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in biology. Each level in the system incorporates the one below it. The language used to discuss genus is also used to discuss species; the one used to discuss orders is also used to discuss genera, etc., up to kingdoms.
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Metalanguages of formal systems all resolve ultimately to natural language, the 'common parlance' in which mathematicians and logicians converse to define their terms and operations and 'read out' their formulae.
1325:, developed in the 1960s by John Backus and Peter Naur, is one of the earliest metalanguages used in computing. Examples of modern-day programming languages which commonly find use in metaprogramming include
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is similar to an ordered metalanguage in that each level represents a greater degree of abstraction. However, a nested metalanguage differs from an ordered one in that each level includes the one below.
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Natural language combines nested and ordered metalanguages. In a natural language there is an infinite regress of metalanguages, each with more specialized vocabulary and simpler syntax.
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Michael J. Reddy (1979) argues that much of the language we use to talk about language is conceptualized and structured by what he refers to as the
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There are several entities commonly expressed in a metalanguage. In logic usually the object language that the metalanguage is discussing is a
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or set of symbols in a metalanguage which stands for a symbol or set of symbols in some object language. For instance, in the sentence:
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Reddy, Michael J. 1979. The conduit metaphor: A case of frame conflict in our language about language. In Andrew Ortony (ed.),
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expressed in a metalanguage. Unlike theorems proved within a given formal system, a metatheorem is proved within a
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280:. Expressions in a metalanguage are often distinguished from those in the object language by the use of italics,
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342:: "... it is in the nature of any formalization of number theory that its metalanguage is embedded within it."
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involves the use of a metalanguage. The act of working with metalanguages in programming is known as
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is a language formally, naturally and firmly fixed in an object language. This idea is found in
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It occurs in natural, or informal, languages, as wellâsuch as in
English, where words such as
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Computers follow programs, sets of instructions in a formal language. The development of a
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and sequel are ordered metalanguages. Since all these metalanguages are sublanguages of
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1408: â Principle in computer science of domain-specific languages for problem solving
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has the form of a metatheory describing the syntactic structure of theories stated in
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Metalogic: An
Introduction to the Metatheory of Standard First-Order Logic
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describe features and concepts pertaining to the
English language itself.
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1673:(in French) (3 ed.). Paris: Gauthier-Villars & Cie. p. 160.
1442: â Communication of additional meaning, nuance, or emotion in speech
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they are all embedded languages with respect to the language as a whole.
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1375: â Communication about how information is meant to be interpreted
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views language as an open pipe spilling mental content into the void:
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whose subject matter is some other theory (a theory about a theory).
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1170:. This paradigm operates through two distinct, related frameworks.
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There are a variety of recognized types of metalanguage, including
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provides insufficient context for those unfamiliar with the subject
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is a language used to describe another language, often called the
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1381: â Branch of ethics seeking to understand ethical properties
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1414: â Ability to consciously reflect on the nature of language
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Speakers and writers eject mental content into an external space
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http://dictionary.cambridge.org/dictionary/british/metalanguage
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A theory of language and information: A mathematical approach
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The
Penguin Dictionary of Literary Terms and Literary Theory
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Listeners and readers extract mental content from this space
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Mental content is reified (viewed as concrete) in this space
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Speakers and writers insert their mental content into words
1454: â Difference between using a word and mentioning it
1448: â Sentence, idea or formula that refers to itself
1395:
Pages displaying short descriptions of redirect targets
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Let me know if you find any good concepts in the essay
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Let me know if you find any new sensations in the poem
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Listeners and readers extract mental content from words
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You have to put each concept into words more carefully
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105:
1762:
Willard McCarty (submitted 2006) Problematic
Metaphors
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and succeeding metalanguages have the same grammar as
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by adding general information and discuss at the
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Since all of these metalanguages are sublanguages of
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The
Concise Oxford Companion to the English Language
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Pages displaying wikidata descriptions as a fallback
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views language as a sealed pipeline between people:
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Language transfers people's thoughts and feelings (
1104:made in the metatheory about the theory are called
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1287:That concept has been floating around for decades
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1431: â Linguistic theory of semantic description
1425: â Investigation of the nature of philosophy
1393: â Experimental form of visual communication
1354: â General theory of mathematical structures
1276:Get those ideas out where they can do some good
400:example of a nested metalanguage comes from the
1787:
8:
1598:Gödel, Escher, Bach: An Eternal Golden Braid
1516:The Concise Oxford Dictionary of Linguistics
1478:Oxford Concise Dictionary of Literary Terms
907:, and very often the metalanguage as well.
