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Logical connective
The material conditional (also known as material implication) is a binary operation commonly used in logic. When the conditional symbol → {\displaystyle
Material_conditional
Family of logics for natural-language and counterfactual conditionals
conditionals more faithfully than the classical material conditional, which gives rise to well-known paradoxes. Conditional logics are used in philosophical logic
Conditional_logic
Type of logical contradiction
The paradoxes of material implication are a group of classically true formulae involving material conditionals whose translations into natural language
Paradoxes of material implication
Paradoxes_of_material_implication
Conditionals that discuss what would have been if things were otherwise
as a challenge for the analysis of conditionals in terms of the material conditional, which would make all counterfactuals with false antecedents trivially
Counterfactual_conditional
Topics referred to by the same term
consequent Material conditional, in propositional calculus, or logical calculus in mathematics Relevance conditional, in relevance logic Conditional logic
Conditional
Formal statement in logic
logical connective of modal logic. It is logically equivalent to the material conditional of classical logic, combined with the necessity operator from modal
Strict_conditional
Logical connective
connective is biconditional (a statement of material equivalence), and can be likened to the standard material conditional ("only if", equal to "if ... then")
If_and_only_if
Topics referred to by the same term
A conditional statement may refer to: A conditional formula in logic and mathematics, which can be interpreted as: Material conditional Strict conditional
Conditional_statement
Conditional statement which is true because the antecedent cannot be satisfied
vacuous truth is a conditional or universal statement (specifically a universal statement that can be converted to a conditional statement) that is true
Vacuous_truth
Sentence expressing an 'if-then' relation
A conditional sentence is a sentence in a natural language that expresses that one thing is contingent on another, e.g., "If it rains, the picnic will
Conditional_sentence
Natural-language "if" sentences about what may be the case
Linguistics portal Conditional logic Counterfactual conditional Logical consequence Material conditional Strict conditional Pragmatics Conditional probability
Indicative_conditional
Test in the study of deductive reasoning
the material conditional, since the natural language conditional is not the material conditional. (See also the paradoxes of the material conditional for
Wason_selection_task
Rule of logical inference
classical two-valued logic, modus ponens can be interpreted from the material conditional (implication) operator. The notion of implication as a rigorous mathematical
Modus_ponens
Symbol connecting formulas in logic
expressions P, Q have side effects. Also, a conditional, which in some sense corresponds to the material conditional connective, is essentially non-Boolean
Logical_connective
Modern alternative name for Hinduism
Varnashrama-dharma (a.k.a. Svadharma) – duties performed according to one's material (conditional) nature and are specific to the individual at that particular time
Sanātana_Dharma
In logic, the corresponding conditional of an argument (or derivation) is a material conditional whose antecedent is the conjunction of the argument's
Corresponding_conditional
True when either but not both inputs are true
of material implication (a material conditional is equivalent to the disjunction of the negation of its antecedent and its consequence) and material equivalence
Exclusive_or
Theory of logic to account for observations from quantum theory
reject quantum logic as a basis for reasoning, because it lacks a material conditional; a common alternative is the system of linear logic, of which quantum
Quantum_logic
Topics referred to by the same term
others Material conditional (also material implication), a logical connective and binary truth function typically interpreted as "If p, then q" Material implication
Implication
If and only if relation
the only case where a logical biconditional is different from a material conditional is the case where the hypothesis (antecedent) is false but the conclusion
Logical_biconditional
Topics referred to by the same term
Human condition, characteristics and key events of human existence Material conditional, a logical connective used to form "if...then..." statements Necessary
Condition
