Understanding Logic: Reasoning, Deduction, and Validity
Understanding Logic and Reasoning
Logic is considered the philosophical discipline that studies the correctness or validity of our reasonings.
Reasonings, Arguments, or Inferences
Our reasonings, also called inferences or arguments, are processes by which we obtain information from known data. Although they are originally mental processes, Logic does not deal with them in this sense (Psychology is responsible for this), but it deals with our reasoning linguistically expressed. Thus, any inference consists of two elements:
- Premises: A set of statements expressing the input data.
- Conclusion: The final statement expressing new information obtained from the premises.
Types of Reasonings or Arguments
There are two types of reasonings or arguments:
- Deduction: Consists of moving from general premises to a less general conclusion.
- Induction: Is a type of reasoning where you come to a general conclusion from less general information which is given in the premises.
Formal Logic
Formal logic focuses exclusively on whether the arguments are well-built or not. It analyzes the relationships between the premises and the conclusion; that is, it analyzes the structure of the reasonings. In this analysis, it does not need to deal with the content or meaning of the premises and the conclusion. A reasoning is well-built or not regardless of what is stated in it.
Informal Logic
Informal logic deals with elements that have nothing to do with the form or structure of our reasonings. In order to determine the validity of an argument, informal logic pays attention to elements such as whether the premises are appropriate, whether the input data can really justify the conclusion, whether there are elements in the context which can distort the validity of our reasoning. That is, non-formal issues are taken into account.
Types of Classical Formal Logic
- Propositional Logic: It interprets the statements as a block, without decomposing them.
- Predicate Logic: It analyzes the internal structure of the statements distinguishing between the subject and the properties which are predicated about it.
- Logic of Classes: It treats individuals as belonging to sets of elements that share certain properties.
- Logic of Relationships: It deals with the relationships between the elements of the statement.
Truth Tables and Validity
As a result of applying the method of truth tables to determine the validity of an argument, three different results may happen:
- Contradiction: This happens when the truth values of the resulting formula are always F, whatever the value of the component statements was.
- Uncertainty or Contingency: This happens, as we have seen in the example above, when the truth values of the last column contain both T and F values; that is, the truth of the main formula depends on the truth or falseness of the component statements.
- Tautology: This occurs when all the values of the last column, which expresses the truth values of the formula, are T. Therefore, whatever the truth values of the atomic statements were, they are combined together so that the resulting formula is always true. Only tautologies are formally valid inferences.