Modal Logic
The logic of necessity and possibility provides the framework for understanding necessary existence, the ontological argument, and the distinction between contingent and necessary being.
The Modal Ontological Argument
Modal logic provides the framework for Plantinga's modal ontological argument, one of the most discussed arguments in contemporary philosophy of religion.
The argument proceeds: (1) It is possible that a maximally great being exists. (2) If it is possible that a maximally great being exists, then a maximally great being exists in some possible world. (3) If a maximally great being exists in some possible world, then it exists in every possible world. (4) If it exists in every possible world, then it exists in the actual world. (5) Therefore, a maximally great being exists.
- Maximal Greatness: A maximally great being has maximal excellence (omnipotence, omniscience, moral perfection) in every possible world. Such a being exists necessarily if it exists at all.
- S5 Modal Logic: In S5, if something is possibly necessary, then it is necessary. This is the key inference: ◇□p → □p. If God's existence is possible, it is necessary.
- The Key Premise: The crucial premise is that maximal greatness is possible—that there is no incoherence in the concept. If this is granted, the conclusion follows by valid modal logic.
- Necessary Existence: God, if possible, exists necessarily—not contingently like created things. This distinguishes God from all contingent beings and grounds the cosmological argument.
Contingency and the Cosmological Argument
Modal distinctions are essential for cosmological arguments. The distinction between contingent and necessary being is the foundation of Leibniz's cosmological argument.
Everything that exists is either contingent (could have failed to exist) or necessary (couldn't have failed to exist). Contingent things require explanation. The chain of contingent explanations cannot be infinite. Therefore, there must be a necessary being that explains the existence of contingent things.
- Contingent Beings: Things that exist but might not have—they require explanation. You exist, but you might not have. The universe exists, but it might not have. Why is there something rather than nothing?
- Necessary Being: Something that exists in all possible worlds—the ultimate explanation. A necessary being doesn't need external explanation; its existence is self-explanatory.
- Principle of Sufficient Reason: Everything that exists has an explanation—contingent things in external causes, necessary things in their own nature. This principle drives the cosmological argument.
- Grounding the Contingent: The totality of contingent things cannot explain itself. Even an infinite series of contingent things is itself contingent. Only a necessary being can ground contingent existence.