The Modal Ontological Argument

Alvin Plantinga

The argument is valid.

Every inference was checked by machine. The objection is answered.

Open in the playground

flowchart TD
    classDef axiom fill:#f6efd9,stroke:#a8842a,color:#23212b;
    classDef premise fill:#e7edf7,stroke:#1f4e9c,color:#23212b;
    classDef deduction fill:#f3f4f1,stroke:#5b6b85,color:#23212b;
    classDef conclusion fill:#d6e1f3,stroke:#1f4e9c,stroke-width:3px,color:#23212b;
    classDef objection fill:#f7e3e1,stroke:#b3261e,color:#23212b;
    classDef reply fill:#f3f4f1,stroke:#7a5c2e,color:#23212b;
    classDef imported stroke-dasharray:4 3;
    classDef defeated fill:#f3f4f1,stroke:#b3261e,stroke-dasharray:6 3,color:#8a8796;
    classDef undecided stroke-dasharray:2 2;
    classDef overruled fill:#f3f4f1,stroke:#c9ccc6,color:#8a8796;
    Nature(["Nature: Alvin Plantinga, The Nature of<br/>Necessity, ch. X"]):::axiom
    MG(["MG: Maximal greatness includes necessary<br/>existence."]):::axiom
    P1["<b>P1</b>: It is possible that a maximally great<br/>being exists.<br/><i>◇M</i>"]:::premise
    P2["<b>P2</b>: Necessarily, if a maximally great being<br/>exists, it exists necessarily.<br/><i>□(M → □M)</i>"]:::premise
    D1["<b>D1</b>: Therefore it is necessary that a<br/>maximally great being exists.<br/><i>□M</i>"]:::deduction
    C1["<b>C1</b>: Therefore a maximally great being<br/>exists.<br/><i>M</i>"]:::conclusion
    O1{{"<b>O1</b>: By parity, it is possible that no<br/>maximally great being exists; in S5 that<br/>premise yields the opposite conclusion."}}:::objection
    R1{{"<b>R1</b>: The two possibility claims are not on a<br/>par: reasons to think maximal greatness<br/>coherent favour P1 over its rival."}}:::reply
    class O1 overruled
    Nature -.-> P1
    MG -.-> P2
    P1 --> D1
    P2 --> D1
    D1 --> C1
    O1 -. objects .-> P1
    R1 -. replies .-> O1

Sources

Nature

Alvin Plantinga, The Nature of Necessity, ch. X

MG

Maximal greatness includes necessary existence.

The argument

Objections and replies