78:Learn how and when to remove these messages
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1976:
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1690:. Berkeley:University of California Press
27:Language used to describe another language
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252:Learn how and when to remove this message
190:Learn how and when to remove this message
128:Learn how and when to remove this message
1252:
1179:
153:This article includes a list of general
1560:Cambridge Advanced Learner's Dictionary
1551:
1207:Try to get your thoughts across better
1034:are not symbols of the object language
470:, which is a sublanguage nested within
1467:The Cambridge Dictionary of Philosophy
1387: â Genre of fiction about fiction
1229:That sentence was filled with emotion
639:, which likewise is a sublanguage of
217:one specialized aspect of the subject
110:providing more context for the reader
7:
1629:. Oxford: Clarendon Press. pp.
1570:Internet. Retrieved 20 November 2010
1566:. Dictionary online. Available from
1671:Leçons sur la theorie des fonctions
1402: â Study of mathematics itself
1504:The Oxford Companion to Philosophy
159:it lacks sufficient corresponding
25:
1667:Borel, FĂ©lix Ădouard Justin Ămile
555:, which is also a sublanguage of
59:This article has multiple issues.
3513:
1358:Jakobson's functions of language
416:Designating the language now as
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89:
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67:or discuss these issues on the
837:is a nested metalanguage, but
779:, differing only in reference.
1:
3474:History of mathematical logic
1579:van Wijngaarden, A., et al. "
1429:Natural semantic metalanguage
1364:Language-oriented programming
1078:Metatheories and metatheorems
215:This article focuses only on
32:Metalanguage (disambiguation)
3399:Primitive recursive function
1366: â programming paradigm
1713:. New York: Simon Schuster
1711:Metatheorizing in Sociology
1128:but not the object theory.
3576:
2463:SchröderâBernstein theorem
2190:Monadic predicate calculus
1849:Foundations of mathematics
1735:Cambridge University Press
1601:. New York: Vintage Books
1564:Cambridge University Press
1471:Cambridge University Press
1406:Metalinguistic abstraction
1360: â Theory of language
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29:
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3496:Philosophy of mathematics
3445:Automated theorem proving
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2570:Von NeumannâBernaysâGödel
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1766:Humanist Discussion Group
1581:Language and metalanguage
1412:Metalinguistic awareness
402:Linnean taxonomic system
290:"noun" is a <noun>
37:Not to be confused with
3550:Linguistics terminology
3146:Self-verifying theories
2967:Tarski's axiomatization
1918:Tarski's undefinability
1913:incompleteness theorems
1539:Oxford University Press
1520:Oxford University Press
1509:Oxford University Press
1482:Oxford University Press
1452:Useâmention distinction
174:more precise citations.
3520:Mathematics portal
3131:Proof of impossibility
2779:propositional variable
2089:Propositional calculus
1514:Matthews, P. H. 1997.
1138:Interpretation (logic)
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3389:Kolmogorov complexity
3342:Computably enumerable
3242:Model complete theory
3034:Principia Mathematica
2094:Propositional formula
1923:BanachâTarski paradox
1755:Principia Cybernetica
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1049:
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884:{\displaystyle L_{0}}
859:
857:{\displaystyle L_{2}}
832:
830:{\displaystyle L_{1}}
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803:{\displaystyle L_{0}}
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772:{\displaystyle L_{3}}
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745:{\displaystyle L_{4}}
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689:{\displaystyle L_{3}}
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548:{\displaystyle L_{2}}
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521:{\displaystyle L_{1}}
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463:{\displaystyle L_{1}}
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436:{\displaystyle L_{0}}
326:embedded metalanguage
296:Types of metalanguage
3337:ChurchâTuring thesis
3324:Computability theory
2533:continuum hypothesis
2051:Square of opposition
1909:Gödel's completeness
1731:Metaphor and Thought
1501:Honderich, T. 1995.
