modal logic Modal logic is a collection of formal systems developed to represent statements about necessity and possibility. It plays a major role in philosophy of language, epistemology, metaphysics, and natural language semantics. Modal logics extend other ...

, modal collapse is the condition in which every true statement is

necessarily true Logical truth is one of the most fundamental concepts in logic. Broadly speaking, a logical truth is a statement which is true regardless of the truth or falsity of its constituent propositions. In other words, a logical truth is a statement whic ...

, and vice versa; that is to say, there are no contingent truths, or to put it another way, that "everything exists necessarily". In the notation of modal logic, this can be written as

\phi \leftrightarrow \Box \phi

. In the context of philosophy, the term is commonly used in critiques of ontological arguments for the existence of God and the principle of

divine simplicity In theology, the doctrine of divine simplicity says that God is simple (without parts). The general idea can be stated in this way: The being of God is identical to the "attributes" of God. Characteristics such as omnipresence, goodness, trut ...

. For example,

Gödel's ontological proof Gödel's ontological proof is a formal argument by the mathematician Kurt Gödel (1906–1978) for the existence of God. The argument is in a line of development that goes back to Anselm of Canterbury (1033–1109). St. Anselm's ontological argum ...

contains

\phi \rightarrow \Box \phi

as a theorem, which combined with the axioms of system S5 leads to modal collapse. Since some regard divine freedom as essential to the nature of God, and modal collapse as negating the concept of

free will Free will is the capacity of agents to choose between different possible courses of action unimpeded. Free will is closely linked to the concepts of moral responsibility, praise, culpability, sin, and other judgements which apply only to actio ...

, this then leads to the breakdown of Gödel's argument.

References

Collapse Collapse or its variants may refer to: Concepts * Collapse (structural) * Collapse (topology), a mathematical concept * Collapsing manifold * Collapse, the action of collapsing or telescoping objects * Collapsing user interface elements ** ...

Philosophical logic Theology Necessity {{mathlogic-stub