← Back to catalogue
Research draft

logical contradiction

vr.tr.logical-contradiction · XCT.QLT

Let an agent recognise and explain logical contradictions, distinguish them from paradoxes, contraries, inconsistencies and rhetorical tension, apply consistency checks to arguments and data, and present contested uses such as debates over texts with attribution.

Thing Registry Cross-cutting context

Research draft, second pass

A second pass drafted this model: the structure a model of this thing needs, and what is known about it in the world. The line under this one says how the second half was obtained - researched against sources, or recalled without web access, in which case nothing here was read anywhere and every claim is a lead to verify. Unreviewed either way.

written by Claude from model knowledge without web access - no source was read, every claim is a lead to verify

Researched by: Claude

Purpose and description

Let an agent recognise and explain logical contradictions, distinguish them from paradoxes, contraries, inconsistencies and rhetorical tension, apply consistency checks to arguments and data, and present contested uses such as debates over texts with attribution.

A statement or set of statements that cannot all be true at once, such as a proposition asserted together with its negation; in logic a contradiction is false under every interpretation, and detecting contradictions is central to reasoning, argument, law and the checking of theories and data.

What it is for: Not for anything; a property of statements.

It can be test whether statements contradict each other; explain the concept with formal and informal examples; distinguish contradiction from paradox and vagueness; check arguments and data for consistency.

Distinguishing features

Cannot all be true together

In classical logic implies anything, hence the need to avoid it

Distinct from paradox, contrary and mere disagreement

Used as a test in proofs, law and data validation

What it looks like

Not visible; expressed in language or formal notation.

How it is recognised

A statement and its negation both asserted

False under every interpretation in classical logic

A paradox is an apparently sound argument to a contradiction; a contrary pair can both be false

Related models

is a kind of - the strongest form

inconsistency

is confused with - a paradox leads to a contradiction by apparently good reasoning

paradox

is used in - a proof method

proof by contradiction

is studied by - the discipline

logic

In practice

Families and kinds

formal contradictions in logic

contradictio in adjecto within a phrase

performative contradictions

inconsistencies in law and pleadings

antinomies in philosophy

alleged contradictions in texts, which are contested claims

Standards and regulation

No regulation; rules of procedure address inconsistent pleadings in some legal systems

Failure modes and hazards

Calling disagreement or vagueness a contradiction

Explosion in inconsistent formal systems

Presenting contested textual claims as settled

Also called

alternative pleadingContradictio in adjectoInternal consistency of the Bibleantinomyperformative contradictionlegal antinomyKant's antinomies

Where this came from

wikidata · CC0 1.0

Source repository Registry entry point

Drafted structure

Bundle to layer to finding to question, as the second pass will find it: 4 bundles · 8 layers · 8 findings · 16 questions.

Concept What a contradiction is.

Definition.

Definition

Definition.

Definition

Definition.

  1. What makes a set of statements contradictory, formally and informally? definition
  2. Is the case a contradiction, a paradox, a contrary pair or vagueness? boundary

Kinds

Kinds.

Kinds

Kinds.

  1. What kinds of contradiction are distinguished in logic, rhetoric and law? definition
  2. Which entry fits paradox? action
Detect Finding contradictions.

Checking.

Arguments

In arguments.

Arguments

Arguments.

  1. How is an argument or theory checked for consistency? action
  2. Which method or tool is used, and what does it prove? measurement

Data

In data and rules.

Data

Data.

  1. How are contradictions found in data sets, specifications and rule systems? action
  2. Which entry fits data validation? action
Theory Logic and philosophy.

Theory.

Logic

Formal treatment.

Logic

Logic.

  1. How do classical and paraconsistent logics treat contradiction, and what is explosion? provenance
  2. Which references are standard? provenance

Philosophy

Philosophical uses.

Philosophy

Philosophy.

  1. How have philosophers used contradiction and antinomy, with positions attributed? provenance
  2. Is the presentation neutral? boundary
Apply Law, texts and teaching.

Application.

Law and texts

Legal and textual claims.

Law

Law.

  1. How do courts treat inconsistent pleadings, and how are alleged contradictions in texts debated with attribution? provenance
  2. Are contested claims about religious or historical texts presented neutrally? boundary

Teach

Teaching.

Teach

Teaching.

  1. How is contradiction taught in logic and critical thinking? action
  2. Which misconceptions arise? provenance

What the second pass must settle

  • Should paradox and antinomy be separate entries?
  • How should paraconsistent logics be represented?
  • The registry entry has merged aliases about legal pleading and the consistency of the Bible, which are separate topics; should they be split off?
Draft as JSON