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What is Truth?

By Alex Korablev · Computer science · Propositional Logic · Graduate · Conceptual / humanities · version 12

A conceptual companion on logical sentences, tautologies, contradictions, consistency, and why R's == is not logical equivalence.

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Licence: CC BY 4.0

Topicslogical equivalencetautologyconsistencypropositional logic

Assumption ledger

  • interpretationSentences are classified in sentential logic: an arithmetic truth such as 2 + 2 = 4 is necessarily true but not a tautology of form, so both answers are accepted as defensible
  • simplificationOnly two variables, p and q, and three expression pairs in the R lab
  • simplificationConsistency of pairs is judged by meaning, not by symbolic translation
  • interpretationDeliberately silly sentences strip away background knowledge so only logic remains
  • simplificationShared state stores only inputs: p, q, the chosen expression pair, whether the truth table is shown, the current sorter index, every sorter and pair answer, and the three written answers. Score, progress, feedback and the table are derived, so a group in a session sees identical results
  • simplificationWritten answers live in memory only (state keys response_s2_backwards, response_s2_charity, response_s2_hurley, capped at 2,000 characters); nothing is saved in the browser
  • dataImage: C. Ribsam & Sons trade card (1880s), Horticultural Artifacts Collection, Smithsonian Gardens; used as illustration directly below the sentence sorter only

Breakout check

✓ Ready for breakouts: every control we tried showed teammates the same thing.

Built-in checks 7 of 7 pass

  • p | q is equivalent to q | p (passes)
  • De Morgan: !(p & q) is equivalent to !p | !q (passes)
  • !p | q is not equivalent to !q | p (passes)
  • setState round-trips getState, including quiz answers, table visibility and written answers (passes)
  • Every sorter item accepts at least one valid category (passes)
  • Scoring with each item first accepted category gives full marks; no answers gives zero (passes)
  • Button state and written answers are written to and read from state (passes)

Cite this

Alex Korablev (2026). What is Truth? [Interactive model], version 12. Ideas at Play. https://ideasatplay.org/play/what-is-truth-da88c0?v=12 (CC BY 4.0)

History

  1. v12Every button effect (including show/hide truth table) and the three written answers are now in shared state and exposed through window.artifact; the browser-storage save was removed because the sandbox forbids it. (generated, Oct 20, 2026)current
  2. v11Sorter and pair-quiz answers, progress and feedback now live in the shared state (new keys sorterIdx, sorterAnswers, pairAnswers; existing keys unchanged), so teammates in a breakout see the same answers, and the score screen now offers Start over instead of a reload. (generated, Oct 20, 2026)View
  3. v10The trade-card figure now shows the image on the left and its caption on the right in a 50/50 width split; nothing else changed. (generated, Oct 19, 2026)View
  4. v9Moved the carrot trade card from a side column to directly beneath the sentence sorter block; nothing else changed. (generated, Oct 19, 2026)View
  5. v8Moved the carrot trade card from a full-page left column to a small figure beside the sentence sorter only; everything else is unchanged. (generated, Oct 19, 2026)View
  6. v7The trade-card image still sits in the same sticky left panel, but now fills half of that panel's width with its caption to the right. (generated, Oct 19, 2026)View
  7. v6The carrot trade-card image now fills the left half of the page (stacked above the content on narrow screens); everything else is unchanged. (generated, Oct 19, 2026)View
  8. v5Removed the sentence 'A man who is a carrot: silly, but still a sentence that is either true or false. Image: ' from the figure caption; nothing else changed. (generated, Oct 19, 2026)View
  9. v4Added the carrot-gentleman trade card (img1) with alt text and the requested citation as a caption in section 01, plus a minimal window.artifact interface; content and styling are otherwise unchanged. (generated, Oct 19, 2026)View
  10. v3The requested remote image URL could not be added because the sandbox blocks network images, so the artifact is unchanged; upload the image as an author image to have it embedded. (generated, Oct 19, 2026)View
  11. v2Changed only the footer text colour to the existing --ink-soft token so it meets the 4.5:1 contrast ratio; nothing else was altered. (generated, Oct 19, 2026)View
  12. v1Imported; lineage before import is not available. (imported, Oct 19, 2026)View

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