Logic as a Branch of Philosophy

Logic comes from the Greek “logos”, which has a variety of meanings including word, thought, idea, argument, account, reason or principle. It is the study of reasoning, or the study of the principles and criteria of valid inference and demonstration. It attempts to distinguish good reasoning from bad reasoning.

‘NEW AND NECESSARY REASONING’
Aristotle

Aristotle had said logic as new and necessary because it allows us to learn things we do not know and the conclusions cannot be escaped. It asks questions like:
“What is correct reasoning?”
“What distinguishes a good argument from a bad one?”
“How can we detect a fallacy in reasoning?”

Logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of inference and through the study of arguments in natural language.

There are three necessary things that must be there in logic:

  1. Consistency : the theorems do not contradicts one another
  2. Soundness: system’s rule of proof will never allow false inferences from a true premise
  3. Completeness: there are no true sentences in the system that cannot, at least in principle, be proved in the system

Back in time: History of Logic

There are various mentions of logic from various parts of the world like in Hindu philosophy, Islamic philosophy, and Greek Philosophy. In Hindu Philosophy, we can see mentions of logic. “Nasadiya Sukta” of the Rig Veda contains various logical divisions that were later recast formally as the four circles of “catuskoti”. The Nyaya school of Indian philosophical speculation is based on texts known as the “Nyaya Sutras” of Aksapada Gautama from around the 2nd Century B.C., and its methodology of inference is based on a system of logic (involving a combination of induction and deduction by moving from particular to particular via generality) that subsequently has been adopted by the majority of the other Indian schools.

In the Ancient Greek tradition, both Plato and Aristotle conceived of logic as the study of argument and from a concern with correctness of argumentation. This is also the root of modern logic. Aristotle produced six works on logic, known collectively as the “Organon”, the first of these, the “Prior Analytics”, being the first explicit work in formal logic. He is perhaps most famous for introducing the syllogism (or term logic).

In medieval times, Aristotelian logic /dialectics was studied, along with grammar and rhetoric, as one of the three main strands of the trivium, the foundation of a medieval liberal arts education

Logic in Islamic philosophy also contributed to the development of modern logic, especially the development of Avicennian logic (which was responsible for the introduction of the hypothetical syllogism, temporal logic, modal logic and inductive logic) as an alternative to Aristotelian logic.

In the 18th Century, Immanuel Kant argued that logic should be conceived as the science of judgment, so that the valid inferences of logic follow from the structural features of judgments, although he still maintained that Aristotle had essentially said everything there was to say about logic as a discipline.

The different types of Logic are listed below.

  1. Formal logic
  2. Informal logic
  3. Symbolic Logic
  4. Mathematical logic

    1. Formal Logic: This is traditional logic or philosophical logic that studies formal rules passed down from Aristotle. It is the study of inference with purely formal and explicit content i.e. it can be expressed as a particular application of a wholly abstract rule.
    2. Informal Logic: It studies natural language or ordinary language and is a discipline that developed recently. Natural language here means a language that is spoken, written or signed by humans for general-purpose communication, as distinguished from formal languages (such as computer-programming languages) or constructed languages (such as Esperanto). It focuses on the reasoning and argument one finds in personal exchange, advertising, political debate, legal argument, and the social commentary that characterizes newspapers, television, the Internet and other forms of mass media.
    3. Symbolic Logic: Symbolic Logic is the study of symbolic abstractions that capture the formal features of logical inference. It deals with the relations of symbols to each other, often using complex mathematical calculus.
    4. Mathematical Logic: Both the application of the techniques of formal logic to mathematics and mathematical reasoning, and, conversely, the application of mathematical techniques to the representation and analysis of formal logic.

 

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