The Argument from Contingency

G. W. Leibniz

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;
    PNC(["PNC: Nothing can both be and not be in the<br/>same respect at the same time."]):::axiom
    PSR(["PSR: Whatever is contingent has an<br/>explanation of its existence."]):::axiom
    ExNihilo(["ExNihilo: Nothing comes from nothing."]):::axiom
    Regress(["Regress: An actually infinite regress of<br/>dependent causes is impossible."]):::axiom
    Monadology(["Monadology: G. W. Leibniz, Monadology, §§ 36–38"]):::axiom
    Origination(["Origination: G. W. Leibniz, On the Ultimate<br/>Origination of Things, 1697"]):::axiom
    NonContradiction["<b>NonContradiction</b>: No proposition is both true and false.<br/><i>∀F:prop. ∀x. ¬(F(x) ∧ ¬F(x))</i>"]:::premise
    class NonContradiction imported
    PSRPremise["<b>PSRPremise</b>: Every contingent being has an<br/>explanation of its existence.<br/><i>∀x. Contingent(x) → (∃y. Explains(y, x))</i>"]:::premise
    class PSRPremise imported
    CausalPrinciple["<b>CausalPrinciple</b>: Whatever begins to exist has a cause.<br/><i>∀x. Began(x) → (∃y. Causes(y, x))</i>"]:::premise
    class CausalPrinciple imported
    P2["<b>P2</b>: The universe is contingent: it might not<br/>have existed.<br/><i>Contingent(universe)</i>"]:::premise
    P3["<b>P3</b>: Whatever explains the existence of the<br/>universe is a necessary being beyond it,<br/>which is God.<br/><i>∀y. Explains(y, universe) → God(y)</i>"]:::premise
    D1["<b>D1</b>: Therefore the universe has an<br/>explanation of its existence.<br/><i>∃y. Explains(y, universe)</i>"]:::deduction
    C1["<b>C1</b>: Therefore God exists.<br/><i>∃y. God(y)</i>"]:::conclusion
    O1{{"<b>O1</b>: The universe might be explained by a<br/>further contingent cause, or by itself<br/>as a brute fact."}}:::objection
    R1{{"<b>R1</b>: A further contingent cause is part of<br/>the universe and needs explaining in<br/>turn; a brute fact is no explanation at<br/>all."}}:::reply
    class O1 overruled
    PNC -.-> NonContradiction
    PSR -.-> PSRPremise
    ExNihilo -.-> CausalPrinciple
    Monadology -.-> P2
    Origination -.-> P3
    PSRPremise --> D1
    P2 --> D1
    D1 --> C1
    P3 --> C1
    O1 -. objects .-> P3
    R1 -. replies .-> O1

Sources

PNC

Nothing can both be and not be in the same respect at the same time.

PSR

Whatever is contingent has an explanation of its existence.

ExNihilo

Nothing comes from nothing.

Regress

An actually infinite regress of dependent causes is impossible.

Monadology

G. W. Leibniz, Monadology, §§ 36–38

Origination

G. W. Leibniz, On the Ultimate Origination of Things, 1697

Definitions

Contingent(x)

◇¬Exists(x)

Necessary(x)

□Exists(x)

The argument

Objections and replies