negative

negatives (plural)
-ve (alternative abbreviation)
−ve (alternative abbreviation)

You can’t prove a negative.

(logic) A statement that something didn’t happen or doesn’t exist.


a priori

en-adj

a priori (comparative more a priori, superlative most a priori)

more a priori (comparative)
most a priori (superlative)
apriori (alternative)

/ˌeɪ pɹaɪˈɔːɹaɪ/

/ˌɑː pɹiˈɔːɹi/

/ˌeɪ pɹaɪˈɔːɹi/

First attested in 1610. Learned borrowing from Medieval Latin ā priōrī (“involving reasoning from cause to effect; from first principles”, literally “from the former”).

lbor

In his opening argument, the student mentioned nothing beyond his a priori knowledge.

(logic) Based on hypothesis and theory rather than experiment or empirical evidence.

مُسَلَّم بِه

logic: based on hypothesis rather than experiment

لَا يُحْتَاجُ إِثْبَاتَة إِلَى تَجْرِبَة


a priori

/ˌeɪ pɹaɪˈɔːɹaɪ/

/ˌɑː pɹiˈɔːɹi/

/ˌeɪ pɹaɪˈɔːɹi/

deductively[Appendix:Glossary#broadly|broadly]] synonymous outside of philosophic arcanity>

(logic) In a way based on theoretical deduction rather than empirical observation.


a priori

NB - Pronunciation of Norwegian Bokmål «a priori».ogg

Borrowed from Medieval Latin ā priōrī (“involving reasoning from cause to effect; from first principles”, literally “from the former”).

bor

førmoderne samfunn … hvor forskjell ennå ikke betraktes a priori som en mangel

pre-modern societies… where difference is not yet considered a priori as a deficiency

viten a priori

(logic, philosophy) a priori; based on hypothesis rather than experiment.


a priori

pl-adj

a priori (not comparable, no derived adverb)

Learned borrowing from Medieval Latin ā priōrī (“involving reasoning from cause to effect; from first principles”, literally “from the former”).


a priori

Unadapted borrowing from Medieval Latin ā priōrī (“involving reasoning from cause to effect; from first principles”, literally “from the former”).


a priori

bor+

Borrowed from Medieval Latin ā priōrī (“involving reasoning from cause to effect; from first principles”, literally “from the former”)


casus

(logic, philosophy, obsolete) A possible world, as a starting point for reasoning.


a posteriori

en-adj

a posteriori (comparative more a posteriori, superlative most a posteriori)

more a posteriori (comparative)
most a posteriori (superlative)

Learned borrowing from Medieval Latin ā posteriōrī (“involving reasoning from effect to cause, from experience to theory”, literally “from what follows”). Popularized from the 19th century in reference to the work of Immanuel Kant.

learned borrowing

What Locke calls "knowledge" they have called "a priori knowledge"; what he calls "opinion" or "belief" they have called "a posteriori" or "empirical knowledge".

1988, R. S. Woolhouse, The empiricists, Oxford University Press:

inductive[Appendix:Glossary#broadly|broadly]] synonymous outside of philosophic arcanity>

empirical

involving induction of theories from facts

(logic) Involving induction of theories from facts.

апастэрыёрны

involving deduction of theories from facts


a posteriori

FALLACIES of the modern worldview have to do with the conception of the world as substance or machinery, mistaking abstractions for reality, confusing origins and truth, failing to attribute feeling to things that feel, recognising ethics as exclusively anthropocentric, thinking a posteriori, objectifying facts as separated from values, reducing the complex to the simple and dividing knowledge into distinct disciplines that produce experts who are often wrong.

inductively[Appendix:Glossary#broadly|broadly]] synonymous outside of philosophic arcanity>

(logic) In a manner that deduces theories from facts.

البعديَة

in a manner that deduces theories from facts


a posteriori

NB - Pronunciation of Norwegian Bokmål «a posteriori».ogg

Learned borrowing from Latin ā posteriōrī (“from what follows; from what [ must ] follow”), first part from Latin ā (“from, away from, out of”), alternative form of ab (“from, away from, out of, down from”) by apocope (not used before a vowel or h), from Proto-Italic *ab, from Proto-Indo-European *h₂epó (“off, away”). Last part from Latin posteriōrī, dative singular of posterior (“after, next”), comparative degree of posterus (“next, after”), from post (“behind, after”), from earlier poste, from Proto-Italic *posti, from Proto-Indo-European *pósti, from *pós (“afterwards; by, at”).

from what follows; from what 􂀿 must 􂁀 follow

der

at 2+2 er 4 som er a priori viten og at vi har sanseerfaring som er a posteriori viten er ikke et bevis for at Jesus ikke eksisterer

that 2 + 2 is 4 which is a priori knowledge and that we have sensory experience which is a posteriori knowledge is not a proof that Jesus does not exist

viten a posteriori

a posteriori knowledge; knowledge based on experience

(logic, philosophy) a posteriori, involving deduction of theories from facts.


a posteriori

pl-adj

a posteriori (not comparable, no derived adverb)

Learned borrowing from Latin ā posteriōrī.

lbor

(literary, logic, philosophy) a posteriori


if and only if

LL-Q1860 (eng)-Vealhurl-if and only if.wav

LL-Q1860 (eng)-Flame, not lame-if and only if.wav

A rectangle is a square if and only if all four of its sides have the same length.

An integer is even if and only if its square is also even.

(logic, mathematics) Is equivalent to; implies and is implied by; is true and false in the same cases as.

тогда́ и то́лько тогда́

, когда́ ...


ratio

la-noun

ratiō f (genitive ratiōnis); third declension

ratiō (canonical feminine)
ratiōnis (genitive)
ratiō (nominative singular)
ratiōnēs (nominative plural)
ratiōnis (genitive singular)
ratiōnum (genitive plural)
ratiōnī (dative singular)
ratiōnibus (dative plural)
ratiōnem (accusative singular)
ratiōnēs (accusative plural)
ratiōne (ablative singular)
ratiōnibus (ablative plural)
ratiō (singular vocative)
ratiōnēs (plural vocative)

Dalmatian:

rasaun, ratiáun

Italo-Romance:

Italian: ragione

Neapolitan: ragiune

Sicilian: ragiuni, raggiuni, raciuni

Padanian:

Friulian: reson

Ladin: reson

Piedmontese: rason

Romansch: raschun, raschung, radschun

Venetan: raxon, rajon

Northern Gallo-Romance:

Old French: raison

French: raison

Walloon: råjhon

→ English: reason

→ Irish: réasún

Southern Gallo-Romance:

Aragonese: razón

Catalan: raó

Occitan: rason

Ibero-Romance:

Asturian: razón

Galician: razón

Portuguese: razão

Spanish: razón

Insular Romance: (newer forms influenced by Italian)

Old Sardinian: rathone, rethone

Middle Sardinian: rasione, rexione, arresoni

Modern Sardinian: regione, rejone, raxoni

Ancient borrowings:

→ Proto-Albanian: *rrësye

Albanian: arsye, arrësye

→ Proto-Brythonic: *rrėd

Breton: ret

Cornish: res

Welsh: rhaid

From the nominative ratiō:

Catalan: ràtio

Dutch: ratio
→ Indonesian: rasio

English: ratio

Esperanto: racio

French: ratio

Italian: ratio

Polish: racja

Portuguese: rácio

Romanian: rație

Spanish: ratio

From the accusative ratiōnem:

Catalan: ració

English: ration

French: ration

Galician: ración

Italian: razione

Portuguese: ração

Romanian: rațiune

Spanish: ración

Turkish: racon

doctrine, system, philosophy (collective body of the teachings of a school of thought)


paradox

en-noun

paradox (countable and uncountable, plural paradoxes)

From Middle French paradoxe, from Latin paradoxum, from Ancient Greek παράδοξος (parádoxos, “unexpected, strange”).

{{t|af|paradoks}

apparent contradiction which is nonetheless true

He is a paradox; you would not expect him in that political party.

You are a paradox of bitch and angel.

1999, Virginia Henley, A Year and a Day, →ISBN, page 315:

A person or thing having contradictory properties.

矛盾的人

person or thing with contradictory properties


perspicuous

en-adj

perspicuous (comparative more perspicuous, superlative most perspicuous)

more perspicuous (comparative)
most perspicuous (superlative)

From Latin perspicuus, in turn from perspiciō (“see through”).

(logic) (Of a language or notation) the process of inference from premises to conclusion is explicitly laid out.


abductive

LL-Q1860 (eng)-Flame, not lame-abductive.wav

(logic, computing) Being or relating to a logical process of abduction or inference.


particular

particular (comparative more particular, superlative most particular)

more particular (comparative)
most particular (superlative)
non-comparable (also)
perticular (alternative)

From Middle English particuler, from Anglo-Norman particuler, Middle French particuler, particulier, from Late Latin particularis (“partial; separate, individual”), from Latin particula (“(small) part”). Equivalent to particle + -ar. Compare particle.

подробен

concerned with, or attentive to, details; minute; precise; fastidious

a particular proposition, opposed to "universal", e.g. (particular affirmative) "Some men are wise"; (particular negative) "Some men are not wise".

(logic) Forming a part of a genus; relatively limited in extension; affirmed or denied of a part of a subject.


conclusion

en-noun

conclusion (countable and uncountable, plural conclusions)

conclusions (plural)
concl. (alternative)

From Middle English, borrowed from Old French conclusion, from Latin conclūsiō, from the past participle stem of conclūdere (“to conclude”), from con- + claudō, ultimately from Proto-Indo-European *kleh₂u- (“key, hook, nail”). By surface analysis, conclude + -sion.

der

He granted him both the major and minor, but denied him the conclusion.

1716 April 20 (Gregorian calendar), Joseph Addison, “The Free-holder: No. 32. Monday, April 9. [1716.]”, in The Works of the Right Honourable Joseph Addison, Esq; […], volume IV, London: […] Jacob Tonson, […], published 1721, →OCLC:

(logic) In an argument or syllogism, the proposition that follows as a necessary consequence of the premises.


proposition

en-noun

proposition (countable and uncountable, plural propositions)

/ˌpɹɑpəˈzɪʃən/

From Middle English proposicioun, from Old French proposicion, from Latin prōpositiō, from the verb prōponō.

“Wiktionary is a good dictionary” is a proposition.

(countable, logic) The content of an assertion that may be taken as being true or false and is considered abstractly without reference to the linguistic sentence that constitutes the assertion; (Aristotelian logic) a predicate of a subject that is denied or affirmed and is connected by a copula.

قَضِيَّة

the abstract contents of a statement, without reference to its formulation


dilemma

PIE word
 *dwóh₁
First attested 1523, from Late Latin dilemma, from Ancient Greek δίλημμα (dílēmma, “ambiguous proposition”), from δι- (di-, “having two of”) + λῆμμα (lêmma, “premise, proposition”).

der

damned if one does and damned if one doesn't

en:syllogism about possibilities A, B, C, and D

(logic) A type of syllogism of the form "if A is true then B is true; if C is true then D is true; either A or C is true; therefore either B or D is true".


trilemma

The word is modelled on dilemma, with di- (“two, twice, double”) replaced by tri- (“three”).

It has been remarked as a characteristic of the late Sir Robert Peel, that in introducing his measures to the House of Commons, he often used the trilemma. "Three courses are before us—to go backward, to stand still, to go forward. We cannot go backward; we cannot stand still; we must, then, go forward."

1851, [James William Gilbart], Logic for the Million: A Familiar Exposition of the Art of Reasoning, London: Longman, Brown, Green & Longmans, →OCLC, part IV (The Points of Reasoning), section V (Reasoning by Compound Syllogism), subsection III (The Trilemma), page 324:

And in anticipation of it, while he [Johann Joseph Ignaz von Döllinger] declares at one moment that it would be profane to limit Divine Providence to an alternative, he affirms in the next that there can be no harm whatever in shutting it up to a supposed exhaustive trilemma.

