1003:
693:, Aquinas writes of natural minima that, "although a body, considered mathematically, is divisible to infinity, the natural body is not divisible to infinity. For in a mathematical body nothing but quantity is considered. And in this there is nothing repugnant to division to infinity. But in a natural body the form also is considered, which form requires a determinate quantity and also other accidents. Whence it is not possible for quantity to be found in the species of flesh except as determined within some termini."
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Aristotle's intuition was that there is some smallest size beyond which matter could no longer be structured as flesh, or bone, or wood, or some other such organic substance that (for
Aristotle, living before the microscope) could be considered homogeneous. For instance, if flesh were divided beyond
923:
Sed dicendum quod licet corpus, mathematice acceptum, sit divisibile in infinitum, corpus tamen naturale non est divisibile in infinitum. In corpore enim mathematico non consideratur nisi quantitas, in qua nihil invenitur divisioni in infinitum repugnans; sed in corpore naturali consideratur forma
452:
Moreover, "ince every body must diminish in size when something is taken from it, and flesh is quantitatively definite in respect both of greatness and smallness, it is clear that from the minimum quantity of flesh no body can be separated out; for the flesh left would be less than the minimum of
448:
On
Anaxagoras' argument in which all things contain all others infinitely, water could be drawn from flesh, then flesh from that water, and water from that flesh, and so on. However, as above, because there is a smallest determinate size beyond which a further divided substance would no longer be
439:
had taught that every thing, and every portion of a thing, contains within itself an infinite number of like and unlike parts. For example, Anaxagoras maintained that there must be blackness as well as whiteness in snow; how, otherwise, could it be turned into dark water? Aristotle criticized
444:
Animals and plants cannot be infinitely small according to
Aristotle; thus the relatively homogeneous substances of which they are composed (e.g., bone and flesh in animals, or wood in plants) could not be infinitely small, either, but must have a smallest determinate size—i.e., a natural
717:
continued to shape philosophical thinking even among these mechanistic philosophers in the transitional centuries between the
Aristotelianism of the medieval Scholastics and the worked-out atomic theory of modern scientists like
685:
principle of infinite divisibility. Commentators like
Philoponus and Aquinas reconciled these aspects of Aristotle's thought by distinguishing between mathematical and "natural" divisibility. For example, in his commentary on
505:
water, and smaller amounts of the other elements (e.g., earth) with which water was thought to mix to form flesh. But whatever was left, the water (or earth, etc.), would no longer have the formal "
497:) that imparts its essential nature and structure. For instance, a rubber ball for a hylomorphist like Aristotle would be rubber (matter) structured by spherical shape (form).
417:
of ancient Greece and the mechanistic philosophy of early modern thinkers like
Descartes, which in turn provided a background for the rigorously mathematical and experimental
1103:
924:
naturalis, quae requirit determinatam quantitatem sicut et alia accidentia. Unde non potest inveniri quantitas in specie carnis nisi infra aliquos terminos determinata.
481:, the Aristotelian natural minimum was not conceptualized as physically indivisible--"atomic" in the contemporary sense. Instead, the concept was rooted in Aristotle's
1928:
733:
in the course of expounding his opposition to
Scholastic Aristotelianism, and his own attempted reconciliation between the atomism of Epicurus and the
1681:
1078:
954:
1128:
1123:
1093:
1083:
1073:
509:" of flesh in particular – the remaining matter would have the form of water (or earth, etc.) rather than the substantial form of flesh.
713:, who were more sympathetic to the ancient Greek atomism of Democritus than to the natural minima of Aristotle. However, the concept of
1133:
1118:
1113:
1098:
506:
413:
in late
Antiquity, in the Islamic world, and by Scholastic and Renaissance thinkers in Europe provided a conceptual bridge between the
395:
1859:
1433:
364:
1166:
784:
is the conventional Latin translation of Greek ἐλάχιστα ("elachista," singular ἐλάχιστον, "elachiston"), which means "minima."
