Logic is an area of philosophy that aims to study the formal structure of statements (propositions) and their rules. In short, logic serves to think correctly, thus being a tool for correct thinking.
Logic comes from the Greek word logos, which means reason, argument or speech. The idea of talking and arguing presupposes that what is being said has a meaning for the listener.
This sense is based on the logical structure, when something "has logic" means that it makes sense, it is a rational argument.
Logic in Philosophy
It was the Greek philosopher Aristotle (384 a. C.-322 a. C.) who created the study of logic, he called it analytic.
For him, any knowledge that pretends to be true and universal knowledge should respect some principles, logical principles.
Logic (or analytics) came to be understood as an instrument of correct thinking and the definition of logical elements that underlie true knowledge.
The Logical Principles
Aristotle developed three basic principles that guide classical logic.
1. identity principle
A being is always identical to itself: THE é THE. If we replace THE for Maria, for example, it is: Maria is Maria.
2. Principle of non-contradiction
It is impossible to be and not to be at the same time, or for a single entity to be also its opposite. it is impossible that THE be THE and not-A, at the same time. Or, following the previous example: it is impossible for Mary to be Mary and not to be Mary.
3. Principle of excluded third party, or excluded third party
In propositions (subject and predicate), there are only two options, either affirmative or negative: THE é x or THE é no-x. Maria is a teacher or Maria is not a teacher. There is no third possibility.
See too:Aristotelian Logic.
The Proposition
In an argument, what is said and has the form of subject, verb and predicate is called a proposition. Propositions are statements, affirmations or denials, and their validity, or falsity, is logically analyzed.
From the analysis of propositions, the study of logic becomes a tool for correct thinking. To think correctly needs (logical) principles that guarantee its validity and truth.
Everything that is said in an argument is the conclusion of a mental process (thought) that evaluates and judges some possible existing relationships.
The Syllogism
From these principles we have a deductive logical reasoning, that is, from two previous certainties (assumptions) a new conclusion is reached, which is not directly referred to in the premises. This is called a syllogism.
Example:
Every man is mortal. (premise 1)
Socrates is a man. (premise 2)
Therefore, Socrates is mortal. (conclusion)
This is the basic structure of the syllogism and the foundation of logic.
The three terms of the syllogism can be classified according to their quantity (universal, particular or singular) and their quality (affirmative or negative)
Propositions may vary as to their quality in:
- Affirmations: S is P. Every human being is mortal, Mary is a worker.
- Negatives: S is not P.Socrates is not an Egyptian.
They can also vary in their quantity in:
- Universals: Every S is P.all men are mortal.
- Private: Some S is P. Some men are Greek.
- Singles: This S is P.Socrates is Greek.
This is the basis of Aristotelian logic and its derivations.
See too: What is syllogism?
Formal Logic
In formal logic, also called symbolic logic, propositions are reduced to well-defined concepts. In this way, what is said is not the most important thing, but its form.
The logical form of the statements is worked through the (symbolic) representation of propositions by letters: P, whatand r. It will also investigate the relationships between propositions through their logical operators: conjunctions, disjunctions and conditioning.
propositional logic
In this way, propositions can be worked on in different ways and serve as a basis for the formal validation of a statement.
Logical operators establish the relationships between propositions and make the logical chaining of their structures possible. Some examples:
Denial
It is the opposite of a term or proposition, represented by the symbol ~ or ¬ (negation of P is ~p or ¬ P). In the table, for p true, we have ~p false. (it's sunny = P, it's not sunny = ~ P or ¬ P).
Conjunction
It is the union between propositions, the symbol ∧ represents the word "and" (today, it's sunny and I go to the beach, P ∧ what). For the conjunction to be true, both must be true.
Disjunction
It is the separation between propositions, the symbol v represents "or" (I'm going to the beach or Stay at home, P v what). For validity, at least one (or another) must be true.
Conditional
It is the establishment of a causal relationship or conditionality, the symbol ⇒ represents "if... then..." (if to rain, then I'll stay at home, P ⇒ what).
bi-conditional
It is the establishment of a two-way conditionality relationship, there is a double implication, the symbol ⇔ represents "if, and only if,". (I go to class if and only if I'm not on vacation, P ⇔ what).
Applying to the truth table, we have:
| P | what | ~p | ~ what | P ∧ what | P v what | P ⇒ what | P ⇔ what |
|---|---|---|---|---|---|---|---|
| V | V | F | F | V | V | V | V |
| V | F | F | V | F | V | F | F |
| F | V | V | F | F | V | V | F |
| F | F | V | V | F | F | V | V |
The letters F and V can be replaced by zero and one. This format is widely used in computational logic (F = 0 and V = 1).
See too: Truth table.
Other types of logic
There are several other types of logic. These types, in general, are derivations of classical formal logic, present a critique of the traditional model or a new approach to problem solving. Some examples are:
1. Mathematical logic
Mathematical logic is derived from Aristotelian formal logic and develops from its value relations of propositions.
In the 19th century, mathematicians George Boole (1825-1864) and Augustus De Morgan (1806-1871) were the responsible for adapting Aristotelian principles to mathematics, giving rise to a new science.
In it, the possibilities of truth and falsehood are evaluated through their logical form. Sentences are transformed into mathematical elements and analyzed based on their relationships between logical values.
See too: Mathematical logic.
2. Computational Logic
Computational logic is derived from mathematical logic, but goes beyond that and is applied to computer programming. Without it, several technological advances, such as artificial intelligence, would be impossible.
This type of logic analyzes the relationships between values and transforms them into algorithms. For this, it also resorts to logical models that break with the model initially proposed by Aristotle.
These algorithms are responsible for a number of possibilities, from encoding and decoding messages to tasks such as facial recognition or the possibility of autonomous cars.
Anyway, the whole relationship that one has with computers, nowadays, goes through this kind of logic. It merges the foundations of traditional Aristotelian logic with elements of the so-called non-classical logics.
3. Non-classical logics
By non-classical, or anti-classical, logic is recognized a series of logical procedures that abandon one or more principles developed by traditional (classical) logic.
For example, fuzzy logic (fuzzy), widely used for the development of artificial intelligence, does not use the exclusion third principle. It assumes any real value between 0 (false) and 1 (true).
Examples of non-classical logics are:
- Logic fuzzy;
- Intuitionist logic;
- Paraconsistent logic;
- Modal logic.
Curiosities
Long before any kind of computational logic, logic served as the foundation of all existing sciences. Some bring this reasoning expressed in their own name by using the suffix "logy", of Greek origin.
Biology, sociology and psychology are some examples that make their relationship with the logos Greek, understood from the idea of a logical and systematic study.
Taxonomy, classification of living beings (kingdom, phylum, class, order, family, genus and species), even today, follows a logical model of classification into categories proposed by Aristotle.
See too:
- Logical Reasoning - Exercises
- Philosophy Exercises