1862 July 1, “Art. VII.—(1.) Kirche und Kirchen, Papstthum und Kirchenstaat. Historisch-politische Bertrachtungen von Joh. Jos. Ign. v. Döllinger. Zweiter unveränderter Abdruck. München: 1861. (2.) The Church and the Churches; or, The Papacy and The Temporal Power. An Historical and Political Review. By Dr. Döllinger. Translated by William Bernard MacCabe. London: 1862.”, in The British Quarterly Review, volume XXXVI, number LXXI, London: Jackson, Walford, & Hodder 18, St. Paul's Churchyard and Simpkin, Marshall and Co., Stationers' Hall Court; Edinburgh: W. Oliphant & Co.; Glasgow: J[ames] MacLehose; Dublin: J. Robertson, →OCLC, page 156:

universe of discourse
universe of discourse

(logic) An argument containing three alternatives, jointly exhaustive either under any condition(s) or under all condition(s) consistent with the universe of discourse of that argument, that each imply the same conclusion.

trilema

(logic) argument containing three alternatives


biner

id-adj

binèr (comparative lebih biner, superlative paling biner)

binèr (canonical)
lebih biner (comparative)
paling biner (superlative)
binari (alternative)

From Dutch binair (“binary”), from French binaire, from Latin bīnārius.

(logic) binary (concerning logic whose subject matter concerns binary states)


problematic

en-adj

problematic (comparative more problematic, superlative most problematic)

more problematic (comparative)
most problematic (superlative)

Borrowed from Middle French problématique, from Late Latin problematicus, from Ancient Greek προβληματικός (problēmatikós), from πρόβλημα (próblēma, “outjutting, barrier, problem”), from προβάλλω (probállō, “I throw, place before”), from πρό (pró, “before”) + βάλλω (bállō, “I throw, place”). By surface analysis, problem + -atic.

der

προβληματικός

(logic, dated) Only affirming the possibility that a predicate be actualised.


apophasis

la-noun

apophasis f (genitive apophasis); third declension

apophasis (genitive)
apophasis (nominative singular)
apophasēs (nominative plural)
apophasis (genitive singular)
apophasium (genitive plural)
apophasī (dative singular)
apophasibus (dative plural)
apophasem (accusative singular)
apophasēs (accusative plural)
apophasīs (accusative plural)
apophase (ablative singular)
apophasibus (ablative plural)
apophasis (singular vocative)
apophasēs (plural vocative)

English: apophasis

French: apophase

Galician: apófase

→ Finnish: apofaasi

Portuguese: apófase

→ Russian: Апофазия (Apofazija)

From Ancient Greek ἀπόφασις (apóphasis, “denial, negation”), ἀπο- (apo-, “away, from, off”) + φάσις (phásis, “statement, proposition”) from ἀπόφημι (apóphēmi, “speak out; say no, refuse, deny”) from Attic Greek φημί (phēmí), Doric Greek φᾱμί (phāmí) from Proto-Hellenic *pʰā́mā from Proto-Indo-European *bʰeh₂; whence via Proto-Italic *fāōr, *fāmā compare fārī, fābula, fāma, hence English fable, fame.

af

(Late Latin, logic, rhetoric) apophasis; ironically alluding to a subject matter by denying that the subject will be mentioned, embedded within a statement or rhetorical question whereby one, as it were, answers himself


scope

en-noun

scope (countable and uncountable, plural scopes)

→ Irish: scóp

From Italian scopo (“purpose”), from Latin scopus (“target”), from Ancient Greek σκοπός (skopós), from σκέπτομαι (sképtomai), from Proto-Indo-European *speḱ-. Etymologically related to skeptic and spectrum.

(logic) The shortest sub-wff of which a given instance of a logical connective is a part.


apodeictic

From Ancient Greek ἀποδεικτικός (apodeiktikós). Compare Latin apodicticus.

uder

ἀποδεικτικός

1855, John Miller Dow Meiklejohn (translator), 1787, Immanuel Kant, Critique of Pure Reason, 2nd Edition,
Thus, moreover, the principles of geometry- for example, that "in a triangle, two sides together are greater than the third," are never deduced from general conceptions of line and triangle, but from intuition, and this a priori, with apodeictic certainty.

Aristotle does, indeed, distinguish between (1) Logic, or Analytic, as the theory or method of arriving at true or apodeictic conclusions; and (2) Dialectic as the method of arriving at conclusions that are accepted or pass current[ly] as true,...

1896, Arthur Schopenhauer, translated by Thomas Bailey Saunders, The Art of Controversy, published 1831:

Descartes sought certainty in the existence of God grounded in apodeictic demonstrations.

2009, Jonathan Dancy, Ernest Sosa, Matthias Steup, A Companion to Epistemology:

(logic) Of the characteristic feature of a proposition that is necessary (or impossible): perfectly certain (or inconceivable) or incontrovertibly true (or false); self-evident.


~p


Introduced by Arend Heyting in “Die formalen Regeln der intuitionistischen Logik” (1930)

(x ≠ y) ↔ ¬(x = y)


conversion

en-noun

conversion (countable and uncountable, plural conversions)

From Middle English conversion, conversioun, borrowed from Anglo-Norman conversion, from Latin conversiō, from convertō.

обръщане

the act of having converted something or someone

המרת דת

to replace one religious faith with another

(logic) The act of interchanging the terms of a proposition, as by putting the subject in the place of the predicate, or vice versa.


valuation

valuation (countable and uncountable, plural valuations)

From Middle French valuation, noun of action from valuer, from Old French valoir.

propositional variable
propositional variable

(logic, propositional logic, model theory) An assignment of truth values to propositional variables, with a corresponding assignment of truth values to all propositional formulas with those variables (obtained through the recursive application of truth-valued functions corresponding to the logical connectives making up those formulas).

propositional logic; model theory; propositional logic; model theory

(logic, first-order logic, model theory) A structure, and the corresponding assignment of a truth value to each sentence in the language for that structure.

first-order logic; model theory; first-order logic; model theory


distribute

en-verb

distribute (third-person singular simple present distributes, present participle distributing, simple past and past participle distributed)

distributes (present singular third-person)
distributing (participle present)
distributed (participle past)
distributed (past)
distribute (infinitive)
distribute (first-person present singular)
distributed (first-person past singular)
distribute (present second-person singular)
distributest (archaic present second-person singular)
distributed (past second-person singular)
distributedst (archaic past second-person singular)
distributes (present singular third-person)
distributeth (archaic present singular third-person)
distributed (past singular third-person)
distribute (plural present)
distributed (past plural)
distribute (present subjunctive)
distributed (past subjunctive)
distribute (imperative present)
distributing (participle present)
distributed (participle past)

PIE word
 *tréyes
From Latin distributus, past participle of distribuere (“to divide, distribute”), from dis- (“apart”) + tribuere (“to give, impart”); see tribute.

A term is said to be distributed when it is taken universal, so as to stand for everything it is capable of being applied to.

1826, Richard Whately, Elements of Logic:

(logic) To employ (a term) in its whole extent; to take as universal in one premise.


obverse

(logic) A proposition obtained by obversion, e.g. All men are mortal => No man is immortal.


consistency

en-noun

consistency (countable and uncountable, plural consistencies)

a foolish consistency is the hobgoblin of little minds

(logic) Freedom from contradiction; the state of a system of axioms such that none of the propositions deduced from them are mutually contradictory.


mutually exclusive

(logic, probability theory) Describing multiple events or propositions such that the occurrence of any one implies the nonoccurrence of all other events or propositions. Boolean function of NOR logic gate

узаемавыключа́льны

describing multiple events being such that the occurrence of any one implies the nonoccurrence of all others


one-sided

en-adj

one-sided (comparative more one-sided, superlative most one-sided)

more one-sided (comparative)
most one-sided (superlative)

(logic, of a modality) That is necessarily or absolutely different than the respective coordinate alethic or temporal modality, but not its opposite.


comprehension

en-noun

comprehension (countable and uncountable, plural comprehensions)

/ˌkɒmpɹɪˈhɛnʃn̩/

/ˌkɑmpɹɪˈhɛnʃn̩/

Borrowed from Middle French compréhension, from Latin comprehensiō (“taking together”), from com- (“with, together”) + prehendō (“take”).

af

(logic) The totality of intensions, that is, attributes, characters, marks, properties, or qualities, that the object possesses, or else the totality of intensions that are pertinent to the context of a given discussion.


conjunctive

From Latin coniunctivus (“serving to connect”), from coniunctus, past participle of coniungere; compare conjoin. From late 15th c; grammatical sense from 1660s.

uder

(logic) Of or relating to logical conjunction.

konjunktiivinen

logic: of or relating to logical conjunction


disjunctive

en-adj

disjunctive (comparative more disjunctive, superlative most disjunctive)

more disjunctive (comparative)
most disjunctive (superlative)

LL-Q1860 (eng)-Flame, not lame-disjunctive.wav

From Middle English disjunctief, disjunctyf, from Middle French disjunctif and Latin disjunctīvus (“placed in opposition”).

der

An opposition of contrariety is not of purely logical concernment; and a disjunctive syllogism with characters opposed in contrariety, in fact, consists of as many pure disjunctive syllogisms as there are opposing predicates.

1873, Sir William Hamilton, Lectures on Metaphysics and Logic, page 235:


disjunctive

L. H. Atwater
Disjunctives may be turned into conditionals.


consistent

en-adj

consistent (comparative more consistent, superlative most consistent)

more consistent (comparative)
most consistent (superlative)

Borrowed from Latin cōnsistēntem, present participle of cōnsistō (“to agree with; to continue”), from con- (prefix indicating a being or bringing together of several objects) (ultimately from Proto-Indo-European *ḱóm (“beside, by, near, with”)) + sistō (“to cause to stand; to place, set”) (ultimately from Proto-Indo-European *stísteh₂ti (“to be standing up; to be getting up”), from the root *steh₂- (“to stand (up)”)).

der

When we ask whether ideas or terms are consistent or inconsistent with each other, the question really is, in what manner the relation presupposed between the ideas qualifies them for being combined as terms of a judgment.

1857, William Spalding, “Introduction”, in An Introduction to Logical Science: Being a Reprint of the Article “Logic” from the Eighth Edition of the Encyclopædia Britannica, Edinburgh: Adam and Charles Black, chapter II (The Function and Axioms of Logical Science), paragraph 12(2), pages 22–23:

Part of establishing a foundation for geometry was demonstrating that the axioms were consistent – that they could never lead to contradictions.

2008, Charles Petzold, “Centuries of Progress”, in The Annotated Turing: A Guided Tour through Alan Turing’s Historic Paper on Computability and the Turing Machine, Indianapolis, Ind.: Wiley Publishing, →ISBN, page 39:

(logic) Of a set of statements: such that no contradiction logically follows from them.


dilemo

eo-head

dilemo (accusative singular dilemon, plural dilemoj, accusative plural dilemojn)

dilemon (accusative singular)
dilemoj (plural)
dilemojn (accusative plural)

From Late Latin dilemma, from Ancient Greek δίλημμα (dílēmma, “ambiguous proposition”).

der

dilemma (a difficult circumstance or problem)


completeness

en-noun

completeness (usually uncountable, plural completenesses)

completenesses (plural)
completenesse (alternative)

THEOREM 37°. (Gödel's completeness theorem 1930.) In the predicate calculus H:
(a) If ⊨F [or even if א₀-⊨F], then ⊢F. If E_1,...,E_k⊨F [or even if E_1,...,E_kא₀-⊨F], then E_1,...,E_k⊢F.
(b) […]

2002, Stephen Cole Kleene, Mathematical Logic, Mineola, New York: Dover Publications, page 314

(logic) The property of a logical theory that whenever a wff is valid then it must also be a theorem. Symbolically, letting T represent a theory within logic L, this can be represented as the property that whenever T⊨ϕ is true, then T⊢ϕ must also be true, for any wff φ of logic L.


