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EXISTENTIAL GENERALIZATION

  • Existential generalization
  • Rule of inference in predicate logic

    In predicate logic, existential generalization (also known as existential introduction, ∃I) is a valid rule of inference that allows one to move from

    Existential generalization

    Existential_generalization

  • Existential quantification
  • Mathematical use of "there exists"

    In predicate logic, an existential quantification is a type of quantifier which asserts the existence of an object with a given property. It is usually

    Existential quantification

    Existential_quantification

  • Universal generalization
  • Rule of inference in predicate logic

    have no free variables. First-order logic Hasty generalization Universal instantiation Existential generalization Copi and Cohen Hurley Moore and Parker

    Universal generalization

    Universal_generalization

  • Existential instantiation
  • Rule of inference in predicate logic

    constant symbol that has not appeared in the proof. Existential fallacy Existential generalization List of rules of inference Universal instantiation Hurley

    Existential instantiation

    Existential_instantiation

  • Faulty generalization
  • Conclusion made on the basis of one or few instances of a phenomenon

    A faulty generalization is an informal fallacy wherein a conclusion is drawn about all or many instances of a phenomenon on the basis of one or a few instances

    Faulty generalization

    Faulty_generalization

  • Rule of inference
  • Method of deriving conclusions

    modus tollens, disjunctive syllogism, constructive dilemma, and existential generalization. Rules of inference include rules of implication, which operate

    Rule of inference

    Rule of inference

    Rule_of_inference

  • Proof by example
  • Erroneous method of proof

    the logical rule known as existential introduction, also known as particularisation or existential generalization: Existential Introduction φ ( β / α )

    Proof by example

    Proof_by_example

  • Distributive property
  • Property involving two mathematical operations

    In mathematics, the distributive property of binary operations is a generalization of the distributive law, which asserts that the equality x ⋅ ( y + z

    Distributive property

    Distributive_property

  • De Morgan's laws
  • Pair of logical equivalences

    generalised to quantifiers, so for example the universal quantifier and existential quantifier are duals: ∀ x P ( x ) ≡ ¬ [ ∃ x ¬ P ( x ) ] ∃ x P ( x ) ≡

    De Morgan's laws

    De Morgan's laws

    De_Morgan's_laws

  • Modus ponens
  • Rule of logical inference

    _{P}^{A}} is absolute TRUE. Hence, subjective logic deduction represents a generalization of both modus ponens and the Law of total probability. Philosophers

    Modus ponens

    Modus_ponens

  • Associative property
  • Property of a mathematical operation

    implication Exportation Tautology Predicate logic Rules of inference Universal generalization / instantiation Existential generalization / instantiation v t e

    Associative property

    Associative property

    Associative_property

  • Double negation
  • Propositional logic theorem

    implication Exportation Tautology Predicate logic Rules of inference Universal generalization / instantiation Existential generalization / instantiation v t e

    Double negation

    Double_negation

  • Modus tollens
  • Rule of logical inference

    law of total probability combined with Bayes' theorem represents a generalization of modus tollens. Modus tollens represents an instance of the abduction

    Modus tollens

    Modus_tollens

  • Hypothetical syllogism
  • Syllogism with conditional premise(s)

    implication Exportation Tautology Predicate logic Rules of inference Universal generalization / instantiation Existential generalization / instantiation v t e

    Hypothetical syllogism

    Hypothetical_syllogism

  • List of fallacies
  • grouped under headings such as relevance, ambiguity, presumption, faulty generalization, and faulty causal reasoning, although the classification and boundaries

    List of fallacies

    List_of_fallacies

  • List of rules of inference
  • quantifying a variable occurring in β {\displaystyle \beta } . Existential Generalization (or Existential Introduction) φ ( β / α ) _ {\displaystyle {\underline

    List of rules of inference

    List_of_rules_of_inference

  • Axiom
  • Statement that is taken to be true

    itself. Aside from this, we can also have existential generalization: Axiom scheme for existential generalization. Given a formula ϕ {\displaystyle \phi

    Axiom

    Axiom

    Axiom

  • Disjunctive syllogism
  • Logical rule of inference

    implication Exportation Tautology Predicate logic Rules of inference Universal generalization / instantiation Existential generalization / instantiation v t e

