Interdefinability

Interdefinability refers to a relationship between two or more concepts, terms, or systems where each can be defined or understood in terms of the others. This means that if you have a definition for one element, you can derive the definition for the others without needing entirely new fundamental concepts. It implies a deep equivalence or interchangeability between the defined entities.

In logic and mathematics, interdefinability is crucial for understanding formal systems. For example, certain logical connectives are interdefinable. The Sheffer stroke (NAND) is interdefinable with the standard conjunction (AND), disjunction (OR), and negation (NOT) because any of these can be expressed using only the Sheffer stroke. This suggests that the Sheffer stroke is a functionally complete connective.

In philosophy, interdefinability can highlight how different conceptual frameworks might be describing the same underlying reality or phenomenon from different perspectives. If two sets of concepts are interdefinable, it suggests that they are not merely different descriptions but rather different ways of specifying the same set of relationships or properties.

The concept also appears in areas like physics and computer science. For instance, in thermodynamics, temperature, pressure, and volume are interdefinable under certain conditions, as described by the ideal gas law. In programming, different data structures or algorithms can sometimes be interdefinable, meaning one can be implemented using the other, though perhaps with different efficiency characteristics. The core idea remains consistent: the ability to express one in terms of the other without introducing new fundamental building blocks.