If α is a wff and a is an individual variable, then (∀a)α is a wff.
An expression $t$ is a term if, and only if, (i) $t$ is an individual variable, or (ii) $t$ is an individual constant, or (iii) $t$ is an expression of the form $f^{n}_{i}t_{1}, \ldots, t_{n}$, where $f^{n}_{i}$ an $n$-place function symbol and $t_1$, …, $t_n $are themselves terms.
So instead of looking at ∃1x T[x], where ∃1 means 'exists a unique' and x is an individual variable, we look at ∃1x T[x], where x is a variable that ranges over n-tuples, and T[x] is the sentence you get by replacing t1 with the first member of x, t2 with the second member of x, …, and tn with the nth member of x.
These findings suggest that SR may be an individual difference variable that cuts across clinical diagnoses, though certain clinical groups (e.g., ADHD) on average tend to be higher in that dimension, leading to greater responses to reinforcement.
The formation rules for well-formed formulas are the obvious ones; in particular universal and existential quantification is allowed for any variable, be it an individual variable, a predicate variable, or a function variable.
If α is a theorem, so is (∀a)α, where a is any individual variable (rule of universal generalization).
If a is any individual variable and α is any wff, every occurrence of a in α is said to be bound (by the quantifiers) when occurring in the wffs (∀a)α and (∃a)α.
A common notation for this purpose is (ιx)ϕx, which may be read as "the thing that is ϕ" or more briefly as "the ϕ." In general, where a is any individual variable and α is any wff, (ιa)α then stands for the single value of a that makes α true.
The other one is an individual human variable: How competent are you?
Each of these data was regarded as an individual variable.
