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480:. Deductively valid arguments can be known to be so without recourse to experience, so they must be knowable a priori. However, formality alone does not guarantee that logical consequence is not influenced by empirical knowledge. So the a priori property of logical consequence is considered to be independent of formality.
1446:-preservational" accounts, according to which the characteristic feature of a good inference is that it never allows one to move from justifiably assertible premises to a conclusion that is not justifiably assertible. This is (roughly) the account favored by
1441:
The accounts considered above are all "truth-preservational", in that they all assume that the characteristic feature of a good inference is that it never allows one to move from true premises to an untrue conclusion. As an alternative, some have proposed
313:
This is in contrast to an argument like "Fred is Mike's brother's son. Therefore Fred is Mike's nephew." Since this argument depends on the meanings of the words "brother", "son", and "nephew", the statement "Fred is Mike's nephew" is a so-called
254:
The most widely prevailing view on how best to account for logical consequence is to appeal to formality. This is to say that whether statements follow from one another logically depends on the structure or
917:
703:
101:
of logical consequence involves the questions: In what sense does a conclusion follow from its premises? and What does it mean for a conclusion to be a consequence of premises? All of
1323:
The conclusion is a logical consequence of the premises because we can not imagine a possible world where (a) all frogs are green; (b) Kermit is a frog; and (c) Kermit is not green.
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Logic and
Scientific Methods: Volume One of the Tenth International Congress of Logic, Methodology and Philosophy of Science, Florence, August 1995
1850:
1556:. It is also possible to specify non-monotonic consequence relations to capture the idea that, e.g., 'Tweety can fly' is a logical consequence of
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Modal-formal accounts of logical consequence combine the modal and formal accounts above, yielding variations on the following basic idea:
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identified three features of an adequate characterization of entailment: (1) The logical consequence relation relies on the
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17:
1886:, Metalogic: An Introduction to the Metatheory of Standard First-Order Logic, University of California Press, 1971, p. 75.
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The two prevailing techniques for providing accounts of logical consequence involve expressing the concept in terms of
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2017:
1976:
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was originally introduced by Frege in 1879, but its current use only dates back to Rosser and Kleene (1934–1935).
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1961:
1st edition, Kluwer
Academic Publishers, Norwell, MA. 2nd edition, Dover Publications, Mineola, NY, 2003.
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1968:
The
Undecidable, Basic Papers on Undecidable Propositions, Unsolvable Problems And Computable Functions
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2007:
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interpretations of the sentences) the sentence must be true if every sentence in the set is true.
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of "Fred is Mike's brother's son", not a formal consequence. A formal consequence must be true
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322:, however this is an incomplete definition of formal consequence, since even the argument "
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27:
Relationship between statements that hold true when one logically follows from another
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2013:
1991:
1972:
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74:
4605:
128:. A sentence is said to be a logical consequence of a set of sentences, for a given
105:
is meant to provide accounts of the nature of logical consequence and the nature of
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2644:
2370:
2365:
2088:
1716:
The
Stanford Encyclopedia of Philosophy (Fall 2009 Edition), Edward N. Zalta (ed.).
1679:
1674:
1599:
741:
171:
82:
52:
1265:
is true if and only if there is no possible world at which all of the elements of
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1999:
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1594:
1309:
Consider the modal account in terms of the argument given as an example above:
1201:
513:
267:
263:
133:
38:
2235:
1392:
if and only if it is impossible for an argument with the same logical form as
919:. Or, in other words, the set of the interpretations that make all members of
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5684:
5659:
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5108:
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1987:
1810:
1624:
1604:
1189:
1188:
Such accounts are called "modal" because they appeal to the modal notions of
547:
227:
113:
106:
970:
accounts of logical consequence are variations on the following basic idea:
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4307:
4154:
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597:
501:
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256:
231:
121:
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5841:
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5013:
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3002:
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2614:
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1939:
967:
243:
143:
Logicians make precise accounts of logical consequence regarding a given
270:. For instance, we can express the logical form of a valid argument as:
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90:
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Necessity, meaning, and rationality: the notion of logical consequence
496:. The study of the syntactic consequence (of a logic) is called (its)
5816:
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5559:
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4402:
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3232:
3044:
3034:
3007:
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2624:
2485:
2396:
1609:
44:"Logical implication" redirects here. For the binary connective, see
2151:(1st ed. 1950), (2nd ed. 1959), (3rd ed. 1972), (4th edition, 1982).
2092:
5729:
5518:
5265:
5194:
5180:
4929:
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4484:
4282:
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3029:
2545:
2248:
242:(sense experience); and (3) The logical consequence relation has a
86:
1983:
5099:
4704:
4080:
2872:
2609:
2540:
2274:
2203:
Theory of
Logical Calculi: Basic Theory of Consequence Operations
1746:
1584:
1568:{Birds can typically fly, Tweety is a bird, Tweety is a penguin}.
97:, because the conclusion is the consequence of the premises. The
94:
66:
2079:
Hanson, William H (1997), "The concept of logical consequence",
500:
whereas the study of (its) semantic consequence is called (its)
5223:
2447:
1995:
1928:
Logical consequences. Theory and applications: An introduction.
259:
of the statements without regard to the contents of that form.
900:
782:
686:
612:
561:
5594:
5190:
3624:
2970:
2815:
2639:
2354:
939:
true is a subset of the set of the interpretations that make
70:
37:"Therefore" redirects here. For the therefore symbol ∴, see
396:, then no information about the possible interpretations of
2599:
2113:
Thought 2 Talk: A Crash Course in
Reflection and Expression
351:
1768:; Kees Doets; Daniele Mundici; Johan van Benthem (eds.).
2323:
5360:
1468:
Belief revision § Non-monotonic inference relation
238:, i.e., it can be determined with or without regard to
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4909:
4884:
4855:
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4779:
4750:
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402:
382:
362:
310:
of arguments constructed using this scheme is valid.
208:
180:
152:
1457:
1079:Alternatively (and, most would say, equivalently):
4981:
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4719:
4690:
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1424:
1404:
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1113:
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697:
659:
639:
619:
588:
568:
534:
468:
448:
428:
408:
388:
368:
262:Syntactic accounts of logical consequence rely on
218:
190:
162:
1958:Boolean Reasoning: The Logic of Boolean Equations
1938:
1196:. 'It is necessary that' is often expressed as a
30:"Entailment" redirects here. For other uses, see
6030:
5827:Segmented discourse representation theory (SDRT)
2198:
912:{\displaystyle \Gamma \models _{\mathcal {FS}}A}
136:, using only logic (i.e., without regard to any
2049:, Metaphysics Research Lab, Stanford University
698:{\displaystyle \Gamma \vdash _{\mathcal {FS}}A}
436:will affect that knowledge. Our knowledge that
306:This argument is formally valid, because every
4558:
1915:
1753:
1476:consequence relations, i.e. ones such that if
344:s nephew" is valid in all cases, but is not a
5346:
5029:
4544:
2786:
2339:
1432:to have true premises and a false conclusion.
728:Syntactic consequence does not depend on any
2247:
2221:A paper on 'implication' from math.niu.edu,
77:that hold true when one statement logically
1759:
1560:{Birds can typically fly, Tweety is a bird}
1204:, so that the accounts above translate as:
5353:
5339:
5043:
5036:
5022:
4551:
4537:
2978:
2793:
2779:
2346:
2332:
2136:The Blackwell Guide to Philosophical Logic
2128:
2071:The Blackwell Guide to Philosophical Logic
2058:
2035:The Blackwell Guide to Philosophical Logic
1864:
1862:
2149:, Cambridge, MA: Harvard University Press
2107:
2040:
2026:
1916:Anderson, A.R.; Belnap, N.D. Jr. (1975),
1902:, The Cambridge Dictionary of Philosophy
1436:
73:which describes the relationship between
1326:
507:
352:A priori property of logical consequence
51:"⊧" redirects here. For the symbol, see
2154:
2053:The Stanford Encyclopedia of Philosophy
2005:
1925:
1920:, vol. 1, Princeton, NJ: Princeton
1859:
1472:The accounts discussed above all yield
735:
120:, by way of examples that explain with
14:
6031:
2800:
2170:
2078:
1931:London: College Publications. Series:
1874:(1952), Van Nostrand Publishing. p.88.
