Logic - Wikiparency

# Logic ## Microsim (three.js) <div class="microsim-player">  <p class="wt-pending"><strong>Microsim staged, not yet on the CDN.</strong> <code>Logic.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> *The formal backbone of computing: propositional connectives evaluate exactly as a Boolean circuit switches, and the valid-argument forms below are the inference rules that automatic theorem provers chain together to certify programs correct.* > Logic is the systematic study of valid inference — which conclusions *must* be true whenever a set of premises is true. Propositional logic builds statements from atomic propositions joined by connectives (and, or, not, if–then) and assigns each the truth value TRUE or FALSE. An argument form is *valid* when no assignment of truth values makes every premise true while the conclusion is false. This microsim lets you pick a classic argument form, flip the shared proposition's truth value, and watch in 3D whether the conclusion is forced — cleanly separating two valid forms from two seductive fallacies. ## About this microsim The scene draws an argument as a linked 3D structure — premises, a conditional, and a conclusion arranged in space. The argument-form selector chooses **Modus Ponens (valid)**, **Modus Tollens (valid)**, **Denying the Antecedent**, or **Affirming the Consequent**; the first two are deductively valid and the last two are formal fallacies. The **TRUE** toggle sets the truth value fed into the shared proposition, so you can test whether the conclusion is genuinely forced or merely suggested. Press **▶ Play** to animate truth propagating step-by-step from premises to conclusion, drag with the mouse to orbit the structure, and use **Reset View** to return the camera to its default angle. Because you *see* the conclusion resolve before reading why, each fallacy shows up as a case where true premises leave the conclusion undetermined. ## Related microsims - Modus ponens — the canonical valid form, isolated and animated - Truth table — the row-by-row method every verdict here rests on - Validity (logic) — the exact property separating the valid forms from the fallacies - Formal fallacy — why affirming the consequent and denying the antecedent fail - Logical connective — the AND/OR/NOT/IF–THEN operators the premises are built from - Propositional calculus — the formal system these argument forms live inside - Negation — related ALGORITHM microsim ## Links (Wikipedia order)  `A_priori_and_a_posteriori` · `Abductive_reasoning` · `Abhidharma` · `Absolute_idealism` · `Achintya_Bheda_Abheda` · `Action_theory_(philosophy)` · `Advaita_Vedanta` · `Aesthetic_emotions` · `Aesthetics` · `African_philosophy` · `Africana_philosophy` · `Agriculturalism` · `Ajñana` · `Albertus_Magnus` · 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[[Inductive_reasoning]] · `Inference` · `Informal_fallacy` · `Informal_logic` · `Internalism_and_externalism` · `Interpretation_(logic)` · `Intuitionistic_logic` · `Iranian_philosophy` · `Irish_philosophy` · `Irving_Copi` · `Islamic_philosophy` · `Italian_idealism` · `Italian_philosophy` · `J._L._Mackie` · `Jaakko_Hintikka` · `Jain_philosophy` · `Jainism` · `Jan_Łukasiewicz` · `Japanese_philosophy` · `Jewish_philosophy` · `Joan_Moschovakis` · `John_P._Burgess` · `John_Rawls` · `John_Stuart_Mill` · `Judeo-Islamic_philosophies_(800–1400)` · `Kalam` · `King_(chess)` · `Knowledge` · `Kokugaku` · `Korean_Confucianism` · `Korean_philosophy` · `Krausism` · `Kurt_Gödel` · `Kyoto_School` · `Language` · `Large_cardinal` · `Law_of_excluded_middle` · `Legal_positivism` · `Legalism_(Chinese_philosophy)` · `Libertarianism_(metaphysics)` · `Linguistic_entailment` · `Linguistics` · `List_of_Boolean_algebra_topics` · `List_of_Slovene_philosophers` · `List_of_fallacies` · `List_of_logic_symbols` · 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`Principle_of_explosion` · `Prior_Analytics` · [[Probability]] · `Process_philosophy` · `Prolog` · `Proof_theory` · [[Property_(philosophy)]] · [[Proposition]] · `Propositional_logic` · `Psychologism` · `Psychology` · `Pudgalavada` · `Pyrrhonism` · `Pythagoreanism` · `Quantifier_(logic)` · `Quantum_logic` · [[Quantum_mechanics]] · `Quietism_(philosophy)` · `Rationalism` · `Rationality` · `Real_number` · `Reality` · `Reason` · `Reductionism` · `Reference` · `Reformed_epistemology` · `Relativism` · `Renaissance_humanism` · `Richard_Montague` · `Robert_Audi` · `Romanian_philosophy` · `Rule_of_inference` · `Russell's_paradox` · `Russian_cosmism` · `Russian_philosophy` · `Samkhya` · `Sarvastivada` · `Sautrāntika` · `Scholasticism` · `School_of_Names` · `School_of_Naturalists` · `School_of_the_Sextii` · `Scientific_method` · `Scientific_realism` · `Scientific_skepticism` · `Scientism` · `Scotism` · `Scottish_philosophy` · `Second_Sophistic` · `Semantics` · `Sense_and_reference` · `Sentence_(linguistics)` · `Sequent_calculus` · [[Set_theory]] · `Sheffer_stroke` · `Shuddhadvaita` · `Simon_Blackburn` · `Singular_term` · `Social_constructionism` · `Social_contract` · `Social_philosophy` · `Socialism` · `Solipsism` · `Sophist` · `Soundness` · `Spanish_philosophy` · `Speech_act` · `Square_of_opposition` · `Stephen_Cole_Kleene` · `Stoicism` · `Structuralism` · `Subject_(grammar)` · `Subjective_idealism` · `Subjectivism` · `Substitution_(logic)` · `Sufi_philosophy` · `Susan_Haack` · `Susanne_Bobzien` · `Svatantrika–Prasaṅgika_distinction` · `Syllogism` · `Symbol_(formal)` · `Syntax` · `Syntax_(logic)` · `Systemics` · `Taoism` · `Tautology_(logic)` · `Ted_Honderich` · `Temporal_logic` · `Term_logic` · `Terminology` · `Theoretical_philosophy` · `Thomism` · `Tiantai` · `Tibetan_Buddhism` · `Transactionalism` · `Transcendental_idealism` · `Transcendentalism` · [[Transistor]] · `Truth` · `Truth-bearer` · `Truth_condition` · `Truth_function` · `Truth_table` · `Truth_value` · `Ubuntu_philosophy` · `Utilitarianism` · `Vaisheshika` · `Validity_(logic)` · `Value_theory` · `Vector_logic` · `Vedanta` · `Vienna_Circle` · `Vietnamese_philosophy` · `Virtue_ethics` · `Vishishtadvaita` · `Well-formed_formula` · `Western_Marxism` · `Western_philosophy` · `Willard_Van_Orman_Quine` · `William_Kneale` · `William_of_Ockham` · `Xuanxue` · `Yangism` · `Yoga_Sutras_of_Patanjali` · `Yogachara` · `Yugoslav_philosophy` · `Zen` · `Zoroastrianism` · `Zurvanism` · `Ājīvika` · `Śūnyatā` ## Overview As a discipline, logic runs from Aristotle's term logic and syllogistic (4th century BC) through George Boole's algebra of thought (1847–1854) to the modern symbolic logic of Frege and Russell. Classical propositional logic rests on the principle of bivalence — every proposition is exactly TRUE or FALSE — and is *truth-functional*: the value of a compound statement is fixed entirely by the values of its parts. This framework underlies mathematical proof, digital hardware, and program verification. Its central lesson, made concrete by the four forms in the sim, is that validity is a property of an argument's *form*, independent of the particular content of its propositions. ## Valid forms and formal fallacies Write the conditional as $P \to Q$ ("if $P$ then $Qquot;). The two valid rules and two fallacies all start from that premise: $\frac{P \to Q,\ \ P}{\therefore\ Q}\ \text{(modus ponens)} \qquad \frac{P \to Q,\ \ \lnot Q}{\therefore\ \lnot P}\ \text{(modus tollens)}$ An argument is valid **iff** in every truth-table row where all premises are TRUE, the conclusion is TRUE too — equivalently, when (premises $\to$ conclusion) is a tautology. The material conditional's table is: | $P$ | $Q$ | $P \to Q$ | |---|---|---| | T | T | T | | T | F | F | | F | T | T | | F | F | T | *Affirming the consequent* infers $P$ from $P \to Q$ and $Q$. Row 3 ($P$ FALSE, $Q$ TRUE) makes both premises TRUE yet the conclusion $P$ FALSE — a countermodel, so the form is invalid. *Denying the antecedent* ($P \to Q,\ \lnot P \vdash \lnot Q$) fails on that very same row. Modus ponens and modus tollens have no such row, which is exactly what the animation reveals. ## Controls -> what each maps to | Control | Maps to | Range / values | Meaning | |---|---|---|---| | Argument-form choice | The inference rule under test | Modus Ponens (valid), Modus Tollens (valid), Denying the Antecedent, Affirming the Consequent | Selects which premise–conclusion pattern is drawn and evaluated | | TRUE | Truth value of the shared proposition | TRUE / FALSE (toggle) | Sets a premise's truth so you can hunt for a counterexample | | ▶ Play | Truth-propagation animation | Play / pause | Steps the inference from premises to conclusion | | Reset View | Camera orientation | Button (no range) | Returns the 3D view to its default angle | ## Learning objective After playing, a learner can predict whether an if–then argument is valid and explain why affirming the consequent and denying the antecedent fail — by pointing to the single truth-table row where true premises meet a false conclusion. ## Limits and connections This sim covers classical, bivalent propositional logic; predicate, modal, and many-valued systems extend it with quantifiers, necessity, or truth values beyond TRUE/FALSE. The same truth-functional evaluation is what a Boolean circuit computes in silicon, tying valid argument directly to hardware design. ## Poster & source <div class="microsim-fallback">  <p><em>Live microsim · <a href="https://wikitube-3d-microsims.netlify.app/Logic.html">open full</a> · source: Microsims for Dissemination/ALGORITHM_microsims/Logic.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/Logic) : [Wikitube](https://en.wikitube.io/wiki/Logic) ## Previous hub tags Tree parent: [[Game_theory]]. Legacy hubs: `ALGORITHM`. --- *Sources: 1 legacy note. Minted wave 1, 2026-07-30 (v1.6 order).*