    Disjunctive syllogism

    Disjunctive_syllogism

  • Material implication (rule of inference)
  • Rule of replacement in propositional logic

    implication Exportation Tautology Predicate logic Rules of inference Universal generalization / instantiation Existential generalization / instantiation v t e

    Material implication (rule of inference)

    Material_implication_(rule_of_inference)

  • Universal instantiation
  • Rule of inference in predicate logic

    According to Willard Van Orman Quine, universal instantiation and existential generalization are two aspects of a single principle, for instead of saying that

    Universal instantiation

    Universal_instantiation

  • Existential fallacy
  • Type of formal fallacy

    The existential fallacy, or existential instantiation, is a formal fallacy. In the existential fallacy, one presupposes that a class has members when one

    Existential fallacy

    Existential_fallacy

  • Destructive dilemma
  • Rule of inference of propositional logic

    implication Exportation Tautology Predicate logic Rules of inference Universal generalization / instantiation Existential generalization / instantiation v t e

    Destructive dilemma

    Destructive_dilemma

  • Exportation (logic)
  • Rule of replacement in propositional logic

    implication Exportation Tautology Predicate logic Rules of inference Universal generalization / instantiation Existential generalization / instantiation v t e

    Exportation (logic)

    Exportation_(logic)

  • Contraposition
  • Mathematical logic concept

    propositions), and their existential impact is dependent upon further propositions where quantification existence is instantiated (existential instantiation),

    Contraposition

    Contraposition

  • Absorption (logic)
  • implication Exportation Tautology Predicate logic Rules of inference Universal generalization / instantiation Existential generalization / instantiation v t e

    Absorption (logic)

    Absorption_(logic)

  • Tautology (rule of inference)
  • Commonly used rules of replacement in propositional logic

    implication Exportation Tautology Predicate logic Rules of inference Universal generalization / instantiation Existential generalization / instantiation v t e

    Tautology (rule of inference)

    Tautology_(rule_of_inference)

  • David Kaplan (philosopher)
  • American philosopher and logician

    (Ungerade, or oblique) discourse, such as substitution failure, existential generalization failure, and the distinction between de re / de dicto propositional

    David Kaplan (philosopher)

    David_Kaplan_(philosopher)

  • Empty domain
  • Concept in first-order logic

    with an existential quantifier is assigned the value falsehood. This follows from the idea that existentially quantified statements have existential import

    Empty domain

    Empty domain

    Empty_domain

  • Disjunction elimination
  • Rule of inference of propositional logic

    implication Exportation Tautology Predicate logic Rules of inference Universal generalization / instantiation Existential generalization / instantiation v t e

    Disjunction elimination

    Disjunction_elimination

  • Free logic
  • Form of logic

    Similar modifications are made to other theorems with existential import (e.g. existential generalization becomes A ( r ) → ( E ! r → ∃ x A ( x ) ) {\displaystyle

    Free logic

    Free_logic

  • Conjunction introduction
  • Rule of inference in propositional logic

    implication Exportation Tautology Predicate logic Rules of inference Universal generalization / instantiation Existential generalization / instantiation v t e

    Conjunction introduction

    Conjunction_introduction

  • First-order logic
  • Type of logical system

    "There exists x such that x is a philosopher and x is not a scholar". The existential quantifier "there exists" expresses the idea that the claim "x is a philosopher

    First-order logic

    First-order_logic

  • Conjunction elimination
  • Inference rule in logic

    implication Exportation Tautology Predicate logic Rules of inference Universal generalization / instantiation Existential generalization / instantiation v t e

    Conjunction elimination

    Conjunction_elimination

  • Negation introduction
  • Logical rule of inference

    implication Exportation Tautology Predicate logic Rules of inference Universal generalization / instantiation Existential generalization / instantiation v t e

    Negation introduction

    Negation_introduction

  • Disjunction introduction
  • Inference introducing a disjunction in logical proofs

    implication Exportation Tautology Predicate logic Rules of inference Universal generalization / instantiation Existential generalization / instantiation v t e

    Disjunction introduction

    Disjunction_introduction

  • Biconditional introduction
  • Inference in propositional logic

    implication Exportation Tautology Predicate logic Rules of inference Universal generalization / instantiation Existential generalization / instantiation v t e

