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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.