Gödel's incompleteness theorem

en-proper noun

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

Gödel's incompleteness theorems (plural)

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


theorem

/ˈθiː.ə.ɹəm/

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

der

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

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


vicious circle

vicious circles (plural)
vicious cycle (alternative)

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

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


apodosis

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

lbor

Coordinate term: protasis

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

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

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

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

جَوَابُ الشَّرْط

the consequential clause in a conditional sentence


unconditional

unconditionals (plural)
inconditional (alternative obsolete)

/ˌʌnkənˈdɪʃənəl/

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


inconsistency

en-noun

inconsistency (countable and uncountable, plural inconsistencies)

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


inconsistent

en-adj

inconsistent (comparative more inconsistent, superlative most inconsistent)

more inconsistent (comparative)
most inconsistent (superlative)

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

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


transduction

en-noun

transduction (countable and uncountable, plural transductions)

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

artificial intelligence
artificial intelligence

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


transduction

Instead of applying a transduction method only once, we can apply different transduction methods to an initial network in sequence. In each sequence, different or identical transduction methods can be applied in different orders. This usually leads to many different final networks.

2003, Wai-Kai Chen, Logic Design, →ISBN:

(logic design) The improvement of an electronic logic network by reduction of redundant components in an initial version, using an established pruning procedure, then applying permissible functions for transformation of the network into a workable form. Thereafter the transformation and reduction may be repeated till no worthwhile further improvement results.


convertible

en-adj

convertible (comparative more convertible, superlative most convertible)

more convertible (comparative)
most convertible (superlative)

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

der

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


induce

en-verb

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

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

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

der

(transitive, logic) To infer by induction.


stronger

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

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


deduction

en-noun

deduction (countable and uncountable, plural deductions)

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

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

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

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

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

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

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

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


cherry-pick

en-verb

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

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

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

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

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

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

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

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

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

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

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

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

de krenten uit de pap halen

to select only the best from a range of options


conclude

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

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

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

der

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


indirect

en-adj

indirect (comparative more indirect, superlative most indirect)

more indirect (comparative)
most indirect (superlative)

/ˌɪndɪˈɹɛkt/

/ˌɪndəˈɹɛkt/

From Middle French indirect, from Late Latin indirectus.

law of the excluded middle
law of the excluded middle

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


equivalence

en-noun

equivalence (countable and uncountable, plural equivalences)

equivalences (plural)
æquivalence (alternative obsolete)

From French équivalence, from Medieval Latin aequivalentia.

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


truth table

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

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


protasis

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

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

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

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


barbara

/ˈbɑɹb(ə)ɹə/

/ˈbɑːb(ə)ɹə/

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

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


induction

induction (countable and uncountable, plural inductions)

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

Meronym: abstraction

(logic) Derivation of general principles from specific instances.

en:reasoning from specific instances to general principles

ինդուկցիա

the derivation of general principles from specific instances


alethiology

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

der

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


disjunction

en-noun

disjunction (countable and uncountable, plural disjunctions)

From Old French disjunction, from Latin disjunctio.

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

disjunkce

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


predicate calculus

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


literal

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

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

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

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


truth value

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


AND

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

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


AND

en-verb

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

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

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

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

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


negation

en-noun

negation (countable and uncountable, plural negations)

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

der

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

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

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

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

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

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


modus ponens

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

1. If P, then Q.

2. P.

3. Therefore, Q.

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

肯定前件

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


petitio principii

/pɪˈtɪʃiˌəʊ prɪnˈkɪpiˌaɪ/

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

uder

τὸ ἐν ἀρχῇ αἰτεῖσθαι

begging the question
begging the question

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

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

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

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

1938, E. Prokosch, A Comparative Germanic Grammar:

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


weaker

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

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


quantify

en-verb

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

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

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

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

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


beg the question

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

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

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

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

uder

τὸ ἐν ἀρχῇ αἰτεῖσθαι

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

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

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

olettaa johtopäätös todeksi

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


conjunct

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

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

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


simplification

en-noun

simplification (countable and uncountable, plural simplifications)


modality

modality (countable and uncountable, plural modalities)

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


subsumption

subsumption (countable and uncountable, plural subsumptions)

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


modal

en-adj

modal (comparative more modal, superlative most modal)

more modal (comparative)
most modal (superlative)

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

der

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

modaal

logic: of or relating to the modality between prepositions


transitivity

en-noun

transitivity (countable and uncountable, plural transitivities)

From French transitivité.
Morphologically transitive + -ity

The hypothetical syllogism inference rule states the transitivity of implication.

(mathematics, logic) The property of being transitive.


salvage

en-verb

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

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

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

der

Prove or disprove, and salvage if possible.

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


subaltern

en-adj

subaltern (comparative more subaltern, superlative most subaltern)

more subaltern (comparative)
most subaltern (superlative)

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

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

alisteinen

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


subaltern

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


Entscheidungsproblem

Unadapted borrowing from German Entscheidungsproblem.

ubor

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

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

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

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


contradictory

Borrowed from Late Latin contradictorius, from Latin contradico.

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

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

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

نَقِيض

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


DM

en-noun

DM (countable and uncountable, plural DMs)

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

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


sublate

en-verb

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

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

From Latin sublatum, past participle of suffero.

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


contingency

en-noun

contingency (countable and uncountable, plural contingencies)

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

kontingenssi

a statement which is neither a tautology nor a contradiction


consequent

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

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

takajäsen

the second half of a hypothetical proposition


turnstile

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


DS

DS (countable and uncountable, plural DSs or DSes)

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

(logic) Initialism of disjunctive syllogism.


analytic

en-adj

analytic (comparative more analytic, superlative most analytic)

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

/ˌænəˈlɪtɪk/

From Ancient Greek ἀναλυτικός (analutikós).

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


inductive

inductive (comparative more inductive, superlative most inductive)

more inductive (comparative)
most inductive (superlative)

From Middle French inductif, from Late Latin inductivus.

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


dirimens copulatio

From Latin dirimēns cōpulātiō (“separating connection”).

bor

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


Polish notation

After the nationality of the logician Jan Łukasiewicz

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

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

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


XOR

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

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


quantifier

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

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

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

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

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

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

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

universal quantifier
universal quantifier

existential quantifier
existential quantifier

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


NAND

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

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


enthymeme

/ˈɛnθɪˌmiːm/

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

uder

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

enthymeem

syllogism with required but unstated assumption


remotion

en-noun

remotion (countable and uncountable, plural remotions)

From Old French or directly from Latin remōtiō.

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

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

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

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

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

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

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

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

(especially logic, largely obsolete) Removal.


defeater

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


free variable

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


rewriting

rewriting (countable and uncountable, plural rewritings)

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

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


distributive

en-adj

distributive (comparative more distributive, superlative most distributive)

more distributive (comparative)
most distributive (superlative)

(logic) Assigning the species of a general term.


consilience

en-noun

consilience (countable and uncountable, plural consiliences)

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

coin

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

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

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

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

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


monadic

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

uder

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

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


desitive

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


sorites

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

der

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

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

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


intension

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

uder

Holonym: comprehension

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

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

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

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


bandwagon fallacy

en-noun

bandwagon fallacy (plural bandwagon fallacies)

argumentum ad populum
argumentum ad populum


argumentum

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Learned borrowing from Latin argūmentum. Doublet of argument.