1311:programming language
1226:Words are containers
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1038:
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963:Metavariable (logic)
945:that can be used to
899:Types of expressions
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366:ordered metalanguage
223:improve this article
30:For other uses, see
3491:Mathematical object
3382:P versus NP problem
3347:Computable function
3141:Reverse mathematics
3067:Logical consequence
2944:primitive recursive
2939:elementary function
2712:Free/bound variable
2565:TarskiâGrothendieck
2084:Logical connectives
2014:Logical equivalence
1864:Logical consequence
1593:Hofstadter, Douglas
1533:McArthur, T. 1996.
1418:Metalocutionary act
1255:
1182:
1150:of meanings to the
927:deductive apparatus
409:In natural language
368:is analogous to an
335:Gödel, Escher, Bach
106:improve the article
3289:Transfer principle
3252:Semantics of logic
3237:Categorical theory
3213:Non-standard model
2727:Logical connective
1854:Information theory
1803:Mathematical logic
1768:, Vol. 20, No. 92.
1476:Baldick, C. 1996.
1373:Meta-communication
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933:) consists of the
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330:Douglas Hofstadter
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3459:Abstract category
3262:Theories of truth
3072:Rule of inference
3062:Natural deduction
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3042:
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2587:
2293:Cartesian product
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2104:Many-valued logic
2079:Boolean functions
1962:Russell's paradox
1937:diagonal argument
1834:First-order logic
1696:978-0-520-01822-8
1640:978-0-19-824224-6
1619:Harris, Zellig S.
1528:978-0-19-280008-4
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911:Deductive systems
316:) metalanguages.
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16:(Redirected from
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3464:Category of sets
3357:Decision problem
3136:Ordinal analysis
3077:Sequent calculus
2975:Boolean algebras
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2860:logical/constant
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2523:ZermeloâFraenkel
2274:Set operations:
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1957:LöwenheimâSkolem
1844:Formal semantics
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1435:Nested quotation
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1323:BackusâNaur form
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1254:Minor framework
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1181:Major framework
1168:conduit metaphor
1162:Role in metaphor
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3450:Category theory
3440:Algebraic logic
3423:
3394:Lambda calculus
3332:Church encoding
3318:
3294:Truth predicate
3150:
3116:Complete theory
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2908:
2904:
2900:
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2887:
2607: and
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2584:
2560:New Foundations
2528:axiom of choice
2511:
2473:Gödel numbering
2413: and
2405:
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2194:
2144:
2125:
2074:Boolean algebra
2060:
2024:Equiconsistency
1989:Classical logic
1966:
1947:Halting problem
1935: and
1911: and
1899: and
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1893:Theorems (
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1465:Audi, R. 1996.
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1400:Metamathematics
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1352:Category theory
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1316:metaprogramming
1307:
1305:Metaprogramming
1248:minor framework
1175:major framework
1164:
1158:of a language.
1140:
1134:
1132:Interpretations
1090:
1082:Main articles:
1080:
1056:
1055:
1036:
1035:
1004:
1003:
1001:formal language
979:variable) is a
965:
959:
953:of the system.
