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Work #159 · Early (both authors)

Principia Mathematica

Alfred North Whitehead and Bertrand Russell
1910 (vol. 1), 1912 (vol. 2), 1913 (vol. 3); 2nd edition 1925-27 · English
Multi-volume formal-logical treatise · Analytic philosophy / philosophy of mathematics / mathematical logic

The logicist programme in its most ambitious form — three volumes deriving arithmetic, set theory, and analysis from a small set of logical primitives

Attribute Fingerprint

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

Attribute Principia Mathematica (Early (both authors))
Time · Extent Infinite
Time · Ontological Status Relational
Time · Grain Continuous
Time · Freedom Deterministic
Time · Traversability Linear
Time · Dimensionality One
Time · Direction Uni-directional
Space · Extent Infinite
Space · Ontological Status Relational
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 Infinite
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

Principia Mathematica

The logical apparatus is timeless; physical time enters only via its mathematical representation.

Space

Principia Mathematica

Pure logical space; physical space is reconstructed as a derivation from arithmetic and set theory.

Matter

Principia Mathematica

Mathematical-logical reality is the focus; physical matter is presupposed but not analysed.

Observer

Principia Mathematica

The mathematician-logician as ideal rational observer, with total knowledge of the logical apparatus and its consequences (the logicist ideal).

Energy

Principia Mathematica

Not addressed; the work's subject is logical structure, not physical dynamics.

Information

Principia Mathematica

Discrete, symbolic, conserved — the information of the proof system is the focus.

Internal Tensions

Where each work's argument pulls against itself.

Principia Mathematica

Gödel's 1931 incompleteness theorems demonstrated that the logicist programme cannot fully succeed: any consistent formal system powerful enough to express arithmetic contains truths it cannot prove. The ramified theory of types proved cumbersome and was replaced by Zermelo-Fraenkel set theory in subsequent foundational work. The two authors diverged sharply after the work: Whitehead to process metaphysics, Russell to political writing. The work's relation to subsequent philosophy of mathematics (intuitionism, structuralism, neo-logicism, mathematical naturalism) remains an active area of research.