    Biconditional introduction

    Biconditional_introduction

  • No true Scotsman
  • Logical fallacy

    Bradley Dowden explains the fallacy as an "ad hoc rescue" of a refuted generalization attempt. The following is a simplified rendition of the fallacy: Person

    No true Scotsman

    No_true_Scotsman

  • Straw man
  • Form of incorrect argument and informal fallacy

    point out the similarity of the selection form to the fallacy of hasty generalization, in which the refutation of an opposing position that is weaker than

    Straw man

    Straw man

    Straw_man

  • Propositional logic
  • Branch of logic

    Conceptual graph Disjunctive syllogism Entitative graph Equational logic Existential graph Implicational propositional calculus Intuitionistic propositional

    Propositional logic

    Propositional_logic

  • Modus ponendo tollens
  • Logical rule of inference

    implication Exportation Tautology Predicate logic Rules of inference Universal generalization / instantiation Existential generalization / instantiation v t e

    Modus ponendo tollens

    Modus_ponendo_tollens

  • Willard Van Orman Quine
  • American philosopher and logician (1908–2000)

    inquiry that a thorough re-examination of the two inferences [existential generalization and universal instantiation] may prove worth our while. Lejewski

    Willard Van Orman Quine

    Willard Van Orman Quine

    Willard_Van_Orman_Quine

  • Biconditional elimination
  • Inference in propositional logic

    implication Exportation Tautology Predicate logic Rules of inference Universal generalization / instantiation Existential generalization / instantiation v t e

    Biconditional elimination

    Biconditional_elimination

  • Godwin's law
  • Internet adage about Nazi comparisons

    from fallacy Masked man Mathematical fallacy In quantificational logic Existential Illicit conversion Proof by example Quantifier shift Syllogistic fallacy

    Godwin's law

    Godwin's_law

  • Ad hominem
  • Attacking the person rather than their argument

    Division Ecological Secundum quid Accident Converse accident Faulty generalization Anecdotal evidence Sampling bias Cherry picking McNamara Base rate /

    Ad hominem

    Ad_hominem

  • Constructive dilemma
  • Rule of inference of propositional logic

    implication Exportation Tautology Predicate logic Rules of inference Universal generalization / instantiation Existential generalization / instantiation v t e

    Constructive dilemma

    Constructive_dilemma

  • Begging the question
  • Logic founded on unproven premises

    Division Ecological Secundum quid Accident Converse accident Faulty generalization Anecdotal evidence Sampling bias Cherry picking McNamara Base rate /

    Begging the question

    Begging_the_question

  • Motte-and-bailey fallacy
  • Type of informal fallacy

    Division Ecological Secundum quid Accident Converse accident Faulty generalization Anecdotal evidence Sampling bias Cherry picking McNamara Base rate /

    Motte-and-bailey fallacy

    Motte-and-bailey_fallacy

  • Correlation does not imply causation
  • Refutation of a logical fallacy

    Division Ecological Secundum quid Accident Converse accident Faulty generalization Anecdotal evidence Sampling bias Cherry picking McNamara Base rate /

    Correlation does not imply causation

    Correlation does not imply causation

    Correlation_does_not_imply_causation

  • Conditional proof
  • Formal proof

    implication Exportation Tautology Predicate logic Rules of inference Universal generalization / instantiation Existential generalization / instantiation v t e

    Conditional proof

    Conditional_proof

  • Burzio's generalization
  • Concept in linguistics

    In generative linguistics, Burzio's generalization is the observation that a verb can assign a theta role (a title used to describe the relationship between

    Burzio's generalization

    Burzio's_generalization

  • Reification (fallacy)
  • Fallacy of treating an abstraction as if it were a real thing

    from fallacy Masked man Mathematical fallacy In quantificational logic Existential Illicit conversion Proof by example Quantifier shift Syllogistic fallacy

    Reification (fallacy)

    Reification_(fallacy)

  • Post hoc ergo propter hoc
  • Fallacy of assumption of causation based on sequence of events

    from fallacy Masked man Mathematical fallacy In quantificational logic Existential Illicit conversion Proof by example Quantifier shift Syllogistic fallacy