Application of logical methods to philosophical problems
truth-functional interpretation of the material conditional by introducing the additional requirement of relevance: for the conditional to be true, its antecedent
Philosophical_logic
Graphical symbol or pictogram used to point or indicate direction
decrease. In mathematical logic, a right-facing arrow indicates material conditional, and a left-right (bidirectional) arrow indicates if and only if
Arrow_(symbol)
Grammatical mood
The conditional mood (abbreviated cond) is a grammatical mood used in conditional sentences to express a proposition whose validity is dependent on some
Conditional_mood
Topics referred to by the same term
connective introduced by Alonzo Church a rule in classical logic that the material conditional ¬p → q is equivalent to the disjunction p ∨ q, so that these two
Conditional_disjunction
Mathematical symbol for "greater than"
operator Mathematical operators and symbols in Unicode Guillemet Material conditional Smith, Charles L. (1964). "On the origin of ">" and "<"". The Mathematics
Greater-than_sign
Topics referred to by the same term
Material implication may refer to: Material conditional, a logical connective Material implication (rule of inference), a rule of replacement for some
Material_implication
Algebraic manipulation of "true" and "false"
operations for all four possible inputs. Material conditional The first operation, x → y, or Cxy, is called material implication. If x is true, then the result
Boolean_algebra
Mathematical symbol
Horseshoe (⊃, \supset in TeX) is a symbol used to represent: Material conditional in propositional logic Superset in set theory It was used by Whitehead
Horseshoe_(symbol)
Probability theory and statistics concept
In probability theory and statistics, the conditional probability distribution is a probability distribution that describes the probability of an outcome
Conditional probability distribution
Conditional_probability_distribution
Mathematical table used in logic
then p ∨ q is p, otherwise p ∨ q is q. Logical implication and the material conditional are both associated with an operation on two logical values, typically
Truth_table
How one process influences another
antecedent is false. The ordinary indicative conditional has somewhat more structure than the material conditional. For instance, although the first is the
Causality
1879 book on logic by Gottlob Frege
in an idiosyncratic two-dimensional notation, based on negation, material conditional and universal quantification. Other connectives and existential quantification
Begriffsschrift
Object that exists in the imagination
are sometimes known as material conditionals. In contrast, indicative conditionals, sometimes known as non-material conditionals, attempt to describe if-then
Object_of_the_mind
argument is assumed in one of the premises. Philonian conditional Another term for the material conditional, emphasizing its use in propositional logic to represent
Glossary_of_logic
Form of reasoning
which happens when one of the premises has the form of a negative material conditional, as in "If the card does not have an A on the left, then it has a
Deductive_reasoning
(P(x)\wedge \neg \exists y\,(P(y)\wedge y\neq x))} . ⇒ 1. Denotes material conditional, and is read as "implies". If P and Q are logical predicates, P ⇒
Glossary of mathematical symbols
Glossary_of_mathematical_symbols
List of symbols used to express logical relations
\to } \to or \rightarrow ⊃ {\displaystyle \supset } \supset material conditional (material implication) implies, if P then Q, it is not the case that P
List_of_logic_symbols
Type of argument
true, and B is true, so A must be true"), but in this example the material conditional logical connective ("A implies B") in the formal fallacy does not
Argumentation_scheme
Sentences of the form "if x, then y"
headings zero conditional, first conditional (or conditional I), second conditional (or conditional II), third conditional (or conditional III) and mixed
English_conditional_sentences
Mathematical logic concept
contraposition, or transposition, refers to the inference of going from a conditional statement into its logically equivalent contrapositive, and an associated
Contraposition
Concept in first-order logic
such that Y" is interpreted as a universal generalization of the material conditional "if anything is such that X then it is such that Y". Also, the quantifiers
Empty_domain
Word used in English for conditional constructions
conjunction", a category covering a broad range of clause-connecting words. Material conditional §Discrepancies with natural language Huddleston, Rodney; Pullum,