919:
913:
905:formal language
901:
871:
866:
865:
844:
839:
838:
817:
812:
811:
790:
785:
784:
759:
754:
753:
732:
727:
726:
703:
698:
697:
676:
671:
670:
669:The grammar of
646:
641:
640:
619:
614:
613:
592:
587:
586:
585:The grammar of
562:
557:
556:
535:
530:
529:
508:
503:
502:
501:The grammar of
477:
472:
471:
450:
445:
444:
423:
418:
417:
411:
378:
362:
322:
298:
282:quotation marks
278:object language
258:
247:
246:
245:
240:
234:
231:
220:
211:
207:
196:
185:
179:
176:
166:Please help to
165:
149:
145:
134:
123:
117:
114:
103:
94:
90:
53:
49:
42:
39:metalinguistics
35:
28:
23:
22:
15:
12:
11:
5:
3573:
3571:
3563:
3562:
3557:
3552:
3547:
3542:
3532:
3531:
3525:
3524:
3510:
3507:
3506:
3504:
3503:
3498:
3493:
3488:
3483:
3482:
3481:
3471:
3466:
3461:
3452:
3447:
3442:
3437:
3435:Abstract logic
3431:
3429:
3425:
3424:
3422:
3421:
3416:
3414:Turing machine
3411:
3406:
3401:
3396:
3391:
3386:
3385:
3384:
3379:
3374:
3369:
3364:
3354:
3352:Computable set
3349:
3344:
3339:
3334:
3328:
3326:
3320:
3319:
3317:
3316:
3311:
3306:
3301:
3296:
3291:
3286:
3281:
3280:
3279:
3274:
3269:
3259:
3254:
3249:
3247:Satisfiability
3244:
3239:
3234:
3233:
3232:
3222:
3221:
3220:
3210:
3209:
3208:
3203:
3198:
3193:
3188:
3178:
3177:
3176:
3171:
3164:Interpretation
3160:
3158:
3152:
3151:
3149:
3148:
3143:
3138:
3133:
3128:
3118:
3113:
3112:
3111:
3110:
3109:
3099:
3094:
3084:
3079:
3074:
3069:
3064:
3059:
3053:
3051:
3045:
3044:
3041:
3040:
3038:
3037:
3029:
3028:
3027:
3026:
3021:
3020:
3019:
3014:
3009:
2989:
2988:
2987:
2985:minimal axioms
2982:
2971:
2970:
2969:
2958:
2957:
2956:
2951:
2946:
2941:
2936:
2931:
2918:
2916:
2897:
2896:
2894:
2893:
2892:
2891:
2879:
2874:
2873:
2872:
2867:
2862:
2857:
2847:
2842:
2837:
2832:
2831:
2830:
2825:
2815:
2814:
2813:
2808:
2803:
2798:
2788:
2783:
2782:
2781:
2776:
2771:
2761:
2760:
2759:
2754:
2749:
2744:
2739:
2734:
2724:
2719:
2714:
2709:
2708:
2707:
2702:
2697:
2692:
2682:
2677:
2675:Formation rule
2672:
2667:
2666:
2665:
2660:
2650:
2649:
2648:
2638:
2633:
2628:
2623:
2617:
2611:
2594:Formal systems
2590:
2589:
2586:
2585:
2583:
2582:
2577:
2572:
2567:
2562:
2557:
2552:
2547:
2542:
2537:
2536:
2535:
2530:
2519:
2517:
2513:
2512:
2510:
2509:
2508:
2507:
2497:
2492:
2491:
2490:
2483:Large cardinal
2480:
2475:
2470:
2465:
2460:
2446:
2445:
2444:
2439:
2434:
2419:
2417:
2407:
2406:
2404:
2403:
2402:
2401:
2396:
2391:
2381:
2376:
2371:
2366:
2361:
2356:
2351:
2346:
2341:
2336:
2331:
2326:
2320:
2318:
2311:
2310:
2308:
2307:
2306:
2305:
2300:
2295:
2290:
2285:
2280:
2272:
2271:
2270:
2265:
2255:
2250:
2248:Extensionality
2245:
2243:Ordinal number
2240:
2230:
2225:
2224:
2223:
2212:
2206:
2200:
2199:
2196:
2195:
2193:
2192:
2187:
2182:
2177:
2172:
2167:
2162:
2161:
2160:
2150:
2149:
2148:
2135:
2133:
2127:
2126:
2124:
2123:
2122:
2121:
2116:
2111:
2101:
2096:
2091:
2086:
2081:
2076:
2070:
2068:
2062:
2061:
2059:
2058:
2053:
2048:
2043:
2038:
2033:
2028:
2027:
2026:
2016:
2011:
2006:
2001:
1996:
1991:
1985:
1983:
1974:
1968:
1967:
1965:
1964:
1959:
1954:
1949:
1944:
1939:
1927:Cantor's
1925:
1920:
1915:
1905:
1903:
1890:
1889:
1887:
1886:
1881:
1876:
1871:
1866:
1861:
1856:
1851:
1846:
1841:
1836:
1831:
1826:
1825:
1824:
1813:
1811:
1807:
1806:
1801:
1799:
1798:
1791:
1784:
1776:
1770:
1769:
1759:
1745:
1744:External links
1742:
1739:
1738:
1722:
1707:Ritzer, George
1699:
1676:
1658:
1646:
1639:
1610:
1585:
1572:
1550:
1549:
1547:
1544:
1543:
1542:
1531:
1512:
1499:
1485:
1474:
1461:
1458:
1456:
1455:
1449:
1446:Self-reference
1443:
1437:
1432:
1426:
1423:Metaphilosophy
1420:
1415:
1409:
1403:
1397:
1388:
1382:
1376:
1370:
1361:
1355:
1348:
1346:
1343:
1306:
1303:
1300:
1299:
1296:
1293:
1289:
1288:
1285:
1282:
1278:
1277:
1274:
1271:
1267:
1266:
1263:
1260:
1242:
1241:
1238:
1235:
1231:
1230:
1227:
1224:
1220:
1219:
1216:
1213:
1209:
1208:
1205:
1202:mental content
1198:
1194:
1193:
1190:
1187:
1163:
1160:
1144:interpretation
1136:Main article:
1133:
1130:
1079:
1076:
1063:
1043:
1024:
1023:
1011:
973:metalinguistic
961:Main article:
958:
955:
939:axiom schemata
915:Main article:
912:
909:
900:
897:
878:
874:
851:
847:
824:
820:
797:
793:
781:
780:
766:
762:
739:
735:
724:
710:
706:
683:
679:
667:
653:
649:
626:
622:
599:
595:
583:
569:
565:
542:
538:
515:
511:
484:
480:
457:
453:
430:
426:
410:
407:
377:
374:
361:
358:
321:
318:
297:
294:
260:
259:
242:
241:
214:
212:
205:
198:
197:
180:September 2010
152:
150:
143:
136:
135:
97:
95:
88:
83:
57:
56:
54:
47:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
3572:
3561:
3558:
3556:
3555:Metalanguages
3553:
3551:
3548:
3546:
3543:
3541:
3538:
3537:
3535:
3522:
3521:
3516:
3508:
3502:
3499:
3497:
3494:
3492:
3489:
3487:
3484:
3480:
3477:
3476:
3475:
3472:
3470:
3467:
3465:
3462:
3460:
3456:
3453:
3451:
3448:
3446:
3443:
3441:
3438:
3436:
3433:
3432:
3430:
3426:
3420:
3417:
3415:
3412:
3410:
3409:Recursive set
3407:
3405:
3402:
3400:
3397:
3395:
3392:
3390:
3387:
3383:
3380:
3378:
3375:
3373:
3370:
3368:
3365:
3363:
3360:
3359:
3358:
3355:
3353:
3350:
3348:
3345:
3343:
3340:
3338:
3335:
3333:
3330:
3329:
3327:
3325:
3321:
3315:
3312:
3310:
3307:
3305:
3302:
3300:
3297:
3295:
3292:
3290:
3287:
3285:
3282:
3278:
3275:
3273:
3270:
3268:
3265:
3264:
3263:
3260:
3258:
3255:
3253:
3250:
3248:
3245:
3243:
3240:
3238:
3235:
3231:
3228:
3227:
3226:
3223:
3219:
3218:of arithmetic
3216:
3215:
3214:
3211:
3207:
3204:
3202:
3199:
3197:
3194:
3192:
3189:
3187:
3184:
3183:
3182:
3179:
3175:
3172:
3170:
3167:
3166:
3165:
3162:
3161:
3159:
3157:
3153:
3147:
3144:
3142:
3139:
3137:
3134:
3132:
3129:
3126:
3125:from ZFC
3122:
3119:
3117:
3114:
3108:
3105:
3104:
3103:
3100:
3098:
3095:
3093:
3090:
3089:
3088:
3085:
3083:
3080:
3078:
3075:
3073:
3070:
3068:
3065:
3063:
3060:
3058:
3055:
3054:
3052:
3050:
3046:
3036:
3035:
3031:
3030:
3025:
3024:non-Euclidean
3022:
3018:
3015:
3013:
3010:
3008:
3007:
3003:
3002:
3000:
2997:
2996:
2994:
2990:
2986:
2983:
2981:
2978:
2977:
2976:
2972:
2968:
2965:
2964:
2963:
2959:
2955:
2952:
2950:
2947:
2945:
2942:
2940:
2937:
2935:
2932:
2930:
2927:
2926:
2924:
2920:
2919:
2917:
2912:
2906:
2901:Example
2898:
2890:
2885:
2884:
2883:
2880:
2878:
2875:
2871:
2868:
2866:
2863:
2861:
2858:
2856:
2853:
2852:
2851:
2848:
2846:
2843:
2841:
2838:
2836:
2833:
2829:
2826:
2824:
2821:
2820:
2819:
2816:
2812:
2809:
2807:
2804:
2802:
2799:
2797:
2794:
2793:
2792:
2789:
2787:
2784:
2780:
2777:
2775:
2772:
2770:
2767:
2766:
2765:
2762:
2758:
2755:
2753:
2750:
2748:
2745:
2743:
2740:
2738:
2735:
2733:
2730:
2729:
2728:
2725:
2723:
2720:
2718:
2715:
2713:
2710:
2706:
2703:
2701:
2698:
2696:
2693:
2691:
2688:
2687:
2686:
2683:
2681:
2678:
2676:
2673:
2671:
2668:
2664:
2661:
2659:
2658:by definition
2656:
2655:
2654:
2651:
2647:
2644:
2643:
2642:
2639:
2637:
2634:
2632:
2629:
2627:
2624:
2622:
2619:
2618:
2615:
2612:
2610:
2606:
2601:
2595:
2591:
2581:
2578:
2576:
2573:
2571:
2568:
2566:
2563:
2561:
2558:
2556:
2553:
2551:
2548:
2546:
2545:KripkeâPlatek
2543:
2541:
2538:
2534:
2531:
2529:
2526:
2525:
2524:
2521:
2520:
2518:
2514:
2506:
2503:
2502:
2501:
2498:
2496:
2493:
2489:
2486:
2485:
2484:
2481:
2479:
2476:
2474:
2471:
2469:
2466:
2464:
2461:
2458:
2454:
2450:
2447:
2443:
2440:
2438:
2435:
2433:
2430:
2429:
2428:
2424:
2421:
2420:
2418:
2416:
2412:
2408:
2400:
2397:
2395:
2392:
2390:
2389:constructible
2387:
2386:
2385:
2382:
2380:
2377:
2375:
2372:
2370:
2367:
2365:
2362:
2360:
2357:
2355:
2352:
2350:
2347:
2345:
2342:
2340:
2337:
2335:
2332:
2330:
2327:
2325:
2322:
2321:
2319:
2317:
2312:
2304:
2301:
2299:
2296:
2294:
2291:
2289:
2286:
2284:
2281:
2279:
2276:
2275:
2273:
2269:
2266:
2264:
2261:
2260:
2259:
2256:
2254:
2251:
2249:
2246:
2244:
2241:
2239:
2235:
2231:
2229:
2226:
2222:
2219:
2218:
2217:
2214:
2213:
2210:
2207:
2205:
2201:
2191:
2188:
2186:
2183:
2181:
2178:
2176:
2173:
2171:
2168:
2166:
2163:
2159:
2156:
2155:
2154:
2151:
2147:
2142:
2141:
2140:
2137:
2136:
2134:
2132:
2128:
2120:
2117:
2115:
2112:
2110:
2107:
2106:
2105:
2102:
2100:
2097:
2095:
2092:
2090:
2087:
2085:
2082:
2080:
2077:
2075:
2072:
2071:
2069:
2067:
2066:Propositional
2063:
2057:
2054:
2052:
2049:
2047:
2044:
2042:
2039:
2037:
2034:
2032:
2029:
2025:
2022:
2021:
2020:
2017:
2015:
2012:
2010:
2007:
2005:
2002:
2000:
1997:
1995:
1994:Logical truth
1992:
1990:
1987:
1986:
1984:
1982:
1978:
1975:
1973:
1969:
1963:
1960:
1958:
1955:
1953:
1950:
1948:
1945:
1943:
1940:
1938:
1934:
1930:
1926:
1924:
1921:
1919:
1916:
1914:
1910:
1907:
1906:
1904:
1902:
1896:
1891:
1885:
1882:
1880:
1877:
1875:
1872:
1870:
1867:
1865:
1862:
1860:
1857:
1855:
1852:
1850:
1847:
1845:
1842:
1840:
1837:
1835:
1832:
1830:
1827:
1823:
1820:
1819:
1818:
1815:
1814:
1812:
1808:
1804:
1797:
1792:
1790:
1785:
1783:
1778:
1777:
1774:
1767:
1763:
1760:
1757:
1756:
1751:
1748:
1747:
1743:
1736:
1733:. Cambridge:
1732:
1726:
1723:
1720:
1719:0-669-25008-2
1716:
1712:
1708:
1703:
1700:
1697:
1693:
1689:
1685:
1680:
1677:
1672:
1668:
1662:
1659:
1655:
1650:
1647:
1642:
1636:
1632:
1627:
1626:
1620:
1614:
1611:
1608:
1607:0-14-017997-6
1604:
1600:
1599:
1594:
1589:
1586:
1582:
1576:
1573:
1569:
1565:
1562:. Cambridge:
1561:
1555:
1552:
1545:
1540:
1536:
1532:
1529:
1525:
1521:
1517:
1513:
1510:
1506:
1505:
1500:
1497:
1496:Penguin Books
1493:
1489:
1488:Cuddon, J. A.
1486:
1483:
1479:
1475:
1472:
1469:. Cambridge:
1468:
1464:
1463:
1459:
1453:
1450:
1447:
1444:
1441:
1438:
1436:
1433:
1430:
1427:
1424:
1421:
1419:
1416:
1413:
1410:
1407:
1404:
1401:
1398:
1392:
1389:
1386:
1383:
1380:
1377:
1374:
1371:
1365:
1362:
1359:
1356:
1353:
1350:
1349:
1344:
1342:
1340:
1336:
1332:
1328:
1324:
1320:
1318:
1317:
1312:
1304:
1297:
1294:
1291:
1290:
1286:
1283:
1280:
1279:
1275:
1272:
1269:
1268:
1264:
1261:
1258:
1257:
1251:
1249:
1239:
1236:
1233:
1232:
1228:
1225:
1222:
1221:
1217:
1214:
1211:
1210:
1206:
1203:
1199:
1196:
1195:
1191:
1188:
1185:
1184:
1178:
1176:
1171:
1169:
1161:
1159:
1157:
1153:
1149:
1145:
1139:
1131:
1129:
1127:
1123:
1119:
1118:formal system
1115:
1111:
1107:
1103:
1099:
1095:
1089:
1085:
1077:
1075:
1061:
1041:
1033:
1029:
1009:
1002:
998:
995:be arbitrary
994:
990:
986:
985:
984:
982:
978:
977:metasyntactic
974:
970:
964:
957:Metavariables
956:
954:
952:
948:
944:
940:
936:
932:
931:formal system
928:
924:
918:
910:
908:
906:
898:
896:
892:
876:
872:
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18:Metalanguages
3560:Proof theory
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3309:Ultraproduct
3156:Model theory
3121:Independence
3057:Formal proof
3049:Proof theory
3032:
3005:
2962:real numbers
2934:second-order
2845:Substitution
2722:Metalanguage
2721:
2663:conservative
2636:Axiom schema
2580:Constructive
2550:MorseâKelley
2516:Set theories
2495:Aleph number
2488:inaccessible
2394:Grothendieck
2278:intersection
2165:Higher-order
2153:Second-order
2099:Truth tables
2056:Venn diagram
1839:Formal proof
1765:
1753:
1750:Metalanguage
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1460:Dictionaries
1440:Paralanguage
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1174:
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1109:
1106:metatheorems
1093:
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1027:
1026:The symbols
1025:
992:
988:
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969:metavariable
968:
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235:January 2013
232:
221:Please help
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124:
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104:Please help
99:
75:
68:
62:
61:Please help
58:
3545:Linguistics
3419:Type theory
3367:undecidable
3299:Truth value
3186:equivalence
2865:non-logical
2478:Enumeration
2468:Isomorphism
2415:cardinality
2399:Von Neumann
2364:Ultrafilter
2329:Uncountable
2263:equivalence
2180:Quantifiers
2170:Fixed-point
2139:First-order
2019:Consistency
2004:Proposition
1981:Traditional
1952:Lindström's
1942:Compactness
1884:Type theory
1829:Cardinality
1385:Metafiction
1262:Description
1204:) to others
1189:Description
1110:metatheorem
1088:Metatheorem
270:linguistics
172:introducing
3534:Categories
3230:elementary
2923:arithmetic
2791:Quantifier
2769:functional
2641:Expression
