The Tractatus, computed

A book that wanted to be run

These snippets are distilled from the text-driven book pass — seven scripts walking the numbered tree 1 → 7, every claim an expect(...), verified against the Ogden translation (all 526 propositions, extracted from Project Gutenberg #5740). The doctrine-driven companion is the logical-atomism pass.

1.1 · The world is the totality of facts, not of things

Introduce a new object and no truth changes; assert a new fact and the world grows. And the totality determines what is not the case (2.05) — absence is closed-world, not mystery.

4.27 / 4.42 · Counting the possible

Wittgenstein gives the combinatorics as sums: K_n = Σ C(n,ν) truth-possibilities of n elementary propositions, and L_n = Σ C(K_n,κ) possible propositions over them. Both formulas, computed as written.

5.101 · The sixteen truth-functions

Proposition 5.101 is a table: every truth-function of two elementary propositions with its truth-condition code, rows running (T,T), (F,T), (T,F), (F,F). The codes below are transcribed from the book and recomputed — all sixteen are checked in the full script.

5.5 / 5.502 · Everything from N(ξ̄)

N takes a multiplicity of propositions and denies them all. One operation regenerates negation, disjunction, conjunction, implication — and the two limiting cases.

5.15 · Probability, before Kolmogorov

The measure r gives to s is the ratio of shared truth-grounds to r's truth-grounds — and because Axioma's / is exact rational arithmetic, the answers come out as the fractions Wittgenstein wrote: independent elementaries give each other 1/2 (5.152), entailment gives 1, a disjunction gives its conjunction 1/3.

6.02 / 6.241 · "A number is the exponent of an operation"

Ω⁰'x = x; Ω^ν+1'x = Ω'Ω^ν'x. Numbers arise as iteration counts — and 6.241's proof of 2 × 2 = 4 says (Ω²)² = Ω⁴ for any operation. Try it with two different Ω.

6.126 · Calculemus, 1921

So let the machine determine it: φ is a tautology exactly when ¬φ excludes every truth-possibility, and the engine's propositional decider ([logic/sat], a DPLL) settles that mechanically. And where logic ends, so does necessity: the sun rising tomorrow is "an hypothesis" (6.36311) — on the grounding ladder it lands as a defeasible conjecture, cancellable, while the tautology survives everything (6.37: only logical necessity).

6.41 / 6.43 / 7 · Value, limits, silence

"In the world there is no value" — a bare fact is axiologically silent until an agent judges from outside. And 6.43: good willing changes the limits of the world, not the facts — after the judgment, the fact extent is untouched; only the overlay differs. "The world of the happy is quite another than that of the unhappy."

The same architecture carries Spinoza's "good and bad indicate no positive quality in things" — see the Ethics study. Whereof one cannot compute, thereof the pass keeps an honest gap ledger.