The 4 most important types of logic (and characteristics)

These are the forms of logic that exist and several examples to understand them.

Logic is the study of reasoning and inferences.. It is a set of questions and analyses that have allowed us to understand how to differentiate valid arguments from fallacies and how we arrive at these.

For this, it has been indispensable to develop different systems and forms of study, which have resulted in four major types of logic. We will see below what each of them is about.

• Recommended article: "The 10 types of logical and argumentative fallacies".

What is logic?

The word "logic" comes from the Greek "logos" which can be translated in different ways: word, thought, argument, principle or reason are some of the main ones. In this sense, logic is the study of principles and reasoning.

The purpose of this study is to understand different criteria of inferences and how we arrive at valid demonstrations, in contrast to invalid demonstrations. Thus, the basic question of logic is what is correct thinking and how can we differentiate between a valid argument and a fallacy?

To answer this question, logic proposes different ways of classifying statements and arguments, whether they occur in formal systems or in natural language. Specifically, it analyzes propositions (declarative sentences) that can be true or false, as well as fallacies, paradoxes, arguments involving causality and, in general, the theory of argumentation.

In general terms, to consider a system as logical, it must meet three criteria:

• Consistency (there is no contradiction between the theorems that compose the system).
• Soundness (test systems do not include false inferences)
• Completeness (all true sentences must be testable)

The 4 types of logic

As we have seen, logic uses different tools to understand the reasoning we use to justify something. Traditionally, four main types of logic are recognized, each with some subtypes and specificities. We will see below what each one is about.

1. Formal logic

Also known as traditional logic or philosophical logic, it deals with the study of inferences with purely formal and explicit content.. It deals with the analysis of formal statements (logical or mathematical), whose meaning is not intrinsic but whose symbols have meaning because of the useful application given to them. The philosophical tradition from which the latter derives is precisely called "formalism".

In turn, a formal system is one that is used to draw a conclusion from one or more premises. The latter can be axioms (self-evident propositions) or theorems (conclusions from a fixed set of rules of inference and axioms).

The conclusions we reach through formal logic, if they are based on valid premises and there are no flaws in the logical operations, are truths in themselves.. In fact, this leads to an open debate about whether formal logic belongs to the world of science or to another field of knowledge, since it does not describe reality but its own rules of operation.

2. Informal logic

Informal logic, on the other hand, is a more recent discipline, which studies, evaluates and analyzes studies, evaluates and analyzes the arguments deployed in natural or everyday language.. This is why it is called "informal". It can be both spoken and written language, or any type of mechanism and interaction used to communicate something. Unlike formal logic, which for example would apply to the study and development of computer languages, formal language refers to languages and languages.

Thus, informal logic can analyze from personal reasoning and arguments to political debates, legal arguments or the premises disseminated by the media such as newspapers, television, the Internet, etcetera.

3. Symbolic logic

As its name indicates, symbolic logic analyzes the relationships between symbols. Sometimes it makes use of complex mathematical language, since it is in charge of studying problems that traditional formal logic finds complicated or difficult to tackle. It is usually divided into two subtypes:

• Predicative or first-order logic.Formal system: a formal system composed of formulas and quantifiable variables.
• PropositionalPropositional: this is a formal system composed of propositions, which are capable of creating other propositions through connectors called "logical connectives". In this system there are almost no quantifiable variables.

4. Mathematical logic

Depending on the author who describes it, mathematical logic can be considered a type of formal logic. Others consider mathematical logic to include both the application of formal logic to mathematics and the application of mathematical reasoning to formal logic.

Broadly speaking, it is the application of mathematical language in the construction of logical systems that makes it possible to reproduce the human mind. For example, this has been very present in the development of artificial intelligence and in the computational paradigms of the study of cognition.

It is usually divided into two subtypes:

• LogicismLogicism: the application of logic in mathematics. Examples of this type are proof theory, model theory, set theory and recursion theory.
• IntuitionismIntuitionism: holds that both logic and mathematics are methods whose application is consistent in order to realize complex mental constructions. But, it says that in themselves, logic and mathematics cannot explain deep properties of the elements they analyze.

Inductive, deductive and modal reasoning

On the other hand, there are three types of reasoning which can also be considered logical systems. These are mechanisms that allow us to draw conclusions from premises. Deductive reasoning makes such extraction from a general premise to a particular premise. A classic example is the one proposed by Aristotle: All humans are mortal (this is the general premise); Socrates is a human (this is the major premise), and finally, Socrates is mortal (this is the conclusion).

Inductive reasoning, on the other hand, is the process by which a conclusion is drawn in the opposite direction: from the particular to the general. An example of this would be "All the crows I can see are black" (particular premise); then, all crows are black (conclusion).

Finally, modal reasoning or logic is based on probabilistic arguments, i.e., expressing a possibility (a modality). It is a system of formal logic that includes terms such as "could", "may", "must", "eventually".

Bibliographical references:

• Groarke, L. (2017). Informal Logic. Stanford Encyclopedia of Philosophy. Retrieved October 02, 2018. Disponible en https://plato.stanford.edu/entries/logic-informal/
• Logic (2018). The basics of philosophy. Recuperado 02 de octubre de 2018. Disponible en https://www.philosophybasics.com/branch_logic.html
• Magnani, L. (2001). Abduction, Reason, and Science: Processes of Discovery and Explanation. Nueva York: Kluwer Academic Plenum Publishers.
• McGinn, C. (2000). Logical Properties: Identity, Existence, Predication, Necessity, Truth. Oxford: Clarendon Press.
• Quine, W.V.O. (1986) (1970). Philosophy of Logic. Cambridge, MA.: Harvard University Press.
• Shapiro, S. y Kouri, S. (2018). Classical Logic. Recuperado 02 de octubre de 2018. Disponible en Logic (2018). The basics of philosophy. Recuperado 02 de octubre de 2018. Disponible en https://www.philosophybasics.com/branch_logic.html
• Garson, J. (2018). Modal Logic. Stanford Encyclopedia of Philosophy. Recuperado 02 de octubre de 2018. Available at https: