free

en-adj

free (comparative freer or more free, superlative freest or most free)

freer (comparative)
more free (comparative)
freest (superlative)
most free (superlative)

From Middle English free, fre, freo, from Old English frēo (“free”), from Proto-West Germanic *frī, from Proto-Germanic *frijaz (“beloved, not in bondage”), from Proto-Indo-European *priHós (“pleased, loved”), from *preyH- (“to please, love”). Related to friend.
cognates, etc
Germanic cognates include West Frisian frij (“free”), Dutch vrij (“free”), Low German free (“free”), German frei (“free”), Danish, Swedish and Norwegian fri (“free”).
Other cognates include Sanskrit प्रिय (priyá-, “beloved”).
Germanic and Celtic are the only Indo-European language branches in which the PIE word with the meaning of "dear, beloved" acquired the additional meaning of "free" in the sense of "not in bondage". This was an extension of the idea of "characteristic of those who are dear and beloved", in other words friends and tribe members (in contrast to unfree inhabitants from other tribes and prisoners of war, many of which were among the slaves – compare the Latin use of liberi to mean both "free persons" and "children of a family").

inh

there ain't no such thing as a free lunch

why buy the cow when you can get the milk for free

z is the free variable in #92;forallx#92;existsy#58;xy#61;z.

(logic, of a variable) Unconstrained by quantifiers.

Unconstrained.
Unconstrained by quantifiers.


A

* (highest rank, grade, music): From the initial position of the letter A in the English alphabet.
* (blood type): From A antigen

The Shorter Oxford English Dictionary on Historical Principles

Oxford University Press
w:Oxford University Press

(logic) A universal affirmative suggestion.


connotation

/ˌkɒnəˈteɪʃən/

/ˌkɑnəˈteɪʃən/

/ˌkɒnəˈteɪʃən/

/ˌkɔnəˈtæɪʃən/

/ˌkɒnəˈtæɪʃən/

Borrowed from Medieval Latin connotātiō, from connotō (“I mark in addition”), from Latin con- (“together, with”) + noto (“I note”); equivalent to connote + -ation.

The two expressions "the morning star" and "the evening star" have different connotations but the same denotation (i.e. the planet Venus).

(logic) The attribute or aggregate of attributes connoted by a term, contrasted with denotation.


denotation

en-noun

denotation (countable and uncountable, plural denotations)

From Late Latin dēnotātiō, from Latin dēnotāre (“to denote, mark out”) + -tiō (suffix forming nouns of action), from dē- (“completely”) + notāre (“to mark”); equivalent to denote + -ation.

The denotations of the two expressions "the morning star" and "the evening star" are the same (i.e. both expressions denote the planet Venus), but their connotations are different.

Regarding denotation, the terms were generally used to refer to a wide range of language contact varieties and features.

2018, James Lambert, “A multitude of ‘lishes’: The nomenclature of hybridity”, in English World-Wide, page 6:

(logic, linguistics, semiotics) The primary, surface, literal, or explicit meaning of a signifier such as a word, phrase, or symbol; that which a word denotes, as contrasted with its connotation; the aggregate or set of objects of which a word may be predicated.

(philosophy, logic) The intension and extension of a word


abdicative

The fourth mood is that which brings together directly a particular abdicative from a particular dedicative and a universal abdicative, e.g., Some just thing is honourable, no honourable thing is base, therefore some just thing is not base.

1987, David Londey, The Logic of Apuleius:


abduction

abduction (countable and uncountable, plural abductions)

From Latin abductiō(n) (“robbing; abduction”), from abdūcō (“take or lead away”), from ab (“away”) + dūcō (“to lead”). By surface analysis, abduct + -ion.
* (physiology): From French, from Latin abductus.
* Compare French abduction.

der

The significance of such a step is that it is not morphologically triggered: it is a step of abduction, and what is required here is a meta-level process of reasoning.

2005, Ronnie Cann, Ruth Kempson, Lutz Marten, The Dynamics of Language, an Introduction, page 256:

(logic) A syllogism or form of argument in which the major premise is evident, but the minor is only probable.


abduction

Learned borrowing from Latin abductiō(n) (“robbing; abduction”), from abdūcō (“take or lead away”) + -tiō(n) (suffix forming nouns relating to actions or their results).

lbor

(logic, computing) abductive reasoning; abduction


on

Etymology tree
Proto-West Germanic *ana
Old English on
Middle English on
English on
From Middle English on, from Old English on, an (“on, upon, onto, in, into”), from Proto-West Germanic *ana, from Proto-Germanic *ana (“on, at”), from Proto-Indo-European *h₂en-.
Cognate with North Frisian a (“on, in”), Saterland Frisian an (“on, at”), West Frisian oan (“on, at”), Dutch aan (“on, at, to”), Low German an (“on, at”), German an (“to, at, on”), Swedish å (“on, at, in”), Faroese á (“on, onto, in, at”), Icelandic á (“on, in”), Gothic 𐌰𐌽𐌰 (ana), Ancient Greek ἀνά (aná, “up, upon”), Albanian në (“in”); and from Old Norse upp á: Danish på, Swedish på, Norwegian på, see upon.

etymon

Southern US, Midland US, Philadelphia, Baltimore

On naturalism, it is therefore difficult to find a ground for ultimate moral hope.

2021, Gavin Ortlund, Why God Makes Sense in a World That Doesn't: The Beauty of Christian Theism, Grand Rapids, MI: Baker Academic, →ISBN:

(philosophy, logic) According to, from the standpoint of; expressing what must follow, whether accepted or not, if a given premise or system is assumed true.


singular

singulars (plural)
sing. (alternative abbreviation)
sg. (alternative abbreviation)
sg (alternative abbreviation)

From Middle English singuler, from Old French, from Latin singulāris (“alone of its kind”), from Latin singulus (“single”).

(logic) That which is not general; a specific determinate instance.


and

Inherited from Middle English and, an, from Old English and, ond, end, from Proto-West Germanic *andi, from Proto-Germanic *andi, *anþi, from Proto-Indo-European *h₂énti (“facing opposite, near, in front of, before”). Cognate with Scots an (“and”), North Frisian en (“and”), West Frisian en, in (“and”), Yiddish און (un, “and”), Low German un (“and”), Dutch en (“and”), German und (“and”), Danish end (“but”), Swedish än (“yet, but”), Icelandic and Norwegian enn (“still, yet”), Albanian edhe (“and”) (dialectal ênde, ênne), ende (“still, yet, therefore”), Latin ante (“opposite, in front of”), and Ancient Greek ἀντί (antí, “opposite, facing”). Doublet of an ("if").

cog

an' (alternative)
'n' (alternative)
n (alternative)

(unstressed form, also for some speakers stressed form) end

-и

used to connect two similar words, phrases, et cetera

-kä (in a negative clause; prefixed with a negation verb)

en

used to string together sentences or sentence fragments in chronological order

as well as

used to connect two similar words or phrases

South Georgia and the South Sandwich Islands

well-formed formulas
well-formed formula

(mathematics, logic) Connecting two well-formed formulas to create a new well-formed formula that requires it to only be true when both of the two formulas are true.


conjunction

en-noun

conjunction (countable and uncountable, plural conjunctions)

/kənˈd͡ʒʌŋk.ʃən/

From Old French conjonction, from Latin coniūnctiō (“joining”), from coniungere (“to join”).

Meronyms: conjunct, logical connective

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

съедине́ние

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


open

en-adj

open (comparative more open or (phonetics) opener, superlative most open or (phonetics) openest)

more open (comparative)
opener (comparative)
most open (superlative)
openest (superlative)

closed-source

antonym(s) of “with a free license and no proprietary components”

Adjective from Middle English open, from Old English open (“open”), from Proto-West Germanic *opan, from Proto-Germanic *upanaz (“open”), from Proto-Indo-European *upo (“up from under, over”).
Cognates
* Scots apen (“open”)
* Saterland Frisian eepen (“open”)
* West Frisian iepen (“open”)
* Dutch open (“open”)
* Low German open, apen (“open”)
* German offen (“open”)
* Danish åben (“open”)
* Swedish öppen (“open”)
* Norwegian Bokmål åpen (“open”)
* Norwegian Nynorsk open (“open”)
* Icelandic opinn (“open”)
 Compare also Latin supinus (“on one's back, supine”), Albanian hap (“to open”). Related to up.
Verb from Middle English openen, from Old English openian (“to open”), from Proto-West Germanic *opanōn, from Proto-Germanic *upanōną (“to raise; lift; open”), from Proto-Germanic *upanaz (“open”, adjective). Cognate with Saterland Frisian eepenje (“to open”), West Frisian iepenje (“to open”), Dutch openen (“to open”), German öffnen (“to open”), Danish åbne (“to open”), Swedish öppna (“to open”), Norwegian Bokmål åpne (“to open”), Norwegian Nynorsk and Icelandic opna (“to open”). Related to English up.
Noun from Middle English open (“an aperture or opening”), from the verb. In the sports sense, however, a shortening of “open competition”.

inh

at church every time the doors swing open

(mathematics, logic, of a formula) Having a free variable.


false

en-adj

false (comparative falser, superlative falsest)

falser (comparative)
falsest (superlative)

From Middle English false, fals, from Old English fals (“false; counterfeit; fraudulent; wrong; mistaken”), from Latin falsus (“counterfeit, false; falsehood”), perfect passive participle of fallō (“deceive”). Reinforced in Middle English by Anglo-Norman and Old French fals, faus. Compare Scots fals, false, Saterland Frisian falsk, German falsch, Dutch vals, Swedish and Danish falsk; all from Latin falsus. Displaced native Middle English les, lese, from Old English lēas (“false”); See lease, leasing. Doublet of faux.
The verb is from Middle English falsen, falsien, from Old French falser, from Latin falsō (“falsify”), itself also from falsus; compare French fausser (“to falsify, to distort”).

cog

(logic) Of a state in Boolean logic that indicates a negative result.


absurd

absurdzik (diminutive)
absurd (nominative singular)
absurdy (nominative plural)
absurdu (genitive singular)
absurdów (genitive plural)
absurdowi (dative singular)
absurdom (dative plural)
absurd (accusative singular)
absurdy (accusative plural)
absurdem (instrumental singular)
absurdami (instrumental plural)
absurdzie (locative singular)
absurdach (locative plural)
absurdzie (singular vocative)
absurdy (plural vocative)
absurdum (alternative obsolete)

Learned borrowing from Latin absurdus. First attested in 1564.

ref

Maria Renata Mayenowa, Stanisław Rospond, Witold Taszycki, Stefan Hrabec, Władysław Kuraszkiewicz (2010-2023) “absurdum”, in Słownik Polszczyzny XVI Wieku [A Dictionary of 16th Century Polish]


ontology

en-noun

ontology (countable and uncountable, plural ontologies)

Learned borrowing from New Latin ontologia (1606, Ogdoas Scholastica, by Jacob Lorhard (Lorhardus), from Ancient Greek ὤν, ὄντος (ṓn, óntos, “being”), present participle of εἰμί (eimí, “being, existing, essence”) + λόγος (lógos, “account”).
First known English use 1663: Archelogia philosophica nova; or, New principles of Philosophy. Containing Philosophy in general, Metaphysicks or Ontology, Dynamilogy or a Discourse of Power, Religio Philosophi or Natural Theology, Physicks or Natural philosophy, by Gideon Harvey (1636–1702), London, Thomson, 1663.
Popularized as a philosophical term by German philosopher Christian Wolff (1679–1754).

der

(logic) A logical system involving theory of classes, developed by Stanislaw Lesniewski (1886-1939).


metaphysics

en-noun

metaphysics (countable and uncountable, plural metaphysics)

1560s; plural of metaphysic, from Middle English methaphesik, methaphisik, methaphisique, metaphesyk, methafisik, metaphesyk, methephysyk, from Old French metafisique, methaphisique and Medieval Latin metaphysica, methephisica, from Byzantine Greek μεταφυσικά (metaphusiká), from the title of the collection by Aristotle μετὰ τὰ φυσικά (metà tà phusiká, “Following The Natural World”), a collection that comes after (μετά (metá)) Aristotle's collection entitled τὰ φυσικά (tà phusiká, “The Natural World”), from φυσικός (phusikós, “natural”). By surface analysis, meta- + physics.

der

Even other universes should be a result of different physics. Without rules, these universes wouldn't exist, because they will have an undefined, thus impossible, nature. We will never understand or guess all possible forms of physics. That's why we have to understand the generic metaphysics.

(logic, uncountable, by extension from the philosophical sense) The metalogic of physics; the logical framework of physics.


or

From Middle English or; partially contracted from other, auther, from Old English āþor, āwþer, āhwæþer ("some, any, either"; > either); and partially from Middle English oththe, from Old English oþþe, from Proto-Germanic *efþau (“or”).

(logic) An operator denoting the disjunction of two propositions or truth values. There are two forms, the inclusive or and the exclusive or.

od

euphonic alt. form used before a vowel, especially "o"


or

(logic, electronics) Alternative form of OR.


antecedent

From Middle English antecedent, borrowed from Old French antecedent, from Latin antecēdēns (“going before”), from antecēdō (“to precede; excel; surpass”).

(logic) The conditional part of a hypothetical proposition, i.e. p→q, where p is the antecedent, and q is the consequent.

antecedent

(logic) The first of two subsets of a sequent, consisting of all the sequent's formulae which are valuated as true.


antecedent

nl-noun

antecedent n (plural antecedenten, diminutive antecedentje n)

antecedenten (plural)
antecedentje (diminutive neuter)

Borrowed from French antécédent, from Latin antecēdēns (“go before”), from antecēdere (“to go or come before”).

(logic) antecedent (condition part of a proposition)


affirmative

en-adj

affirmative (comparative more affirmative, superlative most affirmative)

more affirmative (comparative)
most affirmative (superlative)

/əˈfɜːmətɪv/

From Middle English affirmative, affirmatyve, from Old French affirmatif, from Latin affirmativus, from affirmare (“to assert”).

(logic) Expressing the agreement of the two terms of a proposition.


concrete

en-noun

concrete (countable and uncountable, plural concretes)

Borrowed from Latin concrētus, past participle of concrescō (to curdle) from con- (with, together) + crescō (to grow, rise).

Whence follows, that the Abſtract Terms, [Entity] or [Eſſence] do properly ſignify [A Capacity of Being.] Tho' Entity is often us'd as a Concrete for the Thing it ſelf.

1697, J[ohn] S[ergeant], Solid Philosophy Asserted Against the Fancies of the Ideists: […], London: […] Roger Clavil […] Abel Roper […] Thomas Metcalf, […], page 91:

Conceptualization is man's method of organizing sensory material. To form a concept, one isolates two or more similar concretes from the rest of one's perceptual field, and integrates them into a single mental unit, symbolized by a word.

1982, Leonard Peikoff, The Ominous Parallels: The End of Freedom in America, New York, N.Y.: Stein and Day/Publishers, →ISBN, page 331:

With regard to the physical domain, concretes are as a rule perceived through the senses.

However, how can such a structure of concretes and abstracts be made evident, which after all means that knowledge always aims at the concrete, the unprecedented, the irreducibly dissimilar, although cognition always happens in developing similarity through abstraction?

1997, Joseph A. Bracken, Marjorie Hewitt Suchocki, editors, Trinity in Process: A Relational Theology of God, New York, N.Y.: Continuum, →ISBN, page 154:

On the right-hand sides we have sentences asserting that an equivalence relation holds between concretes—that is, that they are identical in some respect.

2009, Alan Musgrave, “Pleonastic Platonism”, in Heather Dyke, editor, From Truth to Reality: New Essays in Logic and Metaphysics, New York, N.Y.: Routledge, →ISBN, pages 79–80:

(logic) A term designating both a quality and the subject in which it exists; a concrete term.


subject

From Latin subiectus (“a subject, an inferior”), subiectum (“the subject of a proposition”), past participle of subiciō (“throw, lay, place”), from sub (“under, at the foot of”) + iaciō (“throw, hurl”).

der

(logic) That of which something is stated.

subjekti

logic: that of which something is stated


conditional

From French conditionnel, from Old French condicionel, equivalent to condition + -al.

"A implies B" is a conditional statement.

A conditional proposition is one which asserts the dependence of one categorical proposition on another.

1826, Richard Whately, Elements of Logic:

(logic) Stating that one sentence is true if another is true.


conditional

conditionals (plural)
conditionall (alternative)

"A implies B" is a conditional.

Disjunctives may be turned into conditionals

1867, Lyman Hotchkiss Atwater, Manual of Elementary Logic, quoted in OED:

(logic) A statement that one sentence is true if another is.


argument

en-noun

argument (countable and uncountable, plural arguments)

arguments (plural)
arguement (alternative obsolete)

From Middle English argument, from Anglo-Norman and Old French arguement, from Latin argumentum. The English word is analysable as argue + -ment. Doublet of argumentum.
Displaced native Old English racu and ġeflit.

/ˈɑːɡjʊmənt/

/ˈɑɹɡjʊmənt/

وَسِيط

variable that is being passed to a function

Consider the argument: / 15) I am hungry; therefore I am hungry. / Intuitively this should count as valid. But suppose we thought of the components of arguments as sentences, and suppose we imagine the context shifting between the utterance of the premise and the utterance of the conclusion. Suppose you are hungry and utter the premise, and I am not hungry and utter the conclusion. Then we would have a true premise and a false conclusion, so the argument would not be valid. Clearly we need to avoid such problems, and introducing the notion of a proposition, in the style of this section, is one way of doing so.

2001, Mark Sainsbury, “Validity”, in Logical Forms: An Introduction to Philosophical Logic, 2nd edition, Oxford, Oxfordshire: Blackwell Publishing, →ISBN, § 8, page 35:

In ‘The Critic of Arguments’ (1892), [Charles Sanders] Peirce adopts a notion that is even closer to that of a propositional function. There he develops the concept of the ‘rhema’. He says the rhema is like a relative term, but it is not a term. It contains a copula, that is, when joined to the correct number of arguments it produces an assertion. For example, ‘__ is bought by __ from __ for __’ is a four-place rhema. Applying it to four objects a, b, c, and d produces the assertion that a is bought by b from c for d[…].

2011 July 20, Edwin Mares, “Propositional Functions”, in Stanford Encyclopedia of Philosophy, fall 2011 edition, archived from the original on 2020-08-07:

(countable, also figuratively) A fact or statement used to support a proposition; a reason.

(logic, philosophy) A series of propositions organized so that the final proposition is a conclusion which is intended to follow logically from the preceding propositions, which function as premises.


argument

nl-noun

argument n (plural argumenten, diminutive argumentje n)

argumenten (plural)
argumentje (diminutive neuter)

Afrikaans: argument

From Middle Dutch argument, from Old French argument, from Latin argūmentum.

an argument (fact or statement used to support a proposition)

(logic, philosophy) a series of propositions, intended so that the conclusion follows logically from the premises


argument

argumencik (diminutive)
argument (nominative singular)
argumenty (nominative plural)
argumentu (genitive singular)
argumentów (genitive plural)
argumentowi (dative singular)
argumentom (dative plural)
argument (accusative singular)
argumenty (accusative plural)
argumentem (instrumental singular)
argumentami (instrumental plural)
argumencie (locative singular)
argumentach (locative plural)
argumencie (singular vocative)
argumenty (plural vocative)

Learned borrowing from Latin argūmentum.

(philosophy, logic, mathematics, programming) argument


argument

sh-noun

argùment m (Cyrillic spelling аргу̀мент)

argùment (canonical masculine)
аргу̀мент (Cyrillic)
argument (nominative singular)
argumenti (nominative plural)
argumenta (genitive singular)
argumenata (genitive plural)
argumentu (dative singular)
argumentima (dative plural)
argument (accusative singular)
argumente (accusative plural)
argumente (singular vocative)
argumenti (plural vocative)
argumentu (locative singular)
argumentima (locative plural)
argumentom (instrumental singular)
argumentima (instrumental plural)


accident

Borrowed from Latin accidentem, present active participle of accidō (“happen”).


complete

en-adj

complete (comparative more complete or completer, superlative most complete or completest)

more complete (comparative)
completer (comparative)
most complete (superlative)
completest (superlative)
compleat (alternative archaic)

From Middle English compleet (“full, complete”), borrowed from Old French complet or Latin completus, past participle of compleō (“I fill up, I complete”) (whence also complement, compliment), from com- + pleō (“I fill, I fulfill”) (whence also deplete, replete, plenty), ultimately from Proto-Indo-European *pleh₁- (“to fill”) (English full).

пълен

of a proof system: such that any semantically valid formula is also provable

complete androgen insensitivity syndrome

Gödel's first incompleteness theorem showed that Principia could not be both consistent and complete. According to the theorem, for every sufficiently powerful logical system (such as Principia), there exists a statement G that essentially reads, "The statement G cannot be proved." Such a statement is a sort of Catch-22: if G is provable, then it is false, and the system is therefore inconsistent; and if G is not provable, then it is true, and the system is therefore incomplete.ᵂᴾ

(logic, of a proof system of a formal system with respect to a given semantics) In which every semantically valid well-formed formula is provable.


MT

en-noun

MT (countable and uncountable, plural MTs)

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:


SL

SL (countable and uncountable, plural SLs)

sentential logic
sentential logic#English


sound

en-adj

sound (comparative sounder, superlative soundest)

sounder (comparative)
soundest (superlative)
soune (alternative obsolete)
sownd (alternative obsolete)
sowne (alternative obsolete)

→ Volapük: saun

From Middle English sound, sund, isund, ȝesund, from Old English sund, ġesund (“sound, safe, whole, uninjured, healthy, prosperous”), from Proto-West Germanic *sund, from Proto-Germanic *gasundaz, *sundaz (“healthy”), from Proto-Indo-European *sunt-, *swent- (“vigorous, active, healthy”).
Cognate with Scots sound, soun (“healthy, sound”), Saterland Frisian suund, gesuund (“healthy”), West Frisian sûn (“healthy”), Dutch gezond (“healthy, sound”), Low German sund, gesund (“healthy”), German gesund (“healthy, sound”), Danish sund (“healthy”), Swedish sund (“sound, healthy”). Related also to Dutch gezwind (“fast, quick”), German geschwind (“fast, quick”), Old English swīþ (“strong, mighty, powerful, active, severe, violent”). See swith.

cog

With fresh material, taxonomic conclusions are leavened by recognition that the material examined reflects the site it occupied; a herbarium packet gives one only a small fraction of the data desirable for sound conclusions. Herbarium material does not, indeed, allow one to extrapolate safely: what you see is what you get[…]

1992, Rudolf M[athias] Schuster, The Hepaticae and Anthocerotae of North America: East of the Hundredth Meridian, volume V, Chicago, Ill.: Field Museum of Natural History, →ISBN, page vii:

(mathematics, logic) Having the property of soundness.


OR

(logic) Inclusive or; either one proposition or the other is true or both.


OR

(logic) The binary operator inclusive or, true if one at least one of two inputs is true. In infix notation.


predicate

predicates (plural)
prædicate (alternative archaic)

From Middle English predicat(e), from Old French predicat (French prédicat), from Medieval Latin praedicātum (“thing said of a subject, predicate”), substantivized from the nominative neuter singular of praedicātus, the perfect passive participle praedicō (“to proclaim”), see -ate (noun-forming suffix); see also Etymology 2 below.
The adjective was derived from the noun by metanalysis, see -ate (adjective-forming suffix).

der

A propositional variable may be treated as a nullary predicate.

A predicate is either valid, satisfiable, or unsatisfiable.

(logic) A term of a statement, where the statement may be true or false depending on whether the thing referred to by the values of the statement's variables has the property signified by that (predicative) term.