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

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

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

argumentum ab auctoritate est fortissimum in lege

argumentum ab auctoritate plurimum valet in lege

argumentum ab impossibili plurimum valet in lege

argumentum ab inconvenienti est validum in lege

quia lex non permittit aliquod inconveniens


superordinate

en-adj

superordinate (comparative more superordinate, superlative most superordinate)

more superordinate (comparative)
most superordinate (superlative)

subordinate

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

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


NOT function

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


propositional function

en-noun

propositional function (plural propositional functions)

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


truth function

truth functions (plural)
truth-function (alternative)

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


coextensive

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

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

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


quantification

quantification (countable and uncountable, plural quantifications)

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

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


vacuously

en-adv

vacuously (comparative more vacuously, superlative most vacuously)

more vacuously (comparative)
most vacuously (superlative)

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

(logic) Because of being a vacuous truth.


soundness

en-noun

soundness (countable and uncountable, plural soundnesses)

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

cog

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

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


postulation

en-noun

postulation (countable and uncountable, plural postulations)

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


first-order

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


second-order

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


Boolean algebra

Boolean algebra (plural Boolean algebras)

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

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


Boolean function

Boolean function (plural Boolean functions)

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

fonction booléenne

function based on AND, OR and NOT operations


Boolean variable

Boolean variable (plural Boolean variables)

(mathematics, logic, computing) Any variable, from the domain of Boolean algebra, having one of only two values

totuusarvomuuttuja

variable from the domain of Boolean algebra


Boolean logic

Boolean logic (usually uncountable, plural Boolean logics)

Boolean logic can be shown to be "embedded" in integer arithmetic (modulo 2) by assigning polynomials to logical connectives, like so: operatorname NOT(x)=1-x,  operatorname AND(x,y)=xy,  operatorname OR(x,y)=x+y-xy.

(computing, logic, mathematics) A system of symbolic logic that is the basis of Boolean algebra


two-sided

(logic, of a modality) That is necessarily or absolutely different than the respective coordinate alethic or temporal modality as well as its opposite.


individualism

individualism (countable and uncountable, plural individualisms)

collectivism

antonym(s) of “acting without reference to others”

Borrowed from French individualisme. By surface analysis, individual + -ism.

(logic) The doctrine that only individual things are real.


equipollence

equipollence (countable and uncountable, plural equipollences)

equipollences (plural)
equipollency (alternative)

(logic) Sameness of signification of two or more propositions which differ in language.

equipol·lència

sameness of signification of two or more propositions


equipollent

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

From French équipollent, from Latin aequipollēns.

(logic, of each of two statements) able to be deduced from the other


predication

predication (countable and uncountable, plural predications)

predications (plural)
prædication (alternative archaic)

From Middle English predicacion, from Anglo-Norman predicaciun, from Latin praedicātiō, from praedicō.

(logic) The act of making something the subject or predicate of a proposition.

Prädikation

The action of making a term or expression the predicate of a statement


prenex

Borrowed from Late Latin praenexus (“bound up in front”), from Latin prae- (“before”) and nexus, past participle of nectō (“to bind”).

bor+

We say that ϕ is universal iff it can be written in prenex form — i.e. with all quantifiers at the beginning — using only universal quantifiers.

1999, Neil Immerman, Descriptive Complexity, New York: Springer-Verlag, page 12

(mathematics, logic) Of a formula, having all of its quantifiers at the beginning.


prenex

∀x.∃y. is the prenex of the formula ∀x.∃y.P(x,y)

(mathematics, logic) The initial part of a prenex formula where all of the formula's bound variables are bound by logical quantifiers.


predicament

predicaments (plural)
prædicament (alternative obsolete)

From Middle English predicament, from Old French predicament, from Late Latin praedicāmentum (“that which is predicated, a predicament, category”).

der

(logic) That which is predicated; a category.


abjunction

en-noun

abjunction (countable and uncountable, plural abjunctions)

/æbˈd͡ʒʌŋk.ʃən/

From ab- (“away”) + junction (“to join”).

material nonimplication
material nonimplication#English

(logic) Synonym of material nonimplication


predicable

(logic) One of the five most general relations of attributes involved in logical arrangements, namely, genus, species, difference, property, and accident.


categorical

/ˌkætəˈɡɔɹɪk(ə)l/

/ˌkætəˈɡɒɹɪk(ə)l/

/ˌkæʔəˈɡaɹɪk(ə)l/

From Late Latin catēgoricus + -al. By surface analysis, category + -ical.

categorical proposition
categorical proposition


deductive

en-adj

deductive (comparative more deductive, superlative most deductive)

more deductive (comparative)
most deductive (superlative)

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

արտածական

of, pertaining to, or based on deduction

(logic) Based on inferences from general principles.


recursion theory

(logic) A branch of mathematical logic studying computable functions and Turing degrees, concerned with questions such as "What does it mean for a function on the natural numbers to be computable?" and "Can noncomputable functions be classified into a hierarchy based on their level of noncomputability?".


proof by exhaustion

en-noun

proof by exhaustion (plural proofs by exhaustion)

(logic) The indirect verification or falsification of a statement by the verification or falsification of each of the finite number of cases which arise therefrom.


two wrongs make a right

(logic, ethics) A logical informal fallacy whereby a wrongful action is justified by the commission of another.


intuitionistic

Intuitionistic type theory is based on a certain analogy or isomorphism between propositions and types: a proposition is identified with the type of its proofs. This identification is usually called the Curry–Howard isomorphism, which was originally formulated for intuitionistic logic and simply typed lambda calculus. Type Theory extends this identification to predicate logic by introducing dependent types, that is types which contain values. Type Theory internalizes the interpretation of intuitionistic logic proposed by Brouwer, Heyting and Kolmogorov, the so called BHK interpretation. The types of Type Theory play a similar role to sets in set theory but functions definable in Type Theory are always computable.ᵂᴾ

The system, which has come to be known as IZF, or Intuitionistic Zermelo–Fraenkel (ZF refers to ZFC without the axiom of choice), has the usual axioms of extensionality, pairing, union, infinity, separation and power set. The axiom of regularity is stated in the form of an axiom schema of set induction. Also, while Myhill used the axiom schema of replacement in his system, IZF usually stands for the version with collection.ᵂᴾ

proof by contradiction
proof by contradiction

(mathematics, logic) Dealing strictly in constructive proofs, abstaining from proof by contradiction


suppositum

From the past participle of Latin supponere (“to suppose”).

The answer may be that these relation-ships are generated in every possible world, given any suppositum of a certain least complexity.

1977, David Joel, Weissman - Eternal Possibilities: A Neutral Ground for Meaning and Existence:

(logic) Something supposed to be true; an assumption


coinduction

coinduction (countable and uncountable, plural coinductions)

(logic) A form of induction that allows some form of reasoning concerning sets that are not well founded; uses a form of relation called a bisimulation


bisimulation

equivalence relation
equivalence relation

state transition system
state transition system

(logic) an equivalence relation between state transition systems, associating systems which behave in the same way in the sense that one system simulates the other and vice-versa


maximal

(logic) Said of a set of well-formed formulas: that it is as large as it can be without being inconsistent; i.e. that for any well-formed formula φ, the set contains either φ or ~φ.


symbolic logic

symbolic logic (usually uncountable, plural symbolic logics)

(logic) A formal system of deductive logic in which aspects and relationships of natural language are represented by a system of symbols.


sequent

1550s; borrowed from Middle French sequent, from Old French sequent, itself borrowed from Latin sequentem, present participle of sequī (“to follow”).

A sequent a,b⊢c,d could be interpreted to correspond to an Existential Graph, whose expression in Existential Graph Interchange Format would be
~[(a) (b) ~[(c)] ~[(d)]], which in ordinary language could be expressed as "a and b give c or d".

