2774:
181:
655:
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353:; "true" corresponds to the maximal element of the algebra, and "false" corresponds to the minimal element. Intermediate elements of the algebra correspond to truth values other than "true" and "false". The principle of bivalence holds only when the Boolean algebra is taken to be the
307:. The adjective "classical" in logic is not related to the use of the adjective "classical" in physics, which has another meaning. In logic, "classical" simply means "standard". Classical logic should also not be confused with
278:. Russell and Whitehead were influenced by Peano (it uses his notation) and Frege and sought to show mathematics was derived from logic. Wittgenstein was influenced by Frege and Russell and initially considered the
101:
logics. In other words, the overwhelming majority of time spent studying classical logic has been spent studying specifically propositional and first-order logic, as opposed to the other forms of classical logic.
210:, for which Aristotle's system was impotent. Frege, who is considered the founder of analytic philosophy, invented it to show all of mathematics was derivable from logic, and make
1153:
1828:
1911:
1052:
455:(2000). Classical Logic. In Stanford Encyclopedia of Philosophy . Stanford: The Metaphysics Research Lab. Retrieved October 28, 2006, from
202:. It has a wider application than Aristotle's logic and is capable of expressing Aristotle's logic as a special case. It explains the
551:
751:
135:. Classical logic was the reconciliation of Aristotle's logic, which dominated most of the last 2000 years, with the propositional
2225:
299:
Classical logic is the standard logic of mathematics. Many mathematical theorems rely on classical rules of inference such as
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While not entailed by the preceding conditions, contemporary discussions of classical logic normally only include
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109:, meaning all of the possible denotations of propositions can be categorized as either true or false.
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470:, (1994). 'Classical vs non-classical logic'. In D.M. Gabbay, C.J. Hogger, and J.A. Robinson, (Eds),
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in terms of mathematical functions. It was also the first logic capable of dealing with the
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8:
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124:
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177:, who also had the modern understanding of existential import, expanded Boole's system.
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238:
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154:
1731:
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314:
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found in classical logic and not in
Aristotle. Though he never questioned Aristotle,
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82:
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2015:
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118:
86:
123:
Classical logic is a 19th and 20th-century innovation. The name does not refer to
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1587:
1389:
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1205:
999:
903:
452:
330:
261:
198:
150:
31:
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2505:
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1933:
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1741:
1617:
1506:
1501:
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1080:
943:
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401:
246:
245:
also pioneered classical logic with the logic of relations. Peirce influenced
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1963:
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believed that a formal system that allows quantification over predicates (
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128:
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1267:
1030:
644:
432:
338:
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132:
46:
Each logical system in this class shares characteristic properties:
2744:
2542:
1990:
1695:
1289:
619:
223:
219:
529:
472:
Handbook of Logic in
Artificial Intelligence and Logic Programming
292:) didn't meet the requirements to be a logic, saying that it was "
2340:
1132:
142:
1884:
1230:
1075:
407:
Logic, language, and meaning, Volume 1: Introduction to Logic
234:
published a variant of propositional logic two years prior.
437:
Proceedings of the
Twentieth World Congress of Philosophy
30:
is the intensively studied and most widely used class of
654:
373:
503:
Warren
Goldfarb, "Deductive Logic", 1st edition, 2003,
349:), the truth values are the elements of an arbitrary
513:
457:http://plato.stanford.edu/entries/logic-classical/
474:, volume 2, chapter 2.6. Oxford University Press.
410:. University of Chicago Press. pp. 156â157.
139:. The two were sometimes seen as irreconcilable.
2790:
488:Deviant Logic, Fuzzy Logic: Beyond the Formalism
430:
230:. The notation Frege used never much caught on.
439:. Vol. 6. Philosophy Documentation Center.
161:'s algebraic reformulation of logic, so-called
400:
377:The Blackwell dictionary of Western philosophy
149:can be seen as foreshadowing classical logic.
1046:
545:
34:. Classical logic has had much influence on
490:. Chicago: The University of Chicago Press.
424:
367:
282:to have solved all problems of philosophy.
1238:
1053:
1039:
552:
538:
394:
324:
179:
2791:
1060:
357:, which has no intermediate elements.
105:Most semantics of classical logic are
1034:
533:
477:
448:
446:
333:, it became apparent that classical
311:, also known as Aristotelian logic.