If_(preposition)
Type of binary relation
Rational choice theory Hypothetical syllogism — transitivity of the material conditional Smith, Eggen & St. Andre 2006, p. 145 However, the class of von Neumann
Transitive_relation
Metatheorem
3, 5), each subformula is evaluated according to the rules for material conditional, the result being shown below its main operator. Column 6 shows that
Frege's_theorem
Symbolic logic system
Assuming any C {\displaystyle C} , the introduction rule of the material conditional gives B → C {\displaystyle B\to C} , also when B {\displaystyle B}
Minimal_logic
Possessing negative truth value
implication vacuously true). In most logical systems, negation, material conditional and false are related as: ¬p ⇔ (p → ⊥) In fact, this is the definition
False_(logic)
Australian logician
is particularly noted for his views on the interpretation of the material conditional. David Lewis, a frequent visitor to Australian departments of logic
Vic_Dudman
Process in logic
regression. Material inference should not be confused with the following concepts, which refer to formal, not material validity: Material conditional — the
Material_inference
Proof strategy for showing a collection of statements are equivalent
equivalence of the statements then results from the transitivity of the material conditional. For n = 4 {\displaystyle n=4} the proofs are given for φ 1 ⇒ φ 2
Ringschluss
Test for the acceptability of conditionals via hypothetical belief revision
Ramsey test (also called the Ramsey test for conditionals) is a proposal for how to evaluate and accept conditional sentences of the form if p (then) q. Informally
Ramsey_test
Refutation of a logical fallacy
not certain. Indeed, p implies q has the technical meaning of the material conditional: if p then q symbolized as p → q. That is, "if circumstance p is
Correlation does not imply causation
Correlation_does_not_imply_causation
Apparent logical paradox
important to the paradox is that the conditional in classical (and intuitionistic) logic is the material conditional. It has the property that A → B {\displaystyle
Drinker_paradox
Reasoning for mathematical statements
equivalence of the statements then results from the transitivity of the material conditional. A probabilistic proof is one in which an example is shown to exist
Mathematical_proof
Materials with granular size 1 to 100 nm
as protective as a legally mandated OEL for the bulk form of the material (conditional recommendation, low-quality evidence). If specific OELs for MNMs
Nanomaterials
Newspaper in Brighton and Hove, England
found that "the newspaper's decision to make its offer to remove the material conditional on the complainant agreeing not to pursue his complaint further,
The_Argus_(Brighton)
Logical implication Logical negation Logical NOR Majority function Material conditional Minimal axioms for Boolean algebra Peirce arrow Read-once function
List of Boolean algebra topics
List_of_Boolean_algebra_topics
System used to prevent non-paying customers from accessing content that requires payment
Conditional access (CA) is a term commonly used in relation to software and to digital television systems. Conditional access is an evaluation to ensure
Conditional_access
Philosophical problem about what constitutes knowledge
counterfactual conditional), the justified true belief came about, if Smith's purported claims are disputable, as the result of entailment (but see also material conditional)
Gettier_problem
Overview of and topical guide to logic
Logical implication Logical truth Logical consequence Name Necessity Material conditional Meaning (linguistic) Meaning (non-linguistic) Paradox (list) Possible
Outline_of_logic
Topics referred to by the same term
steamship route Horseshoe (symbol), "⊃", a logical connective meaning material conditional in propositional logic Horseshoe cloud, a meteorological phenomenon
Horseshoe_(disambiguation)
first, second or third conditional; there also exist "zero conditional" and mixed conditional sentences. A "first conditional" sentence expresses a future
Uses_of_English_verb_forms
Logical paradox
reductio ad absurdum, discharging assumption 8. 11. p → Kp from line 10 by a classical tautology about the material conditional (negated conditionals)
Fitch's paradox of knowability
Fitch's_paradox_of_knowability
Kind of quantifier in logic
denotes material implication in the metalanguage.) The minimal conditional logic M is characterized by the first six properties, and stronger conditional logics
Conditional_quantifier
Branch of logic
