Translations and notes for Max Jammer's Concepts of Space

7/27/2019 Translations and notes for Max Jammer's Concepts of Space

1/27

Concepts of SpaceMax Jammer

1969 edition adds two pages to introduction of the 1954 edition and merges theappendix into the text , adding one page (199) !here are actua""# $uite a fewuntrans"ated passages em%edded in the text M# trans"ations are rough and "itera"

Comments and corrections we"come &age num%ers refer to '69 edition !he1994 edition from oer (*61 pages) adds a Chapter 6, %ut is otherwise the same

Chapter + !he Concept of Space in nti$uit#-n"# the one untrans"ated passage occurs in this chapterp *6 Morit. Cantor referes to this passage and sa#s / 0ei der 2n%estimmtheitdieser nga%e m3ssen wir a""erdings dahin geste""t sein "assen, o% man g"au%enwi"", es seien in ener Schrift edanen entha"ten gewesen, we"che dem egriffeon 7aumoordinaten nahe ommen0

8rom the indefinitness of these statements we must indeed a""ow to %e stated,

whether one wi"" %e"iee it, that there ma# hae %een in those writings, thoughtswhich came near to the concept of space coordinates:

Chapter ++ Judeo;Christian +deas a%out Spacep *9 eip.ig, 1?4@;41), p 6?1

8!he =e%rews do not hesitate to ca"" od (god), %ecause contained %# nothing,

himse"f %# his tru"# immeasura%"e power containing a"", 0maom0 or (sie)0p"ace0 as often done in "itt"e %oo of &ascha" ritua" which 7itange"ius edited:(wh# is this particu"ar"# interestingA)p BB 7euch"in'sDe verbo mirifico8on the wonderfu", mare"ous word:pB4 7aino"des' Censura librorum apocryphorum Veteris Testamentis 8udgement,criti$ue of the apocr#pha" %oos of the o"d testament:footnote * !homas Campane""a,Medicinalium justa propria principia libriseptem(>#ons, 16B5) 8the correct proper princip"es of medicine %oo seen:pB5 mundus mathematicus seu spatium 8mathematica" wor"d or space:

p B5 +n hisMetaphysicarum rerum juxta (sic. justa?) propria domata/ 80ofmetaph#sica" things c"ose to or near "ie indiidua" or specia" doctrines ordogmas0 or, perhaps, 0correct proper dogmas of metph#sica" matters0:Campane""a characteri.es this mathematica" wor"d or space as the 0omniumdiinitas su%stentas, portans$ue omnia er%o irtutis suae 0

8diinit# of a"" things standing firm and %earing a"" things %# word of his strength(of his word) or in his exce""ent name:

1


2/27

Compane""a states that space is in od, %ut od is not "imited %# space, which is=is 0diina creatura0 !he idea of the identification of space with at "east anattri%ute of the iine eing gains new impetus in the second %oo, where weread/ 0Spatium, entia "ocans inenio primum immorta"e, $uia nu""i est

contrarium0 +n Campane""a's conception, space %ecomes an a%so"ute, a"mostspiritua" entit#, characteri.ed %# diine attri%utes

8Space, giing p"ace to existing things + find (to %e) first immorta", %ecause it hasno contrar# :

p B6 0 , horum c"arissimus erat !homas Campane""a St#"ensis, cuus in corpus!e"esii ingenium transmigrasse dice%atur0

8was of the highest inte""ect, who is said to hae transmigrated into the %od# of!e"esi:

p B 0Dgo sum "ux mundi0ccording to Saint onaenture, od is 0spiritua"is "ux in omnia;modaactua"itate0 8spiritua" "ight in eer# wa# actua" :

pB9 0u"timum continentis immo%i"is,0 in contrast to ristot"e's 0u"timumimmo%i"e continentis0 8highest or fina" containing immo%i"e or immo%i"econtainer:


3/27

comparison to that which that p"ace was defined whence (the) p"ace of heaen is(the) highest p"ace !his howeer has nature of "ight !hat indeed highest iscontaining and presering, as is p"ace :

p 4* !he answer "ies, according to (=enr#) More, in the nature of space, the

c"ear understanding of which can a"one sae phi"osoph# from an otherwiseineita%"e atheism 0t$ue ita per eam ipsam anuam per $uam &hi"osophiaCartesiana eum idetur e""e e Mundo exc"udere, ego, e contra, eum introducererursus enitor et contendo0

8and so going through that same gate through which Cartesian &hi"osoph# wishesto see od exc"uded from the wor"d, + , on the contrar#, strie and contend tointroduce =im again:

p 4B escartes contended that the wa""s of a esse" that is exhausted of air mustnecessari"# co""apse 0Si $uaeratur, $uid fiet, si eus auferat omne corpus $uod in

a"i$uo ase continetur, et nu""um a"iud in a%"ati "ocum enire permittat/7espondendum est/ Gasis "atera si%i inicem hoc ipso fore contiguaA !rincipiaphilosophiae, ++, 1?8if ased, what wi"" happen, if od withdraws eer# %od# which is contained insome esse", and a""ows no other to come in p"ace of the remoed (%odies)/ theresponse is/ the sides of the esse" themse"es in turn (or mutua""#) %# this samewa# sha"" %e touching:

p 44 Sed vasis latera non fierunt contiua"#but in fact the sides of the vessel are not made contiuous$!he existence of space is guaranteed %# its er# measura%i"it# 0par aunes ou par"ieues0 8%# e""es or %# "eagues:

p 4 %ecause Hon entis nu""a est ffectio, according to the 7easonings of #our%e"oed Master

