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Work #801 · Mid

Foundations of Geometry

David Hilbert
1899 (1st ed.); 1903-1971 (multiple subsequent eds) · German
Mathematical treatise · Turn-of-the-century mathematical formalism

Hilbert's 1899 formal axiomatization of Euclidean geometry — the foundation of modern formalism

Attribute Fingerprint

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

Attribute Foundations of Geometry (Mid)
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 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 Partial
Observer · Knowledge Retainment Total
Observer · Physicality Embodied
Observer · Agency Both
Observer · Number Plural
Observer · Metaphysical Agency None
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 Discrete

Dimension-by-Dimension Evidence

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

⧖

Time

Foundations of Geometry

The timeless time of mathematical proof.

✦

Space

Foundations of Geometry

The formal space of Euclidean geometry.

◉

Matter

Foundations of Geometry

Formal primitives — points, lines, planes.

◎

Observer

Foundations of Geometry

The mathematician.

⚡

Energy

Foundations of Geometry

Energies of mathematical reasoning.

⧉

Information

Foundations of Geometry

The axiomatic system as formal information.

Internal Tensions

Where each work's argument pulls against itself.

Foundations of Geometry

Hilbert's Foundations of Geometry: founding work of modern mathematical formalism; central reference for the Hilbert Program and the modern axiomatic method.