Logic (Meaning and Explanation)

We explain what logic is and what its different definitions are. Also, what is formal logic and logical-Aristotelian principles.

What is logic?

The logic is the theory of reasoning. Reasoning is used for many things, including argue. Logic studies the reasoning that is arguments either argument schemes, and your task is to discover if they are valid and why.

It is also a science and a philosophical discipline, which has many uses and is applied in most scientific disciplines. Logic studies reasoning, which in addition to being logical arguments, are the form that thoughts acquire.. Logic governs thoughts and, therefore, also governs the way in which the individual forms concepts, makes judgments and reasons.

Logic works with different tools. Each of these tools is used to determine the validity of arguments. The logical tools are:

Concepts
Definitions
Proposals
formal arguments

Logic is divided into formal, first-order logic and modal logic.

Formal logic. It operates on propositions and systems of propositional logic.
First order logic. Operates on predicates.
Modal logic. Operates on truth values.

Etymology of the word “logic”

The word “logic” comes from Greek logikewhich has its roots in logoswhich means “reason” and “word.” Logic is the study of reason, of the act of reasoning, since the human being can return to himself and reason about his reason itself.

Let the logic come from logos and? logos Be the “reason” implies at least two elements. The first is that logic can study and structure reason. The second is that once reason has been studied and structured, which is the faculty that allows knowledge, the acts of knowledge themselves can be instrumentalized, in order to expand it.

However, and as its name indicates, the second element is no longer a task of logic but one of its effects. As a study of logos, logic is limited to studying the structure of reason and, in any case, the results of the acts of reasoning, not their scope.

Names given to logic

Logic receives different qualifiers depending on the specificity to which it refers and the historical moment in which it was developed.

Some of the most used definitions are:

Eastern logic. It is the logic developed in the systems of Indian philosophy.
Western logic. It is the logic developed in the systems of Western philosophy, from the Greeks to the present.
Traditional logic. It is the logic produced from Aristotle to the time of Gottlob Frege (1848-1925).
ancient logic. It is the Greek and Hellenistic-Roman logic produced from the pre-Socratics to Boethius.
Greek logic. It is the logic produced from the pre-Socratics to Aristotle and the Stoics.
Aristotelian logic. It is the logic set forth in the Organon and some other works of the corpus Aristotelian.
Stoic logic. It is the logic developed by the Megarics and the Stoics.
medieval logic. It is the logic produced between Boethius and the 15th century.
Scholastic and neo-scholastic logic. It is the logic developed by scholastic authors from the 13th to 15th centuries and during the 19th century by the neo-Thomists.
modern logic. It is the logic produced by the authors of the modern era, including the Renaissance. This especially includes Frege.
Contemporary logic. It is the logic produced from the mid-19th century until today.

Reasoning and validity

A reasoning is made by an argumentwhich is a sequence of sentences composed of premises and conclusion. This sequence is arranged so that the premises are at the beginning and the conclusion at the end.

For an argument to be valid, the truth of the premises must imply the truth of the conclusion. This means that as long as the premises are true, the conclusion will also be true.

For example:

Pedro will play soccer or Nicolás will play soccer. (premise)
Pedro will not play soccer. (premise)
Nicolás will play soccer. (conclusion)

What matters about the argument is its form. This can be verified if each of the sentences is replaced with signs. For example: “A or B (p1), A (p2) is not given, B (conclusion) is given.”

In this case, it does not matter whether the premises are true. The important thing is that when accepting the truth of the premises, one must accept, necessarilythe truth of the conclusion. This form is called an “argument outline.”

The formal logic

Formal logic or mathematical logic is the logic that applies to mathematics and science. In order to be applied to these disciplines, logic has to be able to “translate” natural language into logical language. With that in mind, use formal representation systems such as the propositional logic system, the modal logic system or the first order logic system.

Each of these formal presentation systems operates on different elements and uses different variables:

propositional logic operates on propositions. Use propositional variables.
Modal logic It operates on the truth value of the different propositions and predicates.
First-order logic or predicative logic operates on predicates. Use quantifiers and individual variables.

Furthermore, formal logic covers four large areas:

Model theory. This area focuses on the study of axiomatic theories and mathematical logic using mathematical structures such as groups, fields or graphs. Its objective is to attribute semantic meaning to the purely formal constructions of logic.
Demonstration theory. In this area, proofs are proposed using mathematical objects and mathematical techniques as a method to verify logical problems. Proof theory focuses on the syntax and ordering of the formal structures of logic.
Set theory. This area deals with abstract collections of objects, as well as their basic operations and interrelationships. It is a fundamental tool in any mathematical theory.
Computability theory. This area uses set theory to consider computable or non-computable sets. It establishes a connection between mathematics and computer science, and studies the decision problems that can be addressed by an algorithm (equivalent to a Turing machine).

The proper object of logic

The material object of logic is the result of acts of reason. These kinds of objects are “beings of reason” since they only exist in the mind.

There are two types of beings of reason: denial and ratio ratio. Denial is the product of a mental act in which an absence is signaled. The relationship of reason is the product of a mental act that indicates the link between things thought.

The logical-Aristotelian principles

Aristotelian-logical principles were developed by Aristotle (384-322 BC), who is considered the founder of Western logic.

The three most important principles, today considered logical axioms, are:

The principle of non-contradiction. It establishes the impossibility of something being and not being at the same time (A and ¬A cannot be true at the same time).
The identity principle. Establishes the identical identity of something with itself (A is always equal to A).
The principle of the excluded middle. Establish a logical disjunction. Things cannot be true and false at the same time, and there are no possible gradations (A or then ¬A).

A logical-philosophical problem: Logic and reality

One of the most frequent problems faced by those who study logic is the problem of the way in which logical propositions and reality are related. Can logic be applied to reality? Does logic involve different entities?

Many philosophers have wanted to answer these concerns. In general, The answers vary depending on what you think about the nature of logical propositions and language.. These are some solutions:

The Aristotelian conception. Logical principles express necessary connections that respond to real relationships of things.
The empiricist conception. Logical principles are generalizations of empirical relationships that are obtained through a process of total abstraction.
The essentialist conception. Logical principles designate the ideal norms by which ideal objects are governed. Some, like Plato, consider these objects to (metaphysically) exist. Others, like Edmund Husserl, consider them to be subsistent (depending on something else).
The linguistic conception. Logical principles are conventional language rules that may or may not coincide with reality.
The Kantian conception. Logical norms are impositions of the transcendental subject.
The Wittgensteinian conception. Logical formulas are empty tautologies.

References

Gamut, LTF, & Durán, C. (2002). Introduction to logic. Buenos Aires, Argentina: Eudeba.
Deaño, A. (1975). Introduction to formal logic. Madrid: Alliance.
Álvarez, FE (2007). Logic manual. Rosario University.