256:Classical logic reached fruition in
559:
374:Nicholas Bunnin; Jiyuan Yu (2004).
13:
497:
41:
14:
2820:
443:
2772:
653:
516:
380:. Wiley-Blackwell. p. 266.
1020:Tractatus Logico-Philosophicus
625:Problem of multiple generality
461:
275:Tractatus Logico Philosophicus
208:problem of multiple generality
192:, classical logic is found in
165:, was a predecessor of modern
1:
2733:History of mathematical logic
1010:The Principles of Mathematics
360:
2658:Primitive recursive function
706:Commutativity of conjunction
78:Commutativity of conjunction
7:
305:double negation elimination
222:, the doctrine is known as
55:double negation elimination
10:
2825:
1722:SchröderâBernstein theorem
1449:Monadic predicate calculus
1108:Foundations of mathematics
726:Monotonicity of entailment
228:foundations of mathematics
184:Begriffsschrift title page
116:
112:
69:Monotonicity of entailment
2768:
2755:Philosophy of mathematics
2704:Automated theorem proving
2686:
2581:
2413:
2306:
2158:
1875:
1851:
1829:Von NeumannâBernaysâGödel
1774:
1668:
1572:
1470:
1461:
1388:
1323:
1229:
1151:
1068:
992:
896:
851:
805:
739:
698:
662:
651:
615:Idempotency of entailment
567:
431:Akihiro Kanamori (2000).
153:has the understanding of
73:idempotency of entailment
343:Boolean-valued semantics
2405:Self-verifying theories
2226:Tarski's axiomatization
1177:Tarski's undefinability
1172:incompleteness theorems
974:Willard Van Orman Quine
286:Willard Van Orman Quine
60:Law of noncontradiction
2779:Mathematics portal
2390:Proof of impossibility
2038:propositional variable
1348:Propositional calculus
949:Charles Sanders Peirce
792:Hypothetical syllogism
335:propositional calculus
243:Charles Sanders Peirce
185:
171:William Stanley Jevons
64:principle of explosion
51:Law of excluded middle
16:Class of formal logics
2648:Kolmogorov complexity
2601:Computably enumerable
2501:Model complete theory
2293:Principia Mathematica
1353:Propositional formula
1182:BanachâTarski paradox
1015:Principia Mathematica
787:Disjunctive syllogism
772:modus ponendo tollens
325:Generalized semantics
301:disjunctive syllogism
266:Principia Mathematica
183:
169:and classical logic.
147:calculus ratiocinator
2596:ChurchâTuring thesis
2583:Computability theory
1792:continuum hypothesis
1310:Square of opposition
1168:Gödel's completeness
1005:Function and Concept
777:Constructive dilemma
752:Material implication
2750:Mathematical object
2641:P versus NP problem
2606:Computable function
2400:Reverse mathematics
2326:Logical consequence
2203:primitive recursive
2198:elementary function
1971:Free/bound variable
1824:TarskiâGrothendieck
1343:Logical connectives
1273:Logical equivalence
1123:Logical consequence
979:Ludwig Wittgenstein
782:Destructive dilemma
610:Well-formed formula
355:two-element algebra
347:propositional logic
329:With the advent of
319:non-classical logic
270:Ludwig Wittgenstein
125:classical antiquity
36:analytic philosophy
28:FregeâRussell logic
2548:Transfer principle
2511:Semantics of logic
2496:Categorical theory
2472:Non-standard model
1986:Logical connective
1113:Information theory
1062:Mathematical logic
924:Augustus De Morgan
290:higher-order logic
239:Augustus De Morgan
186:
167:mathematical logic
155:existential import
89:is dual to another
2786:
2785:
2718:Abstract category
2521:Theories of truth
2331:Rule of inference
2321:Natural deduction
2302:
2301:
1847:
1846:
1552:Cartesian product
