The Ontological Argument

Anselm of Canterbury

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;
    Proslogion(["Proslogion: Anselm, Proslogion, ch. 2"]):::axiom
    P1["<b>P1</b>: That than which nothing greater can be<br/>conceived exists in the understanding,<br/>even of the fool.<br/><i>InUnderstanding(g)</i>"]:::premise
    P2["<b>P2</b>: If it existed in the understanding<br/>alone, something greater could be<br/>conceived: the same being existing in<br/>reality.<br/><i>InUnderstanding(g) ∧ ¬InReality(g) → (∃x.<br/>Conceivable(x) ∧ Greater(x, g))</i>"]:::premise
    P3["<b>P3</b>: Nothing greater than it can be<br/>conceived.<br/><i>¬∃x. Conceivable(x) ∧ Greater(x, g)</i>"]:::premise
    C1["<b>C1</b>: Therefore that than which nothing<br/>greater can be conceived exists in<br/>reality.<br/><i>InReality(g)</i>"]:::conclusion
    O1{{"<b>O1</b>: Gaunilo (On Behalf of the Fool, § 6):<br/>the same reasoning would prove that the<br/>most excellent island exists."}}:::objection
    R1{{"<b>R1</b>: An island has no intrinsic maximum of<br/>greatness; only a being greatest in<br/>every respect has one, so the parody<br/>fails."}}:::reply
    class O1 overruled
    Proslogion -.-> P1
    Proslogion -.-> P2
    Proslogion -.-> P3
    P1 --> C1
    P2 --> C1
    P3 --> C1
    O1 -. objects .-> P2
    R1 -. replies .-> O1

Sources

Proslogion

Anselm, Proslogion, ch. 2

The argument

Objections and replies