Gödel's incompleteness theorem

en-proper noun

Gödel's incompleteness theorem (plural Gödel's incompleteness theorems)

Gödel's incompleteness theorems (plural)

(logic, mathematics) Either of two theorems in mathematical logic that demonstrate the inherent limitations of every formal axiomatic system containing basic arithmetic.


theorem

/ˈθiː.ə.ɹəm/

From Middle French théorème, from Late Latin theōrēma, from Ancient Greek θεώρημα (theṓrēma, “speculation, proposition to be proved”) (Euclid), from θεωρέω (theōréō, “I look at, view, consider, examine”), from θεωρός (theōrós, “spectator”), from θέα (théa, “a view”) + ὁράω (horáō, “I see, look”). See also theory, and theater.

der

fundamental theorem of calculus for line integrals

Appendix:Roget MICRA thesaurus/Class IV § 454. Topic

(logic) A syntactically correct expression that is deducible from the given axioms of a deductive system.


vicious circle

vicious circles (plural)
vicious cycle (alternative)

LL-Q1860 (eng)-Flame, not lame-vicious circle.wav

(logic) A fallacy in which the premise is used to prove a conclusion which is then used to prove the premise.


apodosis

Learned borrowing from Late Latin apodosis, itself borrowed from Ancient Greek ἀπόδοσις (apódosis).

lbor

In "I will be coming if this weather holds up", "I will be coming" is the apodosis and "this weather holds up" is the protasis.

1943 Dornford Yates An Eye for a Tooth
"If, after that, there is anything more to be done. . ."
"Yes?"
"You’d ----well better do it," said Forecast.
The meaning with which he invested this blunt apodosis was unmistakable. Even I, an eavesdropper, found it most sinister: and I was not surprised when, after a little silence, the other turned on his heel and led the way to the road.

1997 Angeliki Athanasiadou, René Dirven (eds) On Conditionals Again p. 309 by Hansjakob Seiler
There is furthermore the claim that conditionals necessarily involve a causal relation from protasis to apodosis. This may hold for the "conjunctive" types signalling a natural consequence from protasis to apodosis, but becomes increasingly unlikely as we approach disjunctive structures of the type. "May I perish most miserably, if I do not love Xanthia." does not mean "May I perish most miserably, because I do not love Xanthia."

(logic, grammar) The consequential clause in a conditional sentence.

جَوَابُ الشَّرْط

the consequential clause in a conditional sentence


lógica

Borrowed from Latin logica, from Ancient Greek λογική (logikḗ, “logic”), from the feminine form of λογικός (logikós, “of or pertaining to speech or reason or reasoning, rational, reasonable”), from λόγος (lógos, “speech, reason”).


lógico

es-adj

lógico (feminine lógica, masculine plural lógicos, feminine plural lógicas)

lógica (feminine)
lógicos (masculine plural)
lógicas (feminine plural)


unconditional

unconditionals (plural)
inconditional (alternative obsolete)

/ˌʌnkənˈdɪʃənəl/

(logic) A conditional-like structure expressing that the consequent holds true regardless of the particular value of the antecedent.


inconsistency

en-noun

inconsistency (countable and uncountable, plural inconsistencies)

(logic) An incompatibility between two propositions that cannot both be true.


inconsistent

en-adj

inconsistent (comparative more inconsistent, superlative most inconsistent)

more inconsistent (comparative)
most inconsistent (superlative)

LL-Q1860 (eng)-Naomi Persephone Amethyst (NaomiAmethyst)-inconsistent.wav

(logic) Having the property that a contradiction can be derived.


falso

pt-adj

falso (feminine falsa, masculine plural falsos, feminine plural falsas)

falsa (feminine)
falsos (masculine plural)
falsas (feminine plural)

desctree

→ Malay: palsu
Indonesian: palsu
Peranakan Indonesian: palsoe

→? Marathi: फालस (phālas)

From Old Galician-Portuguese falso, from Latin falsus (“deceived”), from fallō (“to deceive”), from Proto-Indo-European *gʰwel- (“to lie, deceive”).


a fortiori

Ellipsis of ā fortiōrī ratiōne (literally “from a stronger reason”).

ellipsis

Cuius rei veritas vt magis elucescat queritur. An malefice valeant membra virilia virtute demonum vere et realiter vel solummodo prestigiosa apparitione auferre? et arguitur quod vere et realiter per argumentum a fortiori.

1486, Heinrich Kramer, “Pars prīma, Quaestiō nōna”, in Malleus maleficarum [The hammer of witches]^(https://la.wikisource.org/wiki/Malleus_maleficarum_(ed._II)):

In order to make the truth of this matter clearer, it is asked whether witches can—with the help of devils—really and actually remove the virile members, or can only take them away through an illusion. And that they can really and actually do so is argued a fortiori.

(rhetoric, logic, Medieval Latin) a fortiori (as a corollary implied by a stronger claim)


a fortiori

NB - Pronunciation of Norwegian Bokmål «a fortiori».ogg

From both Latin ā (“from, away from, out of”), alternative form of ab (“from, away from, out of, down from”) by apocope (not used before a vowel or h), from Proto-Italic *ab, from Proto-Indo-European *h₂epó (“off, away”), and from fortiōrī, comparative of fortis (“strong”), from Proto-Italic *forktis, from Proto-Indo-European *bʰerǵʰ- (“to rise, high, hill”).

der

begrepet «a fortiori» anvendes i matematiske og logiske argumenter, hvis f.eks. a er større enn b og b større enn c, så er «a fortiori» a større enn c

the term «a fortiori» is used in mathematical and logical arguments, if e.g. a is greater than b and b greater than c, then «a fortiori» a is greater than c

Norge … har vært forpliktet til ikke å bestride den danske suverenitet over hele Grønland og à fortiori til å avholde sig fra å okkupere en del av landet

Norway… has been obliged not to contest the Danish sovereignty over the whole of Greenland and a fortiori to refrain from occupying part of the country

hvis man … kan vise at fengslet faktisk ikke er så gjennomsyret av disiplinformer som Foucault vil ha det til, så faller følgelig også a fortiori påstanden om at samfunnet skulle være disiplinært

1997, Espen Schaanning, Vitenskap som skapt viten, page 298:

if one… can show that the prison is in fact not as permeated by forms of discipline as Foucault wants it to be, then consequently also falls a fortiori the claim that society should be disciplinary

de kan ikke a fortiori – desto mer – utelukke å finne semantisk innhold også i religiøse ytringer

they cannot a fortiori - all the more - exclude finding semantic content also in religious utterances

(rhetoric, logic) a fortiori (with stronger or greater reason; as a corollary implied by a stronger claim.)


transduction

en-noun

transduction (countable and uncountable, plural transductions)

1650s, Latin transductionem, form of Latin trānsdūcō (“lead across”). By surface analysis, transduce + -tion.

artificial intelligence
artificial intelligence

(logic) Particularly in the discipline of artificial intelligence, a form of inference, according to which the response appropriate to a particular known case, also is appropriate to another particular case diagnosed to be functionally identical. This contrasts with induction, in which general rules derived from past observations are applied to future cases as a class (compare also analogy).


convertible

en-adj

convertible (comparative more convertible, superlative most convertible)

more convertible (comparative)
most convertible (superlative)

From Old French convertible, from Late Latin convertibilis (“interchangeable”), from Latin convertere (“to turn back, to turn over, to turn around, to turn upside down”), from con- (“with, together”) + vertere (“to turn”), + -ibilis (“-ible: able to”). Equivalent to convert + -ible.

der

(logic) Able to undergo conversion (i.e., inversion) without falsehood.


induce

en-verb

induce (third-person singular simple present induces, present participle inducing, simple past and past participle induced)

induces (present singular third-person)
inducing (participle present)
induced (participle past)
induced (past)

From Middle English enducen, borrowed from Latin indūcere (“lead in, bring in, introduce”), from in + dūcō (“lead, conduct”). Compare also abduce, adduce, conduce, deduce, produce, reduce etc. Doublet of endue.

der

(transitive, logic) To infer by induction.


induce

ro-verb

a induce (third-person singular present induce, past participle indus) 3rd conjugation

a induce 3rd conjugation (canonical)
induce (present singular third-person)
indus (participle past)
a induce (infinitive)
inducând (gerund)
indus (participle past)
induc (first-person indicative present singular)
induci (indicative present second-person singular)
induce (indicative present singular third-person)
inducem (first-person indicative plural present)
induceți (indicative plural present second-person)
induc (indicative plural present third-person)
induceam (first-person imperfect indicative singular)
induceai (imperfect indicative second-person singular)
inducea (imperfect indicative singular third-person)
induceam (first-person imperfect indicative plural)
induceați (imperfect indicative plural second-person)
induceau (imperfect indicative plural third-person)
indusei (first-person indicative perfect singular)
induseși (indicative perfect second-person singular)
induse (indicative perfect singular third-person)
induserăm (first-person indicative perfect plural)
induserăți (indicative perfect plural second-person)
induseră (indicative perfect plural third-person)
indusesem (first-person indicative pluperfect singular)
induseseși (indicative pluperfect second-person singular)
indusese (indicative pluperfect singular third-person)
induseserăm (first-person indicative pluperfect plural)
induseserăți (indicative pluperfect plural second-person)
induseseră (indicative pluperfect plural third-person)
să induc (first-person present singular subjunctive)
să induci (present second-person singular subjunctive)
să inducă (present singular subjunctive third-person)
să inducem (first-person plural present subjunctive)
să induceți (plural present second-person subjunctive)
să inducă (plural present subjunctive third-person)
indu (imperative second-person singular)
induceți (imperative plural second-person)
nu induce (imperative negative second-person singular)
nu induceți (imperative negative plural second-person)

Borrowed from Latin indūcere, with senses based off French induire. First attested in 1875.


stronger

From Middle English strongere, strengere (“stronger”), from Old English strongra, strengra (“stronger”), from Proto-Germanic *strangizô (“*stronger”), comparative of Proto-Germanic *strangaz (“strong”), equivalent to strong + -er. More at strong.

(logic) Said of one proposition with respect to another one: that the former entails the latter, but the latter does not entail the former.


deduction

en-noun

deduction (countable and uncountable, plural deductions)

From Middle French déduction, from Latin deductio.
Equivalent to deduct + -ion or deduce + -tion.

He arrived at the deduction that the butler didn't do it.

An unkinder deduction, considering only the Select Committee's report and discounting rumours of wayward conclusions by the Stedeford Group, would be that if one inquisition doesn't produce the desired answers, the Minister's policy is "try, try again"—or should one say "fight, fight, fight again".

1961 January, “Talking of Trains: Marples out of step”, in Trains Illustrated, page 1:

(logic) A process of reasoning that moves from the general to the specific, in which a conclusion follows necessarily from the premises presented, so that the conclusion cannot be false if the premises are true.

A conclusion; that which is deduced, concluded or figured out

Through his powers of deduction, he realized that the plan would never work.

The ability or skill to deduce or figure out; the power of reason


cherry-pick

en-verb

cherry-pick (third-person singular simple present cherry-picks, present participle cherry-picking, simple past and past participle cherry-picked)

cherry-picks (present singular third-person)
cherry-picking (participle present)
cherry-picked (participle past)
cherry-picked (past)
cherry pick (alternative)
cherrypick (alternative)

A metaphor, from the idea of picking through a bowl of cherries and seeking the best for oneself, or the idea of picking off the cherries for oneself from a cake or dessert.

From all the available statistics, the politician cherry-picked only those that backed up his ideas.

The reason for this concentration is to attempt to alleviate the problems of fragmentation which usually accompany the study of retailing, particularly at the end of the early period, and has so often happened in the past, to curtail the temptation to 'cherry-pick' the best evidence from a wide, but not necessarily related, area.

1999, Nicholas Alexander, Gary Akehurst, The Emergence of Modern Retailing, 1750-1950, page 38:

2001, Ian St. John in sci.environment
You are *asking* for a specific *subset* of the data to *prove* a specific theory. That is 'cherry picking'. It is no more valid to 'cherry pick' data to disprove global warming than it is to 'cherry pick' data to prove it. That is *science*. You *must* deal with the entire data set. What part of this is not clear?

Yes, I do think in principle it is a good idea to have clearing houses where data is assessed and has as objective an account as possible given of the data because of the tendency of all organisations to cherry-pick those studies which may support a pre-existing position.

2006, Scientific developments relating to the Abortion Act 1967: twelfth report of session 2006-07, Vol. 2: Oral and written evidence, page 32:

So it's possible to 'cherry pick' only the evidence that supports a position and ignore the rest. To the reader who does not know about the rest of the evidence, it may seem like a strong case. The whole body of evidence must be considered.

