Definition:Stipulative Definition
Jump to navigation
Jump to search
Definition
A stipulative definition is a definition which defines how to interpret the meaning of a symbol.
It stipulates, or lays down, the meaning of a symbol in terms of previously defined symbols or concepts.
The symbol used for a stipulative definition is:
- $\text {(the symbol being defined)} := \text {(the meaning of that symbol)}$
This can be written the other way round:
- $\text {(a concept being assigned a symbol)} =: \text {(the symbol for it)}$
when it is necessary to emphasise that the symbol has been crafted to abbreviate the notation for the concept.
Notation
The symbol used to introducing a stipulative definition varies throughout the literature.
Here are some instances:
- $\text {(the symbol being defined)} \mathrel{\stackrel {\mathbf {def}} {=\!=}} \text {(the meaning of that symbol)}$
- $\text {(the symbol being defined)} \mathrel{=_{df}} \text {(the meaning of that symbol)}$
- $\text {(the symbol being defined)} = \text {(the meaning of that symbol)} \quad \text{Df.}$
These constructs are not used on $\mathsf{Pr} \infty \mathsf{fWiki}$ through being cumbersome and awkward to reproduce.
Also see
Sources
- 1910: Alfred North Whitehead and Bertrand Russell: Principia Mathematica: Volume $\text { 1 }$ ... (previous) ... (next): Chapter $\text{I}$: Preliminary Explanations of Ideas and Notations
- 1959: A.H. Basson and D.J. O'Connor: Introduction to Symbolic Logic (3rd ed.) ... (previous) ... (next): $\S 2.4$: Relations between Truth-Functions
- 1965: E.J. Lemmon: Beginning Logic ... (previous) ... (next): Chapter $1$: The Propositional Calculus $1$: $4$ The Biconditional
- 1990: H.A. Priestley: Introduction to Complex Analysis (revised ed.) ... (previous) ... (next): Notation and terminology