A Definition is like a Property Line

Oros, the Greek word for ‘definition’, means the boundary that demarcates the edge of a man’s field. Such a line shows where the field begins and everything else ends. Like a boundary line, every definition must include something and exclude something.

A Definition is like a Property Line

Oros, the Greek word for ‘definition’, means the boundary that demarcates the edge of a man’s field. Such a line shows where the field begins and everything else ends. Like a boundary line, every definition must include something and exclude something.

Precision and Imprecision

For a property line to be precise, it must:

1. include what’s supposed to be in

2. exclude what’s supposed to be out.

and

Precision and ImprecisionLikewise,

a precise definition 1. includes everything in the species

and 2. excludes everything outside the species.

An imprecise definition is anything that falls short of this.

Let’s see how a definition can fall short of this.

Precision and ImprecisionA precise definition

1. includes everything in the speciesand

2. excludes everything outside the species.

An imprecise definition 1. excludes something in the species

or 2. includes something outside the species.

Precision and ImprecisionA precise definition

1. includes everything in the species and

2. excludes everything outside the species.

How must we conjoin these two requirements?

How can it fall short of this requirment?

How can it fall short of this requirment?

An imprecise definition 1. excludes something in the species

or 2. includes something outside the species.

Precision and ImprecisionA precise definition

1. includes everything in the species and

2. excludes everything outside the species. A precise definition needs to succeed in both ways…

…so it is imprecise if it fails in either way.

An imprecise definition 1. excludes something in the species

or 2. includes something outside the species.

Precision and Imprecision

If a definition fails in one way, it is called “overly broad”,If it fails in another way,

it is called “overly narrow”,But if it fails both ways, it is overly broad and

overly narrow, and is called “inaccurate”.

Precision and Imprecision

Overly narrow

O v e r l y b r o a d

S P EC I ES

An imprecise definition 1. excludes something in the species

or 2. includes something outside the species.

Precision and Imprecision

Overly narrow

O v e r l y b r o a dAn imprecise definition

1. excludes something in the species or

2. includes something outside the species.

I n a c c u r a t e

S P EC I ES

Quick test for Precision

• There is a quick test to see whether a definition is precise or not. Ask yourself two questions:

Can I think of a counter example, namely:Some __________ that is NOT a __________________.

(definiendum) (definiens)

ORSome __________ that is NOT a __________________.

(definiens) (definiendum)

Quick test for “Too Narrow”

• There is a quick test to see whether a definition is overly narrow.

Some _________is NOT a ____________________. (definiendum) (definiens)

• Is this statement true? If yes, then the definition is too narrow. If not, the definition is not too narrow.

large cat with a maneLion large cat with a maneLion:

(such as a lioness!)

Quick test for “Too Broad”

flowering plantTiger Lily: flowering plant

• There is a quick test to see whether a definition is overly broad.

Some ______________is NOT a ____________. (definiens) (definiendum)

• Is this statement true? If yes, then the definition is too narrow. If not, the definition is not too narrow.

Tiger Lily

(such as a rose!)

Showing a Definition is Imprecise

The definition “ is ” is too narrow/broad (definiendum) (definiens)

because the definiens excludes/includes something that is/isn’t in the definiendum;

viz. which is/isn’t in the definiendum .(counter example) (definiendum)

To formally argue that a definition is imprecise, one uses the

following format.

Showing a Definition is Imprecise

Man: an animal naturally having exactly two legs.

The definition “ is “ is too narrow/broad (definiendum) (definiens)

because the definiens excludes/includes something that is/isn’t in the definiendum;

viz. which is/isn’t in the definiendum .(counter example) (definiendum)

Man an animal w/exactly 2 legs

ManBird

includes isn’t

isn’t

broad,

Showing a Definition is Imprecise

Biology: the science of animal life.

The definition “ is “ is too narrow/broad (definiendum) (definiens)

because the definiens excludes/includes something that is/isn’t in the definiendum;

viz. which is/isn’t in the definiendum .(counter example) (definiendum)

Biology the science of animal life

BiologyBotany

excludes is

is

narrow,

Practice

circle: a curved shape bird: a feathered flying animal Christian: a follower of Martin Lutherpilot: one who flies planes snake: a naturally legless reptile triangle: a polygon w/ 3 equal sideswater: a liquid substance fish: a marine animal spray: a jet of finely divided water

The definition “A is ” is too narrow/broad (definiendum) (definiens)

because the definiens excludes/includes something that is/isn’t in the definiendum;

viz. which is/isn’t in the definiendum .(counter example) (definiendum)

• Use the format below to practice showing the definitions are imprecise.

Homework

Print out the Inprecision worksheet from the class website and complete the exercises.