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Fallacy of Exclusive Premises

Also Known As: Fallacy of Two Negative Premises
Formal Fallacy ID: exclusive_premises

Definition

The fallacy of exclusive premises occurs in a categorical syllogism when both premises are negative. From two negative premises, no valid conclusion can be drawn because negative premises only tell us about exclusion relationships, providing no positive link through which the minor and major terms can be connected. The middle term fails to bridge the other two terms when both premises deny a connection.

Examples

"No fish are mammals. No mammals are reptiles. Therefore, no fish are reptiles." (While the conclusion happens to be true, it does not follow logically from the premises, because two negative premises cannot establish a valid conclusion.)

'No politicians are infallible. No infallible beings are human. Therefore, no politicians are human.' (Both premises are negative; even though the conclusion is false and obviously so, it illustrates that two negative premises cannot yield any valid conclusion.)

'No social media posts are private communications. No private communications are public broadcasts. Therefore, no social media posts are public broadcasts.' (The conclusion does not logically follow from two negative premises, even if it might seem intuitively plausible.)

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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No A are B; No B are C; therefore [invalid conclusion about A and C]
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

    Are both premises of the syllogism negative (containing 'no' or 'not')?

    Type: binary
  2. 2

    Is a conclusion being drawn from two negative premises?

    Type: binary
  3. 3

    Could a valid connection between the terms be established with only negative premises?

    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

→ is a Formal Fallacies

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