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or syntactic structure and by the placement of logical constants. Logical constants determine whether a statement is a logical truth when they are combined with a language that limits its meaning. Therefore, until it is determined how to make a distinction between all logical constants regardless of their language, it is impossible to know the complete truth of a statement or argument.
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of the other. A statement is logically true if, and only if its opposite is logically false. The opposite statements must contradict one another. In this way all logical connectives can be expressed in terms of preserving logical truth. The logical form of a sentence is determined by its semantic
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such as "If p and q, then p" and "All married people are married" are logical truths because they are true due to their internal structure and not because of any facts of the world (whereas "All married people are happy", even if it were true, could not be true solely in virtue of its logical
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of logical truths on empiricist grounds. Empiricists commonly respond to this objection by arguing that logical truths (which they usually deem to be mere tautologies), are analytic and thus do not purport to describe the world. The latter view was notably defended by the
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called into question the distinction between analytic and synthetic statements. It was this second class of analytic statements that caused him to note that the concept of analyticity itself stands in need of clarification, because it seems to depend on the concept of
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was a movement in the early 20th century that tried to reduce the reasoning processes of science to pure logic. Among other things, the logical positivists claimed that any proposition that is not empirically verifiable is neither true nor false, but
160:. Other than logical truths, there is also a second class of analytic statements, typified by "no bachelor is married". The characteristic of such a statement is that it can be turned into a logical truth by substituting synonyms for synonyms
91:. This is to say that they are such that no situation could arise in which they could fail to be true. The view that logical statements are necessarily true is sometimes treated as equivalent to saying that logical truths are true in all
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tautologies. Whereas a tautology or logical truth is true solely because of the logical terms it contains in general (e.g. "
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which turns out to be true under any possible interpretation of its terms (may also be called a
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Logical truths, being analytic statements, do not contain any information about any matters of
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This article is about propositions which are logically true. For the logical property, see
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can be thought of as providing accounts of the nature of logical truth, as well as
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or assignment depending upon the context). This is synonymous to logical truth.
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is also commonly used to refer to what could more specifically be called
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which differ in a significant way from standard logical systems such as