"and" (conjunction), "or" (disjunction), "not" (negation), "if" (material conditional), and "if and only if" (biconditional). Examples of such compound
Propositional_logic
Concept in mathematical logic
∨ {\displaystyle \lor } ); negation ( ¬ {\displaystyle \neg } ); material conditional ( → {\displaystyle \to } ); and possibly the biconditional ( ↔ {\displaystyle
Functional_completeness
Formal proof
A conditional proof is a proof that takes the form of asserting a conditional, and proving that the antecedent of the conditional necessarily leads to
Conditional_proof
Sentence that resists simple formalization
substituting any non-donkey object for y {\displaystyle y} makes the material conditional true (since its antecedent is false), and so existential clause is
Donkey_sentence
Logical biconditional; 10, q, Projection function; 11, if/then, Material conditional; 12, p, Projection function; 13, then/if, Converse implication; 14
List_of_rules_of_inference
Mathematics notation with operators preceding operands
ϕ {\displaystyle \neg \phi } N ϕ {\displaystyle N\phi } negacja Material conditional ϕ → ψ {\displaystyle \phi \to \psi } C ϕ ψ {\displaystyle C\phi \psi
Polish_notation
Critical experiment
(disambiguation) Pierre Duhem § Philosophy of science Falsifiability Material conditional Q.E.D. Scientific method Smoking gun Therefore sign Schwartz, Daniel
Experimentum_crucis
Study of the scope and nature of logic
conceptions: an inference from the premises to a conclusion is valid if the material conditional from the premises to the conclusion is logically true. For example
Philosophy_of_logic
Paradox arising from the question of what constitutes evidence for a statement
{\overline {Rx}}} where → {\displaystyle \rightarrow } indicates the material conditional, according to which "If A {\displaystyle A} then B {\displaystyle
Raven_paradox
Principle of classical logic
thus also in classical logic, where the conditional operator " → {\displaystyle \rightarrow } " is taken as material implication. In the Curry-Howard correspondence
Import–export_(logic)
Uniform restraint of the change in functions
|f(x)-f(y)|<\varepsilon } (where A ⟹ B {\displaystyle A\implies B} is a material conditional statement saying "if A {\displaystyle A} , then B {\displaystyle
Uniform_continuity
Type of formal logic
for the material conditional of LP. For this reason, proponents of LP usually advocate expanding the system to include a stronger conditional connective
Paraconsistent_logic
Text for inclusion in some versions of a document
Conditional text is content within a document that is meant to appear in some renditions of the document, but not other renditions. For example, a writer
Conditional_text
In probability theory, a conditional event algebra (CEA) is an alternative to a standard, Boolean algebra of possible events (a set of possible events
Conditional_event_algebra
Polish Dominican and philosopher (1902–1995)
of modal sentences. Bocheński's understanding of the supernatural and material spheres was greatly influenced by his attachment to the logical method
Józef_Maria_Bocheński
German chemical company
second half of 2025. In November 2025, the EU competition regulator conditionally approved the acquisition after ADNOC offered to ensure the firm aligned
Covestro
Arminian religious doctrine
The conditional preservation of the saints, or conditional perseverance of the saints, or commonly conditional security, is the Arminian Christian belief
Conditional preservation of the saints
Conditional_preservation_of_the_saints
Generalization of conditional expectation
In mathematics, non-commutative conditional expectation is a generalization of the notion of conditional expectation in classical probability. The space
Non-commutative conditional expectation
Non-commutative_conditional_expectation
Software development process
require lifecycle management beyond the conditional statements used to implement them. A study of practitioner material and developers from 38 companies identified
Feature_toggle
Probability theory term
formalized in probability theory by conditioning. Conditional probabilities, conditional expectations, and conditional probability distributions are treated on
Conditioning_(probability)
Type of mechanical component
function as a safeguard designed to break to protect other parts, or as a conditional operator that will not allow a mechanical device to operate until the
Shear_pin
Knowledge representation computer programming language
\mathbb {B} } denotes the booleans, ¬ denotes negation, and ⇒ denotes material conditional. Predicates < and ≥ are built-in and have their usual meaning. Such
FO(.)
