TRI^T HOC, S6 10 (293), T H A N G 10 - 2015
CHUYEN HOA TAM DOAN LUAN TRONG LOGiC HOC ARIXTOT^^^
NGUYIN GIA THO'"'
Chuyen hda tam dogn ludn cd nghia Id biih ddi tam dogn ludn nham bdc bo mgt phdn dodn
• tiin di ndo dd trong tam doan ludn xudt phdt. Trong bdi viet ndy, tdc gid trinh bdy thu phdp cua Arixtdt ditng phdn dodn <ldi lap (hogc mdu thudn) vdi kit lugn roi kii hdp vdi mgt trong cdc tien di cua tam dogn ludn dd cho nhdm bdc bo tiin di cbn lgi. Sii phdn tich cung dd chi ra rdng, ddi vdi cdc tam dogn ludn bd phdn (tdc la tam dogn ludn co kit ludn id phdn dodn bg phdn) thi di bdc bo mot trong cdc tien di khdng the dung phdn dodn ddi ldp vdi kit ludn, md phdi dttng phdn dodn mdu thudn vdi kit ludn kit hdp vdi mgt trong cdc tiin de ciia tam dogn ludn dd cho nhdm rdt ra kit ludn md niu no dung, nd se bdc bo tiin di cbn lgi.
/j^ h u y e n hda t a m d o a n lufin dUdc (1 Arixtdt dmh ngbia n h u sau: "CJhuyen V - / hda t a m d o a n lufin nfira d t r o n g sfl h i n h t h a n h t a m d o a n M a n mdi thdng qua sU t h a y ddi k i t lufin, mfi vdi sflc m ^ n h ciia nd ho§c la < t h u a t ngQ> bidn lfi vd'n ed cua t h u a t ngfl gifla, ho^c lfi thufit ngfl gifla • vdn cd c u a thufit ngfl bidn. C h i n h trong sfl dao ngUdc k i t lufin < t h a n h cai ddl Ifip vdi nd> vfi gifl lai mpt tien d l k h d n g t h a y doi, t i l n d l khfic tfi't y l u t h a y doi, bdi vi nd'u tien d l sau cdn <sflc m a n h > , t h i ca k i t lufin ciing cdn < h i e u lUc>. Thd' nhflng, cd sU k h a c biet, k i t lufin cd dao ngUde chfing bfing each mfiu thufin h a y ddl Ifip, bdi vi khdng p h a i c u n g radt t a m doan lufin xufi't hidn t r o n g nhflng sii ddl Ifip k h a c n h a u ciia sfl dao ngUdc vdi cfic cfich khfic n h a u , t M k h d n g xufi't Men ciing mdt t a m doan lufin, d i l u n a y se dUdc Ifim r o tiep s a u " ( l ) . Ndi cfich khac, c h u y i n hda t a m doan M a n ciing nhU hpc t h u y e t v l chflng rainh vdng q u a n h -
dUdc rflt r a . tfl sfl lufin giai tara doan M a n n h u lfi mdl lidn h e h e qua tinh chfin ly eua k i t lufin tfl t i n h chfin Iy cua t i l n d l . Chflng rainh vdng q u a n h dfla vfio t i n h chdt hg q u a - mfi vdi sflc m a n h cua nd, sU thfla nhfin t i n h chfin thflc cua cai s a u t u nd edn chUa kdo theo mdt each tdt yd'u sU thfla nhfin t i n h chfin thUc cua cfii trUdc va vdi tU cfich bd s u n g tinh tfi't yeu, nen can cd sii md r g n g t r i thfle cd d ragt trong cfic t i e n d l . Chuyin hda tam dogn lufin diia vfio tfnh cha't hd qua, m a vdi sflc m a n h ciia nd, sU p h u d i n h eai sau tfi't y l u kdo theo sU phil dinh cfii trUdc - dUdc tiep nhfin t r o n g t a m doan lufin dUdi Mnh thfle p h u dinh k i t lufin va p h u d i n h mdt t r o n g cfic t i l n d l cua t a m doan lufin.
(*) Nghi§n cCtu nhy dUdc tai tr? b3i Quy phat trien khoa hpc vk cong nghfi Qufic gia (NAFOSTED) trong de tai ma s^Il.6-2012.18.
(**) Ph6 giio su, tig'n si, Vi#n Triet hpc, ViSn HAn lam Khoa hpc xa hfii Vift Nam.
(1) Phdn tick hgc thii nhdt. II, 8,59b 1-8.
Arixtdt ngMen cflu cac tnidng hdp phu dinh k i t Man cua tam doan Man bfing con dudng thfla nhfin chfin ly cua phan dofin mau thufin hay ddl Ifip trong tfi't ca cac modus cua tara doan lufin. Su nghien cflu cM ra rfing, cM cd phu dinh thdng qua mau thufin mdi cho ta sii ehuydn hda, cd nghia la bdc bo mdt trong cdc tiin di, trong tfi't ca cac modus cua tat ca cfic dang Mnh tara doan lufin, kM dd tM sfl phu dinh thdng qua ddi lap cM cho sii chuyen hda trong cac raodus chung cua dang hinh I, II. O dfiy, chung tdi khdng trinh bay tfi't ca cae trUdng hdp chuyen hda, mfi chi ban che d nhflng trUdng hdp (fien hinh, the Men cac thu phap cua Arixtdt.