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The concept of logical truth is closely connected to the concept of a
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regardless of the truth or falsity of its constituent
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443:. Metaphysics Research Lab, Stanford University.
95:. However, the question of which statements are
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48:. Broadly speaking, a logical truth is a
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319:Logical truth and logical positivism
307:Logical truth and rules of inference
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512:Indiana Philosophy Ontology Project
500:Stanford Encyclopedia of Philosophy
263:Logical truth and logical constants
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273:Logical constants, including
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2600:Primitive recursive function
186:Truth values and tautologies
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142:in the early 20th century.
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1664:SchröderâBernstein theorem
1391:Monadic predicate calculus
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459:Language, Truth, and Logic
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2140:elementary function
1913:Free/bound variable
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1285:Logical connectives
1215:Logical equivalence
1065:Logical consequence
604:Philosophy of logic
426:Philosophy of logic
381:Logical truth table
361:and logical truth.
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3591:
3580:
3579:
3577:
3563:
3562:
3560:
3546:
3545:
3543:
3539:quantification
3535:
3530:
3529:
3527:
3523:quantification
3519:
3514:
3513:
3511:
3502:
3501:
3499:
3480:
3479:
3477:
3463:
3462:
3460:
3451:
3450:
3448:
3429:
3428:
3426:
3417:
3416:
3414:
3395:
3394:
3389:
3386:
3385:
3377:
3376:
3369:
3362:
3354:
3345:
3344:
3342:
3341:
3336:
3331:
3321:
3319:
3318:Negation
3315:
3314:
3312:
3311:
3306:
3301:
3295:
3293:
3289:
3288:
3281:
3279:
3277:
3276:
3270:
3268:truth function
3265:
3259:
3257:
3253:
3252:
3243:
3242:
3235:
3228:
3220:
3211:
3210:
3198:
3195:
3194:
3192:
3191:
3180:
3161:
3158:
3157:
3155:
3154:
3143:
3125:
3114:
3100:
3089:
3074:Nonimplication
3071:
3060:
3041:
3038:
3037:
3035:
3034:
3031:Digital buffer
3024:
3013:
2995:
2984:
2966:
2955:
2936:
2933:
2932:
2930:
2929:
2918:
2900:
2889:
2871:
2860:
2846:
2835:
2816:
2813:
2812:
2805:
2803:
2801:
2800:
2789:
2770:
2767:
2766:
2758:
2757:
2750:
2743:
2735:
2726:
2725:
2711:
2708:
2707:
2705:
2704:
2699:
2694:
2689:
2684:
2683:
2682:
2672:
2667:
2662:
2653:
2648:
2643:
2638:
2636:Abstract logic
2632:
2630:
2626:
2625:
2623:
2622:
2617:
2615:Turing machine
2612:
2607:
2602:
2597:
2592:
2587:
2586:
2585:
2580:
2575:
2570:
2565:
2555:
2553:Computable set
2550:
2545:
2540:
2535:
2529:
2527:
2521:
2520:
2518:
2517:
2512:
2507:
2502:
2497:
2492:
2487:
2482:
2481:
2480:
2475:
2470:
2460:
2455:
2450:
2448:Satisfiability
2445:
2440:
2435:
2434:
2433:
2423:
2422:
2421:
2411:
2410:
2409:
2404:
2399:
2394:
2389:
2379:
2378:
2377:
2372:
2365:Interpretation
2361:
2359:
2353:
2352:
2350:
2349:
2344:
2339:
2334:
2329:
2319:
2314:
2313:
2312:
2311:
2310:
2300:
2295:
2285:
2280:
2275:
2270:
2265:
2260:
2254:
2252:
2246:
2245:
2242:
2241:
2239:
2238:
2230:
2229:
2228:
2227:
2222:
2221:
2220:
2215:
2210:
2190:
2189:
2188:
2186:minimal axioms
2183:
2172:
2171:
2170:
2159:
2158:
2157:
2152:
2147:
2142:
2137:
2132:
2119:
2117:
2098:
2097:
2095:
2094:
2093:
2092:
2080:
2075:
2074:
2073:
2068:
2063:
2058:
2048:
2043:
2038:
2033:
2032:
2031:
2026:
2016:
2015:
2014:
2009:
2004:
1999:
1989:
1984:
1983:
1982:
1977:
1972:
1962:
1961:
1960:
1955:
1950:
1945:
1940:
1935:
1925:
1920:
1915:
1910:
1909:
1908:
1903:
1898:
1893:
1883:
1878:
1876:Formation rule
1873:
1868:
1867:
1866:
1861:
1851:
1850:
1849:
1839:
1834:
1829:
1824:
1818:
1812:
1795:Formal systems
1791:
1790:
1787:
1786:
1784:
1783:
1778:
1773:
1768:
1763:
1758:
1753:
1748:
1743:
1738:
1737:
1736:
1731:
1720:
1718:
1714:
1713:
1711:
1710:
1709:
1708:
1698:
1693:
1692:
1691:
1684:Large cardinal
1681:
1676:
1671:
1666:
1661:
1647:
1646:
1645:
1640:
1635:
1620:
1618:
1608:
1607:
1605:
1604:
1603:
1602:
1597:
1592:
1582:
1577:
1572:
1567:
1562:
1557:
1552:
1547:
1542:
1537:
1532:
1527:
1521:
1519:
1512:
1511:
1509:
1508:
1507:
1506:
1501:
1496:
1491:
1486:
1481:
1473:
1472:
1471:
1466:
1456:
1451:
1449:Extensionality
1446:
1444:Ordinal number
1441:
1431:
1426:
1425:
1424:
1413:
1407:
1401:
1400:
1397:
1396:
1394:
1393:
1388:
1383:
1378:
1373:
1368:
1363:
1362:
1361:
1351:
1350:
1349:
1336:
1334:
1328:
1327:
1325:
1324:
1323:
1322:
1317:
1312:
1302:
1297:
1292:
1287:
1282:
1277:
1271:
1269:
1263:
1262:
1260:
1259:
1254:
1249:
1244:
1239:
1234:
1229:
1228:
1227:
1217:
1212:
1207:
1202:
1197:
1192:
1186:
1184:
1175:
1169:
1168:
1166:
1165:
1160:
1155:
1150:
1145:
1140:
1128:Cantor's
1126:
1121:
1116:
1106:
1104:
1091:
1090:
1088:
1087:
1082:
1077:
1072:
1067:
1062:
1057:
1052:
1047:
1042:
1037:
1032:
1027:
1026:
1025:
1014:
1012:
1008:
1007:
1000:
999:
992:
985:
977:
968:
967:
965:
964:
959:
949:
944:
931:
928:
927:
924:
923:
921:
920:
915:
910:
905:
900:
894:
892:
888:
887:
885:
884:
879:
874:
868:
866:
857:
853:
852:
850:
849:
844:
839:
834:
829:
824:
819:
814:
809:
804:
799:
794:
789:
784:
783:
782:
772:
767:
762:
757:
752:
751:
750:
745:
735:
730:
725:
720:
714:
712:
708:
707:
704:
703:
701:
700:
695:
690:
685:
679:
677:
673:
672:
670:
669:
664:
659:
654:
653:
652:
647:
637:
631:
629:
622:
621:
616:
611:
606:
601:
596:
591:
585:
583:
579:
578:
576:
575:
570:
564:
561:
560:
553:
552:
545:
538:
530:
524:
523:
514:
505:
485:
484:External links
482:
479:
478:
471:Theodore Sider
463:
446:
429:
413:
412:
410:
407:
406:
405:
400:
395:
389:
387:Satisfiability
384:
378:
373:
366:
363:
347:formal systems
339:Main article:
336:
333:
320:
317:
308:
305:
267:Main article:
264:
261:
190:Main article:
187:
184:
175:W. V. O. Quine
163:salva veritate
150:Main article:
147:
144:
26:
9:
6:
4:
3:
2:
3714:
3703:
3700:
3698:
3695:
3693:
3690:
3688:
3685:
3683:
3680:
3678:
3677:Logical truth
3675:
3674:
3672:
3659:
3654:
3648:
3636:
3627:
3623:
3618:
3615:
3611:
3606:
3603:
3597:
3592:
3589:
3583:
3578:
3575:
3574:contradiction
3570:
3566:
3561:
3558:
3553:
3549:
3544:
3540:
3533:
3528:
3524:
3517:
3512:
3509:
3505:
3500:
3497:
3493:
3488:
3483:
3478:
3475:
3470:
3466:
3461:
3458:
3454:
3449:
3446:
3442:
3437:
3432:
3427:
3424:
3420:
3415:
3412:
3408:
3403:
3398:
3393:
3392:
3387:
3383:
3375:
3370:
3368:
3363:
3361:
3356:
3355:
3352:
3340:
3339:inconsistency
3337:
3335:
3334:contradiction
3332:
3330:
3326:
3323:
3322:
3320:
3316:
3310:
3307:
3305:
3302:
3300:
3297:
3296:
3294:
3290:
3285:
3275:
3272:⊨
3271:
3269:
3266:
3264:
3261:
3260:
3258:
3254:
3249:
3248:Logical truth
3241:
3236:
3234:
3229:
3227:
3222:
3221:
3218:
3208:
3196:
3170:
3166:
3165:Contradiction
3163:
3162:
3159:
3141:
3133:
3129:
3126:
3112:
3104:
3101:
3087:
3079:
3075:
3072:
3050:
3046:
3043:
3042:
3039:
3032:
3028:
3025:
3003:
2999:
2998:Biconditional
2996:
2982:
2974:
2970:
2967:
2945:
2941:
2938:
2937:
2934:
2916:
2908:
2904:
2901:
2879:
2875:
2872:
2850:
2847:
2825:
