2468:
1447:. Discernibility is usually defined in terms of pure properties only. The reason for this is that taking impure properties into consideration would result in the principle being trivially true since any entity has the impure property of being identical to itself, which it does not share with any other entity.
110:(often considered a valid predicate). As a consequence, there are a few different versions of the principle in the philosophical literature, of varying logical strength—and some of them are termed "the strong principle" or "the weak principle" by particular authors, in order to distinguish between them.
1510:
Black argues that even relational properties (properties specifying distances between objects in space-time) fail to distinguish two identical objects in a symmetrical universe. Per his argument, two objects are, and will remain, equidistant from the universe's plane of symmetry and each other. Even
1543:
This argument is criticized by some modern philosophers on the grounds that it allegedly derives a conclusion about what is true from a premise about what people know. What people know or believe about an entity, they argue, is not really a characteristic of that entity. A response may be that the
1506:
in which there are two distinct (numerically nonidentical) things that have all the same properties. He claimed that in a symmetric universe wherein only two symmetrical spheres exist, the two spheres are two distinct objects even though they have all their properties in common.
105:
Some philosophers have decided, however, that it is important to exclude certain predicates (or purported predicates) from the principle in order to avoid either triviality or contradiction. An example (detailed below) is the predicate that denotes whether an object is equal to
1519:
As stated above, the principle of indiscernibility of identicals—that if two objects are in fact one and the same, they have all the same properties—is mostly uncontroversial. However, one famous application of the indiscernibility of identicals was by
224:, on the other hand, is more controversial in making the converse claim that if two entities have the same properties then they must be identical. This entails that "no two distinct things exactly resemble each other". Note that these are all
683:. In that case, the objects are distinguished by IsA, IsB, and all predicates that are materially equivalent to either of these. This argument can combinatorially be extended to universes containing any number of distinct objects.
1399:
is usually defined in terms of shared properties: two objects are indiscernible if they have all their properties in common. The plausibility and strength of the principle of identity of indiscernibles depend on the
74:. While some think that Leibniz's version of the principle is meant to be only the indiscernibility of identicals, others have interpreted it as the conjunction of the identity of indiscernibles and the
202:
521:
318:
1363:
1502:
has argued against the identity of indiscernibles by counterexample. Notice that to show that the identity of indiscernibles is false, it is sufficient that one provide a
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bringing in an external observer to label the two spheres distinctly does not solve the problem, because it violates the symmetry of the universe.
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Since in proposition 6 we come to a contradiction with proposition 2, we conclude that at least one of the premises is wrong. Either:
1486:
properties are also taken into consideration, the same books become distinct so long as they are discernible through the latter properties.
63:) can be exactly alike, but this is intended as a metaphysical principle rather than one of natural science. A related principle is the
220:
is uncontroversial and states that if two entities are identical with each other then they have the same properties. The principle of
2259:
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to an object if having this property depends on other objects (with or without reference to particular objects), otherwise it is
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If ∀F applies to all such predicates, then the second principle as formulated above reduces trivially and uncontroversially to a
2127:
662:
In a universe of two distinct objects A and B, all predicates F are materially equivalent to one of the following properties:
1763:
78:(the converse principle). Because of its association with Leibniz, the indiscernibility of identicals is sometimes known as
1633:
The application of
Leibniz's law is erroneous; the law is only applicable in cases of monadic, not polyadic, properties; or
1696: – Formal fallacy when one makes an illicit use of Leibniz's law in an argument, a fallacious use of this principle
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Clark Kent is
Superman's secret identity; that is, they're the same person (identical) but people don't know this fact.
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160:: two objects are indiscernible if they have all their properties in common. Formally, this can be expressed as "
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follows from the second. Both principles can be combined into a single axiom by using a biconditional operator (
2490:
2347:
87:
1738:
1684: – Concept in quantum mechanics of perfectly substitutable particles, a similar idea in quantum mechanics
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Therefore
Superman has a property that Clark Kent does not have, namely that Lois Lane thinks that he can fly.
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is an impure property due to the reference to the particular "Socrates". Sometimes, the terms
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is that the inability of
Descartes to doubt the existence of his mind is part of his mind's
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1423:, involve reference to a particular substance in their definition. So, for example,
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2142:
2008:
1848:
1762:
Sandkühler, Hans Jörg (2010). "Ontologie: 4 Aktuelle
Debatten und Gesamtentwürfe".
1530:. Descartes concluded that he could not doubt the existence of himself (the famous
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properties, one cannot regard two books lying on a table as distinct when they are
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is intrinsic. If the identity of indiscernibles is defined only in terms of
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1554:. One may then argue that identical things should have identical essences.
