2805:
650:, which neatly formalizes Quine's dictum. So, Lambert argues, to reject his construction of free logic requires you to reject Quine's philosophy, which requires some argument and also means that whatever logic you develop is always accompanied by the stipulation that you must reject Quine to accept the logic. Likewise, if you reject Quine then you must reject free logic. This amounts to the contribution that free logic makes to ontology.
510:
wrote in 1967: "In fact, one may regard free logic... literally as a theory about singular existence, in the sense that it lays down certain minimum conditions for that concept." The question that concerned the rest of his paper was then a description of the theory, and to inquire whether it gives a
330:
Informally, if F is '=y', G is 'is
Pegasus', and we substitute 'Pegasus' for y, then (4) appears to allow us to infer from 'everything identical with Pegasus is Pegasus' that something is identical with Pegasus. The problem comes from substituting nondesignating constants for variables: in fact, we
653:
The point of free logic, though, is to have a formalism that implies no particular ontology, but that merely makes an interpretation of Quine both formally possible and simple. An advantage of this is that formalizing theories of singular existence in free logic brings out their implications for
526:. He criticizes this approach because it puts too much ideology into a logic, which is supposed to be philosophically neutral. Rather, he points out, not only does free logic provide for Quine's criterionâit even proves it! This is done by brute force, though, since he takes as axioms
325:
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225:
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so vigorously defended a form of logic that only accommodates his famous dictum, "To be is to be the value of a variable," when the logic is supplemented with
335:, since there are no nondesignating constants. Classically, âx(x=y) is deducible from the open equality axiom y=y by particularization (i.e. (3) above).
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409:, where E! is an existence predicate (in some but not all formulations of free logic, E!t can be defined as ∃y(y=t))
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713:. Metaphysics Research Lab, Stanford University – via Stanford Encyclopedia of Philosophy.
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320:{\displaystyle \forall x(Fx\rightarrow Gx)\land \exists xFx\rightarrow \exists x(Fx\land Gx)}
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Similar modifications are made to other theorems with existential import (e.g.
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there are theorems that clearly presuppose that there is something in the
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1013:
Free logics: Their foundations, character, and some applications thereof.
778:. Perspectives in Analytical Philosophy 11. BerlinâNew York: de Gruyter.
1638:
1493:
1270:
965:
857:
810:
789:
Hailperin, Theodore (1957). "A Theory of
Restricted Quantification I".
658:
and George
Nahknikian, which is that to exist is to be self-identical.
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easy analysis. Lambert takes the example of the theory proposed by
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31:
presuppositions than classical logic. Free logics may allow for
587:{\displaystyle \exists xFx\rightarrow (\exists x(E!x\land Fx))}
162:{\displaystyle \forall x\forall rA(x)\Rightarrow \forall rA(r)}
478:{\displaystyle A(r)\rightarrow (E!r\rightarrow \exists xA(x))}
1915:
1261:
1106:
776:
Meinongian Logic. The
Semantics of Existence and Nonexistence
710:
Nonexistent
Objects â The Stanford Encyclopedia of Philosophy
511:
necessary and sufficient condition for existence statements.
488:
402:{\displaystyle \forall xA\rightarrow (E!t\rightarrow A(t/x))}
24:
761:
Abstract
Objects. An Introduction to Axiomatic Metaphysics
643:{\displaystyle Fy\rightarrow (E!y\rightarrow \exists xFx)}
35:
that do not denote any object. Free logics may also allow
834:"Existential Presuppositions and Existential Commitments"
707:
Reicher, Maria (1 January 2016). Zalta, Edward N. (ed.).
491:
of free-logic are given by
Theodore Hailperin (1957),
220:{\displaystyle \forall rA(r)\Rightarrow \exists xA(x)}
600:
532:
423:
348:
244:
177:
113:
73:
63:. Consider the following classically valid theorems.
909:"Objects and existence: Reflections on free logic"
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642:
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477:
401:
319:
219:
161:
97:
2821:
939:
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723:
98:{\displaystyle \forall xA\Rightarrow \exists xA}
773:
1004:âââ, 2001, "Free Logics," in Goble, Lou, ed.,
982:
940:Nakhnikian, George; Salmon, Wesley C. (1957).
43:. A free logic with the latter property is an
1077:
1028:Morscher, Edgar, and Hieke, Alexander, 2001.
