# Outline of logic

The following outline is provided as an overview of and topical guide to logic:

Logicformal science of using reason and is considered a branch of both philosophy and mathematics. 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. 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

Main article: 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

• Formal logic – Mathematical logic, symbolic logic and formal logic are largely, if not completely synonymous. The essential feature of this field is the use of formal languages to express the ideas whose logical validity is being studied.

### Symbols and strings of symbols

#### Strings of symbols

Main article: Well-formed formula

#### Types of propositions

Main article: Proposition

#### Expressions in an object language

Main article: Object language

#### Expressions in a metalanguage

Main article: Metalanguage

### Propositional and boolean logic

#### Propositional logic

Main article: Propositional logic

### Predicate logic and relations

#### Predicate logic

Main article: Predicate logic

#### Relations

Main article: Mathematical relation

## Mathematical logic

### Set theory

Set theory  (list) –

### 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.

## History of logic

Main article: History of logic