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91:
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Associated with this principle is also the question as to whether it is a
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Impossibility for separate objects to have all their properties in common
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1957:
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Numerous counterexamples are given to debunk
Descartes' reasoning via
240:. Formally, the two principles can be expressed in the following way:
2178:. ed., A. Margalit. Dordrecht: D. Reidel, 1979. pp. 239–283
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60:
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The identity of indiscernibles has been used to motivate notions of
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1996:
1604:
24:
1708: – Class of type systems, a similar idea in computer science
1636:
What people think about are not the actual objects themselves; or
1551:
1391:
121:
70:
A form of the principle is attributed to the German philosopher
59:
and vice versa. It states that no two distinct things (such as
1907:"The Identity of Indiscernibles: 1. Formulating the Principle"
1450:
Another important distinction concerns the difference between
228:
expressions. Neither of these principles can be expressed in
2174:
Kripke, Saul. "A Puzzle about Belief". First appeared in,
1332:
can jointly be used to define the equality relation. The
655:. Principle 2, on the other hand, is controversial;
2102:
Between Two Worlds: A Reading of
Descartes's Meditations
1579:
are identical if and only if any predicate possessed by
1672: – Philosophical assertion about rational thought
675:
IsNotAorB, the property that holds of neither A nor B.
2089:. eds. J. Kim and E. Sosa, Blackwell Publishing, 1999
1939:
Honderich, Ted (2005). "identity of indiscernibles".
1839:
Black, Max (1952). "The
Identity of Indiscernibles".
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of equality follow from the first principle, whereas
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611:
591:
571:
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428:
408:
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368:
348:
328:
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236:). Taken together, they are sometimes referred to as
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2063:"Properties: 7a. Intrinsic and Extrinsic Properties"
1874:
Alfred North
Whitehead and Bertrand Russell (1910).
1407:
One important distinction in this regard is between
27:
principle that states that there cannot be separate
1702: – Thought experiment about identity over time
1678: – Classification based on observable evidence
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A person is capable of holding conflicting beliefs.
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Therefore, Superman is not identical to Clark Kent.
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651:Principle 1 is generally regarded as an a priori
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1712:First-order logic § Equality and its axioms
1650:Any of which will undermine Descartes' argument.
672:IsAorB, the property that holds of both A and B;
131:
2042:. Metaphysics Research Lab, Stanford University
1913:. Metaphysics Research Lab, Stanford University
1803:. Metaphysics Research Lab, Stanford University
669:IsB, the property that holds of B but not of A;
666:IsA, the property that holds of A but not of B;
208:are linked by two principles: the principle of
197:{\displaystyle \forall F(Fx\leftrightarrow Fy)}
1392:Indiscernibility and conceptions of properties
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1732:
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1728:
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1563:, such as the following argument based on a
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1880:. Vol. 1. Cambridge: University Press.
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2196:Stanford Encyclopedia of Philosophy entry
2034:Marshall, Dan; Weatherson, Brian (2018).
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2040:The Stanford Encyclopedia of Philosophy
1994:
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1911:The Stanford Encyclopedia of Philosophy
1904:
1886:, Def. 13.01, Lem.13.16.,17., p.176,178
1801:The Stanford Encyclopedia of Philosophy
1743:The Stanford Encyclopedia of Philosophy
1736:
2483:
2168:
1889:
1825:The Cambridge Dictionary of Philosophy
516:{\displaystyle \forall x\,\forall y\,}
313:{\displaystyle \forall x\,\forall y\,}
2204:
1838:
1783:
1494:
2125:
2036:"Intrinsic vs. Extrinsic Properties"
1821:
1795:Noonan, Harold; Curtis, Ben (2018).
1366:) in place of material implication (
244:The indiscernibility of identicals:
90:(famously used in his disputes with
2067:Internet Encyclopedia of Philosophy
1466:is extrinsic while the property of
605:have all the same properties, then
13:
1942:The Oxford Companion to Philosophy
1452:intrinsic and extrinsic properties
471:
461:
454:
280:
258:
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144:are expressed by the word "same".
14:
2542:
2424:New Essays on Human Understanding
2365:Transcendental law of homogeneity
2184:
2060:
1822:Audi, Robert (1999). "identity".
1540:doubt the existence of his body.
1404:used to define indiscernibility.