331:cannot do this in standard formulations of
1269:
1084:
1070:
1006:The Blackwell Guide to Philosophical Logic
906:
499:(1967), and Richard L. Mendelsohn (1989).
924:
891:
876:"Free logic and the concept of existence"
869:
867:
788:
1021:Philosophical applications of free logic
831:
873:
706:
2822:
1091:
864:
1065:
735:. New Haven: Yale University Press.
338:In free logic, (1) is replaced with
1054:Stanford Encyclopedia of Philosophy
234:which exhibits the same feature is
13:
913:Notre Dame Journal of Formal Logic
880:Notre Dame Journal of Formal Logic
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514:Lambert notes the irony in that
230:A valid scheme in the theory of
907:Mendelsohn, Richard L. (1989).
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50:
1:
2764:History of mathematical logic
976:
791:The Journal of Symbolic Logic
2689:Primitive recursive function
7:
988:Free logic: Selected essays
661:
10:
2846:
1753:SchröderâBernstein theorem
1480:Monadic predicate calculus
1139:Foundations of mathematics
415:existential generalization
2799:
2786:Philosophy of mathematics
2735:Automated theorem proving
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1860:Von NeumannâBernaysâGödel
1805:
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1603:
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1492:
1419:
1354:
1260:
1182:
1099:
1030:New essays in free logic.
1015:Sankt Augustin: Academia.
990:. Cambridge Univ. Press.
942:""Exists" as a Predicate"
838:The Journal of Philosophy
946:The Philosophical Review
926:10.1305/ndjfl/1093635243
893:10.1305/ndjfl/1093956251
832:Hintikka, Jaako (1959).
774:Jacquette, Dale (1996).
693:
2436:Self-verifying theories
2257:Tarski's axiomatization
1208:Tarski's undefinability
1203:incompleteness theorems
874:Lambert, Karel (1967).
516:Willard Van Orman Quine
2810:Mathematics portal
2421:Proof of impossibility
2069:propositional variable
1379:Propositional calculus
688:Table of logic symbols
683:Triangle of opposition
644:
588:
479:
403:
321:
221:
163:
99:
2679:Kolmogorov complexity
2632:Computably enumerable
2532:Model complete theory
2324:Principia Mathematica
1384:Propositional formula
1213:BanachâTarski paradox
645:
589:
480:
404:
322:
222:
164:
100:
2627:ChurchâTuring thesis
2614:Computability theory
1823:continuum hypothesis
1341:Square of opposition
1199:Gödel's completeness
763:. Dordrecht: Reidel.
678:Square of opposition
598:
530:
421:
346:
242:
175:
111:
71:
2830:Non-classical logic
2781:Mathematical object
2672:P versus NP problem
2637:Computable function
2431:Reverse mathematics
2357:Logical consequence
2234:primitive recursive
2229:elementary function
2002:Free/bound variable
1855:TarskiâGrothendieck
1374:Logical connectives
1304:Logical equivalence
1154:Logical consequence
1025:Oxford Univ. Press.
731:Nonexistent Objects
61:domain of discourse
2579:Transfer principle
2542:Semantics of logic
2527:Categorical theory
2503:Non-standard model
2017:Logical connective
1144:Information theory
1093:Mathematical logic
1032:Dordrecht: Kluwer.
640:
584:
524:description theory
475:
399:
317:
217:
159:
95:
2817:
2816:
2749:Abstract category
2552:Theories of truth
2362:Rule of inference
2352:Natural deduction
2333:
2332:
1878:
1877:
1583:Cartesian product
1488:
1487:
1394:Many-valued logic
1369:Boolean functions
1252:Russell's paradox
1227:diagonal argument
1124:First-order logic
333:first-order logic
2837:
2808:
2807:
2759:History of logic
2754:Category of sets
2647:Decision problem
2426:Ordinal analysis
2367:Sequent calculus
2265:Boolean algebras
2205:
2204:
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2150:logical/constant
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1813:ZermeloâFraenkel
1564:Set operations:
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1247:LöwenheimâSkolem
1134:Formal semantics
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757:Zalta, Edward N.
