ABSTRACT
First published in the most ambitious international philosophy project for a generation; the Routledge Encyclopedia of Philosophy.
Logic from A to Z is a unique glossary of terms used in formal logic and the philosophy of mathematics.
Over 500 entries include key terms found in the study of:
* Logic: Argument, Turing Machine, Variable
* Set and model theory: Isomorphism, Function
* Computability theory: Algorithm, Turing Machine
* Plus a table of logical symbols.
Extensively cross-referenced to help comprehension and add detail, Logic from A to Z provides an indispensable reference source for students of all branches of logic.
TABLE OF CONTENTS
letter |13 pages
A
entry |1 pages
Abacus machine
entry |1 pages
Abstract term
entry |1 pages
Abstraction
entry |1 pages
Ad hominem argument
entry |1 pages
Ad ignorantiam argument
entry |1 pages
Adicity
entry |1 pages
Adjunction
entry |1 pages
Affirmative (proposition)
entry |1 pages
Affirming the consequent, fallacy of
entry |1 pages
Alephs
entry |1 pages
Algorithm
entry |1 pages
Algorithmic function
entry |1 pages
Alternative denial
entry |1 pages
Ambiguity, fallacy of
entry |1 pages
Ampliation
entry |1 pages
Analytic/synthetic (judgment or proposition)
entry |1 pages
Ancestral (of a relation)
entry |1 pages
Antecedent
entry |1 pages
Antisymmetric relation/order
entry |1 pages
Apparent variable
entry |1 pages
Argument
entry |1 pages
Argument ad hominem
entry |1 pages
Argument ad ignorantiam
entry |1 pages
Argument, converse of an
entry |1 pages
Argument, diagonal
entry |1 pages
Argument, dialectical
entry |1 pages
Argument (of a relation/function)
entry |1 pages
Arity
entry |1 pages
Asymmetric relation/order
entry |1 pages
Atomic (sentence or formula)
entry |1 pages
Automaton
entry |1 pages
Automorphism
entry |1 pages
Axiom
entry |1 pages
Axiom of abstraction
entry |1 pages
Axiom of choice
entry |1 pages
Axiom of comprehension
entry |1 pages
Axiom of constructibility
entry |1 pages
Axiom of determinateness
entry |1 pages
Axiom of extensionality
entry |1 pages
Axiom of foundation
entry |1 pages
Axiom of infinity
entry |1 pages
Axiom of pairing
entry |1 pages
Axiom of power set
entry |1 pages
Axiom of reducibility
entry |1 pages
Axiom of regularity
entry |1 pages
Axiom of replacement
entry |1 pages
Axiom of separation
entry |1 pages
Axiom of substitution
entry |1 pages
Axiom of sumset
entry |1 pages
Axiom of union
entry |1 pages
Axiom schema
entry |1 pages
Axiomatic theory
entry |1 pages
Axioms, set-theoretic
letter |2 pages
B
entry |1 pages
Bamalip
entry |1 pages
Bamana
entry |1 pages
Baralipton
entry |1 pages
Barbara
entry |1 pages
Barbari
entry |1 pages
Baroco
entry |1 pages
Base component
entry |1 pages
Base (of propositional operators/connectives)
entry |1 pages
Begging the question
entry |1 pages
Bernays-Gödel set theory
entry |1 pages
Berry's paradox
entry |1 pages
Beths
entry |1 pages
Biconditional
entry |1 pages
Bijection
entry |1 pages
Bivalence
entry |1 pages
Bocardo
entry |1 pages
Bound (occurrence of a) variable
entry |1 pages
Bound (of a set)
entry |1 pages
Bramantip
entry |1 pages
Brouwer's continuity theorem
entry |1 pages
Burali-Forti's paradox
letter |15 pages
C
entry |1 pages
Calculus
entry |1 pages
Calemes
entry |1 pages
Calemop
entry |1 pages
Calemos
entry |1 pages
Camene
entry |1 pages
Camenes
entry |1 pages
Camenop
entry |1 pages
Camestres
entry |1 pages
Camestrop
entry |1 pages
Cantor's paradox
entry |1 pages
Cantor's theorem
entry |1 pages
Cardinal (number)
entry |1 pages
Cardinality
entry |1 pages
Cartesian product
entry |1 pages
Categoremata
entry |1 pages
Categorical in power
entry |1 pages
Categorical proposition
entry |1 pages
Categorical syllogism
entry |1 pages
Categorical theory
entry |1 pages
Celantes
entry |1 pages
Celantop
entry |1 pages
Celantos
entry |1 pages
Celarent
entry |1 pages
Celaro
entry |1 pages
Celaront
entry |1 pages
Cesare
entry |1 pages
Cesaro
entry |1 pages
Characteristic function
entry |1 pages
Choice, axiom of
entry |1 pages
Choice sequence
entry |1 pages
Choice set/function
entry |1 pages
Church's theorem
entry |1 pages
Church's thesis
entry |1 pages
Church-Turing thesis
entry |1 pages
Circular reasoning, fallacy of
entry |1 pages
Class
entry |1 pages
Class/set distinction
entry |1 pages
Closure (deductive, logical)
entry |1 pages
Codomain
entry |1 pages
Compact cardinal
entry |1 pages
Compactness
entry |1 pages
Comparability
entry |1 pages
Complement
entry |1 pages
Complete relation/order
entry |1 pages
Complete set of connectives
entry |1 pages
Completeness (of a logical calculus)
entry |1 pages
Completeness (of a theory)
entry |1 pages
Completeness theorem
entry |1 pages
Composition, fallacy of
entry |1 pages
Comprehension
entry |1 pages
Computable function
entry |1 pages
Conclusion
entry |1 pages
Conditional, counterfactual
entry |1 pages
Conditional, material
entry |1 pages
Conditional proof
entry |1 pages
Conjunction
entry |1 pages
Conjunctive normal form
entry |1 pages
Connected relation/order
entry |1 pages
Connotation
entry |1 pages
Consequent
entry |1 pages
Consequentiae
entry |1 pages
Conservative extension (of a theory)
entry |1 pages
Consistency
entry |1 pages
Constant
entry |1 pages
Constant function
entry |1 pages
Constructibility, axiom of
entry |1 pages
Constructive choices, principle of
entry |1 pages
Constructive existence proof
entry |1 pages
Continuity theorem
entry |1 pages
Continuous set
entry |1 pages
Continuum hypothesis
entry |1 pages
Contraction
entry |1 pages
Contradiction
entry |1 pages
Contradiction, law of
entry |1 pages
Contradictories
entry |1 pages
Contraposition
entry |1 pages
Contraries
entry |1 pages
Contrary to fact conditional
entry |1 pages
Converse domain
entry |1 pages
Converse (of an argument)
entry |1 pages
Converse (of a conditional)
entry |1 pages
Converse (of a relation)
entry |1 pages
Conversion per
entry |1 pages
Conversion, simple
entry |1 pages
Copula
entry |1 pages
Countable
entry |1 pages
Counter domain
entry |1 pages
Counterfactual (conditional)
entry |1 pages
Cross product (of sets)
entry |1 pages
Curry's paradox
entry |1 pages
Cut-elimination theorems
letter |10 pages
D
entry |1 pages
Dabitis
entry |1 pages
Darapti
entry |1 pages
Daraptis
entry |1 pages
Darii
entry |1 pages
Datisi
entry |1 pages
De dicto
entry |1 pages
De Morgan's laws
entry |1 pages
De relde dicto
entry |1 pages
Decidability
entry |1 pages
Decision problem
entry |1 pages
Decision procedure
entry |1 pages
Deducibility
entry |1 pages