    Post hoc ergo propter hoc

    Post_hoc_ergo_propter_hoc

  • Marina Palei
  • Russian-Dutch writer and poet

    The motif of homelessness and insecurity, always going to the existential generalization, also has been reflected in her works. In 1972, Paley began studying

    Marina Palei

    Marina Palei

    Marina_Palei

  • Base rate fallacy
  • Logic error due to ignoring the base rate

    from fallacy Masked man Mathematical fallacy In quantificational logic Existential Illicit conversion Proof by example Quantifier shift Syllogistic fallacy

    Base rate fallacy

    Base rate fallacy

    Base_rate_fallacy

  • Conjunction fallacy
  • Formal fallacy, aka Linda Problem

    from fallacy Masked man Mathematical fallacy In quantificational logic Existential Illicit conversion Proof by example Quantifier shift Syllogistic fallacy

    Conjunction fallacy

    Conjunction_fallacy

  • Argument from ignorance
  • Informal fallacy

    Division Ecological Secundum quid Accident Converse accident Faulty generalization Anecdotal evidence Sampling bias Cherry picking McNamara Base rate /

    Argument from ignorance

    Argument from ignorance

    Argument_from_ignorance

  • Glossary of logic
  • logics, that asserts the existence of the referent of a constant. existential generalization A rule of inference allowing the conclusion that something exists

    Glossary of logic

    Glossary_of_logic

  • Circular reasoning
  • Logical fallacy in which the conclusion provides the premise

    Division Ecological Secundum quid Accident Converse accident Faulty generalization Anecdotal evidence Sampling bias Cherry picking McNamara Base rate /

    Circular reasoning

    Circular reasoning

    Circular_reasoning

  • Texas sharpshooter fallacy
  • Statistical fallacy

    from fallacy Masked man Mathematical fallacy In quantificational logic Existential Illicit conversion Proof by example Quantifier shift Syllogistic fallacy

    Texas sharpshooter fallacy

    Texas sharpshooter fallacy

    Texas_sharpshooter_fallacy

  • Argument from authority
  • Logical fallacy

    from fallacy Masked man Mathematical fallacy In quantificational logic Existential Illicit conversion Proof by example Quantifier shift Syllogistic fallacy

    Argument from authority

    Argument_from_authority

  • Quantifier (logic)
  • Mathematical use of "for all" and "there exists"

    numbers domain, but false for the integer domain. On the other hand, the existential quantifier ∃ {\displaystyle \exists } in the formula ∃ x x 2 − 5 x +

    Quantifier (logic)

    Quantifier_(logic)

  • Affirming the consequent
  • Type of fallacious argument (logical fallacy)

    Division Ecological Secundum quid Accident Converse accident Faulty generalization Anecdotal evidence Sampling bias Cherry picking McNamara Base rate /

    Affirming the consequent

    Affirming_the_consequent

  • Loaded question
  • Question containing an unjustified assumption

    from fallacy Masked man Mathematical fallacy In quantificational logic Existential Illicit conversion Proof by example Quantifier shift Syllogistic fallacy

    Loaded question

    Loaded_question

  • Formal fallacy
  • Faulty deductive reasoning due to a logical flaw

    from fallacy Masked man Mathematical fallacy In quantificational logic Existential Illicit conversion Proof by example Quantifier shift Syllogistic fallacy

    Formal fallacy

    Formal_fallacy

  • Gambler's fallacy
  • Mistakenly drawing statistical inference from independent events

    Division Ecological Secundum quid Accident Converse accident Faulty generalization Anecdotal evidence Sampling bias Cherry picking McNamara Base rate /

    Gambler's fallacy

    Gambler's_fallacy

  • Association fallacy
  • Formal fallacy

    from fallacy Masked man Mathematical fallacy In quantificational logic Existential Illicit conversion Proof by example Quantifier shift Syllogistic fallacy

    Association fallacy

    Association_fallacy

  • Slippery slope
  • Rhetorical argument

    Division Ecological Secundum quid Accident Converse accident Faulty generalization Anecdotal evidence Sampling bias Cherry picking McNamara Base rate /

    Slippery slope

    Slippery slope

    Slippery_slope

  • Argument from incredulity
  • Informal logical fallacy

    from fallacy Masked man Mathematical fallacy In quantificational logic Existential Illicit conversion Proof by example Quantifier shift Syllogistic fallacy