2008, Warren Davies, How to Study Psychology, page 80:

(rhetoric, logic, by extension) To select only evidence which supports an argument, and reject or ignore contradictory evidence.

de krenten uit de pap halen

to select only the best from a range of options


conclude

conclude (third-person singular simple present concludes, present participle concluding, simple past and past participle concluded)

concludes (present singular third-person)
concluding (participle present)
concluded (participle past)
concluded (past)

From Middle English concluden, borrowed from Latin conclūdere (“to shut up, close, end”).

der

(logic) to deduce, to infer (develop a causal relation)


indirect

en-adj

indirect (comparative more indirect, superlative most indirect)

more indirect (comparative)
most indirect (superlative)

/ˌɪndɪˈɹɛkt/

/ˌɪndəˈɹɛkt/

From Middle French indirect, from Late Latin indirectus.

law of the excluded middle
law of the excluded middle

(mathematics, logic, of a proof) Employing argument by contradiction; making use the law of the excluded middle; arguing via the contrapositive.


equivalence

en-noun

equivalence (countable and uncountable, plural equivalences)

equivalences (plural)
æquivalence (alternative obsolete)

From French équivalence, from Medieval Latin aequivalentia.

(uncountable, logic) The relationship between two propositions that are either both true or both false.


truth table

Each row of a truth table corresponds to a distinct interpretation. The columns on the left side assign truth values to the letters (of the truth table's given formula), and the column on the right side shows the truth value for the entire formula, which computably depends on the truth values of its letters.

(logic) A table showing all possible truth values for an expression, derived from the truth values of its components.


protasis

From Late Latin protasis, from Ancient Greek πρότασις (prótasis), from προτείνω (proteínō, “put forward, tender, propose”), from πρό (pró) + τείνω (teínō, “stretch”).

In "I will be coming if this weather holds up", "if this weather holds up" is the protasis, and "I will be coming" is the apodosis.

2005 B. P. Bairan: An Introduction to Syllogistic Logic
Every conditional statement is made up of two component statements. The component statement that follows the "if" is called antecedent (or the "implicans" or — rarely — the "protasis"), and the component statement that follows the "then" is the "consequent"(or the "implicate" or — rarely — the "apodosis").

(logic, grammar) A clause that expresses a contingent element in a conditional sentence.


protasis

la-noun

protasis f (genitive protasis); third declension

protasis (genitive)
protasis (nominative singular)
protasēs (nominative plural)
protasis (genitive singular)
protasium (genitive plural)
protasī (dative singular)
protasibus (dative plural)
protasem (accusative singular)
protasēs (accusative plural)
protasīs (accusative plural)
protase (ablative singular)
protasibus (ablative plural)
protasis (singular vocative)
protasēs (plural vocative)

English: protasis

Italian: protasi

From the Ancient Greek πρότασις (prótasis).


Con

ZFC ⊨ Con(PA)

(mathematics, logic) consistency predicate


Logik

de-noun

Logik f (genitive Logik, plural Logiken)

Logik (genitive)
Logiken (plural)
Logik (nominative singular)
Logiken (definite nominative plural)
Logik (genitive singular)
Logiken (definite genitive plural)
Logik (dative singular)
Logiken (dative definite plural)
Logik (accusative singular)
Logiken (accusative definite plural)

Borrowed from Latin logica, from Ancient Greek λογική (logikḗ, “logic”).


Q

English: max Q

Ancient Greek language
Egyptian language
Etruscan language
Phoenician language
Q

From the Etruscan letter 𐌒 (q, “cu”), from the Ancient Greek letter Ϙ (Q, “qoppa”), derived from the Phoenician letter 𐤒 (q, “qop”), from the Egyptian hieroglyph 𓃻.

(logic, mathematics) Robinson arithmetic.


Π

arithmetical hierarchy
arithmetical hierarchy

polynomial hierarchy
polynomial hierarchy

universal quantifier
universal quantifier

(mathematics, logic, computer science) A class (in some hierarchy of formulae, like the arithmetical hierarchy or polynomial hierarchy) of those formulae whose outermost quantifiers are universal quantifiers.


barbara

/ˈbɑɹb(ə)ɹə/

/ˈbɑːb(ə)ɹə/

From the name Barbara; chosen because it has three A's in it representing universal affirmatives.

(logic) A syllogism in which all three propositions are of the form "All X are Y" or "X is a Y".


induction

en-noun

induction (countable and uncountable, plural inductions)

Inherited from Middle English induction, from Old French induction, from Latin inductiō, from indūcō (“I lead”). By surface analysis, induct + -ion or induce + -tion.

Meronym: abstraction

(logic) Derivation of general principles from specific instances.

en:reasoning from specific instances to general principles

ինդուկցիա

the derivation of general principles from specific instances


ZF

(Mainland China, Internet slang) initialism of 政府 (zhèngfǔ)


alethiology

From Ancient Greek ἀλήθεια (alḗtheia, “truth”) + -λογία (-logía).

der

(logic) The branch of logic dealing with truth and error.


disjunction

en-noun

disjunction (countable and uncountable, plural disjunctions)

From Old French disjunction, from Latin disjunctio.

(logic) The proposition resulting from the combination of two or more propositions using the or operator.

disjunkce

logic: proposition resulting from the combination of two or more propositions using the or operator


predicate calculus

(logic) The branch of logic that deals with quantified statements such as "there exists an x such that..." or "for any x, it is the case that...", where x is a member of the domain of discourse.


literal

literals (plural)
litteral (alternative obsolete)
lit. (alternative)

LL-Q1860 (eng)-Mélange a trois-literal.wav

From Middle English literal, from Old French literal, from Late Latin litteralis, also literalis (“of or pertaining to letters or to writing”), from Latin littera, litera (“a letter”); see letter.

(logic) A propositional variable or the negation of a propositional variable. ᵂᵖ


truth value

(logic) A value indicating to what extent a statement is true; in classical logic, these are the values "true" and "false".


icke

icke (indefinite nominative singular)
ickes (genitive indefinite singular)
icket (definite nominative singular)
ickets (definite genitive singular)

[ˈî̝k̟ʰːɛ̠̂]

From Old Swedish ækki, ække, ikke, originally the nominative neuter of ængin (“no one, nobody”). Related to Danish ikke, Norwegian Bokmål ikke and Norwegian Nynorsk ikkje.


AND

(logic) Alternative form of ∧, the conjunction operator.

(logic) The binary operator and, only true if both of two inputs is true. In infix notation.


AND

en-verb

AND (third-person singular simple present ANDs, present participle ANDing, simple past and past participle ANDed)

ANDs (present singular third-person)
ANDing (participle present)
ANDed (participle past)
ANDed (past)

If an internal node is encountered that contains a mask, the search key is logically ANDed with the mask and another search is made of the subtree...

2006, Gary R Wright, W Richard Stevens, The Implementation:

(logic, transitive) To combine (a value) with another value by means of this operator.


negation

en-noun

negation (countable and uncountable, plural negations)

From Middle English negacioun, from Old French negacion, from Latin negātiō (“a denial; negative word”).
Morphologically negate + -ion

der

You get the negation of a proposition if you insert "not" (or some equivalent expression) into it in such a way as to form a contradictory of it.

2001, Mark Sainsbury, chapter 1, in Logical Forms — An Introduction to Philosophical Logic, 2nd edition, Blackwell Publishing, →ISBN, §4, page 19:

(logic, countable) A proposition which is the contradictory of another proposition and which can be obtained from that other proposition by the appropriately placed addition/insertion of the word "not". (Or, in symbolic logic, by prepending that proposition with the symbol for the logical operator "not".)

Although some of the logicians working in term logic have very complicated treatments of negation, we can see the origin of the modern conception in the extensional tradition as well. In Boole and most of his followers, the negation of a term is understood as the set theoretic complement of the class represented by that term. For this reason, the negation of classical propositional logic is often called ‘Boolean negation’.

2011 July 20, Edwin Mares, “Propositional Functions”, in The Stanford Encyclopedia of Philosophy, retrieved 2012-07-15:

(logic) The logical operation which obtains such (negated) propositions.


modus ponens

From Latin modus ponendo ponens (roughly, “mode where affirming affirms”).

1. If P, then Q.

2. P.

3. Therefore, Q.

(philosophy, logic) A valid form of argument in which the antecedent of a conditional proposition is affirmed, thereby entailing the affirmation of the consequent. Modus ponens has the form

肯定前件

a valid form of argument in which the antecedent of a conditional proposition is affirmed, thereby entailing the affirmation of the consequent


petitio principii

/pɪˈtɪʃiˌəʊ prɪnˈkɪpiˌaɪ/

From Latin petītiō prīncipiī (literally “an assumption from the beginning”), calque of Ancient Greek τὸ ἐν ἀρχῇ αἰτεῖσθαι (tò en arkhêi aiteîsthai, “to assume from the beginning”).

uder

τὸ ἐν ἀρχῇ αἰτεῖσθαι

begging the question
begging the question

(philosophy, logic, uncountable) The logical fallacy of begging the question (i.e., "assuming the conclusion").

A somewhat similar objection has been made by Locke and others, to the effect that the ordinary demonstrative syllogism is a petitio principii.

1869, C. S. Pierce, “Grounds of Validity of the laws of Logic: Further Consequences of Four Incapacities.”, in Journal of Speculative Philosophy:

The Streitberg-Michels Theory is evidently a petitio principii. To explain ē in gēbum, it is from the outset taken for granted, for inadequate reasons of method, that the form must be a perfect. [italics original]

1938, E. Prokosch, A Comparative Germanic Grammar:

(philosophy, logic, countable) A particular argument which commits the fallacy of begging the question; a circular argument.


Funktion

de-noun

Funktion f (genitive Funktion, plural Funktionen)

Funktion (genitive)
Funktionen (plural)
Funktion (nominative singular)
Funktionen (definite nominative plural)
Funktion (genitive singular)
Funktionen (definite genitive plural)
Funktion (dative singular)
Funktionen (dative definite plural)
Funktion (accusative singular)
Funktionen (accusative definite plural)

(computing, logic, mathematics) function


sss

(mathematics, logic) if and only if; used to show that the predicate that follows it has the same truth value as the predicate that precedes it


weaker

LL-Q1860 (eng)-Flame, not lame-weaker.wav

(logic) Said of one proposition with respect to another one: that the latter entails the former, but the former does not entail the latter.


quantify

en-verb

quantify (third-person singular simple present quantifies, present participle quantifying, simple past and past participle quantified)

quantifies (present singular third-person)
quantifying (participle present)
quantified (participle past)
quantified (past)

From Medieval Latin quantifico (introduced by Sir William Hamilton in logic).

The statement (#92;forallx#92;in#92;mathbb#123;R#125;)#92;,2x#61;x#43;x quantifies over the real numbers.

(logic) To relate a statement (called a predicate) to a given set using a quantifier—either for all (denoted ∀) or there exists (denoted ∃).


beg the question

beg the question (third-person singular simple present begs the question, present participle begging the question, simple past and past participle begged the question)

begs the question (present singular third-person)
begging the question (participle present)
begged the question (participle past)
begged the question (past)

LL-Q1860 (eng)-Sapaa-beg the question.wav

From Latin petitio principii, from Ancient Greek τὸ ἐν ἀρχῇ αἰτεῖσθαι (tò en arkhêi aiteîsthai, “to assume from the beginning”).

uder

τὸ ἐν ἀρχῇ αἰτεῖσθαι

The objection is that the argument begs the question, meaning that the premise, that God has all the virtues, assumes the conclusion, that God is benevolent.

1994, D. N. Walton, “Begging the question as a pragmatic fallacy.”, in Synthese, volume 100, number 1:

(philosophy, logic, law) To engage in the logical fallacy of begging the question (petitio principii).

olettaa johtopäätös todeksi

to engage in the logical fallacy of begging the question (petitio principii)


conjunct

From Latin conjunctus, the perfect past participle of conjungō. Doublet of conjoint. See conjoin.

Asserting a conjunction would be irrational if the epistemic grounds for one conjunct defeat those for the other, for example when the two conjuncts are logically inconsistent.

