Relevant and Related Concepts in logic
There are certain key terms that cannot be separated from our study of logic. It is therefore important that before any progress made, we should be able to identify and know what some of these terms mean. The list below is not exhaustive. Others will be be encountered and treated in subsequent sections of this work.
Reasoning
It is the otherwise known as inference ( from the verb to infer which means to draw or to develop something new from another ). This is the process of making judgement or drawing conclusions from one or more premises. It is thinking that is coherent and logical.
An Argument: This is a set of propositions, which are so related that from the ideas expressed in one or more, called the premises, a new idea or judgement is drawn in the last, called the conclusion. So, every argument comprises of two elements namely; the premise(s) and the conclusion.
A Proposition: This is a statement that has a truth value. In other words, It is a statement that expresses an idea that can either be true or false.
Truth: It is the possibility of an idea expressed in a proposition being correct and factual or true. In other words, the content expressed in the propositional is not a fact.
Falsity: The possibility of the idea expressed in a propositional statement to be non-factual or incorrect. In other words, the content expressed in the proposition is not a fact.
Validity: The capacity of the conclusion of an argument to follow from the premises of the argument. In other words, it is the extent to which the conclusion of an argument is related to its premises. An argument can either be valid or in valid.
A Valid argument: This is an argument whose conclusion follows or can be derived from the premises. The conclusion is perfectly related to the premises. In other words, a valid argument is one in which it is not possible for the conclusion to be false if the premises are true. So, for a valid argument, if the premises are true, then the conclusion too will be true.
An invalid argument: This is an argument whose conclusion does not follow or cannot be derived from its premises. The conclusion is either only partly related or not at all related to the premises. In other words, an invalid argument is one in which it is possible fr the premises to be true but the conclusion false.
Types of reasoning
As we indicated previously in the preceding sub-sections, reasoning is a very important aspect of human mind. Logic is particularly concerned with this process. As we defined it previously, reasoning is the process of making judgements or drawing conclusions from one or more premises. Logicians have identified three basic types of this process viz.
Deductive Reasoning: It is equally known as deductive or reasoning by deductive. this is reasoning that proceeds from general cases to particular cases. Characteristics that are observed to be true or false of a general class of things or a group are attributed to be true or false in the same to individual elements that belong to such a class of things or group. So that which is true of a whole group is true to every individual member of that group.
Example 1
Every student is an exam-cheat.
Mbua is a student.
Consequently, he is an exam-cheat.
Example 2
Students are not learners.
Ebai is a student.
Therefore, he is not a learner.
Inductive Reasoning: This type of reasoning is equally known as induction or reasoning by induction. This is reasoning from particular cases to general cases. Characteristics that are observed to be true or false of individual objects, persons and situations are attributed to be true or false in a similar way to groups or general or whole classes of objects, person and situations of which such individuals are members. So, that which is true of an individual is generalized to be true in the whole class or group. In the same way, that which is false of an individual is generalized to be false for the whole class or group. In the same way, that which is false of an individual is generalized to be false for the whole class or group.
Example 1
Bingo is a dog.
Bingo eats bones
Therefore, all dogs eats bones.
Example 2
Mr. Mbah is a farmer.
He does not go to church.
So, No farmer goes to church.
Analogical Reasoning: This type of reasoning is known as analogy or reasoning by analogy. It is a form of reasoning or logical inference that is based on the assumption that if two things are known to be similar/ dissimilar in some respects, then they must be similar/dissimilar in other respects. It is based on comparisons between two or more things, ideas or persons. So a conclusion or a judgement is inferred about two things, persons or ideas on the basis of some characteristics that unite or separate them.
Example 1
It rained heavily and Buea experienced floods last rainy season
It has has rained heavily and Buea has experienced floods this year.
Therefore, if it rains heavily next year, Buea will experience floods
* Inference or analogy based on similarity