Proof by example¶

The invalid inference that a universal claim has been proved merely by exhibiting one or several favorable instances.

Version: v1 · 2026-09-08 · History
Domain-specific #: 6247
Origin domain: informal logic
Subdomain: informal logic

Core Idea¶

Proof by example treats confirming cases as sufficient for a universally quantified conclusion even though one counterexample would refute it and exhaustive coverage has not been shown. Salient instances make the conclusion seem plausible, and the reasoner silently replaces the universal quantifier with an existential or sampled claim. The abstraction is therefore identified by a declared carrier, a transformation or constraint over that carrier, and an invariant that tells an analyst whether the named structure is genuinely present.

The load-bearing residual is not the broad topic of informal logic. It is the domain-specific identity determined by a nonexhaustive set of instances is offered as conclusive support for a universal proposition without a valid general argument.

Scope of Application¶

Proof by example belongs to informal logic and is useful where the analyst can specify the typed informal logic carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, then evaluate a nonexhaustive set of instances is offered as conclusive support for a universal proposition without a valid general argument. The scope is broad within that domain but bounded by the need for a nonexhaustive set of instances is offered as conclusive support for a universal proposition without a valid general argument. The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.

Clarity¶

The abstraction clarifies a crowded vocabulary by making a nonexhaustive set of instances is offered as conclusive support for a universal proposition without a valid general argument the center of the account. A claim should name the carrier, the governing operation or relation, the applicable assumptions, and the recognition test. A bare label is insufficient because the name Proof by example can be used for a formal identity, an implementation, or a neighboring result unless carrier and convention are stated.

Manages Complexity¶

Without the abstraction, an analyst must reason directly over many local details: the carrier roles, admissibility assumptions, competing conventions, derived invariants, boundary cases, and proof or validation obligations specific to Proof by example. Proof by example compresses them into the roles in the structural signature. That compression permits comparison across instances without erasing the variables that determine validity. It also exposes which details may be varied safely and which are constitutive.

Abstract Reasoning¶

Identify the carrier. State what the elements, states, objects, or observations are: the typed informal logic carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets. Reject examples whose alleged carrier belongs to a different problem. 2. Lock the constitutive rule. Express a nonexhaustive set of instances is offered as conclusive support for a universal proposition without a valid general argument independently of one notation or implementation.

Knowledge Transfer¶

Knowledge transfers strongly among subfields of informal logic because they reuse the typed informal logic carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, Salient instances make the conclusion seem plausible, and the reasoner silently replaces the universal quantifier with an existential or sampled claim., and type the carrier, state every parameter and convention in the definition, test that a nonexhaustive set of instances is offered as conclusive support for a universal proposition without a valid general argument, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.

Relationships to Other Abstractions¶

Current abstraction Proof by example Domain-specific

Parents (1) — more general patterns this builds on

Proof by example is a kind of Informal Fallacy Prime

The proposed strict upward parent is prime:informal_fallacy.

Hierarchy path (1) — routes to 1 parentless root

Proof by example → Informal Fallacy

Neighborhood in Abstraction Space¶

Proof by example sits in a crowded region of the domain-specific corpus (8^th percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.

Family — Truth, Semantics & Logical Systems (18 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-09-08