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2795:
2740:Category theory
2730:Algebraic logic
2713:
2684:Lambda calculus
2622:Church encoding
2608:
2584:Truth predicate
2440:
2406:Complete theory
2329:
2198:
2194:
2190:
2185:
2177:
1897: and
1893:
1888:
1874:
1850:New Foundations
1818:axiom of choice
1801:
1763:Gödel numbering
1703: and
1695:
1599:
1484:
1434:
1415:
1364:Boolean algebra
1350:
1314:Equiconsistency
1279:Classical logic
1256:
1237:Halting problem
1225: and
1201: and
1189: and
1188:
1183:Theorems (
1178:
1095:
1090:
1039:
1018:âââ, ed. 1991.
998:
979:
974:
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958:10.2307/2182749
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934:
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850:10.2307/2021988
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803:10.2307/2964055
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673:Logical hexagon
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522:assumptions of
505:
493:Jaakko Hintikka
489:Axiomatizations
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2537:Satisfiability
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2454:Interpretation
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2275:minimal axioms
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2014:
2009:
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1982:
1972:
1967:
1965:Formation rule
1962:
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1884:Formal systems
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1773:Large cardinal
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1538:Extensionality
1535:
1533:Ordinal number
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1217:Cantor's
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1037:External links
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1016:
1009:
1002:
996:
984:Lambert, Karel
978:
975:
972:
971:
952:(4): 535â542.
932:
899:
863:
844:(3): 125â137.
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504:
503:Interpretation
501:
474:
471:
468:
465:
462:
459:
456:
453:
450:
447:
444:
441:
438:
435:
432:
429:
426:
411:
410:
398:
395:
392:
388:
384:
381:
378:
375:
372:
369:
366:
363:
360:
357:
354:
351:
328:
327:
316:
313:
310:
307:
304:
301:
298:
295:
292:
289:
286:
283:
280:
277:
274:
271:
268:
265:
262:
259:
256:
253:
250:
247:
228:
227:
216:
213:
210:
207:
204:
201:
198:
195:
192:
189:
186:
183:
180:
169:
158:
155:
152:
149:
146:
143:
140:
137:
134:
131:
128:
125:
122:
119:
116:
105:
94:
91:
88:
85:
82:
79:
76:
52:
49:
15:
9:
6:
4:
3:
2:
2842:
2831:
2828:
2827:
2825:
2812:
2811:
2806:
2798:
2792:
2789:
2787:
2784:
2782:
2779:
2777:
2774:
2770:
2767:
2766:
2765:
2762:
2760:
2757:
2755:
2752:
2750:
2746:
2743:
2741:
2738:
2736:
2733:
2731:
2728:
2726:
2723:
2722:
2720:
2716:
2710:
2707:
2705:
2702:
2700:
2699:Recursive set
2697:
2695:
2692:
2690:
2687:
2685:
2682:
2680:
2677:
2673:
2670:
2668:
2665:
2663:
2660:
2658:
2655:
2653:
2650:
2649:
2648:
2645:
2643:
2640:
2638:
2635:
2633:
2630:
2628:
2625:
2623:
2620:
2619:
2617:
2615:
2611:
2605:
2602:
2600:
2597:
2595:
2592:
2590:
2587:
2585:
2582:
2580:
2577:
2575:
2572:
2568:
2565:
2563:
2560:
2558:
2555:
2554:
2553:
2550:
2548:
2545:
2543:
2540:
2538:
2535:
2533:
2530:
2528:
2525:
2521:
2518:
2517:
2516:
2513:
2509:
2508:of arithmetic
2506:
2505:
2504:
2501:
2497:
2494:
2492:
2489:
2487:
2484:
2482:
2479:
2477:
2474:
2473:
2472:
2469:
2465:
2462:
2460:
2457:
2456:
2455:
2452:
2451:
2449:
2447:
2443:
2437:
2434:
2432:
2429:
2427:
2424:
2422:
2419:
2416:
2415:from ZFC
2412:
2409:
2407:
2404:
2398:
2395:
2394:
2393:
2390:
2388:
2385:
2383:
2380:
2379:
2378:
2375:
2373:
2370:
2368:
2365:
2363:
2360:
2358:
2355:
2353:
2350:
2348:
2345:
2344:
2342:
2340:
2336:
2326:
2325:
2321:
2320:
2315:
2314:non-Euclidean
2312:
2308:
2305:
2303:
2300:
2298:
2297:
2293:
2292:
2290:
2287:
2286:
2284:
2280:
2276:
2273:
2271:
2268:
2267:
2266:
2262:
2258:
2255:
2254:
2253:
2249:
2245:
2242:
2240:
2237:
2235:
2232:
2230:
2227:
2225:
2222:
2220:
2217:
2216:
2214:
2210:
2209:
2207:
2202:
2196:
2191:Example
2188:
2180:
2175:
2174:
2173:
2170:
2168:
2165:
2161:
2158:
2156:
2153:
2151:
2148:
2146:
2143:
2142:
2141:
2138:
2136:
2133:
2131:
2128:
2126:
2123:
2119:
2116:
2114:
2111:
2110:
2109:
2106:
2102:
2099:
2097:
2094:
2092:
2089:
2087:
2084:
2083:
2082:
2079:
2077:
2074:
2070:
2067:
2065:
2062:
2060:
2057:
2056:
2055:
2052:
2048:
2045:
2043:
2040:
2038:
2035:
2033:
2030:
2028:
2025:
2023:
2020:
2019:
2018:
2015:
2013:
2010:
2008:
2005:
2003:
2000:
1996:
1993:
1991:
1988:
1986:
1983:
1981:
1978:
1977:
1976:
1973:
1971:
1968:
1966:
1963:
1961:
1958:
1954:
1951:
1949:
1948:by definition
1946:
1945:
1944:
1941:
1937:
1934:
1933:
1932:
1929:
1927:
1924:
1922:
1919:
1917:
1914:
1912:
1909:
1908:
1905:
1902:
1900:
1896:
1891:
1885:
1881:
1871:
1868:
1866:
1863:
1861:
1858:
1856:
1853:
1851:
1848:
1846:
1843:
1841:
1838:
1836:
1835:KripkeâPlatek
1833:
1831:
1828:
1824:
1821:
1819:
1816:
1815:
1814:
1811:
1810:
1808:
1804:
1796:
1793:
1792:
1791:
1788:
1786:
1783:
1779:
1776:
1775:
1774:
1771:
1769:
1766:
1764:
1761:
1759:
1756:
1754:
1751:
1748:
1744:
1740:
1737:
1733:
1730:
1728:
1725:
1723:
1720:
1719:
1718:
1714:
1711:
1710:
1708:
1706:
1702:
1698:
1690:
1687:
1685:
1682:
1680:
1679:constructible
1677:
1676:
1675:
1672:
1670:
1667:
1665:
1662:
1660:
1657:
1655:
1652:
1650:
1647:
1645:
1642:
1640:
1637:
1635:
1632:
1630:
1627:
1625:
1622:
1620:
1617:
1615:
1612:
1611:
1609:
1607:
1602:
1594:
1591:
1589:
1586:
1584:
1581:
1579:
1576:
1574:
1571:
1569:
1566:
1565:
1563:
1559:
1556:
1554:
1551:
1550:
1549:
1546:
1544:
1541:
1539:
1536:
1534:
1531:
1529:
1525:
1521:
1519:
1516:
1512:
1509:
1508:
1507:
1504:
1503:
1500:
1497:
1495:
1491:
1481:
1478:
1476:
1473:
1471:
1468:
1466:
1463:
1461:
1458:
1456:
1453:
1449:
1446:
1445:
1444:
1441:
1437:
1432:
1431:
1430:
1427:
1426:
1424:
1422:
1418:
1410:
1407:
1405:
1402:
1400:
1397:
1396:
1395:
1392:
1390:
1387:
1385:
1382:
1380:
1377:
1375:
1372:
1370:
1367:
1365:
1362:
1361:
1359:
1357:
1356:Propositional
1353:
1347:
1344:
1342:
1339:
1337:
1334:
1332:
1329:
1327:
1324:
1322:
1319:
1315:
1312:
1311:
1310:
1307:
1305:
1302:
1300:
1297:
1295:
1292:
1290:
1287:
1285:
1284:Logical truth
1282:
1280:
1277:
1276:
1274:
1272:
1268:
1265:
1263:
1259:
1253:
1250:
1248:
1245:
1243:
1240:
1238:
1235:
1233:
1230:
1228:
1224:
1220:
1216:
1214:
1211:
1209:
1206:
1204:
1200:
1197:
1196:
1194:
1192:
1186:
1181:
1175:
1172:
1170:
1167:
1165:
1162:
1160:
1157:
1155:
1152:
1150:
1147:
1145:
1142:
1140:
1137:
1135:
1132:
1130:
1127:
1125:
1122:
1120:
1117:
1113:
1110:
1109:
1108:
1105:
1104:
1102:
1098:
1094:
1087:
1082:
1080:
1075:
1073:
1068:
1067:
1064:
1056:
1055:
1050:
1046:
1041:
1040:
1031:
1027:
1024:
1022:
1017:
1014:
1010:
1007:
1003:
999:
997:9780511039195
993:
989:
985:
981:
980:
967:
963:
959:
955:
951:
947:
943:
936:
927:
922:
918:
914:
910:
903:
894:
889:
885:
881:
877:
870:
868:
859:
855:
851:
847:
843:
839:
835:
828:
820:
816:
812:
808:
804:
800:
796:
792:
785:
777:
770:
762:
758:
752:
744:
742:9780300024043
738:
733:
732:
726:
720:
712:
711:
703:
699:
689:
686:
684:
681:
679:
676:
674:
671:
669:
666:
665:
659:
657:
651:
634:
631:
628:
619:
616:
613:
604:
601:
575:
572:
569:
566:
563:
560:
554:
542:
539:
536:
525:
521:
517:
512:
509:
508:Karel Lambert
500:
498:
497:Karel Lambert
494:
490:
486:
466:
460:
457:
448:
445:
442:
430:
424:
416:
390:
386:
382:
376:
370:
367:
364:
355:
352:
341:
340:
339:
336:
334:
311:
308:
305:
302:
299:
293:
284:
281:
278:
272:
266:
263:
257:
254:
248:
237:
236:
235:
233:
211:
205:
202:
190:
184:
181:
170:
153:
147:
144:
132:
126:
123:
117:
106:
92:
89:
80:
77:
66:
65:
64:
62:
58:
48:
46:
42:
39:that have an
38:
34:
30:
26:
22:
16:Form of logic
2801:
2599:Ultraproduct
2446:Model theory
2411:Independence
2347:Formal proof
2339:Proof theory
2322:
2295:
2252:real numbers
2224:second-order
2135:Substitution
2012:Metalanguage
1953:conservative
1926:Axiom schema
1870:Constructive
1840:MorseâKelley
1806:Set theories
1785:Aleph number
1778:inaccessible
1684:Grothendieck
1568:intersection
1464:
1455:Higher-order
1443:Second-order
1389:Truth tables
1346:Venn diagram
1129:Formal proof
1052:
1045:"Free logic"
1043:Nolt, John.
1029:
1019:
1012:
1008:. Blackwell.
1005:
987:
949:
945:
935:
916:
912:
902:
883:
879:
841:
837:
827:
797:(1): 19â35.
794:
790:
784:
775:
769:
760:
751:
730:
719:
709:
702:
668:Logical cube
652:
513:
506:
487:
412:
337:
329:
229:
54:
44:
41:empty domain
20:
18:
2709:Type theory
2657:undecidable
2589:Truth value
2476:equivalence
2155:non-logical
1768:Enumeration
1758:Isomorphism
1705:cardinality
1689:Von Neumann
1654:Ultrafilter
1619:Uncountable
1553:equivalence
1470:Quantifiers
1460:Fixed-point
1429:First-order
1309:Consistency
1294:Proposition
1271:Traditional
1242:Lindström's
1232:Compactness
1174:Type theory
1119:Cardinality
1011:âââ, 1997.
51:Explanation
29:existential
27:with fewer
2520:elementary
2213:arithmetic
2081:Quantifier
2059:functional
1931:Expression
1649:Transitive
1593:identities
1578:complement
1511:hereditary
1494:Set theory
977:References
520:Russellian
21:free logic
2791:Supertask
2694:Recursion
2652:decidable
2486:saturated
2464:of models
2387:deductive
2382:axiomatic
2302:Hilbert's
2289:Euclidean
2270:canonical
2193:axiomatic
2125:Signature
2054:Predicate
1943:Extension
1865:Ackermann
1790:Operation
1669:Universal
1659:Recursive
1634:Singleton
1629:Inhabited
1614:Countable
1604:Types of
1588:power set
1558:partition
1475:Predicate
1421:Predicate
1336:Syllogism
1326:Soundness
1299:Inference
1289:Tautology
1191:paradoxes
626:∃
623:→
608:→
570:∧
552:∃
546:→
534:∃
455:∃
452:→
437:→
374:→
359:→
350:∀
306:∧
291:∃
288:→
276:∃
273:∧
261:→
246:∀
200:∃
197:⇒
179:∀
142:∀
139:⇒
121:∀
115:∀
87:∃
84:⇒
75:∀
2824:Category
2776:Logicism
2769:timeline
2745:Concrete
2604:Validity
2574:T-schema
2567:Kripke's
2562:Tarski's
2557:semantic
2547:Strength
2496:submodel
2491:spectrum
2459:function
2307:Tarski's
2296:Elements
2283:geometry
2239:Robinson
2160:variable
2145:function
2118:spectrum
2108:Sentence
2064:variable
2007:Language
1960:Relation
1921:Automata
1911:Alphabet
1895:language
1749:-jection
1727:codomain
1713:Function
1674:Universe
1644:Infinite
1548:Relation
1331:Validity
1321:Argument
1219:theorem,
986:(2003).