2821:
2818:
2817:
2814:
2809:
2779:
2775:
2772:
2771:
2768:
2764:
2756:
2751:
2749:
2744:
2742:
2737:
2736:
2733:
2723:
2722:
2717:
2709:
2703:
2700:
2698:
2695:
2693:
2690:
2688:
2685:
2681:
2678:
2677:
2676:
2673:
2671:
2668:
2666:
2663:
2661:
2657:
2654:
2652:
2649:
2647:
2644:
2642:
2639:
2637:
2634:
2633:
2631:
2627:
2621:
2618:
2616:
2613:
2611:
2610:Recursive set
2608:
2606:
2603:
2601:
2598:
2596:
2593:
2591:
2588:
2584:
2581:
2579:
2576:
2574:
2571:
2569:
2566:
2564:
2561:
2560:
2559:
2556:
2554:
2551:
2549:
2546:
2544:
2541:
2539:
2536:
2534:
2531:
2530:
2528:
2526:
2522:
2516:
2513:
2511:
2508:
2506:
2503:
2501:
2498:
2496:
2493:
2491:
2488:
2486:
2483:
2479:
2476:
2474:
2471:
2469:
2466:
2465:
2464:
2461:
2459:
2456:
2454:
2451:
2449:
2446:
2444:
2441:
2439:
2436:
2432:
2429:
2428:
2427:
2424:
2420:
2419:of arithmetic
2417:
2416:
2415:
2412:
2408:
2405:
2403:
2400:
2398:
2395:
2393:
2390:
2388:
2385:
2384:
2383:
2380:
2376:
2373:
2371:
2368:
2367:
2366:
2363:
2362:
2360:
2358:
2354:
2348:
2345:
2343:
2340:
2338:
2335:
2333:
2330:
2327:
2326:from ZFC
2323:
2320:
2318:
2315:
2309:
2306:
2305:
2304:
2301:
2299:
2296:
2294:
2291:
2290:
2289:
2286:
2284:
2281:
2279:
2276:
2274:
2271:
2269:
2266:
2264:
2261:
2259:
2256:
2255:
2253:
2251:
2247:
2237:
2236:
2232:
2231:
2226:
2225:non-Euclidean
2223:
2219:
2216:
2214:
2211:
2209:
2208:
2204:
2203:
2201:
2198:
2197:
2195:
2191:
2187:
2184:
2182:
2179:
2178:
2177:
2173:
2169:
2166:
2165:
2164:
2160:
2156:
2153:
2151:
2148:
2146:
2143:
2141:
2138:
2136:
2133:
2131:
2128:
2127:
2125:
2121:
2120:
2118:
2113:
2107:
2102:Example
2099:
2091:
2086:
2085:
2084:
2081:
2079:
2076:
2072:
2069:
2067:
2064:
2062:
2059:
2057:
2054:
2053:
2052:
2049:
2047:
2044:
2042:
2039:
2037:
2034:
2030:
2027:
2025:
2022:
2021:
2020:
2017:
2013:
2010:
2008:
2005:
2003:
2000:
1998:
1995:
1994:
1993:
1990:
1988:
1985:
1981:
1978:
1976:
1973:
1971:
1968:
1967:
1966:
1963:
1959:
1956:
1954:
1951:
1949:
1946:
1944:
1941:
1939:
1936:
1934:
1931:
1930:
1929:
1926:
1924:
1921:
1919:
1916:
1914:
1911:
1907:
1904:
1902:
1899:
1897:
1894:
1892:
1889:
1888:
1887:
1884:
1882:
1879:
1877:
1874:
1872:
1869:
1865:
1862:
1860:
1859:by definition
1857:
1856:
1855:
1852:
1848:
1845:
1844:
1843:
1840:
1838:
1835:
1833:
1830:
1828:
1825:
1823:
1820:
1819:
1816:
1813:
1811:
1807:
1802:
1796:
1792:
1782:
1779:
1777:
1774:
1772:
1769:
1767:
1764:
1762:
1759:
1757:
1754:
1752:
1749:
1747:
1746:KripkeâPlatek
1744:
1742:
1739:
1735:
1732:
1730:
1727:
1726:
1725:
1722:
1721:
1719:
1715:
1707:
1704:
1703:
1702:
1699:
1697:
1694:
1690:
1687:
1686:
1685:
1682:
1680:
1677:
1675:
1672:
1670:
1667:
1665:
1662:
1659:
1655:
1651:
1648:
1644:
1641:
1639:
1636:
1634:
1631:
1630:
1629:
1625:
1622:
1621:
1619:
1617:
1613:
1609:
1601:
1598:
1596:
1593:
1591:
1590:constructible
1588:
1587:
1586:
1583:
1581:
1578:
1576:
1573:
1571:
1568:
1566:
1563:
1561:
1558:
1556:
1553:
1551:
1548:
1546:
1543:
1541:
1538:
1536:
1533:
1531:
1528:
1526:
1523:
1522:
1520:
1518:
1513:
1505:
1502:
1500:
1497:
1495:
1492:
1490:
1487:
1485:
1482:
1480:
1477:
1476:
1474:
1470:
1467:
1465:
1462:
1461:
1460:
1457:
1455:
1452:
1450:
1447:
1445:
1442:
1440:
1436:
1432:
1430:
1427:
1423:
1420:
1419:
1418:
1415:
1414:
1411:
1408:
1406:
1402:
1392:
1389:
1387:
1384:
1382:
1379:
1377:
1374:
1372:
1369:
1367:
1364:
1360:
1357:
1356:
1355:
1352:
1348:
1343:
1342:
1341:
1338:
1337:
1335:
1333:
1329:
1321:
1318:
1316:
1313:
1311:
1308:
1307:
1306:
1303:
1301:
1298:
1296:
1293:
1291:
1288:
1286:
1283:
1281:
1278:
1276:
1273:
1272:
1270:
1268:
1267:Propositional
1264:
1258:
1255:
1253:
1250:
1248:
1245:
1243:
1240:
1238:
1235:
1233:
1230:
1226:
1223:
1222:
1221:
1218:
1216:
1213:
1211:
1208:
1206:
1203:
1201:
1198:
1196:
1195:Logical truth
1193:
1191:
1188:
1187:
1185:
1183:
1179:
1176:
1174:
1170:
1164:
1161:
1159:
1156:
1154:
1151:
1149:
1146:
1144:
1141:
1139:
1135:
1131:
1127:
1125:
1122:
1120:
1117:
1115:
1111:
1108:
1107:
1105:
1103:
1097:
1092:
1086:
1083:
1081:
1078:
1076:
1073:
1071:
1068:
1066:
1063:
1061:
1058:
1056:
1053:
1051:
1048:
1046:
1043:
1041:
1038:
1036:
1033:
1031:
1028:
1024:
1021:
1020:
1019:
1016:
1015:
1013:
1009:
1005:
998:
993:
991:
986:
984:
979:
978:
975:
963:
960:
957:
953:
950:
948:
945:
943:
933:
932:
929:
919:
918:Logic symbols
916:
914:
911:
909:
906:
904:
901:
899:
896:
895:
893:
889:
883:
880:
878:
875:
873:
870:
869:
867:
865:
861:
858:
854:
848:
845:
843:
840:
838:
835:
833:
830:
828:
825:
823:
820:
818:
815:
813:
810:
808:
805:
803:
800:
798:
797:Logical truth
795:
793:
790:
788:
785:
781:
778:
777:
776:
773:
771:
768:
766:
763:
761:
758:
756:
753:
749:
746:
744:
741:
740:
739:
738:Contradiction
736:
734:
731:
729:
726:
724:
721:
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683:Argumentation
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662:Non-classical
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517:Logical truth
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508:Logical truth
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376:False (logic)
374:
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371:Contradiction
369:
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351:propositional
348:
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169:In his essay
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38:Logical truth
33:
19:
3486:
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3401:
3324:
3304:formal proof
3247:
3045:Joint denial
2969:Exclusive or
2777:
2712:
2510:Ultraproduct
2357:Model theory
2322:Independence
2258:Formal proof
2250:Proof theory
2233:
2206:
2163:real numbers
2135:second-order
2046:Substitution
1923:Metalanguage
1864:conservative
1837:Axiom schema
1781:Constructive
1751:MorseâKelley
1717:Set theories
1696:Aleph number
1689:inaccessible
1595:Grothendieck
1479:intersection
1366:Higher-order
1354:Second-order
1300:Truth tables
1257:Venn diagram
1194:
1040:Formal proof
837:Substitution
796:
657:Mathematical
582:Major fields
498:
474:
466:
457:
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344:
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209:
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123:structure).
120:propositions
115:
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107:
101:
96:
88:
86:
58:propositions
37:
36:
3537:existential
3263:truth value
3256:Functional:
3128:Conjunction
3078:NIMPLY gate
2903:Disjunction
2874:Implication
2620:Type theory
2568:undecidable
2500:Truth value
2387:equivalence
2066:non-logical
1679:Enumeration
1669:Isomorphism
1616:cardinality
1600:Von Neumann
1565:Ultrafilter
1530:Uncountable
1464:equivalence
1381:Quantifiers
1371:Fixed-point
1340:First-order
1220:Consistency
1205:Proposition
1182:Traditional
1153:Lindström's
1143:Compactness
1085:Type theory
1030:Cardinality
952:WikiProject
822:Proposition
817:Probability
770:Description
711:Foundations
454:Alfred Ayer
292:conjunction
279:quantifiers
218:proposition
202:truth value
127:Rationalist
97:necessarily
70:tautologies
3671:Categories
2878:IMPLY gate
2431:elementary
2124:arithmetic
1992:Quantifier
1970:functional
1842:Expression
1560:Transitive
1504:identities
1489:complement
1422:hereditary
1405:Set theory
882:Set theory
780:Linguistic
775:Entailment
765:Definition
733:Consequent
728:Antecedent
521:PhilPapers
473:, (2010).