Bfic bd cae tien de cua modus khfing dinh chung dang hinh I (Barbara) bang each thfla nhfin phfin doan ddl lap vdi kit Man la chfin thflc, dUdc Arixtdt trinh bay bdng each sau: "Gia sfl A nfim trong mdl quan he vdi G thdng qua
<thufit ngQ> gifla B. Nd'u thfla nhfin rfing, A khdng vd'n cd cua mdt G nfio, nhUng vdn cd cua tofin bd B, thi <se rut ra rfing> B khdng vd'n cd cua radt G nfio, nhUng B vd'n cd cua tofin bp G, tM chi <rut ra dUdc dilu> la A khdng <vd'n cd> cua mdt so B (khdng phai tdt ca B), mfi khdng phai (fieu lfi <A khdng vd'n cd> cua mdt <B> nao, bdi vi cai ehung khdng dUdc chiing mmh thdng qua dang hinh cudi. Ndi chung, tien de ed
<thuat ngfl> ldn khdng t h l bi bac bd bdi cfii chung thdng qua chuyen hda, vi sfl bfic bd nd dUdc tiln hfinh ludn ludn thdng qua dang hinh ba, bdi ca hai tien de can dUdc lay trong mdl quan hd vdi
<thuat ngQ> nhd"(2). Chuyen hda modus Barbara thdng qua cai ddl lap cd the dUdc the Men bfing each sau:
A vd'n cd cua toan bd B B vd'n cd cua toan bg G A vdn cd cua tofin bd G.
Ta coi phan doan ddl lap "A khdng vd'n cd cua mdt G nfio" la chfin thfle. Khi dd, de bac bd tien d l nhd, ta kit hdp phan dofin ddl Ifip vdi kd't lufin vdi tien dl ldn:
A vdn cd cua tofin bd B A khdng vd'n ed cua mdt G nfio B khdng von cd cua radt G nao (Caraestres II).
Kit lufin khdng tUdng tMch vdi tien d l nhd: "B vd'n cd cua toan bd G" vfi nhU la phan doan ddl lap vdi nd. Do dd, neu kd't Man: "B khdng vd'n co cua radt G nao" chfin thiic, thi gia ddl thupc ve tien dl nhd "B vd'n cd cua tofin bd G" (tflc tien d l nhd hi bac bd).
De bfic bd tiln d l ldn (AB), phan dofin ddl lap vdi ket Man cdn kit hdp vdi tien de nhd:
A khdng voii cd cua radt G nfio B vd'n cd cua tofin bd G
A khdng vd'n cd cua mot so B (Felapton III)
Chflng ta lai nhfin dugc kit lufin mdu thudn vdi tien d l ldn cua tam doan Man ban ddu, va do vfiy, kM dUdc thfla nhfin lfi chfin ly, no bac bd tiln d l 16n:
"A vd'n cd cua toan bg B".
(2) Phdn tich bgc thvC nhdt. II, 8, 59b 11-20.
60
NGUYEN GIA THO Ta thfi'y rfing, tien dl nhd (BG) cua
modus Barbara dang hinh I cd the bfic bd thdng qua phan doan mfiu thufin vdi kit lufin (A khdng vd'n cd cua mdt so' G) nhd raodus Baroco dang Mnh II, cdn tien de ldn bi bac bd thdng qua chinh phfin doan do nhd modus Bocardo dang Mnh m .
Cac tiln de cua raodus Celarent dang hinh I bi bfic bd thdng qua phan doan ddi Ifip vfi raau thufin nhd cae modus tUdng flng cua cae dang hinh II, III. Dd chinh lfi nhd sfl chuyen hda thdng qua phfin doan ddl Ifip tien dl nhd bi bae bd nhd modus Cesare dang hinh II, cdn tien dl ldn, nhd modus Darapti dang hinh III; chuyin hda thdng qua phfin doan mau thufin tiln de nhd hi bfic bd nhd modus Festino dang hinh II, cdn tiln d l ldn tM nhd modus Disarais dang Mnh i n .
Trong cfic modus bd phfin dang hinh I chuyen hda cd nghia lfi bac bd tiln de nhd hay ldn, chi c6 t h l thdng qiia phfin doan mfiu thufin; khdng the bfic bd thdng qua phan dofin ddl Ifip.
Chung ta hay xem xet modus Daril dang hinh ddu:
A vd'n cd cua tofin bd B B vd'n cd cua mdt so G A vd'n cd cua radt so' G Vdi tu each phan doan ddl Ifip, Arixtd't lfi'y phan dofin: "A khdng vd'n cd ciia radt so' G". Ndu k i t hdp nd vdi tiln dl Idn cua tam doan lufin xufi't phat vdi muc dich bac bd tiln d l nhd, tM ta cd
A vd'n cd cua tofin bd B A khdng vdn cd cua mgt so G B khdng vd'n cd cua mgt sd' G Phan doan ke't lufin tUdng tMch vdi tien de nhd: "B vdn cd cua mdt so' G"- hai phfin dofin cd t h l cflng ehan thflc, vi the khdng bfic bd dUdc gi.
