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 and incorrect inferences. Logicians study the criteria for the evaluation of arguments.
Foundations of logic
- Analytic-synthetic distinction
- Antinomy
- A priori and a posteriori
- Definition
- Description
- Entailment
- Identity
- Inference
- Logical form
- Logical implication
- Logical truth
- Logical consequence
- Name
- Necessity
- Material conditional
- Meaning
- Meaning
- Paradox
- Possible world
- Presupposition
- Probability
- Quantification
- Reason
- Reasoning
- Reference
- Semantics
- Strict conditional
- Syntax
- Truth
- Truth value
- Validity
Branches of logic
- Affine logic
- Alethic logic
- Aristotelian logic
- Boolean logic
- Buddhist logic
- Bunched logic
- Categorical logic
- Classical logic
- Computability logic
- Deontic logic
- Dependence logic
- Description logic
- Deviant logic
- Doxastic logic
- Epistemic logic
- First-order logic
- Formal logic
- Free logic
- Fuzzy logic
- Higher-order logic
- Infinitary logic
- Informal logic
- Intensional logic
- Intermediate logic
- Interpretability logic
- Intuitionistic logic
- Linear logic
- Many-valued logic
- Mathematical logic
- Metalogic
- Minimal logic
- Modal logic
- Non-Aristotelian logic
- Non-classical logic
- Noncommutative logic
- Non-monotonic logic
- Ordered logic
- Paraconsistent logic
- Philosophical logic
- Predicate logic
- Propositional logic
- Provability logic
- Quantum logic
- Relevance logic
- Sequential logic
- Spatial logic
- Strict logic
- Substructural logic
- Syllogistic logic
- Symbolic logic
- Temporal logic
- Term logic
- Topical logic
- Traditional logic
- Zeroth-order logic
Philosophical logic
Informal logic and critical thinking
- Argument
- Argument map
- Accuracy and precision
- Ad hoc hypothesis
- Ambiguity
- Analysis
- Attacking Faulty Reasoning
- Belief
- Belief bias
- Bias
- Cognitive bias
- Confirmation bias
- Credibility
- Critical reading
- Critical thinking
- Decidophobia
- Decision making
- Dispositional and occurrent belief
- Emotional reasoning
- Evidence
- Expert
- Explanation
- Explanatory power
- Fact
- Fallacy
- Higher-order thinking
- Inquiry
- Interpretive discussion
- Occam's razor
- Opinion
- Practical syllogism
- Precision questioning
- Propaganda
- Propaganda techniques
- Problem Solving
- Prudence
- Pseudophilosophy
- Reasoning
- Relevance
- Rhetoric
- Rigour
- Socratic questioning
- Source credibility
- Source criticism
- Theory of justification
- Topical logic
- Vagueness
Deductive reasoning
Theories of deduction
- Anti-psychologism
- Conceptualism
- Constructivism
- Conventionalism
- Counterpart theory
- Deflationary theory of truth
- Dialetheism
- Fictionalism
- Formalism
- Game theory
- Illuminationist philosophy
- Logical atomism
- Logical holism
- Logicism
- Modal fictionalism
- Nominalism
- Polylogism
- Pragmatism
- Preintuitionism
- Proof theory
- Psychologism
- Ramism
- Semantic theory of truth
- Sophism
- Trivialism
- Ultrafinitism
Fallacies
- Fallacy - incorrect argumentation in reasoning resulting in a misconception or presumption. By accident or design, fallacies may exploit emotional triggers in the listener or interlocutor, or take advantage of social relationships between people. 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 variables
- *Propositional variable
- *Predicate variable
- *Literal
- *Metavariable
- Logical constants
- *Logical connective
- *Quantifier
- *Identity
- *Brackets
Logical connectives
- Converse implication
- Converse nonimplication
- Exclusive or
- Logical NOR
- Logical biconditional
- Logical conjunction
- Logical disjunction
- Material implication
- Material nonimplication
- Negation
- Sheffer stroke
Strings of symbols
- Atomic formula
- Open sentence
Types of propositions
- Analytic proposition
- Axiom
- Atomic sentence
- Clause
- Contingent proposition
- Contradiction
- Logical truth
- Propositional formula
- Rule of inference
- Sentence
- Sequent
- Statement
- Subalternation
- Tautology
- Theorem
Rules of inference
- Biconditional elimination
- Biconditional introduction
- Case analysis
- Commutativity of conjunction
- Conjunction introduction
- Constructive dilemma
- Contraposition
- Conversion
- De Morgan's laws
- Destructive dilemma
