Computability Theory And Ontological Emergence
by
Jon Cogburn and Mark Silcox
It is often helpful in metaphysics to reflect upon the principles that govern how existence claims are made in logic and mathematics. Consider, for example, the different ways in which mathematicians construct inductive definitions. In order to provide an inductive definition of a class of mathematical entities, one must first define a base class and then stipulate further conditions for inclusion by reference to the properties of members of the base class. These conditions can be deflationary, so that the target class is a subclass of the base class, or inflationary, so that the base class is an important subclass of the target class. For example, in defining the set of wellformed sentences of first order logic, one can begin with the set of all possible strings and, in a deflationary manner, exclude the nonsentences. Or one can begin with the set of atomic formulae, and in an inflationary manner, build more complicated sentences out of the atomic formulae.

