This discussion on composite bodies would seem more appropriate to
Book I with respect to modes. Yet, Spinoza delves into this issue as he
is addressing the concept that the mind is the idea of the body. His
prior proposition articulates that the body is the object of the mind.
So he explores the basic operation of simple and composite bodies so
that the ideation of the mind is more clear. The patterns described here
are the fundamentals that give rise to thought. The mind's operation is
based on an understanding of the operating principles of the composite
bodies which form the body that is the object of the mind. This
"understanding" includes such things as sensation and emotion.
DEFINITIO: Cum corpora aliquot ejusdem aut diversæ magnitudinis a reliquis ita coercentur ut invicem incumbant vel si eodem aut diversis celeritatis gradibus moventur ut motus suos invicem certa quadam ratione communicent, illa corpora invicem unita dicemus et omnia simul unum corpus sive individuum componere quod a reliquis per hanc corporum unionem distinguitur.
Translated as,
When some bodies of the same or of diverse magnitudes are forced by the other [bodies] so that they lay on one another or if they are moved by the same or by varying degrees of speed so that they communicate their own motions to each other by some fixed means, we say that those bodies are united with each other and that everything at the same time makes up one body or individual which is distinguished from others by this union of bodies.
AXIOMA III: Quo partes individui vel corporis compositi secundum majores vel minores superficies sibi invicem incumbunt, eo difficilius vel facilius cogi possunt ut situm suum mutent et consequenter eo difficilius vel facilius effici potest ut ipsum individuum aliam figuram induat. Atque hinc corpora quorum partes secundum magnas superficies invicem incumbunt, dura, quorum autem partes secundum parvas, mollia et quorum denique partes inter se moventur, fluida vocabo.
Translated as,
As parts of an individual or composite body lay in line with larger or smaller surfaces among each other, so they are able to be compelled with difficulty or ease so as to change their place and consequently are able to be effected with difficulty or ease that the individual itself is led to another shape. And from here bodies whose parts lay on large surfaces among each other, are hard, moreover those whose parts in line with small [surfaces], are soft and whose parts are moved from all sides among themselves, I will call fluid.
LEMMA IV: Si corporis sive individui quod ex pluribus corporibus componitur, quædam corpora segregentur et simul totidem alia ejusdem naturæ eorum loco succedant, retinebit individuum suam naturam uti antea absque ulla ejus formæ mutatione.
Translated as,
If something of a body or an individual is composed from more bodies, certain bodies are separated and at the same time as many others of the same nature follow in place of them, it [the body] will retain its individual nature as before without any change of its form.
DEMONSTRATIO: Corpora enim (per lemma 1) ratione substantiæ non distinguuntur; id autem quod formam individui constituit, in corporum unione (per definitionem præcedentem) consistit; atqui hæc (per hypothesin) tametsi corporum continua fiat mutatio, retinetur : retinebit ergo individuum tam ratione substantiæ quam modi suam naturam uti ante. Q.E.D.
Translated as,
For bodies (by IIL1) are not distinguished by reason of substance; moreover that which constitutes the form of the individual, consists in a union of bodies (by preceding definition); and so this [union] (by hypothesis) is retained as if a continuous change of bodies occurred. Therefore it will retain the individuality not only by reason of substance but also due to its own nature of the mode as before.
LEMMA V : Si partes individuum componentes majores minoresve evadant, ea tamen proportione ut omnes eandem ut antea ad invicem motus et quietis rationem servent, retinebit itidem individuum suam naturam ut antea absque ulla formæ mutatione.
Translated as,
If the parts composing an individual become either more or less, nevertheless by that proportion so that all might save the same ratio as before for movement and rest, it [body] will retain likewise its same individual nature as before without any change of form.
DEMONSTRATIO: Hujus eadem est ac præcedentis lemmatis.
Translated as,
The demonstration of this is the same as of the preceding lemma.