Deduction
entry |1 pages
Deduction theorem
entry |1 pages
Degree (of a relation)
entry |1 pages
Denial
entry |1 pages
Denotation
entry |1 pages
Dense relation/order
entry |1 pages
Denumerable
entry |1 pages
Denying the antecedent, fallacy of
entry |1 pages
Derivability conditions
entry |1 pages
Derivation
entry |1 pages
Determinateness, axiom of
entry |1 pages
Dialectical argument
entry |1 pages
Dilemma
entry |1 pages
Dilution
entry |1 pages
Dimaris
entry |1 pages
Dimatis
entry |1 pages
Direct product (of sets)
entry |1 pages
Direct proof
entry |1 pages
Disamis
entry |1 pages
Discourse, domain of
entry |1 pages
Discrete set
entry |1 pages
Disjunction
entry |1 pages
Disjunctive normal form
entry |1 pages
Disjunctive syllogism
entry |1 pages
Distributed term (of a syllogism)
entry |1 pages
Division, fallacy of
entry |1 pages
Domain (of a relation/function)
entry |1 pages
Domain of discourse
entry |1 pages
Downward Löwenheim-Skolem theorem
entry |1 pages
Duality
letter |4 pages
E
entry |1 pages
Effective procedure
entry |1 pages
Effectively calculable function
entry |1 pages
Effectively computable function
entry |1 pages
Elementarily equivalent structures
entry |1 pages
Empty set
entry |1 pages
Endomorphism
entry |1 pages
Enthymeme
entry |1 pages
Entscheidungsproblem
entry |1 pages
Epimenides' paradox
entry |1 pages
Equinumerosity/equipollence
entry |1 pages
Equivalence class
entry |1 pages
Equivalence relation
entry |1 pages
Essentialism
entry |1 pages
Eubulides' paradox
entry |1 pages
Ex falso quodlibet
entry |1 pages
Excluded middle
entry |1 pages
Exclusive disjunction
entry |1 pages
Existential generalization
entry |1 pages
Existential import
entry |1 pages
Existential instantiation
entry |1 pages
Extension
entry |1 pages
Extension (of a theory)
entry |1 pages
Extensionality, axiom of
letter |4 pages
F
entry |1 pages
Fallacy
entry |1 pages
Fapesmo
entry |1 pages
Felapto
entry |1 pages
Felapton
entry |1 pages
Ferio
entry |1 pages
Ferison
entry |1 pages
Fesapo
entry |1 pages
Festino
entry |1 pages
Field (of a relation/function)
entry |1 pages
Figure (of a categorical syllogism)
entry |1 pages
Fimeno
entry |1 pages
Finite
entry |1 pages
Finite character
entry |1 pages
First-order/higher-order
entry |1 pages
Forcing
entry |1 pages
Formal language
entry |1 pages
Formal proof
entry |1 pages
Formal system
entry |1 pages
Foundation, axiom of
entry |1 pages
Fraenkel set theory
entry |1 pages
Free (occurrence of a) variable
entry |1 pages
Fresison
entry |1 pages
Frisesomorum
entry |1 pages
Function
letter |1 pages
G
entry |1 pages
Generalized continuum hypothesis
entry |1 pages
Gödel sentence
entry |1 pages
Gödel's theorems
entry |1 pages
Greatest lower bound
entry |1 pages
Greatest ordinal, paradox of the
entry |1 pages
Grelling–Nelson paradox
entry |1 pages
Grelling's paradox
letter |2 pages
H
entry |1 pages
Halting problem
entry |1 pages
Hauptsatz
entry |1 pages
Heap, paradox of the
entry |1 pages
Henkin sentence
entry |1 pages
Henkin's problem
entry |1 pages
Heterologicality, paradox of
entry |1 pages
Higher-order
entry |1 pages
Homomorphism
entry |1 pages
Horned syllogism
entry |1 pages
Hypothetical syllogism
letter |6 pages
I
entry |1 pages
Identity function
entry |1 pages
