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Work #1564 · Middle-to-late

What is Cantor's Continuum Problem?

Kurt Gödel
1947 (revised and expanded 1964) · English
Philosophical-mathematical paper · Mathematical logic / philosophy of mathematics / mathematical Platonism

Gödel's 1947/1964 'What Is Cantor's Continuum Problem?' — the Platonist statement of his philosophy of mathematics

Attribute Fingerprint

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

Attribute What is Cantor's Continuum Problem? (Middle-to-late)
Time · Extent Infinite
Time · Ontological Status Substantival
Time · Grain Continuous
Time · Freedom Deterministic
Time · Traversability Linear
Time · Dimensionality One
Time · Direction Uni-directional
Space · Extent Infinite
Space · Ontological Status Substantival
Space · Curvature Curved
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 Total
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 Conserved
Information · Granularity Continuous

Dimension-by-Dimension Evidence

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

Time

What is Cantor's Continuum Problem?

1947 first version; 1964 substantially expanded version (after Cohen's 1963 independence proof).

Space

What is Cantor's Continuum Problem?

Institute for Advanced Study, Princeton — Gödel's institutional base from 1940 until his 1978 death.

Matter

What is Cantor's Continuum Problem?

Single philosophical paper (~10 pages in original 1947; ~30 pages with 1964 supplement). Form is essay-philosophical: Gödel sets out the mathematical situation, then the philosophical interpretation.

Observer

What is Cantor's Continuum Problem?

Middle-to-late Gödel. The 1947 paper is by the Gödel who had proven the consistency of CH (1940); the 1964 supplement is by the Gödel responding to Cohen's just-published independence result.

Energy

What is Cantor's Continuum Problem?

Philosophical-Platonist energies. The paper is Gödel's most explicit philosophical statement of his mathematical realism.

Information

What is Cantor's Continuum Problem?

Short paper plus substantial 1964 supplement. Together they constitute Gödel's principal philosophical-mathematical statement.

Internal Tensions

Where each work's argument pulls against itself.

What is Cantor's Continuum Problem?

Canonical twentieth-century statement of mathematical Platonism. Continuously cited in philosophy of mathematics; the central reference point for the realist position against constructivism (Brouwer), formalism (late Hilbert), nominalism (Field, Burgess and Rosen), and structuralism (Shapiro, Resnik). The 'large cardinal' research programme since Gödel has been driven in part by his proposal that new axioms might settle CH.