(logic) A disjunctive set of logical formulae which is partitioned into two subsets; the first subset, called the antecedent, consists of formulae which are valuated as false, and the second subset, called the succedent, consists of formulae which are valuated as true. (The set is written without set brackets and the separation between the two subsets is denoted by a turnstile symbol, which may be read "give(s)".)


defeasible

en-adj

defeasible (comparative more defeasible, superlative most defeasible)

more defeasible (comparative)
most defeasible (superlative)

Back-formation from defeasance + -ible, from Anglo-Norman defesaunce, Old French desfaisance, a deverbal noun from desfaire (“to undo”) (Modern French défaire), from des- (“un-, apart”) + fere, faire (“to do”) + -able, reflecting Latin dis- + facere + -ābilis. Near-doublet of defeatable.

The accounting charge for the non-callable debt is defeasible by an escrow.

(law, logic) Capable of being defeated, terminated, annulled, voided or invalidated.

breekbaar

capable of being defeated, invalidated, …


factored

A radical in final factored form is written last, proceeded by the other factors listed with numbers before letters (variables); and variables are usually listed in alphabetical order.

1998, Walter W. Leffin, George L. Henderson, Mary Van Beck Voelker, Introduction to Technical Mathematics:

An alternative representation (to sum-of-product form) of a logic function which is closer to the physical implementation of the logic is the factored form.

2005, Gary D. Hachtel, Fabio Somenzi, Logic Synthesis and Verification Algorithms, page 417:

It follows from this definition that in factored expressions, complements are permitted only for the literals.

2018, Vlad P. Shmerko, Svetlana N. Yanushkevich, Sergey Edward Lyshevski, Computer Arithmetics for Nanoelectronics, page 333:

(mathematics, logic) Expressed in terms of factors (values that are multiplied together to form a whole)


reductio ad absurdum

en-noun

reductio ad absurdum (usually uncountable, plural reductio ad absurdums)

Unadapted borrowing from Latin reductiō ad absurdum.

ubor

“You, gentlemen, as representatives of that institution which recognizes only truths that are deduced from reductio ad absurdums will probably have no difficulty in perceiving the truth of this absurdity and hence be ready to excuse the outcome of it—my absence.”

1894, Flora Helm, “Concerns a Talk in Which Anarchy and Love Are Blended”, in Between Two Forces: A Record of a Theory and a Passion, Boston, Mass.: Arena Publishing Company. […], pages 149–150:

Constructing representations out of atoms that are already themselves representations cannot address the origins of the atoms per se. Careful pursuit of such approaches has yielded bizarre reductio ad absurdums such as the implication that virtually all concepts that human beings are capable of having are already in the genes.

1998, Mark H. Bickhard, “Constructivisms and Relativisms: A Shopper’s Guide”, in Michael R[obert] Matthews, editor, Constructivism in Science Education: A Philosophical Examination, Dordrecht, Boston, Mass., London: Kluwer Academic Publishers, →ISBN, page 106:

One way to argue against a position is to demonstrate that it proves too much. Proponents of an HWR analysis of negligence may insist that the conceptual and normative arguments that have been directed against their project ultimately generate reductio ad absurdums suggesting that I have proved too much.

2009, Michael S. Moore, “Normative Problems in Applying the Harm-within-the-Risk Test to Crimes/Torts of Negligence”, in Causation and Responsibility: An Essay in Law, Morals, and Metaphysics, Oxford University Press, published 2010, →ISBN, section III (The First Blind Alley: The Attempt to Replace Proximate Causation with Culpability as a Prerequisite for Legal Liability), page 208:

(mathematics, logic) The method of disproving a statement by assuming the statement is true and, with that assumption, arriving at a blatant contradiction.


zero-knowledge

(logic) Describing situations in which the veracity of a statement may be shown to be true without revealing any other information.


dormitive principle

en-noun

dormitive principle (plural dormitive principles)

A modern translation of Latin, virtus dormitiva, coined by Molière in The Imaginary Invalid (1673). In the play, he lampoons a group of physicians providing an explanation in macaronic Latin of the sleep-inducing properties of opium as stemming from its "virtus dormitiva". The currency of this phrase as a critique of scientific claims is due to Gregory Bateson (1976, Steps to an Ecology of Mind p. 5), as is the translation of virtus as 'principle'.

We note Bateson's (1968) dormitive principle at work in which behaviors are described as traits such as LD, which then are used to explain the behavior.

1988, Doreen Kronick, New Approaches to Learning Disabilities: Cognitive, Metacognitive, and Holistic:

For Arrow, many socioeconomic phenomena are explained in terms of the "dormitive principle", which, he says, simply repeats the phenomenon being explained.

2000, “Rational Choice and Rationallity”, in The Paradox of Social Order: Linking Psychology and Sociology, page 14:

If we examine traditional explanations of behavior through the lens of recursion, we will sometimes find what Bateson called "dormitive principles," a form of circular description. A "dormitive principle" is a more abstract repackaging of a description of the item you claim to be explaining. To paraphrase Bateson, this occurs when the cause of a simple action, as for example, when aggression is explained as being caused by an "aggressive instinct" or psychotic symptomatology is attributed to "madness."

2002, Bradford Keeney, Aesthetics of Change, The Guilford Press,, →ISBN, page 33:

And to any intelligent reader, explanation of an 'inherent ability' was reminiscent of Molière's mock explanation of the soporific effects of opium - that it contained a 'dormitive principle'.

2003, Ian Glynn, An Anatomy of Thought: The Origin and Machinery of the Mind:

Similarly, to view “leadership" as something that resides in a person is to generate a dormitive principle. This would inspire such pseudoexplanations as “He leads because he possesses leadership qualities.”

2017, Bradford P. Keeney, Aesthetics of Change, page 38:

Prevent disability from becoming a dormitive principle that can, per se, justify any conduct or event in the interaction of the disabled person

2018, Roberto Pereira, Juan Luis Linares, Clinical Interventions in Systemic Couple and Family Therapy, page 215:

To say that "he only uses drugs because he is the black sheep” is to mix up these logical types, also called invoking the dormitive principle.

2018, Michael D. Reiter, Systems Theories for Psychotherapists: From Theory to Practice:

(idiomatic, rhetoric, logic, linguistics) A type of tautology in which an item is explained in terms of the item itself, only put in different (usually more abstract) words.


circular argument

circular argument (plural circular arguments)

circular arguments (plural)
circular logic (alternative)

A logically circular argument’s conclusion is included as one of its premises.

2004 Nov, M Bergmann, “Epistemic Circularity: Malignant and Benign.”, in Philosophy and Phenomenological Research, volume 69, number 3, p. 710 n3:

(philosophy, logic) An argument which commits the logical fallacy of assuming what it is attempting to prove.


significate

Latin significatus, past participle of significare.

“Britain is an island;” “all tyrants are miserable; ” “no miser is rich; ” are universal propositions, and their subjects are therefore said to be distrubted. being understood to stand, each, for the whole of its Significates: but, “some islands are fertile;” “all tyrants are not assassinated;" are Particular, and their subjects, consequently, not distributed, being taken to stand for a part only of their Significates

1826, Richard Whately, Elements of Logic:

(logic) One of several things signified by a common term.


adicity

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From -adic (taken from monadic/dyadic/triadic [function/operator]) + -ity, or alternatively from -ad (taken from monad/duad/triad) + -icity. Compare Latinate equivalent arity, based on -ary.