2007 July 14, Timothy Chan, “Belief, assertion and Moore’s Paradox”, in Philosophical Studies, volume 139, number 3, →DOI:


elementary equivalence
elementary equivalence


simplification

en-noun

simplification (countable and uncountable, plural simplifications)


scientia

la-noun

scientia f (genitive scientiae); first declension

scientiae (genitive)
scientia (nominative singular)
scientiae (nominative plural)
scientiae (genitive singular)
scientiārum (genitive plural)
scientiae (dative singular)
scientiīs (dative plural)
scientiam (accusative singular)
scientiās (accusative plural)
scientiā (ablative singular)
scientiīs (ablative plural)
scientia (singular vocative)
scientiae (plural vocative)

> Aromanian: shtiintsã (inherited)

Old Galician-Portuguese:

Galician: chencha

> Romanian: știință (inherited)

→ Albanian: shkencë

⇒ Breton: skiant

→ Catalan: ciència

→ Esperanto: scienco
→ Ido: cienco

⇒ Friulian: sience

desctree

→ Italian: scienza, scenza (misspelling), scienzia (archaic)
→ Ido: cienco
→ Maltese: xjenza

→ Occitan: sciéncia

→ Old French: science, escience (learned)
→ Middle English: science, scyence, syens, sciens, sciense, sience
> English: science (inherited) (see there for further descendants)
Scots: science
Middle French: science
French: science (see there for further descendants)
Norman: scienche

desc

→ Old Galician-Portuguese: ciencia (learned)

Fala: ciencia

Galician: ciencia

Portuguese: ciência

desctree

→ Old Spanish: çiençia, sçencia, sciencia, sçiençia, siençia (learned)
> Ladino: sensia (inherited)
> Spanish: ciencia, esciencia (archaic) (inherited)
→ Asturian: ciencia
→ Basque: zientzia
→ Ido: cienco
→ Tagalog: siyensiya

→ Sardinian: iscièntzia

→ Sicilian: scènzia, scienza

⇒ Venetan: sienza, siensa

From sciēns, scientem (“knowing, aware; having expertise”) + -ia (“abstract noun suffix”). Attested from Varro onwards (early 1st century BCE).

af

scientia propter quid

a knowledge derived from cause to effect

scientia quia

a knowledge derived from effect to cause

plūs differunt scientia adquīsīta per dēmōnstrātiōnem et scientia adquīsīta per experientiam, quam scientia quia et scientia propter quid

William of Ockham, Commentary on the Sentences of Peter Lombard I.89

there's a greater difference between knowledge acquired through logical proof and knowledge acquired through practical experience, than between knowledge from effect and knowledge from cause

(philosophy) that which is known (as opposed to a mere belief, translating Ancient Greek ἐπιστήμη (epistḗmē))

(Medieval Latin, logic) knowledge (as distinguished according to the direction: from cause to effect or vice versa, corr. to Ancient Greek διότι (dióti) vs. ὅτι (hóti))


формула

bg-noun

фо́рмула • (fórmula) f

фо́рмула (canonical)
fórmula (romanization)
фо́рмула (indefinite singular)
фо́рмули (indefinite plural)
фо́рмулата (definite singular)
фо́рмулите (definite plural)


формула

formula (romanization)
формула (nominative singular)
формулалар (nominative plural)
формуланың (genitive singular)
формулалардың (genitive plural)
формулаға (dative singular)
формулаларға (dative plural)
формуланы (accusative singular)
формулаларды (accusative plural)
формулада (locative singular)
формулаларда (locative plural)
формуладан (ablative singular)
формулалардан (ablative plural)
формуламен (instrumental singular)
формулалармен (instrumental plural)

kk-decl-noun

формулалардың

формулаларға

формулаларды

формулаларда

формулалардан

формулалармен

Borrowed from Russian фо́рмула (fórmula), from Latin formula.

Kazakh alphabets#Arabic script
Kazakh alphabets#Cyrillic script
Kazakh alphabets#Latin script


формула

formula (romanization)
формула (indefinite singular)
формули (indefinite plural)
формулата (definite singular unspecified)
формулите (definite plural unspecified)
формулава (definite proximal singular)
формуливе (definite plural proximal)
формулана (definite distal singular)
формулине (definite distal plural)
формуло (singular vocative)
формули (plural vocative)


формула

ru-noun+

фо́рмула • (fórmula) f inan (genitive фо́рмулы, nominative plural фо́рмулы, genitive plural фо́рмул, relational adjective фо́рмульный, diminutive фо́рмулка)

фо́рмула (canonical)
fórmula (romanization)
фо́рмулы (genitive)
фо́рмулы (nominative plural)
фо́рмул (genitive plural)
фо́рмульный (adjective relational)
фо́рмулка (diminutive)
фо́рмула (nominative singular)
фо́рмулы (nominative plural)
фо́рмулы (genitive singular)
фо́рмул (genitive plural)
фо́рмуле (dative singular)
фо́рмулам (dative plural)
фо́рмулу (accusative singular)
фо́рмулы (accusative plural)
фо́рмулой (instrumental singular)
фо́рмулою (instrumental singular)
фо́рмулами (instrumental plural)
фо́рмуле (prepositional singular)
фо́рмулах (plural prepositional)
фо́рмула (dated nominative singular)
фо́рмулы (dated nominative plural)
фо́рмулы (dated genitive singular)
фо́рмулъ (dated genitive plural)
фо́рмулѣ (dated dative singular)
фо́рмуламъ (dated dative plural)
фо́рмулу (accusative dated singular)
фо́рмулы (accusative dated plural)
фо́рмулой (dated instrumental singular)
фо́рмулою (dated instrumental singular)
фо́рмулами (dated instrumental plural)
фо́рмулѣ (dated prepositional singular)
фо́рмулахъ (dated plural prepositional)

Ru-формула.ogg


формула

фо̑рмула (canonical feminine)
fȏrmula (romanization)
формула (nominative singular)
формуле (nominative plural)
формуле (genitive singular)
формула (genitive plural)
формули (dative singular)
формулама (dative plural)
формулу (accusative singular)
формуле (accusative plural)
формуло (singular vocative)
формуле (plural vocative)
формули (locative singular)
формулама (locative plural)
формулом (instrumental singular)
формулама (instrumental plural)


формула

uk-noun

фо́рмула • (fórmula) f inan (genitive фо́рмули, nominative plural фо́рмули, genitive plural фо́рмул)

фо́рмула (canonical)
fórmula (romanization)
фо́рмули (genitive)
фо́рмули (nominative plural)
фо́рмул (genitive plural)
фо́рмула (nominative singular)
фо́рмули (nominative plural)
фо́рмули (genitive singular)
фо́рмул (genitive plural)
фо́рмулі (dative singular)
фо́рмулам (dative plural)
фо́рмулу (accusative singular)
фо́рмули (accusative plural)
фо́рмулою (instrumental singular)
фо́рмулами (instrumental plural)
фо́рмулі (locative singular)
фо́рмулах (locative plural)
фо́рмуло (singular vocative)
фо́рмули (plural vocative)

Uk-формула.ogg


modality

en-noun

modality (countable and uncountable, plural modalities)

(logic) The classification of propositions on the basis on whether they claim possibility, impossibility, contingency or necessity; mode.


háttur

is-noun

háttur m (genitive singular háttar, nominative plural hættir)

háttar (genitive singular)
hættir (nominative plural)
háttur (indefinite nominative singular)
hátturinn (definite nominative singular)
hættir (indefinite nominative plural)
hættirnir (definite nominative plural)
hátt (accusative indefinite singular)
háttinn (accusative definite singular)
hætti (accusative indefinite plural)
háttu (accusative archaic indefinite literary plural)
hættina (accusative definite plural)
hætti (dative indefinite singular)
hættinum (dative definite singular)
háttum (dative indefinite plural)
háttunum (dative definite plural)
háttar (genitive indefinite singular)
háttarins (definite genitive singular)
hátta (genitive indefinite plural)
háttanna (definite genitive plural)

From Old Norse háttr, from Proto-Germanic *hahtuz.

(logic) mode, modality; (the classification of propositions on the basis on whether they claim possibility, impossibility, contingency or necessity)


spor

sporeček (diminutive)
spor (nominative singular)
spory (nominative plural)
sporu (genitive singular)
sporů (genitive plural)
sporu (dative singular)
sporům (dative plural)
spor (accusative singular)
spory (accusative plural)
spore (singular vocative)
spory (plural vocative)
sporu (locative singular)
sporech (locative plural)
sporem (instrumental singular)
spory (instrumental plural)


subsumption

en-noun

subsumption (countable and uncountable, plural subsumptions)

(logic) The premise of a syllogism that contains the minor term.


modal

en-adj

modal (comparative more modal, superlative most modal)

more modal (comparative)
most modal (superlative)

From Middle French modal, from Medieval Latin modālis (“pertaining to a mode”), from Latin modus (“mode”). Compare to French, Spanish, and Portuguese modal and Italian modale. By surface analysis, mod(e) + -al.

der

(logic) Of, or relating to the modality between propositions.

modaal

logic: of or relating to the modality between prepositions


transitivity

en-noun

transitivity (countable and uncountable, plural transitivities)

From French transitivité.
Morphologically transitive + -ity

The hypothetical syllogism inference rule states the transitivity of implication.

(mathematics, logic) The property of being transitive.


salvage

en-verb

salvage (third-person singular simple present salvages, present participle salvaging, simple past and past participle salvaged)

salvages (present singular third-person)
salvaging (participle present)
salvaged (participle past)
salvaged (past)

From Old French salver (see also save, from a variant form), from Late Latin salvare (“to make safe, secure, save”), from Latin salvus (“safe”) with the English suffix -age.

der

Prove or disprove, and salvage if possible.

(transitive, logic) To modify (a false proposition) to create a true proposition.


post hoc ergo propter hoc

See post (“after”), propter (“because of”), hoc – neuter accusative of hic (“this”), and ergō (“therefore”).

(logic) after this, therefore because of this


subaltern

en-adj

subaltern (comparative more subaltern, superlative most subaltern)

more subaltern (comparative)
most subaltern (superlative)

From Middle French subalterne, from Late Latin subalternus, from Latin sub- + alternus, from alter.

(logic) Asserting only a part of what is asserted in a related proposition.

alisteinen

asserting only a part of what is asserted in a related proposition


subaltern

(logic) A subaltern proposition; a proposition implied by a universal proposition.


Entscheidungsproblem

Unadapted borrowing from German Entscheidungsproblem.

ubor

‘The Entscheidungsproblem,’ Rudy said. ‘Meaning?’ Alan explained, ‘Hilbert wanted to know whether any given statement could, in principle, be found true or false.’

Turing was attending Max Newman's lectures on the foundations of mathematics when the Entscheidungsproblem first attracted his attention.

2012, George Dyson, Turing's Cathedral, Penguin, published 2013, page 279:

(mathematics, logic) A decision problem of finding a way to decide whether a formula is true or provable within a given system.