Identity, law of
entry |1 pages
Identity of indiscernibles
entry |1 pages
Ignoratio elenchi
entry |1 pages
Illicit process, fallacy of
entry |1 pages
Image (of a function)
entry |1 pages
Immediate inference
entry |1 pages
Implication, logical
entry |1 pages
Implication, material
entry |1 pages
Implication, strict
entry |1 pages
Impredicative definition
entry |1 pages
Inaccessible cardinal
entry |1 pages
Inclusive disjunction
entry |1 pages
Incompleteness theorems
entry |1 pages
Inconsistent triad
entry |1 pages
Indefinite categorical proposition
entry |1 pages
Independence
entry |1 pages
Indirect proof
entry |1 pages
Indiscernibility of identicals
entry |1 pages
Induction, mathematical
entry |1 pages
Infimum
entry |1 pages
Infinite
entry |1 pages
Infinity, axiom of
entry |1 pages
Injection
entry |1 pages
Input (of a function)
entry |1 pages
Intension
entry |1 pages
Interpretation
entry |1 pages
Intersection (of
entry |1 pages
Into function
entry |1 pages
Inverse (of a function)
entry |1 pages
Inverse (of a relation)
entry |1 pages
Isomorphism
letter |1 pages
J
entry |1 pages
Join
entry |1 pages
Joint denial
letter |1 pages
K
entry |1 pages
Kleene's second recursion theorem
entry |1 pages
König's lemma
letter |5 pages
L
entry |1 pages
Large cardinal
entry |1 pages
Law of comparability
entry |1 pages
Law of contradiction
entry |1 pages
Law of (the) excluded middle
entry |1 pages
Law of identity
entry |1 pages
Law of trichotomy
entry |1 pages
Least upper bound
entry |1 pages
Left field (of a relation)
entry |1 pages
Lekton
entry |1 pages
Lemma, König's
entry |1 pages
Lemma, Zorn's
entry |1 pages
Liar paradox
entry |1 pages
Limit ordinal
entry |1 pages
Limitation of size
entry |1 pages
Linear relation/order
entry |1 pages
Löb's theorem
entry |1 pages
Logical constant
entry |1 pages
Logical implication
entry |1 pages
Logistic system
entry |1 pages
Löwenheim–Skolem theorem(s)
entry |1 pages
Lower bound
letter |7 pages
M
entry |1 pages
Mahlo cardinal
entry |1 pages
Major premise (of a syllogism)
entry |1 pages
Major term (of a syllogism)
entry |1 pages
Many-valued logics
entry |1 pages
Mapping (map)
entry |1 pages
Markov's principle
entry |1 pages
Material implication
entry |1 pages
Maximal consistent set
entry |1 pages
Measurable cardinal
entry |1 pages
Meet
entry |1 pages
Middle term (of a syllogism)
entry |1 pages
Minor premise (of a syllogism)
entry |1 pages
Minor term (of a syllogism)
entry |1 pages
Mnemonics, syllogistic
entry |1 pages
Modal syllogism
entry |1 pages
Model
entry |1 pages
Modus ponendo tollens
entry |1 pages
Modus tollendo ponens
entry |1 pages
Modus tollens
entry |3 pages
Mood (of a categorical syllogism)
entry |1 pages
Multiplicative axiom
letter |2 pages
N
entry |1 pages
Negation
entry |1 pages
Negation-completeness
entry |1 pages
Negative (proposition)
entry |1 pages
Neumann–Bernays–Gödel set theory
entry |1 pages
Non sequitur
entry |1 pages
Noncontradiction, law of
entry |1 pages
Nonstandard model
entry |1 pages
Normal form (conjunctive)
entry |1 pages
Normal form (disjunctive)
entry |1 pages
Normal form (Skolem)
entry |1 pages
N-tuple
entry |1 pages
Null set
letter |3 pages
O
entry |1 pages
Obversion
entry |1 pages
Omega
entry |1 pages
Omega-completeness
entry |1 pages