- Disjunction elimination
- Disjunction introduction
- Disjunctive syllogism
- Double negation elimination
- Generalization
- Hypothetical syllogism
- Law of excluded middle
- Law of identity
- Modus ponendo tollens
- Modus ponens
- Modus tollens
- Obversion
- Principle of contradiction
- Resolution
- Simplification
- Transposition
Formal theories
- Formal proof
- List of first-order theories
Expressions in a metalanguage
- Metalinguistic variable
- Deductive system
- Metatheorem
- Metatheory
- Interpretation
Propositional and Boolean logic
Propositional logic
- Absorption law
- Clause
- Deductive closure
- Distributive property
- Entailment
- Formation rule
- Functional completeness
- Intermediate logic
- Literal
- Logical connective
- Logical consequence
- Negation normal form
- Open sentence
- Propositional calculus
- Propositional formula
- Propositional variable
- Rule of inference
- Strict conditional
- Substitution instance
- Truth table
- Zeroth-order logic
Boolean logic
- Boolean algebra
- Boolean logic
- Boolean algebra
- Boolean algebras canonically defined
- Introduction to Boolean algebra
- Complete Boolean algebra
- Free Boolean algebra
- Monadic Boolean algebra
- Residuated Boolean algebra
- Two-element Boolean algebra
- Modal algebra
- Derivative algebra
- Relation algebra
- Absorption law
- Laws of Form
- De Morgan's laws
- Algebraic normal form
- Canonical form
- Boolean conjunctive query
- Boolean-valued model
- Boolean domain
- Boolean expression
- Boolean ring
- Boolean function
- Boolean-valued function
- Parity function
- Symmetric Boolean function
- Conditioned disjunction
- Field of sets
- Functional completeness
- Implicant
- Logic alphabet
- Logic redundancy
- Logical connective
- Logical matrix
- Product term
- True quantified Boolean formula
- Truth table
Predicate logic and relations
Predicate logic
- Atomic formula
- Atomic sentence
- Domain of discourse
- Empty domain
- Extension
- First-order logic
- First-order predicate
- Formation rule
- Free variables and bound variables
- Generalization
- Monadic predicate calculus
- Predicate
- Predicate logic
- Predicate variable
- Quantification
- Second-order predicate
- Sentence
- Universal instantiation
Relations
- Finitary relation
- Antisymmetric relation
- Asymmetric relation
- Bijection
- Bijection, injection and surjection
- Binary relation
- Composition of relations
- Congruence relation
- Connected relation
- Converse relation
- Coreflexive relation
- Covering relation
- Cyclic order
- Dense relation
- Dependence relation
- Dependency relation
- Directed set
- Equivalence relation
- Euclidean relation
- Homogeneous relation
- Idempotence
- Intransitivity
- Involutive relation
- Partial equivalence relation
- Partial function
- Partially ordered set
- Preorder
- Prewellordering
- Propositional function
- Quasitransitive relation
- Reflexive relation
- Serial relation
- Surjective function
- Symmetric relation
- Ternary relation
- Transitive relation
- Trichotomy
- Well-founded relation
Mathematical logic
Set theory
- Set theory list
- Aleph null
- Bijection, injection and surjection
- Binary set
- Cantor's diagonal argument
- Cantor's first uncountability proof
- Cantor's theorem
- Cardinality of the continuum
- Cardinal number
- Codomain
- Complement
- Constructible universe
- Continuum hypothesis
- Countable set
- Decidable set
- Denumerable set
- Disjoint sets
- Disjoint union
- Domain of a function
- Effective enumeration
- Element
- Empty function
- Empty set
- Enumeration
- Extensionality
- Finite set
- Forcing
- Function
- Function composition
- Generalized continuum hypothesis
- Index set
- Infinite set
- Intension
- Intersection
- Inverse function
- Large cardinal
- Löwenheim–Skolem theorem
- Map
- Multiset
- Morse–Kelley set theory
- Naïve set theory
- One-to-one correspondence
- Ordered pair
- Partition of a set
- Pointed set
- Power set
- Projection
- Proper subset
- Proper superset
- Range of a function
- Russell's paradox
- Sequence
- Set
- Set of all sets
- Simple theorems in the algebra of sets
- Singleton
- Skolem paradox
- Subset
- Superset
- Tuple
- Uncountable set
- Union
- Von Neumann–Bernays–Gödel set theory
- Zermelo set theory
- Zermelo–Fraenkel set theory