LEMMA VI: Si corpora quædam individuum componentia motum quem versus unam partem habent, aliam versus flectere cogantur at ita ut motus suos continuare possint atque invicem eadem qua antea ratione communicare, retinebit itidem individuum suam naturam absque ulla formæ mutatione.
Translated as,
If certain bodies composing an individual have motion which turns one part, [and] they [certain bodies] are compelled to bend against another and so are able to continue their movements and communicate among each other as before, then it [the individual] will retain likewise its own individual nature without any change of form.
DEMONSTRATIO: Per se patet. Id enim omne retinere supponitur quod in ejusdem definitione formam ipsius constituere diximus.
Translated as,
This is clear by itself. For it is supposed to retain everything which in its same definition that we said constitutes its form.
LEMMA VII: Retinet præterea individuum sic compositum suam naturam sive id secundum totum moveatur sive quiescat sive versus hanc sive versus illam partem moveatur dummodo unaquæque pars motum suum retineat eumque uti antea reliquis communicet.
Translated as,
Besides an individual thus composed retains its own nature whether it is moved all together or it is resting or this or that part is moved as long as each and every part retains its own motion and communicates this [motion] to the remaining parts as before.
DEMONSTRATIO: Patet ex ipsius definitione, quam vide ante lemma 4.
Translated as,
It is clear from the definition of itself, on which see IIL4 above.
SCHOLIUM: His itaque videmus qua ratione individuum compositum possit multis modis affici, ejus nihilominus natura servata. Atque hucusque individuum concepimus quod non nisi ex corporibus quæ solo motu et quiete, celeritate et tarditate inter se distinguuntur hoc est quod ex corporibus simplicissimis componitur. Quod si jam aliud concipiamus ex pluribus diversæ naturæ individuis compositum, idem pluribus aliis modis posse affici reperiemus, ipsius nihilominus natura servata. Nam quandoquidem ejus unaquæque pars ex pluribus corporibus est composita, poterit ergo (per lemma præcedens) unaquæque pars absque ulla ipsius naturæ mutatione jam tardius jam celerius moveri et consequenter motus suos citius vel tardius reliquis communicare. Quod si præterea tertium individuorum genus ex his secundis compositum concipiamus, idem multis aliis modis affici posse reperiemus absque ulla ejus formæ mutatione. Et si sic porro in infinitum pergamus, facile concipiemus totam naturam unum esse Individuum cujus partes hoc est omnia corpora infinitis modis variant absque ulla totius Individui mutatione. Atque hæc, si animus fuisset de corpore ex professo agere, prolixius explicare et demonstrare debuissem. Sed jam dixi me aliud velle nec alia de causa hæc adferre quam quia ex ipsis ea quæ demonstrare constitui, facile possum deducere.
Translated as,
With these, we see thus by what means a composite individual is able to be affected in many ways, whose nature is, nevertheless, preserved. And so to this point we have conceived the individual which exists not unless from bodies which are distinguished by motion or rest alone, by speed or slowness among themselves, that is, which is composed out of the simplest bodies. What if now we might conceive of another [body] made up of more individuals of diverse nature, we might find the same [body] is able to be affected in even more other ways, whose nature, nevertheless, is preserved. For since each and every part of it is composed of more bodies, each and every part will be able therefore (by IIL7) without any change of its own nature, be moved now slowly now quickly and consequently communicate its motions to the remaining parts more quickly or slowly. Which if moreover we might conceive of a third kind of individuals composed from these second [type], we might find that the same is able to be affected by many other modes without any change of its form. And if thus we proceed again into infinity, we may easily conceive all nature to be one Individual whose parts, that is, all bodies change by infinite modes without any change of the whole Individual. And these things, if it had been my mind to discuss the body especially, I ought to explain more fully and demonstrate. But already I have said that I wish something else and not to raise other things concerning this cause which because I am easily able to deduce [them] from these, I have decided to demonstrate them.
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