1457:
1456:
1363:Many-valued logic
1338:Boolean functions
1221:Russell's paradox
1196:diagonal argument
1093:First-order logic
1028:
1027:
892:
891:
524:Philosophy portal
417:978-0-226-28085-1
387:978-1-4051-0679-5
127:, which used the
83:De Morgan duality
2816:
2804:History of logic
2777:
2776:
2728:History of logic
2723:Category of sets
2616:Decision problem
2395:Ordinal analysis
2336:Sequent calculus
2234:Boolean algebras
2174:
2173:
2148:
2119:logical/constant
1873:
1872:
1859:
1782:ZermeloâFraenkel
1533:Set operations:
1468:
1467:
1405:
1236:
1235:
1216:LöwenheimâSkolem
1103:Formal semantics
1055:
1048:
1041:
1032:
1031:
964:Henry M. Sheffer
954:Bertrand Russell
919:Richard Dedekind
803:
802:
747:De Morgan's laws
721:Noncontradiction
663:Classical logics
657:
554:
547:
540:
531:
530:
526:
521:
520:
519:
491:
481:
475:
465:
459:
453:Shapiro, Stewart
450:
441:
440:
428:
422:
421:
398:
392:
391:
371:
258:Bertrand Russell
237:The writings of
119:History of logic
87:logical operator
2824:
2823:
2819:
2818:
2817:
2815:
2814:
2813:
2799:Classical logic
2789:
2788:
2787:
2782:
2771:
2764:
2709:Category theory
2699:Algebraic logic
2682:
2653:Lambda calculus
2591:Church encoding
2577:
2553:Truth predicate
2409:
2375:Complete theory
2298:
2167:
2163:
2159:
2154:
2146:
1866: and
1862:
1857:
1843:
1819:New Foundations
1787:axiom of choice
1770:
1732:Gödel numbering
1672: and
1664:
1568:
1453:
1403:
1384:
1333:Boolean algebra
1319:
1283:Equiconsistency
1248:Classical logic
1225:
1206:Halting problem
1194: and
1170: and
1158: and
1157:
1152:Theorems (
1147:
1064:
1059:
1029:
1024:
1000:Begriffsschrift
988:
984:Jan Ćukasiewicz
904:Bernard Bolzano
888:
859:Double negation
847:
818:Double negation
801:
735:
711:Excluded middle
694:
658:
649:
563:
561:Classical logic
558:
522:
517:
515:
500:
498:Further reading
495:
494:
482:
478:
466:
462:
451:
444:
429:
425:
418:
399:
395:
388:
372:
368:
363:
351:Boolean algebra
345:(for classical
331:algebraic logic
327:
315:Jan Ćukasiewicz
262:A. N. Whitehead
199:Begriffsschrift
151:Bernard Bolzano
121:
115:
44:
42:Characteristics
32:deductive logic
20:Classical logic
17:
12:
11:
5:
2822:
2812:
2811:
2806:
2801:
2784:
2783:
2769:
2766:
2765:
2763:
2762:
2757:
2752:
2747:
2742:
2741:
2740:
2730:
2725:
2720:
2711:
2706:
2701:
2696:
2694:Abstract logic
2690:
2688:
2684:
2683:
2681:
2680:
2675:
2673:Turing machine
2670:
2665:
2660:
2655:
2650:
2645:
2644:
2643:
2638:
2633:
2628:
2623:
2613:
2611:Computable set
2608:
2603:
2598:
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2585:
2579:
2578:
2576:
2575:
2570:
2565:
2560:
2555:
2550:
2545:
2540:
2539:
2538:
2533:
2528:
2518:
2513:
2508:
2506:Satisfiability
2503:
2498:
2493:
2492:
2491:
2481:
2480:
2479:
2469:
2468:
2467:
2462:
2457:
2452:
2447:
2437:
2436:
2435:
2430:
2423:Interpretation
2419:
2417:
2411:
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2408:
2407:
2402:
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2353:
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2268:
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2246:
2244:minimal axioms
2241:
2230:
2229:
2228:
2217:
2216:
2215:
2210:
2205:
2200:
2195:
2190:
2177:
2175:
2156:
2155:
2153:
2152:
2151:
2150:
2138:
2133:
2132:
2131:
2126:
2121:
2116:
2106:
2101:
2096:
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2090:
2089:
2084:
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2067:
2062:
2057:
2047:
2042:
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2020:
2019:
2018:
2013:
2008:
2003:
1998:
1993:
1983:
1978:
1973:
1968:
1967:
1966:
1961:
1956:
1951:
1941:
1936:
1934:Formation rule
1931:
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1925:
1924:
1919:
1909:
1908:
1907:
1897:
1892:
1887:
1882:
1876:
1870:
1853:Formal systems
1849:
1848:
1845:
1844:
1842:
1841:
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1821:
1816:
1811:
1806:
1801:
1796:
1795:
1794:
1789:
1778:
1776:
1772:
1771:
1769:
1768:
1767:
1766:
1756:
1751:
1750:
1749:
1742:Large cardinal
1739:
1734:
1729:
1724:
1719:
1705:
1704:
1703:
1698:
1693:
1678:
1676:
1666:
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1650:
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1566:
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1549:
1544:
1539:
1531:
1530:
1529:
1524:
1514:
1509:
1507:Extensionality
1504:
1502:Ordinal number
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1489:
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1482:
1471:
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1458:
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1409:
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1198:
1186:Cantor's
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1179:
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1145:
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1120:
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1100:
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1083:
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1026:
1025:
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1007:
1002:
996:
994:
990:
989:
987:
986:
981:
976:
971:
966:
961:
959:Ernst Schröder
956:
951:
946:
944:Giuseppe Peano
941:
936:
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916:
911:
906:
900:
898:
894:
893:
890:
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718:
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708:
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687:
682:
677:
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664:
660:
659:
652:
650:
648:
647:
642:
637:
632:
627:
622:
617:
612:
607:
602:
600:Truth function
597:
592:
587:
582:
577:
571:
569:
565:
564:
557:
556:
549:
542:
534:
528:
527:
512:
511:
499:
496:
493:
492:
476:
460:
442:
433:"Introduction"
423:
416:
402:L. T. F. Gamut
393:
386:
365:
364:
362:
359:
326:
323:
296:in disguise".
251:Ernst Schröder
247:Giuseppe Peano
117:Main article:
114:
111:
91:
90:
80:
75:
66:
57:
43:
40:
24:standard logic
15:
9:
6:
4:
3:
2:
2821:
2810:
2807:
2805:
2802:
2800:
2797:
2796:
2794:
2781:
2780:
2775:
2767:
2761:
2758:
2756:
2753:
2751:
2748:
2746:
2743:
2739:
2736:
2735:
2734:
2731:
2729:
2726:
2724:
2721:
2719:
2715:
2712:
2710:
2707:
2705:
2702:
2700:
2697:
2695:
2692:
2691:
2689:
2685:
2679:
2676:
2674:
2671:
2669:
2668:Recursive set
2666:
2664:
2661:
2659:
2656:
2654:
2651:
2649:
2646:
2642:
2639:
2637:
2634:
2632:
2629:
2627:
2624:
2622:
2619:
2618:
2617:
2614:
2612:
2609:
2607:
2604:
2602:
2599:
2597:
2594:
2592:
2589:
2588:
2586:
2584:
2580:
2574:
2571:
2569:
2566:
2564:
2561:
2559:
2556:
2554:
2551:
2549:
2546:
2544:
2541:
2537:
2534:
2532:
2529:
2527:
2524:
2523:
2522:
2519:
2517:
2514:
2512:
2509:
2507:
2504:
2502:
2499:
2497:
2494:
2490:
2487:
2486:
2485:
2482:
2478:
2477:of arithmetic
2475:
2474:
2473:
2470:
2466:
2463:
2461:
2458:
2456:
2453:
2451:
2448:
2446:
2443:
2442:
2441:
2438:
2434:
2431:
2429:
2426:
2425:
2424:
2421:
2420:
2418:
2416:
2412:
2406:
2403:
2401:
2398:
2396:
2393:
2391:
2388:
2385:
2384:from ZFC
2381:
2378:
2376:
2373:
2367:
2364:
2363:
2362:
2359:
2357:
2354:
2352:
2349:
2348:
2347:
2344:
2342:
2339:
2337:
2334:
2332:
2329:
2327:
2324:
2322:
2319:
2317:
2314:
2313:
2311:
2309:
2305:
2295:
2294:
2290:
2289:
2284:
2283:non-Euclidean
2281:
2277:
2274:
2272:
2269:
2267:
2266:
2262:
2261:
2259:
2256:
2255:
2253:
2249:
2245:
2242:
2240:
2237:
2236:
2235:
2231:
2227:
2224:
2223:
2222:
2218:
2214:
2211:
2209:
2206:
2204:
2201:
2199:
2196:
2194:
2191:
2189:
2186:
2185:
2183:
2179:
2178:
2176:
2171:
2165:
2160:Example
2157:
2149:
2144:
2143:
2142:
2139:
2137:
2134:
2130:
2127:
2125:
2122:
2120:
2117:
2115:
2112:
2111:
2110:
2107:
2105:
2102:
2100:
2097:
2095:
2092:
2088:
2085:
2083:
2080:
2079:
2078:
2075:
2071:
2068:
2066:
2063:
2061:
2058:
2056:
2053:
2052:
2051:
2048:
2046:
2043:
2039:
2036:
2034:
2031:
2029:
2026:
2025:
2024:
2021:
2017:
2014:
2012:
2009:
2007:
2004:
2002:
1999:
1997:
1994:
1992:
1989:
1988:
1987:
1984:
1982:
1979:
1977:
1974:
1972:
1969:
1965:
1962:
1960:
1957:
1955:
1952:
1950:
1947:
1946:
1945:
1942:
1940:
1937:
1935:
1932:
1930:
1927:
1923:
1920:
1918:
1917:by definition
1915:
1914:
1913:
1910:
1906:
1903:
1902:
1901:
1898:
1896:
1893:
1891:
1888:
1886:
1883:
1881:
1878:
1877:
1874:
1871:
1869:
1865:
1860:
1854:
1850:
1840:
1837:
1835:
1832:
1830:
1827:
1825:
1822:
1820:
1817:
1815:
1812:
1810:
1807:
1805:
1804:KripkeâPlatek
1802:
1800:
1797:
1793:
1790:
1788:
1785:
1784:
1783:
1780:
1779:
1777:
1773:
1765:
1762:
1761:
1760:
1757:
1755:
1752:
1748:
1745:
1744:
1743:
1740:
1738:
1735:
1733:
1730:
1728:
1725:
1723:
1720:
1717:
1713:
1709:
1706:
1702:
1699:
1697:
1694:
1692:
1689:
1688:
1687:
1683:
1680:
1679:
1677:
1675:
1671:
1667:
1659:
1656:
1654:
1651:
1649:
1648:constructible
1646:
1645:
1644:
1641:
1639:
1636:
1634:
1631:
1629:
1626:
1624:
1621:
1619:
1616:
1614:
1611:
1609:
1606:
1604:
1601:
1599:
1596:
1594:
1591:
1589:
1586:
1584:
1581:
1580:
1578:
1576:
1571:
1563:
1560:
1558:
1555:
1553:
1550:
1548:
1545:
1543:
1540:
1538:
1535:
1534:
1532:
1528:
1525:
1523:
1520:
1519:
1518:
1515:
1513:
1510:
1508:
1505:
1503:
1500:
1498:
1494:
1490:
1488:
1485:
1481:
1478:
1477:
1476:
1473:
1472:
1469:
1466:
1464:
1460:
1450:
1447:
1445:
1442:
1440:
1437:
1435:
1432:
1430:
1427:
1425:
1422:
1418:
1415:
1414:
1413:
1410:
1406:
1401:
1400:
1399:
1396:
1395:
1393:
1391:
1387:
1379:
1376:
1374:
1371:
1369:
1366:
1365:
1364:
1361:
1359:
1356:
1354:
1351:
1349:
1346:
1344:
1341:
1339:
1336:
1334:
1331:
1330:
1328:
1326:
1325:Propositional
1322:
1316:
1313:
1311:
1308:
1306:
1303:
1301:
1298:
1296:
1293:
1291:
1288:
1284:
1281:
1280:
1279:
1276:
1274:
1271:
1269:
1266:
1264:
1261:
1259:
1256:
1254:
1253:Logical truth
1251:
1249:
1246:
1245:
1243:
1241:
1237:
1234:
1232:
1228:
1222:
1219:
1217:
1214:
1212:
1209:
1207:
1204:
1202:
1199:
1197:
1193:
1189:
1185:
1183:
1180:
1178:
1175:
1173:
1169:
1166:
1165:
1163:
1161:
1155:
1150:
1144:
1141:
1139:
1136:
1134:
1131:
1129:
1126:
1124:
1121:
1119:
1116:
1114:
1111:
1109:
1106:
1104:
1101:
1099:
1096:
1094:
1091:
1089:
1086:
1082:
1079:
1078:
1077:
1074:
1073:
1071:
1067:
1063:
1056:
1051:
1049:
1044:
1042:
1037:
1036:
1033:
1021:
1018:
1016:
1013:
1011:
1008:
1006:
1003:
1001:
998:
997:
995:
991:
985:
982:
980:
977:
975:
972:
970:
969:Alfred Tarski
967:
965:
962:
960:
957:
955:
952:
950:
947:
945:
942:
940:
937:
935:
932:
930:
929:Gottlob Frege
927:
925:
922:
920:
917:
915:
912:
910:
907:
905:
902:
901:
899:
895:
885:
882:
880:
877:
875:
874:Biconditional
872:
870:
867:
865:
862:
860:
857:
856:
854:
850:
844:
841:
839:
836:
834:
833:Biconditional
831:
829:
826:
824:
821:
819:
816:
814:
811:
810:
808:
804:
798:
795:
793:
790:
788:
785:
783:
780:
778:
775:
773:
770:
768:
767:modus tollens
765:
763:
760:
758:
757:Transposition
755:
753:
750:
748:
745:
744:
742:
738:
732:
729:
727:
724:
722:
719:
717:
714:
712:
709:
707:
704:
703:
701:
697:
691:
688:
686:
683:
681:
678:
676:
675:Propositional
673:
671:
668:
667:
665:
661:
656:
646:
643:
641:
638:
636:
633:
631:
630:Associativity
628:
626:
623:
621:
618:
616:
613:
611:
608:
606:
603:
601:
598:
596:
593:
591:
588:
586:
583:
581:
578:
576:
573:
572:
570:
566:
562:
555:
550:
548:
543:
541:
536:
535:
532:
525:
514:
510:
509:0-87220-660-2
506:
502:
501:
489:
485:
480:
473:
469:
464:
458:
454:
449:
447:
438:
434:
427:
419:
413:
409:
408:
403:
397:
389:
383:
379:
378:
370:
366:
358:
356:
352:
348:
344:
340:
337:admits other
336:
332:
322:
320:
316:
312:
310:
306:
302:
297:
295:
291:
287:
283:
281:
277:
276:
271:
267:
263:
259:
254:
252:
248:
244:
240:
235:
233:
229:
225:
221:
218:had done for
217:
216:David Hilbert
213:
209:
205:
201:
200:
195:
194:Gottlob Frege
191:
188:The original
182:
178:
176:
172:
168:
164:
163:Boolean logic
160:
156:
152:
148:
144:
140:
138:
134:
130:
126:
120:
110:
108:
103:
100:
96:
95:propositional
88:
84:
81:
79:
76:
74:
70:
67:
65:
61:
58:
56:
52:
49:
48:
47:
39:
37:
33:
29:
25:
21:
2770:
2568:Ultraproduct
2415:Model theory
2380:Independence
2316:Formal proof
2308:Proof theory
2291:
2264:
2221:real numbers
2193:second-order
2104:Substitution
1981:Metalanguage
1922:conservative
1895:Axiom schema
1839:Constructive
1809:MorseâKelley
1775:Set theories
1754:Aleph number
1747:inaccessible
1653:Grothendieck
1537:intersection
1424:Higher-order
1412:Second-order
1358:Truth tables
1315:Venn diagram
1247:
1098:Formal proof
939:Hugh MacColl
914:Georg Cantor
909:George Boole
806:Introduction
762:modus ponens
690:Higher-order
685:Second-order
635:Distribution
595:Truth tables
560:
487:
484:Haack, Susan
479:
471:
463:
436:
426:
406:
396:
376:
369:
328:
313:
298:
284:
279:
273:
265:
255:
236:
232:Hugh MacColl
214:rigorous as
197:
187:
159:George Boole
141:
122:
104:
92:
45:
27:
23:
19:
18:
2678:Type theory
2626:undecidable
2558:Truth value
2445:equivalence
2124:non-logical
1737:Enumeration
1727:Isomorphism
1674:cardinality
1658:Von Neumann
1623:Ultrafilter
1588:Uncountable
1522:equivalence
1439:Quantifiers
1429:Fixed-point
1398:First-order
1278:Consistency
1263:Proposition
1240:Traditional
1211:Lindström's
1201:Compactness
1143:Type theory
1088:Cardinality
884:Disjunction
879:Conjunction
864:Existential
852:Elimination
843:Disjunction
838:Conjunction
823:Existential
680:First-order
605:Truth value
575:Quantifiers
468:Gabbay, Dov
204:quantifiers
190:first-order
137:Stoic logic
99:first-order
2793:Categories
2489:elementary
2182:arithmetic
2050:Quantifier
2028:functional
1900:Expression
1618:Transitive
1562:identities
1547:complement
1480:hereditary
1463:Set theory
934:Kurt Gödel
797:Absorption
699:Principles
585:Connective
486:, (1996).
