Concepts, Definitions and Classifications: Where Error Arises Even Before Inference

“Definition is an explanation of the content of a concept.”

Georgy Chelpanov, “Logic Textbook”, in modern orthography

Scene: “normal apartment”

Two people are choosing an apartment. One says: “We need a normal one.” For him this means a quiet area and a separate kitchen. For the other — a new building and a commute to work no longer than half an hour. Both agree with the phrase, but agree with different thoughts.

A word is a term. The mental boundary it denotes is a concept. A specific apartment is an object. It is premature to argue about an object’s properties until the participants agree on the concept.

Repair: replace the evaluative word with observable criteria: «no more than 35 minutes from work, not the first floor, no major roads are audible at night».

Contents and Scope

The concept has two sides:

• content — features by which we recognize an object;
• scope — all objects that fit these features.

The more required properties, the narrower the circle of suitable objects. «Book» is a broad concept. «Paper children’s book in the Russian language» is narrower.

Second example

The announcement promises a discount for “regular customers”. Who is regular: someone who has bought twice, someone who buys every month, or a cardholder? Without a boundary, the seller can change the meaning after the customer’s decision.

Repair: specify the criterion and the moment of its verification: «no less than three purchases in the 90 days prior to the start of the campaign».

How to build a definition

A useful definition answers three questions:

1. What definitely is included?
2. What definitely is not included?
3. What to do with edge cases?

A definition is not required to reveal the “eternal essence” of a thing. Sometimes an operational definition is sufficient: a procedure by which we make a decision. For example, for a study, “regular reader” might mean “read at least one book per month over the last six months.” This is not the only correct meaning, but it can be uniformly applied to all participants.

Common Breakages

Too Broad

A bicycle is a wheeled vehicle.

Cars and trains come here.

Too Narrow

A bicycle is a two-wheeled vehicle for city rides.

Three-wheeled models and sports rides drop out.

In a Circle

A reliable person is one you can depend on.

The second part repeats the first word, but does not provide a check.

Through the Unknown

Abduction is a retroductive inference.

If the second word is no clearer to the reader than the first, the definition has failed its job.

Division and Classification

Scene: in the family budget, expenses are divided into “food”, “mandatory”, “major”, and “entertainment”. Buying a refrigerator is both major and mandatory, while food delivery is food and entertainment. Categories are built on different grounds.

Division rule: use one question per level. For example:

• by purpose: housing, food, transport, leisure;
• separately by size: regular and large;
• separately by obligation: mandatory and non-mandatory.

Several independent scales are called faceted classification. It is often more honest than one tree.

Short practice

Take the word “useful” in the phrase “useful course”.

1. For whom is it useful?
2. What result should change?
3. Within what timeframe?
4. What will be the edge case?
5. Can the word be replaced with an observable criterion?

Possible repair: “After the course, the participant without hints walks through the argument, finds the missing premise, and offers a checkable fix.”

Chapter Rule: You cannot require exact output from fuzzy boundaries. First, agree on inclusion, exclusion, and boundary criteria.