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Work #1243 · Mature

Grundgesetze der Arithmetik (Basic Laws of Arithmetic)

Gottlob Frege
1893 (vol. 1), 1903 (vol. 2) · German
Formal-logical mathematical treatise · Mathematical logic / Logicism / Analytic philosophy

Frege's 1893-1903 systematic derivation of arithmetic from logic — the formal statement of logicism

Attribute Fingerprint

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

Attribute Grundgesetze der Arithmetik (Basic Laws of Arithmetic) (Mature)
Time · Extent Infinite
Time · Ontological Status Substantival
Time · Grain Discrete
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 Non-Local
Matter · Extent Infinite
Matter · Ontological Status Substantival
Matter · Conservation Conserved
Matter · Dimensionality Three
Matter · Locality Non-Local
Observer · Time Instance Single
Observer · Space Instance Single
Observer · Knowledge Extent Total
Observer · Knowledge Retainment Total
Observer · Physicality Embodied
Observer · Agency Active
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

Grundgesetze der Arithmetik (Basic Laws of Arithmetic)

The 1893-1903 mature-Frege Jena period.

Space

Grundgesetze der Arithmetik (Basic Laws of Arithmetic)

The Jena University setting.

Matter

Grundgesetze der Arithmetik (Basic Laws of Arithmetic)

The abstract-mathematical objects.

Observer

Grundgesetze der Arithmetik (Basic Laws of Arithmetic)

Frege as proper-mathematical-logical-philosophical investigator.

Energy

Grundgesetze der Arithmetik (Basic Laws of Arithmetic)

The intellectual-formal-logical energies.

Information

Grundgesetze der Arithmetik (Basic Laws of Arithmetic)

The systematic formal content of the two volumes.

Internal Tensions

Where each work's argument pulls against itself.

Grundgesetze der Arithmetik (Basic Laws of Arithmetic)

Russell's 1902 paradox letter revealed the system's inconsistency; Frege's 1903 appendix attempted a fix; subsequent work (Russell-Whitehead Principia, Zermelo-Fraenkel set theory) reconstructed the foundations.