The circle and the void 2
A house divided - The logical schism at the heart of the ontological syllogism
“Minor Premise 2: A contingent being is one that exists in some but not all possible worlds. Formally:◇G ∧ ¬□G”
If the first premise of the Modal Ontological Argument acts as the engine of its own conclusion, then the introduction of a second, contradictory premise represents a profound and irreconcilable schism at the argument’s core. The spectacle initially unfolds as a failed proof and then advances to a logical system in a state of civil war with itself. This internal conflict arises when one juxtaposes the definitive, almost imperial, claim of Major Premise 1, that a Maximally Great Being must exist necessarily if it exists at all, with the altogether more modest and earthbound assertion of Minor Premise 2, which claims that this same being is merely contingent. The resulting dissonance is not just a minor technicality to be smoothed over; it is a catastrophic failure of coherence that reduces the entire syllogism to a nullity.
To appreciate the depth of this contradiction, we must first understand the particular modal territory each premise seeks to occupy. Major Premise 1, formally expressed as □(G → □G), functions as a kind of metaphysical decree. It describes a property of the Maximally Great Being and legislates its very mode of existence across the entirety of logical space. It declares that in every conceivable world, the instantiation of G carries an inescapable consequence with it: G’s ubiquitous presence in all worlds. This premise, by its very structure, abolishes the very possibility of a contingent God. It creates a strict, binary universe of discourse: the Maximally Great Being is either a necessary fixture of reality, present in every possible world without exception or it is an impossible one, absent from all. There is no middle ground, no realm of some-but-not-all worlds where such a being might reside.
Minor Premise 2 wanders into this rigid, absolutist landscape with an air of naive innocence, proposing precisely that excluded middle. Its formulation, ◇G ∧ ¬□G, is the very definition of contingency in modal logic. It asserts that the Maximally Great Being is possible, that there is at least one world in which it finds a home, while simultaneously denying its necessity, insisting that there exists at least one other world from which it is absent. This is the ontological status of ordinary things: of trees, of human beings, of empires. It is the logic of the ephemeral, of that which depends on the right confluence of circumstances to spring into being and can just as easily pass away. By applying this logic to the Maximally Great Being as defined in Premise 1, we commit a category error of the highest order.
The inevitable collision is both swift and fatal. If we were to entertain, for a moment, the truth of Minor Premise 2, we would be required to believe that there is some possible world, let us call it W1, in which G exists. But from Major Premise 1, which holds in all worlds, we know that in W1, the conditional G → □G must be true. Given that G is true in W1, it follows with logical force that □G is true. This means that G must be true in every possible world without exception. Yet this conclusion, □G, stands in direct and violent contradiction to the second clause of Minor Premise 2, which is ¬□G. We are now left holding two mutually exclusive propositions: that God exists in all worlds and that God does not exist in all worlds. The law of non-contradiction, a most fundamental principle in classical logical, is violated in a single, breath-taking move.
The implications of this internal collapse are fatal for the syllogism in which it appears. A valid argument, whatever its other merits or demerits, must at a minimum be based on a set of premises that could all be true at the same time. This is a basic condition of sound reasoning. The simultaneous assertion of Premise 1 and Premise 2, however, fails this most elementary test. They cannot be jointly affirmed without plunging the argument into incoherence. What we are presented with is not a pathway to a conclusion but a philosophical absurdity. The syllogism, in this configuration, does not so much argue for the existence of God as it demonstrates the impossibility of its own premises.
This confrontation also serves, with unwelcome clarity, to illuminate the arbitrary nature of the definitional game being played. The proponent of the Modal Ontological Argument typically wishes to have it only one way: they insist upon the rigorous, necessity-entailing definition of Premise 1 while quietly setting aside any notion of contingency. The introduction of Premise 2 into the fray forces this trick into the open. It highlights that the definition of ‘maximal greatness’ is not a discovered, neutral fact, but a stipulated one, designed to produce a specific outcome. The acceptance of Premise 1 already decided the question against contingency; insisting upon Premise 2 is rejecting the foundational definition upon which the entire argument is built. We cannot have both without succumbing to nonsense.
In the final analysis, the spectacle of these two premises at war with one another is a sobering lesson in philosophical rigour. It demonstrates that the sheer formal beauty of a logical structure is no guarantee of its substance or its sanity. The argument, in this instance, is defeated by a profound internal inconsistency. It is a house divided and like any such house, it cannot stand. The contradiction between the necessary being of Premise 1 and the contingent being of Premise 2 does not simply weaken the Modal Ontological Argument; it reduces it to a mere curiosity, a testament to the fact that even the most sophisticated logical machinery will seize and fail when its foundational parts are engineered to work against one another.