2359:Transitive
2303:identities
2288:complement
2221:hereditary
2204:Set theory
1546:References
1537:. Oxford:
1518:. Oxford:
1507:. Oxford:
1494:. London:
1480:. Oxford:
1391:Metagraphy
1379:Metaethics
1148:assignment
1126:metatheory
1122:metatheory
1102:Statements
1094:metatheory
1084:Metatheory
286:metasyntax
155:references
118:April 2021
64:improve it
3540:Metalogic
3501:Supertask
3404:Recursion
3362:decidable
3196:saturated
3174:of models
3097:deductive
3092:axiomatic
3012:Hilbert's
2999:Euclidean
2980:canonical
2903:axiomatic
2835:Signature
2764:Predicate
2653:Extension
2575:Ackermann
2500:Operation
2379:Universal
2369:Recursive
2344:Singleton
2339:Inhabited
2324:Countable
2314:Types of
2298:power set
2268:partition
2185:Predicate
2131:Predicate
2046:Syllogism
2036:Soundness
2009:Inference
1999:Tautology
1901:paradoxes
1656:. p. 277.
332:'s book,
227:talk page
70:talk page
3486:Logicism
3479:timeline
3455:Concrete
3314:Validity
3284:T-schema
3277:Kripke's
3272:Tarski's
3267:semantic
3257:Strength
3206:submodel
3201:spectrum
3169:function
3017:Tarski's
3006:Elements
2993:geometry
2949:Robinson
2870:variable
2855:function
2828:spectrum
2818:Sentence
2774:variable
2717:Language
2670:Relation
2631:Automata
2621:Alphabet
2605:language
2459:-jection
2437:codomain
2423:Function
2384:Universe
2354:Infinite
2258:Relation
2041:Validity
2031:Argument
1929:theorem,
1709:. 1991.
1686:. 1971.
1669:(1928).
1621:(1991).
1595:. 1980.
1345:See also
1265:Example
1192:Example
997:formulas
951:theorems
352:or even
320:Embedded
302:embedded
3428:Related
3225:Diagram
3123: (
3102:Hilbert
3087:Systems
3082:Theorem
2960:of the
2905:systems
2685:Formula
2680:Grammar
2596: (
2540:General
2253:Forcing
2238:Element
2158:Monadic
1933:paradox
1874:Theorem
1810:General
1152:symbols
360:Ordered
306:ordered
168:improve
3191:finite
2954:Skolem
2907:
2882:Theory
2850:Symbol
2840:String
2823:atomic
2700:ground
2695:closed
2690:atomic
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2609:syntax
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2349:Finite
2114:finite
1972:Logics
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1879:Theory
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1558:2010.
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1146:is an
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947:derive
941:) and
935:axioms
382:nested
376:Nested
310:nested
308:, and
157:, but
3181:Model
2929:Peano
2786:Proof
2626:Arity
2555:Naive
2442:image
2374:Fuzzy
2334:Empty
2283:union
2228:Class
1869:Model
1859:Lemma
1817:Axiom
1259:Stage
1186:Stage
1156:words
1112:is a
1096:is a
999:of a
929:of a
925:(or,
350:verb,
347:noun,
266:logic
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2411:Maps
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2175:Free
2145:list
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1822:list
1715:ISBN
1692:ISBN
1654:Ibid
1635:ISBN
1603:ISBN
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1331:Lisp
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