Definition:Singular Statement
Definition
A singular statement is a statement whose subject is identified by means of a proper name.
More generally, it is a statement which contains no variables, either bound or free.
Individuating Description
An individuating description is a predicate whose purpose is to uniquely identify a particular object.
Designatory Function
A designatory function is a propositional function which, on replacement of the operand with a constant, becomes an individuating description.
Examples
Rain is wet is a singular statement.
It expresses the fact that rain (a proper name identifying the liquid which falls from the sky under certain meteorological conditions) has the property being-wet.
In the language of symbolic logic, this could be written as follows:
- Let $\mathbf r$ be rain.
- Let $W$ be the property being wet.
Thus we symbolize Rain is wet as $W \left({\mathbf r}\right)$.
- $2 + 3 = 3 + 2$ is a singular statement.
It expresses a specific relation between the proper names $3$ and $2$.
Also known as
A singular statement is also known as a singular proposition or a singular sentence.
Also see
Sources
- 1946: Alfred Tarski: Introduction to Logic and to the Methodology of Deductive Sciences (2nd ed.) ... (previous) ... (next): $\S 1.3$: Universal and Existential Sentences
- 1973: Irving M. Copi: Symbolic Logic (4th ed.) ... (previous) ... (next): $4$: Propositional Functions and Quantifiers: $4.1$: Singular Propositions and General Propositions
- 1980: D.J. O'Connor and Betty Powell: Elementary Logic ... (previous) ... (next): $\S \text{III}$: The Logic of Predicates $(1): \ 2$: Predicate expressions