Meta Ontology

Perhaps this is unimportant but there are two ways of reasoning that I am fond of and they are incompatable. This relates weakly to model theory for predicate calculus. In those models you suppose some fixed set of individual objects and describe what it means for a proposition to be about those objects. Another example is when we do arithmetic, we assume that the integers are there and our calculations merely designate new integers that existed before our calculation.

In other contexts we have languages where we speak of new things popping into existence at compile time, if not at run time. In Scheme or Lisp we explain the meaning of “(cons 3 6)” as the creation of a new cell whose contents are 3 and 6. The brings with it the notion that the value of that expression provides exclusive access to the place where 3 and 6 were put. Any programmer born before 1980 will know that that same place was probably used by someone else and at best access to that place has somehow been expunged and the new value now uniquely provides access.

Church’s lambda calculus and early attempts at mathematics foundations found it frequently necessary to speak of choosing some variable that does not appear in some given expression.

I don’t know where to take this.