8not %eing nothing is an affection:

p 4? !he attri%utes of space are attri%utes of od "ist of these attri%utes isgien in More'sEnchiridion metaphysicum%He$ue enim 7ea"e duntaxat, ($uod u"timo "oco nota%imus) sed iinum $uiddamide%itur hoc Dxtensum infinitum ac immo%i"e, ($uod tam certo in rerum naturadeprehenditur) post$uam iina i""a Homina e" !itu"os $ui examussim ipsicongruunt enumeraimus, $ui I u"teriorem fidem facient i""ud non posse essenihi", utpote cui tot tam$ue praec"ara ttri%uta competunt

>itera""#/ 8or not on"# the 7ea" (concerning which we write %e"ow) %ut a"so thisinfinite and immo%i"e Dxtension wi"" %e seen a ind of iinit# (%ecause ie theDxtension so certain"# found in things produced natura""#) when we hae

B


4/27

enumerated those Hames or !it"es which agree perfect"# and which producegreater confidence that a thing cannot %e nothing, inasmuch as what so man#er# c"ear ttri%utes are agree:

Dd Cr#er suggests/ 8!his infinite and motion"ess Dxtension (which is found so

certain"# in nature) wi"" appear not on"# 7ea" (on which we sha"" comment at theend) %ut somewhat iine after we hae enumerated those iine Hames, or!it"es rather, which agree so precise"# with each other, and which wi"" proidefurther proof that a thing cannot %e nothing when so man# such distinct ttri%utescoincide in it:

Cuusmodi sunt $uae se$uuntur, $uae$ue Metaph#sici &rimo Dnti speciatimattri%unt8-f such ind are those (ie tit"es) which fo""ow, and which Metaph#siciansattri%ute to &rime eing as species:

2t unum, Simp"ex, +mmo%i"e, eternum, Comp"etum, +ndependens, se extens,&er se su%stens, +ncorrupti%i"e, Hecessarium, +mmensum, +ncreatum,+ncircumscriptum, +ncomprehensi%i"e, -mnipraesens, +ncorporeum, -mniapermeans I comp"ectans, Dns per Dssentiam, Dns actu, &urus ctus

8s one, Sing"e, +mmoa%"e, Dterna", Comp"ete, +ndependent, Se"f Caused, Se"fSu%sisting, +ncorrupti%"e, Hecessar#, Gast, 2ncreated, 2n%ounded,+ncomprehensi%"e, -mnipresent, +ncorporea", "" &erading and Dm%racing ,Dxisting in Su%stance, eing in ctua"it#, &ure ction:

Hon pauciores $uam iginti !itu"i sunt $ui%us insigniri so"et iinum Humen, $uiinfinito huic >oco interno, $uem in rerum natura esse demonstraimus, aptissimeconeniunt/ ut omittam ipsam iinum Humen apud Ca%%a"istes appe"ari0maom,0 id est, >ocum

>itera""#/ 8 Hot fewer than twent# !it"es (there) are (with) which we areaccustomed to mar the Sacred


5/27

p 4?&im'umis introduced as though we a"" new what it means +t is a =e%rewword which means 0contraction0 footnote * 0eus creaturus mundos contraxitpraesentiam suam,0 (abbala denudata(Sa".%ach, 16), part ++, p 15@8od to create the wor"d contacted ("it withdrew) his presence:

p 49 +ndeed, a simi"ar inte""ectua" process was most pro%a%"# in f"uentia" on thephi"osoph# of Spino.a ei%ni./ 0Gerissimum est, Spino.am Ca%%a"a =e%raeorum esse a%usum08+t is most true, Spino.a Ca%%a"a of =e%rews to %e wasted or a%used: (+ don't$uite get this one)

5


6/27

Chapter B!he Dmancipation of the Space Concept from ristote"ianism

p 55 !hemistius!araphrasis in libros 1uatuor 2ristotelis de caelo.8ristot"e's e Cae"o paraphrased in four %oos:

p 5 +t is this tendenc#, inherent in the moing %od# and not in the medium or inspace, that corresponds to the 0impetus0 in the case of forced motion &hi"oponus'exp"anation of the fa"" of hea# %odies shows a remara%"e resem%"ance to theexp"anation of grait# suggested %# Copernicus/0D$uidem existimo graitatem non a"iud esse,$uam appententiam (sic.3perhaps appetentiam ) $uandam natura"em parti%usinditam a diina proidentia opificis uniersorum,ut in unitatem integritatem$ue suam sese conferant in forman (sic.3perhapsformam) g"o%i coKuntes0De revolutionibus orbium coelestium3 liber 4 cap. 45.8+ndeed + thin grait# not to %e different,than (a) "onging for a certain natura" region introduced %# diine proidence of

architect (framer, artisan, worman) of wor"ds ,in order that in unit# and oneness the# (ie things) gather themse"es in form of adense mass (g"o%i) co""ected together:

p 5? amascius' treatise!eri arithmou ai topou ai chronou 8-n the num%ersand p"aces and periods (of time):p5? ; Simp"icius Corollarium de locoof Commentariato ristot"e's!hysics

p 59 or examp"e, !hemistius in his!araphrasis in libros 1uatuor 2ristotelis decaelosa#s/0Sed conersio,immo omnis motus,super manente ac $uiescente a"i$uo omnino ce"e%ratur 1

8%ut on the contrar#,rather a"" that is moed,performs entire"# oer some other remaining and resting (thing):

+n iis autem,$uae e nima"ium Motu a no%is dicta sunt,monstratum est id,$uod manet ac $uiescit,i""ius autem partem esse non posse,$uod super ipso moetur08+n the same howeer,

1Lce"e%ratur

ce"e%ratur G 1 1 &7DS &SS+GD +H B Sce"e%ro, ce"e%rare, ce"e%rai, ce"e%ratus G (1st) !7HS 8NNN-:ce"e%rateFperformE fre$uentE honorFg"orif#E pu%"ici.eFadertiseE discussF%and#E

