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Affirming a Disjunct

Also Known As: Affirming One Disjunct Fallacy of the Alternative Disjunct
Formal Fallacy ID: affirming_disjunct

Definition

Affirming a disjunct is a formal fallacy that occurs with inclusive disjunctions (OR statements). Given 'A or B' and knowing A is true, the fallacy concludes that B must be false. This is invalid because 'or' in logic is inclusive by default -- both A and B can be true simultaneously. The error lies in treating an inclusive 'or' as exclusive.

Examples

"She's either at the library or at the coffee shop. I just confirmed she's at the library. Therefore, she's definitely not at the coffee shop." (She could have been at both at different times, or the statement could allow both.)

The ad says 'Buy our juice for vitamins or great taste!' A customer thinks: 'I bought it for the vitamins, so it definitely can't also taste great.' But both could be true simultaneously — the disjunction doesn't exclude the other option just because one is confirmed.

A manager tells the team: 'We'll succeed if we cut costs or improve quality.' After cutting costs, a colleague concludes: 'We cut costs, so improving quality is now off the table.' In reality, both strategies could be pursued at the same time.

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 OR B; A; therefore NOT B
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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Not formally decidable

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

    Is a disjunction (or-statement) being used as a premise?

    Type: binary
  2. 2

    Is the truth of one disjunct being used to conclude the other is false?

    Type: binary
  3. 3

    Is the 'or' being treated as exclusive when it could be inclusive?

    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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Related Aspects

← related to
Denying a Conjunct

Denying a conjunct is a formal fallacy that occurs when, from the premise that a conjunction is false (not both A and B), and the premise that one conjunct is false, it is concluded that the other conjunct must be true. This confuses the logical conjunction (AND) with the exclusive disjunction (XOR). If 'not both A and B' is true, denying A only tells us the conjunction fails — it does not tell us anything about B, which could be either true or false.

Hierarchical Context

→ is a Formal Fallacies

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