The 4 most important types of logic (and characteristics)

Logic is the study of reasoning and inferences. It is a set of questions and analyzes that have made it possible 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 essential, which have resulted in four main 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.

This study has the purpose of understanding different criteria of inferences and how it is that we arrive at valid proofs, in contrast to the invalid proofs. So 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, they must meet three criteria:

• Consistency (there is no contradiction between the theorems that make up the system)
• Solidity (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. Four major types of logic are traditionally 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 the study of inferences with purely formal and explicit content. It is about analyzing formal statements (logical or mathematical), whose meaning is not intrinsic but rather its symbols make sense due to the useful application that they are given. 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 inferences and axioms).

The conclusions we reached through formal logic, if they are based on valid premises and there are no failures in the logical operations, they are true in themselves. In fact, this leads to an open debate about whether formal logic belongs to the world of science. or they belong to another field of knowledge, as they do not describe reality but rather their own rules of functioning.

2. Informal logic

For its part, informal logic is a more recent discipline, which studies, evaluates and analyzes the arguments deployed in natural or everyday language. Hence, it receives the category of "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 everything from personal reasoning and arguments to political debates, legal arguments or premises disseminated by the media such as the newspaper, television, the internet, etc.

3. Symbolic logic

As the name implies, symbolic logic analyzes the relationships between symbols. Sometimes it uses 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: it is a formal system composed of formulas and quantifiable variables
• Propositional: it is a formal system composed of propositions, which are capable of creating other propositions through connectors called "logical connectives". 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, it is about 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:

• Logicism: it is about the application of logic in mathematics. Examples of this type are proof theory, model theory, set theory, and recursion theory.
• Intuitionism: maintains that both logic and mathematics are methods whose application is consistent to carry out complex mental constructions. But, he says that by 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 that can also be considered logical systems. These are mechanisms that allow us to draw conclusions from premises. Deductive reasoning makes this 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 human (it is the major premise), and finally, Socrates is mortal (this is the conclusion).

For its part, 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); so all 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", "may", "must", "eventually".

Bibliographic references:

• Groarke, L. (2017). Informal Logic. Stanford Encyclopedia of Philosophy. Retrieved October 2, 2018. Available in https://plato.stanford.edu/entries/logic-informal/
• Logic (2018). The basics of philosophy. Retrieved October 2, 2018. Available in https://www.philosophybasics.com/branch_logic.html
• Magnani, L. (2001). Abduction, Reason, and Science: Processes of Discovery and Explanation. New 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. and Kouri, S. (2018). Classical Logic. Retrieved October 2, 2018. Available in Logic (2018). The basics of philosophy. Retrieved October 2, 2018. Available in https://www.philosophybasics.com/branch_logic.html
• Garson, J. (2018). Modal Logic. Stanford Encyclopedia of Philosophy. Retrieved October 2, 2018. Available in https://plato.stanford.edu/entries/logic-modal/