6


7/27

such things in e nima"ium Motu0 hae dec"ared to us,(where) it is demonstrated,insofar as (something) moes and rests,howeer that cannot %e part, which oer itse"f is moed:(ie that oer which it is moed cannot itse"f %e part of the thing moed)

p 6@ an o%ect which appears to %e at rest to an o%serer who regards himse"f as%eing moed wou"d appear to %e retrogressing to the same o%serer if he regardshimse"f at rest

ootnote 15 0Si a"i$ui%us "atis p"uri%us inae$ua"i ce"eritate simu" transportetur ineasdem partes et ocu"us, $uae $uidem ocu"o ae$ua"i ce"eritate feruntur, ide%unturstare, tardiora ero in contrarium ferri, ce"eriora ero in praecedentia ; Sia"i$ui%us "atis appareat a"i$uid, $uod non feratur, ide%itur i""ud non "atumretrorsum ferri0 + > =ei%erg and = Menge, edEuclidis opera omnia(>eip.ig,1??B;1916) o" , 6ptica, p 11@

p64 M uttmann draws our attention in this connection to the fo""owing phrasein >ei%ni.'sEpistolae ad !. des )osses/ 0Su%stantia nempe simp"ex etsi nonha%eat in se extensionem, ha%et tamen positionem, $uae est fundamentumextensionis08Certain"# simp"e su%stances een if the# hae not extension in themse"es,hae #et positionwhich is the foundation of extension:

p 65 modus tollens 7

p 6 +t wi"" %e reca""ed that a"i"ei a"so discusses the pro%"em in hisDiscorsi edimostra'ioni matematiche3 intorno a due nuove scien'e38iscourses andmathematica" demonstrations a%out to two new sciences:

p 69 0+ndiisi%i"e indiisi%i"i additum non facit maius,0 8 +ndiisi%"e added toindiisi%"e does not mae "arger:

2Modus !o""ens (M!)

ru"e of inference of the form/

p O $

P $ QQQQQQQ

P p

Dxamp"e/ 0+f it had rained this morning, then the grass wou"d sti"" %e wet ut the grass is notwet !herefore, it did not rain this morning0

simp"e truth;ta%"e shows that an# argument of this form must %e a"id


8/27

p B !hat this pro%"em was rea""# one of the maor incitements to Copernicus'drastic reision of the accepted cosmo"ogica" conception ma# %e seen fromarious remars in hisDe revolutionibus orbium caelestium(154B) +n chapter Gof the first %oo he sa#s/

0Cum$ue cae"um sit,$uod continet et cae"at omnia,communis uniersorum "ocus,non statim apparet,cur non magis contento $uam continent,"ocato $uam "ocant motus attri%uatur0

M# "itera" trans"ation/ 8whi"e to heaen (moement ma# %e attri%uted ),which contains and finishes a"",common p"ace of a"" things,

(it) does not immediate"# appear,wh# not rather to contained than containing,to "ocated than "ocating, moement ma# %e attri%uted (ie to containing and"ocating as we"" as to heaen):

Dd Cr#er suggests/ 8


9/27

he fee"s ustified in sa#ing/ 0&rima et suprema omnium est ste""arum fixarumsphaera, se ipsam et omnia continens, ideo$ue immo%i"isE nempe uniersi "ocus,ad $uem motus et positio caeterorum omnium s#derum conferatur0

8irst and highest of a"" is the sphere of fixed stars in itse"f itse"f and a""containing, therefore immo%i"eE tru"# uniersa" p"ace, on which confering motionand position on a"" remaining (caeterorum) stars :

p 4 So, for examp"e, among the errors condemned in 1* there is this/ 0uodeus non possit moere Coe"um motu rectu Dt ratio est $uia tunc re"in$ueretacuum08!hat od is not a%"e to moe heaen %# recti"inear motion (motu rectu)and (the) reason is %ecause then it wou"d "eae %ehind empt# (p"ace, locum):

p 5 from 7ichard of Midd"eton's Super 1uattuor libros sententiarum

1uaestiones subtilissimae.8four %oos a%out the most su%t"e $uestions ofthining:

ootnote 46 gies >atin text

p?* Cusanus comes to the conc"usion/ 0ui igitur est Centrum mundusAsci"icet est eus %enedictus, i""e est Centrum terrae, et omnium sphaerarum0Hicho"as of Cusa,De docta inorantia3 443 88 #of learned inorance3 on teachininorance?$8


10/27

Cusanus, o%ecting the spatia" hierarch# of a"ues, states exp"icit"#/ 0He$ue dicide%et, $uod $uia terra est minor so"e et a% eo recipit inf"uentiam, $uod proptereasit i"ior08Heither ought it to %e saidthat %ecause this earth is sma""er than the sun and from it receies inf"uence

that for this reason it shou"d %e meaner:p ?4 Den in Cardan'sDe subtilitate, space is sti"" conceied in accord withristote"ian tradition as the concae surace of the "imiting %od# 0Dst igitur"ocus u"tima corporis superficies, corpus contentum am%icus0 Jerome Cardan,De subtilitate3 lib. 4.