Omega-consistency
entry |1 pages
Onto function
entry |1 pages
Open term/formula
entry |1 pages
Opposition
entry |1 pages
Order
entry |1 pages
Ordering
entry |1 pages
Order type
entry |1 pages
Ordered n-tuple
entry |1 pages
Ordered pair
entry |1 pages
Ordinal (number)
entry |1 pages
Output (of a function)
letter |9 pages
P
entry |1 pages
Pairing axiom
entry |1 pages
Paradox, Berry's
entry |1 pages
Paradox, Burali-Forti's
entry |1 pages
Paradox, Cantor's
entry |1 pages
Paradox, Curry's
entry |1 pages
Paradox, Epimenides'
entry |1 pages
Paradox of the greatest ordinal
entry |1 pages
Paradox, Grelling's
entry |1 pages
Paradox of the heap
entry |1 pages
Paradox of heterologicality
entry |1 pages
Paradox, liar
entry |1 pages
Paradox, Russell's
entry |1 pages
Paradox, sorites
entry |1 pages
Paradoxes of material and strict implication
entry |1 pages
Paralogism
entry |1 pages
Parameter
entry |1 pages
Parameter theorem
entry |1 pages
Parametrization theorem
entry |1 pages
Partial function
entry |1 pages
Particular (proposition)
entry |1 pages
Particular to general reasoning
entry |1 pages
Partition
entry |1 pages
Peano postulates (Peano arithmetic)
entry |1 pages
Petitio principii
entry |1 pages
Philonian conditional
entry |1 pages
Polish notation
entry |1 pages
PolysyUogism
entry |1 pages
Post completeness
entry |1 pages
Postulates, Peano
entry |1 pages
Power (of a set)
entry |1 pages
Power set
entry |1 pages
Power set axiom
entry |1 pages
Predecessor
entry |1 pages
Predicate
entry |1 pages
Predicate-functor logic
entry |1 pages
Predicate logic
entry |1 pages
Prenex normal form
entry |1 pages
Pre-ordering
entry |1 pages
Primitive recursive function
entry |1 pages
Principle of constructive choices
entry |1 pages
Problem
entry |1 pages
Product (of sets)
entry |1 pages
Projection function
entry |1 pages
Proof
entry |1 pages
Proper class
entry |1 pages
Proposition
entry |1 pages
Proposition, categorical
entry |1 pages
Propositional function
entry |1 pages
Propositional logic
entry |1 pages
Propositional operator/connective
entry |1 pages
Provability predicate
letter |1 pages
Q
entry |1 pages
Quality (of a categorical proposition)
entry |1 pages
Quantifier
entry |1 pages
Quantity (of a categorical proposition)
entry |1 pages
Quasi-ordering
letter |5 pages
R
entry |1 pages
Ramified theory of types
entry |1 pages
Range (of a relation/function)
entry |1 pages
Real variable
entry |1 pages
Reasoning from particular to general
entry |1 pages
Recursion theorem
entry |1 pages
Recursive function
entry |1 pages
Recursive set
entry |1 pages
Reducibility, axiom of
entry |1 pages
Reductio absurdum
entry |1 pages
Reduction, syllogistic
entry |1 pages
Reflexive relation/order
entry |1 pages
Register machine
entry |1 pages
Regularity, axiom of
entry |1 pages
Relations (properties of)
entry |1 pages
Relative complement
entry |1 pages
Replacement, axiom of
entry |1 pages
Restriction, axiom of
entry |1 pages
Richard's paradox
entry |1 pages
Right field (of a relation)
entry |1 pages
Rules of inference
entry |1 pages
Russell's paradox
letter |9 pages
S
entry |1 pages
Satisfaction
entry |1 pages
Sentence
entry |1 pages
Separation, axiom of
entry |1 pages
Sequence
entry |1 pages
Series
entry |1 pages
