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Work #659 · Early

On Formally Undecidable Propositions of Principia Mathematica and Related Systems

Kurt Gödel
1931 · German
Mathematical-logical paper · Foundations of mathematics

Gödel's 1931 foundational paper — the incompleteness theorems

Attribute Fingerprint

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

Attribute On Formally Undecidable Propositions of Principia Mathematica and Related Systems (Early)
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 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 Continuous

Dimension-by-Dimension Evidence

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

Time

On Formally Undecidable Propositions of Principia Mathematica and Related Systems

The eternal time of mathematical truth.

Space

On Formally Undecidable Propositions of Principia Mathematica and Related Systems

The formal-system space.

Matter

On Formally Undecidable Propositions of Principia Mathematica and Related Systems

The world arithmetized via Gödel-numbering.

Observer

On Formally Undecidable Propositions of Principia Mathematica and Related Systems

The mathematical proof-theorist.

Energy

On Formally Undecidable Propositions of Principia Mathematica and Related Systems

Energies of mathematical proof.

Information

On Formally Undecidable Propositions of Principia Mathematica and Related Systems

Foundational mathematical-incompleteness framework.

Internal Tensions

Where each work's argument pulls against itself.

On Formally Undecidable Propositions of Principia Mathematica and Related Systems

Gödel's incompleteness theorems foundational for foundations of math, logic, and theory of computation.