1276:(everything is equal to itself),
2467:
2466:
1739:"The Identity of Indiscernibles"
1358:{\displaystyle \leftrightarrow }
1268:expressed by the sign "=" is an
447:The identity of indiscernibles:
67:of identicals, discussed below.
2119:
2092:
2080:
2054:
1547:Meditations on First Philosophy
1527:Meditations on First Philosophy
1462:. For example, the property of
2105:. Princeton University Press.
1949:
1867:
1832:
1815:
1515:Indiscernibility of identicals
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510:
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156:, on the other hand, concerns
88:principle of sufficient reason
76:indiscernibility of identicals
1:
2453:Leibniz–Clarke correspondence
2099:Carriero, John Peter (2008).
1956:Rosenkrantz, Gary S. (1979).
1828:. Cambridge University Press.
1717:
1241:the empty relation satisfies
442:have all the same properties.
132:Identity and indiscernibility
100:Leibniz–Clarke correspondence
84:principle of noncontradiction
39:in common. That is, entities
2128:"Alter Egos and Their Names"
2126:Pitt, David (October 2001),
1997:"Non-Qualitative Properties"
1741:. In Edward N. Zalta (ed.).
1737:Forrest, Peter (Fall 2008).
1419:are properties that, unlike
1380:{\displaystyle \rightarrow }
659:famously argued against it.
7:
2273:Characteristica universalis
2255:Best of all possible worlds
1682:Indistinguishable particles
1658:
1622:A person's knowledge about
1489:
841:
811:
791:
753:
715:
10:
2547:
2294:Identity of indiscernibles
1945:. Oxford University Press.
1619:Leibniz's law is wrong; or
1429:being the wife of Socrates
1330:identity of indiscernables
222:identity of indiscernibles
214:identity of indiscernibles
117:within quantum mechanics.
21:identity of indiscernibles
2501:Gottfried Wilhelm Leibniz
2464:
2395:
2238:
2232:Gottfried Wilhelm Leibniz
2135:The Journal of Philosophy
2087:Metaphysics: An Anthology
2013:10.1007/s10670-014-9626-9
1958:"The Pure and the Impure"
1427:is a pure property while
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72:Gottfried Wilhelm Leibniz
2414:Discourse on Metaphysics
1853:10.1093/mind/LXI.242.153
1768:. Meiner. Archived from
1765:Enzyklopädie Philosophie
1670:Disquotational principle
1402:conception of properties
124:principle, or merely an
2526:Metaphysical principles
2387:Well-founded phenomenon
2338:Pre-established harmony
2250:Alternating series test
1905:Forrest, Peter (2020).
1536:argument), but that he
1476:intrinsically identical
47:are identical if every
2511:Philosophical theories
1706:Structural type system
1626:is not a predicate of
1603:Lois Lane thinks that
1468:having a mass of 60 kg
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2491:Identity (philosophy)
2266:Calculus ratiocinator
1995:Cowling, Sam (2015).
1877:Principia Mathematica
1688:Identity (philosophy)
1665:1st axiom of a metric
1583:is also possessed by
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212:and the principle of
204:". The two senses of
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55:is also possessed by
2404:De Arte Combinatoria
2332:Mathesis universalis
2260:Calculus controversy
2141:(10): 531–552, 550,
1560:reductio ad absurdum
1439:are used instead of
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158:qualitative sameness
35:that have all their
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2516:Philosophical logic
234:nonfirstorderizable
216:. The principle of
2319:Leibniz's notation
1962:Logique et Analyse
1694:Masked-man fallacy
1495:Symmetric universe
1377:
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1236:When used as '=',
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150:numerical sameness
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2375:Universal science
2348:Sufficient reason
2304:Law of continuity
1417:Impure properties
1266:equality relation
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638:{\displaystyle y}
618:{\displaystyle x}
598:{\displaystyle y}
578:{\displaystyle x}
558:{\displaystyle y}
538:{\displaystyle x}
435:{\displaystyle y}
415:{\displaystyle x}
395:{\displaystyle y}
375:{\displaystyle x}
355:{\displaystyle y}
335:{\displaystyle x}
230:first-order logic
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1454:. A property is
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1968:(88): 515–523.
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1847:(242): 153–64.
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1421:pure properties
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2007:(2): 275–301.
