The 4 most important types of logic (and features)
Logic is the study of reasoning and inference . It is a set of questions and analyses that have allowed us to understand how valid arguments are differentiated from fallacies and how we arrive at them.
To this end, it has been essential to develop different systems and forms of study, which have led to four major types of logic. We will now see what each of them is about.
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 aims to understand different criteria for inferences and how we arrive at valid demonstrations, as opposed to invalid ones. 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 a formal system or in natural language. Specifically, it analyzes propositions (declarative sentences) that may be true or false, as well as fallacies, paradoxes, arguments involving causality and, in general, the theory of argumentation.
Generally speaking, to be considered logical, a system 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)
- Completeness (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 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, is the study of inferences with a purely formal and explicit content . It is a matter of analysing 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 may be axioms (self-evident propositions) or theorems (conclusions from a fixed set of rules of inferences and axioms).
2. Informal logic
For its part, informal logic is a more recent discipline, which studies, evaluates and analyzes the arguments displayed in natural or everyday language . This is why it receives the category of “informal”. It can be both spoken and written language or any kind of mechanism and interaction used to communicate something. Unlike formal logic, which would apply, for example, to the study and development of computer languages, formal language refers to languages and idioms.
Thus, informal logic can analyse everything from personal reasoning and arguments to political debates, legal arguments or the premises spread by the media such as the newspaper, television, internet, etc.
3. Symbolic logic
As its name suggests, symbolic logic analyzes the relationships between symbols. Sometimes it uses complex mathematical language, as it studies problems that traditional formal logic finds complicated or difficult to address. It is usually divided into two subtypes:
- Predictive 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 able to create other propositions through connectors called “logical connectives”. There are almost no quantifiable variables in this one.
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 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 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 perform complex mental constructions. But, he 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 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 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 the crows are black (conclusion).
Finally, the reasoning or modal logic is based on probabilistic arguments, that is, they express a possibility (a modality). It is a system of formal logic 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 at https://plato.stanford.edu/entries/logic-informal/
- Logic (2018). The basics of philosophy. Retrieved October 2, 2018. Available at https://www.philosophybasics.com/branch_logic.html
- Shapiro, S. and Kouri, S. (2018). Classical Logic. Recovered October 2, 2018. Available in Logic (2018). The basics of philosophy. Retrieved October 2, 2018. Available at https://www.philosophybasics.com/branch_logic.html
- Garson, J. (2018). Modal Logic. Stanford Encyclopedia of Philosophy. Retrieved October 2, 2018. Available at https://plato.stanford.edu/entries/logic-modal/