8fina" p"ace is therefore surface of %od#,%od# contained (%# encirc"ing thing):

p ?5 Sca"iger presupposes the acuum as a necessar# condition of motion 0+nnatura acuum dari necesse est0 J C Sca"iger,Exotericarum exercitationum

liberi ad 9ieronymum Cardanum(>utet, 155)8in nature empt# (p"ace) is necessar# to a""ow:0+dem$ue esse acuum et "ocumE ne$ue differre, nisi nomine08and a"so to empt# and p"aceE neither differing, except on"# in name:

!e"esio+f a %od# "eaes its p"ace or is expe""ed from it, p"ace itse"f does not "eae, nor is itexpe""ed, %ut remains the same, prompt"# %ecoming the receptac"e of another%od#

+ta$ue "ocus entium $uorumis receptor fieri $ueatet in existenti%us enti%us recedenti%us expu"sisenihi" ipse recedat expe""ature,

sed idem perpetuo remaneatet succedentia entia promptissime suscipiat omnia,

tantus$ue assidue ipse sit,$uanta$uae (sic.) in ipso "ocantur sunt entiaEperpetio (sic.) nimirum iis,$uiae (sic.) in ea (sic.eoA) "ocata sunt,ae$ua"is,at eorum nu""i idem sit nec fiat un$uam,sed penitus a% omni%us diersus sit

8ccording"# the p"ace of an# %od# whateer can %e made the receierand in "eaing the %eing which withdraws or drien outnothing at a"" of itse"f ma# %e withdrawn or expe""ed,

%ut remans a"wa#s the sameand readi"# reciee a"" succeeding %eings,

as much ma# continue to %e itse"f,

1@


11/27

as in itse"f %eings are "ocatedEperpetua""# dou%t"ess the same,which are in that p"ace,e$ua" (e$ua""#A),%ut of them none ma# %e nor eer %e made the same,

%ut deep"# ma# %e separated from a"":

Dd Cr#er suggests/ !hus a "ocation cou"d %ecome the receier of an# %eings at a""and in the withdrawa" or expu"sion of existing %eings wou"d itse"f not withdraw or%e expe""ed one ot, %ut wou"d sta# constant"# the same and tae in most readi"#a"" things that come there, and %e a"wa#s as "arge itse"f as great as %e the %eings"ocated in itE constant"# indeed on a par with the things "ocated in it, and #et neer%eing or %ecoming the same as an# of them, %ut deep"# separated from a"" things

!e"esioDe natura rerum juxta propria principia libri novem(Hap"es, 15?6), +,

*5 8-n the Hature of !hings ccording to !heir -wn &rincip"es:p ?6 !he considerations adduced %# !e"esio show c"ear"# the new spirit of +ta"iannatura" phi"osoph# of the sixteenth centur# Hothing "ess than the formu"ation ofa new ph#sics is at issue ut another o%stac"e has sti"" to %e remoed %eforethese ideas cou"d %e assimi"ated and a new machanics reared on their %asis !hetraditiona" su%stance;accident doctrine, the great %u"war of scho"astic thought,had to %e set aside +t was not enough to reise the ph#sica" foundations of thetheor# of spaceE it had to %e proied with a new metaph#sica" foundation as we""

ranciscus &atritius undertoo this tas

uid ergo estAh#postasis, diastema, est (sic.), diastasis (sic.), ectasis (sic.) est, extensio est,intera""um est, capedo est, at$ue intercapedoDrgo $uantitasA Drgo accidensA Drgo accidens ante su%stantiamA I ante corpusArchitas uter$ue, I senior thagorae auditor, I iunior &"atonis amicus,I $uicos (sic.) secuti sunt scriptores categoriam,hoc spacium non cognoere &atritius,:ova de universis philosophia libris1uin1uointa comprehensa (Genice, 159B), fo" 658


12/27

p ? &atritius 0+d enim ante omnia necesse est esse, $uo posito a"ia poni possuntomniaE $uo a%"ato a"ia omnia to""antur08+t (space) howeer %efore a"" is necessar# to %e existing (existance),which postu"ated a"" others can %e p"aced,

which remoed a"" others are remoed:Dd Cr#er suggests/ or this must %e %efore a"" other things &osit this and a"" otherthings can %e positedE tae it awa# and a"" other things are taen awa#

0Hu""a ergo categoriarum spatium comp"ectiturE ante eas est, extra eas omnes est08Hone howeer of the categories inc"udes space,it is %efore them,it is %e#ond them a"":

+ta$ue a"iter de eo phi"osophandum est $uam ex categoriis Spatium ergo extensio

est h#postatica per se su%stans, nu""i inhaerens Hon est $uantitas Dt si $uantitasest, non est i""a categoriarum, sed ante eam eus$ue fons et origo &atritius,!ancosmia. De spatio physico, 65 f8and so of that ought to %e phi"osophi.ed other than (a"iter $uam) from thecategoriesSpace therefore is h#postaticBextension , su%sisting of itse"f,adhering in nothing+t is not $uantit#nd if it (extension) is $uantit#,it (that $uantit#) is not (one) of categories,%ut %efore it (ie that one of the categories) and fountain and origin of the er#same thing (ie of that categor#):

p ?9 +t is therefore on"# natura" that runo expresses a new conception of infinitespace on the ground that 0Si non superficies sed spatium $uoddam "ocus est,nu""um corpus ne$ue u""a corporis i""ocata erit sie maximum, sie minimum siefinitum sit ipsum, sie infinitum08+f a certain p"ace (or, if a defined p"ace) is not surface %ut, so to spea, (or a indof) space,no %od# nor an#thing wi"" %e un"ocated %# %od# whether "argest,whether "east whether itse"f "imited,whether un"imited:

p 9@ Campane""a dee"ops &atritius' theor# of space sti"" further, maintainingthat space is the immoa%"e %asis of a"" existence/ 0%asin omnis creati, omnia$uepraecedere esse sa"tem origine et natura08foundation of a"" created,

3 h#postati.eE to construe (a conceptua" entit#) as a rea" existent/ reif#

1*


13/27

and to precede a"" existence at "east %# origin and nature:

!homas Campane""a,De sensu rerum(16*@), +, c 1* t another p"ace he ca""sspace 0"ocus, %asis existentiae, in $uo pu"crum -pificium, hoc est mundus, sedet08p"ace, %ase of existence,

in which the %eaut# of the una moetur, nec Mercurii,aut Generis ste""a, propter "ocum a"i$uem in mundo, nec ste""ae fixae $uietaemanent propter "ocum8%ut not p"ace in nature (to do) an#thing ($uic$uam) is a%"eEp"ace is nothing,does not exist,has no strengthEthe power of eer# thing in %od# itse"f+ndeed the moon is not moed,nor Mercur#,or the star of Genus,on accountF%# means of an# p"ace in the wor"dnor do the fixed stars remain resting %ecause of p"ace:


14/27

assendi, Syntama philosophicum("orence, 1*), part ++, sec 1, "i% ++, cap 1ccording to assendi, this priorit# is not on"# "ogica" or onto"ogica, %ut a"sotempora", for he sa#s exp"icit"#/ 02num est, spatia immensa fuisse, ante$uameus conderet mundum08one is,

immeasura%"e spaces hae %een,%efore od made the wor"d:

+t is certain"# no fiction, not een the mode of a su%stance 0Cum ex deductisconstet posse $uidem ea spatia dici nihi" corporeum, seu$ua"e (sic.3 sie$ua"e)su%stantia, aut accidens est, sed non nihi" incorporeum ac specia"is sui generis/constat $uo$ue esse ea posse, etsi inte""ectus non cogitet, ac non $uemadmodumchimaeram merum esse opus imaginationis0

8when %# reason of deduction (deductie reasoning) certain"# to %e a%"e indeedthese spaces are ca""ed nothing corporea",

or if (it is) a ind of su%stance,or is accident,%ut not nothing incorpora" and of its own specia" ind/it is "iewise understood,constant"# "iewise a%"e to %e the same,and #et (a"though) the inte""ect does not imagine (it),and not as to %e a chimaera, a mere wor of imagination:

Dd Cr#er suggests/


15/27

Chapter 4!he Concept of %so"ute Space

p 9 +n 0e $uadratura curarum0 Hewton writes/ 0uantitates mathematicas,non ut ex parti%us $uam minimis constantes, sed ut motu continuo descriptas, hic

considero =ae geneses in rerum nature (sic., perhaps natura"e) "ocum ereha%ent et in motu corporum $uotidie cernuntur08+ consider here mathematica" $uantities not as consisting of parts as sma"" aspossi%"e, %ut as descri%ed %# continuous motion !hese tru"# hae %eginning innatura" p"ace of things and in moement of %odies ordinari"#understoodFdistinguished:

or a"though Hewton ca""s the "aws of motion 0axioms0 (2xiomata sive leesmotus), 8axioms or "aws of motion: the term 0axiom0 as emp"o#ed %# Hewton inthis context certain"# does not hae the modern meaning of an ar%itrar#assumptionE phrases "ie 0"ex tertia per theoriam compro%ata est0 8third "aw

ustified %# theor#: or 0certa sit "ex tertia motus0 show c"ear"# that Hewton %# hisuse of the term axiom 8"et the third "aw of motion %e fixed :

!hese trans"ations do not seem to me to support Jammer's thesis re axioms eeractua""# ar%itrar#A

p 1@4 ere"e#/ Hewton's cosmo"ogica" assumption that the center of the wor"dis at rest escapes a"" possi%i"it# of experimenta" or o%serationa" erification !hefact was c"ear"# recogni.ed %# ere"e#, one of the great opponents of the theor#of a%so"ute space +n 0e motu0 he writes/02ti e" ex eo patet $uod,$uum secundam i""orum principia

$ui motum a%so"utum inducunt,nu""o s#mptomate scire "iceat,utrum integra rerum compages $uiescat,an moeatur uniformiter in directum,perspicuum sit motum a%so"utum nu""ius corporis cognosci posse08s een from that it is seen (patior, to %e isi%"e) that ,whi"e fo""owing from the princip"es of those

who induce a%so"ute motionno s#mptom is a""owed to %e nown,whether the entire framewor (compages, a oining, connection, structure) ofthings ma# (%e at) rest,or %e moed uniform"# in direction,eident"# a%so"ute motion of no %od# can %e nown:

Dd Cr#er suggests/ s for instance is seen from the fact that, since, according to(secundum) the princip"es of those who infer a%so"ute motion, %# no eent can it%e nown whether the who"e structure of things is at rest or is moing uniform"#

15


16/27

straight ahead, it is c"ear that a%so"ute motion cannot %e recognised in an#particu"ar %od#

p 1@6 !hus Hewton's first argument with regard to a%so"ute motion is %ased onthe idea that rea" force creates rea" motion !o Hewton, at "east in this context,

forces are metaph#sica" entities conceied anthropomorphica""# =oweer, if we"eae out of account the import of forces for the determination of a%so"ute space,the notion of force in Hewton's mechanics ma# %e interpreted in the modernfunctiona" wa#, as in =einrich =ert.'sDie !rin'ipien der Mechani(>eip.ig,1?94, p B*)%0egi%us contra Cartesianos0 8 -n the cause of grait#, and defense of theauthor's opinion a%out the true "aws of nature against Cartesians: >ei%ni. tried todemonstrate that grait# is not exp"ica%"e as a force acting at a distance, %ut isreduci%"e to the contiguous action of the surrounding ether +n other words, hetried to reduce grait# to a centrifuga" force, sa#ing/ 0Dtsi a"de duduminc"inaerim ipse ad graitatem a i centrifuga materiae aethereae circu"antisrepetendam, sunt tamen a"i$ua $uae du%itationes graissimas inecere08"though former"# + ma# hae great"# inc"ined m#se"f to grait# from centrifuga"(center f"eeing) force of returned (repetendam, fa""ing %ac) encirc"ing etherea"matter, there are #et some which hae in some wa# introduced serious dou%ts:

oes this support JammerA

p 1*1ff!he su%ect occurs in =u#gens' first "etter to >ei%ni., which reads/

Je ous dira# seu"ement, $ue dans os notes sur des Cartes 'a# remar$u $ue ouscroie. absonum esse nullum dari motum realem3 sed tantum relativum Ce $uepourtant e tiens pour tres constant, sans m'arrester au raisonnement etexperiences de Hewton dans ses &rincip"es de &hi"osophie, $ue e sca# (sic. sTa#A,now) estre dans "'erreur, et 'a# enie de oir s'i" ne se retractera pas dans "anoue""e edition de ce "ire, $ue doit procurer aid regorius