    Argument from incredulity

    Argument_from_incredulity

  • Sorites paradox
  • Logical paradox from vague predicates

    vague; moreover, representations of propositions are vague. A formal generalization of the paradoxical sorites argument is as follows: F a 1 {\displaystyle

    Sorites paradox

    Sorites paradox

    Sorites_paradox

  • Anecdotal evidence
  • Evidence relying on personal testimony

    conclusion rather than a logical conclusion, it is considered a faulty generalization. In medicine, anecdotal evidence may be subject to the placebo effect

    Anecdotal evidence

    Anecdotal_evidence

  • Equivocation
  • Misleading use of a term with multiple meanings

    Division Ecological Secundum quid Accident Converse accident Faulty generalization Anecdotal evidence Sampling bias Cherry picking McNamara Base rate /

    Equivocation

    Equivocation

  • Fallacy of composition
  • Fallacy of inferring on the whole from a part

    parts. The fallacy of composition is related to the fallacy of hasty generalization, in which an unwarranted inference is made from a statement about a

    Fallacy of composition

    Fallacy_of_composition

  • Secundum quid
  • Informal fallacy

    or fails to recognize the difference between rules of thumb (soft generalizations, heuristics that hold true as a general rule but leave room for exceptions)

    Secundum quid

    Secundum_quid

  • Tu quoque
  • Fallacy regarding hypocrisy

    from fallacy Masked man Mathematical fallacy In quantificational logic Existential Illicit conversion Proof by example Quantifier shift Syllogistic fallacy

    Tu quoque

    Tu_quoque

  • Poisoning the well
  • Type of informal fallacy

    Division Ecological Secundum quid Accident Converse accident Faulty generalization Anecdotal evidence Sampling bias Cherry picking McNamara Base rate /

    Poisoning the well

    Poisoning the well

    Poisoning_the_well

  • False equivalence
  • Logical fallacy of inconsistency

    Division Ecological Secundum quid Accident Converse accident Faulty generalization Anecdotal evidence Sampling bias Cherry picking McNamara Base rate /

    False equivalence

    False equivalence

    False_equivalence

  • Modus non excipiens
  • implication Exportation Tautology Predicate logic Rules of inference Universal generalization / instantiation Existential generalization / instantiation v t e

    Modus non excipiens

    Modus_non_excipiens

  • Sampling bias
  • Bias in the sampling of a population

    from fallacy Masked man Mathematical fallacy In quantificational logic Existential Illicit conversion Proof by example Quantifier shift Syllogistic fallacy

    Sampling bias

    Sampling bias

    Sampling_bias

  • Stimulus control
  • Key tenet of behavioral analysis

    wavelengths. This procedure yielded sharper generalization gradients than did the simple generalization procedure used in the first procedure. In addition

    Stimulus control

    Stimulus_control

  • Availability heuristic
  • Bias towards recently acquired information

    Division Ecological Secundum quid Accident Converse accident Faulty generalization Anecdotal evidence Sampling bias Cherry picking McNamara Base rate /

    Availability heuristic

    Availability_heuristic

  • Denying the antecedent
  • Logical fallacy

    Division Ecological Secundum quid Accident Converse accident Faulty generalization Anecdotal evidence Sampling bias Cherry picking McNamara Base rate /

    Denying the antecedent

    Denying_the_antecedent

  • Naturalistic fallacy
  • Purported fallacy in explaining good reductively

    from fallacy Masked man Mathematical fallacy In quantificational logic Existential Illicit conversion Proof by example Quantifier shift Syllogistic fallacy

    Naturalistic fallacy

    Naturalistic_fallacy

  • Ad nauseam
  • Discussion that has continued to the point of nausea

    Division Ecological Secundum quid Accident Converse accident Faulty generalization Anecdotal evidence Sampling bias Cherry picking McNamara Base rate /

    Ad nauseam

    Ad_nauseam

  • Universal algebra
  • Theory of algebraic structures in general

    including universal quantification (∀) except before an equation, and existential quantification (∃) logical connectives other than conjunction (∧) relations