1343:
1108:
1032:
879:
1982:
1042:
1027:
977:
871:
The
Scientist's Atom and the Philosopher's Stone: How Science Succeeded and Philosophy Failed to Gain Knowledge of Atoms
512:
This is suggestive of modern chemistry, in which, e.g., a bar of gold can be continually divided until one has a single
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761:, one of the founders of modern chemistry. Boyle occasionally referred to his postulated corpuscles as
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In the early modern period, Aristotelian hylomorphism fell out of favor with the rise of the
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nature. Thus, "natural minimum" may be taken to mean "formal minimum": the minimum amount of
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of gold, but further division of that atom of gold yields only subatomic particles (
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833:(1 January 2001). "The Medieval and Renaissance Tradition of Minima Naturalia".
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worldview, which held that every physical thing is a compound of matter (Greek
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prompted further speculations by later philosophers. The idea was taken up by
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gold. Just as water alone is not flesh, electrons alone are not gold.
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390:(e.g., flesh, bone, or wood) could be divided and still retain its
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flesh, any further cycle of such drawings out would be impossible.
440:
Anaxagoras' theory on multiple grounds, among them the following:
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were discussed by
Scholastic and Renaissance thinkers including
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151:
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1637:
1550:
1495:
521:
670:. Of this list, the most influential Scholastic thinkers on
513:
836:
Late Medieval and Early Modern Corpuscular Matter Theories
386:
as the smallest parts into which a homogeneous natural
757:, who in turn influenced the corpuscularian alchemist
501:
its natural minimum, what would remain might be some
1929:On Youth, Old Age, Life and Death, and Respiration
560:in late Antiquity and by the Islamic Aristotelian
2134:
2057:
696:
677:A chief theme in later commentary is reconciling
424:
2423:
662:, Didacus de Astudillo, Ludovicus Buccaferrea,
860:
858:
856:
1427:
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864:
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358:
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642:, Facinus de Ast, Peter Alboinis of Mantua,
853:
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1420:
1372:
955:
941:
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893:
891:
810:
365:
351:
531:
406:necessary to instantiate a certain form.
674:were Duns Scotus and Gregory of Rimini.
888:
2424:
962:
2276:
2185:
1415:
936:
382:("natural minima") were theorized by
1983:On Melissus, Xenophanes, and Gorgias
1441:
919:In octo libros Physicorum expositio
13:
2344:Transmission of the Greek Classics
35:
14:
2463:
2018:The Situations and Names of Winds
993:History and philosophy of science
2404:
2394:
2393:
1395:
1394:
1382:
1371:
1001:
524:, etc.) which are no longer the
332:
320:
1924:On Length and Shortness of Life
1514:Correspondence theory of truth
907:
787:
775:
697:Influence on corpuscularianism
536:Aristotle's brief comments on
425:Aristotle's initial suggestion
1:
1860:Constitution of the Athenians
803:
394:character. In this context, "
1762:On Generation and Corruption
874:. Springer. pp. 75–96.
473:, and also unlike the later
429:According to Aristotle, the
7:
1344:Neurology and neurosurgery
829:; Christoph Herbert Lüthy;
118:Libri Quattuor Sententiarum
10:
2468:
2003:On Marvellous Things Heard
1622:Potentiality and actuality
839:. BRILL. pp. 91–133.
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2366:Commentaries on Aristotle
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970:
634:, John Marsilius Inguen,
793:Not to be confused with
768:
295:Protestant scholasticism
2452:Philosophy of Aristotle
1734:Sophistical Refutations
1058:20th century in science
1053:19th century in science
703:"mechanical philosophy"
307:Protoscholastic writing
231:("Doctor Scholasticus")
189:("Doctor Invincibilis")
1919:On Divination in Sleep
1605:Horror vacui (physics)
978:Theories and sociology
532:Scholastic elaboration
339:Catholicism portal
207:("Doctor Universalis")
40:
2411:Philosophy portal
2033:Rhetoric to Alexander
1038:Scientific Revolution
831:William Royall Newman
558:Simplicius of Cilicia
327:Philosophy portal
301:Problem of universals
219:("Doctor Seraphicus")
39:
2442:History of chemistry
2122:Andronicus of Rhodes
2023:On Virtues and Vices
1978:On Indivisible Lines
1899:Sense and Sensibilia
1869:Rhetoric and poetics
1682:mathematical realism
1291:Agricultural science
1043:Age of Enlightenment
652:Alessandro Achillini
596:Richard of Middleton
223:Anselm of Canterbury
177:("Doctor Angelicus")
157:John Scotus Eriugena
2092:Strato of Lampsacus
1724:Posterior Analytics
1476:Ideas and interests
1329:Veterinary medicine
1023:Classical Antiquity
795:Marsilius of Inghen
737:faith. Aristotle's
664:Francisco de Toledo
421:of modern science.