твърде́ние

logic: a term of a statement, where the statement may be true or false


predicate

en-verb

predicate (third-person singular simple present predicates, present participle predicating, simple past and past participle predicated)

predicates (present singular third-person)
predicating (participle present)
predicated (participle past)
predicated (past)
prædicate (alternative archaic)

From Latin praedicātus, perfect passive participle of praedicō (“to publish, declare, proclaim”) (see -ate (verb-forming suffix)), further from prae- (“before”) + dicō (“to proclaim, dedicate”), related to dīcō (“to say, tell”). Doublet of preach.

1911, Encyclopedia Britannica, Conceptualism
This quality becomes real as a mental concept when it is predicated of all the objects possessing it (“quod de pluribus natum est praedicari”).

(transitive, logic) To assert or state as an attribute or quality of something.

твърдя

logic: to assert or state as an attribute or quality of something


law

en-noun

law (countable and uncountable, plural laws)

From Middle English lawe, laȝe, from Old English lagu (“law”), borrowed from Old Norse lǫg (“law”, literally “things laid down or firmly established”), originally the plural of lag (“layer, stratum, a laying in order, measure, stroke”), from Proto-Germanic *lagą (“that which is laid down”), from Proto-Indo-European *legʰ- (“to lie”). Cognate with Scots law (“law”), Icelandic lög (“things laid down, law”), Faroese lóg (“law”), Norwegian lov (“law”), Swedish lag (“law”), Danish lov (“law”), Finnish laki (“law”). Displaced native Old English ǣ and ġesetnes. More at lay.
Not related to legal, nor to French loi, Spanish ley, all of which ultimately derive from Latin lēx, from Proto-Indo-European *leǵ- (“to gather”).

азакуан

body of rules established in a community by its authorities

Mathematical laws can be proved purely through mathematics, without scientific experimentation.

(mathematics, logic) A statement (of relation) that is true under specified conditions; a mathematical or logical rule.

օրենք

mathematics: statement that is true under specified conditions


bound

From Middle English bound, bund (preterite) and bounden, bunden, ibunden, ȝebunden (past participle), from Old English bund- and bunden, ġebunden respectively. See bind.

(mathematics, logic, of a variable) Constrained by a quantifier.

свързан

constrained by something, or constrained to something


sentence

Borrowed from Middle French sentence, from Latin sententia (“way of thinking, opinion, sentiment”), from sentiēns, present participle of sentiō (“to feel, think”), ultimately from Proto-Indo-European *sent- (“to feel”).

(logic) A formula with no free variables.


circle

Pitcairn-Norfolk: sirkil

From Middle English circle, cercle, from Old French cercle and Latin circulus, diminutive of Latin circus (“circle, circus”), from Ancient Greek κίρκος (kírkos, “circle, ring”), related to Old English hring (“ring”). Compare also Old English ċircul (“circle, zodiac”), which came from the same Latin source.

That heavy Bodies deſcend by gravity, is no better an account then we might expect from a Ruſtick: and again; that Gravity is a quality whereby an heavy body deſcends, is an impertinent Circle, and teacheth nothing.

1661, Joseph Glanvill, chapter XVIII, in The Vanity of Dogmatizing: Or Confidence in Opinions. […], London: […] E. C[otes] for Henry Eversden […], →OCLC, page 171:

(logic) A form of argument in which two or more unproved statements are used to prove each other; inconclusive reasoning.


theory

en-noun

theory (countable and uncountable, plural theories)

From Middle French théorie, from Late Latin theōria, from Ancient Greek θεωρία (theōría, “contemplation, divine perspective, speculation, a looking at, a seeking”), from θεωρέω (theōréō, “I look at, view, see, consider, examine”), from θεωρός (theōrós, “spectator”), from θέα (théa, “view, perspective, sight”) + ὁράω (horáō, “I see, look”) [i. e. θέαν ὁράω (théan horáō, “see, look at a view; survey + genitive”)].

der

A theory is consistent if it has a model.

(countable, logic) A set of axioms together with all statements derivable from them; or, a set of statements which are deductively closed. Equivalently, a formal language plus a set of axioms (from which can then be derived theorems). The statements may be required to all be bound (i.e., to have no free variables).

teoria

in logic: a set of axioms and all statements derivable from them


simple

Inherited from Middle English symple, simple, from Old French and French simple, from Latin simplex (“simple”, literally “onefold”) (as opposed to duplex (“double”, literally “twofold”)), from semel (“the same”) + plicō (“I fold”). See same and fold. Compare single, singular, simultaneous, etc.
Partially displaced native English onefold.

Peter van Inwagen, for example, believes that there are no ordinary objects, no chairs or shirts or shoes. Right here there are just some simples — atoms or whatever — arranged shoe-wise.

2021 September 14, Michael David Stevens, 10:41 from the start, in Do Chairs Exist?:


analysis

en-noun

analysis (countable and uncountable, plural analyses)

From Medieval Latin analysis, from Ancient Greek ἀνάλυσις (análusis), from ἀναλύω (analúō, “I unravel, investigate”), from ἀνα- (ana-, “thoroughly”) + λύω (lúō, “I loosen”).

language analysis for the determination of origin

List of terms used in mathematical analysis

(countable, logic) Proof by deduction from known truths.

analizë

logic: proof by deduction from known truths


vel

(logic) The ∨ symbol used to represent the inclusive or, which is a logical connective.


distribution

distribution (countable and uncountable, plural distributions)

distributions (plural)
distribucion (alternative obsolete)

From Old French, from Latin distributio, from distribuere 'to distribute', itself from dis- 'apart' + tribuere 'to' (from tribus).

(logic) The resolution of a whole into its parts.

erittely

logic: resolution of a whole into its parts


difference

difference (countable and uncountable, plural differences)

From Middle English difference, from Old French difference, from Latin differentia (“difference”), from differēns (“different”), present participle of differre. Doublet of differentia. Morphologically differ + -ence.

know the difference between one's ass and a hole in the ground

know the difference between one's ass and one's elbow

(logic) The quality or attribute which is added to those of the genus to constitute a species; a differentia.


depth

depth (countable and uncountable, plural depths)

From Middle English depthe, from Old English *dīepþ (“depth”), from Proto-Germanic *diupiþō (“depth”), equivalent to deep + -th (abstract nominal suffix). Cognate with Scots deepth (“depth”), Saterland Frisian Djüpte (“depth”), West Frisian djipte (“depth”), Dutch diepte (“depth”), Low German Deepde (“depth”), Danish dybde (“depth”), Icelandic dýpt (“depth”), Gothic 𐌳𐌹𐌿𐍀𐌹𐌸𐌰 (diupiþa, “depth”).

(logic) the number of simple elements which an abstract conception or notion includes; the comprehension or content


logic

logic (countable and uncountable, plural logics)

→ Chinese: 邏輯 /逻辑 (luójí)

From Middle English logik, from Old French logike, from Latin logica, from Ancient Greek λογική (logikḗ, “logic”), from feminine of λογικός (logikós, “of or pertaining to speech or reason or reasoning, rational, reasonable”), from λόγος (lógos, “speech, reason”). Displaced native Old English flitcræft (literally “art of arguing”).

ncog

An old tradition has it that there are two branches of logic: deductive logic and inductive logic. More recently, the differences between these disciplines have become so marked that most people nowadays use "logic" to mean deductive logic, reserving terms like "confirmation theory" for at least some of what used to be called inductive logic. I shall follow the more recent practice, and shall construe "philosophy of logic" as "philosophy of deductive logic".

2001, Mark Sainsbury, Logical Forms - An Introduction to Philosophical Logic, Second Edition, Blackwell Publishing, page 9:

(philosophy, logic) The study of the principles and criteria of valid inference and demonstration.


true

en-adj

true (comparative truer or more true, superlative truest or most true)

truer (comparative)
more true (comparative)
truest (superlative)
most true (superlative)
trew (alternative obsolete)
trewe (alternative obsolete)
troo (alternative nonstandard)

[t̠ɹ̠̊˔ʷu̠ː]

From Middle English trewe, from Old English trīewe, (Mercian) trēowe (“trusty, faithful”), from Proto-Germanic *triwwiz (compare Saterland Frisian trjou (“honest”), Dutch getrouw and trouw, German treu, Norwegian and Swedish trygg (“safe, secure’”), from pre-Germanic *drewh₂yos, from Proto-Indo-European *drewh₂- (“steady, firm”) (compare Irish dearbh (“sure”), Old Prussian druwis (“faith”), Ancient Greek δροόν (droón, “firm”)), extension of *dóru (“tree”) (possibly also Proto-Slavic *sъdorvъ (“healthy”) from the same root). More at tree. For the semantic development, compare Latin robustus (“tough”) from robur (“red oak”).

der

the course of true love never did run smooth

"A and B" is true if and only if "A" is true and "B" is true.

(logic) Of the state in Boolean logic that indicates an affirmative or positive result.


e

Guinea-Bissau Creole: i, e

Indo-Portuguese: e

Kabuverdianu: y, i, e

Papiamentu: i, y

From Old Galician-Portuguese e (“and”), from Latin et (“and”), from Proto-Indo-European *éti.

Verdadeiro e falso dá falso.

(logic) and (indicates a conjunction operation)


mark

marks (plural)
marke (alternative obsolete)
merk (alternative obsolete)
marc (alternative obsolete)

→ Bengali: মার্কা (marka)

→ Cantonese: 嘜 /唛 (mak¹, maak¹)

desc

→ Shanghainese: 麥克麥克 /麦克麦克 (⁸maq-kheq₇-maq₈-kheq₇)

→ Japanese: マーク (māku)

→ Korean: 마크 (makeu)

From Middle English mark, merk, merke, from Old English mearc (“mark, sign, line of division; standard; boundary, limit, term, border; defined area, district, province”), from Proto-West Germanic *marku, from Proto-Germanic *markō (“boundary; boundary marker”), from Proto-Indo-European *mórǵs (“edge, boundary, border”).
Compare march.
Cognates
* Dutch mark, merk (“mark, brand”)
* German Mark (“mark; borderland”), Marke (“mark, brand”)
* Swedish mark (“mark, land, territory”)
* Icelandic mark (“mark, sign”)
* Latin margo (“edge, margin”)
* Persian مرز (marz, “limit, boundary”)
* Sanskrit मर्या (maryā, “limit, mark, boundary”), मार्ग (mārga, “mark, section”).

cog

(heading) Indicator of position, objective etc.

(logic) A characteristic or essential attribute; a differential.


reason

en-noun

reason (countable and uncountable, plural reasons)

From Middle English resoun, reson, from Anglo-Norman raisun (Old French raison), from Latin ratiō, from ratus, past participle of reor (“reckon”), ultimately from Proto-Indo-European *h₂reh₁- (“to think”), reanalysed root of *h₂er- (“to put together”). Displaced native Middle English reden (found in compounds), from Old English rǣden (“condition, stipulation, calculation, direction”), from the same Proto-Indo-European source (compare West Frisian reden (“reason”), Dutch reden (“reason”)). Doublet of ration and ratio.

cog

(logic) A premise placed after its conclusion.

A cause:
A premise placed after its conclusion.


偽

/ŋui/ → /ɡwi/ → /ɡi/
From Middle Chinese 僞 (MC ngjweH).

