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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.
1314:, 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.
361:. An example of an ordered metalanguage is the construction of one metalanguage to discuss an object language, followed by the creation of another metalanguage to discuss the first, etc.
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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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269:. Expressions in a metalanguage are often distinguished from those in the object language by the use of italics,
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331:: "... 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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1397: 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
517:, which has the form of a factual description, is a discourse in the metametalanguage
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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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2019:
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1662:(in French) (3 ed.). Paris: Gauthier-Villars & Cie. p. 160.
1431: 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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939:
1364: 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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1159:. This paradigm operates through two distinct, related frameworks.
327:, in a discussion of the relationship between formal languages and
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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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1960:
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is a language used to describe another language, often called the
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1370: â Branch of ethics seeking to understand ethical properties
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1403: 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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128:
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32:
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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
1443: â Difference between using a word and mentioning it
1437: â Sentence, idea or formula that refers to itself
1384:
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
1226:
Listeners and readers extract mental content from words
1207:
You have to put each concept into words more carefully
211:
94:
1751:
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
1113:, and may reference concepts that are present in the
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Since all of these metalanguages are sublanguages of
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1524:
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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1968:
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Language transfers people's thoughts and feelings (
1093:made in the metatheory about the theory are called
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1276:That concept has been floating around for decades
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1420: â Linguistic theory of semantic description
1414: â Investigation of the nature of philosophy
1382: â Experimental form of visual communication
1343: â General theory of mathematical structures
1265:Get those ideas out where they can do some good
389:example of a nested metalanguage comes from the
1776:
8:
1587:Gödel, Escher, Bach: An Eternal Golden Braid
1505:The Concise Oxford Dictionary of Linguistics
1467:Oxford Concise Dictionary of Literary Terms
896:, and very often the metalanguage as well.
67:Learn how and when to remove these messages
2602:
2197:
1965:
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1679:. Berkeley:University of California Press
16:Language used to describe another language
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241:Learn how and when to remove this message
179:Learn how and when to remove this message
117:Learn how and when to remove this message
1241:
1168:
142:This article includes a list of general
1549:Cambridge Advanced Learner's Dictionary
1540:
1196:Try to get your thoughts across better
1023:are not symbols of the object language
459:, which is a sublanguage nested within
1456:The Cambridge Dictionary of Philosophy
1376: â Genre of fiction about fiction
1218:That sentence was filled with emotion
628:, which likewise is a sublanguage of
206:one specialized aspect of the subject
99:providing more context for the reader
7:
1618:. Oxford: Clarendon Press. pp.
1559:Internet. Retrieved 20 November 2010
1555:. Dictionary online. Available from
1660:Leçons sur la theorie des fonctions
1391: â Study of mathematics itself
1493:The Oxford Companion to Philosophy
148:it lacks sufficient corresponding
14:
1656:Borel, FĂ©lix Ădouard Justin Ămile
544:, which is also a sublanguage of
48:This article has multiple issues.
3502:
1347:Jakobson's functions of language
405:Designating the language now as
195:
133:
78:
37:
56:or discuss these issues on the
826:is a nested metalanguage, but
768:, differing only in reference.
1:
3463:History of mathematical logic
1568:van Wijngaarden, A., et al. "
1418:Natural semantic metalanguage
1353:Language-oriented programming
1067:Metatheories and metatheorems
204:This article focuses only on
21:Metalanguage (disambiguation)
3388:Primitive recursive function
1355: â programming paradigm
1702:. New York: Simon Schuster
1700:Metatheorizing in Sociology
1117:but not the object theory.