Set/class distinction
entry |1 pages
Set theory
entry |1 pages
Set-theoretic axioms
entry |1 pages
Sheffer stroke
entry |1 pages
Signature
entry |1 pages
Signification
entry |1 pages
Simple relation/order
entry |1 pages
Simple theory of types
entry |1 pages
Singular proposition
entry |1 pages
Skolem theorem
entry |1 pages
Skolem normal form
entry |1 pages
S-M-N theorem
entry |1 pages
Solvable problem
entry |1 pages
Sophism
entry |1 pages
Sorites
entry |1 pages
Soundness (of an argument)
entry |1 pages
Soundness (of a formal system)
entry |1 pages
Soundness (of a logical calculus)
entry |1 pages
Soundness (of a theory)
entry |1 pages
Square of opposition
entry |1 pages
Strengthened liar paradox
entry |1 pages
Strict implication
entry |1 pages
Structure
entry |1 pages
Subalternation
entry |1 pages
Subcontradictories
entry |1 pages
Subject
entry |1 pages
Subjunctive conditional
entry |1 pages
Subset
entry |1 pages
Substitution, axiom of
entry |1 pages
Subtheory
entry |1 pages
Successor
entry |1 pages
Successor function
entry |1 pages
Sumset axiom
entry |1 pages
Superset
entry |1 pages
Supremum
entry |1 pages
Surjection
entry |1 pages
Syllogism
entry |1 pages
Syllogism, categorical
entry |1 pages
Syllogism, horned
entry |1 pages
Syllogism, hypothetical
entry |1 pages
Syllogism, modal
entry |1 pages
Symmetric difference of sets
entry |1 pages
Symmetric relation/order
entry |1 pages
Syncategoremata
entry |1 pages
Synthetic (judgment or proposition)
letter |5 pages
T
entry |1 pages
Tarski's undefinability theorem
entry |1 pages
Tautology, tautological implication
entry |1 pages
T-equivalence
entry |1 pages
Tertium non datur
entry |1 pages
Theorem
entry |1 pages
Theory, axiomatic
entry |1 pages
Theory, categorical
entry |1 pages
Theory, completeness of a
entry |1 pages
Theory, (conservative) extension of a
entry |1 pages
Theory, soundness of a
entry |1 pages
Theory of types
entry |1 pages
Thinning
entry |1 pages
Total function
entry |1 pages
Total relation/order
entry |1 pages
Transfinite cardinal
entry |1 pages
Transfinite induction
entry |1 pages
Transitive closure
entry |1 pages
Transitive relation/order
entry |1 pages
Trichotomy
entry |1 pages
Truth-function
entry |1 pages
Truth in a model
entry |1 pages
Truth table
entry |1 pages
Truth-value
entry |1 pages
-Tuple
entry |1 pages
Turing computable function
entry |1 pages
Turing machine
entry |1 pages
Types, theory of
letter |2 pages
U
entry |1 pages
Union, axiom of
entry |1 pages
Union (of sets)
entry |1 pages
Universal generalization
entry |1 pages
Universal instantiation
entry |1 pages
Universal machine theorem
entry |1 pages
Universal (proposition)
entry |1 pages
Universal quantifier
entry |1 pages
Universal set
entry |1 pages
Universal Turing machine
entry |1 pages
Upper bound
entry |1 pages
Upward Löwenheim–Skolem theorem
letter |2 pages
V
entry |1 pages
Validity
entry |1 pages
Valuation
entry |1 pages
Value (of a function)
entry |1 pages
Variable
entry |1 pages
Vicious-circle principle
entry |1 pages
Von Neumann–Bernays–Gödel set theory
letter |1 pages
W
entry |1 pages
Weakening
entry |1 pages
Well-founded relation/order
entry |1 pages
Well-ordering
letter |1 pages
Z
entry |1 pages
Zermelo–Fraenkel set theory
entry |1 pages
Zorn's lemma