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Work #105

The Foundations of Arithmetic

Gottlob Frege
1884 · German
Logico-philosophical treatise · Analytic philosophy / logicism / philosophy of mathematics

Arithmetic is reducible to logic — numbers are not subjective ideas but objective abstract entities accessible to reason

Attribute Fingerprint

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

Attribute The Foundations of Arithmetic
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 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 Finite
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 Discrete

Dimension-by-Dimension Evidence

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

Time

The Foundations of Arithmetic

Numbers are timeless abstract objects. Real time in physical reality is the standard nineteenth-century framework.

Space

The Foundations of Arithmetic

Numbers are not in space. Standard treatment of physical space.

Matter

The Foundations of Arithmetic

Material objects are real but not the subject of arithmetic. Standard scientific realism.

Observer

The Foundations of Arithmetic

The Fregean observer is the rational agent capable of grasping objective thoughts. The "third realm" of objective thoughts is accessible to all rational minds.

Energy

The Foundations of Arithmetic

Not engaged.

Information

The Foundations of Arithmetic

Numbers and thoughts are substantival abstract informational entities. Personal information not philosophically privileged.

Internal Tensions

Where each work's argument pulls against itself.

The Foundations of Arithmetic

Russell's paradox destroyed the formal program of the Foundations; Frege's appendix to the Grundgesetze volume II (1903) acknowledged the catastrophe but could not resolve it. The philosophical achievements survived independently of the formal failure, and the twenty-first-century neo-logicism (Crispin Wright, Bob Hale) has attempted to recover the program with new principles.