undefined terms

USAGE SUMMARY

The phrase "undefined terms" is correct and usable in written English. You can use it in contexts related to mathematics, logic, or philosophy where certain concepts are not explicitly defined. For example, "In geometry, points, lines, and planes are often considered undefined terms." Alternative expressions include "basic concepts" and "primitive terms."

✓ Grammatically correct

Encyclopedias

News & Media

Science

Academia

Human-verified examples from authoritative sources

Exact Expressions

22 human-written examples

Thus, in an axiomatic theory of sets, set and the membership relation ∊ are undefined terms.

Encyclopedia Britannica

The Government's proposal outlines three "patterns of behavior" that would trigger action, but all three have undefined terms.

The New York Times

Steve Hunter The proposal reads like an insurance policy: lots of references to other documents, lots of undefined terms, lots of loopholes and no fixed price tag.

The New York Times

In the last analysis all definitions have to fall back on undefined terms (to be accepted like axioms) that symbolize first-order experience of life.

Britannica

Hence, he began the Elements with some undefined terms, such as "a point is that which has no part" and "a line is a length without breadth".

Encyclopedia Britannica

Undefined terms involving the application of partial functions and operators are common in program specifications and in discharging proof obligations that arise in design.

Information Processing Letters

Human-verified similar examples from authoritative sources

Similar Expressions

37 human-written examples

By using the word 'artificial,' the courts have avoided coming to grips with the problem of defining 'manipulation'; they have simply substituted one undefined term for another".

The New York Times - Magazine

Article 50 states that any member state may leave "in accordance with its own constitutional requirements", an undefined term that has allowed both sides to pursue rival interpretations.

The Guardian

Since the article in May, its reporting has not aggressively challenged the administration's description of those killed as "militants" — itself an undefined term.

The New York Times

The legal dispute focused on article 50 of the treaty on European Union, which says any member state may leave "in accordance with its own constitutional requirements" – an undefined term that has allowed both sides to pursue rival interpretations.

The Guardian

The legal dispute focuses on article 50 of the treaty on European Union, which states that any member state may leave "in accordance with its own constitutional requirements" – an undefined term that has allowed both sides to pursue rival interpretations.

The Guardian

Expert writing Tips

Best practice

When using "undefined terms" in technical writing, acknowledge that these terms are being used as primitives and explain why they are not being defined within the scope of your work. This clarifies your assumptions and avoids ambiguity.

Common error

A common mistake is to assume your audience understands the meaning of "undefined terms" without any context. Always provide sufficient background or examples to illustrate how these terms function within your specific domain.

Linguistic Context

The phrase "undefined terms" functions primarily as a noun phrase, often serving as the subject or object in sentences discussing foundational concepts in mathematics, logic, and formal systems. Ludwig highlights its use in academic and technical contexts.

Expression frequency: Common

Frequent in

Encyclopedias

20%

News & Media

20%

Science

35%

Less common in

Academia

15%

Wiki

5%

Formal & Business

5%

Ludwig's WRAP-UP

The phrase "undefined terms" refers to fundamental concepts in a system that are deliberately left without formal definition, serving as the foundation for axioms and theorems. As Ludwig confirms, this phrase is grammatically correct and frequently appears in academic, scientific, and formal contexts. Common usage involves acknowledging these "terms" as primitives to avoid circular definitions. Related phrases include "primitive terms" and "basic concepts". When writing about "undefined terms", it's crucial to provide context and avoid assuming the reader's prior knowledge. Though it may seem counterintuitive to leave some terms without a definition, this is often necessary to construct a logical system.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

primitive terms

Focuses on the foundational aspect of the terms, suggesting they are accepted without prior definition.

basic concepts

Emphasizes the fundamental nature of the terms, indicating they are core ideas that don't require definition.

unspecified terms

Highlights the lack of specific details or constraints associated with the terms.

vague terms

Indicates the terms are not clearly defined, leading to potential ambiguity.

imprecise terms

Suggests a lack of exactness or accuracy in the definition of the terms.

ill-defined terms

Implies that the terms are poorly defined, making their meaning unclear.

ambiguous terms

Highlights the potential for multiple interpretations of the terms.

terms lacking definition

States directly that the terms have not been formally defined.

terms without clear meaning

Focuses on the absence of a distinct or easily understood meaning for the terms.

axiomatic terms

Suggests that the terms are accepted as self-evident truths, similar to axioms, and thus do not require definition.

FAQs

How are "undefined terms" used in mathematics?

In mathematics, "undefined terms" serve as the foundation upon which axioms and theorems are built. They are accepted without formal definition to avoid infinite regress. Examples include point, line, and plane in geometry.

What's the difference between "undefined terms" and axioms?

"Undefined terms" are the basic concepts we accept without definition, while axioms are statements we accept as true without proof. Axioms use undefined terms to express fundamental relationships.

Why are some "terms" left "undefined" in formal systems?

Leaving some "terms" "undefined" is essential to avoid circular definitions and infinite regression. These "terms" are the starting points for building a logical system.

Can I use "primitive terms" instead of "undefined terms"?

Yes, "primitive terms" is often used synonymously with "undefined terms". Both refer to terms that are not formally defined but are taken as a starting point in a system of thought.