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2320:
2317:
2315:
2314:Leibniz's gap
2312:
2310:
2309:Leibniz wheel
2307:
2305:
2302:
2300:
2299:Individuation
2297:
2295:
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2197:
2194:
2192:
2191:Leibniz's Law
2189:
2188:
2177:
2171:
2164:on 2006-05-08
2160:
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2018:
2014:
2010:
2006:
2002:
1998:
1991:
1983:
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1967:
1963:
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1787:
1772:on 2021-03-11
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1464:being an aunt
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1135:, see above)
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671:
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664:
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653:logical truth
632:
612:
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524:
523:
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301:
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274:
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261:
254:
243:
242:
241:
239:
238:Leibniz's law
235:
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227:
223:
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215:
211:
207:
188:
185:
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176:
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159:
155:
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129:
127:
123:
118:
116:
111:
109:
103:
101:
97:
93:
89:
85:
81:
80:Leibniz's law
77:
73:
68:
66:
62:
58:
54:
51:possessed by
50:
46:
42:
38:
34:
30:
26:
22:
2442:
2432:
2422:
2412:
2402:
2379:
2352:
2330:
2323:
2293:
2271:
2264:
2175:
2170:
2159:the original
2138:
2134:
2121:
2101:
2094:
2086:
2082:
2070:. Retrieved
2066:
2056:
2044:. Retrieved
2039:
2029:
2004:
2000:
1990:
1965:
1961:
1951:
1941:
1915:. Retrieved
1910:
1883:
1876:
1869:
1844:
1840:
1834:
1824:
1817:
1805:. Retrieved
1800:
1774:. Retrieved
1770:the original
1764:
1757:
1746:. Retrieved
1742:
1627:
1623:
1596:thinks that
1584:
1580:
1576:
1572:
1558:
1556:
1545:
1542:
1537:
1531:
1525:
1518:
1509:
1498:
1483:
1479:
1475:
1471:
1467:
1463:
1459:
1455:
1449:
1444:
1440:
1436:
1432:
1428:
1425:being a wife
1424:
1420:
1416:
1415:properties.
1412:
1408:
1406:
1401:
1396:
1395:
1367:
1345:
1341:
1338:transitivity
1337:
1333:
1329:
1325:
1321:
1320:is equal to
1317:
1313:
1312:is equal to
1309:
1305:
1304:is equal to
1301:
1293:
1292:is equal to
1289:
1285:
1284:is equal to
1281:
1263:
1251:
1242:
1227:
1219:
1215:
1200:
1196:
1186:
1176:
1168:
1164:
1149:
1143:
1132:
1128:
1124:
1120:
1114:
1104:
1098:
1085:
1075:
1071:
1067:
1058:
1054:
1050:
1046:
1042:
1032:
1024:
1020:
1016:
1001:
995:
985:
981:
975:
965:
959:
949:
943:
933:
929:
925:
916:
912:
908:
898:
890:
886:
882:
866:
862:
858:
851:
847:
843:
836:
828:
824:
817:
813:
806:
799:
793:
786:
778:
774:
770:
766:
759:
755:
748:
740:
736:
732:
728:
721:
717:
710:
701:
689:
678:
661:
650:
237:
226:second-order
221:
217:
213:
209:
205:
157:
153:
149:
145:
141:
137:
135:
119:
112:
107:
104:
79:
75:
69:
56:
52:
44:
40:
20:
18:
2370:Rationalism
1600:cannot fly.
1433:qualitative
1342:reflexivity
1148:by Def. of
1103:by Def. of
1000:by Def. of
964:by Def. of
128:principle.
25:ontological
2485:Categories
2444:Monadology
2284:Difference
2242:philosophy
2072:25 January
2046:25 January
2001:Erkenntnis
1917:25 January
1797:"Identity"
1776:2021-01-27
1748:2012-04-12
1718:References
1598:Clark Kent
1298:transitive
1053:such that
915:such that
61:snowflakes
37:properties
2531:Semantics
2434:Théodicée
2343:Plenitude
2021:122265064
1974:0024-5836
1807:4 January
1676:Duck test
1594:Lois Lane
1571:Entities
1500:Max Black
1480:extrinsic
1478:. But if
1460:intrinsic
1456:extrinsic
1375:→
1353:↔
1278:symmetric
1274:reflexive
1272:in being
690:Proof box
657:Max Black
499:→
487:↔
472:∀
462:∀
455:∀
296:↔
281:∀
278:→
259:∀
252:∀
183:↔
168:∀
148:is about
126:empirical
49:predicate
2506:Ontology
2472:Category
2381:Vis viva
2360:Theodicy
2289:Dynamism
1982:44085165
1884:Identity
1659:See also
1607:can fly.