Scientific study of digital information
The conditional entropy or conditional uncertainty of X given random variable Y (also called the equivocation of X about Y) is the average conditional entropy
Information_theory
English scholastic philosopher (1270s–1340s)
to have taken the position that, in line with modern views on the material conditional, the principle that "from the impossible anything follows" ("ex impossibili
Walter_Burley
school were (i) their account of modality, (ii) their theory of the material conditional, and (iii) their account of meaning and truth. Modality. According
History_of_logic
Table in statistics
statistics, the conditional probability table (CPT) is defined for a set of discrete and mutually dependent random variables to display conditional probabilities
Conditional_probability_table
Austrian philosopher (1879–1944)
binary relation A requires B, i.e. A materially implies !B. (All entailment in the axioms is material conditional.) It is defined by axiom III, whereas
Ernst_Mally
Intelligence of machines
expensive. For inference to be tractable, most observations must be conditionally independent of one another. AdSense uses a Bayesian network with over
Artificial_intelligence
Class of polymers with a silicon-nitrogen backbone
polysilazanes. Polysilazanes are colorless to pale yellow liquids or solid materials. Conditional of manufacturing, the liquids often contain dissolved ammonia that
Polysilazane
Form of conditionals in computer programming
alternative to conditional transfer of control, as implemented by conditional branch machine instructions. Predication works by having conditional (predicated)
Predication (computer architecture)
Predication_(computer_architecture)
English singer-songwriter (born 1989)
(2016), A Brief Inquiry into Online Relationships (2018), Notes on a Conditional Form (2020) and Being Funny in a Foreign Language (2022). Each of their
Matty_Healy
Lawful permanent residency in the United States
resident under the conditional clause may receive an I-551 stamp as well as a permanent resident card. The expiration date of the conditional period is two
Green_card
Overview of how Japanese verbs conjugate
present and past tense, volition, passive voice, causation, imperative and conditional mood, and ability. There are also special forms for conjunction with
Japanese_conjugation
Digital circuit implementation method
previous stage carry equal. A conditional sum adder is a recursive structure based on the carry-select adder. In the conditional sum adder, the MUX level chooses
Carry-select_adder
115–334 (text) (PDF) 115-335 December 20, 2018 Nicaraguan Investment Conditionality Act (NICA) of 2017 To oppose loans at international financial institutions
List of acts of the 115th United States Congress
List_of_acts_of_the_115th_United_States_Congress
Ongoing armed conflict in West Asia
be included as part of a ceasefire deal, thereby making a ceasefire conditional on an end to the 2026 Lebanon war against Hezbollah. On 24 March, Israel
2026_Iran_war
MATERIAL CONDITIONAL
MATERIAL CONDITIONAL
Girl/Female
Hindu, Indian
Musk; A Fragrant Material
Boy/Male
Muslim
Paternal
Girl/Female
Tamil
Chitragandha | சிதà¯à®°à®•à®‚தா
A fragrant material
Chitragandha | சிதà¯à®°à®•à®‚தா
Girl/Female
Indian, Punjabi, Sikh
Lady of Maternal Family
Biblical
paternal; that pursues the steps of his father
Boy/Male
Indian, Sanskrit
Material
Boy/Male
Arabic, Indian, Iranian, Muslim, Parsi
Paternal
Girl/Female
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sindhi, Telugu
A Fragrant Material
Girl/Female
Indian
A fragrant material
Boy/Male
Biblical
Paternal; that pursues the steps of his father.
