Deductive reasoning concerns what follows necessarily from given premises (i.e. from a general premise to a particular one). An inference is deductively valid if (and only if) there is no possible situation in which all the premises are true and the conclusion false. However, it should be remembered that a false premise can possibly lead to a false conclusion.
Deductive reasoning was developed by Aristotle, Thales, Pythagoras and other Greek philosophers of the Classical Period. At the core of deductive reasoning is the syllogism (also known as term logic),usually attributed to Aristotle), where one proposition (the conclusion) is inferred from two others (the premises), each of which has one term in common with the conclusion. For example:
Major premise: All humans are mortal.
Minor premise: Socrates is human.
Conclusion: Socrates is mortal.
An example of deduction is:
All apples are fruit.
All fruits grow on trees.
Therefore all apples grow on trees.
One might deny the initial premises, and therefore deny the conclusion. But anyone who accepts the premises must accept the conclusion. Today, some academics claim that Aristotle's system has little more than historical value, being made obsolete by the advent of Predicate Logic and Propositional Logic (see the sections below).