# Deductive Logical Reasoning, Validity and Soundness

15 Mar

Deduction is a method for applying a general rule in specific situations of which conclusions can be drawn. It is the method of non contradictory identification and based on the classical axioms of Aristotelean logic.

Most Known example for Deduction is :

1. All humans are mortal.

Bertrand Russell’s views on philosophy (Photo credit: Wikipedia)

2. Aristotle is human.
3. Therefore, Aristotle is mortal.

The first statement is major premise, the second is minor premise, and third statement is conclusion. In deduction to reach conclusion both premises must be true, or it would be a fallacious argument.

Validity : In valid deductive argument, a conclusion must follow from premises. If you want to reach from point A to point E, therefore you must go through points B, C, and D. If you do wrong turn, you will end up somewhere else. Consider this example :

1. If p is true, then q is true.
2. If q is true, then r is true.
3. Therefore, if p is true, then r is true.

As you see, 2nd premise is connected to first premise, and conclusion was derived through step by step: prem1→prem2→conc.

Soundness : If all premises of valid argument are true, then it is sound argument, and there is no choice but accept the conclusion.