8+ wi"" on"# sa# to #ou, that in #our notes on escartes + hae o%sered that #outhin inconruous ;for< nothin to have been iven real motion3 but only relative.!hat which howeer + ho"d er# steadfast, without hendering the reasoning and

16


17/27

experiences of Hewton in his &rincip"es of &hi"osoph#, which + now to %e inerror, and + hae a mind to see if he wi"" retract in the new edition of his %oo,which owes (perhaps, is %ound toA) to agent (pu%"isherA) aid regorius :

-n another page, Jammer offers his own trans"ation of the >atin/

0that it wou"d %e a%surd, if there exists no rea", %ut on"# re"atie motion0>ei%ni.'s rep"# to this "etter (June **, 1694) is extreme"# interesting/+n addition to $uaint spe""ing and o%so"ete words, these passages are ridd"ed witht#pographica" errors>ei%ne. uses the wordsubjectumwhich "oos "ie >atin %ut used interchangea%"#withsujet Since 0su%ect of motion0 doesn't mean much in Dng"ish + trans"ate%othsubjectum

uant U "a difference entre "e mouuement a%so"u et re"atif, e cro# (sic. croieA )$ue si "e mouuement ou p"us tost (p"utVt) "a force mouuante des corps est $ue"$ue

chose de ree" comme i" sem%"e $u'on droit reconnoistre (sic. reconnaWtreA), i"faudra %ien $u'e""e 8fem, ie "a force: ait un su%ectum 8as to the difference %etween a%so"ute moement and re"atie, + %e"iee that if themoement, or rather the force moing the %od# is something rea" (or hassomething of rea" in it) ust as it seems that ought to recogni.ed direct"#, it wi"" %enecessar# that it ( ie the force) has asubjectum:

8= "exander (introduction to >ei%nit.;C"are Correspondence) gies/ 0sfor the difference %etween a%so"ute and re"atie motion, + %e"iee that if motion,or rather the moing force of %odies is something rea", as it seems one mustadmit, it is necessar# that it has asubjectum0

+ am p"eased to see he a"so prefers not to trans"ate subjectum:

Car a et % (the# hae apparent"# %een discussing two %odies, a and %) a""ant "'uncontre "'autre, 'aoue $ue tous "es phenomenes arrieront tout "e meme, $ue" $uesoit ce"u# dans "e $ue" on posera "e mouuement ou "e reposE et $uand i" # auroit(sic.A) 1@@@ corps, e demeure d'accord $ue "es phenomenes ne nous scauroient(sic.,sTauroient L sauraient, from saoir, to %e a%"e) fournir (n# mXme aux anges)une raison infa""i%"e pour determiner "esujetdu mouuement ou de son degrE et$ue chacun pourroit (sic.pourraWtA) estre concY U part comme estant (sic. ZtantA)en repos, et c'est aussi tout ce $ue e crois $ue ous demandesE mais ous nenieres pas e crois $ue erita%"ement chacun a un certain degr de mouuement on(sic.ouA) , si ous ou"s de "a forceE non;o%stant "'e$uia"ence des =ipotheses(sic.)8ecause a and % go (moe) the one contrar# to the other, + acnow"edge that a""the phenomena happen a"" the same, whicheer ma# %e that in which the# sha""suppose the moement or rest (ie which one is supposed to %e at rest)E and ifthere shou"d %e 1@@@ %odies, + agree that the phenomena cou"d not furnish us (not

1


18/27

een to the ange"s) an infa""i%"e argument to determine thesubjectum ofmoement or of its degreeE and that %esides (U part) each is a%"e to %e concededas %eing at rest, and it is thus a"" that which + now that #ou asE %ut #ou wou"dnot den#, + %e"iee, that indeed each has a certain degree of moement or, if #ouwish, of forceE not withstanding the e$uia"ence of the h#potheses:

+" est ra# $ue 'en tire cette conse$uence $u'i" # a dans "a nature $ue"$ue autrechose $ue ce $ue "a eometrie # peut determiner

8it is true that + draw out of it (en tire) this conse$uence that there is in naturesomething e"se which the geometr# is a%"e to determine:

Dt parm# p"usieurs raisons dont e me sers pour prouuer $u'outre "'etendue et sesariations, $ui sont des choses purement eometri$ues, i" faut reconnoistre (sic.reconnaWtreA) $ue"$ue chose de superieur, $ui est "a forceE ce""e;c# n'est pas desmoindres

8and among man# reasons the# gie + aai" m#se"f for proing that %e#ond theextension and its ariations (aria%i"it#A), which are pure geometric things, thereneeds to %e recogni.ed something superior, which is forceE the "atter is not the"east:

Monsieur Hewton reconnoist (sic.reconnaWtA) "'e$uia"ence des =#pothese en casdes mouuements recti"ineaires E mais a (sic.3[A) "'egard des Circu"aires, i" croit$ue "'effort $ue font "es corps circu"ans de s'e"oigner du centre ou de "'axe de "acircu"ation fait connoistre (sic. connaWtreA) "eur mouuement a%so"u8 Monsieur Hewton recogni.es the e$uia"ence of the h#potheses in the case ofrecti"inear moement %ut in regard to circu"ar, he %e"iees that, the effort that thereo"ing %odies mae to remoe themse"es from the center or the axis ofrotation, maes nown their a%so"ute moement:

Mais 'a# des raisons $ui me font croire $ue rien ne rompt "a "o# genera"e de"'D$uia"ence +" me sem%"e cependant $ue ous meme , Monsieur, estis autresfois du sentiment de M Heuton (sic.) [ "'egard du mouuement circu"aire8 %ut + hae some reasons which mae me %e"iee that nothing %reas the genera""aw of e$uia"ence +t seems to me neerthe"ess that #ou #ourse"f , Monsieur,were former"# of the opinion of M Heuton in regard to circu"ar moement:

exander gies/ 0or if there are 1@@@ %odies, + sti"" ho"d that phenomena cannotgie us an# infa""i%"e wa# of determining which are moing and in what degreeEand that each separate"# cou"d %e considered as %eing at rest Mr Hewtonrecogni.es the e$uia"ence of h#potheses in the case of recti"inear motion, %utwith regard to circu"ar motion he %e"iees that the effort which reo"ing %odiesmae to recede from the axis of rotation ena%"es one to now their a%so"ute

1?


19/27

motion ut + hae reasons for %e"ieing that nothing %reas this genera" "aw ofe$uia"ence0

p 1** ut =u#gens is opposed to an# compromise !hus he writes in a "etterdated ugust *4, 1694/

&our ce $ui est du mouement a%so"u et re"atif, 'a# admire ostre memoire, de ce$ue ous ous estes souenu , $u'autrefois 'estois du sentiment de Mr Hewton,en ci $ui regard "e mouement circu"aireCe $ui est ra#,et i" n'# a $ue * ou B $ue 'a# troue ce"u# $ui est p"us erita%"e, du$ue" i" sem%"e$ue ous n'estes pas e"oigne non p"us maintenant,si non ence (sic.en ceA) $ue ous ou"e.,$ue "ors$ue p"usieurs corps ont entre eux du mouement re"atif, i"s aient chacunun certain degre de mouement erita%"e , ou de force, en$uo# e ne suis point deostre ais

8as regards what is a%so"ute or re"atie motion, + am astonished (wonder) at #ourmemor# (or note), of that which #ou hae reca""ed to #our mind, that former"# +was of the opinion of Mr Hewton, in that which regards circu"ar moement


20/27

so it ino"es to some degree respectie"#and a"so not to %e a%"e to %e gien phenomena out of which a%so"ute motion orrest is determinedEmoement consists therefore in change of position or "ocation:

p 1*B efore =u#gens' death in 1695, >ei%nit.' fina" "etter to him/ Comme e ous disois (sic.disaisA) un our U &aris $u'on aoit de "a peine Uconnoistre (sic. connaWtreA) "e erita%"e suet du Mouuement ous me rpondites$ue ce"a se pouuoit (sic. se pouvoir3 to be possibleA) par "e mo#en du mouuementcircu"aire, ce"a m'arresta (sic. arr=terA) E et e m'en souuins (sic. souvenir3 souvins34 recalledA) en "isant U peu prZs "a mXme chose dans "e "iure de Mons HewtonEmais ce fut "ors$ue e cro#ois da oir $ue "e mouuement circu"aire n'a point deprii"ege en ce"a 8


21/27

Je ne suis pas mXme fort e"ogne (sic. eloin>A) de "a ostre, et dans un petitpapier $ue e communi$ua# U Mr Giiani, et $ui me paroissoit (sic. paratre3appear3 mae planeA) propre U persuader Messieurs de 7ome a permettre"'opinion de Copernic, e m'en accomodois

8+ am not so far from #ou, and through a "itt"e paper which + communicated toMr Giiani, and which seems to me suita%"e to persuade the ent"emen(Messieurs) of 7ome to permit the opinion of Copernicus, + hae adusted m#se"fto it:

Cependant si ous estes dans ces sentimens sur "a rea"it du mouument, em'imagine $ue ous deuris (sic. devrie'A) en aoir sur "a nature du corps dedifferens de ceux $u'on a coustume d'aoir J'en a# d'asse. singu"iers (A) et $ui meparoissent (sic. paratreA) demonstrs

8Heerthe"ess if #ou are of these opinions on the rea"it# of moement, + thin that#ou ought to hae different (opinions) on the nature of %odies than one isaccustomed to hae + hae them (opinionsA) sufficient"# uni$ue (singu"iers A)and which appear to me to %e demonstrated:

p 1*4iu putai in circu"ari motu ha%eri eri motus %ut Jammer trans"ates this\

sa"a eritate

>atin for 0saing the truth0 +f two expressions can %e interchanged without changing the truth;a"ue of the statements in which occur, the# are said to %e su%stituta%"e sa"a eritate ictionar# of &hi"osophica" !erms and Hames

*1


22/27

Chapter 5!he Concept of Space in Modern Science

p 1*? 0Coe"i enarrant g"oriam ei0, 8the heaens exp"ain fu""# the g"or# of od,0the heaens proc"aim the g"or# of the >ord0:

p 1*9 >eonhard Du"er grapp"ed with the pro%"em for more than thirt# #ears +nhisMechanica sive motus scientiae analytice exposita8ana"#tica" now"edge ofmechanics or moement expounded:Du"er dee"ops his mechanics on Hewtonian"ines and introduces the concept of a%so"ute space and a%so"ute motion in thespirit of the!rincipia So his second definition reads/ 0>ocus est pars spatiiimmensi seu infiniti in $uo uniersus mundus consistit Gocari hoc sensuacceptus "ocus so"et a%so"utus, ut distinguatur a "oco re"atio, cuius mox fietmentio08>ocation (space) is portion of space immense or %ound"ess in which the who"ewor"d stands together, (comes a%out, is esta%"ished, consists) 7eceiing "ocationis usua""# ca""ed a%so"ute in this sense , in order to %e distinguished from re"atie