1762:"Logical consequence: a turn in style"
234:of the sentences: (2) The relation is
5782:Discourse representation theory (DRT)
5334:
5017:
4786:{\displaystyle \not \leftrightarrow }
4532:
2774:
2327:
2176:On the concept of logical consequence
2141:
2068:
1964:
1955:
1740:
1738:
1706:
1704:
1702:
1700:
1698:
1696:
1750:Internet Encyclopedia of Philosophy.
1536:is a consequence of any superset of
483:
5695:Quantificational variability effect
5362:Formal semantics (natural language)
2521:Analytic and synthetic propositions
2392:Formal semantics (natural language)
2292:Indiana Philosophy Ontology Project
2280:Internet Encyclopedia of Philosophy
2266:Stanford Encyclopedia of Philosophy
2115:, New York: Automatic Press / VIP,
24:
4976:
4751:
4585:
2165:A Companion to Philosophical Logic
2061:The Concept of Logical Consequence
1933:Mathematical logic and foundations
1735:
1693:
1543:
1503:
1399:
1341:
1272:
1214:
1151:
1089:
1042:
980:
926:
897:
888:
848:
826:
804:
779:
683:
674:
654:
609:
583:
558:
249:
211:
183:
155:
25:
6090:
2241:
2181:Logic, Semantics, Metamathematics
1838:Cambridge University Press, 371p.
1819:Cambridge University Press, 136p.
1458:Non-monotonic logical consequence
962:
817:if and only if there is no model
5315:
5304:
4998:
4815:{\displaystyle \leftrightarrow }
4604:
4512:
2733:
2009:The Logical Basis of Metaphysics
1801:Harvard University Press, p.82ff
2179:Reprinted in Tarski, A., 1983.
1889:
1877:
1871:Introduction to Metamathematics
1848:FOLDOC: "syntactic consequence"
1035:that if all of the elements of
790:{\displaystyle {\mathcal {FS}}}
620:{\displaystyle {\mathcal {FS}}}
569:{\displaystyle {\mathcal {FS}}}
5777:Combinatory categorial grammar
4856:
4809:
4685:
4656:
4631:
1841:
1822:
1804:
1786:
1719:
834:{\displaystyle {\mathcal {I}}}
219:{\displaystyle {\mathcal {L}}}
191:{\displaystyle {\mathcal {L}}}
163:{\displaystyle {\mathcal {L}}}
13:
1:
5555:Antecedent-contained deletion
4891:{\displaystyle \nrightarrow }
4473:History of mathematical logic
1956:Brown, Frank Markham (2003),
1950:, Stanford: CSLI Publications
1835:Cambridge companion to Carnap
1710:Beall, JC and Restall, Greg,
1140:is true if and only if it is
1031:is true if and only if it is
4916:{\displaystyle \nleftarrow }
4691:{\displaystyle \rightarrow }
4398:Primitive recursive function
2234:A definition of 'implicant'
2012:, Harvard University Press,
1909:
456:is a logical consequence of
7:
4862:{\displaystyle \downarrow }
4662:{\displaystyle \leftarrow }
2312:Encyclopedia of Mathematics
2041:Edgington, Dorothy (2006),
2027:Edgington, Dorothy (2001),
1965:Davis, Martin, ed. (1965),
1572:
1319:Therefore, Kermit is green.
1144:for all of the elements of
333:s brother's son, therefore
170:, either by constructing a
10:
6095:
5436:Syntax–semantics interface
3462:Schröder–Bernstein theorem
3189:Monadic predicate calculus
2848:Foundations of mathematics
2187:. Originally published in
2129:Planchette, P. A. (2001),
2063:, Harvard University Press
2051:in Edward N. Zalta (ed.),
1982:. Papers include those by
1461:
881:is false. This is denoted
770:within some formal system
739:
596:of formulas if there is a
511:
81:one or more statements. A
50:
43:
36:
29:
5965:
5928:Question under discussion
5878:Conversational scoreboard
5855:
5759:
5752:
5655:Intersective modification
5640:Homogeneity (linguistics)
5547:
5456:
5449:
5368:
5301:
5052:
4995:
4958:
4838:
4733:
4637:{\displaystyle \uparrow }
4613:
4602:
4567:
4508:
4495:Philosophy of mathematics
4444:Automated theorem proving
4426:
4321:
4153:
4046:
3898:
3615:
3591:
3569:Von Neumann–Bernays–Gödel
3514:
3408:
3312:
3210:
3201:
3128:
3063:
2969:
2891:
2808:
2728:
2688:
2660:
2653:
2605:Necessity and sufficiency
2508:
2473:
2425:
2379:
2361:
2353:
2199:Ryszard Wójcicki (1988).
2059:Etchemendy, John (1990),
2043:"Indicative Conditionals"
2006:Dummett, Michael (1991),
1971:, New York: Raven Press,
1948:Language, Proof and Logic
1926:Augusto, Luis M. (2017),
1772:. Springer. p. 292.
5983:Distributional semantics
2081:The Philosophical Review
2069:Goble, Lou, ed. (2001),
1766:Maria Luisa Dalla Chiara
1726:Quine, Willard Van Orman
1686:
1660:Tautological consequence
1645:Sole sufficient operator
1580:Abstract algebraic logic
841:in which all members of
476:cannot be influenced by
126:models of interpretation
5978:Computational semantics
5720:Subsective modification
5524:Propositional attitudes
4901:Converse nonimplication
4145:Self-verifying theories
3966:Tarski's axiomatization
2917:Tarski's undefinability
2912:incompleteness theorems
2269:(Winter 2016 ed.).
2185:Oxford University Press
1590:Boolean algebra (logic)
1549:{\displaystyle \Gamma }
1509:{\displaystyle \Gamma }
1405:{\displaystyle \Gamma }
1366:{\displaystyle \vdash }
1347:{\displaystyle \Gamma }
1278:{\displaystyle \Gamma }
1239:{\displaystyle \vdash }
1220:{\displaystyle \Gamma }
1157:{\displaystyle \Gamma }
1114:{\displaystyle \vdash }
1095:{\displaystyle \Gamma }
1048:{\displaystyle \Gamma }
1005:{\displaystyle \vdash }
986:{\displaystyle \Gamma }
932:{\displaystyle \Gamma }
854:{\displaystyle \Gamma }
810:{\displaystyle \Gamma }
797:of a set of statements
718:{\displaystyle \vdash }
705:. The turnstile symbol
660:{\displaystyle \Gamma }
589:{\displaystyle \Gamma }
376:follows logically from
112:Logical consequence is
32:Entail (disambiguation)
6054:Propositional calculus
6008:Philosophy of language
5650:Inalienable possession
5630:Free choice inferences
5625:Faultless disagreement
5396:Generalized quantifier
5322:Mathematics portal
4983:
4946:
4945:{\displaystyle \land }
4917:
4892:
4863:
4816:
4787:
4758:
4721:
4692:
4663:
4638:
4592:
4519:Mathematics portal
4130:Proof of impossibility
3778:propositional variable
3088:Propositional calculus
2163:in D. Jacquette, ed.,
1798:philosophy of language
1640:Propositional calculus
1550:
1530:
1510:
1490:
1437:Warrant-based accounts
1426:
1406:
1386:
1367:
1348:
1299:
1279:
1259:
1240:
1221:
1178:
1158:
1134:
1115:
1096:
1069:
1049:
1025:
1006:
987:
953:
933:
913:
875:
855:
835:
811:
791:
760:
732:of the formal system.
719:
699:
661:
641:
621:
590:
570:
536:
470:
450:
430:
410:
390:
370:
226:. The Polish logician
220:
192:
164:
99:philosophical analysis
5908:Plural quantification
5802:Inquisitive semantics
5767:Alternative semantics
5311:Philosophy portal
5005:Philosophy portal
4984:
4982:{\displaystyle \bot }
4947:
4918:
4893:
4864:
4817:
4788:
4759:
4757:{\displaystyle \neg }
4722:
4720:{\displaystyle \lor }
4693:
4664:
4639:
4593:
4591:{\displaystyle \top }
4388:Kolmogorov complexity
4341:Computably enumerable
4241:Model complete theory
4033:Principia Mathematica
3093:Propositional formula
2922:Banach–Tarski paradox
2740:Philosophy portal
2275:"Logical consequence"
2257:"Logical Consequence"
2109:Hendricks, Vincent F.
1828:Creath, Richard, and
1551:
1531:
1511:
1491:
1427:
1407:
1387:
1368:
1349:
1327:Modal-formal accounts
1300:
1280:
1260:
1241:
1222:
1179:
1159:
1135:
1116:
1097:
1070:
1050:
1026:
1007:
988:
954:
934:
914:
876:
856:
836:
812:
792:
761:
720:
700:
662:
642:
622:
591:
571:
544:syntactic consequence
537:
508:Syntactic consequence
471:
451:
431:
411:
391:
371:
221:
193:
165:
5893:Function application
5700:Responsive predicate
5690:Privative adjectives
4973:
4936:
4907:
4882:
4853:
4806:
4777:
4748:
4711:
4682:
4653:
4647:Converse implication
4628:
4582:
4336:Church–Turing thesis
4323:Computability theory
3532:continuum hypothesis
3050:Square of opposition
2908:Gödel's completeness
2134:in Goble, Lou, ed.,
2033:in Lou Goble (ed.),
1760:Kosta Dosen (1996).
1540:
1520:
1500:
1496:is a consequence of
1480:
1416:
1396:
1376:
1357:
1338:
1313:All frogs are green.
1289:
1269:
1249:
1230:
1211:
1198:universal quantifier
1168:
1148:
1124:
1105:
1086:
1059:
1039:
1015:
996:
977:
943:
923:
885:
865:
845:
821:
801:
774:
768:semantic consequence
750:
736:Semantic consequence
709:
671:
651:
631:
604:
580:
553:
526:
460:
440:
420:
400:
380:
360:
356:If it is known that
316:material consequence
206:
178:
150:
89:is one in which the
46:Material conditional
18:Consequence relation
6064:Deductive reasoning
6044:Philosophical logic
6039:Logical consequence
5973:Cognitive semantics
5888:Existential closure
5832:Situation semantics
5735:Temperature paradox
5705:Rising declaratives
5670:Modal subordination
5645:Hurford disjunction
5605:Discourse relations
4561:logical connectives
4490:Mathematical object
4381:P versus NP problem
4346:Computable function
4140:Reverse mathematics
4066:Logical consequence
3943:primitive recursive
3938:elementary function
3711:Free/bound variable
3564:Tarski–Grothendieck
3083:Logical connectives
3013:Logical equivalence
2863:Logical consequence
2402:Philosophy of logic
2297:Logical consequence
2288:Logical consequence
2131:Logical Consequence
1900:Logical consequence
1747:Logical Consequence
1730:Philosophy of Logic
1713:Logical Consequence
1635:Probabilistic logic
1615:Deductive reasoning
1464:Non-monotonic logic
1194:logical possibility
478:empirical knowledge
103:philosophical logic
93:is entailed by the
65:) is a fundamental
59:Logical consequence
6018:Semantics of logic
5943:Strict conditional
5918:Quantifier raising
5883:Downward entailing
5863:Autonomy of syntax
5792:Generative grammar
5772:Categorial grammar
5710:Scalar implicature
5615:Epistemic modality
5590:De dicto and de re
4979:
4942:
4913:
4888:
4859:
4812:
4783:
4754:
4717:
4688:
4659:
4634:
4618:Alternative denial
4588:
4288:Transfer principle
4251:Semantics of logic
4236:Categorical theory
4212:Non-standard model
3726:Logical connective
2853:Information theory
2802:Mathematical logic
2701:Rules of inference
2670:Mathematical logic
2412:Semantics of logic
2228:2014-10-21 at the
1853:2013-04-03 at the
1816:and Logical Theory
1670:Turnstile (symbol)
1650:Strict conditional
1546:
1526:
1506:
1486:
1422:
1402:
1382:
1363:
1344:
1305:is false (untrue).
1295:
1275:
1255:
1236:
1217:
1174:
1154:
1130:
1111:
1092:
1065:
1045:
1021:
1002:
983:
949:
929:
909:
871:
851:
831:
807:
787:
756:
715:
695:
667:. This is denoted
657:
637:
617:
586:
566:
532:
466:
446:
426:
406:
386:
366:
240:empirical evidence
216:
200:intended semantics
188:
160:
6079:Binary operations
6069:Concepts in logic
6026:
6025:
5998:Logic translation
5961:
5960:
5953:Universal grinder
5938:Squiggle operator
5898:Meaning postulate
5837:Supervaluationism
5807:Intensional logic
5787:Dynamic semantics
5748:
5747:
5580:Crossover effects
5529:Tense–aspect–mood
5509:Lexical semantics
5328:
5327:
5296:
5295:
5011:
5010:
4526:
4525:
4458:Abstract category
4261:Theories of truth
4071:Rule of inference
4061:Natural deduction
4042:
4041:
3587:
3586:
3292:Cartesian product
3197:
3196:
3103:Many-valued logic
3078:Boolean functions
2961:Russell's paradox
2936:diagonal argument
2833:First-order logic
2768:
2767:
2724:
2723:
2558:Deductive closure
2504:
2503:
2443:Critical thinking
2214:978-90-277-2785-5
2122:978-87-991013-7-5
1830:Friedman, Michael
1779:978-0-7923-4383-7
1744:McKeon, Matthew,
1655:Tautology (logic)
1529:{\displaystyle A}
1489:{\displaystyle A}
1425:{\displaystyle A}
1385:{\displaystyle A}
1316:Kermit is a frog.
1298:{\displaystyle A}
1258:{\displaystyle A}
1190:logical necessity
1177:{\displaystyle A}
1133:{\displaystyle A}
1068:{\displaystyle A}
1024:{\displaystyle A}
952:{\displaystyle A}
874:{\displaystyle A}
759:{\displaystyle A}
640:{\displaystyle A}
535:{\displaystyle A}
484:Proofs and models
469:{\displaystyle P}
449:{\displaystyle Q}
429:{\displaystyle Q}
409:{\displaystyle P}
389:{\displaystyle P}
369:{\displaystyle Q}
16:(Redirected from
6086:
6003:Linguistics wars
5933:Semantic parsing
5822:Montague grammar
5757:
5756:
5600:Deontic modality
5454:
5453:
5441:Truth conditions
5376:Compositionality
5369:Central concepts
5355:
5348:
5341:
5332:
5331:
5320:
5319:
5309:
5308:
5307:
5239:
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5068:
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5024:
5015:
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5002:
5001:
4988:
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4897:
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4868:
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4792:
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4784:
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4755:
4726:
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4666:
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4641:
4640:
4635:
4608:
4597:
4595:
4594:
4589:
4553:
4546:
4539:
4530:
4529:
4517:
4516:
4468:History of logic
4463:Category of sets
4356:Decision problem
4135:Ordinal analysis
4076:Sequent calculus
3974:Boolean algebras
3914:
3913:
3888:
3859:logical/constant
3613:
3612:
3599:
3522:Zermelo–Fraenkel
3273:Set operations:
3208:
3207:
3145:
2976:
2975:
2956:Löwenheim–Skolem
2843:Formal semantics
2795:
2788:
2781:
2772:
2771:
2738:
2737:
2736:
2658:
2657:
2423:
2422:
2387:Computer science
2348:
2341:
2334:
2325:
2324:
2320:
2284:
2270:
2261:Zalta, Edward N.
2218:
2206:
2178:
2162:
2156:Shapiro, Stewart
2150:
2147:Methods of Logic
2133:
2125:
2103:
2074:
2064:
2050:
2032:
2022:
1981:
1960:
1951:
1944:Etchemendy, John
1930:
1921:
1903:
1896:Etchemendy, John
1893:
1887:
1884:Hunter, Geoffrey
1881:
1875:
1866:
1857:
1845:
1839:
1826:
1820:
1808:
1802:
1793:Dummett, Michael
1790:
1784:
1783:
1757:
1751:
1742:
1733:
1723:
1717:
1708:
1675:Double turnstile
1600:Boolean function
1555:
1553:
1552:
1547:
1535:
1533:
1532:
1527:
1515:
1513:
1512:
1507:
1495:
1493:
1492:
1487:
1431:
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1423:
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1391:
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1372:
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1369:
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1120:
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938:
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541:
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455:
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387:
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343:
332:
225:
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217:
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197:
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172:deductive system
169:
167:
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161:
159:
158:
53:Double turnstile
21:
6094:
6093:
6089:
6088:
6087:
6085:
6084:
6083:
6029:
6028:
6027:
6022:
5957:
5851:
5812:Lambda calculus
5744:
5715:Sloppy identity
5675:Opaque contexts
5610:Donkey anaphora
5575:Counterfactuals
5543:
5445:
5364:
5359:
5329:
5324:
5314:
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5305:
5303:
5297:
5292:
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5209:
5205:
5197:
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5175:
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5159:
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5147:
5139:
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5133:
5125:
5122:
5119:
5111:
5107:
5102:
5094:
5090:
5085:
5077:
5073:
5064:
5048:
5046:logical symbols
5042:
5012:
5007:
4999:
4997:
4991:
4974:
4971:
4970:
4954:
4937:
4934:
4933:
4908:
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4904:
4883:
4880:
4879:
4854:
4851:
4850:
4834:
4807:
4804:
4803:
4778:
4775:
4774:
4749:
4746:
4745:
4729:
4712:
4709:
4708:
4683:
4680:
4679:
4654:
4651:
4650:
4629:
4626:
4625:
4609:
4600:
4583:
4580:
4579:
4563:
4557:
4527:
4522:
4511:
4504:
4449:Category theory
4439:Algebraic logic
4422:
4393:Lambda calculus
4331:Church encoding
4317:
4293:Truth predicate
4149:
4115:Complete theory
4038:
3907:
3903:
3899:
3894:
3886:
3606: and
3602:
3597:
3583:
3559:New Foundations
3527:axiom of choice
3510:
3472:Gödel numbering
3412: and
3404:
3308:
3193:
3143:
3124:
3073:Boolean algebra
3059:
3023:Equiconsistency
2988:Classical logic
2965:
2946:Halting problem
2934: and
2910: and
2898: and
2897:
2892:Theorems (
2887:
2804:
2799:
2769:
2764:
2734:
2732:
2720:
2684:
2675:Boolean algebra
2649:
2500:
2491:Metamathematics
2469:
2421:
2375:
2357:
2352:
2305:
2273:
2244:
2230:Wayback Machine
2215:
2123:
2093:10.2307/2998398
2020:
1979:
1912:
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1906:
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1855:Wayback Machine
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1470:
1460:
1452:Michael Dummett
1439:
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1397:
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1355:
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1246:
1231:
1228:
1227:
1212:
1209:
1208:
1202:possible worlds
1169:
1166:
1165:
1164:to be true and
1149:
1146:
1145:
1125:
1122:
1121:
1106:
1103:
1102:
1087:
1084:
1083:
1060:
1057:
1056:
1055:are true, then
1040:
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1016:
1013:
1012:
997:
994:
993:
978:
975:
974:
965:
944:
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802:
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751:
748:
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738:
710:
707:
706:
682:
681:
677:
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669:
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652:
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632:
629:
628:
608:
607:
605:
602:
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581:
578:
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486:
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418:
417:
401:
398:
397:
381:
378:
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361:
358:
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341:
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294:Therefore, all
268:inference rules
252:
250:Formal accounts
210:
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49:
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35:
28:
23:
22:
15:
12:
11:
5:
6092:
6082:
6081:
6076:
6074:Syntax (logic)
6071:
6066:
6061:
6059:Semantic units
6056:
6051:
6046:
6041:
6024:
6023:
6021:
6020:
6015:
6010:
6005:
6000:
5995:
5993:Inferentialism
5990:
5988:Formal grammar
5985:
5980:
5975:
5969:
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5925:
5920:
5915:
5913:Possible world
5910:
5905:
5900:
5895:
5890:
5885:
5880:
5875:
5870:
5865:
5859:
5857:
5853:
5852:
5850:
5849:
5844:
5839:
5834:
5829:
5824:
5819:
5814:
5809:
5804:
5799:
5797:Glue semantics
5794:
5789:
5784:
5779:
5774:
5769:
5763:
5761:
5760:Formal systems
5754:
5750:
5749:
5746:
5745:
5743:
5742:
5737:
5732:
5727:
5722:
5717:
5712:
5707:
5702:
5697:
5692:
5687:
5685:Polarity items
5682:
5677:
5672:
5667:
5662:
5657:
5652:
5647:
5642:
5637:
5632:
5627:
5622:
5617:
5612:
5607:
5602:
5597:
5592:
5587:
5582:
5577:
5572:
5570:Conservativity
5567:
5562:
5557:
5551:
5549:
5545:
5544:
5542:
5541:
5536:
5534:Quantification
5531:
5526:
5521:
5516:
5511:
5506:
5501:
5496:
5491:
5486:
5481:
5476:
5471:
5466:
5460:
5458:
5451:
5447:
5446:
5444:
5443:
5438:
5433:
5428:
5423:
5418:
5413:
5411:Presupposition
5408:
5403:
5398:
5393:
5388:
5383:
5378:
5372:
5370:
5366:
5365:
5358:
5357:
5350:
5343:
5335:
5326:
5325:
5302:
5299:
5298:
5294:
5293:
5289:quantification
5285:
5280:
5279:
5277:
5273:quantification
5269:
5264:
5263:
5261:
5252:
5251:
5249:
5230:
5229:
5227:
5213:
5212:
5210:
5201:
5200:
5198:
5179:
5178:
5176:
5167:
5166:
5164:
5155:
5154:
5152:
5143:
5142:
5140:
5129:
5128:
5126:
5115:
5114:
5112:
5098:
5097:
5095:
5081:
5080:
5078:
5059:
5058:
5053:
5050:
5049:
5041:
5040:
5033:
5026:
5018:
5009:
5008:
4996:
4993:
4992:
4990:
4989:
4978:
4959:
4956:
4955:
4953:
4952:
4941:
4923:
4912:
4898:
4887:
4872:Nonimplication
4869:
4858:
4839:
4836:
4835:
4833:
4832:
4829:Digital buffer
4822:
4811:
4793:
4782:
4764:
4753:
4734:
4731:
4730:
4728:
4727:
4716:
4698:
4687:
4669:
4658:
4644:
4633:
4614:
4611:
4610:
4603:
4601:
4599:
4598:
4587:
4568:
4565:
4564:
4556:
4555:
4548:
4541:
4533:
4524:
4523:
4509:
4506:
4505:
4503:
4502:
4497:
4492:
4487:
4482:
4481:
4480:
4470:
4465:
4460:
4451:
4446:
4441:
4436:
4434:Abstract logic
4430:
4428:
4424:
4423:
4421:
4420:
4415:
4413:Turing machine
4410:
4405:
4400:
4395:
4390:
4385:
4384:
4383:
4378:
4373:
4368:
4363:
4353:
4351:Computable set
4348:
4343:
4338:
4333:
4327:
4325:
4319:
4318:
4316:
4315:
4310:
4305:
4300:
4295:
4290:
4285:
4280:
4279:
4278:
4273:
4268:
4258:
4253:
4248:
4246:Satisfiability
4243:
4238:
4233:
4232:
4231:
4221:
4220:
4219:
4209:
4208:
4207:
4202:
4197:
4192:
4187:
4177:
4176:
4175:
4170:
4163:Interpretation
4159:
4157:
4151:
4150:
4148:
4147:
4142:
4137:
4132:
4127:
4117:
4112:
4111:
4110:
4109:
4108:
4098:
4093:
4083:
4078:
4073:
4068:
4063:
4058:
4052:
4050:
4044:
4043:
4040:
4039:
4037:
4036:
4028:
4027:
4026:
4025:
4020:
4019:
4018:
4013:
4008:
3988:
3987:
3986:
3984:minimal axioms
3981:
3970:
3969:
3968:
3957:
3956:
3955:
3950:
3945:
3940:
3935:
3930:
3917:
3915:
3896:
3895:
3893:
3892:
3891:
3890:
3878:
3873:
3872:
3871:
3866:
3861:
3856:
3846:
3841:
3836:
3831:
3830:
3829:
3824:
3814:
3813:
3812:
3807:
3802:
3797:
3787:
3782:
3781:
3780:
3775:
3770:
3760:
3759:
3758:
3753:
3748:
3743:
3738:
3733:
3723:
3718:
3713:
3708:
3707:
3706:
3701:
3696:
3691:
3681:
3676:
3674:Formation rule
3671:
3666:
3665:
3664:
3659:
3649:
3648:
3647:
3637:
3632:
3627:
3622:
3616:
3610:
3593:Formal systems
3589:
3588:
3585:
3584:
3582:
3581:
3576:
3571:
3566:
3561:
3556:
3551:
3546:
3541:
3536:
3535:
3534:
3529:
3518:
3516:
3512:
3511:
3509:
3508:
3507:
3506:
3496:
3491:
3490:
3489:
3482:Large cardinal
3479:
3474:
3469:
3464:
3459:
3445:
3444:
3443:
3438:
3433:
3418:
3416:
3406:
3405:
3403:
3402:
3401:
3400:
3395:
3390:
3380:
3375:
3370:
3365:
3360:
3355:
3350:
3345:
3340:
3335:
3330:
3325:
3319:
3317:
3310:
3309:
3307:
3306:
3305:
3304:
3299:
3294:
3289:
3284:
3279:
3271:
3270:
3269:
3264:
3254:
3249:
3247:Extensionality
3244:
3242:Ordinal number
3239:
3229:
3224:
3223:
3222:
3211:
3205:
3199:
3198:
3195:
3194:
3192:
3191:
3186:
3181:
3176:
3171:
3166:
3161:
3160:
3159:
3149:
3148:
3147:
3134:
3132:
3126:
3125:
3123:
3122:
3121:
3120:
3115:
3110:
3100:
3095:
3090:
3085:
3080:
3075:
3069:
3067:
3061:
3060:
3058:
3057:
3052:
3047:
3042:
3037:
3032:
3027:
3026:
3025:
3015:
3010:
3005:
3000:
2995:
2990:
2984:
2982:
2973:
2967:
2966:
2964:
2963:
2958:
2953:
2948:
2943:
2938:
2926:Cantor's
2924:
2919:
2914:
2904:
2902:
2889:
2888:
2886:
2885:
2880:
2875:
2870:
2865:
2860:
2855:
2850:
2845:
2840:
2835:
2830:
2825:
2824:
2823:
2812:
2810:
2806:
2805:
2798:
2797:
2790:
2783:
2775:
2766:
2765:
2763:
2762:
2757:
2747:
2742:
2729:
2726:
2725:
2722:
2721:
2719:
2718:
2713:
2708:
2703:
2698:
2692:
2690:
2686:
2685:
2683:
2682:
2677:
2672:
2666:
2664:
2655:
2651:
2650:
2648:
2647:
2642:
2637:
2632:
2627:
2622:
2617:
2612:
2607:
2602:
2597:
2592:
2587:
2582:
2581:
2580:
2570:
2565:
2560:
2555:
2550:
2549:
2548:
2543:
2533:
2528:
2523:
2518:
2512:
2510:
2506:
2505:
2502:
2501:
2499:
2498:
2493:
2488:
2483:
2477:
2475:
2471:
2470:
2468:
2467:
2462:
2457:
2452:
2451:
2450:
2445:
2435:
2429:
2427:
2420:
2419:
2414:
2409:
2404:
2399:
2394:
2389:
2383:
2381:
2377:
2376:
2374:
2373:
2368:
2362:
2359:
2358:
2351:
2350:
2343:
2336:
2328:
2322:
2321:
2303:
2294:
2285:
2271:
2255:(2013-11-19).
2243:
2242:External links
2240:
2239:
2238:
2232:
2219:
2213:
2196:
2172:Tarski, Alfred
2168:
2152:
2139:
2126:
2121:
2105:
2087:(3): 365–409,
2076:
2066:
2056:
2038:
2024:
2018:
2003:
1977:
1962:
1953:
1936:
1923:
1911:
1908:
1905:
1904:
1888:
1876:
1868:S. C. Kleene,
1858:
1840:
1821:
1811:Lear, Jonathan
1803:
1785:
1778:
1752:
1734:
1718:
1691:
1690:
1688:
1685:
1683:
1682:
1677:
1672:
1667:
1665:Therefore sign
1662:
1657:
1652:
1647:
1642:
1637:
1632:
1627:
1622:
1617:
1612:
1607:
1602:
1597:
1595:Boolean domain
1592:
1587:
1582:
1576:
1574:
1571:
1570:
1569:
1562:
1561:
1545:
1525:
1505:
1485:
1459:
1456:
1438:
1435:
1434:
1433:
1421:
1401:
1381:
1362:
1343:
1328:
1325:
1321:
1320:
1317:
1314:
1307:
1306:
1294:
1274:
1254:
1235:
1216:
1186:
1185:
1173:
1153:
1129:
1110:
1091:
1077:
1076:
1064:
1044:
1020:
1001:
982:
964:
963:Modal accounts
961:
948:
928:
908:
902:
899:
894:
890:
870:
850:
828:
806:
784:
781:
755:
737:
734:
730:interpretation
714:
694:
688:
685:
680:
676:
656:
636:
614:
611:
585:
563:
560:
531:
509:
506:
485:
482:
465:
445:
425:
405:
385:
365:
353:
350:
304:
303:
292:
282:
251:
248:
213:
185:
157:
134:if and only if
39:Therefore sign
26:
9:
6:
4:
3:
2:
6091:
6080:
6077:
6075:
6072:
6070:
6067:
6065:
6062:
6060:
6057:
6055:
6052:
6050:
6047:
6045:
6042:
6040:
6037:
6036:
6034:
6019:
6016:
6014:
6011:
6009:
6006:
6004:
6001:
5999:
5996:
5994:
5991:
5989:
5986:
5984:
5981:
5979:
5976:
5974:
5971:
5970:
5968:
5964:
5954:
5951:
5949:
5946:
5944:
5941:
5939:
5936:
5934:
5931:
5929:
5926:
5924:
5921:
5919:
5916:
5914:
5911:
5909:
5906:
5904:
5901:
5899:
5896:
5894:
5891:
5889:
5886:
5884:
5881:
5879:
5876:
5874:
5871:
5869:
5866:
5864:
5861:
5860:
5858:
5854:
5848:
5845:
5843:
5840:
5838:
5835:
5833:
5830:
5828:
5825:
5823:
5820:
5818:
5815:
5813:
5810:
5808:
5805:
5803:
5800:
5798:
5795:
5793:
5790:
5788:
5785:
5783:
5780:
5778:
5775:
5773:
5770:
5768:
5765:
5764:
5762:
5758:
5755:
5751:
5741:
5738:
5736:
5733:
5731:
5728:
5726:
5723:
5721:
5718:
5716:
5713:
5711:
5708:
5706:
5703:
5701:
5698:
5696:
5693:
5691:
5688:
5686:
5683:
5681:
5680:Performatives
5678:
5676:
5673:
5671:
5668:
5666:
5663:
5661:
5660:Logophoricity
5658:
5656:
5653:
5651:
5648:
5646:
5643:
5641:
5638:
5636:
5633:
5631:
5628:
5626:
5623:
5621:
5618:
5616:
5613:
5611:
5608:
5606:
5603:
5601:
5598:
5596:
5593:
5591:
5588:
5586:
5583:
5581:
5578:
5576:
5573:
5571:
5568:
5566:
5563:
5561:
5558:
5556:
5553:
5552:
5550:
5546:
5540:
5537:
5535:
5532:
5530:
5527:
5525:
5522:
5520:
5517:
5515:
5512:
5510:
5507:
5505:
5502:
5500:
5497:
5495:
5494:Evidentiality
5492:
5490:
5487:
5485:
5482:
5480:
5477:
5475:
5472:
5470:
5467:
5465:
5462:
5461:
5459:
5455:
5452:
5448:
5442:
5439:
5437:
5434:
5432:
5429:
5427:
5424:
5422:
5419:
5417:
5414:
5412:
5409:
5407:
5404:
5402:
5399:
5397:
5394:
5392:
5389:
5387:
5384:
5382:
5379:
5377:
5374:
5373:
5371:
5367:
5363:
5356:
5351:
5349:
5344:
5342:
5337:
5336:
5333:
5323:
5318:
5312:
5300:
5290:
5283:
5278:
5274:
5267:
5262:
5259:
5255:
5250:
5247:
5243:
5238:
5233:
5228:
5225:
5220:
5216:
5211:
5208:
5204:
5199:
5196:
5192:
5187:
5182:
5177:
5174:
5170:
5165:
5162:
5158:
5153:
5150:
5146:
5141:
5138:
5132:
5127:
5124:
5118:
5113:
5110:
5109:contradiction
5105:
5101:
5096:
5093:
5088:
5084:
5079:
5076:
5072:
5067:
5062:
5057:
5056:
5051:
5047:
5039:
5034:
5032:
5027:
5025:
5020:
5019:
5016:
5006:
4994:
4968:
4964:
4963:Contradiction
4961:
4960:
4957:
4939:
4931:
4927:
4924:
4910:
4902:
4899:
4885:
4877:
4873:
4870:
4848:
4844:
4841:
4840:
4837:
4830:
4826:
4823:
4801:
4797:
4796:Biconditional
4794:
4780:
4772:
4768:
4765:
4743:
4739:
4736:
4735:
4732:
4714:
4706:
4702:
4699:
4677:
4673:
4670:
4648:
4645:
4623:
4619:
4616:
4615:
4612:
4607:
4577:
4573:
4570:
4569:
4566:
4562:
4554:
4549:
4547:
4542:
4540:
4535:
4534:
4531:
4521:
4520:
4515:
4507:
4501:
4498:
4496:
4493:
4491:
4488:
4486:
4483:
4479:
4476:
4475:
4474:
4471:
4469:
4466:
4464:
4461:
4459:
4455:
4452:
4450:
4447:
4445:
4442:
4440:
4437:
4435:
4432:
4431:
4429:
4425:
4419:
4416:
4414:
4411:
4409:
4408:Recursive set
4406:
4404:
4401:
4399:
4396:
4394:
4391:
4389:
4386:
4382:
4379:
4377:
4374:
4372:
4369:
4367:
4364:
4362:
4359:
4358:
4357:
4354:
4352:
4349:
4347:
4344:
4342:
4339:
4337:
4334:
4332:
4329:
4328:
4326:
4324:
4320:
4314:
4311:
4309:
4306:
4304:
4301:
4299:
4296:
4294:
4291:
4289:
4286:
4284:
4281:
4277:
4274:
4272:
4269:
4267:
4264:
4263:
4262:
4259:
4257:
4254:
4252:
4249:
4247:
4244:
4242:
4239:
4237:
4234:
4230:
4227:
4226:
4225:
4222:
4218:
4217:of arithmetic
4215:
4214:
4213:
4210:
4206:
4203:
4201:
4198:
4196:
4193:
4191:
4188:
4186:
4183:
4182:
4181:
4178:
4174:
4171:
4169:
4166:
4165:
4164:
4161:
4160:
4158:
4156:
4152:
4146:
4143:
4141:
4138:
4136:
4133:
4131:
4128:
4125:
4124:from ZFC
4121:
4118:
4116:
4113:
4107:
4104:
4103:
4102:
4099:
4097:
4094:
4092:
4089:
4088:
4087:
4084:
4082:
4079:
4077:
4074:
4072:
4069:
4067:
4064:
4062:
4059:
4057:
4054:
4053:
4051:
4049:
4045:
4035:
4034:
4030:
4029:
4024:
4023:non-Euclidean
4021:
4017:
4014:
4012:
4009:
4007:
4006:
4002:
4001:
3999:
3996:
3995:
3993:
3989:
3985:
3982:
3980:
3977:
3976:
3975:
3971:
3967:
3964:
3963:
3962:
3958:
3954:
3951:
3949:
3946:
3944:
3941:
3939:
3936:
3934:
3931:
3929:
3926:
3925:
3923:
3919:
3918:
3916:
3911:
3905:
3900:Example
3897:
3889:
3884:
3883:
3882:
3879:
3877:
3874:
3870:
3867:
3865:
3862:
3860:
3857:
3855:
3852:
3851:
3850:
3847:
3845:
3842:
3840:
3837:
3835:
3832:
3828:
3825:
3823:
3820:
3819:
3818:
3815:
3811:
3808:
3806:
3803:
3801:
3798:
3796:
3793:
3792:
3791:
3788:
3786:
3783:
3779:
3776:
3774:
3771:
3769:
3766:
3765:
3764:
3761:
3757:
3754:
3752:
3749:
3747:
3744:
3742:
3739:
3737:
3734:
3732:
3729:
3728:
3727:
3724:
3722:
3719:
3717:
3714:
3712:
3709:
3705:
3702:
3700:
3697:
3695:
3692:
3690:
3687:
3686:
3685:
3682:
3680:
3677:
3675:
3672:
3670:
3667:
3663:
3660:
3658:
3657:by definition
3655:
3654:
3653:
3650:
3646:
3643:
3642:
3641:
3638:
3636:
3633:
3631:
3628:
3626:
3623:
3621:
3618:
3617:
3614:
3611:
3609:
3605:
3600:
3594:
3590:
3580:
3577:
3575:
3572:
3570:
3567:
3565:
3562:
3560:
3557:
3555:
3552:
3550:
3547:
3545:
3544:Kripke–Platek
3542:
3540:
3537:
3533:
3530:
3528:
3525:
3524:
3523:
3520:
3519:
3517:
3513:
3505:
3502:
3501:
3500:
3497:
3495:
3492:
3488:
3485:
3484:
3483:
3480:
3478:
3475:
3473:
3470:
3468:
3465:
3463:
3460:
3457:
3453:
3449:
3446:
3442:
3439:
3437:
3434:
3432:
3429:
3428:
3427:
3423:
3420:
3419:
3417:
3415:
3411:
3407:
3399:
3396:
3394:
3391:
3389:
3388:constructible
3386:
3385:
3384:
3381:
3379:
3376:
3374:
3371:
3369:
3366:
3364:
3361:
3359:
3356:
3354:
3351:
3349:
3346:
3344:
3341:
3339:
3336:
3334:
3331:
3329:
3326:
3324:
3321:
3320:
3318:
3316:
3311:
3303:
3300:
3298:
3295:
3293:
3290:
3288:
3285:
3283:
3280:
3278:
3275:
3274:
3272:
3268:
3265:
3263:
3260:
3259:
3258:
3255:
3253:
3250:
3248:
3245:
3243:
3240:
3238:
3234:
3230:
3228:
3225:
3221:
3218:
3217:
3216:
3213:
3212:
3209:
3206:
3204:
3200:
3190:
3187:
3185:
3182:
3180:
3177:
3175:
3172:
3170:
3167:
3165:
3162:
3158:
3155:
3154:
3153:
3150:
3146:
3141:
3140:
3139:
3136:
3135:
3133:
3131:
3127:
3119:
3116:
3114:
3111:
3109:
3106:
3105:
3104:
3101:
3099:
3096:
3094:
3091:
3089:
3086:
3084:
3081:
3079:
3076:
3074:
3071:
3070:
3068:
3066:
3065:Propositional
3062:
3056:
3053:
3051:
3048:
3046:
3043:
3041:
3038:
3036:
3033:
3031:
3028:
3024:
3021:
3020:
3019:
3016:
3014:
3011:
3009:
3006:
3004:
3001:
2999:
2996:
2994:
2993:Logical truth
2991:
2989:
2986:
2985:
2983:
2981:
2977:
2974:
2972:
2968:
2962:
2959:
2957:
2954:
2952:
2949:
2947:
2944:
2942:
2939:
2937:
2933:
2929:
2925:
2923:
2920:
2918:
2915:
2913:
2909:
2906:
2905:
2903:
2901:
2895:
2890:
2884:
2881:
2879:
2876:
2874:
2871:
2869:
2866:
2864:
2861:
2859:
2856:
2854:
2851:
2849:
2846:
2844:
2841:
2839:
2836:
2834:
2831:
2829:
2826:
2822:
2819:
2818:
2817:
2814:
2813:
2811:
2807:
2803:
2796:
2791:
2789:
2784:
2782:
2777:
2776:
2773:
2761:
2758:
2755:
2751:
2748:
2746:
2743:
2741:
2731:
2730:
2727:
2717:
2716:Logic symbols
2714:
2712:
2709:
2707:
2704:
2702:
2699:
2697:
2694:
2693:
2691:
2687:
2681:
2678:
2676:
2673:
2671:
2668:
2667:
2665:
2663:
2659:
2656:
2652:
2646:
2643:
2641:
2638:
2636:
2633:
2631:
2628:
2626:
2623:
2621:
2618:
2616:
2613:
2611:
2608:
2606:
2603:
2601:
2598:
2596:
2595:Logical truth
2593:
2591:
2588:
2586:
2583:
2579:
2576:
2575:
2574:
2571:
2569:
2566:
2564:
2561:
2559:
2556:
2554:
2551:
2547:
2544:
2542:
2539:
2538:
2537:
2536:Contradiction
2534:
2532:
2529:
2527:
2524:
2522:
2519:
2517:
2514:
2513:
2511:
2507:
2497:
2494:
2492:
2489:
2487:
2484:
2482:
2481:Argumentation
2479:
2478:
2476:
2472:
2466:
2465:Philosophical
2463:
2461:
2460:Non-classical
2458:
2456:
2453:
2449:
2446:
2444:
2441:
2440:
2439:
2436:
2434:
2431:
2430:
2428:
2424:
2418:
2415:
2413:
2410:
2408:
2405:
2403:
2400:
2398:
2395:
2393:
2390:
2388:
2385:
2384:
2382:
2378:
2372:
2369:
2367:
2364:
2363:
2360:
2356:
2349:
2344:
2342:
2337:
2335:
2330:
2329:
2326:
2318:
2314:
2313:
2308:
2307:"Implication"
2304:
2302:
2298:
2295:
2293:
2289:
2286:
2282:
2281:
2276:
2272:
2268:
2267:
2262:
2258:
2254:
2253:Restall, Greg
2250:
2246:
2245:
2237:
2233:
2231:
2227:
2224:
2220:
2216:
2210:
2205:
2204:
2197:
2194:
2190:
2186:
2182:
2177:
2173:
2169:
2166:
2161:
2157:
2153:
2148:
2144:
2140:
2137:
2132:
2127:
2124:
2118:
2114:
2110:
2106:
2102:
2098:
2094:
2090:
2086:
2082:
2077:
2072:
2067:
2062:
2057:
2054:
2048:
2044:
2039:
2036:
2030:
2025:
2021:
2019:9780674537866
2015:
2011:
2010:
2004:
2001:
1997:
1993:
1989:
1985:
1980:
1978:9780486432281
1974:
1970:
1969:
1963:
1959:
1954:
1949:
1945:
1941:
1937:
1934:
1929:
1924:
1919:
1914:
1913:
1901:
1897:
1892:
1885:
1880:
1873:
1872:
1865:
1863:
1856:
1852:
1849:
1844:
1837:
1836:
1831:
1825:
1818:
1817:
1812:
1807:
1800:
1799:
1794:
1789:
1781:
1775:
1771:
1767:
1763:
1756:
1749:
1748:
1741:
1739:
1731:
1727:
1722:
1715:
1714:
1707:
1705:
1703:
1701:
1699:
1697:
1692:
1681:
1678:
1676:
1673:
1671:
1668:
1666:
1663:
1661:
1658:
1656:
1653:
1651:
1648:
1646:
1643:
1641:
1638:
1636:
1633:
1631:
1628:
1626:
1625:Logical graph
1623:
1621:
1618:
1616:
1613:
1611:
1608:
1606:
1605:Boolean logic
1603:
1601:
1598:
1596:
1593:
1591:
1588:
1586:
1583:
1581:
1578:
1577:
1567:
1566:
1565:
1559:
1558:
1557:
1523:
1483:
1475:
1469:
1465:
1455:
1453:
1449:
1448:intuitionists
1445:
1419:
1379:
1360:
1334:
1333:
1332:
1324:
1318:
1315:
1312:
1311:
1310:
1292:
1285:are true and
1252:
1233:
1207:
1206:
1205:
1203:
1199:
1195:
1191:
1171:
1143:
1127:
1108:
1082:
1081:
1080:
1062:
1034:
1018:
999:
973:
972:
971:
969:
960:
946:
906:
892:
868:
861:are true and
769:
753:
743:
733:
731:
726:
712:
692:
678:
647:from the set
634:
599:
549:
548:formal system
545:
529:
519:
515:
505:
503:
499:
495:
491:
481:
479:
463:
443:
423:
403:
383:
363:
349:
347:
340:
336:
329:
325:
321:
317:
311:
309:
301:
297:
293:
291:
287:
283:
281:
277:
273:
272:
271:
269:
265:
260:
258:
247:
245:
241:
237:
233:
229:
228:Alfred Tarski
202:for language
201:
198:or by formal
173:
146:
141:
139:
135:
131:
127:
123:
119:
115:
110:
108:
107:logical truth
104:
100:
96:
92:
88:
84:
80:
76:
72:
68:
64:
60:
54:
47:
40:
33:
19:
5948:Type shifter
5923:Quantization
5873:Continuation
5740:Veridicality
5620:Exhaustivity
5585:Cumulativity
5504:Indexicality
5484:Definiteness
5479:Conditionals
5406:Logical form
5236:
5185:
5148:
5065:
4843:Joint denial
4767:Exclusive or
4510:
4308:Ultraproduct
4155:Model theory
4120:Independence
4065:
4056:Formal proof
4048:Proof theory
4031:
4004:
3961:real numbers
3933:second-order
3844:Substitution
3721:Metalanguage
3662:conservative
3635:Axiom schema
3579:Constructive
3549:Morse–Kelley
3515:Set theories
3494:Aleph number
3487:inaccessible
3393:Grothendieck
3277:intersection
3164:Higher-order
3152:Second-order
3098:Truth tables
3055:Venn diagram
2862:
2838:Formal proof
2635:Substitution
2572:
2455:Mathematical
2380:Major fields
2310:
2278:
2264:
2207:. Springer.
2202:
2180:
2175:
2167:. Blackwell.
2164:
2159:
2146:
2138:. Blackwell.
2135:
2130:
2112:
2084:
2080:
2070:
2060:
2052:
2047:Conditionals
2046:
2034:
2029:Conditionals
2028:
2008:
1967:
1957:
1947:
1940:Barwise, Jon
1927:
1917:
1899:
1891:
1879:
1869:
1843:
1834:
1824:
1815:
1806:
1797:
1788:
1769:
1755:
1745:
1729:
1721:
1711:
1630:Peirce's law
1563:
1471:
1440:
1330:
1322:
1308:
1187:
1141:
1078:
1032:
966:
767:
745:
727:
598:formal proof
546:within some
543:
521:
502:model theory
498:proof theory
493:
489:
487:
355:
345:
338:
334:
327:
323:
320:in all cases
319:
312:
305:
299:
295:
289:
285:
279:
275:
261:
257:logical form
253:
232:logical form
142:
137:
122:formal proof
111:
79:follows from
78:
62:
58:
57:
5868:Context set
5842:Type theory
5725:Subtrigging
5489:Disjunction
5416:Proposition
5287:existential
4926:Conjunction
4876:NIMPLY gate
4701:Disjunction
4672:Implication
4418:Type theory
4366:undecidable
4298:Truth value
4185:equivalence
3864:non-logical
3477:Enumeration
3467:Isomorphism
3414:cardinality
3398:Von Neumann
3363:Ultrafilter
3328:Uncountable
3262:equivalence
3179:Quantifiers
3169:Fixed-point
3138:First-order
3018:Consistency
3003:Proposition
2980:Traditional
2951:Lindström's
2941:Compactness
2883:Type theory
2828:Cardinality
2750:WikiProject
2620:Proposition
2615:Probability
2568:Description
2509:Foundations
2223:Implication
2143:Quine, W.V.
2073:, Blackwell
2031:, Blackwell
1564:but not of
246:component.
6033:Categories
6013:Pragmatics
5665:Mirativity
5431:Speech act
5386:Entailment
5381:Denotation
4676:IMPLY gate
4229:elementary
3922:arithmetic
3790:Quantifier
3768:functional
3640:Expression
3358:Transitive
3302:identities
3287:complement
3220:hereditary
3203:Set theory
2680:Set theory
2578:Linguistic
2573:Entailment
2563:Definition
2531:Consequent
2526:Antecedent
2301:PhilPapers
2183:, 2nd ed.
1918:Entailment
1620:Logic gate
1462:See also:
1142:impossible
746:A formula
740:See also:
522:A formula
512:See also:
348:argument.
