the determination of the strength of analogical arguments.

To assess the value of an analogy the number and importance of the points of resemblance between the particulars are given due weightage. Sometimes the number of instances counts important to add to the probability of the conclusion.

Suppose I gave a shirt-cloth to a tailor. Even though he had taken the measurement the shirt did not fit me well. On further occasions other friends also patronise with similar experience that their shirts were not tailored properly to fit them by the same tailor.

A number of instances •helps draw the conclusion that the tailor does not stitch properly for good fitting. Thus a single instance may not be sufficient to lend support to the conclusion but if a number of instances are there they add to the degree of probability. Of course there is no mathematical ratio between the number of instances and the conclusion.

The degree of probability of analogical arguments would be more on the modesty of the conclusion. If my motor-cycle shows less oil consumption and gives high mileage I infer that my friend's motor-cycle which is of the same model and brand would be giving the same mileage.

Further the strength of the analogical inference will be more if the things compared are similar on important and relevant points. Things must resemble on essential points and not on superficial points.

A doctor's inference that a will be relieved of his pain by a particular drug as the same drug has relieved the pain of b,c and d having somewhat similar symptoms is a reasonable analogical argument. Because there is similarity in their symptoms and the drug has worked in case of b,c and d, it will be reasonable to think that it will work on a. But suppose p,q and r belong to a particular locality, speak the same language and have the sme number of children.

It is found that they suffer from stomach- trouble."It will be silly to infer that s who also belongs to the same locality, speak the same language and have the same number of children is having stomach trouble.

This argument by analogy is very weak for the pints of similarity cited are quite irrelevant to the matter with which the inference is concerned. But in case of the former example the similarities are quite relevant to the conclusion. Thus the strength of the analogy will be more when the points of similarity will be relevant to the conclusion.

From the above illustration it follows that if the points of difference or dissimilarity in analogical argument will be more in number and importance the strength of the analogy will be less. If two things are similar on unimportant or irrelevant points and the point to be inferred has no useful link with their similarities the probability of the conclusion will be very weak.

Suppose two persons belong to the same age group, village, caste and religion. If one is a poet it cannot be inferred that the other person is also a poet. For the conclusion of being a poet has no relevant link with the points of similarity.

Similarly the value of an analogical inference will be less if the unknown sphere between the things compared is larger than their known region. Sometimes our information is inadequate or we are ignorant when we compare two particulars.

If we are not sure what are the similarities or dissimilarities between the things then also our conclusion can have less probability. That is if the number and importance of the unknown points will be more then the probability of the conclusion will be weak.

Thus the value of an analogical argument depends on the important points of resemblance between the instance in the premise and that of the conclusion.

It is not on how many points the phenomena are similar or dissimilar, but their relevance with the point to be inferred in an analogy is important.

The importance of similarity between the instance in the premise and that of the conclusion adds to the probability of the conclusion whereas more disimilarities or the unknown points between the instance mentioned in the premise and the conclusion weaken it and reduce the probability of the conclusion.

Some logicians express the value of analogical argument mathematically by means of a fraction in the following manner-

Known ponts of resemblance Known points of difference + Unknown points In a fraction if the numerator increases, its value increases and if the denominator increases the value of the fraction decreases.

Similarly the value of a particular analogical argument is more if the known points of resemblance, the numerator, will be more. That makes the analogical argument more probable. But if the denominator is more, then the value of the argument will be less i.e. the probability will be weak.

But the value of analogy cannot be decided with accurate precision unlike that of a mathematical fraction. For while a mathematical fraction is constant, the fraction in the analogy is quite uncertain and even vague. Because in the analogy the unknown points always remain uncertain and vague. If some points are unknown, their exact nature and number cannot be determined.

However the value of an analogy mostly depends on the connection between the points of resemblance and the inferred similarity. If the points of resemblance have some determining effect and that is what is inferred in the conclusion, then the value of the analogy would be more.

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