In logic, an axiom is a premise that is used in order to achieve the demonstration of other propositions.
Logic is the discipline that is based on the laws, modalities and forms of scientific knowledge . It is a formal science that lacks content since it focuses on the study of valid inference alternatives . That is, it proposes studying the appropriate methods and principles to identify correct reasoning versus incorrect reasoning.
Etymology allows us to know that the term logic has its origin in the Latin word logĭca , which in turn derives from the Greek logikós (from logos , "reason" or "study" ). The Greek philosopher Aristotle , experts in historical issues indicate, was a pioneer in using the notion to name the testing of arguments as indicators of truth within science, and in presenting the syllogism as a valid argument.
Historical development of logic
We cannot ignore that throughout history there have been many other figures who have contributed with their ideas and approaches to developing this science. Thus, for example, during the Middle Ages we must highlight the role played by Averroes , the philosopher from Córdoba who, among other things, stated that it was essential to study the logic of the ancient masters in order, from there, to proceed to « “philosophize” in the right way.
Already in the 18th and 19th centuries, one of the figures who most addressed the topic of logic was Immanuel Kant . He is considered one of the most important and influential thinkers in history and stands out for the fact that in this matter at hand he established a new concept: transcendental logic .
A term with which this philosopher of Prussian origin tried to define the process by which the human being must carry out an investigation of the pure concepts of categories of a transcendental type or also of what exact understanding is.
Hegel, Augustus De Morgan,John Venn y Gottlob Frege son otros de los autores que han destacado en el campo de la lógica. Especialmente este último causó una auténtica revolución con sus teorías y es considerado, junto al mencionado Aristotle, como el lógico más importante de toda la historia. Y es que estableció los conceptos de prueba, lógica de predicados y formal language.
When the truth of the premises necessarily leads to the truth of the conclusion, it is a solid argument for logic.
Classification according to type
Aristotle is considered the father of formal logic . On the other hand, informal logic refers to the methodical examination of probable arguments based on oratory, rhetoric and philosophy , among other sciences. Its objective is the recognition of paradoxes and fallacies, as well as being an effective resource to construct discourses correctly.
Natural logic is the natural ability to reason without appealing to science. The so-called fuzzy logic or fuzzy logic , on the other hand, is that which contemplates a certain uncertainty when analyzing the true or false nature of propositions, similar to the reasoning typical of human beings.
On the other hand, mathematical logic or symbolic logic is characterized by using an artificial symbolic language and making an abstraction of the contents, generally aiming to prove theorems. When applied in computer science, we speak of computational logic .
In logic, principles are foundations that explain the functioning of a system, such as the correspondence principle, the consistency principle, and the coherence principle.
Other logic classes
There are other types or classes of logic, such as so-called binary logic , which works with variables that only take two discrete values.
Modal logic , meanwhile, is a logical or formal system that analyzes the structure of those reasoning formed by modal operators. These operators are terms that refer to the truth contained in the judgments. Epistemic logic , deontic logic , doxastic logic and temporal logic are part of modal logic.
The formal system that revolves around contradictions is called paraconsistent logic . Boolean logic or Boolean algebra , on the other hand, is an algebraic structure that makes possible the schematization of logical procedures.
Propositional logic , statement logic or propositional calculus ; intuitionist logic or constructivist logic ; probability logic or probabilistic logic ; and philosophical logic are other frequently used classifications.
Different reasonings
Different types of logic are associated with different reasoning . We can mention that inductive logic , for example, examines the probability that a certain conclusion is true. With inductive reasoning , the truth of the premises functions as a support for the conclusion although without ensuring it.
Deductive reasoning , on the other hand, presents a conclusion that is logically arrived at from each previous proposition . If all the premises are true, the conclusion will be valid according to deductive logic .
At this point we must refer to the rules of inference , which are logical forms based on a function that studies the formal syntax of the premises and generates a conclusion. Modus Ponens and Modus Tollens are rules of this type.