1997, Robert W. Burch, 13: Peirce's Reduction Thesis, Nathan Houser, Don D. Roberts, James Van Evra (editor), Studies in the Logic of Charles Sanders Peirce, Indiana University Press, page 233,
Equivalently, it says that all relations of adicity greater than 3 may be reduced to relations of adicities 1, 2, and/or 3. The negative component of the Thesis says, first, that relations of adicity 2 may not in general be constructed from (reduced to) relations exclusively of adicity 1; and, second, that relations of adicity 3 and greater may not in general be constructed from (equivalently: reduced to) relations exclusively of adicities 1 and/or 2.

What can be predicted is that the adicity of any syntactic predicate is the same: since its adicity is a grammatical and not a thematic fact, semantic differences between predicates cannot affect their grammatical structure.

2004, Susan Rothstein, Predicates and Their Subjects, Springer, page 47:

2007, Helier J. Robinson, Relation Philosophy of Mathematics, Science, and Mind, Sharebooks Publishing, 2nd Edition, page 68,
We have seen that every relation, without exception, necessarily has a term set, and the necessary properties of simplicity and an adicity: relations without these are impossible, merely nominal.

(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.


heuretic

(logic) The branch of logic concerned with discovery or invention


decidable

en-adj

decidable (comparative more decidable, superlative most decidable)

more decidable (comparative)
most decidable (superlative)

intuitionistic logic
intuitionistic logic

(logic) in intuitionistic logic, a proposition P is decidable in a given theory if it can be proven from the theory that "either P or not P", i.e. in symbols: P∨¬P.


deflationary

(philosophy, logic) Belonging or relating to a family of theories claiming that assertions that predicate truth of a statement do not attribute a property called truth to such a statement.


predesignate

From pre- + designate. Adjective coined by Sir William Hamilton.

(logic, of a proposition) Having its quantity indicated by a verbal sign, as with "all", "none", etc.


unlesss

Attributed to John Horton Conway. From unless, by analogy with the formation of iff from if.

1990, James Glimm, The Legacy of John Von Neumann, American Mathematical Society, →ISBN, page 279,
Partial Order: G ≥ H unlesss (unless and only unless) H ≥ some Gᴿ or some Hᴸ ≥ G.

A subset S is called absorbing if to each x#92;inX there is a real number #92;epsilon#61;#92;epsilon#95;xgt;0 such that #92;lambdax#92;inS for all #92;lambda with 0lt;#92;left#124;#92;lambda#92;right#124;#92;le#92;epsilon. Trivially the set X is absorbing; on the other hand #92;#123;0#92;#125; can never be absorbing (unlesss X#61;#92;#123;0#92;#125;).

1999, V. K. Balachandran, Topological Algebras, North-Holland, published 2000, →ISBN, pages 78–79:

2004, William Fraser, Susan Hirshberg, and David Wolfe, "The Structure of the Distributive Lattice of Games Born by Day n", in Integers: Electronic Journal of Combinatorial Number Theory 5(2) (2005), page 2,
G ≥ H unlesss H ≥ Gᴿ or Hᴸ ≥ G for some Gᴿ ∈ Gᴿ or some Hᴸ ∈ Hᴸ. ¶ (Analogous to “iff”, the term “unlesss” means “unless and only unless”.)


precisely unless

(mathematics, logic) implies a negative and is implied by a negative; i.e. B implies not-A and not-B implies A


contrapositive

(logic) The inverse of the converse of a given logical implication.

kontrapositio

the inverse of the converse of a given proposition


self-contradiction

en-noun

self-contradiction (countable and uncountable, plural self-contradictions)

(logic) A statement that contains a contradiction, or a premise from which one could be derived.


major premise

(logic) In a categorical syllogism, the premise whose terms are the syllogism's major term and middle term.

pääpremissi

premise whose terms are the major term and middle term


comparate

(logic) One of two things being compared.


alethic

en-adj

alethic (comparative more alethic, superlative most alethic)

more alethic (comparative)
most alethic (superlative)

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

der

The modal operators □ and ◊ stand for alethic necessity and possibility.

2003, Nicholas Asher, Alex Lascarides, Logics of Conversation, page 46:

(logic) Of or pertaining to the various modalities of truth, such as the possibility or impossibility of something being true.

alethisch

logic: pertaining to the modalities of truth


forward reasoning

(philosophy, logic) In artificial intelligence, modus ponens.


material conditional

en-noun

material conditional (plural material conditionals)

'A ⊃ B' represents a material conditional.

(logic) A type of conditional statement used in formal logic and defined as true whenever its antecedent is false or its consequent is true, and false when its antecedent is true and its consequent is false.


modus tollens

From Latin modus tollendō tollēns (“the mode where the denying denies”), from modus (“mode”) and forms of tollō (“I take away”).

der

1. If P, then Q.

2. Not Q.

3. Therefore, not P.

(philosophy, logic) A valid form of argument in which the consequent of a conditional proposition is denied, thus implying the denial of the antecedent. Modus tollens has this form:

Modus tollens

a valid form of argument in which the consequent of a condition proposition is denied


just in case

The negation of a disjunction is true just in case both disjuncts are false.


adjunctive

(logic) The property of two operations x and y, such that ax(ayb) = a, and ay(axb) = a.


well-formed formula

en-noun

well-formed formula (plural well-formed formulas or well-formed formulae)

well-formed formulas (plural)
well-formed formulae (plural)

This program works correctly on all well-formed formulas but it blows up on illegal input.

(logic) A statement that is expressed in a valid, syntactically correct, manner.


infinitate

en-verb

infinitate (third-person singular simple present infinitates, present participle infinitating, simple past and past participle infinitated)

infinitates (present singular third-person)
infinitating (participle present)
infinitated (participle past)
infinitated (past)

(logic, transitive) To transform a term, concept, or similar idea into its opposite by adding a negative prefix


minor premise

minor premises (plural)
minor (alternative)

The minor premise in John Stuart Mill's famous syllogism is 'Socrates is a man'.

(logic) The second premise in a categorical syllogism, whose subject is the minor term and whose predicate is the middle term.


NOT

(mathematics, logic) A unary operation on logical values that changes true to false, and false to true.


structurality

en-noun

structurality (countable and uncountable, plural structuralities)

(mathematics, logic) A property satisfied by structural translations from sequents into equations or from equations into sequents.


contraposition

contraposition (countable and uncountable, plural contrapositions)

(countable, logic) The statement of the form "if not Q then not P", given the statement "if P then Q".


rhetorical induction

(logic) reasoning from specific examples to general laws


colligation

colligation (countable and uncountable, plural colligations)

From Latin colligātiō. By surface analysis, colligate + -ion.

Induction is a term applied to describe the process of a true Colligation of Facts by means of an exact and appropriate Conception.

1840, William Whewell, “Aphorisms Concerning Science”, in The Philosophy of the Inductive Sciences, Founded upon Their History. […], volume I, London: John W[illiam] Parker, […]; Cambridge, Cambridgeshire: J. and J. J. Deighton, →OCLC, paragraph XIII, page xxxix:

the colligation of facts

1843, John Stuart Mill, A System of Logic, Ratiocinative and Inductive, being a Connected View of the Principles of Evidence, and the Methods of Scientific Investigation. […], volume (please specify |volume=I or II), London: John W[illiam] Parker, […], →OCLC:

In order to have knowledge of the physical world, we use our ideas and concepts as the "thread" on which we string the facts about the world, the "pearls." We do this by a process Whewell called colligation.

2011, Laura J. Snyder, The Philosophical Breakfast Club Broadway Books, page 252 (in a discussion of William Whewell's Philosophy of the Inductive Sciences, Founded upon Their History (1840))

(logic) The formulation of a general hypothesis which seeks to connect two or more facts.


common knowledge

(logic, game theory) A special kind of knowledge for a group of agents, such that when all the agents in a group G know p, they all know that they know p, they all know that they all know that they know p, and so on ad infinitum.


disjunct

Holonym: disjunction

(logic) One of multiple propositions, any of which, if true, confirm the validity of another proposition (a disjunction).


