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Fallacy of the Consequent

Also Known As: Consequent Fallacy
Formal Fallacy ID: fallacy_of_the_consequent

Definition

A broad category of formal fallacies involving incorrect reasoning about the consequent of a conditional statement. It encompasses both affirming the consequent and related errors where the logical role of the consequent is mishandled.

Examples

If a person is a genius, they passed the test. John passed the test. Therefore, John is a genius.

If there is a gas leak, the carbon monoxide detector will go off. The carbon monoxide detector is going off. Therefore, there must be a gas leak. (Affirms the consequent — the alarm could be triggered by a malfunction, low battery, or other gas sources.)

If a student cheated on the exam, their score would improve dramatically. Maria's score improved dramatically. Therefore, Maria must have cheated. (Affirming the consequent — many legitimate explanations, such as extra study or reduced anxiety, could account for the improvement.)

Formal Logic Pattern
FOL Pattern
The First-Order Logic formula representing this reasoning pattern's logical structure.
FOL (First-Order Logic) uses quantifiers (∀ = for all, ∃ = there exists), connectives (∧ = and, ∨ = or, ⇒ = implies, ¬ = not), and predicates to capture the essential form of a reasoning pattern. For example, the Ad Hominem fallacy: Person(x) ∧ HasFlaw(x) ⇒ Invalid(Claim(x)). These patterns allow automated verification of logical validity.
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(A ⇒ B) ∧ B ⇒ A (variant with negation chains)
Formal Verification:
Formal Verification
Checks whether a reasoning pattern is logically valid or invalid using an automated theorem prover.
Formal verification uses an SMT (Satisfiability Modulo Theories) solver — specifically Z3 — to mathematically check whether an argument's logical structure is valid. Each reasoning pattern is translated into First-Order Logic and tested: Can the premises be true while the conclusion is false? If yes, it's formally invalid. If no, it's formally valid. Many real-world patterns (analogies, heuristics) cannot be fully captured in formal logic — these are marked as not formally decidable, which doesn't mean they're wrong.
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Formally invalid

Verification Steps
Verification Steps
Binary yes/no questions that an AI must answer to detect a reasoning pattern in a text.
Each of the 452 aspects has verification steps — simple yes/no questions designed to systematically detect whether a pattern appears in a text. For ad hominem: "Does the argument attack a person rather than their claim?" For false dichotomy: "Are only two options presented when more exist?" This ensures consistent, reproducible analysis.
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Binary (yes/no) questions an LLM must answer to identify this aspect:

  1. 1

    Does the argument contain a conditional premise?

    Type: binary
  2. 2

    Does the argument confuse the consequent with the antecedent in drawing its conclusion?

    Type: binary
  3. 3

    Is the conclusion drawn by incorrectly manipulating the conditional relationship?

    Type: binary
Deep Dive
The expandable detail section on each aspect page with examples, psychology, and counter-strategies.
The Deep Dive section provides in-depth information about each aspect: a real-world example showing the pattern in action, an explanation of why it works psychologically, practical advice on how to counter it, alternative names, and links to related aspects.
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Hierarchical Context

→ sub type of Formal Fallacies

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⚗️ Argument Lab

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