(logic) a false statement (usually based without facts)


或

CJKV/code

Sino-Xenic (或):
* → Vietnamese: hoặc (或)

Characters in the same phonetic series (或) (Zhengzhang, 2003)
Ideogrammic compound (會意 /会意): 戈 (“dagger-axe (used to defend the territory)”) + 囗 (“city wall”) + 一, “territory”. The most ancient version is 戓, then modified into 或; the stroke was added perhaps when the pronunciation of the character evolved.
Borrowed for abstract meanings. The derivative 國 (OC *kʷɯːɡ), 域 (OC *ɢʷrɯɡ), and perhaps 淢 refer to the original word. The last character can be seen in the ancient name of the Han river, 㵄.
或 (OC *ɡʷɯːɡ, “someone; some”) is the result of the distributive suffix *-k being added to 有 (OC *ɢʷɯʔ, “there is”).
Cognate with 又 (OC *ɢʷɯs, “again”) (Schuessler, 2007).


postulate

From Latin postulātus or Latin postulātum. Alternatively, a substantivation of Latin postulātus, perfect passive participle of postulō (“to request”), see -ate (noun-forming suffix) for more. Compare French postulat.


context

en-noun

context (countable and uncountable, plural contexts)

en:finite set of variables concerning a formula, in logic

(logic) For a formula: a finite set of variables, which set contains all the free variables in the given formula.


derive

en-verb

derive (third-person singular simple present derives, present participle deriving, simple past and past participle derived)

derives (present singular third-person)
deriving (participle present)
derived (participle past)
derived (past)

From Middle English deriven, from Old French deriver, from Latin dērīvō (“to lead, turn, or draw off (a liquid), draw off, derive”), from dē (“away”) + rīvus (“a stream”); see rival. Unrelated to arrive.

der

(transitive, logic) To deduce (a conclusion) by reasoning.


order

en-noun

order (countable and uncountable, plural orders)

orders (plural)
ordre (alternative obsolete)

→ Swahili: oda

From Middle English ordre, from Old French ordre, ordne, ordene (“order, rank”), from Latin ōrdinem, accusative of ōrdō (“row, rank, regular arrangement”, literally “row of threads in a loom”), from Proto-Italic *ordō (“to arrange”), probably ultimately from Proto-Indo-European *h₂or-d-, from *h₂er-.
Related to Latin ōrdior (“begin”, literally “begin to weave”). In sense “request for purchase”, compare bespoke. Doublet of ordo.

cog

on another order

(sciences, engineering, logic) Scale: size or scope.


與

Phono-semantic compound (形聲 /形声, OC *la, *laʔ, *las): phonetic 舁 (OC *la, “raised hands”) + phonetic 牙 (OC *ŋraː). Both components are phonetic. The closest version to the original is 𦥸.
; "to be with; to associate with"
; "to give"

Han compound

与
𠔔
𠔜
𦥸
𦦲
𫝌
𫟋
𫤰
𭁇
𭁈
𭁉
𭁕
𮍫
𮍬
𮍭
𮍰


sphere

spheres (plural)
sphære (alternative archaic)
sphear (alternative archaic)
spheare (alternative obsolete)

From Middle English spere, from Old French sphere, from Late Latin sphēra, earlier Latin sphaera (“ball, globe, celestial sphere”), from Ancient Greek σφαῖρα (sphaîra, “ball, globe”), of unknown origin. Not related to superficially similar Persian سپهر (sepehr, “sky”) .

uder

In point of fact, so often as we think a subject as partially included within the sphere of a predicate, eo ipso we think it as partially, that is, particularly, excluded therefrom.

a. 1856, William Hamilton, “Appendix III: Quantification of Predicate,—Immediate Inference,—Conversion,—Opposition”, in Lectures on Metaphysics and Logic, volume 2, published 1860, page 526:

All categorical propositions necessarily imply the existence of their subjects in the appropriate sphere; in affirmative propositions this involves the existence of the predicate in the same sphere; but in negative propositions the predicate does not necessarily exist in that particular sphere, though it does in some sphere.

1896, James Welton, A Manual of Logic, 2nd edition, volume 1, page 213:

Finally, the disjunctive judgment contains a relation of two or more propositions to each other—a relation not of consequence, but of logical opposition, in so far as the sphere of the one proposition excludes that of the other.

1900 [1781], Immanuel Kant, translated by J. M. D. Meiklejohn, Critique of Pure Reason, page 58:

(logic, dated) The domain of reference of a proposition, subject, or predicate, or the totality of the particular subjects to which it applies.


arity

en-noun

arity (countable and uncountable, plural arities)

From -ary (taken from unary/binary/ternary [function/operator]) + -ity. Compare adicity and adinity.

(logic, mathematics, computer science) The number of arguments or operands a function or operation takes. For a relation, the number of domains in the corresponding Cartesian product.


逆

ja-adj

逆(ぎゃく) • (gyaku) -na (adnominal 逆(ぎゃく)な (gyaku na), adverbial 逆(ぎゃく)に (gyaku ni))

逆 (canonical)
gyaku (romanization)
逆な (adnominal)
逆に (adverbial)
逆だろ (imperfective stem)
ぎゃくだろ (imperfective stem)
gyaku daro (imperfective)
逆で (continuative stem)
ぎゃくで (continuative stem)
gyaku de (continuative)
逆だ (stem terminative)
ぎゃくだ (stem terminative)
gyaku da (terminative)
逆な (attributive stem)
ぎゃくな (attributive stem)
gyaku na (attributive)
逆なら (hypothetical stem)
ぎゃくなら (hypothetical stem)
gyaku nara (hypothetical)
逆であれ (imperative stem)
ぎゃくであれ (imperative stem)
gyaku de are (imperative)
逆ではない (informal negative)
逆じゃない (informal negative)
ぎゃくではない (informal negative)
ぎゃくじゃない (informal negative)
gyaku de wa nai (informal negative)
gyaku ja nai (informal negative)
逆だった (informal past)
ぎゃくだった (informal past)
gyaku datta (informal past)
逆ではなかった (informal negative past)
逆じゃなかった (informal negative past)
ぎゃくではなかった (informal negative past)
ぎゃくじゃなかった (informal negative past)
gyaku de wa nakatta (informal negative past)
gyaku ja nakatta (informal negative past)
逆です (formal)
ぎゃくです (formal)
gyaku desu (formal)
逆ではありません (formal negative)
逆じゃありません (formal negative)
ぎゃくではありません (formal negative)
ぎゃくじゃありません (formal negative)
gyaku de wa arimasen (formal negative)
gyaku ja arimasen (formal negative)
逆でした (formal past)
ぎゃくでした (formal past)
gyaku deshita (formal past)
逆ではありませんでした (formal negative past)
逆じゃありませんでした (formal negative past)
ぎゃくではありませんでした (formal negative past)
ぎゃくじゃありませんでした (formal negative past)
gyaku de wa arimasen deshita (formal negative past)
gyaku ja arimasen deshita (formal negative past)
逆で (conjunctive)
ぎゃくで (conjunctive)
gyaku de (conjunctive)
逆なら（ば） (conditional)
ぎゃくなら（ば） (conditional)
gyaku nara (ba) (conditional)
逆だったら (conditional past)
ぎゃくだったら (conditional past)
gyaku dattara (conditional past)
逆だろう (volitional)
ぎゃくだろう (volitional)
gyaku darō (volitional)
逆に (adverbial)
ぎゃくに (adverbial)
gyaku ni (adverbial)
逆さ (noun-from-adj)
ぎゃくさ (noun-from-adj)
gyakusa (noun-from-adj)

ja-adj-infl

逆

. で は ありません でした

. じゃ ありません でした


量

Characters in the same phonetic series (量) (Zhengzhang, 2003)
Inconclusive. In the oracle bone and bronze scripts, the most common form was 日 (“sun”) + 東 (“bag; east”). Here are a few proposed interpretations as an ideogrammic compound (會意 /会意):
* 日 was sometimes replaced with 田, so Qiu Xigui thinks that it may be the original character of 糧 (OC *raŋ, “grain field”).
* Yu Xingwu interprets it as measuring something under the sun.
* Guo Moruo interprets it as the sun rising in the east – original character of 亮 (OC *raŋs).
* Huang Dekuan suspects the 日 is actually 昜 (OC *laŋ) as the phonetic component.
Shuowen interprets this as a phono-semantic compound (形聲 /形声, OC *raŋ, *raŋs): phonetic 曏 (OC *qʰjaŋʔ, *qʰjaŋs, *qʰaŋʔ, *qʰaŋs) + semantic 重 (“weight; heavy”).
From Proto-Sino-Tibetan *k-raŋ (“to count, to measure”) (STEDT under *(g/k)raŋ; Schuessler, 2007). Cognate to Tibetan བགྲང (bgrang, “to count”), Khaling ʾkhran-ne, Burmese ခြင် (hkrang, “to measure capacity”), Nusu xɹɯ³¹ (“to count”).
Pronunciation 2 is possibly a *-s suffixed exopassive derivation of Pronunciation 1; thus it means "what is measured → a measure" and is cognate to Tibetan གྲངས (grangs, “number”) (see also Unger (1983))


量

量 (canonical)
ryō (romanization)
ryau (romanization)
りやう (hiragana historical)

From Middle Chinese 量 (MC ljangH, “measure”).

比量


門

CJKV/code

Sino-Xenic (門):
* → Japanese: 門(もん) (mon)
* → Korean: 문(門) (mun)
* → Vietnamese: môn (門)

Wutunhua: men

Characters in the same phonetic series (門) (Zhengzhang, 2003)
Pictogram (象形): a gate. Compare 戶 (OC *ɡʷaːʔ, “(one) door”), which is half of this character (𠁣).
From Proto-Sino-Tibetan *mur (“mouth; lip; to hold in mouth; to chew; face; gills”) (STEDT). Cognate with Tibetan མུར་བ (mur ba, “to masticate”), Tibetan མུར་འགྲམ (mur 'gram, “jawbone; cheek”), Mizo hmûi (“lips; upper lip”) and 吻 (OC *mɯnʔ, “lips; corner of the lips”).
; “-gate”


非

CJKV/code

Sino-Xenic (非):
* → Japanese: 非(ひ) (hi)
* → Korean: 비(非) (bi)
* → Vietnamese: phi (非)

Characters in the same phonetic series (非) (Zhengzhang, 2003)
Pictogram (象形) - two wings facing opposite directions. Originally, it represented wings; then, according to Xu Shen, its meaning changed into "leave; disobey" (違). Eventually, it was used perhaps as a phonetic loan to mean "not to be".
Unrelated to the Kangxi radical 韭.
非 (OC *pɯj) is the fusion of the negation particle 不 (OC *pɯ, *pɯʔ, *pɯ', “not”) and the copula 惟 (OC *ɢʷi, “to be”), attested in oracle bone inscriptions.


SO

second-order logic
second-order logic#English

(logic, computer science) Initialism of second-order logic.


verifiable

(logic) A statement or observation that can be verified.


Boolean

From Boole + -ean, named after English mathematician, philosopher and logician George Boole (1815–1864).

named-after

boolean (alternative)
Boolian (alternative)

Oh, Boolean operators! "Blue and ones"! Good idea!

2005 May 9, Michael Chapman; Matthew Chapman, “Bug In Mouth Disease”, in Homestar Runner, spoken by Strong Sad (Matthew Chapman):

(logic, computing) Pertaining to data items that can have “true” and “false” (or, equivalently, 1 and 0 respectively) as their only possible values and to operations on such values.

booleà

logic: pertaining to data items that have values “true” and “false”


Boolean

Booleans (plural)
boolean (alternative)
Boolian (alternative)

(logic, computing) A variable that can hold a single true/false (1/0) value.


degree

→ Burmese: ဒီဂရီ (diga.ri)

→ Juba Arabic: digrii

→ Swahili: digrii

→ Tagalog: digri

From Middle English degre, borrowed from Old French degré (French: degré), itself from Latin gradus, with the prefix de-.

Appendix:Roget MICRA thesaurus/Class I § 26. Degree

Appendix:Roget MICRA thesaurus/Class I § 31. Greatness

Appendix:Roget MICRA thesaurus/Class I § 32. Smallness

(logic) The number of logical connectives in a formula.


closed

(mathematics, logic, of a formula) Lacking a free variable.


discharge

en-verb

discharge (third-person singular simple present discharges, present participle discharging, simple past and past participle discharged)

discharges (present singular third-person)
discharging (participle present)
discharged (participle past)
discharged (past)

/dɪsˈtʃɑːdʒ/

/ˈdɪstʃɑːdʒ/

/dɪsˈtʃɑɹdʒ/

/ˈdɪstʃɑɹdʒ/

-ɪstʃɑː(ɹ)dʒ

From Middle English dischargen, from Old French deschargier (“to unload”), from Late Latin discarricāre (“unload”). By surface analysis, dis- + charge.

