Proposition - Wikiparency

# Proposition ## Microsim (three.js) <div class="microsim-player">  <p class="wt-pending"><strong>Microsim staged, not yet on the CDN.</strong> <code>Proposition.html</code> is built and deploy-ready in <code>Microsims for Dissemination/</code>, but the Netlify project still serves the geometry+spintronics set only. The player is disabled until the deploy lands; the explanatory text below is unchanged.</p>   </div> *A proposition is the atom of truth that Propositional calculus is built from — the smallest thing classical logic asks to be true or false under the Principle of bivalence, long before any Logical connective or Truth function combines it with another.* > A **proposition** is the content of a declarative statement — something that is definitely either true or false. It is not a question, a command, or an exclamation, and it is not the sentence itself but the claim the sentence makes. This microsim deals you a deck of "statement cards" and lets you sort the ones that carry a truth value from the ones that do not. Each card is a candidate, and your job is to decide whether it is truth-apt. Pressing **Shuffle New Examples** deals a fresh hand so the boundary between proposition and non-proposition comes into focus. ## About this microsim The sim presents individual **statement cards** — short sentences such as "7 is prime," "Close the door," or "What time is it?" — and invites you to judge each one as a proposition or not. Because a proposition must be capable of being true or false, declaratives pass while questions (interrogatives), commands (imperatives), and exclamations fail; open sentences like "x > 5" also fail until their variable is fixed. The one real control, **🔄 Shuffle New Examples**, resamples the deck: each press draws a new mix of true declaratives, false declaratives, and non-truth-apt sentences, so you see the pattern repeatedly rather than memorizing one set. The show-before-tell move is to shuffle a few times and try to predict, before reading closely, which cards will and will not carry a truth value. ## Related microsims - Propositional calculus — see how propositions become the atoms of a full formal system. - Truth table — enumerate the true/false assignments a proposition can take. - Principle of bivalence — the assumption that every proposition is exactly true or false. - Logical connective — combine atomic propositions into compound ones. - Predicate (mathematical logic) — what an open sentence becomes once its variable is bound. - Argument — propositions in their working role as premises and conclusion. - Existential quantification — related ALGORITHM microsim - Possible world — related ALGORITHM microsim ## Links (Wikipedia order)  `A._J._Ayer` · `A_priori_and_a_posteriori` · `Abductive_reasoning` · `Al-Farabi` · `Alciphron_(book)` · `Alethic_modality` · `Alternative_semantics` · `Ambiguity` · 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`Xunzi_(philosopher)` · `Zhuang_Zhou` ## Overview In logic and analytic philosophy, a **proposition** is the primary bearer of truth value. It is the meaning or content expressed by a declarative sentence, abstracted from the particular words: the English "Snow is white" and the German "Schnee ist weiß" express the same proposition. The notion is central to classical logic, where the principle of bivalence holds that every proposition is exactly one of true or false. Propositions are what arguments are made of — the premises and conclusion of an inference are propositions — and they are the atoms that propositional logic combines with connectives such as *and*, *or*, *not*, and *if…then*. The distinction between a proposition and the sentence expressing it, sharpened by Frege and Russell in the early analytic tradition, underlies modern formal semantics and automated reasoning. ## What counts as a proposition A sentence expresses a proposition only if it is **truth-apt** — capable, in principle, of being true or false. This immediately separates declarative sentences from other grammatical moods: | Statement | Mood / type | Proposition? | Truth value | |---|---|---|---| | "9 is divisible by 3" | Declarative | Yes | True | | "Paris is in Asia" | Declarative | Yes | False | | "Is it raining?" | Interrogative | No | — | | "Shut the window." | Imperative | No | — | | "x > 5" | Open sentence | No (a predicate) | Depends on x | | "This sentence is false." | Self-referential | Contested | Paradox | An **atomic** (simple) proposition makes a single claim; **compound** propositions are built from atomic ones with logical connectives, and their value is a truth function of their parts. Formally, if $P$ and $Q$ are propositions, so are $\neg P$, $P \wedge Q$, $P \vee Q$, and $P \rightarrow Q$, and each takes a value in $\{\text{true}, \text{false}\}$. Under bivalence there are exactly $2^n$ truth-value assignments to $n$ atomic propositions — the rows of a truth table. ## Controls -> what each maps to | Control | Maps to | Range / values | Meaning | |---|---|---|---| | 🔄 Shuffle New Examples | Resampling the example deck | Button (single action) | Deals a fresh set of statement cards — a new mix of true declaratives, false declaratives, questions, commands, and open sentences — so you can re-test the proposition / non-proposition boundary on unfamiliar cases. | ## Learning objective After playing, a learner can look at an arbitrary sentence and decide whether it expresses a proposition — that is, whether it is truth-apt — and explain why questions, commands, and open sentences do not. ## Limits and connections The sim treats truth-aptness classically: it assumes bivalence and sidesteps borderline cases such as the liar paradox, vague predicates, and future contingents, which many-valued and other non-classical logics handle differently. It also shows propositions in isolation; their real power appears once they are assembled into formulas and arguments and evaluated by truth tables. ## Poster & source <div class="microsim-fallback">  <p><em>Live microsim · <a href="https://wikitube-3d-microsims.netlify.app/Proposition.html">open full</a> · source: Microsims for Dissemination/ALGORITHM_microsims/Proposition.html</em></p> </div>  *Built to the [[WT!Three_js_Microsim_Master_Class|three.js Master Class]].*  ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Proposition) : [Wikitube](https://en.wikitube.io/wiki/Proposition) ## Previous hub tags Tree parent: [[Reliability_engineering]]. Legacy hubs: `ALGORITHM`. --- *Sources: 1 legacy note. Minted wave 1, 2026-07-30 (v1.6 order).*