819:34062434
759:(1983).
727:(1980).
662:See also
495:(1959),
417:becomes
232:equality
2718:Related
2515:Diagram
2413: (
2392:Hilbert
2377:Systems
2372:Theorem
2250:of the
2195:systems
1975:Formula
1970:Grammar
1886: (
1830:General
1543:Forcing
1528:Element
1448:Monadic
1223:paradox
1164:Theorem
1100:General
1051:(ed.).
966:2182749
886:(1â2).
858:2021988
811:2964055
2481:finite
2244:Skolem
2197:
2172:Theory
2140:Symbol
2130:String
2113:atomic
1990:ground
1985:closed
1980:atomic
1936:ground
1899:syntax
1795:binary
1722:domain
1639:Finite
1404:finite
1262:Logics
1221:
1169:Theory
994:
964:
856:
817:
809:
739:
37:models
2471:Model
2219:Peano
2076:Proof
1916:Arity
1845:Naive
1732:image
1664:Fuzzy
1624:Empty
1573:union
1518:Class
1159:Model
1149:Lemma
1107:Axiom
1047:. In
962:JSTOR
919:(4).
854:JSTOR
815:S2CID
807:JSTOR
694:Notes
33:terms
25:logic
23:is a
2594:Type
2397:list
2201:list
2178:list
2167:Term
2101:rank
1995:open
1889:list
1701:Maps
1606:sets
1465:Free
1435:list
1185:list
1112:list
992:ISBN
737:ISBN
594:and
342:1b.
2281:of
2263:of
2211:of
1743:Sur
1717:Map
1524:Ur-
1506:Set
954:doi
921:doi
888:doi
846:doi
799:doi
238:4.
171:3.
107:2.
67:1.
55:In
2826::
2667:NP
2291::
2285::
2215::
1892:),
1747:Bi
1739:In
960:.
950:66
948:.
944:.
917:30
915:.
911:.
882:.
878:.
866:^
852:.
842:56
840:.
836:.
813:.
805:.
795:22
793:.
485:.
47:.
19:A
2747:/
2662:P
2417:)
2203:)
2199:(
2096:â
2091:!
2086:â
2047:=
2042:â
2037:â
2032:â§
2027:âš
2022:ÂŹ
1745:/
1741:/
1715:/
1526:)
1522:(
1409:â
1399:3
1187:)
1085:e
1078:t
1071:v
1057:.
1023:.
1000:.
968:.
956::
929:.
923::
896:.
890::
884:8
860:.
848::
821:.
801::
745:.
638:)
635:x
632:F
629:x
620:y
617:!
614:E
611:(
605:y
602:F
582:)
579:)
576:x
573:F
567:x
564:!
561:E
558:(
555:x
549:(
543:x
540:F
537:x
473:)
470:)
467:x
464:(
461:A
458:x
449:r
446:!
443:E
440:(
434:)
431:r
428:(
425:A
397:)
394:)
391:x
387:/
383:t
380:(
377:A
371:t
368:!
365:E
362:(
356:A
353:x
315:)
312:x
309:G
303:x
300:F
297:(
294:x
285:x
282:F
279:x
270:)
267:x
264:G
258:x
255:F
252:(
249:x
215:)
212:x
209:(
206:A
203:x
194:)
191:r
188:(
185:A
182:r
157:)
154:r
151:(
148:A
145:r
136:)
133:x
130:(
127:A
124:r
118:x
93:A
90:x
81:A
78:x
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