3565:
2452:SchröderâBernstein theorem
2179:Monadic predicate calculus
1838:Foundations of mathematics
1724:Cambridge University Press
1590:. New York: Vintage Books
1553:Cambridge University Press
1460:Cambridge University Press
1395:Metalinguistic abstraction
1349: â Theory of language
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1070:
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903:
25:
18:
3498:
3485:Philosophy of mathematics
3434:Automated theorem proving
2605:
2559:Von NeumannâBernaysâGödel
2200:
1755:Humanist Discussion Group
1570:Language and metalanguage
1401:Metalinguistic awareness
391:Linnean taxonomic system
279:"noun" is a <noun>
26:Not to be confused with
3539:Linguistics terminology
3135:Self-verifying theories
2956:Tarski's axiomatization
1907:Tarski's undefinability
1902:incompleteness theorems
1528:Oxford University Press
1509:Oxford University Press
1498:Oxford University Press
1471:Oxford University Press
1441:Useâmention distinction
163:more precise citations.
3509:Mathematics portal
3120:Proof of impossibility
2768:propositional variable
2078:Propositional calculus
1503:Matthews, P. H. 1997.
1127:Interpretation (logic)
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3378:Kolmogorov complexity
3331:Computably enumerable
3231:Model complete theory
3023:Principia Mathematica
2083:Propositional formula
1912:BanachâTarski paradox
1744:Principia Cybernetica
1058:
1038:
1006:
875:
873:{\displaystyle L_{0}}
848:
846:{\displaystyle L_{2}}
821:
819:{\displaystyle L_{1}}
794:
792:{\displaystyle L_{0}}
763:
761:{\displaystyle L_{3}}
736:
734:{\displaystyle L_{4}}
707:
705:{\displaystyle L_{2}}
680:
678:{\displaystyle L_{3}}
650:
648:{\displaystyle L_{0}}
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621:{\displaystyle L_{3}}
596:
594:{\displaystyle L_{2}}
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564:{\displaystyle L_{0}}
539:
537:{\displaystyle L_{2}}
512:
510:{\displaystyle L_{1}}
481:
479:{\displaystyle L_{0}}
454:
452:{\displaystyle L_{1}}
427:
425:{\displaystyle L_{0}}
315:embedded metalanguage
285:Types of metalanguage
3326:ChurchâTuring thesis
3313:Computability theory
2522:continuum hypothesis
2040:Square of opposition
1898:Gödel's completeness
1720:Metaphor and Thought
1490:Honderich, T. 1995.
1300:programming language
1215:Words are containers
1047:
1027:
995:
952:Metavariable (logic)
934:that can be used to
888:Types of expressions
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605:
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355:ordered metalanguage
212:improve this article
19:For other uses, see
3480:Mathematical object
3371:P versus NP problem
3336:Computable function
3130:Reverse mathematics
3056:Logical consequence
2933:primitive recursive
2928:elementary function
2701:Free/bound variable
2554:TarskiâGrothendieck
2073:Logical connectives
2003:Logical equivalence
1853:Logical consequence
1582:Hofstadter, Douglas
1522:McArthur, T. 1996.
1407:Metalocutionary act
1244:
1171:
1139:of meanings to the
916:deductive apparatus
398:In natural language
357:is analogous to an
324:Gödel, Escher, Bach
95:improve the article
3278:Transfer principle
3241:Semantics of logic
3226:Categorical theory
3202:Non-standard model
2716:Logical connective
1843:Information theory
1792:Mathematical logic
1757:, Vol. 20, No. 92.
1465:Baldick, C. 1996.
1362:Meta-communication
1242:
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1105:statement about a
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932:rules of inference
922:) consists of the
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319:Douglas Hofstadter
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3448:Abstract category
3251:Theories of truth
3061:Rule of inference
3051:Natural deduction
3032:
3031:
2577:
2576:
2282:Cartesian product
2187:
2186:
2093:Many-valued logic
2068:Boolean functions
1951:Russell's paradox
1926:diagonal argument
1823:First-order logic
1685:978-0-520-01822-8
1629:978-0-19-824224-6
1608:Harris, Zellig S.
1517:978-0-19-280008-4
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1056:{\displaystyle L}
1036:{\displaystyle L}
1004:{\displaystyle L}
900:Deductive systems
305:) metalanguages.