NOT operator

(mathematics, logic) An operation on logical values that changes true to false, and false to true.


domain of discourse

domain of discourse (plural domains of discourse)

(logic) In predicate logic, an indication of the relevant set of entities that are being dealt with by quantifiers.


false analogy

(logic) An informal fallacy applying to inductive arguments, in which the similarity in one respect of two concepts, objects, or events is taken as sufficient to establish that they are similar in another respect in which they actually are dissimilar.


differentia

/dɪfəˈɹɛnʃɪə/

From Latin differentia. Doublet of difference.

That character, it seems to me, should be regarded as the practically important differentia of religion for our purpose; and just what it is can easily be brought out by comparing the mind of an abstractly conceived Christian with that of a moralist similarly conceived.

1902, William James, “Lecture II: Circumscription of the Topic”, in The Varieties of Religious Experience: A Study in Human Nature […] , New York, N.Y.; London: Longmans, Green, and Co. […], →OCLC, page 45:

If genera are different and co-ordinate, their differentiae are themselves different in kind. Take as an instance the genus ‘animal’ and the genus ‘knowledge’. ‘With feet’, ‘two-footed’, ‘winged’, ‘aquatic’, are differentiae of ‘animal’; the species of knowledge are not distinguished by the same differentiae.

1928, E. M. Edghill, Categories, translation of original by Aristotle:

In the case of a word like “surfboard,” the differentiae seem pretty clear. How is this board different from all other boards?

2017, Kory Stamper, Word By Word, Vintage, published 2018, page 116:

(logic, semantics, taxonomy) A distinguishing feature which marks a species off from other members of the same genus.


chicken-or-egg question

chicken-or-egg question (plural chicken-or-egg questions)

chicken-or-egg questions (plural)
chicken or egg question (alternative)
chicken-and-egg question (alternative)
chicken and egg question (alternative)
chicken-and-egg problem (alternative)
hen and egg question (alternative)
hen-and-egg question (alternative)
hen or egg question (alternative)
hen-or-egg question (alternative)
hen-and-egg problem (alternative)

(logic, philosophy) A supposed paradox concerning whether chickens or chicken eggs existed first.


counterexample

(logic) An example that counters a general rule; an exception to a general rule; a specific instance of the falsity of (and falsifiability of) any proposed universal applicability of a rule or statement.


predicate logic

predicate logic (plural predicate logics)

(logic) The generic term for symbolic formal systems like first-order logic, second-order logic, many-sorted logic or infinitary logic.


monadic predicate logic

monadic predicate logic (plural monadic predicate logics)

(logic) The fragment of predicate logic in which all predicate letters are monadic (that is, they take only one argument), and there are no function letters.


first-order logic

first-order logic (countable and uncountable, plural first-order logics)

(logic) A formal deductive system extended from propositional logic with the possibility to quantify over individuals of the domain of discourse.

منطق الرتبَة الأولى

formal deductive system expanded from propositional logic


FOL

first-order logic
first-order logic#English

(logic) Initialism of first-order logic.


propositional logic

propositional logic (plural propositional logics)

(logic) A formal deductive system in which formulae representing propositions can be formed by combining atomic propositions using logical connectives.


intensional logic

intensional logic (plural intensional logics)

(logic) A formal deductive system able to represent the distinction between intension and extension of a term.


infinite regress

infinite regress (plural infinite regresses)

(logic) A regress into an infinite sequence of propositions in an attempt to found the truth of the proposition Pᵢ on the truth of the proposition Pᵢ₊₁.


mereology

mereology (countable and uncountable, plural mereologies)

/ˌmɪəɹiˈɒləd͡ʒi/

Coined by Stanisław Leśniewski in 1927, from Ancient Greek μέρος (méros, “part”) + -logy (“study, discussion, science”).

2001, Lech Polkowski, Spatial Reasoning via Rough Sets, Wojciech Ziarko, Yiyu Yao (editors), Rough Sets and Current Trends in Computing: 2nd International Conference RSCTC 2000, Revised Papers, Springer, LNAI 2005, page 479,
In [13] a new paradigm for approximate reasoning, rough mereology, has been introduced. Rough mereology is based on the notion of a part to a degree and thus falls in the province of part–based mereologies.

2007, Achille C. Varzi, Antony Galton (second reader), Chapter 15: Spatial Reasoning and Ontology: Parts, Wholes, and Locations, Marco Aiello, Ian Pratt-Hartmann, Johan van Benthem (editors), Handbook of Spatial Logics, Springer, page 947,
Let us begin with mereology. This is often defined as the theory of the part-whole relation, but such a definition is misleading. It suggests that mereology has something to say about both parts and wholes, which is not true. As we shall see in Sec. 2, the notion of a whole goes beyond the conceptual resources of mereology and calls for topological concepts and principles of various sorts. By itself, mereology is best understood as the theory of the parthood relation, regardless of whether the second term of the relation may be said to qualify as a whole entity.

In 1926 Tarski drew Leśniewski's attention to the similarity existing between his mereology and Whitehead's theory of events.[…]In the United States, mereology is known as the “calculus of individuals” — a designation that is etymologically somewhat paradoxical, since the objects of mereology are anything but indivisible individua.

2012, Guido Küng, Ontology and the Logistic Analysis of Language: An Enquiry into the Contemporary Views on Universals, Revised edition, Springer, page 107:

(logic) The discipline which deals with the relationship of parts with their respective wholes.

mereologie

logic: theory dealing with parts in relation to wholes


falsidical

en-adj

falsidical (comparative more falsidical, superlative most falsidical)

more falsidical (comparative)
most falsidical (superlative)

From Latin falsidicus (“speaking falsehood”), from falsi- (“false”) + dicus (“speaker”).


informal fallacy

en-noun

informal fallacy (plural informal fallacies)

(logic) A fallacy whose error cannot be represented by the symbols used in formal logic.


formal fallacy

formal fallacy (plural formal fallacies)

(logic) A pattern of reasoning which is always wrong, due to a flaw in the structure of the argument.


mathematical logic

mathematical logic (usually uncountable, plural mathematical logics)

(logic) A subfield of logic and mathematics consisting of both the mathematical study of logic and the application of this study to other areas of mathematics, exemplified by questions on the expressive power of formal logics and the deductive power of formal proof systems.


formal logic

formal logic (countable and uncountable, plural formal logics)


formal system

(logic) The grouping of a formal language and a set of inference rules and/or axioms.

formeel systeem

combination of formal language and inference rules


logical calculus

logical calculus (plural logical calculi)


propositional calculus

propositional calculus (countable and uncountable, plural propositional calculi)


strict implication

strict implication (plural strict implications)

material implication
material implication

(logic) A material implication that is acted upon by the necessity operator from modal logic.


material implication

material implication (countable and uncountable, plural material implications)

material conditional
material conditional#English


necessary condition

necessary condition (plural necessary conditions)

(logic) A statement Q in relation to statement P such that P implies Q.


sufficient condition

sufficient condition (plural sufficient conditions)

(logic) A statement P in relation to statement Q such that P implies Q.


modal logic

modal logic (countable and uncountable, plural modal logics)

(logic) Any formal system that attempts to deal with modalities, such as possibility and necessity, but also obligation and permission.


deontic logic

deontic logic (countable and uncountable, plural deontic logics)

(logic) The study of obligation, permission, and related concepts.

