Logic (from the Ancient Greek: λογική, logike)chas two meanings: 

  • first, it describes the use of valid reasoning in some activity; 
  • second, it names the normative study of reasoning or a branch thereof.

In the latter sense, it features most prominently in the subjects of philosophy, mathematics, and computer science.

Logic was studied in several ancient civilizations, including India,  China, Persia and Greece. 


Aristotle one of the founders of western logic. image: Jastrow/ wikipedia

In the West, logic was established as a formal discipline by Aristotle, who gave it a fundamental place in philosophy. The study of logic was part of the classical trivium, which also included grammar and rhetoric. 

Logic was further extended by Al-Farabi who categorized it into two separate groups (idea and proof). 

Later, Avicenna revived the study of logic and developed relationship between temporalis and the implication. In the East, logic was developed by Buddhists and Jains.

Logic is often divided into three parts: 

  • inductive reasoning, 
  • abductive reasoning, and 
  • deductive reasoning.

How logic is studied

The concept of logical form is central to logic, it being held that the validity of an argument is determined by its logical form, not by its content. Traditional Aristotelian syllogistic logic and modern symbolic logic are examples of formal logics.

Informal logic 

is the study of natural language arguments. The study of fallacies is an especially important branch of informal logic. The dialogues of Plato  are good examples of informal logic.

Formal logic is the study of inference with purely formal content. An inference possesses a purely formal content if it can be expressed as a particular application of a wholly abstract rule, that is, a rule that is not about any particular thing or property. The works of Aristotle contain the earliest known formal study of logic. Modern formal logic follows and expands on Aristotle. 

 In many definitions of logic, logical inference and inference with purely formal content are the same. This does not render the notion of informal logic vacuous, because no formal logic captures all of the nuance of natural language.

Symbolic logic 

is the study of symbolic abstractions that capture the formal features of logical inference.  Symbolic logic is often divided into two branches: propositional logic and predicate logic.

Mathematical logic

 is an extension of symbolic logic into other areas, in particular to the study of model theory, proof theory, set theory, and recursion theory.