# Outline of logic

Logic is the formal science of using reason and is considered a branch of both philosophy and mathematics and to a lesser extent computer science. Logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of inference and the study of arguments in natural language. The scope of logic can therefore be very large, ranging from core topics such as the study of fallacies and paradoxes, to specialized analyses of reasoning such as probability, correct reasoning, and arguments involving causality. One of the aims of logic is to identify the correct (or valid) and incorrect (or fallacious) inferences. Logicians study the criteria for the evaluation of arguments.

## Foundations of logic

Philosophy of logic

## Philosophical logic

#### Fallacies

• Fallacy  (list) incorrect argumentation in reasoning resulting in a misconception or presumption. By accident or design, fallacies may exploit emotional triggers in the listener or interlocutor (appeal to emotion), or take advantage of social relationships between people (e.g. argument from authority). Fallacious arguments are often structured using rhetorical patterns that obscure any logical argument. Fallacies can be used to win arguments regardless of the merits. There are dozens of types of fallacies.

## Formal logic

#### Symbols and strings of symbols

##### Logical symbols
###### Logical connectives

Logical connective

Proposition

Object language

Metalanguage

#### Propositional and boolean logic

##### Propositional logic

Propositional logic

#### Predicate logic and relations

Predicate logic

##### Relations

Mathematical relation

## Mathematical logic

Mathematical logic

#### Metalogic

Metalogic The study of the metatheory of logic.

##### Proof theory

Proof theory The study of deductive apparatus.

##### Model theory

Model theory The study of interpretation of formal systems.

#### Computability theory

Computability theory branch of mathematical logic that originated in the 1930s with the study of computable functions and Turing degrees. The field has grown to include the study of generalized computability and definability. The basic questions addressed by recursion theory are "What does it mean for a function from the natural numbers to themselves to be computable?" and "How can noncomputable functions be classified into a hierarchy based on their level of noncomputability?". The answers to these questions have led to a rich theory that is still being actively researched.

## Semantics of natural language

Formal semantics (natural language)

• Formal systems
• Concepts

Classical logic

Modal logic

## Non-classical logic

Non-classical logic

## Concepts of logic

Mathematical logic

History of logic