(logic) A formal system capturing the concepts of obligation and permission.


monome

From mono- + -ome; compare binomial, polynomial.

(mathematics, logic, computing) An expression with a single term, such as a product of numeric variables (with no addition) or a conjunction of possibly negated Boolean variables (with no disjunction).


propositional variable

propositional variable (plural propositional variables)

A propositional variable is typically a letter (possibly with a subscripted number) whose truth value is contingent upon some interpretation or valuation.

(logic) A variable that can either be true or false.


fallacy fallacy

fallacy fallacy (plural fallacy fallacies)

From the fact that assuming a conclusion is false because of a fallacy in the reasoning is itself a fallacy.

(logic) The formal fallacy of inferring that if an argument contains a fallacy, its conclusion must be false.


affirming the consequent

(logic) A formal fallacy, committed by reasoning in the form:

A formal fallacy, committed by reasoning in the form:
If P, then Q.
Q.
Therefore, P.


retrospective determinism

retrospective determinism (usually uncountable, plural retrospective determinisms)

(logic) A fallacy consisting in reasoning that because something happened, it was therefore bound to happen.


accentus

(logic) Ambiguity arising when the meaning of a sentence is changed by placing an unusual prosodic stress, or when, in a written passage, it is left unclear which word the emphasis was supposed to fall on.


proof by example

proof by example (plural proofs by example)

(logic) A logical fallacy consisting of providing one or more examples as a proof of a more general statement.


decidability

decidability (countable and uncountable, plural decidabilities)

(logic, computer science) The state or condition of being decidable.


term logic

term logic (countable and uncountable, plural term logics)

(logic) An approach to logic that splits propositions into two terms—subject and predicate.


subnector

(logic) a functor which takes as input one or more sentences and outputs a term.


obligatum

(logic) That which is, or must be, granted.


negatum

(logic) The proposition that is to be negated.

Something that is negated.
The proposition that is to be negated.


supervenient

en-adj

supervenient (comparative more supervenient, superlative most supervenient)

more supervenient (comparative)
most supervenient (superlative)

From Latin supervenient-, stem of superveniens, present participle of supervenio (“to come to or in addition to, to overtake”).

If mental properties are supervenient on physical properties, people with identical bodies will also have identical minds.

(logic, philosophy, of a set of properties) In a relationship with another set such that membership in the other set implies membership in the present set


paraconsistent

Coined in 1976 by the Peruvian philosopher Francisco Miró Quesada, from para- + consistent.

(logic) Dealing with contradictions in a discriminating way, in order to avoid acceptance of one from entailing acceptance of all contradictions.


equiprobable

The random number generator is designed to generate random numbers with an equiprobable law of distribution with the limits +1 to -1.

1964, I. A. Turyev et al., A Laboratory computer for joint operation with a simulator:

(mathematics, logic) Having equal probability, such as any number from 1 to 6 being the equiprobable outcome of the fair toss of fair dice.


universe of discourse

en-noun

universe of discourse (plural universes of discourse)

(logic) The set of all entities over which quantifiers—including "for all" and "there exists"—range.


compositionality

Coordinate term: (in pragmatics) contextuality

(especially logic, semantics, mathematics) The property of being compositional.


argument form

argument forms (plural)
argument-form (alternative)

(logic) The result of replacing parts of an argument with letters, leaving only logic words such as "if" and "for all" unreplaced.


relatum

From Latin relatum, neuter past participle of referre.

And with respect to secondary processes, whether a PDT becomes an ADT will vary according to both the ADTs a person has acquired through primary acquisition processes (for this determines which objects can be the relata in the relational properties) and according to the individual’s experiential and epistemic history with respect to disgust elicitors.

2003, Christopher Knapp, “De-moralizing Disgustingness”, in Philosophy and Phenomenological Research, LXVI, № 2, page 265:

For according to the externalist, the opposing view rests on the idea that “being conscious of” is a genuine relation, that is, a relation whose obtaining entails the existence of its relata.

2007 July 12, Harold Langsam, “Rationality, Justification, and the Internalism/Externalism Debate”, in Erkenntnis, volume 68, number 1, →DOI:

However we understand the defect, most divine determinists will likely wish to say that the relation of inconformity between act and law obtains (when it does obtain) merely in virtue of the intrinsic natures of the relata. In other words, the relation of inconformity follows merely upon the nonrelational characteristics of the relata.

2019, Peter Furlong, The Challenges of Divine Determinism: A Philosophical Analysis, page 94:

(logic, philosophy) A term that is related to the referent.


interdefinable

(logic, philosophy) Able to be defined in terms of each other.


mereological

/ˌmɪəɹiəˈlɒd͡ʒɪkəl/

Join is a mereological relation which can be interpreted as union set-theoretically.

I think that theories like mereological nihilism are interesting in the way that epistemological skepticism is interesting, the main question for both being how do we avoid this?

2008 August 13, Jonathan Schaffer, “Truthmaker commitments”, in Philosophical Studies, volume 141, number 1, →DOI:

(philosophy, logic) Of or pertaining to mereology, a collection of axiomatic first-order theories dealing with parts and their respective wholes.


biconditional

Although (MR) is discussed here as simply (CP ), in actuality (MR) is a biconditional of which one part is (CP ).

2008 January 3, Anand Vaidya, “Modal Rationalism and Modal Monism”, in Erkenntnis, volume 68, number 2, →DOI:

(logic) An "if and only if" conditional wherein the truth of each term depends on the truth of the other


commutant

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

The basic mathematical entity to be used here in elucidating the different senses of superselection rules is a von Neumann algebra #123;#92;mathfrak#123;M

2008 September 27, John Earman, “Superselection Rules for Philosophers”, in Erkenntnis, volume 69, number 3, →DOI:

(algebra, logic) The subset of all elements of a semigroup that commute with the elements of a given subset


Turing degree

(computer science, logic) A measure of the level of algorithmic unsolvability of the decision problem of whether a given set of natural numbers contains any given number.


Peano arithmetic

Peano arithmetic (countable and uncountable, plural Peano arithmetics)

Named after Italian mathematician Giuseppe Peano (1858–1932).

named-after

(logic) A set of axioms of first-order logic for the natural numbers specifying the operations of zero, successor, addition and multiplication, including a first-order schema of induction.


Presburger arithmetic

Introduced in 1929 by Mojżesz Presburger.

(logic) A set of axioms of first-order logic for the natural numbers specifying the operations of zero, successor, and addition, including a first-order schema of induction, without multiplication.

Mojżesz Presburger
Presburger arithmetic


axiomatic system

en-noun

axiomatic system (plural axiomatic systems)

(logic) A set of axioms from which theorems can be derived.


many-sorted logic

many-sorted logic (plural many-sorted logics)

(logic) A logic that directly supports classification of entities into disjunct sorts.


arithmetical hierarchy

arithmetical hierarchy (plural arithmetical hierarchies)

(logic) A hierarchy which classifies the complexity of first-order formulae (and sets defined by them) based on the number of alternations between series of unbounded existential quantifiers and universal quantifiers.


arithmetic hierarchy

arithmetic hierarchy (plural arithmetic hierarchies)

arithmetical hierarchy
arithmetical hierarchy#English

(logic) Alternative form of arithmetical hierarchy


arithmetical set

arithmetical set (plural arithmetical sets)

(logic) A set of natural numbers that can be defined by a formula of first-order Peano arithmetic.


