Let $\mathbb{X}=\{1,2,3,4,5\}$ be a set and $x$ be an element of the set. Then 1 is also an element of the set. We say that $x$ is a "variable". I am searching for a word that conveys the idea of something that is an placeholder for an element of the set, but not a specific one (and not the entire set). I want to convey the idea of something being a schema. Compared to programming I mean something like a class (= placeholder/schema), in contrast to an object (= concrete instance) and in contrast to the set of all created objects.
The reason why I am hesitant to call this thing a "variable", because I do not mean the symbol, but the concept. For example, if I say $x\in\mathbb X$ and $y\in\mathbb X$, then $x$ and $y$ are different variables, but they are both notate the same "abstract thing for which I am searching a word for.
Another idea is to call this a universal, following
- https://en.wikipedia.org/wiki/Universal_(metaphysics)
- or https://www.csus.edu/indiv/p/pynetf/metaphysics_toolkit.htm
An entity is a universal if it is repeatable. It is capable of having instances, occurrences, examples, tokens, members, cases…, whatever. There can be more than one square, more than one blue triangle, etc.
So in this case $x$ and $y$ would denote the same universal. The universal does not convey the idea of a placeholder that much, but maybe this does not matter?