Entscheidungsproblem

de-noun

Entscheidungsproblem n (strong, genitive Entscheidungsproblems, plural Entscheidungsprobleme)

Entscheidungsproblems (genitive)
Entscheidungsprobleme (plural)
Entscheidungsproblem (nominative singular)
Entscheidungsprobleme (definite nominative plural)
Entscheidungsproblems (genitive singular)
Entscheidungsprobleme (definite genitive plural)
Entscheidungsproblem (dative singular)
Entscheidungsproblemen (dative definite plural)
Entscheidungsproblem (accusative singular)
Entscheidungsprobleme (accusative definite plural)

→ English: Entscheidungsproblem


γένος

grc-noun

γένος • (génos) n (genitive γένεος or γένους); third declension

génos (romanization)
γένεος (genitive)
γένους (genitive)
τὸ γένος (nominative singular)
γένει (dual nominative)
τᾰ̀ γένη (nominative plural)
τοῦ γένους (genitive singular)
γενοῖν (dual genitive)
γενῶν (genitive plural)
τῷ γένει (dative singular)
γενοῖν (dative dual)
τοῖς γένεσῐ (dative plural)
γένεσῐν (dative plural)
toîs génesĭ (dative plural)
toîs génesĭn (dative plural)
τὸ γένος (accusative singular)
γένει (accusative dual)
τᾰ̀ γένη (accusative plural)
γένος (singular vocative)
γένει (dual vocative)
γένη (plural vocative)
γένος (nominative singular)
γένει (dual nominative)
γένεε (dual nominative)
γένεᾰ (nominative plural)
γένεος (genitive singular)
γένευς (genitive singular)
γενέοιν (dual genitive)
γενέων (genitive plural)
γένει (dative singular)
γένεῐ̈ (dative singular)
γενέοιν (dative dual)
γένεσῐ (dative plural)
γένεσῐν (dative plural)
génesĭ (dative plural)
génesĭn (dative plural)
γένος (accusative singular)
γένει (accusative dual)
γένεε (accusative dual)
γένεᾰ (accusative plural)
γένος (singular vocative)
γένει (dual vocative)
γένεε (dual vocative)
γένεᾰ (plural vocative)
τὸ γένος (nominative singular)
γένει (dual nominative)
γένεε (dual nominative)
τᾰ̀ γένεᾰ (nominative plural)
τοῦ γένεος (genitive singular)
γένευς (genitive singular)
γενέοιν (dual genitive)
γενέων (genitive plural)
τῷ γένει (dative singular)
γένεῐ̈ (dative singular)
γενέοιν (dative dual)
τοῖσῐ (dative plural)
τοῖσῐν γένεσῐ (dative plural)
γένεσῐν (dative plural)
toîsĭ génesĭ (dative plural)
toîsĭ génesĭn (dative plural)
toîsĭnĭ (dative plural)
toîsĭnĭn (dative plural)
τὸ γένος (accusative singular)
γένει (accusative dual)
γένεε (accusative dual)
τᾰ̀ γένεᾰ (accusative plural)
γένος (singular vocative)
γένει (dual vocative)
γένεε (dual vocative)
γένεᾰ (plural vocative)

desc

→ Aramaic: גניסא, גנסא

→ Aramaic: גניסא, גנסא

Greek: γένος (génos)

From Proto-Hellenic *génos. Cognate with Latin genus, Sanskrit जनस् (jánas), Old Armenian ծին (cin), among others; see also γίγνομαι (gígnomai, “to be born”).

τὰ γένη δ᾽ εἰς εἴδη πλείω καὶ διαφέροντα διαιρεῖται

384 BCE – 322 BCE, Aristotle, Metaphysics 1059β.36

(please add an English translation of this quotation)

tà génē d’ eis eídē pleíō kaì diaphéronta diaireîtai

(logic) the opposite of εἶδος (eîdos, “species”)


injection

→ Romanian: injecție

→ Turkish: enjeksiyon

(mathematics, logic, set theory) injection


contradictory

Borrowed from Late Latin contradictorius, from Latin contradico.

If one proposition is the negation of another, it follows trivially from the definition that the two propositions are contradictories. The converse does not hold. Two propositions can be contradictories without either being the negation of the other. For example:
 3) John is more than six feet tall
and
 4) John is either exactly six feet tall or else less than six feet tall
 are contradictories, but neither is the negation of the other. Negation is one way, but not the only way, of forming a contradictory.

2001, Mark Sainsbury, chapter 1, in Logical Forms — An Introduction to Philosophical Logic, 2nd edition, Blackwell Publishing, →ISBN, §4, page 20:

(logic) Either of a pair of propositions, that cannot both be true or both be false.

نَقِيض

any of a pair of propositions, that cannot both be true or both be false


DM

en-noun

DM (countable and uncountable, plural DMs)

Let ‘F’ stand for the state of affairs that consists in finite persons possessing and exercising free will. Let ‘p’ stand for ‘God exists’; ‘q’ for ‘F obtains’; ‘r’ for ‘F poses a serious risk of evil’; and ‘s’ for ‘There is no option available to God that counters F.’ With this in place, the argument may be formalized as follows:
(1) [(p & q) & r] → s Premiss
(2) ~s Premiss
(3) ~[(p & q) & r] 1, 2 MT
(4) ~(p & q) v ~r 3 DM
(5) r Premiss
(6) ~(p & q) 4, 5 DS
(7) ~p v ~q 6 DM
(3) follows from the conjunction of (1) and (2) by modus tollens; De Morgan’s law applied to (3) yields (4); (4) and (5) together lead to (6) by disjunctive syllogism; and another application of De Morgan’s law takes us from (6) to the final conclusion, according to which either God exists or there is free will (but not both).

2004 August, J. L. Schellenberg, “The Atheist’s Free Will Offence”, in International Journal for Philosophy of Religion, volume 56, № 1, pages 11-12:


sublate

en-verb

sublate (third-person singular simple present sublates, present participle sublating, simple past and past participle sublated)

sublates (present singular third-person)
sublating (participle present)
sublated (participle past)
sublated (past)

From Latin sublatum, past participle of suffero.

(transitive, logic) To negate, deny or contradict.


contingency

en-noun

contingency (countable and uncountable, plural contingencies)

(logic, countable) A statement which is neither a tautology nor a contradiction.

kontingenssi

a statement which is neither a tautology nor a contradiction


consequent

Borrowed from Middle French conséquent, from Latin consequens, consequentem, present participle of consequi (“to follow”), from con- + sequi (“to follow”). Compare French conséquent.

(logic) The second half of a hypothetical proposition; Q, if the form of the proposition is "If P, then Q."

takajäsen

the second half of a hypothetical proposition


konjunktion

konjunktion (indefinite nominative singular)
konjunktions (genitive indefinite singular)
konjunktionen (definite nominative singular)
konjunktionens (definite genitive singular)
konjunktioner (indefinite nominative plural)
konjunktioners (genitive indefinite plural)
konjunktionerna (definite nominative plural)
konjunktionernas (definite genitive plural)

(logic) a conjunction, more specifically logisk konjunktion


turnstile

(mathematics, logic) The ⊢ symbol used to represent logical entailment (deducibility relation), especially of the syntactic type; i.e., syntactic consequence. (Such symbol can be read as "prove(s)" or "give(s)". )


(logic) intensional conjunction, as in some relevant logics.


DS

DS (countable and uncountable, plural DSs or DSes)

DSs (plural)
DSes (plural)
D. S. (alternative)
D.S. (alternative)

(logic) Initialism of disjunctive syllogism.


analytic

en-adj

analytic (comparative more analytic, superlative most analytic)

more analytic (comparative)
most analytic (superlative)
analytick (alternative)

/ˌænəˈlɪtɪk/

From Ancient Greek ἀναλυτικός (analutikós).

(logic, of a proposition) that follows necessarily by definition; tautologous.


inductive

inductive (comparative more inductive, superlative most inductive)

more inductive (comparative)
most inductive (superlative)

From Middle French inductif, from Late Latin inductivus.

(logic) Of, or relating to logical induction, by generalizing a universal claim or principle from the observed particular instances.


válido

pt-adj

válido (feminine válida, masculine plural válidos, feminine plural válidas)

válida (feminine)
válidos (masculine plural)
válidas (feminine plural)

Borrowed from Latin validus (“healthy; valid”), from valeō (“to be healthy”).

(logic) valid (that evaluates to true regardless of the input values)


dirimens copulatio

From Latin dirimēns cōpulātiō (“separating connection”).

bor

(logic, rhetoric) Mentioning a balancing or opposing fact to prevent the argument from being one-sided or unqualified.


Polish notation

After the nationality of the logician Jan Łukasiewicz

In Polish Notation, the connectives are placed before the wffs. The virtue of this sentence is that its grammar is simpler, for it has no need for parentheses. Sider’s examples: (P ∧ Q) → R and P ∧ (Q → R) become → ∧PQR and ∧P → QR.
If you actually look at a text in this tradition, you’ll find something slightly different. “C” stands for “consequence”, i.e., implication (→) and “N” for negation (∼).
So,consider the following from Tarski and Łukasiewicz’s Investigations into the Sentential Calculus. The claim there is that there are three axioms:
 ‘CCpqCCqrCpr’
 ‘CCNppp’
 ‘CpCNpq’

2009, Brandon C. Look, “Symbolic Logic II, Lecture 6”, in www.uky.edu/~look, archived from the original on 2011-11-09:

(arithmetic, logic) A notation for arithmetic (and logical) formulae in which operations (respectively, quantifiers and operands) are written immediately before their operands, used to avoid the need for parentheses; for example, 3 * (4 + 7) is written as * 3 + 4 7 and A AND B is written as AND A B.


XOR

The XOR of (0,0) is 0; (0,1) is 1; (1,0) is 1; and (1,1) is 0.

(logic) The connective "exclusive or". One way to state its meaning in plain English is "if either A or B, but not if both."


quantifier

Appendix:Roget MICRA thesaurus/Class I § 4. Unsubstantiality

Appendix:Roget MICRA thesaurus/Class I § 78. Generality

Appendix:Roget MICRA thesaurus/Class I § 100. Plurality

Appendix:Roget MICRA thesaurus/Class I § 101. Zero

Appendix:Roget MICRA thesaurus/Class I § 102. Multitude

Appendix:Roget MICRA thesaurus/Class I § 103. Fewness

Appendix:Roget MICRA thesaurus/Class I § 105. Infinity

existential quantifier
existential quantifier

(logic) An operator, such as the universal quantifier (written as ∀) or the existential quantifier (∃), used in predicate calculus to indicate the degree that predicate is true for a specified set.


NAND

Blend of NOT + AND, by analogy with NOR reinterpreted as NOT + OR or negation + OR

(logic) A binary operator composite of NOT AND; negation of AND function.


enthymeme

/ˈɛnθɪˌmiːm/

From Ancient Greek ἐνθύμημα (enthúmēma, “thought, consideration”), from ἐν (en, “within, with”) + θυμός (thumós, “soul, life”).

uder

(logic) A syllogism with a required but unstated assumption.

enthymeem

syllogism with required but unstated assumption


remotion

en-noun

remotion (countable and uncountable, plural remotions)

From Old French or directly from Latin remōtiō.

This act persuades me / That this remotion of the Duke and her / Is practice only.

c. 1603–1606, William Shakespeare, “The Tragedie of King Lear”, in Mr. William Shakespeares Comedies, Histories, & Tragedies […] (First Folio), London: […] Isaac Iaggard, and Ed[ward] Blount, published 1623, →OCLC, [Act II, scene ii]:

A syllogism disjunctive from the enumeration of the parts is that, in which from the remotion of all the parts the remotion of the whole is concluded.

1847, Murray's Compendium of logic, with a corrected Latin text, page 155:

We may proceed from the remotion of the consequent to the remotion of the antecedent.

1857, John Daniel Morell, Handbook of logic, page 51:

The remotion of Cr3+ from the wastewater prevents its possible oxidation.

