• What is logic?
• Philosophical logic
• Aristotelian logic
• Mathematical logic
• Computational logic
• Formal and informal logic

We explain what logic is and the characteristics of philosophical, Aristotelian, mathematical, computational, formal and informal logic.

Logic is used in various processes such as proof, inference, or deduction.

What is logic?

Logic is a formal science, which is part of the philosophy and of the math. It focuses on the study of valid and invalid procedures of thought, that is, in processes such as demonstration, inference or deduction, as well as in concepts such as fallacies, paradoxes and the truth.

Logic is a discipline extremely ancient, independently born among the thinkers of the great classical and ancient civilizations, like the Chinese, the Greek or the Indian. From its beginnings, it was understood as a way of judging thought to check its formal validity, that is, to recognize what is the ideal procedure of reasoning, the one that really leads to the truth.

However, from the 20th century on, it has been considered as a field more akin to mathematics, as the applications of the latter gained great industrial, social and technological importance.

The word "logic" has its origin in the Greek voice logiké ("Endowed with reason"), from the term logos, equivalent to "word" or "thought" alike.

However, in everyday language we use this word as a synonym for "common sense", that is, in a valuable or valued way of thinking, in their respective contexts possible. It is also used as a synonymous of "way of thinking", as when referring to "sports logic", "military logic", and so on.

Philosophical logic

With this term we call the areas of philosophy in which the methods of logic to resolve or advance certain philosophical dilemmas, being able to be handled within the considered traditional logic or, on the contrary, non-classical logic. In other words, logic within the framework of philosophy.

It is a discipline very close to the philosophy of language, and is essentially a continuation of the logic of antiquity, centered on thought and natural language. We commonly use this name to distinguish it from the latest mathematical logic.

Aristotelian logic

Within philosophical logic, the tradition of thought that begins with the works of the Greek philosopher Aristotle de Estagira (384-322 BC), considered the western founder of logic and one of the most important authors, is known as Aristotelian logic. important parts of the world's philosophical tradition.

Aristotle's main works on logic are gathered in his Organ (from the Greek "instrument"), compiled by Andronicus of Rhodes several centuries after writing. In them a whole logical system unfolds that was extremely influential in Europe and the Middle East until after Middle Ages.

In this work, moreover, Aristotle postulated the fundamental axioms of logic:

• The principle of non-contradiction. According to which something cannot be and not be at the same time (A and ¬A cannot be true at the same time).
• The principle of identity. According to which something is always identical to itself (A is always equal to A).
• The principle of the excluded third. According to which something is or is not true, without any possible gradations (A or then ¬A).

Mathematical logic

It is known as mathematical logic, also called symbolic logic, formal logic, theoretical or logistical logic, to the application of the logical thinking to certain areas of mathematics and science.

This implies the study of the process of inference, through formal systems of representation, such as propositional logic, modal logic or first-order logic, which allow "translating" natural language into mathematical language in order to develop rigorous demonstrations.

Mathematical logic encompasses four major areas, which are:

• Model theory. Which proposes the study of axiomatic theories and mathematical logic through mathematical structures known as groups, bodies or graphs, thus attributing a semantic content to the purely formal constructions of logic.
• Demonstration theory. Also called proof theory, it proposes proofs by means of mathematical objects and techniques mathematics as the way to check logic problems. Thus, where model theory deals with giving a semantics (a meaning) to the formal structures of logic, the Theory of Proof deals rather with their syntax (its ordering).
• Theory of sets. Focused on the study of abstract collections of objects, understood in themselves as objects, as well as their basic operations and interrelations. This branch of mathematical logic is one of the most fundamental that exists, so much so that it constitutes a basic tool of any mathematical theory.
• Computability theory. Shared area between mathematics and computing or computing, studies the decision problems to which a algorithm (equivalent to a Turing machine) can cope. To do this, he uses set theory, understanding them as computable or non-computable sets.

Computational logic

Computational logic creates intelligent computing systems.

Computational logic is the same mathematical logic but applied to the field of computing, that is, at various fundamental levels of computing: computational circuits, programming logic, and management algorithms. Artificial intelligence, a relatively recent field in the area, is also part of it.

It could be said that, broadly speaking, computational logic aspires to feed a computer system through logical structures that express, in a mathematical language, the different possibilities of human thought, thus creating intelligent computer systems.

Formal and informal logic

A distinction is also often made between two separate fields of logic: formal and informal, based on their approach to the language in which statements are expressed.

• Formal logic. It is the one that attends to the formal language, that is, to the way of expressing its contents, using them strictly, without ambiguities, in such a way that the deductive path can be analyzed from the validity of its contents. shapes (hence its name).
• Informal logic. Instead, study their arguments a posteriori, distinguishing valid and invalid forms from the information given, regardless of its logical form or its formal language. This variant emerged in the mid-20th century as a discipline within philosophy.