409:References
131:empiricism
3614:therefore
3602:therefore
3557:tautology
3521:universal
3274:tautology
3179:⊥
3142:∧
3113:↚
3088:↛
3059:↓
3027:Statement
3012:↔
3002:XNOR gate
2954:¬
2917:∨
2888:→
2859:←
2834:↑
2824:NAND gate
2788:⊤
2774:Tautology
2702:Supertask
2605:Recursion
2563:decidable
2397:saturated
2375:of models
2298:deductive
2293:axiomatic
2213:Hilbert's
2200:Euclidean
2181:canonical
2104:axiomatic
2036:Signature
1965:Predicate
1854:Extension
1776:Ackermann
1701:Operation
1580:Universal
1570:Recursive
1545:Singleton
1540:Inhabited
1525:Countable
1515:Types of
1499:power set
1469:partition
1386:Predicate
1332:Predicate
1247:Syllogism
1237:Soundness
1210:Inference
1200:Tautology
1102:paradoxes
913:Fallacies
908:Paradoxes
898:Logicians
832:Statement
827:Reference
792:Induction
755:Deduction
718:Abduction
688:Metalogic
635:Classical
599:Inference
229:tautology
222:valuation
210:tautology
135:knowledge
52:which is
50:statement
3600:entails,
3586:entails,
3474:superset
3132:AND gate
3049:NOR gate
2983:↮
2973:XOR gate
2944:NOT gate
2940:Negation
2687:Logicism
2680:timeline
2656:Concrete
2515:Validity
2485:T-schema
2478:Kripke's
2473:Tarski's
2468:semantic
2458:Strength
2407:submodel
2402:spectrum
2370:function
2218:Tarski's
2207:Elements
2194:geometry
2150:Robinson
2071:variable
2056:function
2029:spectrum
2019:Sentence
1975:variable
1918:Language
1871:Relation
1832:Automata
1822:Alphabet
1806:language
1660:-jection
1638:codomain
1624:Function
1585:Universe
1555:Infinite
1459:Relation
1242:Validity
1232:Argument
1130:theorem,
947:Category
847:Validity
748:Antinomy
676:Theories
640:Informal
403:Validity
365:See also
329:nonsense
300:negation
255:", and "
180:synonymy
42:concepts
3626:because
3490:
3469:implies
3457:implies
3439:
3405:
3380:Common
3309:theorem
3292:Formal:
3250: â€
3134:)
3130: (
3080:)
3076: (
3051:)
3047: (
3029: (
3004:)
3000: (
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2971: (
2946:)
2942: (
2909:)
2907:OR gate
2905: (
2880:)
2876: (
2826:)
2822: (
2761:Common
2629:Related
2426:Diagram
2324: (
2303:Hilbert
2288:Systems
2283:Theorem
2161:of the
2106:systems
1886:Formula
1881:Grammar
1797: (
1741:General
1454:Forcing
1439:Element
1359:Monadic
1134:paradox
1075:Theorem
1011:General
962:changes
954: (
812:Premise
743:Paradox
573:History
568:Outline
510:at the
493:(ed.).
398:Theorem
247:(e.g. "
214:formula
206:"false"
3588:proves
3484:
3433:
3399:
3327:
3299:theory
3171:
3105:
2851:
2780:
2392:finite
2155:Skolem
2108:
2083:Theory
2051:Symbol
2041:String
2024:atomic
1901:ground
1896:closed
1891:atomic
1847:ground
1810:syntax
1706:binary
1633:domain
1550:Finite
1315:finite
1173:Logics
1132:
1080:Theory
864:topics
650:Reason
628:Logics
619:Syntax
290:their
3697:Truth
3569:false
3407:&
3329:false
3169:False
2382:Model
2130:Peano
1987:Proof
1827:Arity
1756:Naive
1643:image
1575:Fuzzy
1535:Empty
1484:union
1429:Class
1070:Model
1060:Lemma
1018:Axiom
891:other
856:Lists
842:Truth
609:Proof
557:Logic
237:every
104:facts
46:logic
32:Truth
3552:true
3508:nand
2778:True
2505:Type
2308:list
2112:list
2089:list
2078:Term
2012:rank
1906:open
1800:list
1612:Maps
1517:sets
1376:Free
1346:list
1096:list
1023:list
956:talk
802:Name
787:Form
353:and
277:and
251:", "
241:some
239:", "
158:fact
116:this
54:true
3496:iff
3445:not
3411:and
2192:of
2174:of
2122:of
1654:Sur
1628:Map
1435:Ur-
1417:Set
698:Set
519:at
257:nor
253:and
216:or
110:or
44:in
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3487:or
3436:or
3423:or
3402:or
2578:NP
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1658:Bi
1650:In
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