The 4 most important types of logic (and features)

March 24, 2024

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

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

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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.

This study has the purpose of understanding different criteria of inferences and how we arrive at valid demonstrations, in contrast to the invalid demonstrations. So, the basic question of logic is what is the 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 a formal system or in natural language. Specifically, it analyzes propositions (declarative sentences) that can be true or false, as well as fallacies, paradoxes, arguments that involve causality and, in general, the theory of argumentation.

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

Consistency (there is no contradiction between the theorems that make up the system)
Solidity (the test systems do not include false inferences)
Completud (all true sentences must be able to be proved)

The 4 types of logic

As we have seen, logic uses different tools to understand the reasoning we use to justify something. Traditionally, four major 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 is about the study of inferences with purely formal and explicit content . It is about analyzing the formal statements (logical or mathematical), whose meaning is not intrinsic but its symbols have meaning because of the useful application they are given. The philosophical tradition from which the latter derives is called precisely "formalism".

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

2. Informal logic

For its part, informal logic is a more recent discipline, which study, evaluate and analyze the arguments displayed in the natural or everyday language . Hence, it receives the category of "informal". It can be either spoken or 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 premises disseminated by the media, such as newspapers, television, the Internet, and so on.

3. Symbolic logic

As the name implies, symbolic logic analyzes the relationships between symbols. Sometimes it uses complex mathematical language, since it is responsible for studying problems that traditional formal logic finds complicated or difficult to address. It is usually divided into two subtypes:

Predicative logic or first order : it is a formal system composed of formulas and quantifiable variables
Propositional : it is a formal system composed of propositions, which are able to create other propositions through connectors called "logical connective". In this 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 that mathematical logic includes both the application of formal logic to mathematics, and the application of mathematical reasoning to formal logic.

Broadly speaking, the application of mathematical language in the construction of logical systems 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:

Logicism : it is about the application of logic in mathematics. Examples of this type are the theory of proof, model theory, set theory and the theory of recursion.
Intuition : argues that both logic and mathematics are methods whose application is consistent to perform complex mental constructions. But, he says that in themselves, logic and mathematics can not explain deep properties of the elements they analyze.

Inductive, deductive and modal reasoning

On the other hand, There are three types of reasoning that 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 that proposed by Aristotle: All humans are mortal (this is the general premise); Socrates is a human (it is the major premise), and finally, Socrates is mortal (this is the conclusion).

For its part, an inductive reasoning 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 the crows are black (conclusion).

Finally, reasoning or modal logic is based on probabilistic arguments, that is, they express a possibility (a modality). It is a formal logic system that includes terms such as "could", "can", "should", "eventually".

Bibliographic references:

Groarke, L. (2017). Informal Logic. Stanford Encyclopedia of Philosophy. Retrieved October 2, 2018. Available at //plato.stanford.edu/entries/logic-informal/
Logic (2018). The basics of philosophy. Retrieved October 2, 2018. Available at //www.philosophybasics.com/branch_logic.html
Shapiro, S. and Kouri, S. (2018). Classical Logic. Retrieved October 2, 2018. Available in Logic (2018). The basics of philosophy. Retrieved October 2, 2018. Available at //www.philosophybasics.com/branch_logic.html
Garson, J. (2018). Modal Logic. Stanford Encyclopedia of Philosophy. Retrieved October 2, 2018. Available at //plato.stanford.edu/entries/logic-modal/