(logic) To release (an auxiliary assumption) from the list of assumptions used in arguments, and return to the main argument.


attribute

From Latin attributus past participle of attribuere.

(logic) That which is predicated or affirmed of a subject; a predicate; an accident.

attribuutti

logic: that which is predicated or affirmed of a subject


operation

en-noun

operation (countable and uncountable, plural operations)

→ Japanese: オペレーション (operēshon)

→ Scottish Gaelic: opairèisean

/ˌɒp.əˈɹeɪ.ʃən/

/ˌɑ.pəˈɹeɪ.ʃən/

From Middle French operation, from Old French operacion, from Latin operātiō, from the verb operor (“I work”), from opus, operis (“work”). Equivalent to operate + -ion.

عَمَلِيَّة

The number of operands associated with an operation is called its arity; an operation of arity 2 is called a binary operation.

(computing, logic, mathematics, countable) A procedure for generating a value from one or more other values (the operands).

(mathematics, more formally, countable) A function which maps zero or more (but typically two) operands to a single output value.


strong

en-adj

strong (comparative stronger, superlative strongest)

stronger (comparative)
strongest (superlative)
strang (alternative)
stronk (alternative)

Sranan Tongo: tranga

Aukan: taanga

Saramaccan: taánga

From Middle English strong, strang, from Old English strang, from Proto-West Germanic *strang, from Proto-Germanic *strangaz (“tight, strict, straight, strong”), from Proto-Indo-European *strengʰ- (“taut, stiff, tight”). Cognate with Scots strang (“strong”), Saterland Frisian strang, West Frisian string (“austere, strict, harsh, severe, stern, stark, tough”), Dutch streng (“strict, severe, tight”), German streng (“strict, severe, austere”), Swedish sträng, strang (“severe, strict, harsh”), Norwegian strang (“strong, harsh, bitter”), Norwegian streng (“strong, hard”), Icelandic strangur (“strict”), Latin stringō (“tighten”).

cog

a chain is only as strong as its weakest link

the strong do what they can and the weak suffer what they must

(mathematics, logic) Having a wide range of logical consequences; widely applicable. (Often contrasted with a weak statement which it implies.)


innuendo

en-noun

innuendo (plural innuendoes or innuendos or innuendis)

innuendoes (plural)
innuendos (plural)
innuendis (plural)
inuendo (alternative)

LL-Q1860 (eng)-I learned some phrases-innuendo.wav

From the Latin innuendō (“by nodding”), ablative singular form of innuendum (“a nodding”), gerund of innuō (“I give a nod”).

(logic) A rhetorical device with an omitted, but obvious conclusion, made to increase the force of an argument.


weak

en-adj

weak (comparative weaker, superlative weakest)

weaker (comparative)
weakest (superlative)
weake (alternative obsolete)

healthy

antonym(s) of “lacking in force or ability”

potent

antonym(s) of “lacking in taste or potency”

From Middle English weyk, wayk, weik, waik, from Old Norse veikr (“weak”), from Proto-Germanic *waikwaz (“weak, yielded, pliant, bendsome”), from Proto-Indo-European *weyk- (“to bend, wind”).
Cognate with Old English wāc (“weak, bendsome”), Saterland Frisian wook (“soft, gentle, tender”), West Frisian weak (“soft”), Dutch week (“soft, weak”), German weich (“weak, soft”), Norwegian veik (“weak”), Swedish vek (“weak, pliant”), Icelandic veikur (“bendsome, weak”). Related to Old English wīcan (“to yield”). Doublet of week and wick.

cog

the spirit is willing but the flesh is weak

(mathematics, logic) Having a narrow range of logical consequences; narrowly applicable. (Often contrasted with a strong statement which implies it.)


crocodile

→ Maori: kokorotaera, karakotaera

→ Niuean: kirokotaili

→ Tokelauan: kolokotaila

→ Tongan: kalokataile

→ Welsh: crocodeil

From Middle English cocodrill, cokadrill, cokedril, from Old French cocodril (modern French crocodile), from Medieval Latin cocodrillus, from Latin crocodilus, from Ancient Greek κροκόδειλος (krokódeilos). The word was later refashioned after the Latin and Greek forms. Doublet of krokodil.

[ˈkʰɹɑkədaɪɫ]

We have seen syllogisms, crocodiles, enthymemas, sorites, &c. explained and tried upon a boy of nine or ten years old in playful conversation[…]

1798, Maria Edgeworth, Practical Education:

(logic) A fallacious dilemma, mythically supposed to have been first used by a crocodile.


minor

en-adj

minor (comparative more minor, superlative most minor)

more minor (comparative)
most minor (superlative)
miner (alternative)
maner (alternative)
minore (alternative)
minour (alternative)
mynor (alternative)
mynour (alternative)
mynowr (alternative)
mi (alternative)

antonym(s) of

serious, grave, severe, dangerous, fatal, life-threatening, acute (informal)

From Middle English minor, menor, menour, etc., from Latin minor (“lesser; young; young person”) both directly and via Norman and Middle French menor, menour, etc. Doublet of minus but not mini-. Cognate with minister, minify, Minorca, Menshevik, and possibly minnow. Compare Latin minimum and minuō, Old High German minniro, Cornish minow.

der

The minor term of John Stuart Mill's famous syllogism—usually mistakenly credited to Aristotle—is Socrates; the major term is mortal.

Lesser, smaller in importance, size, degree, seriousness, or significance compared to another option, particularly:

(logic) Acting as the subject of the second premise of a categorical syllogism, which then also acts as the subject of its conclusion.


minor

minors (plural)
miner (alternative)
maner (alternative)
minore (alternative)
minour (alternative)
mynor (alternative)
mynour (alternative)
mynowr (alternative)
mi (alternative)

And so musten oure clerkis argue whan þai aleggen for her lordeschip þe lyuynge of her patrons & sayntis, & sayen þus: "Seynt thomas & seynt hwe & seynt Swiþune wer þus lordis, & in þis þai suyd cristis lyuynge & his lore; þerfor we may lefulli be þus lordis." And I wote wel þat gabriel schal blow his horne or þai han preuyd þe mynor; þat is, þat þes seyntes or patrons in þis suyden þe lore or þe life of ihesu criste.

c. 1450, anonymous author, The Clergy May Not Hold Property, page 31:

(logic) Ellipsis of minor term or minor premise.


major

en-adj

major (comparative more major, superlative most major)

more major (comparative)
most major (superlative)
majour (alternative obsolete)

[ˈmeɪ̯d͡ʒɚ(ɹ)]

[ˈmeɪ̯d͡ʒə(ɹ)]

[ˈmæɪ̯d͡ʒə(ɹ)]

From Middle English major, from Latin maior, comparative of magnus (“great, large; noble, important”), from Proto-Indo-European *méǵh₂yōs (“greater”), comparative of *meǵh₂- (“great”). Compare West Frisian majoar (“major”), Dutch majoor (“major”), French majeur. Doublet of mayor.

Occurring as the predicate in the conclusion of a categorical syllogism. (of a term)

Containing the major term in a categorical syllogism. (of a premise)


major

majors (plural)
majour (alternative obsolete)

[ˈmeɪ̯d͡ʒɚ(ɹ)]

[ˈmeɪ̯d͡ʒə(ɹ)]

[ˈmæɪ̯d͡ʒə(ɹ)]

pääaineopiskelija

student specializing in a specified subject


horseshoe

/ˈhɔːɹs.ʃuː/

From Middle English horsscho, horssho, horscho, hors schoo, equivalent to horse + shoe.

almost only counts in horseshoes and hand grenades

close only counts in horseshoes and darts

close only counts in horseshoes and hand grenades


formula

en-noun

formula (countable and uncountable, plural formulas or formulae or formulæ)

formulas (plural)
formulae (plural)
formulæ (plural)

Irish: foirmle

Scottish Gaelic: foirmle

Learned borrowing from Latin fōrmula (“a small pattern or mold, form, rule, principle, method, formula”), diminutive of forma (“a form”). See form.

lbor

(logic) A syntactic expression of a proposition, built up from quantifiers, logical connectives, variables, relation and operation symbols, and, depending on the type of logic, possibly other operators such as modal, temporal, deontic or epistemic ones.

論理式

logic: syntactic expression of a proposition


formula

fȏrmula (canonical feminine)
фо̑рмула (Cyrillic)
formula (nominative singular)
formule (nominative plural)
formule (genitive singular)
formula (genitive plural)
formuli (dative singular)
formulama (dative plural)
formulu (accusative singular)
formule (accusative plural)
formulo (singular vocative)
formule (plural vocative)
formuli (locative singular)
formulama (locative plural)
formulom (instrumental singular)
formulama (instrumental plural)


medium

Borrowed from Latin medium, neuter of medius (“middle”), from Proto-Italic *meðjos, from Proto-Indo-European *médʰyos (“between”). Compare middle. Doublet of mid, medio, media, and meson.

(countable, logic) The mean or middle term of a syllogism, that by which the extremes are brought into connection.


parenthesis

en-noun

parenthesis (countable and uncountable, plural parentheses)

/pəˈɹɛnθəsɪs/

Learned borrowing from Late Latin parenthesis (“addition of a letter to a syllable in a word”), itself borrowed from Ancient Greek παρένθεσις (parénthesis, “insertion”).

der

(mathematics, logic) Such brackets as used to clarify expressions by grouping those terms affected by a common operator, or to enclose the components of a vector or the elements of a matrix.

փակագծեր

(mathematics, logic) brackets used to clarify expressions by grouping terms affected by a common operator


synthesis

en-noun

synthesis (countable and uncountable, plural syntheses)

From Latin synthesis, from Ancient Greek σύνθεσις (súnthesis, “a putting together; composition”), from συντίθημι (suntíthēmi, “put together, combine”), from συν- (sun-, “together”) + τίθημι (títhēmi, “set, place”). Doublet of sandhi.

der

(logic) A deduction from the general to the particular, by applying the rules of logic to a premise.

համադրություն

logic: deduction from the general to the particular


tableau

Unadapted borrowing from French tableau, from Old French tablel (“a surface which is used primarily for painting”).


thesis

Georg Wilhelm Friedrich Hegel
Johann Gottlieb Fichte

From Late Middle English thesis (“lowering of the voice”) and also borrowed directly from its etymon Latin thesis (“proposition, thesis; lowering of the voice”), from Ancient Greek θέσῐς (thésĭs, “arrangement, placement, setting; conclusion, position, thesis; lowering of the voice”), from τῐ́θημῐ (tĭ́thēmĭ, “to place, put, set; to put down in writing; to consider as, regard”) (ultimately from Proto-Indo-European *dʰeh₁- (“to do; to place, put”)) + -σῐς (-sĭs, suffix forming abstract nouns or nouns of action, process, or result). The English word is a doublet of deed.
Sense 1.1 (“proposition or statement supported by arguments”) is adopted from antithesis. Sense 1.4 (“initial stage of reasoning”) was first used by the German philosopher Johann Gottlieb Fichte (1762–1814), and later applied to the dialectical method of his countryman, the philosopher Georg Wilhelm Friedrich Hegel (1770–1831).
The plural form theses is borrowed from Latin thesēs, from Ancient Greek θέσεις (théseis).

der

Senses relating to logic, rhetoric, etc.