Boy/Male
Tamil
Yudhajit | யà¯à®¤à®¾à®œà®¿à®¤
Victor in war, A hero, Soldier, Of a king of the kekayas and maternal uncle of Bharata
Yudhajit | யà¯à®¤à®¾à®œà®¿à®¤
Boy/Male
Hindu
Victor in war, A hero, Soldier, Of a king of the kekayas and maternal uncle of Bharata
Girl/Female
Afghan, Arabic, Indian, Iranian, Latin, Muslim, Parsi, Sindhi
Dry Earth; Detached; Free of Material Things; Noble; Freedom; Princess
Boy/Male
Indian
Maternal Uncle of God Krishna
Girl/Female
Arabic, Assamese, Bengali, Celebrity, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Muslim, Oriya, Sanskrit, Tamil, Telugu
Musk; A Fragrant Material; Earth; Scented with Musk; Scented; Fragrant
Boy/Male
Tamil
Yudhajith | யà¯à®¤à®¾à®œà¯€à®¤
Victor in war, A hero, Soldier, Of a king of the kekayas and maternal uncle of Bharata
Yudhajith | யà¯à®¤à®¾à®œà¯€à®¤
Girl/Female
Tamil
Chithragandha | சிதà¯à®°à®•à®‚தா
A fragrant material
Chithragandha | சிதà¯à®°à®•à®‚தா
Boy/Male
Hindu
Bird, Uncle of kauravas (Younger brother of Gandhari; maternal uncle of Duryodhana; An expert dice player.)
Male
African
materials for building.
Boy/Male
Tamil
Bird, Uncle of kauravas (Younger brother of Gandhari; maternal uncle of Duryodhana; An expert dice player.)
MATERIAL CONDITIONAL
MATERIAL CONDITIONAL
Girl/Female
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Telugu
Holy River
Male
Native American
Native American Navajo name TSIISHCHILI means "curly-haired."
Boy/Male
Hindu, Indian, Marathi
Wanted
Boy/Male
Bengali, Hindu, Indian, Tamil, Telugu
Worshipper of God
Boy/Male
Latin
Innocent.
Boy/Male
Indian
Stands for Peace; Chinese Zodiac
Biblical
son of Hadad, or noise
Boy/Male
Hindu
Boy/Male
Indian
Courageous and generous
Girl/Female
American, British, Christian, English, French, Swedish
Star; Myrtle Leaf
MATERIAL CONDITIONAL
MATERIAL CONDITIONAL
MATERIAL CONDITIONAL
MATERIAL CONDITIONAL
MATERIAL CONDITIONAL
adv.
In an important manner or degree; essentaily; as, it materially concern us to know the real motives of our actions.
a.
Not material; immaterial.
a.
Of no substantial consequence; without weight or significance; unimportant; as, it is wholly immaterial whether he does so or not.
a.
Of or pertaining to an artery, or the arteries; as, arterial action; the arterial system.
a.
Of or pertaining to a father; fatherly; showing the disposition of a father; guiding or instructing as a father; as, paternal care.
a.
Consisting of matter; not spiritual; corporeal; physical; as, material substance or bodies.
a.
See Manorial.
a.
Having a body; consisting of, or pertaining to, a material body or substance; material; -- opposed to spiritual or immaterial.
a.
Of or pertaining to a lover or to love making; amatory; as, amatorial verses.
a.
Received or derived from a father; hereditary; as, a paternal estate.
a.
Growing, forming, or existing in the air, as opposed to growing or existing in earth or water, or underground; as, aerial rootlets, aerial plants.
a.
Of or pertaining to a mother; becoming to a mother; motherly; as, maternal love; maternal tenderness.
a.
Directed to the side; as, a lateral view of a thing.
a.
Rising aloft in air; high; lofty; as, aerial spires.
n.
A patrial noun. Thus Romanus, a Roman, and Troas, a woman of Troy, are patrial nouns, or patrials.
n.
That in a complex system which constitutes the materials, or instruments employed, in distinction from the personnel, or men; as, the baggage, munitions, provisions, etc., of an army; or the buildings, libraries, and apparatus of a college, in distinction from its officers.
n.
The substance or matter of which anything is made or may be made.
a.
Of or pertaining to the sides; as, the lateral walls of a house; the lateral branches of a tree.
v. t.
To form from matter; to materialize.