361:References
317:pioneered
309:term logic
294:set theory
212:arithmetic
129:term logic
62:, and the
2760:Supertask
2663:Recursion
2621:decidable
2455:saturated
2433:of models
2356:deductive
2351:axiomatic
2271:Hilbert's
2258:Euclidean
2239:canonical
2162:axiomatic
2094:Signature
2023:Predicate
1912:Extension
1834:Ackermann
1759:Operation
1638:Universal
1628:Recursive
1603:Singleton
1598:Inhabited
1583:Countable
1573:Types of
1557:power set
1527:partition
1444:Predicate
1390:Predicate
1305:Syllogism
1295:Soundness
1268:Inference
1258:Tautology
1160:paradoxes
869:Universal
828:Universal
731:Explosion
716:Bivalence
645:Soundness
590:Tautology
580:Predicate
339:semantics
280:Tractatus
175:John Venn
133:Aristotle
2745:Logicism
2738:timeline
2714:Concrete
2573:Validity
2543:T-schema
2536:Kripke's
2531:Tarski's
2526:semantic
2516:Strength
2465:submodel
2460:spectrum
2428:function
2276:Tarski's
2265:Elements
2252:geometry
2208:Robinson
2129:variable
2114:function
2087:spectrum
2077:Sentence
2033:variable
1976:Language
1929:Relation
1890:Automata
1880:Alphabet
1864:language
1718:-jection
1696:codomain
1682:Function
1643:Universe
1613:Infinite
1517:Relation
1300:Validity
1290:Argument
1188:theorem,
813:Negation
640:Validity
620:Logicism
404:(1991).
303:and the
224:logicism
220:geometry
107:bivalent
85:: every
2687:Related
2484:Diagram
2382: (
2361:Hilbert
2346:Systems
2341:Theorem
2219:of the
2164:systems
1944:Formula
1939:Grammar
1855: (
1799:General
1512:Forcing
1497:Element
1417:Monadic
1192:paradox
1133:Theorem
1069:General
568:General
226:in the
143:Leibniz
113:History
2450:finite
2213:Skolem
2166:
2141:Theory
2109:Symbol
2099:String
2082:atomic
1959:ground
1954:closed
1949:atomic
1905:ground
1868:syntax
1764:binary
1691:domain
1608:Finite
1373:finite
1231:Logics
1190:
1138:Theory
897:People
507:
414:
384:
268:, and
2809:Logic
2440:Model
2188:Peano
2045:Proof
1885:Arity
1814:Naive
1701:image
1633:Fuzzy
1593:Empty
1542:union
1487:Class
1128:Model
1118:Lemma
1076:Axiom
993:Works
740:Rules
341:. In
26:) or
2563:Type
2366:list
2170:list
2147:list
2136:Term
2070:rank
1964:open
1858:list
1670:Maps
1575:sets
1434:Free
1404:list
1154:list
1081:list
670:Term
505:ISBN
412:ISBN
382:ISBN
260:and
249:and
241:and
173:and
97:and
71:and
53:and
22:(or
2250:of
2232:of
2180:of
1712:Sur
1686:Map
1493:Ur-
1475:Set
272:'s
264:'s
196:'s
145:'s
131:of
2795::
2636:NP
2260::
2254::
2184::
1861:),
1716:Bi
1708:In
445:^
435:.
321:.
253:.
38:.
2716:/
2631:P
2386:)
2172:)
2168:(
2065:â
2060:!
2055:â
2016:=
2011:â
2006:â
2001:â§
1996:âš
1991:ÂŹ
1714:/
1710:/
1684:/
1495:)
1491:(
1378:â
1368:3
1156:)
1054:e
1047:t
1040:v
553:e
546:t
539:v
420:.
390:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
