Work Classification Layer
Compare Works
Pick two or more works to set their attribute fingerprints, dimension-by-dimension passages, and shared school embodiments side by side. Especially useful for author-stage comparisons (Wittgenstein early vs late) and for setting a single tradition's foundational texts against each other.
The Consistency of the Axiom of Choice and the Generalized Continuum Hypothesis
Gödel's 1940 monograph — relative consistency of the Axiom of Choice and the Generalized Continuum Hypothesis with ZF set theory
Attribute Fingerprint
Rows where works disagree are highlighted in gold. The full ontology grid is shown.
| Attribute | The Consistency of the Axiom of Choice and the Generalized Continuum Hypothesis (Middle) |
|---|---|
| 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 | Curved |
| 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 | Mediated |
| Observer · Knowledge Retainment | Total |
| Observer · Physicality | Embodied |
| Observer · Agency | Active |
| Observer · Number | Plural |
| Observer · Metaphysical Agency | Impersonal |
| 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
The Consistency of the Axiom of Choice and the Generalized Continuum Hypothesis
1940. Gödel was 33; he had emigrated from Vienna to Princeton in early 1940 after escaping Nazi-occupied Europe via the Trans-Siberian Railway and Pacific crossing.
Space
The Consistency of the Axiom of Choice and the Generalized Continuum Hypothesis
Institute for Advanced Study, Princeton. The 1938-39 lectures (delivered before his emigration to America was permanent) were the basis for the published monograph.
Matter
The Consistency of the Axiom of Choice and the Generalized Continuum Hypothesis
Single mathematical monograph (~70 pages). Form is technical-mathematical: definitions, theorems, proofs in standard set-theoretic notation.
Observer
The Consistency of the Axiom of Choice and the Generalized Continuum Hypothesis
Middle Gödel. The observer is the logician already famous for the 1931 incompleteness theorems, now turning to set theory's foundational questions.
Energy
The Consistency of the Axiom of Choice and the Generalized Continuum Hypothesis
Foundational-mathematical energies. The book is one of the major twentieth-century contributions to set theory, comparable in importance to Zermelo's 1908 axiomatisation and Cohen's 1963 independence proof.
Information
The Consistency of the Axiom of Choice and the Generalized Continuum Hypothesis
Single lecture-derived monograph plus subsequent editions. The constructible-universe construction has become a central tool in modern set theory.
Internal Tensions
Where each work's argument pulls against itself.
Gödel's major set-theoretic contribution; the constructible-universe construction remains a central tool. Together with Cohen's 1963 independence proof for the negations of AC and GCH, it definitively established the independence of these axioms from ZF — answering a question Cantor had posed in the 1870s and Hilbert had placed first on his 1900 list of mathematical problems.