2003, 2001. a Clay Odyssey, →ISBN, page 619:

(especially logic, largely obsolete) Removal.


teori

teori (indefinite nominative singular)
teoris (genitive indefinite singular)
teorin (definite nominative singular)
teorins (definite genitive singular)
teorier (indefinite nominative plural)
teoriers (genitive indefinite plural)
teorierna (definite nominative plural)
teoriernas (definite genitive plural)


defeater

(logic, philosophy) a belief which, if proved to be true, would imply outright or indirectly that another belief were false.


sav

head

sav (definite accusative savı, plural savlar)

savı (accusative definite)
savlar (plural)
sav (nominative singular)
savlar (nominative plural)
savı (accusative definite singular)
savları (accusative definite plural)
sava (dative singular)
savlara (dative plural)
savda (locative singular)
savlarda (locative plural)
savdan (ablative singular)
savlardan (ablative plural)
savın (genitive singular)
savların (genitive plural)
savım (first-person nominative singular)
savlarım (first-person nominative singular)
savın (nominative second-person singular)
savların (nominative second-person singular)
savı (nominative singular third-person)
savları (nominative singular third-person)
savımız (first-person nominative plural)
savlarımız (first-person nominative plural)
savınız (nominative plural second-person)
savlarınız (nominative plural second-person)
savları (nominative plural third-person)
savımı (accusative definite first-person singular)
savlarımı (accusative definite first-person singular)
savını (accusative definite second-person singular)
savlarını (accusative definite second-person singular)
savını (accusative definite singular third-person)
savlarını (accusative definite singular third-person)
savımızı (accusative definite first-person plural)
savlarımızı (accusative definite first-person plural)
savınızı (accusative definite plural second-person)
savlarınızı (accusative definite plural second-person)
savlarını (accusative definite plural third-person)
savıma (dative first-person singular)
savlarıma (dative first-person singular)
savına (dative second-person singular)
savlarına (dative second-person singular)
savına (dative singular third-person)
savlarına (dative singular third-person)
savımıza (dative first-person plural)
savlarımıza (dative first-person plural)
savınıza (dative plural second-person)
savlarınıza (dative plural second-person)
savlarına (dative plural third-person)
savımda (first-person locative singular)
savlarımda (first-person locative singular)
savında (locative second-person singular)
savlarında (locative second-person singular)
savında (locative singular third-person)
savlarında (locative singular third-person)
savımızda (first-person locative plural)
savlarımızda (first-person locative plural)
savınızda (locative plural second-person)
savlarınızda (locative plural second-person)
savlarında (locative plural third-person)
savımdan (ablative first-person singular)
savlarımdan (ablative first-person singular)
savından (ablative second-person singular)
savlarından (ablative second-person singular)
savından (ablative singular third-person)
savlarından (ablative singular third-person)
savımızdan (ablative first-person plural)
savlarımızdan (ablative first-person plural)
savınızdan (ablative plural second-person)
savlarınızdan (ablative plural second-person)
savlarından (ablative plural third-person)
savımın (first-person genitive singular)
savlarımın (first-person genitive singular)
savının (genitive second-person singular)
savlarının (genitive second-person singular)
savının (genitive singular third-person)
savlarının (genitive singular third-person)
savımızın (first-person genitive plural)
savlarımızın (first-person genitive plural)
savınızın (genitive plural second-person)
savlarınızın (genitive plural second-person)
savlarının (genitive plural third-person)
savım (first-person singular)
savlarım (first-person singular)
savsın (second-person singular)
savlarsın (second-person singular)
sav (singular third-person)
savdır (singular third-person)
savlar (singular third-person)
savlardır (singular third-person)
savız (first-person plural)
savlarız (first-person plural)
savsınız (plural second-person)
savlarsınız (plural second-person)
savlar (plural third-person)
savlardır (plural third-person)

Learned borrowing from Ottoman Turkish ساو (sav) or from other historic Turkic varieties. The term fell out of use in Turkey in the XVII-th century and was reintroduced during the language reform in order to replace داعیه (dâiye, “incitement, cause, motive”) and ادعا (iddiâ). The last term is still in use, however, see iddia.
Ultimately from Proto-Turkic *sāb.


head

∧ or #92;land (English symbol name wedge)

land (canonical)
wedge (English name symbol)

(mathematics, logic) The conjunction operator, forming a Boolean-valued function, typically with two arguments, returning true only if all of its arguments are true.


lause

lause (nominative singular)
lauseet (nominative plural)
lause (accusative nominative singular)
lauseet (accusative nominative plural)
lauseen (accusative genitive singular)
lauseet (accusative genitive plural)
lauseen (genitive singular)
lauseiden (genitive plural)
lauseitten (genitive plural)
lausetta (partitive singular)
lauseita (partitive plural)
lauseessa (inessive singular)
lauseissa (inessive plural)
lauseesta (elative singular)
lauseista (elative plural)
lauseeseen (illative singular)
lauseisiin (illative plural)
lauseihin (illative plural)
lauseella (adessive singular)
lauseilla (adessive plural)
lauseelta (ablative singular)
lauseilta (ablative plural)
lauseelle (allative singular)
lauseille (allative plural)
lauseena (essive singular)
lauseina (essive plural)
lauseeksi (singular translative)
lauseiksi (plural translative)
lauseetta (abessive singular)
lauseitta (abessive plural)
lausein (instructive plural)
See the possessive forms below. (comitative)
lauseeni (nominative singular)
lauseeni (nominative plural)
lauseeni (accusative nominative singular)
lauseeni (accusative nominative plural)
lauseeni (accusative genitive singular)
lauseeni (accusative genitive plural)
lauseeni (genitive singular)
lauseideni (genitive plural)
lauseitteni (genitive plural)
lausettani (partitive singular)
lauseitani (partitive plural)
lauseessani (inessive singular)
lauseissani (inessive plural)
lauseestani (elative singular)
lauseistani (elative plural)
lauseeseeni (illative singular)
lauseisiini (illative plural)
lauseihini (illative plural)
lauseellani (adessive singular)
lauseillani (adessive plural)
lauseeltani (ablative singular)
lauseiltani (ablative plural)
lauseelleni (allative singular)
lauseilleni (allative plural)
lauseenani (essive singular)
lauseinani (essive plural)
lauseekseni (singular translative)
lauseikseni (plural translative)
lauseettani (abessive singular)
lauseittani (abessive plural)
lauseineni (comitative plural)
lauseesi (nominative singular)
lauseesi (nominative plural)
lauseesi (accusative nominative singular)
lauseesi (accusative nominative plural)
lauseesi (accusative genitive singular)
lauseesi (accusative genitive plural)
lauseesi (genitive singular)
lauseidesi (genitive plural)
lauseittesi (genitive plural)
lausettasi (partitive singular)
lauseitasi (partitive plural)
lauseessasi (inessive singular)
lauseissasi (inessive plural)
lauseestasi (elative singular)
lauseistasi (elative plural)
lauseeseesi (illative singular)
lauseisiisi (illative plural)
lauseihisi (illative plural)
lauseellasi (adessive singular)
lauseillasi (adessive plural)
lauseeltasi (ablative singular)
lauseiltasi (ablative plural)
lauseellesi (allative singular)
lauseillesi (allative plural)
lauseenasi (essive singular)
lauseinasi (essive plural)
lauseeksesi (singular translative)
lauseiksesi (plural translative)
lauseettasi (abessive singular)
lauseittasi (abessive plural)
lauseinesi (comitative plural)
lauseemme (nominative singular)
lauseemme (nominative plural)
lauseemme (accusative nominative singular)
lauseemme (accusative nominative plural)
lauseemme (accusative genitive singular)
lauseemme (accusative genitive plural)
lauseemme (genitive singular)
lauseidemme (genitive plural)
lauseittemme (genitive plural)
lausettamme (partitive singular)
lauseitamme (partitive plural)
lauseessamme (inessive singular)
lauseissamme (inessive plural)
lauseestamme (elative singular)
lauseistamme (elative plural)
lauseeseemme (illative singular)
lauseisiimme (illative plural)
lauseihimme (illative plural)
lauseellamme (adessive singular)
lauseillamme (adessive plural)
lauseeltamme (ablative singular)
lauseiltamme (ablative plural)
lauseellemme (allative singular)
lauseillemme (allative plural)
lauseenamme (essive singular)
lauseinamme (essive plural)
lauseeksemme (singular translative)
lauseiksemme (plural translative)
lauseettamme (abessive singular)
lauseittamme (abessive plural)
lauseinemme (comitative plural)
lauseenne (nominative singular)
lauseenne (nominative plural)
lauseenne (accusative nominative singular)
lauseenne (accusative nominative plural)
lauseenne (accusative genitive singular)
lauseenne (accusative genitive plural)
lauseenne (genitive singular)
lauseidenne (genitive plural)
lauseittenne (genitive plural)
lausettanne (partitive singular)
lauseitanne (partitive plural)
lauseessanne (inessive singular)
lauseissanne (inessive plural)
lauseestanne (elative singular)
lauseistanne (elative plural)
lauseeseenne (illative singular)
lauseisiinne (illative plural)
lauseihinne (illative plural)
lauseellanne (adessive singular)
lauseillanne (adessive plural)
lauseeltanne (ablative singular)
lauseiltanne (ablative plural)
lauseellenne (allative singular)
lauseillenne (allative plural)
lauseenanne (essive singular)
lauseinanne (essive plural)
lauseeksenne (singular translative)
lauseiksenne (plural translative)
lauseettanne (abessive singular)
lauseittanne (abessive plural)
lauseinenne (comitative plural)
lauseensa (nominative singular)
lauseensa (nominative plural)
lauseensa (accusative nominative singular)
lauseensa (accusative nominative plural)
lauseensa (accusative genitive singular)
lauseensa (accusative genitive plural)
lauseensa (genitive singular)
lauseidensa (genitive plural)
lauseittensa (genitive plural)
lausettaan (partitive singular)
lausettansa (partitive singular)
lauseitaan (partitive plural)
lauseitansa (partitive plural)
lauseessaan (inessive singular)
lauseessansa (inessive singular)
lauseissaan (inessive plural)
lauseissansa (inessive plural)
lauseestaan (elative singular)
lauseestansa (elative singular)
lauseistaan (elative plural)
lauseistansa (elative plural)
lauseeseensa (illative singular)
lauseisiinsa (illative plural)
lauseihinsa (illative plural)
lauseellaan (adessive singular)
lauseellansa (adessive singular)
lauseillaan (adessive plural)
lauseillansa (adessive plural)
lauseeltaan (ablative singular)
lauseeltansa (ablative singular)
lauseiltaan (ablative plural)
lauseiltansa (ablative plural)
lauseelleen (allative singular)
lauseellensa (allative singular)
lauseilleen (allative plural)
lauseillensa (allative plural)
lauseenaan (essive singular)
lauseenansa (essive singular)
lauseinaan (essive plural)
lauseinansa (essive plural)
lauseekseen (singular translative)
lauseeksensa (singular translative)
lauseikseen (plural translative)
lauseiksensa (plural translative)
lauseettaan (abessive singular)
lauseettansa (abessive singular)
lauseittaan (abessive plural)
lauseittansa (abessive plural)
lauseineen (comitative plural)
lauseinensa (comitative plural)

lausua (“to speak, utter”) + -e. First attested in 1845.

(logic) proposition (assertion which may be true or false)


free variable

(mathematics, logic) A variable (occurring within some expression or well-formed formula) which is not bound by a quantifier or analogous symbol (such as a lambda abstractor, the "differential d" near the end of an integral or differential form, or a summation symbol).


rewriting

en-noun

rewriting (countable and uncountable, plural rewritings)

LL-Q1860 (eng)-Naomi Persephone Amethyst (NaomiAmethyst)-rewriting.wav

(logic, computer science) Any of wide range of potentially non-deterministic methods of replacing subterms of a formula with other terms.


distributive

en-adj

distributive (comparative more distributive, superlative most distributive)

more distributive (comparative)
most distributive (superlative)

(logic) Assigning the species of a general term.


tautologous

tautologous (comparative more tautologous, superlative most tautologous)

more tautologous (comparative)
most tautologous (superlative)

Pertaining to a tautology; tautological.


تالی

Turkish: tali

Borrowed from Arabic تَالٍ (tālin, “following, subsequent”), active participle of تَلَا (talā, “to follow”).

bor+

(logic) consequent, the second half of a hypothetical proposition, which follows the term then


量詞

/li̯ɑŋ⁵¹ t͡sʰz̩³⁵/

/lœːŋ²² t͡sʰiː²¹/

/lyɒŋ¹¹ ɬo¹³/

/lyøŋ²¹ ɬo²⁴/

/liɔŋ²²⁻²¹ su²⁴/

/liɔŋ⁴¹⁻²² sɯ²⁴/

/liaŋ²²⁻²¹ su¹³/

/liaŋ⁵⁵⁻¹¹ sɯ⁵⁵/

/li̯ɑŋ⁵¹ t͡sʰz̩³⁵/

/lœːŋ²² t͡sʰiː²¹/

/lyɒŋ¹¹ ɬo¹³/

/lyøŋ²¹ ɬo²⁴/

/liɔŋ²²⁻²¹ su²⁴/

/liɔŋ⁴¹⁻²² sɯ²⁴/

/liaŋ²²⁻²¹ su¹³/

/liaŋ⁵⁵⁻¹¹ sɯ⁵⁵/

專用動量詞

動量詞／动量词 (dòngliàngcí)

专用动量词

動量詞／动量词 (dòngliàngcí)

借用動量詞

動量詞／动量词 (dòngliàngcí)

借用动量词

動量詞／动量词 (dòngliàngcí)


consilience

en-noun

consilience (countable and uncountable, plural consiliences)

From Latin con- (prefix indicating a being or bringing together of several objects) + saliō (“to bound, jump, leap”) (modelled after resiliēns (“rebounding”)) + -ence, influenced by concurrent. Coined by English polymath William Whewell in 1840 in his book The Philosophy of the Inductive Sciences.

coin

Indeed in all cases in which from propositions of considerable generality, propositions of a still higher degree are obtained, there is a convergence of inductions; and if in one of the lines which thus converge, the steps be rapidly and suddenly made in order to meet the other line, we may consider that we have an example of Consilience.