(logic) An affirmation, or distinction from a supposition or hypothesis.


direct

en-adj

direct (comparative more direct, superlative most direct)

more direct (comparative)
most direct (superlative)
darect (alternative India)

/daɪ̯əˈɹɛkt/

Borrowed from Latin dīrectus, perfect passive participle of dīrigō (“straighten, direct”), from dis- (“asunder, in pieces, apart, in two”) + regō (“make straight, rule”). Compare dress. Doublet of derecho.
For the meaning development compare with Russian напра́вить (naprávitʹ, “to direct, to turn, to aim, to level, to point”), отпра́вить (otprávitʹ, “to send, to dispatch, to forward”) connected with пра́вить (právitʹ, “to govern, to rule, to drive, to steer”).

m+

law of the excluded middle
law of the excluded middle

(mathematics, logic, of a proof) Not employing the law of the excluded middle or argument by contradiction.


assertoric

/ˌæsɚˈtɔɹɪk/

(logic) Stating that which is actual, usually in contrast with modal sentences.


mode

Borrowed from Latin modus. Doublet of moda, a borrowing through French.


opposition

/ˌɒp.əˈzɪʃ.ən/

/ˌɑ.pəˈzɪʃ.ən/

From Middle English opposicioun, from Old French oposicion (whence French opposition), from Late Latin oppositiō, translating Ancient Greek ἀντίθεσις (antíthesis), from the past participle stem of classical Latin oppōnō (“I set against”).

(logic) The difference of quantity or quality between two propositions having the same subject and predicate.


figure

→ Japanese: フィギュア (figyua)

From Middle English figure, borrowed from Old French figure, from Latin figūra (“form, shape, form of a word, a figure of speech, Late Latin a sketch, drawing”), from fingō (“to form, shape, mold, fashion”), from Proto-Indo-European *dʰeyǵʰ- (“to mold, shape, form, knead”). Cognate with Ancient Greek τεῖχος (teîkhos), Sanskrit देग्धि (dégdhi), Old English dāg (“dough”). More at dough. Doublet of figura.

der

(logic) The form of a syllogism with respect to the relative position of the middle term.


non sequitur

en-noun

non sequitur (plural non sequiturs or non sequuntur)

non sequiturs (plural)
non sequuntur (plural)
non-sequitur (alternative)
nonsequitur (alternative)

Learned borrowing from Latin phrase nōn sequitur (“it does not follow”).

what does that have to do with the price of tea in China

(logic) Any invalid argument in which the conclusion cannot be logically deduced from the premises.


dom

head

dom c (singular definite dommen, plural indefinite domme)

dommen (definite singular)
domme (indefinite plural)
dom (indefinite nominative singular)
dommen (definite nominative singular)
domme (indefinite nominative plural)
dommene (definite nominative plural)
doms (genitive indefinite singular)
dommens (definite genitive singular)
dommes (genitive indefinite plural)
dommenes (definite genitive plural)

From Old Norse dómr (“judgement”), from Proto-Germanic *dōmaz, from Proto-Indo-European *dʰóh₁mos.


alternation

en-noun

alternation (countable and uncountable, plural alternations)

Learned borrowing from Latin alternatio; compare French alternation. By surface analysis, alternate + -ion.

(logic) The "inclusive or" truth function.


tilde

Borrowed from Spanish tilde, from Latin titulus (“superscript”) or from tildar. Doublet of titer/titre, title, titlo, tittle, and titulus. Compare Portuguese til.

apex

visually similar diacritic in Middle Vietnamese that is often confused with the tilde

A symbol ⟨~⟩, with various names and uses, also known as swung dash or wave dash. In the computer industry, various other names may be used, such as squiggle and twiddle.

(logic) An alternate form of the logical negation operator, which is usually written as ¬.


ancestral

ancestrals (plural)
ancestrall (alternative)
auncestral (alternative)

From Anglo-Norman ancestrel, from ancestre (“ancestor”).

Like all ordinary ancestrals, remote successor is logically reflexive.

1992, Diane Brentari, Gary N. Larson, Lynn A. MacLeod, The Joy of Grammar: A festschrift in honor of James D. McCawley, page 309:

One can take advantage of the ancestrals of basic relations such as RemoteSuccessor, to define Quace structure as follows internal to Proposal A:

2004, Paul Martin Postal, Skeptical Linguistic Essays, page 61:

I thus naturally extend the notation introduced for the ancestrals of structural relations between arcs to the nonstructural relations Sponsor and Erase, and to relations defined in terms of them like Successor.

2010, Paul Martin Postal, Edge-based Clausal Syntax, page 32:

(logic) A relationship in which something is a precursor.


member

→ Japanese: メンバー (menbā)

→ Korean: 멤버 (membeo)

→ Malay: member

→ Punjabi: ਮੈਂਬਰ (maimbar)

From Middle English membre, from Old French membre, from Latin membrum (“limb, body part”), from Proto-Italic *memzrom, from Proto-Indo-European *mḗms, *mēms-rom (“flesh”). Akin to Gothic 𐌼𐌹𐌼𐌶 (mimz, “meat, flesh”), Crimean Gothic menus.
Coexists with native Middle English lim, limb (“member, limb, joint”) (from Old English lim (“limb, joint, main branch”)), and displaced Middle English lith (“limb, joint, member”) (from Old English liþ (“limb, member, join, tip”)).

cog

(logic) One of the propositions making up a syllogism.


binary

en-adj

binary (comparative more binary, superlative most binary)

more binary (comparative)
most binary (superlative)

From Late Latin bīnārius (“consisting of two”), from Latin bīnī (“two-by-two, pair”). By surface analysis, bin- + -ary.

двайко́вы

being in a state of one of two mutually exclusive conditions such as on or off

Near-synonym: Boolean

en:concerning logic of mutually exclusive states

(logic) Concerning logic whose subject matter concerns such states.


reduce

en-verb

reduce (third-person singular simple present reduces, present participle reducing, simple past and past participle reduced)

reduces (present singular third-person)
reducing (participle present)
reduced (participle past)
reduced (past)

From Middle English reducen, from Old French reduire, from Latin redūcō (“reduce”); from re- (“back”) + dūcō (“lead”). See duke, and compare with redoubt.

(transitive, logic) To convert a syllogism to a clearer or simpler form.

herleiden

logic: to convert a syllogism to a clearer or simpler form


inverse

Recorded since 1440, from Latin inversus, the past participle of invertere (“to invert”), itself from in- (“in, on”) + vertere (“to turn”).

противоположност

opposite of a given due to contrary effects or nature

"Anything that isn't a dog doesn't go to heaven" is the inverse of "All dogs go to heaven." More generally, ¬ mathsf p→¬ mathsf q is the inverse of mathsf p→ mathsf q and is equivalent to the converse proposition mathsf q→ mathsf p.

Inversion is the inferring, from a given proposition, another proposition whose subject is the contradictory of the subject of the original proposition. The given proposition is called the Invertend, that which is inferred from it is termed the Inverse... The rule for Inversion is: Convert either the Obverted Converse or the Obverted Contrapositive.

1896, James Welton, A Manual of Logic, 2nd edition, Bk iii, Ch. iii, §102:

The result of an inversion, particularly:

(logic) The non-truth-preserving proposition constructed by negating both the premise and conclusion of an initially given proposition.


nor

From Etymology 1 (sense 2 above), reinterpreted as not + or or negation + or.

(logic, electronics) Alternative form of NOR.


xor

(logic) xor; exclusive or (logical operation that outputs true only when both inputs differ)


atomic

نَوَوِيّ

of, or employing nuclear energy or processes

en:unatomizable
en:unsimplifiable in logic

(logic, of a proposition) Lacking logical operators; unable to be made simpler in logical form.


syllogism

From Old French silogisme (“syllogism”), from Latin syllogismus, from Ancient Greek συλλογισμός (sullogismós, “inference, conclusion”). Doublet of syllogismus.

der

Meronyms: major premise, minor premise

Ever since Aristotle, syllogism has occupied a central place in logic and cast a fateful shadow upon the power of reason. Recognized to be the great conveyor of rationality, allowing reason to reach conclusions of unparalleled universality and necessity, syllogism has equally been acknowledged to be beset by limits.

2006, Richard Dien Winfield, From Concept to Objectivity: Thinking Through Hegel's Subjective Logic, Ashgate Publishing, Ltd., →ISBN, page 107:

(logic) An argument whose conclusion is supported by two premises, of which one contains the term that is the predicate of the conclusion, and the other contains the term that is the subject of the conclusion; common to both premises is a term that is excluded from the conclusion.


determine

en-verb

determine (third-person singular simple present determines, present participle determining, simple past and past participle determined)

determines (present singular third-person)
determining (participle present)
determined (participle past)
determined (past)
determin (alternative obsolete)

/ɖiˈʈɜː(ɾ)ˌmaɪn/

From Middle English determinen, from Old French determiner, French déterminer, from Latin determināre (“to bound, limit, prescribe, fix, determine”), from de + termināre (“to limit”), from terminus (“bound, limit, end”).

der

(logic) To define or limit by adding a differentia.


complement

en-noun

complement (countable and uncountable, plural complements)

From Middle English complement, from Latin complēmentum (“that which fills up or completes”), from compleō (“I fill up, I complete”) (English complete). Doublet of compliment. The verb is from the noun.

der

(logic) An expression related to some other expression such that it is true under the same conditions that make other false, and vice versa.

komplementti

expression which is true when the other is false, and vice versa


term

From Middle English terme, borrowed from Old French terme, from Latin terminus (“a bound, boundary, limit, end; in Medieval Latin, also a time, period, word, covenant, etc.”), ultimately from Proto-Indo-European *térmn̥ (“stump, end, boundary”).
Doublet of terminus and termon. Old English had termen, from the same source.

términu

one of the addends in a sum or in another mathematical operation

The subject and predicate of a proposition are, after Aristotle, together called its terms or extremes.

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) The subject or the predicate of a proposition; one of the three component parts of a syllogism, each one of which is used twice.

terminus

one of three component parts of a syllogism


term

tèrm (canonical)
term-term (plural)
terma (alternative)

From Dutch term, from French terme, from Old French terme, from Latin terminus (“a bound, boundary, limit, end; in Medieval Latin, also a time, period, word, covenant, etc.”).

(logic) term (the subject or the predicate of a proposition)


converse

From Latin conversus (“turned around”), past participle of converto (“turn about”).

All trout are fish, but the converse, that all fish are trout, is not true.

(logic) Of a proposition or theorem consisting of a statement of the form "If A is true, then B is true", the statement "If B is true, then A is true" which need not be equivalent to the first one.


sequor

la-verb

sequor (present infinitive sequī, perfect active secūtus sum or sequūtus sum); third conjugation, deponent

sequī (infinitive present)
secūtus sum (active perfect)
sequūtus sum (active perfect)
sequor (active first-person indicative present singular)
sequeris (active indicative present second-person singular)
sequere (active indicative present second-person singular)
sequitur (active indicative present singular third-person)
sequimur (active first-person indicative plural present)
sequiminī (active indicative plural present second-person)
sequuntur (active indicative plural present third-person)
sequēbar (active first-person imperfect indicative singular)
sequēbāris (active imperfect indicative second-person singular)
sequēbāre (active imperfect indicative second-person singular)
sequēbātur (active imperfect indicative singular third-person)
sequēbāmur (active first-person imperfect indicative plural)
sequēbāminī (active imperfect indicative plural second-person)
sequēbantur (active imperfect indicative plural third-person)
sequar (active first-person future indicative singular)
sequēris (active future indicative second-person singular)
sequēre (active future indicative second-person singular)
sequētur (active future indicative singular third-person)
sequēmur (active first-person future indicative plural)
sequēminī (active future indicative plural second-person)
sequentur (active future indicative plural third-person)
secūtus (active indicative perfect)
secūtus (active indicative pluperfect)
secūtus (active future indicative perfect)
sequar (active first-person present singular subjunctive)
sequāris (active present second-person singular subjunctive)
sequāre (active present second-person singular subjunctive)
sequātur (active present singular subjunctive third-person)
sequāmur (active first-person plural present subjunctive)
sequāminī (active plural present second-person subjunctive)
sequantur (active plural present subjunctive third-person)
sequerer (active first-person imperfect singular subjunctive)
sequerēris (active imperfect second-person singular subjunctive)
sequerēre (active imperfect second-person singular subjunctive)
sequerētur (active imperfect singular subjunctive third-person)
sequerēmur (active first-person imperfect plural subjunctive)
sequerēminī (active imperfect plural second-person subjunctive)
sequerentur (active imperfect plural subjunctive third-person)
secūtus (active perfect subjunctive)
secūtus (active pluperfect subjunctive)
sequere (active imperative present second-person singular)
sequiminī (active imperative plural present second-person)
sequitor (active future imperative second-person singular)
sequitor (active future imperative singular third-person)
sequuntor (active future imperative plural third-person)
sequī (active infinitive present)
sequēns (active participle present)
secūtūrum esse (active future infinitive)
sequūtūrum esse (active future infinitive)
secūtūrus (active future participle)
sequūtūrus (active future participle)
sequendus (future participle passive)
secūtum esse (active infinitive perfect)
sequūtum esse (active infinitive perfect)
secūtus (active participle perfect)
sequūtus (active participle perfect)
secūtum fore (active future infinitive perfect)
sequūtum fore (active future infinitive perfect)
secūtūrum fuisse (active infinitive perfect potential)
sequūtūrum fuisse (active infinitive perfect potential)
sequendī (genitive gerund noun-from-verb)
sequendō (dative gerund noun-from-verb)
sequendum (accusative gerund noun-from-verb)
sequendō (ablative gerund noun-from-verb)
secūtum (accusative noun-from-verb supine)
sequūtum (accusative noun-from-verb supine)
secūtū (ablative noun-from-verb supine)
sequūtū (ablative noun-from-verb supine)

