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

Branches of logic

Philosophical logic

Informal logic and critical thinking

Informal logic Critical thinking Argumentation theory

Deductive reasoning

Theories of deduction

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.
- List of mathematical logic topics

Symbols and strings of symbols

Logical symbols

Logical connectives

Logical connective

Strings of symbols

Types of propositions

Proposition

Rules of inference

Rule of inference (list)

Formal theories

Expressions in a metalanguage

Metalanguage

Propositional and boolean logic

Propositional logic

Boolean logic

Predicate logic and relations

Predicate logic

Relations

Mathematical relation

Mathematical logic

Set theory

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)

Classical logic

Properties of classical logics:
- Law of the excluded middle
- Double negation elimination
- Law of noncontradiction
- Principle of explosion
- Monotonicity of entailment
- Idempotency of entailment
- Commutativity of conjunction
- De Morgan duality – every logical operator is dual to another
Term logic
Outline of logic

Modal logic

Non-classical logic

Concepts of logic

Mathematical logic

History of logic

Literature about logic

Journals

Books

Logic organizations

Association for Symbolic Logic

Logicians

References

^ Marco Aiello; Ian Pratt-Hartmann; Johan van Benthem, eds. (2007). Handbook of Spatial Logics. p. 1. doi:10.1007/978-1-4020-5587-4. ISBN 978-1-4020-5586-7. any formal language interpreted over a class of structures featuring geometrical entities and relations, broadly construed
^ "octagon of prophecies - Google Search". www.google.com. Retrieved 2024-10-29.

External links

Taxonomy of Logical Fallacies
forall x: an introduction to formal logic, by P.D. Magnus, covers sentential and quantified logic
Translation Tips, by Peter Suber, for translating from English into logical notation
Math & Logic: The history of formal mathematical, logical, linguistic and methodological ideas. In The Dictionary of the History of Ideas.
Logic test Test your logic skills
Logic Self-Taught: A Workbook (originally prepared for on-line logic instruction)

[1] Marco Aiello; Ian Pratt-Hartmann; Johan van Benthem, eds. (2007). Handbook of Spatial Logics. p. 1. doi:10.1007/978-1-4020-5587-4. ISBN 978-1-4020-5586-7. any formal language interpreted over a class of structures featuring geometrical entities and relations, broadly construed

[2] "octagon of prophecies - Google Search". www.google.com. Retrieved 2024-10-29.

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v t e Common logical connectives
Tautology/True $\top$
Alternative denial (NAND gate) ${\overline {\wedge }}$ Converse implication $\Leftarrow$ Implication (IMPLY gate) $\Rightarrow$ Disjunction (OR gate) $\lor$
Negation (NOT gate) $\neg$ Exclusive or (XOR gate) $\oplus$ Biconditional (XNOR gate) $\odot$ Statement (Digital buffer)
Joint denial (NOR gate) ${\overline {\vee }}$ Nonimplication (NIMPLY gate) $\nRightarrow$ Converse nonimplication $\nLeftarrow$ Conjunction (AND gate) $\land$
Contradiction/False $\bot$
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Outline of logic

Foundations of logic

Branches of logic

Philosophical logic

Informal logic and critical thinking

Deductive reasoning

Theories of deduction

Fallacies

Formal logic

Symbols and strings of symbols

Logical symbols

Logical connectives

Strings of symbols

Types of propositions

Rules of inference

Formal theories

Expressions in a metalanguage

Propositional and boolean logic

Propositional logic

Boolean logic

Predicate logic and relations

Predicate logic

Relations

Mathematical logic

Set theory

Metalogic

Proof theory

Model theory

Computability theory

Semantics of natural language

Classical logic

Modal logic

Non-classical logic

Concepts of logic

History of logic

Literature about logic

Journals

Books

Logic organizations

Logicians

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