# Parity of reasoning is another process Of simulating induction

Parity of reasoning is another process Of simulating induction. This process of inference is applied in formal science like mathematics. Particularly it is applied in geometry.

Though parity of reasoning gives the appearance of making a generalization, in reality it is not at all a form of induction. On the contrary it is substantially a deductive form of reasoning and has nothing to do with induction. Hence it is considered as simulating induction.

Induction by parity of reasoning is the generalization of a truth on the basis that the same reasoning which has proved a particular case will apply in every other similar case.

Suppose we prove in geometry that the two adjacent angles make two right angles; or that the three interior angles of a triangle make two right angles.

The proof that is given in one case is applicable in every other similar case. Whatever proof justifies the case that two adjacent angles are 180°, will be applicable in every case of adjacent angles. Or the proof that justifies that the interior angles of a triangle are 180°, will hold good in case of every triangle.

In algebra we also apply the same procedure of reasoning. Suppose we prove that a2 – b2 = (a + b) (a – b). On this basis we conclude that the difference of the square of any two numbers is equal to the product of their sum and difference. The symbolic expression of this form of reasoning is: ‘ •

Si is necessarily P.

All S’s are necessarily P.

It is to be noted that conclusion in parity of reasoning is a mathematical proposition. And a mathematical proposition is necessarily true as it is drawn from some axioms, definitions and theorems.

The conclusion appears as if there is a generalization but it is not on the basis of observation of facts. The conclusion is a deductive one and the basis for this deduction is similarity in reasoning.

The reasoning or proof that justifies a mathematical proposition will also apply in every other similar case. In fact any single proof makes a theorem. In the examples, the concept of an adjacent triangle stands for any adjacent angle or a triangle represents every triangle.