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3458:History of logic
3453:Category of sets
3346:Decision problem
3125:Ordinal analysis
3066:Sequent calculus
2964:Boolean algebras
2904:
2903:
2878:
2849:logical/constant
2603:
2589:
2512:ZermeloâFraenkel
2263:Set operations:
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2135:
1966:
1946:LöwenheimâSkolem
1833:Formal semantics
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1673:Hunter, Geoffrey
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1424:Nested quotation
1385:
1358:
1312:BackusâNaur form
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1243:Minor framework
1172:
1170:Major framework
1157:conduit metaphor
1151:Role in metaphor
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1059:
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912:deductive system
906:Deductive system
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3439:Category theory
3429:Algebraic logic
3412:
3383:Lambda calculus
3321:Church encoding
3307:
3283:Truth predicate
3139:
3105:Complete theory
3028:
2897:
2893:
2889:
2884:
2876:
2596: and
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2587:
2573:
2549:New Foundations
2517:axiom of choice
2500:
2462:Gödel numbering
2402: and
2394:
2298:
2183:
2133:
2114:
2063:Boolean algebra
2049:
2013:Equiconsistency
1978:Classical logic
1955:
1936:Halting problem
1924: and
1900: and
1888: and
1887:
1882:Theorems (
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1454:Audi, R. 1996.
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1389:Metamathematics
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1341:Category theory
1336:
1305:metaprogramming
1296:
1294:Metaprogramming
1237:minor framework
1164:major framework
1153:
1147:of a language.
1129:
1123:
1121:Interpretations
1079:
1071:Main articles:
1069:
1045:
1044:
1025:
1024:
993:
992:
990:formal language
968:variable) is a
954:
948:
942:of the system.
908:
902:
894:formal language
890:
860:
855:
854:
833:
828:
827:
806:
801:
800:
779:
774:
773:
748:
743:
742:
721:
716:
715:
692:
687:
686:
665:
660:
659:
658:The grammar of
635:
630:
629:
608:
603:
602:
581:
576:
575:
574:The grammar of
551:
546:
545:
524:
519:
518:
497:
492:
491:
490:The grammar of
466:
461:
460:
439:
434:
433:
412:
407:
406:
400:
367:
351:
311:
287:
271:quotation marks
267:object language
247:
236:
235:
234:
229:
223:
220:
209:
200:
196:
185:
174:
168:
165:
155:Please help to
154:
138:
134:
123:
112:
106:
103:
92:
83:
79:
42:
38:
31:
28:metalinguistics
24:
17:
12:
11:
5:
3562:
3560:
3552:
3551:
3546:
3541:
3536:
3531:
3521:
3520:
3514:
3513:
3499:
3496:
3495:
3493:
3492:
3487:
3482:
3477:
3472:
3471:
3470:
3460:
3455:
3450:
3441:
3436:
3431:
3426:
3424:Abstract logic
3420:
3418:
3414:
3413:
3411:
3410:
3405:
3403:Turing machine
3400:
3395:
3390:
3385:
3380:
3375:
3374:
3373:
3368:
3363:
3358:
3353:
3343:
3341:Computable set
3338:
3333:
3328:
3323:
3317:
3315:
3309:
3308:
3306:
3305:
3300:
3295:
3290:
3285:
3280:
3275:
3270:
3269:
3268:
3263:
3258:
3248:
3243:
3238:
3236:Satisfiability
3233:
3228:
3223:
3222:
3221:
3211:
3210:
3209:
3199:
3198:
3197:
3192:
3187:
3182:
3177:
3167:
3166:
3165:
3160:
3153:Interpretation
3149:
3147:
3141:
3140:
3138:
3137:
3132:
3127:
3122:
3117:
3107:
3102:
3101:
3100:
3099:
3098:
3088:
3083:
3073:
3068:
3063:
3058:
3053:
3048:
3042:
3040:
3034:
3033:
3030:
3029:
3027:
3026:
3018:
3017:
3016:
3015:
3010:
3009:
3008:
3003:
2998:
2978:
2977:
2976:
2974:minimal axioms
2971:
2960:
2959:
2958:
2947:
2946:
2945:
2940:
2935:
2930:
2925:
2920:
2907:
2905:
2886:
2885:
2883:
2882:
2881:
2880:
2868:
2863:
2862:
2861:
2856:
2851:
2846:
2836:
2831:
2826:
2821:
2820:
2819:
2814:
2804:
2803:
2802:
2797:
2792:
2787:
2777:
2772:
2771:
2770:
2765:
2760:
2750:
2749:
2748:
2743:
2738:
2733:
2728:
2723:
2713:
2708:
2703:
2698:
2697:
2696:
2691:
2686:
2681:
2671:
2666:
2664:Formation rule
2661:
2656:
2655:
2654:
2649:
2639:
2638:
2637:
2627:
2622:
2617:
2612:
2606:
2600:
2583:Formal systems
2579:
2578:
2575:
2574:
2572:
2571:
2566:
2561:
2556:
2551:
2546:
2541:
2536:
2531:
2526:
2525:
2524:
2519:
2508:
2506:
2502:
2501:
2499:
2498:
2497:
2496:
2486:
2481:
2480:
2479:
2472:Large cardinal
2469:
2464:
2459:
2454:
2449:
2435:
2434:
2433:
2428:
2423:
2408:
2406:
2396:
2395:
2393:
2392:
2391:
2390:
2385:
2380:
2370:
2365:
2360:
2355:
2350:
2345:
2340:
2335:
2330:
2325:
2320:
2315:
2309:
2307:
2300:
2299:
2297:
2296:
2295:
2294:
2289:
2284:
2279:
2274:
2269:
2261:
2260:
2259:
2254:
2244:
2239:
2237:Extensionality
2234:
2232:Ordinal number
2229:
2219:
2214:
2213:
2212:
2201:
2195:
2189:
2188:
2185:
2184:
2182:
2181:
2176:
2171:
2166:
2161:
2156:
2151:
2150:
2149:
2139:
2138:
2137:
2124:
2122:
2116:
2115:
2113:
2112:
2111:
2110:
2105:
2100:
2090:
2085:
2080:
2075:
2070:
2065:
2059:
2057:
2051:
2050:
2048:
2047:
2042:
2037:
2032:
2027:
2022:
2017:
2016:
2015:
2005:
2000:
1995:
1990:
1985:
1980:
1974:
1972:
1963:
1957:
1956:
1954:
1953:
1948:
1943:
1938:
1933:
1928:
1916:Cantor's
1914:
1909:
1904:
1894:
1892:
1879:
1878:
1876:
1875:
1870:
1865:
1860:
1855:
1850:
1845:
1840:
1835:
1830:
1825:
1820:
1815:
1814:
1813:
1802:
1800:
1796:
1795:
1790:
1788:
1787:
1780:
1773:
1765:
1759:
1758:
1748:
1734:
1733:External links
1731:
1728:
1727:
1711:
1696:Ritzer, George
1688:
1665:
1647:
1635:
1628:
1599:
1574:
1561:
1539:
1538:
1536:
1533:
1532:
1531:
1520:
1501:
1488:
1474:
1463:
1450:
1447:
1445:
1444:
1438:
1435:Self-reference
1432:
1426:
1421:
1415:
1412:Metaphilosophy
1409:
1404:
1398:
1392:
1386:
1377:
1371:
1365:
1359:
1350:
1344:
1337:
1335:
1332:
1295:
1292:
1289:
1288:
1285:
1282:
1278:
1277:
1274:
1271:
1267:
1266:
1263:
1260:
1256:
1255:
1252:
1249:
1231:
1230:
1227:
1224:
1220:
1219:
1216:
1213:
1209:
1208:
1205:
1202:
1198:
1197:
1194:
1191:mental content
1187:
1183:
1182:
1179:
1176:
1152:
1149:
1133:interpretation
1125:Main article:
1122:
1119:
1068:
1065:
1052:
1032:
1013:
1012:
1000:
962:metalinguistic
950:Main article:
947:
944:
928:axiom schemata
904:Main article:
901:
898:
889:
886:
867:
863:
840:
836:
813:
809:
786:
782:
770:
769:
755:
751:
728:
724:
713:
699:
695:
672:
668:
656:
642:
638:
615:
611:
588:
584:
572:
558:
554:
531:
527:
504:
500:
473:
469:
446:
442:
419:
415:
399:
396:
366:
363:
350:
347:
310:
307:
286:
283:
249:
248:
231:
230:
203:
201:
194:
187:
186:
169:September 2010
141:
139:
132:
125:
124:
86:
84:
77:
72:
46:
45:
43:
36:
15:
13:
10:
9:
6:
4:
3:
2:
3561:
3550:
3547:
3545:
3544:Metalanguages
3542:
3540:
3537:
3535:
3532:
3530:
3527:
3526:
3524:
3511:
3510:
3505:
3497:
3491:
3488:
3486:
3483:
3481:
3478:
3476:
3473:
3469:
3466:
3465:
3464:
3461:
3459:
3456:
3454:
3451:
3449:
3445:
3442:
3440:
3437:
3435:
3432:
3430:
3427:
3425:
3422:
3421:
3419:
3415:
3409:
3406:
3404:
3401:
3399:
3398:Recursive set
3396:
3394:
3391:
3389:
3386:
3384:
3381:
3379:
3376:
3372:
3369:
3367:
3364:
3362:
3359:
3357:
3354:
3352:
3349:
3348:
3347:
3344:
3342:
3339:
3337:
3334:
3332:
3329:
3327:
3324:
3322:
3319:
3318:
3316:
3314:
3310:
3304:
3301:
3299:
3296:
3294:
3291:
3289:
3286:
3284:
3281:
3279:
3276:
3274:
3271:
3267:
3264:
3262:
3259:
3257:
3254:
3253:
3252:
3249:
3247:
3244:
3242:
3239:
3237:
3234:
3232:
3229:
3227:
3224:
3220:
3217:
3216:
3215:
3212:
3208:
3207:of arithmetic
3205:
3204:
3203:
3200:
3196:
3193:
3191:
3188:
3186:
3183:
3181:
3178:
3176:
3173:
3172:
3171:
3168:
3164:
3161:
3159:
3156:
3155:
3154:
3151:
3150:
3148:
3146:
3142:
3136:
3133:
3131:
3128:
3126:
3123:
3121:
3118:
3115:
3114:from ZFC
3111:
3108:
3106:
3103:
3097:
3094:
3093:
3092:
3089:
3087:
3084:
3082:
3079:
3078:
3077:
3074:
3072:
3069:
3067:
3064:
3062:
3059:
3057:
3054:
3052:
3049:
3047:
3044:
3043:
3041:
3039:
3035:
3025:
3024:
3020:
3019:
3014:
3013:non-Euclidean
3011:
3007:
3004:
3002:
2999:
2997:
2996:
2992:
2991:
2989:
2986:
2985:
2983:
2979:
2975:
2972:
2970:
2967:
2966:
2965:
2961:
2957:
2954:
2953:
2952:
2948:
2944:
2941:
2939:
2936:
2934:
2931:
2929:
2926:
2924:
2921:
2919:
2916:
2915:
2913:
2909:
2908:
2906:
2901:
2895:
2890:Example
2887:
2879:
2874:
2873:
2872:
2869:
2867:
2864:
2860:
2857:
2855:
2852:
2850:
2847:
2845:
2842:
2841:
2840:
2837:
2835:
2832:
2830:
2827:
2825:
2822:
2818:
2815:
2813:
2810:
2809:
2808:
2805:
2801:
2798:
2796:
2793:
2791:
2788:
2786:
2783:
2782:
2781:
2778:
2776:
2773:
2769:
2766:
2764:
2761:
2759:
2756:
2755:
2754:
2751:
2747:
2744:
2742:
2739:
2737:
2734:
2732:
2729:
2727:
2724:
2722:
2719:
2718:
2717:
2714:
2712:
2709:
2707:
2704:
2702:
2699:
2695:
2692:
2690:
2687:
2685:
2682:
2680:
2677:
2676:
2675:
2672:
2670:
2667:
2665:
2662:
2660:
2657:
2653:
2650:
2648:
2647:by definition
2645:
2644:
2643:
2640:
2636:
2633:
2632:
2631:
2628:
2626:
2623:
2621:
2618:
2616:
2613:
2611:
2608:
2607:
2604:
2601:
2599:
2595:
2590:
2584:
2580:
2570:
2567:
2565:
2562:
2560:
2557:
2555:
2552:
2550:
2547:
2545:
2542:
2540:
2537:
2535:
2534:KripkeâPlatek
2532:
2530:
2527:
2523:
2520:
2518:
2515:
2514:
2513:
2510:
2509:
2507:
2503:
2495:
2492:
2491:
2490:
2487:
2485:
2482:
2478:
2475:
2474:
2473:
2470:
2468:
2465:
2463:
2460:
2458:
2455:
2453:
2450:
2447:
2443:
2439:
2436:
2432:
2429:
2427:
2424:
2422:
2419:
2418:
2417:
2413:
2410:
2409:
2407:
2405:
2401:
2397:
2389:
2386:
2384:
2381:
2379:
2378:constructible
2376:
2375:
2374:
2371:
2369:
2366:
2364:
2361:
2359:
2356:
2354:
2351:
2349:
2346:
2344:
2341:
2339:
2336:
2334:
2331:
2329:
2326:
2324:
2321:
2319:
2316:
2314:
2311:
2310:
2308:
2306:
2301:
2293:
2290:
2288:
2285:
2283:
2280:
2278:
2275:
2273:
2270:
2268:
2265:
2264:
2262:
2258:
2255:
2253:
2250:
2249:
2248:
2245:
2243:
2240:
2238:
2235:
2233:
2230:
2228:
2224:
2220:
2218:
2215:
2211:
2208:
2207:
2206:
2203:
2202:
2199:
2196:
2194:
2190:
2180:
2177:
2175:
2172:
2170:
2167:
2165:
2162:
2160:
2157:
2155:
2152:
2148:
2145:
2144:
2143:
2140:
2136:
2131:
2130:
2129:
2126:
2125:
2123:
2121:
2117:
2109:
2106:
2104:
2101:
2099:
2096:
2095:
2094:
2091:
2089:
2086:
2084:
2081:
2079:
2076:
2074:
2071:
2069:
2066:
2064:
2061:
2060:
2058:
2056:
2055:Propositional
2052:
2046:
2043:
2041:
2038:
2036:
2033:
2031:
2028:
2026:
2023:
2021:
2018:
2014:
2011:
2010:
2009:
2006:
2004:
2001:
1999:
1996:
1994:
1991:
1989:
1986:
1984:
1983:Logical truth
1981:
1979:
1976:
1975:
1973:
1971:
1967:
1964:
1962:
1958:
1952:
1949:
1947:
1944:
1942:
1939:
1937:
1934:
1932:
1929:
1927:
1923:
1919:
1915:
1913:
1910:
1908:
1905:
1903:
1899:
1896:
1895:
1893:
1891:
1885:
1880:
1874:
1871:
1869:
1866:
1864:
1861:
1859:
1856:
1854:
1851:
1849:
1846:
1844:
1841:
1839:
1836:
1834:
1831:
1829:
1826:
1824:
1821:
1819:
1816:
1812:
1809:
1808:
1807:
1804:
1803:
1801:
1797:
1793:
1786:
1781:
1779:
1774:
1772:
1767:
1766:
1763:
1756:
1752:
1749:
1746:
1745:
1740:
1737:
1736:
1732:
1725:
1722:. Cambridge:
1721:
1715:
1712:
1709:
1708:0-669-25008-2
1705:
1701:
1697:
1692:
1689:
1686:
1682:
1678:
1674:
1669:
1666:
1661:
1657:
1651:
1648:
1644:
1639:
1636:
1631:
1625:
1621:
1616:
1615:
1609:
1603:
1600:
1597:
1596:0-14-017997-6
1593:
1589:
1588:
1583:
1578:
1575:
1571:
1565:
1562:
1558:
1554:
1551:. Cambridge:
1550:
1544:
1541:
1534:
1529:
1525:
1521:
1518:
1514:
1510:
1506:
1502:
1499:
1495:
1494:
1489:
1486:
1485:Penguin Books
1482:
1478:
1477:Cuddon, J. A.
