more from David Bostock

### Single Idea 13811

#### [catalogued under 5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic]

Full Idea

Usually we allow that a function is defined for arguments of a suitable kind (a 'partial' function), but we can say that each function has one value for any object whatever, from the whole domain that our quantifiers range over (a 'total' function).

Gist of Idea

A 'total' function ranges over the whole domain, a 'partial' function over appropriate inputs

Source

David Bostock (Intermediate Logic [1997], 8.2)

Book Reference

Bostock,David: 'Intermediate Logic' [OUP 1997], p.333

A Reaction

He points out (p.338) that 'the father of..' is a functional expression, but it wouldn't normally take stones as input, so seems to be a partial function. But then it doesn't even take all male humans either. It only takes fathers!

Related Ideas

Idea 10074
A 'total function' maps every element to one element in another set **[Smith,P]**

Idea 13700
A 'total' function must always produce an output for a given domain **[Sider]**

Idea 10075
A 'partial function' maps only some elements to another set **[Smith,P]**