Gödel number

Named after Austrian mathematician and logician Kurt Gödel

named-after

(logic) A number uniquely assigned to each symbol, and to each well-formed formula of some formal language.


description logic

en-noun

description logic (plural description logics)

knowledge representation
knowledge representation

(logic) One of a family of knowledge representation languages which can be used to represent the concept definitions of an application domain (known as terminological knowledge) in a structured and formally well-understood way.


Peirce's law

Named after the logician and philosopher Charles Sanders Peirce.

Consider Peirce's law, ((P→Q)→P)→P). If Q is true, then P→Q is also true so the law reads "If truth implies P then deduce P" which certainly makes sense. If Q is false, then (P→Q)→P≡(P→⊥)→P≡¬P→P≡¬P→P and ¬P≡¬P→⊥≡¬¬P so the law reads ¬¬P→P, which is intuitionistically false but equivalent to the classical axiom ¬P∨P.

propositional calculus
propositional calculus

law of excluded middle
law of excluded middle

implicational propositional calculus
implicational propositional calculus

(logic) The classically valid but intuitionistically non-valid formula ((P→Q)→P)→P of propositional calculus, which can be used as a substitute for the law of excluded middle in implicational propositional calculus.


implicational propositional calculus

implicational propositional calculus (uncountable)

(logic) A minimalist version of propositional calculus which uses only the logical connectives → ("implies") and ⊥ ("false").


intuitionistic logic

intuitionistic logic (plural intuitionistic logics)

law of double negation
law of double negation

(mathematics, logic) A type of logic which rejects the axiom law of excluded middle or, equivalently, the law of double negation and/or Peirce's law. It is the foundation of intuitionism.

intuïtionistische logica

a type of logic which rejects the axiom "law of excluded middle"


proof by contradiction

proof by contradiction (countable and uncountable, plural proofs by contradiction)

(mathematics, logic) The proof of a statement adduced by deriving a contradiction from the statement's negation.


law of double negation

The law of double negation is not valid intuitionistically. To show this with Heyting algebra semantics, let A=(0,1)∪(1,2). Then ¬A=(-∞,0)∪(2,∞), ¬¬A=(0,2), ¬¬A→A=(-∞,1)∪(1,∞) ne ℝ.

(logic) The statement that the negation of the negation of A implies A, for any proposition A. Stated symbolically: ¬¬A→A.


proof system

(logic) A set of axioms and a set of inference rules which are jointly used to deduce tautologies, thereby providing proofs of them.


valuation function

valuation function (plural valuation functions)

Say that a model's interpration assigns true to A and false to B. Then the valuation function assigns false to "not A", true to "not B", false to "A implies B", false to "A and B", and true to "A or B".

(logic) A function which assigns a truth value to every well-formed formula, which is identical to the model's interpretation function when applied to atomic propositions, and which otherwise assigns a truth value recursively depending on the formula's top logical connective and the truth values of the subformulae surrounding that logical connective.


law of excluded middle

law of the excluded middle (alternative)

(logic) A logical principle which states all statements must be either true or false, i.e. in symbols: P∨¬P.


Kleene star

After Stephen Cole Kleene (1909-1994), American mathematician.

Coordinate term: Kleene plus

(logic, computing theory) The asterisk, *, used as an operator to concatenate zero or more strings from a given set, widely used in regular expressions.


intensionality

intensionality (countable and uncountable, plural intensionalities)

(logic, mathematics) The condition of having an intension


dialetheism

dialetheism (usually uncountable, plural dialetheisms)

Coined by Graham Priest and Richard Routley, from di- + Ancient Greek ἀλήθεια (alḗtheia, “truth”), in 1981.

der

[It] is important to point out that endorsing dialetheism is not the same as rejecting logic or rational argumentation.

2005, Laurence Goldstein, Logic: key concepts in philosophy, page 158:

(logic) The theory that statements can be both true and false at the same time and in the same sense. The opposite of the law of noncontradiction.


falsum

(logic) An arbitrary contradiction, denoted ⊥.


summum genus

Summum genus, in its strictest sense, is that all-extensive term under which every object of whatever kind may be classed, and of every one of which it may be affirmatively predicated: the word which is generally used to denote such genus is substance, or, as some call it, being. ... ; thus by ornithologist, bird would be regarded as the summum genus under which he would arrange the different subdivisions of birds ...

1827, John Huyshe, A Treatise on Logic, on The Basis of Aldrich:

(logic, semantics) The highest, most all-inclusive genus; the one that is not a species of any other genus.


axiom schema

en-noun

axiom schema (plural axiom schemas or axiom schemata)

axiom schemas (plural)
axiom schemata (plural)

(logic) A formula in the language 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.


subformula

subformula (plural subformulas or subformulae)

subformulas (plural)
subformulae (plural)

(logic) A formula that is part of another formula.


schematic variable

schematic variable (plural schematic variables)

universe of discourse
universe of discourse

(logic) A variable that appears in an axiom schema and ranges over formulas, distinguished from the variables of the axiom schema that are quantified over and that range over the individuals of the universe of discourse.


nonliteral

(programming, logic) That which is not a literal.


tetrachotomy

tĕtrəkŏʹtəmĭ

/tɛtɹəˈkɒtəmɪ/

From τέτραχα (tétrakha, “quadripartite”) + τόμος (tómos, “slice, piece”) (from τέμνω (témnō, “I cut”)).


pons asinorum

From New Latin pons asinorum, from Latin pōns (“bridge”) + genitive plural of asinus (“donkey”). Literally, “bridge of donkeys”.

(logic) A method for finding the middle term of a syllogism in Aristotlean analytics.


dormitive virtue

dormitive virtue (plural dormitive virtues)

A calque translation of Latin, virtus dormitiva, coined by Molière in The Imaginary Invalid. In the play, he lampoons a group of physicians providing an explanation in macaronic Latin of the sleep-inducing properties of opium as stemming from its "virtus dormitiva".

The inevitable next suggestion -— that aesthetic experience is distinguished not by pleasure at all but by a special aesthetic emotion can be dropped on the waste-pile of "dormitive virtue” explanations

1968, Proceedings and Addresses of the American Philosophical Association, American Philosophical Association, page 6:

Solidity now has all the defects of a dormitive virtue, obscurity, unobservability, something-we-know-notwhattery — and none of the advantages of a dormitive virtue

1998, Rae Langton, Kantian Humility: Our Ignorance of Things in Themselves, page 176:

Because (1) is postulated and at the same time used as a covering law, the putative explanations are vacuous in the sense in which explanatory appeals to dormitive virtue are.

2003, Henry E. Kyburg, Mariam Thalos, Probability is the Very Guide of Life, page 66:

Now admittedly, this has the look of a dormitive virtue argument: the reason the intellect can recollect its own activity is that it possesses just such a recollective capacity.

2013, Charles Bolyard, Rondo Keele, Later Medieval Metaphysics: Ontology, Language, and Logic, page 147:

But if talk of such facts just arises via hypostatizations out of the relevant truths, then the facts posited can't explain the truths except via a blatant dormitive virtue explanation.

2021, Karen Bennett, Dean W. Zimmerman, Oxford Studies in Metaphysics, volume 12, page 29:

Fitness is not the empty idea of a dormitive virtue. The point is that although fitness is explanatory, it seems to be a placeholder for a deeper account that dispenses with the concept of fitness [again the propensity concept].