1475:
1472:
1468:
1464:
1461:
1458:. Cambridge:
1457:
1453:
1452:
1448:
1442:
1439:
1436:
1433:
1430:
1427:
1425:
1422:
1419:
1416:
1413:
1410:
1408:
1405:
1402:
1399:
1396:
1393:
1390:
1387:
1381:
1378:
1375:
1372:
1369:
1366:
1363:
1360:
1354:
1351:
1348:
1345:
1342:
1339:
1338:
1333:
1331:
1329:
1325:
1321:
1317:
1313:
1309:
1307:
1306:
1301:
1293:
1286:
1283:
1280:
1279:
1275:
1272:
1269:
1268:
1264:
1261:
1258:
1257:
1253:
1250:
1247:
1246:
1240:
1238:
1228:
1225:
1222:
1221:
1217:
1214:
1211:
1210:
1206:
1203:
1200:
1199:
1195:
1192:
1188:
1185:
1184:
1180:
1177:
1174:
1173:
1167:
1165:
1160:
1158:
1150:
1148:
1146:
1142:
1138:
1134:
1128:
1120:
1118:
1116:
1112:
1108:
1107:formal system
1104:
1100:
1096:
1092:
1088:
1084:
1078:
1074:
1066:
1064:
1050:
1030:
1022:
1018:
998:
991:
987:
984:be arbitrary
983:
979:
975:
974:
973:
971:
967:
966:metasyntactic
963:
959:
953:
946:Metavariables
945:
943:
941:
937:
933:
929:
925:
921:
920:formal system
917:
913:
907:
899:
897:
895:
887:
885:
881:
865:
861:
838:
834:
811:
807:
784:
780:
753:
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3549:Proof theory
3500:
3298:Ultraproduct
3145:Model theory
3110:Independence
3046:Formal proof
3038:Proof theory
3021:
2994:
2951:real numbers
2923:second-order
2834:Substitution
2711:Metalanguage
2710:
2652:conservative
2625:Axiom schema
2569:Constructive
2539:MorseâKelley
2505:Set theories
2484:Aleph number
2477:inaccessible
2383:Grothendieck
2267:intersection
2154:Higher-order
2142:Second-order
2088:Truth tables
2045:Venn diagram
1828:Formal proof
1754:
1742:
1739:Metalanguage
1719:
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1449:Dictionaries
1429:Paralanguage
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1234:
1163:
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1132:
1130:
1098:
1095:metatheorems
1082:
1080:
1020:
1016:
1015:The symbols
1014:
981:
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961:
958:metavariable
957:
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387:paradigmatic
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224:January 2013
221:
210:Please help
205:
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166:
147:
113:
104:
93:Please help
88:
64:
57:
51:
50:Please help
47:
3534:Linguistics
3408:Type theory
3356:undecidable
3288:Truth value
3175:equivalence
2854:non-logical
2467:Enumeration
2457:Isomorphism
2404:cardinality
2388:Von Neumann
2353:Ultrafilter
2318:Uncountable
2252:equivalence
2169:Quantifiers
2159:Fixed-point
2128:First-order
2008:Consistency
1993:Proposition
1970:Traditional
1941:Lindström's
1931:Compactness
1873:Type theory
1818:Cardinality
1374:Metafiction
1251:Description
1193:) to others
1178:Description
1099:metatheorem
1077:Metatheorem
259:linguistics
161:introducing
3523:Categories
3219:elementary
2912:arithmetic
2780:Quantifier
2758:functional
2630:Expression
2348:Transitive
2292:identities
2277:complement
2210:hereditary
2193:Set theory
1535:References
1526:. Oxford:
1507:. Oxford:
1496:. Oxford:
1483:. London:
1469:. Oxford:
1380:Metagraphy