1605:Superman
1490:Critique
1334:symmetry
1250:but not
1189:; hence
1123:, since
1090:assumed
984:, since
525:For any
322:For any
206:sameness
146:Identity
138:identity
86:and the
33:entities
2155:3649468
1861:2252291
1552:essence
1524:in his
1324:). The
1243:IndscID
1216:IndscID
1201:IDIndsc
1187:Fx ⇔ Fx
1165:IDIndsc
1121:IndscID
1078:, then
1066:define
1017:IndscID
982:IndscID
936:, then
924:define
883:IndscID
749:IDIndsc
711:IndscID
402:, then
122:logical
98:in the
29:objects
2448:(1714)
2438:(1710)
2428:(1704)
2418:(1686)
2408:(1666)
2153:
2109:
2019:
1980:
1972:
1859:
1533:cogito
1484:impure
1445:impure
1413:impure
1296:) and
1127:(from
1041:Given
907:Given
96:Clarke
92:Newton
23:is an
2396:Works
2162:(PDF)
2151:JSTOR
2131:(PDF)
2017:S2CID
1978:JSTOR
1857:JSTOR
1538:could
1504:model
1316:then
1288:then
1197:x = x
1177:Proof
1144:x = z
1129:x = y
1125:y = x
1086:y = z
1076:v = z
1074:) as
1059:y = z
1055:x = y
1033:Proof
1025:Trans
996:y = x
986:x = y
944:x = x
934:v = x
932:) as
917:x = y
899:Proof
867:x = z
863:y = z
859:x = y
837:Trans
829:y = x
825:x = y
800:x = x
779:x = y
729:x = y
565:, if
362:, if
232:(are
136:Both
2107:ISBN
2074:2021
2048:2021
1970:ISSN
1919:2021
1841:Mind
1809:2021
1630:; or
1575:and
1482:and
1443:and
1441:pure
1435:and
1411:and
1409:pure
1336:and
1328:and
1308:and
1300:(if
1280:(if
1264:The
1252:Refl
1220:Refl
1169:Refl
1133:Symm
1131:and
1057:and
1021:Refl
950:Refl
891:Symm
887:Refl
807:Symm
787:Refl
777:) →
585:and
545:and
422:and
342:and
140:and
94:and
43:and
19:The
2143:doi
2009:doi
1849:doi
1388:).
1199:by
1119:by
980:by
948:by
743:))
731:→ ∀
102:).
31:or
2487::
2149:,
2139:98
2137:,
2133:,
2065:.
2038:.
2015:.
2005:80
2003:.
1999:.
1976:.
1966:22
1964:.
1960:.
1927:^
1909:.
1891:^
1855:.
1845:61
1843:.
1799:.
1785:^
1725:^
1567::
1254:.
1245:,
1218:⇸
1167:→
1115:Fx
1099:Fy
1061:,
1049:,
1045:,
1023:→
1019:∧
976:Fy
960:Fx
919:,
911:,
889:→
885:∧
869:)
865:→
861:∧
831:)
827:→
781:)
775:Fy
771:Fx
765:(∀
741:Fy
737:Fx
2224:e
2217:t
2210:v
2145::
2115:.
2076:.
2050:.
2023:.
2011::
1984:.
1921:.
1863:.
1851::
1811:.
1779:.
1751:.
1628:x
1624:x
1585:y
1581:x
1577:y
1573:x
1322:z
1318:x
1314:z
1310:y
1306:y
1302:x
1294:x
1290:y
1286:y
1282:x
1230::
1179::
1150:F
1140:→
1111:→
1105:F
1095:→
1072:v
1070:(
1068:F
1051:z
1047:y
1043:x
1035::
1002:F
992:→
972:→
966:F
956:→
930:v
928:(
926:F
913:y
909:x
901::
857:(
854:.
852:z
850:,
848:y
846:,
844:x
842:∀
839::
823:(
820:.
818:y
816:,
814:x
812:∀
809::
796:.
794:x
792:∀
789::
773:⇔
769:(
767:F
762:.
760:y
758:,
756:x
754:∀
751::
739:⇔
735:(
733:F
727:(
724:.
722:y
720:,
718:x
716:∀
713::
704::
645:.
633:y
613:x
593:y
573:x
553:y
533:x
511:]
508:y
505:=
502:x
496:)
493:y
490:F
484:x
481:F
478:(
475:F
469:[
465:y
458:x
430:y
410:x
390:y
370:x
350:y
330:x
308:]
305:)
302:y
299:F
293:x
290:F
287:(
284:F
275:y
272:=
269:x
266:[
262:y
255:x
192:)
189:y
186:F
180:x
177:F
174:(
171:F
108:x
57:y
53:x
45:y
41:x
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