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 essential, which have resulted in four major types of logic. We will see below what each of them is about.
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 inference criteria and how we arrive at valid demonstrations, in contrast to invalid demonstrations. So, the basic question of logic is what is the correct thought 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:
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 the study of inferences with purely formal and explicit content It involves analyzing formal statements (logical or mathematical), whose meaning is not intrinsic but rather their symbols make sense due to 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 extract a conclusion from one or more premises. The latter can be axioms (self-evident propositions) or theorems (conclusions from a fixed set of inference rules 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, they are truths in themselves In fact, this leads to an open debate about whether formal logic belongs to the world of science or belongs to another area of knowledge, as it does not describe reality but rather its own rules of operation.
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 newspapers, television, the Internet, etc.
3. Symbolic logic
As its name indicates, 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:
4. Mathematical logic
Depending on the author describing 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:
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 a human (this is the major premise), and finally, Socrates is mortal (this is the conclusion).
For its part, inductive reasoning is the process through 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 system of formal logic that includes terms such as “could”, “may”, “should”, “eventually”.
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