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Work #1560 · Earliest

A Completeness Theorem in Modal Logic

Saul Kripke
1959 (Kripke aged 18) · English
Mathematical-logical paper · Mathematical logic / modal logic / analytic metaphysics

Kripke's 1959 founding paper — the possible-worlds semantics for modal logic

Attribute Fingerprint

Rows where works disagree are highlighted in gold. The full ontology grid is shown.

Attribute A Completeness Theorem in Modal Logic (Earliest)
Time · Extent Infinite
Time · Ontological Status Substantival
Time · Grain Continuous
Time · Freedom Non-Deterministic
Time · Traversability Linear
Time · Dimensionality One
Time · Direction Uni-directional
Space · Extent Infinite
Space · Ontological Status Substantival
Space · Curvature Flat
Space · Dimensionality Three
Space · Locality Local
Matter · Extent Infinite
Matter · Ontological Status Substantival
Matter · Conservation Conserved
Matter · Dimensionality Three
Matter · Locality Local
Observer · Time Instance Single
Observer · Space Instance Single
Observer · Knowledge Extent Mediated
Observer · Knowledge Retainment Partial
Observer · Physicality Embodied
Observer · Agency Active
Observer · Number Plural
Observer · Metaphysical Agency Impersonal
Observer · Moral Authority Reason
Observer · Theological Method
Energy · Extent Infinite
Energy · Ontological Status Substantival
Energy · Conservation Conserved
Energy · Dispersibility Irreversible
Information · Ontological Status Substantival
Information · Cosmic Conservation Conserved
Information · Personal Conservation Non-conserved
Information · Granularity Continuous

Dimension-by-Dimension Evidence

What each work's passages reveal about its stance on each of the six dimensions.

Time

A Completeness Theorem in Modal Logic

1959 (published; submitted 1958). Kripke was eighteen at submission, an undergraduate at Harvard.

Space

A Completeness Theorem in Modal Logic

Omaha (Kripke's high-school years) / Harvard. Kripke had been working on these ideas since high school in Omaha.

Matter

A Completeness Theorem in Modal Logic

Single 14-page mathematical paper introducing the Kripke-frame structure (a set of possible worlds and an accessibility relation).

Observer

A Completeness Theorem in Modal Logic

Teenage Kripke. The author is an exceptional logician working at the foundations of modal logic before age twenty.

Energy

A Completeness Theorem in Modal Logic

Founding-logical energies. The paper inaugurates the framework that would shape modal logic, modal metaphysics, and philosophical logic for the next sixty years.

Information

A Completeness Theorem in Modal Logic

Single founding paper. The Kripke-semantic framework (worlds + accessibility relation + valuation) is the canonical model for modal-logical reasoning.

Internal Tensions

Where each work's argument pulls against itself.

A Completeness Theorem in Modal Logic

Founding paper of Kripke semantics — written by an 18-year-old Kripke as an undergraduate. The 1959 paper plus the 1963 follow-up made possible David Lewis's modal realism, Robert Stalnaker's possible-worlds semantics for conditionals, Alvin Plantinga's modal ontological argument, and the entire late-twentieth-century revival of analytic metaphysics of modality.