Question

Explain what is meant by deductive reasoning. Give an example of the Law of Detachment and the law of Syllogism.

Answer 1

Deductive Reasoning

Deductive reasoning is the process by which a person makes conclusions based on a previously known fact/facts. Deduction starts with an assumed hypothesis or theory. Here the assumption for the argument sake is not questioned. Deductive reasoning is the method by which conclusions are drawn in geometric proofs.

Deductive reasoning is sometimes known as 'top-down' reasoning, often to differentiate it from the bottom-up approach of Inductive Reasoning.

For example,

A Platoon Commander knows that all the men in a room are soldiers, that all soldiers get up early for exercise in the morning, and that Steve is in that specific room.

Knowing these statements to be true, Platoon commander could deductively reason that Steve gets up early in the morning. Such a method of reasoning is a step-by-step process of drawing conclusions based on previously known truths.

Law of Detachment

Law of detachment basically tells us

P -> Q .

∴ If P happens the Q will happen.

That is if hypothesis happens then the conclusion will happen.

Law of detachment involves 2 quantities which is “hypothesis” and “conclusion”.

Here the flow is always unidirectional and the reverse is not always true.

Example 1 : If you study then you will get good grade.

It is always unidirectional .

If i reverse the same, for example -> If I get good grade then it doesn’t always mean that I have studied well. I might have cheated also.

example 2) If rain increases then yield of the crop increases.

If yield of crop increases it doesn’t mean that rain has increased . It may be the fertilizer used is better , farmer had worked hard and many other reasons which might have resulted in increase of yield of crop.

Law of Syllogism.

Law of syllogism is similar to that of transitive property( ie if A=B and B=C the A=C).

If P- > Q ,

If Q - > R ,

∴ If P then R.

That is if first event occurs , then event R will occur after a chain of events between P and R.

In Law of syllogism there are three or more quantities involved.

Here the conclusion of a statement becomes the hypothesis in the next statement which leads to another event. This is like a chain of events leading to final conclusion.

Example :

If you study then you will get good grade.

If you get good grade then you will go on to next class.

Based on the above given statements , if we were given a statement like “Sally Studied” and was asked to derive a conclusion out of it. We will compare this with above statements and derive a conclusion as shown below.

If Sally Studied then she will get good grade.

If she get good grade then she will go on to next class.

Based on this we can conclude that if Sally Studied, she will go on to next class.

The reverse is not always true.

For example if we were given a statement that “John went on to next class”.

We cannot always conclude that he got a good grade and he studied well.

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