The goal of logic is to make explicit our intuitions of good reasoning, such that we can distinguish between good reasoning and bad reasoning in terms of an explicit procedure that does not need to rely on intuitions.

To do this, logicians formulate the information and the inferences involved in reasoning as propositions. As we have seen the propositions of the information from which we derive inferences are called premises, while the propositions of the inferences are called conclusions.

Information		Reasoning		Inferences
Premises				Conclusions

How do we distinguish between good reasoning and bad reasoning? Take the following examples:

Intuitively, we recognize example 1 to be an instance of good reasoning and example 2 to be an instance of bad reasoning. We therefore expect logic to tell us why this is so.
In order to unearth what is bad about example 2, the first step is to express the propositions in such a way that their logical structure becomes clear. The proposition expressed by the sentence All humans are mammals is the same as “For any x, if x is a human, x is a mammal.” We can now restate examples 1 and 2 as:

Let us denote x is a human as P and x is a mammal as Q:

We now see that the sentence All humans are mammals expresses a complex proposition consisting of two propositions P and Q, and is of the form:

If P, then Q. Logicians use an arrow to denote the “if…then” relation, and write “If P, then Q” as: P Q

We can now express the logical structure of examples 1and 2 as:

	Example 1	Example 2
Premise 1:	P Q	P Q
Premise 2:	P	P
Conclusion:	Therefore Q	Therefore P

Why is the structure in example 2 bad, in contrast to that in example 1? The response to this question calls for the concept of rules of inference, the abstract pattern that sanctions a conclusion from a given set of premises. An important rule of inference in deductive logic, for instance, is what is called Modus Ponens, which says:

Rule of inference: Modus ponens

Given that: P Q is true   P is true it is reasonable to conclude that: Q is true

Modus Ponens sanctions the reasoning in example 1, but not in example 2. We can now say that the reasoning in example 2 is bad because there is no rule of inference that sanctions the conclusion based on the premises provided.

Contributed by K P Mohanan ().