1840, William Whewell, “Of the Logic of Induction”, in The Philosophy of the Inductive Sciences, Founded upon Their History. […], volume II, London: John W[illiam] Parker, […]; Cambridge, Cambridgeshire: J. and J. J. Deighton, →OCLC, part II (Of Knowledge), book XI (Of the Construction of Science), paragraph 4, pages 242–243:

CONSILIENCE of INDUCTIONS takes place when an induction obtained from one class of facts coincides with an induction obtained from a different class. This consilience is the test of the truth of the theory in which it occurs.

1858, William Fleming, “CONSILIENCE of INDUCTIONS”, in The Vocabulary of Philosophy, Mental, Moral, and Metaphysical; […], 2nd revised and enlarged edition, London, Glasgow: Richard Griffin and Company, publishers to the University of Glasgow, →OCLC, page 114:

(logic) The concurrence of multiple inductions drawn from different data sets.


monadic

From Ancient Greek μοναδικός (monadikós, “single”), from μονάς (monás, “a unit”); see monad. By surface analysis, monad + -ic.

uder

"The monadic existential quantifier ∃, as in ∃x, may express existence of x in formal logic or mathematics]]".

(mathematics, logic) having an arity of one (taking a single argument or operand)


desitive

(obsolete, logic) An argument that leads to a conclusion.


sorites

From the Latin sōrītēs, from the Ancient Greek σωρείτης (sōreítēs, “fallacy of the heap”), from σωρός (sōrós, “heap”).

der

Why?—he would ask, making use of the sorites or syllogism of Zeno and Chrysippus without knowing it belonged to them.—Why? why are we a ruined people?—Because we are corrupted.——Whence is it, dear Sir, that we are corrupted?—Because we are needy [...] ——And wherefore, he would add,—are we needy?——From the neglect, he would answer

1760, Laurence Sterne, The Life & Opinions of Tristram Shandy, Gentleman, Penguin, published 2003, page 130:

(logic, rhetoric) A series of propositions whereby each conclusion is taken as the subject of the next.


conséquence

la conséquence logique

la conséquence matérielle

la conséquence syntaxique et la conséquence sémantique

syntactic consequence and semantic consequence


جنس

fa-noun

جنس • (jens) (plural اجناس (ajnâs), or جنسها (jens-hâ))


intension

From Latin intēnsiō (“straining, effort; intensifying”), from intēnsus (“stretched”), perfect passive participle of intendō (“strain or stretch toward”).

uder

'Is a plant', 'has a trunk', 'has leaves' are intensions of the concept tree. Its extension is the set of all trees existing in the real world.

This law is, that the intension of our knowledge is in the inverse ratio of its extension.

1859–1860, William Hamilton, edited by H[enry] L[ongueville] Mansel and John Veitch, Lectures on Metaphysics and Logic […], volume (please specify |volume=I to IV), Edinburgh, London: William Blackwood and Sons, →OCLC:

(logic, semantics) Any property or quality connoted by a word, phrase or other symbol, contrasted with actual instances in the real world to which the term applies.


bandwagon fallacy

en-noun

bandwagon fallacy (plural bandwagon fallacies)

argumentum ad populum
argumentum ad populum


argumentum

LL-Q1860 (eng)-Flame, not lame-argumentum.wav

Learned borrowing from Latin argūmentum. Doublet of argument.

Argumentum anti-Normannicum: or, An argument proving, from ancient histories and records, that William, Duke of Normandy, made no absolute conquest of England by the sword; in the sense of our modern writers.

1682: Sir Edward Coke, Argumentum anti-Normannicum, main title (John Darby)

(chiefly formal, in law, logic, etc.) Used in numerous Latin phrases (and occasionally alone) in the sense of “appeal” or “argument”.

argumentum ab auctoritate est fortissimum in lege

argumentum ab auctoritate plurimum valet in lege

argumentum ab impossibili plurimum valet in lege

argumentum ab inconvenienti est validum in lege

quia lex non permittit aliquod inconveniens


logic gate

There are six non-trivial, symmetric, two-input, Boolean logic gates: AND, OR, XOR, NAND, NOR and XNOR.

A physical device, typically electronic, which computes a Boolean logical output (0 or 1) from Boolean input or inputs according to the rules of some logical operator.


functor

LL-Q1860 (eng)-Flame, not lame-functor.wav

In the category of categories, #92;mathbb#123;CAT#125;, the objects are categories and the morphisms are functors.

1991, Natalie Wadhwa (translator), Yu. A. Brudnyǐ, N. Ya. Krugljak, Interpolation Functors and Interpolation Spaces, Volume I, Elsevier (North-Holland), page 143,
Choosing for U the operation of closure, regularization or relative completion, we obtain from a given functor ℱ∈𝒥ℱ the functors
◌̅F: overrightarrow X→◌̅F( overrightarrow X),F⁰: overrightarrow X→F( overrightarrow X)⁰,Fᶜ: overrightarrow X→F( overrightarrow X)ᶜ.

Given a homotopical category X and a functor u#58;A#92;rightarrowB, a homotopical u-colimit (resp. u-limit) functor on X will be a homotopically terminal (resp. initial) Kan extension of the identity (50.2) along the induced diagram functor Xᵘ#58;Xᴮ#92;rightarrowXᴬ (47.1).

2004, William G. Dwyer, Philip S. Hirschhorn, Daniel M. Kan, Jeffrey H. Smith, Homotopy Limit Functors on Model Categories and Homotopical Categories, American Mathematical Society, page 165:

2009, Benoit Fresse, Modules Over Operads and Functors, Springer, Lecture Notes in Mathematics: 1967, page 35,
In this chapter, we recall the definition of the category of Σ_*-objects and we review the relationship between Σ_*-objects and functors. In short, a Σ_*-object (in English words, a symmetric sequence of objects, or simply a symmetric object) is the coefficient sequence of a generalized symmetric functor S(M):X→S(M,X), defined by a formula of the form
S(M,X)=⨁ ᪲ᵣ₌₀(M(r)⊗X)_(Σᵣ).

(category theory) A category homomorphism; a morphism from a source category to a target category which maps objects to objects and arrows to arrows (either covariantly or contravariantly), in such a way as to preserve morphism composition and identities.


implicand

By surface analysis, implic(ate) + -and.

(propositional calculus) The conclusion of an implication.


implicant

electrical engineering
electrical engineering

(electrical engineering) On a Karnaugh map: a set of ones (whose quantity is a power of two) which are related by adjacency (i.e., the set is connected, if the Karnaugh map is considered to be a graph which "wraps around" its edges, like a torus; and all elements of the subgraph induced by the set have the same degree). Equivalently, in terms of Boolean algebra, a product term which, when true, always implies that the given Boolean function is true.


superordinate

en-adj

superordinate (comparative more superordinate, superlative most superordinate)

more superordinate (comparative)
most superordinate (superlative)

subordinate

antonym(s) of “lower in rank or position”

(logic) The relation of a universal proposition to a specific proposition of the same form with the universal quantified variable replaced by a specific instance.


異或

/i⁵¹⁻⁵³ xu̯ɔ⁵¹/

/i⁵¹⁻⁵³ xu̯ɔ⁵¹/


NOT function

(logic, mathematics) A function that is equivalent to the NOT operator.


propositional function

en-noun

propositional function (plural propositional functions)

(logic) An expression containing algebraic symbols that serve to represent words or other elements of a sentence or proposition


truth function

truth functions (plural)
truth-function (alternative)

(mathematics, logic) A Boolean function whose value is interpreted as truth or falsity


coextensive

Coextensive expressions with different intensions cannot in general be substituted for one another within an expression e while preserving the extension of e (assuming that the extension of a declarative sentence is its truth value).

1995, Jaegwon Kim, Ernest Sosa, A Companion to Metaphysics:

(logic) Having the same extension—the object or set of objects to which a term refers.


quantification

quantification (countable and uncountable, plural quantifications)

Coined by Scottish philosopher Sir William Hamilton: "quantification of the predicate".

(logic) A limitation that is imposed on the variables of a proposition.


vacuously

en-adv

vacuously (comparative more vacuously, superlative most vacuously)

more vacuously (comparative)
most vacuously (superlative)

The statement is vacuously true because P is false and P implies Q.

(logic) Because of being a vacuous truth.


soundness

en-noun

soundness (countable and uncountable, plural soundnesses)

From Middle English soundenes, soundnes, from Old English *sundnes, *ġesundnes (attested in onsundnes), from Proto-West Germanic *sundnassī (“soundness, health”); equivalent to sound + -ness. Cognate with West Frisian sûnens (“soundness, health”), Middle Low German suntnisse (“soundness, health”), Middle High German suntnisse (“soundness, health”), German Gesundnis (“health”).

cog

(logic) The property (of an argument) of not only being valid, but also of having true premises.

(logic) The property of a logical theory that whenever a wff is a theorem then it must also be valid. Symbolically, letting T represent a theory within logic L, this can be represented as the property that whenever T⊢φ is true, then T⊨φ must also be true, for any wff φ of logic L.


termino

Borrowed from Esperanto termino, English terminus, French terminus, German Terminus, Termin, Italian termine, Russian термин (termin), Spanish término, all ultimately from Latin terminus.

io-bor

(logic, in syllogism) the major premise, minor premise or the middle


terminas

lt-noun

ter̃minas m (plural ter̃minai) stress pattern 1

ter̃minas m (plural terminai̇̃) stress pattern 3ᵇ

ter̃minas (canonical masculine stress-pattern-1)
ter̃minai (plural)
ter̃minas m stress pattern 3ᵇ (canonical)
terminai̇̃ (plural)
ter̃minas (nominative singular)
ter̃minai (nominative plural)
ter̃mino (genitive singular)
ter̃minų (genitive plural)
ter̃minui (dative singular)
ter̃minams (dative plural)
ter̃miną (accusative singular)
ter̃minus (accusative plural)
ter̃minu (instrumental singular)
ter̃minais (instrumental plural)
ter̃mine (locative singular)
ter̃minuose (locative plural)
ter̃mine (singular vocative)
ter̃minai (plural vocative)
ter̃minas (nominative singular)
terminai̇̃ (nominative plural)
ter̃mino (genitive singular)
terminų̃ (genitive plural)
ter̃minui (dative singular)
termináms (dative plural)
ter̃miną (accusative singular)
ter̃minus (accusative plural)
ter̃minu (instrumental singular)
terminai̇̃s (instrumental plural)
terminè (locative singular)
terminuosè (locative plural)
ter̃mine (singular vocative)
terminai̇̃ (plural vocative)


In its original sense "disjunction", probably from the initial letter of Latin vel (“or”).


prova

From Old Galician-Portuguese prova, either regressively derived from the verb provar or from Late Latin proba (“proof”), from Latin probō (“to approve; to prove”), from probus (“good”).

(logic, mathematics) proof (sequence of statements which concludes with a statement that is the object of the proof)


postulation

en-noun

postulation (countable and uncountable, plural postulations)

(logic) Something self-evident that can be assumed as the basis of an argument.


first-order

(mathematics, logic) Of one of a series of models, languages, relationship, forms of logical discourse, etc., being the simplest one or the first in a sequence.


second-order

(mathematics, logic) Denoting the second in a numerical sequence of models, languages, relationships, forms of logical discourse etc.


Boolean algebra

Boolean algebra (plural Boolean algebras)

Named after George Boole (1815–1864), an English mathematician, educator, philosopher and logician.

(algebra, logic, computing) Specifically, an algebra in which all elements can take only one of two values (typically 0 and 1, or "true" and "false") and are subject to operations based on AND, OR and NOT


Boolean function

Boolean function (plural Boolean functions)

(algebra, logic, computing) Any function based on the operations AND, OR and NOT, and whose elements are from the domain of Boolean algebra

fonction booléenne

function based on AND, OR and NOT operations