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Logical Definitions

A definition explains the meaning of a word. It has three parts: the word being explained (definiendum), a connector such as 'means' or 'is', and the explaining words (definiens). Kinds: classical (class plus difference), ostensive (pointing), enumerative (listing) and contextual (using the word in a sentence). A good definition is not too wide, not too narrow, not circular and uses clearer words than the word it explains.

🎬 Step-by-step story

  1. Here are many shapes. We want to define one word, 'cube'. The word we want to explain is the definiendum.
  2. Classical definition: start with a known group, 'solid', then add the difference, 'six equal square faces'. Only cubes glow.
  3. Ostensive definition: no words, just point at a cube and say 'this is a cube'.
  4. Enumerative definition: name every member. 'Primary colours are red, yellow and blue.'
  5. Now bad definitions. Too wide lets boxes in. Too narrow leaves cubes out. A circular one tells us nothing new.
  6. Free play: press the buttons and watch which shapes get in. A good definition picks exactly the cubes.

Tip: drag the 3D scene to turn it. Use two fingers to zoom.

🤔 Common doubts, cleared

Which word are we actually defining?

The definiendum. In the 3D it is the word 'Cube' hovering over the red cube.

Why do we start with 'solid' in a classical definition?

Because we first put the thing in a known group, then say how it differs from other members of that group. Only cubes glow once we add 'six equal square faces'.

Is pointing really a definition?

Yes, an ostensive one. It works well for colours and tastes, but may be unclear: the finger could mean the colour, the size or the object.

When is listing enough?

When the group is small and fixed, like primary colours. For endless groups, like all triangles, a list is impossible and we need a classical definition.

How do I see that a definition is too wide?

Press 'Too wide'. The two boxes glow although they are not cubes, so the definition lets in too much.

What does a circular definition show in the 3D?

Press 'Circular'. Nothing glows, because it gives no new information about which shapes are cubes.

What is a definition?

A definition tells us what a word means. When two people use the same word in different ways, they talk past each other. A clear definition fixes this.

Every definition has three parts:

Sentence form: definiendum + connector + definiens.

Four kinds of definition

1. Classical definition. Give the bigger group (the genus) and then what makes this thing special inside the group (the difference). 'A triangle is a closed shape (group) with three sides (difference).'

2. Ostensive definition. You show an example by pointing. 'Red is this colour.' It is how a baby learns 'dog'. It is weak when the pointing is unclear: does 'this' mean the colour, the shape or the object?

3. Enumerative definition. You list all the members. 'The Indian national symbols are the flag, the emblem and the anthem.' It works only when the list is short and complete.

4. Contextual definition. You do not explain the word alone. You explain what a whole sentence with the word means. 'Someone is a bachelor' can be explained by 'he is an unmarried man'. Scientists use it when a word is only meaningful inside a sentence or a formula.

Mistakes in definitions

Inadequacy (wrong size). The definition catches the wrong things.

Ignotum per ignotum (Latin: 'the unknown by the unknown'). The explaining words are harder than the word. 'Lamp means a luminiferous apparatus.' You now need a second dictionary.

Circularity. The word is used in its own explanation. 'A teacher is a person who teaches.' Or a loop: 'Brave means not cowardly', 'cowardly means not brave'.

Try it: build and test a definition

In the 3D, press Too wide, Too narrow and Circular and count how many shapes get in. Then try at home: define 'chair' in one sentence and test it on a stool, a sofa and a tree stump. Is your definition too wide or too narrow? Fix it, then test again. This 'test with a tricky example' is exactly how philosophers improve definitions.

Key formulas and definitions

Worked examples

1. Split 'A square is a rectangle with four equal sides' into its three parts.

Definiendum: square. Connector: 'is'. Definiens: 'a rectangle with four equal sides'. It is a classical definition: genus = rectangle, difference = four equal sides.

2. Which kind of definition is: 'The vowels are a, e, i, o, u'?

Enumerative. It lists all the members of the group.

3. A teacher says, 'A mango is a fruit that is yellow.' Is this too wide or too narrow? Why?

Both. Too wide: bananas and lemons are yellow fruits but are not mangoes. Too narrow: raw mangoes are green, so real mangoes are left out.

4. 'Justice is the state of being just.' Name the error.

Circularity. 'Just' is the same word family as 'justice', so the definiens needs the definiendum to be understood.

5. A child asks what 'photosynthesis' means and is told 'it is the autotrophic anabolic assimilation of carbon by chlorophyllous organisms'. What is wrong?

Ignotum per ignotum. The explaining words are harder than the word. Better: 'the way green plants use sunlight to make food from water and carbon dioxide'.

Common mistakes

Practice quiz

1. In 'A cube is a solid with six equal square faces', the definiendum is:
2. Pointing at a bicycle and saying 'this is a bicycle' is:
3. 'A fish is an animal that lives in water' is mainly wrong because it is:
4. 'Sad means not happy; happy means not sad.' This is:
5. Which is the genus in 'A triangle is a closed shape with three sides'?

Practice: answer these yourself

Type or choose your answer, then press Check. Use a hint if you are stuck; the full solution appears after you answer.

Frequently asked questions

What are the three parts of a definition?

The definiendum (the word being explained), the connector (like 'is' or 'means') and the definiens (the words that explain it).

What is the difference between a classical and an enumerative definition?

A classical definition gives a group and a special feature, so it can cover endless members. An enumerative definition simply lists the members, so it works only for a small, complete list.

Why is a circular definition bad?

Because to understand the explanation you must already understand the word. It goes round in a loop and teaches nothing new.

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