Catalan: seguir

Franco-Provençal: siuvre

Old French: segre, siure, sivre, siudre; suiant, sivant; sieute, suite

Bourguignon: seugre

Gallo: sieude

→ Middle English: suant, suit

English: sue; suant; suit

Middle French: suyvre

French: suivre; suite

→ English: suite

Picard: suire

Norman: sieuvre, suuvre

Walloon: shuve

Italian: seguire

→ English: segue

Occitan: seguir, sègre

Old Galician-Portuguese: seguir

Galician: seguir

Portuguese: seguir

→ Papiamentu: sigui

Sardinian: sichire

Sicilian: sicutari (from *sequitare)

Spanish: seguir

→ Esperanto: sekvi

Inherited from Proto-Italic *sekʷōr, from Proto-Indo-European *sekʷ- (“to follow”). Cognates include Sanskrit सचते (sácate), Avestan 𐬵𐬀𐬗𐬀𐬌𐬙𐬉 (hacaitē) and Ancient Greek ἕπομαι (hépomai).


tautology

en-noun

tautology (countable and uncountable, plural tautologies)

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

From Late Latin tautologia, from Ancient Greek ταὐτολογία (tautología) from ταὐτός (tautós, “the same”) + λόγος (lógos, “explanation”). By surface analysis, tauto- + -logy.

propositional variable
propositional variable

(countable, logic, propositional logic) A statement that is true for all truth values of its propositional variables.

(countable, logic, first-order logic) A statement that is true for all truth values of its Boolean atoms.


Introduced by Gerhard Gentzen who based it on the Latin letter A, by analogy with ∃.

universal quantifier
universal quantifier

(mathematics, logic) The symbol used in predicate calculus, etc, to represent the universal quantifier, meaning “for all”.


Introduced by Giuseppe Peano in Formulaire de mathematiqués (1897), from the uppercase Latin letter E. The modern variable-binding syntax first appeared in Principia Mathematica (1910).

existential quantifier
existential quantifier

(mathematics, logic) The existential quantifier, meaning "there exists (at least one)".


universal quantifier

universal quantifier (plural universal quantifiers)

(logic) The operator, represented by the symbol ∀, used in predicate calculus to indicate that a predicate is true for all members of a specified set. Verbal equivalents include "for each" and "for every".


existential quantifier

existential quantifier (plural existential quantifiers)

(logic) The operator, represented by the symbol ∃, used in predicate calculus to indicate that a predicate is true for at least one member of a specified set. Verbal equivalents include "there exists" and "there is".


iff

A rectangle is a square iff all four of its sides have the same length.

(mathematics, logic) Abbreviation of if and only if.


ou

From Old Galician-Portuguese ou, from Latin aut.

(logic) inclusive or (connective which yields true when at least one of the predicates is true)


inclusive or

(logic, computing) A logical connective joining two or more predicates that yields the logical value "true" when at least one of the predicates is true.


exclusive or

exclusive ors (plural)
exclusive-or (alternative)
XOR (alternative)
xor (alternative)
EOR (alternative)
eor (alternative)

Exclusive disjunction
exclusive disjunction

(logic, computing) Exclusive disjunction: the use of or to indicate that of two predicates, one is true and one is false (without specifying which is which); contrasted with inclusive or, which does not imply that one must be false.

(logic, computing, more generally) Exclusive disjunction: the use of or to indicate that of two or more predicates, an odd number are true (without specifying which or how many); contrasted with inclusive or, which indicates only that one or more is true.

exclusive disjunction
exclusive disjunction

(logic, computing) An exclusive disjunction; the result of applying the above-described exclusive or to two or more predicates; contrasted with an inclusive or, which is the result of applying an inclusive or.


connective

For connexive, borrowed from Latin connexīvus. Displacement of x by ct in Latin loanwords is very common. Compare connect, connectivum, connection.

Condition iii) ensures that the truth-rules for the sentential connectives and quantifiers are satisfied within one and the same valuation νₛ.

2008 October 8, Holger Andreas, “Another Solution to the Problem of Theoretical Terms”, in Erkenntnis, volume 69, number 3, →DOI:

(logic) A function that operates on truth values to give another truth value.


axiom

Oxford University Museum of Natural History

From Middle French axiome in the 15th century, from Latin axiōma (“axiom; principle”), from Ancient Greek ἀξίωμα (axíōma, “that which is thought to fit, a requisite, that which a pupil is required to know beforehand, a self-evident principle”), from ἀξιόω (axióō, “to think fit or worthy, to require, to demand”), from ἄξιος (áxios, “fit, worthy”, literally “weighing as much as; of like value”), from ἄγω (ágō, “to weigh (down)”).

der

[…] Geometry, an excellent Logic, as you obſerve, where the definitions are clear, where the Poſtulata cannot be refuſed, nor the Axioms denied; […]

1734 April 10, “Philalethes Cantabrigiensis” [pseudonym; James Jurin], Geometry No Friend to Infidelity: Or, A Defence of Sir Isaac Newton and the British Mathematicians, in a Letter to the Author of The Analyst, London: Printed for T. Cooper at the Globe in Ivy-Lane, →OCLC, page 28:

The axioms read as follows. For every composable pair f and g the composite f#92;circg goes from the domain of g to the codomain of f. For each object A the identity arrow 1#95;A goes from A to A. Composing any arrow with an identity arrow (supposing that the two are composable) gives the original arrow. And composition is associative.

1992, Colin McLarty, “Rudimentary Structures in a Category”, in Elementary Categories, Elementary Toposes (Oxford Logic Guides; 21), Oxford: Clarendon Press; New York, N.Y.: Oxford University Press, →ISBN, page 13:

(logic, mathematics, proof theory) A fundamental assumption that serves as a basis for deduction of theorems; a postulate (sometimes distinguished from postulates as being universally applicable, whereas postulates are particular to a certain science or context).


logika

logika (nominative singular)
logiki (genitive singular)
logice (dative singular)
logikę (accusative singular)
logiką (instrumental singular)
logice (locative singular)
logiko (singular vocative)

Learned borrowing from Latin logica, from Ancient Greek λογική (logikḗ). Displaced Old Polish wielemowna.


proof

en-noun

proof (countable and uncountable, plural proofs)

→ Russian: пруф (pruf), пру́фы (prúfy)

desc

⇒ Russian: пруфли́нк (pruflínk, literally “proof + link”)

From Middle English proof, from Old French prove, from Late Latin proba (“a proof”), from Latin probō (“to prove”); see prove; compare also the doublet probe.

the proof of the pudding is in the eating

(countable, logic, mathematics) A sequence of statements consisting of axioms, assumptions, statements already demonstrated in another proof, and statements that logically follow from previous statements in the sequence, and which concludes with a statement that is the object of the proof.


denial

en-noun

denial (countable and uncountable, plural denials)

The denial of "There might be X" is the null, "False, there is no X."


contradiction

contradiction (countable and uncountable, plural contradictions)

tautology

antonym(s) of “proposition that is false for all values of its variables”

/ˌkɒntɹəˈdɪkʃən/

/ˌkɑːntɹəˈdɪkʃən/

From Middle English contradiccioun, contradiction, from Old French contradiction, from Latin contrādictiō, from contrādīcō (“speak against”).

(logic, countable) A proposition that is false for all values of its propositional variables or Boolean atoms.


material

en-adj

material (comparative more material, superlative most material)

more material (comparative)
most material (superlative)

From Middle English material, from Late Latin māteriālis, from Latin māteria (“wood, material, substance”), from māter (“mother”). Displaced native Middle English andweorc, andwork (“material, matter”) (from Old English andweorc (“matter, substance, material”)). Doublet of materiel.

ncog

material cause

the material aspect of being

(logic) Of or relating to the matter of reasoning, as distinguished from the form of it, especially empirical.


structure

en-noun

structure (countable and uncountable, plural structures)

/ˈstɹʌkt͡ʃɚ/

[ˈstʃɹɐktʃə]

From Middle French structure, from Latin structūra (“a fitting together, adjustment, building, erection, a building, edifice, structure”), from struere, past participle structus (“pile up, arrange, assemble, build”). Compare construct, instruct, destroy, etc.

der

(logic) A set along with a collection of finitary functions and relations.


limit

German: Limit

From Middle English limit, from Old French limit, from Latin līmes (“a cross-path or balk between fields, hence a boundary, boundary line or wall, any path or road, border, limit”). Displaced native Old English ġemǣre. Doublet of limes.

(logic, metaphysics) A determining feature; a distinguishing characteristic.


model

desc

→ Cantonese: 模特兒 /模特儿 (mou⁴ dak⁶ ji⁴), 摩度

→ Cebuano: model

→ German: Model

→ Japanese: モデル

→ Korean: 모델 (model)

→ Mandarin: 模特兒 /模特儿, 麻豆 (neologism)

→ Swahili: modeli

→ Welsh: model

From Middle French modelle, from Old Italian modello, from Vulgar Latin *modellus, diminutive form of modulus (“measure, standard”), diminutive of modus (“measure”); see mode, and compare module, modulus, mould, mold.

عارض أزياء

ʕāriḍ ʔazyāʔ

(logic) An interpretation function which assigns a truth value to each atomic proposition.

(logic) An interpretation which makes a set of sentences true, in which case that interpretation is called a model of that set.


convert

en-verb

convert (third-person singular simple present converts, present participle converting, simple past and past participle converted)

converts (present singular third-person)
converting (participle present)
converted (participle past)
converted (past)

[kʰə̥ɱˈvɜːt]

From Old French convertir, from Latin converto (“turn around”).

(transitive, logic) To change (one proposition) into another, so that what was the subject of the first becomes the predicate of the second.


contrary

/kənˈtɹɛəɹi/

From Middle English contrarie, compare French contraire, from Old French contraire, from Latin contrārius (“opposite, opposed, contrary”), from contrā (“against”).

der

If two universals differ in quality, they are contraries; as, every vine is a tree; no vine is a tree. These can never be both true together; but they may be both false.