"ocation, of which next wi"" %e made mention:p 1B@ in his 07Zf"exions sur "'espaces et "e temps/ emphasi.ed the necessar#existence of a%so"ute spaceE for he had come to the conc"usion that some rea"existing su%stratum is indispensa%"e to the determination of motion Since thissu%stratum appears not to exist in the casua" surrounding materia", it must %espace itse"f that exists in this capacit# 0-n en deroit p"utVt conc"ure, $ue tant"'espace a%so"u, $ue "e temps, te"s $ue "es Mathmaticiens se "es figurent, toientdes choses re""es, $ui su%sistent mXmes hors de notre imagination0 8one ratherought to conc"ude , that as much a%so"ute space, as time, such as themathematiciens imagine them, were rea" things, which su%sist themse"es(memes) out of our imagination:

Du"er's demonstration of the rea"it# of a%so"ute space on the %asis of the "aw ofinertia appears fina""# in hisTheoria motus corporum solidorum seu riidorum,8theor# of motion of %odies so"id or rigid: though theMechanicaa"read# insiststhat the "aws of motion presuppose the existence of a%so"ute space 0Si hacsignificatione expositae oces accipiantur, ocari so"ent motus a%so"utus,$uies$ue a%so"uta t$ue hae sunt erae et genuinae istarum ocum definitiones,sunt enim accomodatae ad "eges motus, $uae in se$uenti%us exp"ica%untur08whether in this meaning (significatione ) the expressions set forth are accepted,(the# are) ordinari"# ca""ed a%so"ute motion, a%so"ute rest ut as these are trueand authentic, natura" definitions of these expressions, the# are indeed suita%"e to"aws of motion, which are in the fo""owing set forth:

!he "aw is formu"ated in xioma *p 1B1 as fo""ows/ 0Corpus, $uod a%so"ute $uiescit, si nu""i externae actioni fueritsu%ectum, perpetuo in $uiete perseera%it0 8%od#, which a%so"ute"# rests, if it%e su%ect to no externa" action, persists perpetua""# in rest: +n the 0Dxp"icatio0

**


23/27


24/27

for training in the princip"es of machanics +ts approach is much more ac"arifi#ing or, more c"ear"# stated, an anti;metaph#sica" one:

+n the conc"uding passage of his foreword to the seenth edition (191*) of hisMechaniMach sa#s 0e.3g"ich der egriffsunget3me des a%so"uten 7aumes

und der a%so"uten ^eit onnte ich nichts .ur3cnehmen +ch ha%e hier nurdeut"icher a"s orher ge.eigt, dass Hewton .war manches 3%er diese inge redet,a%er durchaus eine ernste nwendung on dense"%en gemacht hat Sein Coro""G (!rincipia, 16?, p 19) enth]"t das ein.ig pratisch %rauch%are(wahrschein"ich angen]hrte) +nertia"s#stem0 D Mach,Die Mechani in ihrerEnt*iclun (>eip.ig, 1??B) 8in re"ation to the conceptiona" monsters of a%so"utespace and a%so"ute time + can tae %ac nothing + hae here on"# c"ear"# as%efore shown that Hewton indeed said much a%out these things, howeerthroughout had made no serious app"ication of the same =is Coro"" G containsthe on"# practica""# usea%"e (pro%a%"# approximate) inertia" s#stem:

p 14B 02e%er den a%so"uten 7aum und die a%so"ute ewegung ann niemandetwas aussagen, sie sind %"osse edanendinge, die in der Drfahrung nichtaufge.eigt werden `nnen0 8a%out a%so"ute space and a%so"ute time no one canstate an#thing, the# are mere 0thought things0, which in experience cannot %epointed out:+n the fourth edition ofDie MechaniMach summari.es his ideas concerningspace in a er# c"ear statement (which curious"# is omitted in the "ater editions)/

3r mich gi%t es 3%erhaupt nur eine re"atie ewegung und ich ann darin einen2nterschied .wischen 7otation und !rans"ation nicht machen reht sich einR`rper re"atie gegen den ixsternhimme", so treten "iehr]fte auf, dreht er sichre"ati gegen einen anderen R`rper, nicht a%er gegen den ixsternhimme", sofeh"en die "iehr]fte +ch ha%e nichts dagegen, wenn man die erstere 7otationeine a%so"ute nennt, wenn man nur nicht ergisst, dass dies nichts anderes heisst,a"s eine re"atie rehung gegen den ixsternhimme" R`nnen wir ie""eicht das


25/27

indistinguisha%"e + ho"d according"# %oth cases to %e the same and theHewtonian distinction an i""usion:

p 15? Gon Staudt, whom R"ein ca""s 0einen der am tiefsten eindringendeneometere, die e ge"e%t ha%en,0 8one of the deepest penetrating geometers which

hae eer "ied:p 16@ ootnote 7a3me onstanten Rr3mmungsmasses, Spaces of constantcurature massp 161parturiunt montes3 nascetur ridiculus mus8the mountains "a%or to %ringforth a ridicu"ous mouse:p 161 footnote 64 0Ds muss a"so entweder das dem 7aume .u runde "iegendeewis and Short>atin >exicon

*5


26/27

8 thus whereer either more or "ess essentia" in an#thing where it is contained thatwhich compares widthFthicness of these, there we %ecome ac$uanted with thisfourth dimension, which + name the essentia" densit#Fthicness:

p 1?*


27/27

Chapter 67ecent ee"opments

p *1? 0meta%asis eis a""o genos0 reemetabasis% moing oer, shifting, eg of the %od# in wa"ing, from one "eg to the

otherE change of position, transition from one su%ect to anothereis%prep with acc on"# 7adica" sense, into, and then to/allo% an#thing e"se,enos3 eos or ous3 to% in >ogic, opp eidos (species),c"ass, sort, ind, ta

*

Documents

Translations and notes for Max Jammer's Concepts of Space