>>12209025If we take classical propositional logic, then the symbols are
where the first is binary and the second nullary.
We can already form propositons, such as and we may add some more letters and rules to form propositions, as we do below. We may take some propositions as given (axioms).
In the metalogic, we use greek letters for propositional variables. Given any proposition and another , then we also take as given.
If you got an equalitarian theory, then you also have
If you got a first-order theory, then you add a quantifier and some alphabet for variables
and you allow for propositions to be indexed by those (we may use notation to be explicit about that)
If you got a set theory, then you also add
Finally we add brackets in the standard sense that everybody can parse out.
I draw a line here.
Because this is already the full name of the game. We can make abbreviations
for
for
for
for
for
Similarly, there is no curly brackets in formal set theory, but we like to write
for any false proposition such as .
And we write
for
Any set is some class any class is a property. From that perspective, set theory (a colleciton of axioms to start the game) is about turning class into something you can quantify over - do higher order logic in a first-order theory.
And the emptyset is already there before you can even define a subset.