1725, Isaac Watts, Logick: Or, The Right Use of Reason in the Enquiry after Truth, […], 2nd edition, London: […] John Clark and Richard Hett, […], Emanuel Matthews, […], and Richard Ford, […], published 1726, →OCLC:

(logic) One of a pair of propositions that cannot both be simultaneously true, though they may both be false.


satisfy

en-verb

satisfy (third-person singular simple present satisfies, present participle satisfying, simple past and past participle satisfied)

satisfies (present singular third-person)
satisfying (participle present)
satisfied (participle past)
satisfied (past)

From Middle English satisfyen, satisfien, from Old French satisfiier, satisfier (also Old French satisfaire), from Latin satisfacere, from satis (“enough, sufficient”) + faciō (“I make, I do”).

The complex numbers satisfy #92;existsx#58;x²#43;1#61;0.

(mathematics, logic, transitive) To cause (a sentence) to be true when the sentence is interpreted in one's universe.


dyadic

en-adj

dyadic (comparative more dyadic, superlative most dyadic)

more dyadic (comparative)
most dyadic (superlative)
diadic (alternative)

From dyad + -ic. The mathematics sense was coined by American scientist Josiah Willard Gibbs in 1884 in the second half of his book Elements of Vector Analysis.

coin

Up to now, all the expressions we have called predicates have stood for properties which it makes sense to attribute to a single individual. Such predicates are known as monadic, or one-place, predicates. There are, however, many expressions which we cannot meaningfully apply to single objects, but only to groups of two, three or more objects. We cannot e.g. sensibly say 'x is greater than', but only 'x is greater than y'. Nor can we say 'x is between', or even 'x is between y', but only 'x is between y and z'. We shall say that an expression such as 'greater than' or 'between' stands not for a property of an individual, but for a relation between individuals. Since 'greater than' stands for a relation between two individuals, we shall say that the relation in question is a dyadic or a two-place relation. Similarly, 'between' stands for a triadic or three-place relation; and we can also have four-place, five-place, etc., relations. . . . A dyadic relation holds not simply between a pair of objects, but between those objects in a certain order. It is one thing to say that Bill is father of Tom, and another thing to say that Tom is father of Bill. . . . There are, it is true, certain dyadic relations whose direction is unimportant, in the sense that whenever they hold between x and y, they also hold between y and x; 'parallel to' and 'cousin of' are examples.

1965 G. E. Hughes and D. G. Londey: The Elements of Formal Logic p.270

Pertaining to a dyad, the number two; of two parts or elements.

(mathematics, logic) having an arity of two (taking two arguments or operands)


joss

Calque of English iff, jos with the final consonant doubled


schema

Unadapted borrowing from Latin schēma, from Ancient Greek σχῆμα (skhêma, “form, shape”). Doublet of scheme.

der

(logic) A formula in the metalanguage of an axiomatic system, in which one or more schematic variables appear, which stand for any term or subformula of the system, which may or may not be required to satisfy certain conditions.


antinomy

en-noun

antinomy (countable and uncountable, plural antinomies)

LL-Q1860 (eng)-I learned some phrases-antinomy.wav

Learned borrowing from Latin antinomia + English -y (suffix forming abstract nouns denoting a condition, quality, or state); antinomia is derived from Ancient Greek ἀντινομία (antinomía), from ἀντι- (anti-, prefix meaning ‘against’) (ultimately from Proto-Indo-European *h₂ent- (“face; forehead; front”)) + νόμος (nómos, “custom, usage; law, ordinance”) + -ῐ́ᾱ (-ĭ́ā, suffix forming feminine abstract nouns), with νόμος (nómos) derived from νέμω (némō, “to deal out, dispense, distribute”) (from Proto-Indo-European *nem- (“to distribute; to give; to take”)) + -ος (-os, suffix forming nouns indicating actions or their results). The English word may be analysed as anti- (prefix meaning ‘against; opposite of’) + -nomy (suffix indicating a system of laws, rules, or knowledge about a body of a particular field).

confix

This introduces the antinomy that has followed us through the whole study. The solution of this antinomy is found in making the Not-me, which interrupts self-consciousness, really reflect self-consciousness, by manifesting the nature of the I—in other words, by making it conform to the ideal of the soul.

1884, Charles Carroll Everett, Fichte’s Science of Knowledge: A Critical Exposition, page 12:

Of the work that has been done on the liar antinomy, possibly the most profound and certainly the most influential has been that of Tarski

1991, Vann McGee, Truth, Vagueness, & Paradox: An Essay on the Logic of Truth, page 67:

(by extension) Any contradiction or paradox.

(specifically, epistemology, logic) In the thought of the German philosopher Immanuel Kant (1724–1804): an apparent contradiction between valid conclusions; a paradox.

التضاد

(epistemology, logic) apparent contradiction between valid conclusions


valid

en-adj

valid (comparative more valid, superlative most valid)

more valid (comparative)
most valid (superlative)

Borrowed from Middle French valide (“healthy, sound, in good order”), from Latin validus, from valeō (“I am strong, I am healthy, I am worth”) + -idus, from Proto-Indo-European *h₂welh₁- (“be strong”).

der

(logic) Of a formula or system: such that it evaluates to true regardless of the input values.

An argument is valid if and only if the set consisting of both (1) all of its premises and (2) the contradictory of its conclusion is inconsistent.

(logic) Of an argument: whose conclusion is always true whenever its premises are true.

sound

in logic: argument whose conclusion is always true whenever its premises are all true


assumption

en-noun

assumption (countable and uncountable, plural assumptions)

From Middle English assumpcioun, from Medieval Latin assumptio (“a taking up (into heaven)”) and Latin assumptio (“a taking up, adoption, the minor proposition of a syllogism”). Doublet of assumptio; see assume.

der

categorical syllogism
categorical syllogism

(logic) The minor or second proposition in a categorical syllogism.

asumpción

the minor or second proposition in a categorical syllogism


dichotomy

en-noun

dichotomy (countable and uncountable, plural dichotomies)

Audio (GA)

Audio (AU)

From Ancient Greek διχοτομία (dikhotomía, “dichotomy”).

der

But in the fallacy of false dichotomy, not only do the two alternatives fail to be jointly exhaustive, but they are not even likely. As a result, the disjunctive premise is false, or at least probably false.

2011, Patrick J. Hurley, A Concise Introduction to Logic, page 162:

2011, Tomasz A. Gorarzd, Jacek Krzaczkowski, The Complexity of Problems Connected with Two-Element Algebras, Paweł M. Idziak, Andrzej Wronski, Reports on Mathematical Logic: No. 46, page 92,
One can ask if for any algebra the considered problem is always in P or NP-complete (P or coNP-complete)? For example, the problem of the satisfiability of a system of polynomial equations over a group G is in P if G is abelian and NP-complete otherwise ([7, 13]).
One of the most widely known subclasses of NP which exhibits such a dichotomy, is the class of constraint satisfaction problems (CSP) on the set {0,1}, see [16]. Recently Bulatov proved the dichotomy for CSP on a three-element set [3].

(logic) The division of a class into two disjoint subclasses that are together comprehensive, as the division of human into female and male.

dikotomi

logic: division of a class into two disjoint subclasses that are together comprehensive


elimination

en-noun

elimination (countable and uncountable, plural eliminations)

(logic) The act of obtaining by separation, or as the result of eliminating; deduction.


equivocation

equivocation (countable and uncountable, plural equivocations)

equivocations (plural)
æquivocation (alternative)

/ɪˌkwɪvəˈkeɪʃən/

/ɪˌkwɪvəˈkeɪʃn̩/

c. 1380, from Middle English equivocacion, from Old French equivocation, from Medieval Latin aequivocātiō, from aequivocō, from Late Latin aequivocus (“ambiguous, equivocal”), from Latin aequus (“equal”) + vocō (“call”); a calque of Ancient Greek ὁμωνυμία (homōnumía).

der

(logic) A logical fallacy resulting from the use of multiple meanings of a single expression.


exportation

en-noun

exportation (countable and uncountable, plural exportations)

(logic) Either the logical law ((P∧Q)→R)⇒(P→(Q→R)), or the rule of replacement ((P∧Q)→R)⇔(P→(Q→R)).


extension

extension (countable and uncountable, plural extensions)

From Middle English extensioun, from Old French estension, from Latin extensiō, extensiōnem.

(logic) The set of tuples of values that, used as arguments, satisfy the predicate.


fallacy

From Middle English fallaci, fallace, fallas, from Old French fallace, from Latin fallācia (“deception, deceit”), from fallāx (“deceptive, deceitful”), from fallere (“to deceive”).

Baldridge also showed the "one molecule of blood," usually held to be the stimulus for attracting sharks, to be another common fallacy, since a molecule of blood does not exist.

1983, Richard Ellis, The Book of Sharks, Knopf, →ISBN, page 163:

(logic) An argument, or apparent argument, which professes to be decisive of the matter at issue, while in reality it is not; a specious argument.


corollary

/ˈkɔɹəˌlɛɹi/

/kɔˈɹoʊˌlɛɹi/

From Middle English, from Late Latin corōllārium (“money paid for a garland; gift, gratuity, corollary; consequence, deduction”), from corōlla (“small garland”), diminutive of corōna (“crown”).

der

We have proven that this set is finite and well ordered; as a corollary, we now know that there is an order-preserving map from it to the natural numbers.

(mathematics, logic) A proposition which follows easily from the statement or proof of another proposition.


implication

en-noun

implication (countable and uncountable, plural implications)

From Middle French implication, from Latin implicationem (accusative of implicatio).Equivalent to implicate + -ion.

propositional calculus
propositional calculus

(countable, logic) The connective in propositional calculus that, when joining two predicates A and B in that order, has the meaning "if A is true, then B is true".


importation

importation (countable and uncountable, plural importations)

(logic) The logical law (P→(Q→R))⇒((P∧Q)→R).


interpretation

interpretation (countable and uncountable, plural interpretations)

/ɪnˌtɜːpɹəˈteɪʃən/

/ɪnˌtɝpɹəˈteɪʃən/

/ɪnˌtɜːpɹəˈtæɪʃən/

From Middle English [Term?], from Anglo-Norman [Term?], from Old French [Term?], from Latin interpretātiō, noun of action from interpretor (“to explain, expound, interpret, understand, conclude, infer, comprehend”)
Morphologically interpret + -ation

(countable, logic, model theory) An assignment of a truth value to each propositional symbol of a propositional calculus.


premise

premises (plural)
premiss (alternative)
præmise (alternative archaic)
præmiss (alternative archaic)

From Middle English premise, premisse, from Old French premisse, from Medieval Latin premissa (“set before”) (premissa propositio (“the proposition set before”)), feminine past participle of Latin praemittere (“to send or put before”), from prae- (“before”) + mittere (“to send”).
The sense "a piece of real estate" arose from the misinterpretation of the word by property owners while reading title deeds where the word was used with the legal sense.

der

While the premises stand firm, 'tis impossible to shake the conclusion.

1667, attributed to Richard Allestree, The Causes of the Decay of Christian Piety. […], London: […] R. Norton for T. Garthwait, […], →OCLC:

(logic) Any of the first propositions of a syllogism, from which the conclusion is deduced.

مُقَدِّمَة

either of the first two propositions of a syllogism, from which the conclusion is deduced


tacit

en-adj

tacit (comparative more tacit, superlative most tacit)

more tacit (comparative)
most tacit (superlative)

Borrowed from late Middle French tacite, or from Latin tacitus (“that is passed over in silence, done without words, assumed as a matter of course, silent”), from tacere (“to be silent”).

bor

(logic) Not derived from formal principles of reasoning; based on induction rather than deduction.

подразби́ращ се

not derived from formal principles of reasoning


formal

Learned borrowing from Latin fōrmālis. By surface analysis, forma + -al.

(logic) formal (involving mere manipulations of symbols)


(logic) Intensional disjunction, as in some relevant logics.


negative

en-adj

negative (comparative more negative, superlative most negative)

more negative (comparative)
most negative (superlative)
-ve (alternative abbreviation)
−ve (alternative abbreviation)

From Middle English negative, negatif, from Old French negatif, from Latin negātīvus (“that denies, negative”), from negāre (“to deny”); see negate.

der

(linguistics, logic) Denying a proposition; negating a concept.


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