1368:Metaethics
1137:assignment
1115:metatheory
1111:metatheory
1091:Statements
1083:metatheory
1073:Metatheory
275:metasyntax
144:references
107:April 2021
53:improve it
3529:Metalogic
3490:Supertask
3393:Recursion
3351:decidable
3185:saturated
3163:of models
3086:deductive
3081:axiomatic
3001:Hilbert's
2988:Euclidean
2969:canonical
2892:axiomatic
2824:Signature
2753:Predicate
2642:Extension
2564:Ackermann
2489:Operation
2368:Universal
2358:Recursive
2333:Singleton
2328:Inhabited
2313:Countable
2303:Types of
2287:power set
2257:partition
2174:Predicate
2120:Predicate
2035:Syllogism
2025:Soundness
1998:Inference
1988:Tautology
1890:paradoxes
1645:. p. 277.
321:'s book,
216:talk page
59:talk page
3475:Logicism
3468:timeline
3444:Concrete
3303:Validity
3273:T-schema
3266:Kripke's
3261:Tarski's
3256:semantic
3246:Strength
3195:submodel
3190:spectrum
3158:function
3006:Tarski's
2995:Elements
2982:geometry
2938:Robinson
2859:variable
2844:function
2817:spectrum
2807:Sentence
2763:variable
2706:Language
2659:Relation
2620:Automata
2610:Alphabet
2594:language
2448:-jection
2426:codomain
2412:Function
2373:Universe
2343:Infinite
2247:Relation
2030:Validity
2020:Argument
1918:theorem,
1698:. 1991.
1675:. 1971.
1658:(1928).
1610:(1991).
1584:. 1980.
1334:See also
1254:Example
1181:Example
986:formulas
940:theorems
341:or even
309:Embedded
291:embedded
3417:Related
3214:Diagram
3112: (
3091:Hilbert
3076:Systems
3071:Theorem
2949:of the
2894:systems
2674:Formula
2669:Grammar
2585: (
2529:General
2242:Forcing
2227:Element
2147:Monadic
1922:paradox
1863:Theorem
1799:General
1141:symbols
349:Ordered
295:ordered
157:improve
3180:finite
2943:Skolem
2896:
2871:Theory
2839:Symbol
2829:String
2812:atomic
2689:ground
2684:closed
2679:atomic
2635:ground
2598:syntax
2494:binary
2421:domain
2338:Finite
2103:finite
1961:Logics
1920:
1868:Theory
1706:
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1622:â318.
1594:
1547:2010.
1515:
1479:1999.
1326:, and
1135:is an
1087:theory
970:symbol
936:derive
930:) and
924:axioms
371:nested
365:Nested
299:nested
297:, and
146:, but
3170:Model
2918:Peano
2775:Proof
2615:Arity
2544:Naive
2431:image
2363:Fuzzy
2323:Empty
2272:union
2217:Class
1858:Model
1848:Lemma
1806:Axiom
1248:Stage
1175:Stage
1145:words
1101:is a
1085:is a
988:of a
918:of a
914:(or,
339:verb,
336:noun,
255:logic
3293:Type
3096:list
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2877:list
2866:Term
2800:rank
2694:open
2588:list
2400:Maps
2305:sets
2164:Free
2134:list
1884:list
1811:list
1704:ISBN
1681:ISBN
1643:Ibid
1624:ISBN
1592:ISBN
1513:ISBN
1328:Yacc
1320:Lisp
1235:The
1162:The
1143:and
1103:true
1097:. A
1075:and
1019:and
980:and
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960:(or
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385:The
373:(or
343:word
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2416:Map
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2205:Set
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313:An
253:In
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