91:conclusion
75:statements
63:entailment
6049:Metalogic
5817:Mereology
5753:Formalism
5635:Givenness
5560:Cataphora
5548:Phenomena
5539:Vagueness
5469:Ambiguity
5421:Reference
5401:Intension
5391:Extension
5271:universal
5149:therefore
5137:therefore
5092:tautology
4977:⊥
4940:∧
4911:↚
4886:↛
4857:↓
4825:Statement
4810:↔
4800:XNOR gate
4752:¬
4715:∨
4686:→
4657:←
4632:↑
4622:NAND gate
4586:⊤
4572:Tautology
4500:Supertask
4403:Recursion
4361:decidable
4195:saturated
4173:of models
4096:deductive
4091:axiomatic
4011:Hilbert's
3998:Euclidean
3979:canonical
3902:axiomatic
3834:Signature
3763:Predicate
3652:Extension
3574:Ackermann
3499:Operation
3378:Universal
3368:Recursive
3343:Singleton
3338:Inhabited
3323:Countable
3313:Types of
3297:power set
3267:partition
3184:Predicate
3130:Predicate
3045:Syllogism
3035:Soundness
3008:Inference
2998:Tautology
2900:paradoxes
2711:Fallacies
2706:Paradoxes
2696:Logicians
2630:Statement
2625:Reference
2590:Induction
2553:Deduction
2516:Abduction
2486:Metalogic
2433:Classical
2397:Inference
2317:EMS Press
2249:Beall, Jc
1910:Resources
1610:Causality
1544:Γ
1504:Γ
1474:monotonic
1400:Γ
1361:⊢
1342:Γ
1273:Γ
1234:⊢
1215:Γ
1152:Γ
1109:⊢
1090:Γ
1043:Γ
1033:necessary
1000:⊢
981:Γ
927:Γ
893:⊨
889:Γ
849:Γ
805:Γ
713:⊢
679:⊢
675:Γ
655:Γ
584:Γ
576:of a set
114:necessary
5966:See also
5856:Concepts
5730:Telicity
5565:Coercion
5519:Negation
5514:Modality
5464:Anaphora
5224:superset
5135:entails,
5121:entails,
4930:AND gate
4847:NOR gate
4781:↮
4771:XOR gate
4742:NOT gate
4738:Negation
4485:Logicism
4478:timeline
4454:Concrete
4313:Validity
4283:T-schema
4276:Kripke's
4271:Tarski's
4266:semantic
4256:Strength
4205:submodel
4200:spectrum
4168:function
4016:Tarski's
4005:Elements
3992:geometry
3948:Robinson
3869:variable
3854:function
3827:spectrum
3817:Sentence
3773:variable
3716:Language
3669:Relation
3630:Automata
3620:Alphabet
3604:language
3458:-jection
3436:codomain
3422:Function
3383:Universe
3353:Infinite
3257:Relation
3040:Validity
3030:Argument
2928:theorem,
2745:Category
2645:Validity
2546:Antinomy
2474:Theories
2438:Informal
2236:AllWords
2226:Archived
2174:(1936),
2158:(2002),
2145:(1982),
2111:(2005),
2104:365–409.
1946:(2008),
1851:Archived
1680:Validity
1573:See also
1450:such as
1075:is true.
492:and via
308:instance
236:a priori
145:language
138:personal
130:language
95:premises
87:argument
85:logical
5474:Binding
5240:
5219:implies
5207:implies
5189:
5161:because
5069:
5044:Common
4932:)
4928: (
4878:)
4874: (
4849:)
4845: (
4827: (
4802:)
4798: (
4773:)
4769: (
4744:)
4740: (
4707:)
4705:OR gate
4703: (
4678:)
4674: (
4624:)
4620: (
4559:Common
4427:Related
4224:Diagram
4122: (
4101:Hilbert
4086:Systems
4081:Theorem
3959:of the
3904:systems
3684:Formula
3679:Grammar
3595: (
3539:General
3252:Forcing
3237:Element
3157:Monadic
2932:paradox
2873:Theorem
2809:General
2760:changes
2752: (
2610:Premise
2541:Paradox
2371:History
2366:Outline
2319:, 2001
2290:at the
2263:(ed.).
2101:2998398
1832:(2007)
1813:(1986)
1795:(1993)
1585:Ampheck
1516:, then
1444:warrant
264:schemes
67:concept
5903:Monads
5450:Topics
5234:
5183:
5123:proves
5063:
4969:
4903:
4649:
4578:
4190:finite
3953:Skolem
3906:
3881:Theory
3849:Symbol
3839:String
3822:atomic
3699:ground
3694:closed
3689:atomic
3645:ground
3608:syntax
3504:binary
3431:domain
3348:Finite
3113:finite
2971:Logics
2930:
2878:Theory
2662:topics
2448:Reason
2426:Logics
2417:Syntax
2211:
2193:German
2189:Polish
2119:
2099:
2016:
1998:, and
1996:Kleene
1992:Rosser
1988:Church
1975:
1776:
1184:false.
959:true.
494:models
490:proofs
346:formal
266:using
118:formal
61:(also
5595:De se
5499:Focus
5457:Areas
5426:Scope
5104:false
5071:&
4967:False
4180:Model
3928:Peano
3785:Proof
3625:Arity
3554:Naive
3441:image
3373:Fuzzy
3333:Empty
3282:union
3227:Class
2868:Model
2858:Lemma
2816:Axiom
2689:other
2654:Lists
2640:Truth
2407:Proof
2355:Logic
2259:. In
2097:JSTOR
1984:Gödel
1764:. In
1687:Notes
1200:over
968:Modal
766:is a
542:is a
342:'
331:'
244:modal
83:valid
71:logic
5258:nand
5087:true
4576:True
4303:Type
4106:list
3910:list
3887:list
3876:Term
3810:rank
3704:open
3598:list
3410:Maps
3315:sets
3174:Free
3144:list
2894:list
2821:list
2754:talk
2600:Name
2585:Form
2209:ISBN
2191:and
2117:ISBN
2014:ISBN
2000:Post
1973:ISBN
1774:ISBN
1466:and
1192:and
516:and
298:are
288:are
284:All
278:are
274:All
174:for
124:and
116:and
5847:TTR
5246:iff
5195:not
5075:and
3990:of
3972:of
3920:of
3452:Sur
3426:Map
3233:Ur-
3215:Set
2496:Set
2299:at
2089:doi
2085:106
627:of
600:in
416:or
337:is
326:is
69:in
6035::
5237:or
5186:or
5173:or
5066:or
4376:NP
4000::
3994::
3924::
3601:),
3456:Bi
3448:In
2315:,
2309:,
2277:.
2251:;
2095:,
2083:,
2045:,
1994:,
1990:,
1986:,
1942:;
1898:,
1861:^
1737:^
1728:,
1695:^
1454:.
504:.
132:,
109:.
5354:e
5347:t
5340:v
5282:∃
5266:∀
5254:|
5242:≡
5232:↔
5221:,
5215:⊃
5203:→
5191:~
5181:¬
5169:∨
5157:∵
5145:∴
5131:⊨
5117:⊢
5106:,
5100:⊥
5089:,
5083:⊤
5061:∧
5037:e
5030:t
5023:v
4965:/
4831:)
4574:/
4552:e
4545:t
4538:v
4456:/
4371:P
4126:)
3912:)
3908:(
3805:∀
3800:!
3795:∃
3756:=
3751:↔
3746:→
3741:∧
3736:∨
3731:¬
3454:/
3450:/
3424:/
3235:)
3231:(
3118:∞
3108:3
2896:)
2794:e
2787:t
2780:v
2756:)
2347:e
2340:t
2333:v
2283:.
2217:.
2195:.
2091::
2075:.
2065:.
2055:.
2037:.
2023:.
2002:.
1952:.
1935:.
1922:.
1782:.
1732:.
1524:A
1484:A
1442:"
1420:A
1412:/
1380:A
1293:A
1253:A
1172:A
1128:A
1063:A
1019:A
947:A
907:A
901:S
898:F
869:A
827:I
783:S
780:F
754:A
742:⊨
693:A
687:S
684:F
635:A
613:S
610:F
562:S
559:F
530:A
518:⊢
514:∴
464:P
444:Q
424:Q
404:P
384:P
364:Q
339:Q
335:P
328:Q
324:P
302:.
300:Z
296:X
290:Z
286:Y
280:Y
276:X
212:L
184:L
156:L
55:.
48:.
41:.
34:.
20:)
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