225:("Doctor Marianus")
201:("The Commentator")
183:("Doctor Subtilis")
2136:Islamic Golden Age
2059:Peripatetic school
1845:Nicomachean Ethics
1540:Future contingents
964:History of science
827:John Emery Murdoch
739:mininima naturalia
275:Islamic philosophy
195:("Doctor Eximius")
137:Augustine of Hippo
41:
2419:
2418:
2371:Metabasis paradox
2332:
2331:
2272:
2271:
2259:Pietro Pomponazzi
2201:
2200:
2181:
2180:
2130:
2129:
2082:Eudemus of Rhodes
2072:Clearchus of Soli
2046:
2045:
1714:On Interpretation
1657:Temporal finitism
1545:Genus–differentia
1502:Category of being
1409:
1408:
1301:Materials science
1263:Political science
1028:Medieval European
881:978-90-481-2362-9
705:of thinkers like
681:with the general
648:Gaetano of Thiene
624:Gregory of Rimini
608:William of Ockham
592:Boethius of Dacia
434:Greek philosopher
375:
374:
290:Neo-scholasticism
270:Catholic theology
187:William of Ockham
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2409:
2408:
2407:
2397:
2396:
2274:
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2254:Jacopo Zabarella
2203:
2202:
2183:
2182:
2132:
2131:
2112:Diodorus of Tyre
2055:
2054:
1697:
1696:
1627:Substance theory
1588:Moderate realism
1582:Minima naturalia
1483:Active intellect
1436:
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1422:
1413:
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1402:
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1386:
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1296:Computer science
1144:Natural sciences
1109:Medieval Islamic
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782:Minima naturalia
779:
763:minima naturalia
731:minima naturalia
715:minima naturalia
679:minima naturalia
672:minima naturalia
668:Benedict Pereira
654:, Luis Coronel,
640:Albert of Saxony
588:Siger of Brabant
568:Minima naturalia
538:minima naturalia
526:chemical element
491:substantial form
411:minima naturalia
379:Minima naturalia
367:
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337:
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265:Franciscan Order
193:Francisco Suárez
97:Summa Grammatica
83:Summa Theologica
16:
15:
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2264:Cesar Cremonini
2220:Albertus Magnus
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2042:
1998:Physiognomonics
1993:On Things Heard
1988:On the Universe
1949:
1933:
1891:Parva Naturalia
1885:
1864:
1850:Eudemian Ethics
1830:
1814:
1776:
1738:
1719:Prior Analytics
1686:
1610:Rational animal
1471:
1445:
1443:Aristotelianism
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1381:
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1235:Social sciences
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904:1.4, 187b14–21.
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868:(4 June 2009).
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727:Pierre Gassendi
699:
660:Domingo de Soto
616:Adam de Wodeham
614:, Walter Bury,
612:William Alnwick
576:Albertus Magnus
554:John Philoponus
534:
427:
409:Speculation on
371:
331:
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260:Dominican Order
255:Aristotelianism
243:
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205:Albertus Magnus
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2376:Views on women
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1489:Antiperistasis
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983:Historiography
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915:Thomas Aquinas
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755:Daniel Sennert
725:The mechanist
698:
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656:Juan de Celaya
644:Paul of Venice
628:John Dumbleton
604:John of Jandun
580:Thomas Aquinas
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213:("The Master")
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175:Thomas Aquinas
171:
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152:Alcuin of York
149:
147:Pope Gregory I
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50:
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32:
31:
25:
24:
9:
6:
4:
3:
2:
2464:
2453:
2450:
2448:
2447:Scholasticism
2445:
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2435:
2433:
2430:
2429:
2427:
2412:
2402:
2400:
2392:
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2381:Wheel paradox
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2289:Trendelenburg
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2221:
2218:
2216:
2215:Peter Lombard
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2212:
2210:
2208:
2207:Scholasticism
2204:
2194:
2191:
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2188:
2184:
2172:
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2168:
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2160:
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2110:
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2100:
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2097:Lyco of Troas
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2068:
2065:
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2060:
2056:
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2049:
2039:
2038:Magna Moralia
2036:
2034:
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2029:
2026:
2024:
2021:
2019:
2016:
2014:
2011:
2009:
2006:
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1991:
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1677:Virtue ethics
1675:
1673:
1672:Unmoved mover
1670:
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1200:Combinatorics
1198:
1196:
1193:
1191:
1188:
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1179:
1173:
1170:
1168:
1167:Earth science
1165:
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1024:
1021:
1019:
1018:Ancient world
1016:
1015:
1013:
1009:
1004:
994:
991:
989:
988:Pseudoscience
986:
984:
981:
979:
976:
975:
973:
969:
965:
958:
953:
951:
946:
944:
939:
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925:
920:
916:
910:
903:
899:
894:
892:
883:
877:
873:
872:
867:
866:Alan Chalmers
861:
859:
857:
848:
846:90-04-11516-1
842:
838:
837:
832:
828:
822:
820:
818:
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796:
790:
783:
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774:
766:
764:
760:
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752:
748:
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736:
732:
728:
723:
721:
716:
712:
708:
704:
694:
692:
691:
684:
680:
675:
673:
669:
665:
661:
657:
653:
649:
645:
641:
637:
636:John Wycliffe
633:
632:Nicole Oresme
629:
625:
621:
617:
613:
609:
605:
601:
597:
593:
589:
585:
584:Giles of Rome
581:
577:
573:
569:
565:
564:(Ibn Rushd).
563:
559:
555:
551:
550:
545:
544:
539:
529:
527:
523:
519:
515:
510:
508:
504:
498:
496:
492:
488:
484:
480:
476:
475:atomic theory
472:
468:
464:
460:
451:
447:
443:
442:
441:
438:
435:
432:
422:
420:
419:atomic theory
416:
412:
407:
405:
401:
397:
393:
389:
385:
381:
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368:
363:
361:
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286:
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273:
271:
268:
266:
263:
261:
258:
256:
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251:
250:
246:
245:
239:
238:
230:
229:Peter Abelard
227:
224:
221:
218:
215:
212:
211:Peter Lombard
209:
206:
203:
200:
197:
194:
191:
188:
185:
182:
179:
176:
173:
172:
166:
165:
158:
155:
153:
150:
148:
145:
143:
140:
138:
135:
134:
128:
127:
120:
119:
115:
113:
112:
108:
106:
105:
104:Summa logicae
101:
99:
98:
94:
92:
91:
90:Cur Deus Homo
87:
85:
84:
80:
79:
73:
72:
65:
62:
60:
57:
55:
52:
51:
45:
44:
38:
34:
33:
30:
29:Scholasticism
27:
26:
22:
18:
17:
2361:Neoplatonism
2087:Theophrastus
1945:Protrepticus
1838:and politics
1649:
1636:
1632:hypokeimenon
1630:
1614:
1597:
1581:
1580:
1573:
1561:
1557:Hylomorphism
1549:
1527:
1506:
1494:
1487:
1339:Neuroscience
1243:Anthropology
1225:Trigonometry
922:
918:
909:
901:
870:
835:
789:
781:
777:
762:
759:Robert Boyle
743:"corpuscles"
738:
730:
724:
714:
700:
689:
688:Aristotle's
683:Aristotelian
678:
676:
671:
620:Jean Buridan
567:
566:
547:
541:
537:
535:
511:
499:
494:
486:
456:
431:Pre-Socratic
428:
410:
408:
378:
377:
376:
299:
285:Neoplatonism
247:
169:Philosophers
116:
109:
102:
95:
88:
81:
2237:Duns Scotus
2077:Dicaearchus
2067:Aristoxenus
1826:Metaphysics
1819:Metaphysics
1805:Progression
1772:On the Soul
1767:Meteorology
1569:Magnanimity
1535:Four causes
1306:Engineering
1248:Archaeology
1215:Probability
1182:Mathematics
1048:Romanticism
1033:Renaissance
600:Duns Scotus
572:Roger Bacon
549:Meteorology
483:hylomorphic
479:John Dalton
457:Unlike the
217:Bonaventure
181:Duns Scotus
76:Major works
2426:Categories
2319:Hursthouse
2193:Maimonides
2159:Avicennism
1810:Generation
1782:On Animals
1709:Categories
1529:Eudaimonia
1283:Technology
1268:Psychology
1220:Statistics
1067:By culture
971:Background
804:References
747:alchemical
729:discussed
711:John Locke
467:Democritus
437:Anaxagoras
280:Empiricism
249:Philosophy
131:Precursors
2354:Platonism
2309:MacIntyre
2171:Averroism
2149:Al-Farabi
2107:Critolaus
2051:Followers
2028:Economics
2008:Mechanics
1973:On Plants
1968:On Colors
1963:On Breath
1914:On Dreams
1904:On Memory
1667:Haecceity
1645:Syllogism
1616:Phronesis
1508:Catharsis
1457:Aristotle
1377:Timelines
1354:Pathology
1349:Nutrition
1273:Sociology
1253:Economics
1162:Chemistry
1152:Astronomy
1089:Byzantine
1084:Brazilian
1079:Argentine
898:Aristotle
749:works of
707:Descartes
518:electrons
503:elemental
463:Leucippus
392:essential
388:substance
384:Aristotle
2399:Category
2324:Nussbaum
2294:Brentano
2166:Averroes
2154:Avicenna
2144:Al-Kindi
2117:Erymneus
2013:Problems
1909:On Sleep
1876:Rhetoric
1855:Politics
1800:Movement
1662:Quiddity
1523:accident
1450:Overview
1400:Category
1359:Pharmacy
1316:Medicine
1205:Geometry
1195:Calculus
1114:Japanese
735:Catholic
562:Averroes
489:) and a
471:Epicurus
445:minimum.
398:" means
199:Averroes
142:Boethius
64:Occamism
21:a series
19:Part of
2437:Atomism
2242:Scotism
2230:Thomism
1881:Poetics
1790:History
1752:Physics
1744:Physics
1701:Organon
1629: (
1575:Mimesis
1519:Essence
1334:Anatomy
1258:History
1190:Algebra
1172:Physics
1157:Biology
1134:Spanish
1129:Russian
1124:Mexican
1099:Chinese
1074:African
902:Physics
745:in the
741:became
690:Physics
543:Physics
540:in the
493:(Greek
459:atomism
453:flesh."
415:atomism
242:Related
59:Scotism
54:Thomism
48:Schools
2284:Newman
2277:Modern
2186:Jewish
1836:Ethics
1729:Topics
1599:Philia
1593:Mythos
1467:Lyceum
1388:Portal
1119:Korean
1104:Indian
1094:French
1011:By era
878:
843:
720:Dalton
666:, and
522:quarks
507:nature
495:morphe
469:, and
404:matter
400:formal
396:nature
2349:Plato
2314:Smith
2299:Adler
1795:Parts
1692:Works
1651:Telos
1638:ousia
1563:Lexis
1551:Hexis
1496:Arete
1462:Logic
1210:Logic
769:Notes
751:Geber
2304:Foot
1938:Lost
876:ISBN
841:ISBN
753:and
709:and
556:and
546:and
514:atom
487:hyle
477:of
461:of
2428::
1635:,
921:.
917:.
900:,
890:^
855:^
812:^
765:.
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658:,
650:,
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630:,
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366:e
359:t
352:v
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