    Universal algebra

    Universal_algebra

  • Just-world fallacy
  • Idea that everyone faces consequence as they deserve

    Division Ecological Secundum quid Accident Converse accident Faulty generalization Anecdotal evidence Sampling bias Cherry picking McNamara Base rate /

    Just-world fallacy

    Just-world_fallacy

  • Mathematical fallacy
  • Certain type of mistaken proof

    Division Ecological Secundum quid Accident Converse accident Faulty generalization Anecdotal evidence Sampling bias Cherry picking McNamara Base rate /

    Mathematical fallacy

    Mathematical_fallacy

  • Alternating Turing machine
  • Abstract computation model

    problem, which is a generalization of the Boolean satisfiability problem in which each variable can be bound by either an existential or a universal quantifier

    Alternating Turing machine

    Alternating_Turing_machine

  • Argumentum ad populum
  • Fallacy of claiming the majority is always correct

    from fallacy Masked man Mathematical fallacy In quantificational logic Existential Illicit conversion Proof by example Quantifier shift Syllogistic fallacy

    Argumentum ad populum

    Argumentum_ad_populum

  • Inductivism
  • Traditional, still commonplace view of scientific method to develop scientific theories

    verifiability criterion implies that existential generalizations are meaningful, but that universal generalizations are not, even though they include general

    Inductivism

    Inductivism

  • Argument to moderation
  • Informal fallacy that the truth is always a compromise

    from fallacy Masked man Mathematical fallacy In quantificational logic Existential Illicit conversion Proof by example Quantifier shift Syllogistic fallacy

    Argument to moderation

    Argument_to_moderation

  • Reductio ad Hitlerum
  • Logical fallacy

    Division Ecological Secundum quid Accident Converse accident Faulty generalization Anecdotal evidence Sampling bias Cherry picking McNamara Base rate /

    Reductio ad Hitlerum

    Reductio ad Hitlerum

    Reductio_ad_Hitlerum

  • Universal quantification
  • Mathematical use of "for all"

    sometimes by "(x)" alone). Universal quantification is distinct from existential quantification ("there exists"), which only asserts that the property

    Universal quantification

    Universal_quantification

  • Descriptivist theory of names
  • Theory in philosophy of language

    turn, be reduced, to a certain very specific logical form of existential generalization as follows: "The king of France is bald." becomes ∃ x ( K ( x

    Descriptivist theory of names

    Descriptivist_theory_of_names

  • In-group favoritism
  • Psychological bias towards favoring members of one's in-group

    from fallacy Masked man Mathematical fallacy In quantificational logic Existential Illicit conversion Proof by example Quantifier shift Syllogistic fallacy

    In-group favoritism

    In-group_favoritism

  • Tone policing
  • Distraction technique and anti-debate tactic

    from fallacy Masked man Mathematical fallacy In quantificational logic Existential Illicit conversion Proof by example Quantifier shift Syllogistic fallacy

    Tone policing

    Tone_policing

  • Sealioning
  • Type of trolling or harassment

    Division Ecological Secundum quid Accident Converse accident Faulty generalization Anecdotal evidence Sampling bias Cherry picking McNamara Base rate /

    Sealioning

    Sealioning

  • Informal fallacy
  • Form of incorrect argument in natural language

    fallacies of generalization, the false premise is due to an erroneous generalization. In the case of the fallacy of sweeping generalization, a general rule

    Informal fallacy

    Informal fallacy

    Informal_fallacy

  • Rage-baiting
  • Internet rage incitement technique

    Division Ecological Secundum quid Accident Converse accident Faulty generalization Anecdotal evidence Sampling bias Cherry picking McNamara Base rate /

    Rage-baiting

    Rage-baiting

    Rage-baiting

  • Argument from fallacy
  • Fallacy that since an argument contains a logical fallacy, its conclusion must be false

    from fallacy Masked man Mathematical fallacy In quantificational logic Existential Illicit conversion Proof by example Quantifier shift Syllogistic fallacy

    Argument from fallacy

    Argument_from_fallacy

  • Overwhelming exception
  • Informal fallacy of generalization

    An overwhelming exception is an informal fallacy of generalization. It is a generalization that is accurate, but comes with one or more qualifications

    Overwhelming exception

    Overwhelming_exception

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