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Weak Analogy (Formal)

Also Known As: Faulty Analogy False Analogy
Informal Fallacy ID: argument_from_analogy_fallacy

Definition

An informal fallacy where an argument relies on an analogy between two cases that are not sufficiently similar in the relevant respects. While analogies can be useful, they become fallacious when the dissimilarities outweigh the similarities for the conclusion being drawn.

Examples

Running a country is like running a business. Therefore, a successful CEO would make a great president.

The brain is just like a computer, so we should be able to simply 'reprogram' people with mental illness the way we update buggy software.

A sports team needs a strong captain to win championships, so what this country needs is a strong, authoritarian leader — democracy just slows things down.

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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Similar(A,B) ∧ P(A) ⇒ P(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

    Does the argument draw a comparison between two things to transfer a property from one to the other?

    Type: binary
  2. 2

    Are the two things being compared dissimilar in ways relevant to the conclusion?

    Type: binary
  3. 3

    Does the argument ignore critical differences that would undermine the analogy?

    Type: binary
  4. 4

    Is the conclusion presented as established rather than merely suggested by the analogy?

    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 Informal Fallacies

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