2021, Richard E. Michod, Darwinian Dynamics: Evolutionary Transitions in Fitness and Individuality, page 186:

(idiomatic, rhetoric, logic, linguistics) A type of tautology in which an item is explained in terms of the item itself, only put in different (usually more abstract) words.


precisive

en-adj

precisive (comparative more precisive, superlative most precisive)

more precisive (comparative)
most precisive (superlative)

precisive censure

precisive abstraction

(logic) Exactly limiting by cutting off all that is not absolutely relevant.


conjunctive normal form

en-noun

conjunctive normal form (countable and uncountable, plural conjunctive normal forms)

(logic) The form of a Boolean formula that the formula has if the formula is a conjunction of disjunctions of literals, such as “(A or B or C) and (D or E or not F)”.


disjunctive normal form

(logic) The form of a boolean formula that the formula has if the formula is a disjunction of conjunctions of literals, such as “(A and B and C) or (D and E and not F)”.

disjunktiivinen normaalimuoto

the form of a boolean formula that the formula has if the formula is a disjunction of conjunctions of literals, such as “(A and B and C) or (D and E and not F)”


LEM

What constructive mathematicians know is that there are mathematical universes in which sets are like topological spaces and properties are like open sets. In fact, these universes are well-known to classical mathematicians (they are called toposes), but they look at them from “the outside”. When we consider what mathematicians who live in such a universe see, we discover many fascinating kinds of mathematics, which tend to be constructive. The universe of classical mathematics is special because in it all sets are like discrete topological spaces. In fact, one way of understanding LEM is “all spaces/sets are discrete”. Is this really such a smart thing to assume? If for no other reason, LEM should be abandoned because it is quite customary to consider “continuous” and “discrete” domains in applications in computer science and physics. So what gives mathematicians the idea that all domains are discrete?

2005, Andrej Bauer, Mathematics and Computation: The Law of Excluded Middle:

Law of excluded middle
law of excluded middle#English


infinitary

(mathematics, logic) Of or pertaining to expressions of infinite length


paralogy

paralogy (countable and uncountable, plural paralogies)


superaltern

(logic) A universal proposition from which can be inferred a corresponding subaltern


FO

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


finitary

(logic) Pertaining to finite-length proofs, each using a finite set of axioms.


succedent

(logic) The formulas on the right-hand side of a sequent.


accidens

An Accidens (or accident) of an individual, genus, or species is any attribute which is possessed by it, and which does not follow from, or form a part of, its comprehension. […] If, on the other hand, an accidens is sometimes present and sometimes absent in an individual, […]

1886, Prasanna K. Roy, A Text-book of Deductive Logic: For the Use of Students, page 83:

But, where there is no apparent reason why the attribute should always be found in the individuals of a class, it is called an Accidens.

1896, James Welton, A Manual of Logic, volume 1, page 86:

(logic) Synonym of accident (“a property, fact, or relation that is the result of chance or is nonessential or nonsubstantive”)


categorematic

From Ancient Greek κατηγόρημα (katēgórēma, “a predicate”) + -atic.

uder

The word "man" is categorematic; the word "many" is not.

(logic, of a word) Capable of being employed alone as a term.


shallow embedding

en-noun

shallow embedding (plural shallow embeddings)

(logic, uncountable) The act of representing one logic or language with another by providing a syntactic translation.

(logic, countable) A specific mechanism for such a syntactic translation.


deep embedding

(logic, uncountable) The act of representing one language, typically a logic or programming language, with another by modeling expressions in the former as data in the latter.

(logic, countable) A specific such representation.


subcontrary

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(logic) Denoting the relation of opposition between the particular affirmative and particular negative. Of these both may be true and only one can be false.


subcontrary

(logic) Either of a pair of propositions at least one of which must be true


ignotum per ignotius

From Latin ignōtum per ignōtius, “[to explain] the unknown by the more unknown”.

(logic) A type of fallacious argument in which one attempts to prove something unknown by relying upon an assumption that is also unknown.


discursus

Borrowed from Latin discursus. Doublet of discourse.

(logic) argumentation; ratiocination; discursive reasoning


obvert

en-verb

obvert (third-person singular simple present obverts, present participle obverting, simple past and past participle obverted)

obverts (present singular third-person)
obverting (participle present)
obverted (participle past)
obverted (past)

(transitive, logic) To infer by obversion; too convert a proposition to its obverse.


explicandum

(logic) That which is to be explained or explicated


implicator

Residuated implicators are quite important since a t-norm T and an implicator I can only satisfy the residuation principle T(x,y) ≤_L z ⇔ y ≤_L I(x,z) if and only if the implicator I equals the residuated implicator I_T.

2008, M. Nachtegael, P. Sussner, T. Mélange, E.E. Kerre, “An Interval-Valued Fuzzy Morphological Model Based on Lukasiewicz-Operators”, in Jacques Blanc-Talon, Salah Bourennane, Wilfried Philips, Dan Popescu, Paul Scheunders, editors, Advanced Concepts for Intelligent Vision Systems: 10th International Conference, ACIVS 2008, Juan-les-Pins, France, October 2008, Proceedings (Lecture Notes in Computer Science; 5259), Springer, →ISBN, page 605:

(logic) The antecedent of an implication.


hyperjump

(mathematics, logic) A form of Turing jump in hyperarithmetic.


graphoid

(logic) A set of statements of the form, "X is irrelevant to Y given that we know Z" where X, Y and Z are sets of variables, which can be manipulated by a set of axioms concerning informational irrelevance and its graphical representation.


counterproof

It seems that ghosts and legendary encounters in general thrive under the protection of law because their extranormal statements and implications require proof and provoke the less convincing counterproof.

2001, Linda Dégh, Legend and Belief: Dialectics of a Folklore Genre, page 4:

(logic) A proof that contradicts a given statement.


apodictically

en-adv

apodictically (comparative more apodictically, superlative most apodictically)

more apodictically (comparative)
most apodictically (superlative)


positive logic

(logic) A logical system or fragment thereof not containing a negation operator.


classical logic

en-noun

classical logic (countable and uncountable, plural classical logics)

The Lindenbaum-Tarski algebra of propositional classical logic is a Boolean algebra.

(logic) A kind of logic based on the principles that each proposition has a truth value of either "true" or "false", but not both, and that if a proposition were to be both true and false or neither true nor false then a result would be that all propositions would be both true and false.


De Morgan's law

De Morgan's law (plural De Morgan's laws)

De Morgan's laws (plural)
DM (alternative)

/dɨˈmɔɹɡɪnzˌlɔ/

Named after the British mathematician and logician Augustus De Morgan (1806–1871), who first formulated the laws in formal propositional logic.

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:

(mathematics, logic) Either of two laws in formal logic which state that:

The negation of a conjunction is the disjunction of the negations; expressed in propositional logic as: ¬ (𝑝 ∧ 𝑞) ⇔ (¬ 𝑝) ∨ (¬ 𝑞)

The negation of a disjunction is the conjunction of the negations; expressed in propositional logic as: ¬ (𝑝 ∨ 𝑞) ⇔ (¬ 𝑝) ∧ (¬ 𝑞)


supervaluationism

(logic) A semantics for dealing with irreferential singular terms and vagueness.


supertruth

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(logic) In supervaluationism, the quality of being supertrue.


supertrue

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"I am happy or I am not happy" is supertrue, because I must be one or the other.

(logic) In supervaluationism, necessarily true regardless of the values of variables.


superfalse

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"I am asleep and I am not asleep" is superfalse, because I can never be both.

(logic) In supervaluationism, necessarily false regardless of the values of variables.


Sheffer stroke

Sheffer strokes (plural)
Sheffer's stroke (alternative)

(logic) The vertical bar symbol ( | ), denoting the NAND operation.


SLD

selective linear definite
w:SLD resolution

(logic) Initialism of selective linear definite.


abstract model

(engineering, logic, mathematics) A model that contains an abstraction or abstractions of the reality.