Nd'u bfic bd tien d l ldn, kM Hdn kit phfin doan ddl lap vdi kd't Man vdi tien de nhd, thi ta se cd tam doan lufin:
A khdng vd'n cd eua mgt sd' G B vd'n cd cua radt sd^ G
Tfl eac tiln dl trdn khdng thl rut ra kit Man mdt each tfi't yd'u, vi ca hai diu lfi phfin doan bd phfin.
Nhu vfiy, cac tien dl cua raodus Darii khdng t h l hi bac bd thdng qua phfin doan dot lap.
Bfic bd cac tiln dl cua modus Darii thdng qua phdn dodn mdu thudn dUdc tid'n hfinh ve cfin ban bfing cfich sau:
A vd'n ed cua toan bd B B vd'n cd cua mdt sd' G A vd'n cd cua mdt sd' G Phan doan mfiu thufin vdi kd't lufin se lfi: "A khdng vd'n ed cua radt G nfio".
Tiln de nhd hi bac bd thdng qua modus Caraestres dang hinh II:
A vd'n cd cua tofin bg B A khdng vd'n cd eua radt G nao B khdng vd'n cd cua mgt G nfio.
Kit lufin mau thufin vdi tiln d l nhd cua tara doan lufin xudt phat: "B vdn cd ciia mdt so G", do vfiy, ndu "B khdng vdn ed cua radt G nfio" chfin thUe, tM tiln de nhd cua tam doan lufin xudt
phfit "B von cd cua radt sd'G" se gia ddl. Kit lufin mfiu thufin vdi tiln de tflc nd bi bfic bd. ldn: "A vo'n cd ciia tofin bg B", do vfiy,
Tiln dl ldn (A vd'n cd eua toan bd B) ne'u nd chfin thflc, tien de ldn "A vdn hi bac bd thdng qua modus Ferison cd cua tofin bg B" se gia ddl, tflc la bi dang hmh ba:
A khdng vd'n cd cua mdt G nfio B vdn cd cua mdt so' G A khdng vd'n cd cua radt so' B
Barbara I: A vdn ed eua tofin bg B (1) B vdn cd cua tofin bd G (2)
bac bd.
Bac bd chinh cac tien de dd (cua raodus Barbara) thdng qua phan doan raau thufin vdi ket Man, dfldc the Men nhu sau:
A vd'n cd cua tofin bd G (3)
A khdng vdn cd cua mdt so" G (4) (Phfin doan mfiu thufin vdi k i t lufin).
Baroco II Bocardo III A vd'n cd eua toan bd B (1) A khdng vd'n cd eua radt sd'G (4) A khdng vdn c6 cua radt so G (4) B vdn cd cua toan bd G (2) B khdng vd'n cd cua radt so' G (5)
Nhfin xdt: - Neu chfin thflc (5), tM (2) gia ddl,
- Nlu chfin thUc (6), tM (1) gia ddl, - Nlu chfin thUc (4), tM (5) ehan thflc, Cac tien d l cua raodus Ferio dang hinh I cung ddng thdi bi bac bd khdng phai thdng qua phan doan ddl lap, mfi thdng qua cac phan doan mau thufin vdi kit Man: Tien d l nhd bi bfic bd thdng qua modus Cesare dang Mnh II, cdn tiln dl Idn, thdng qua modus Datisi dang hinh III.
Trong hgc thuylt ve chuyen hda dang hmh I, Arixtd't cH ra nguydn tfic mm Hdn he cua ba dang Mnh tara doan Man mfi theo dd, ed sii nit ra tfi't ca cac raodus dang Mnh II, III tfl dang Mnh I nhd phU(3ng phfip mfiu thufin. Nguydn
A khdng vd'n cd cua mdt so' B (6) tfic nfiy trong logic hge Men dai lfi nguydn tfic cho phep thdng qua viec thfla nhfin phan doan khdng tUdng tMch do mfiu thufin vdi kit Man cua dang Mnh I, tao ra bang tfi't ca cfic raodus cd the cd cua ca ba dang hinh (sau kM loai bd cac modus rafi trong dd, tfl hai tiln de chung nit ra ke't lufin bd phfin (Darapti va Felapton). Thflc vay, hgc thuylt Arixtd't vl chuyin hda thdng qua mfiu thufin tMd't Ifip mdl Hen he tfnh bfic bd Ifin nhau vfi tfnh chflng minh dUdc cfic raodus dang Mnh I, II, III trong eac cfip ba tam doan Man sau:
Barbara I, Baroco II, Bocardo III, Celarent I, Festmo II, Disamis III, Darii I, Caraestres II, Ferison III Ferio I, Cesare II, Datisi III.
62
NGUYEN GIA THO De bac bo mdt tiln dl nfio dd ciia tam
doan lufin dang Mnh I nhd dang hinh II, III, tM cdn thfla nhfin phan dofin mfiu thufin vdi kit lufin la chfin thUc vfi kd't hdp vdi tiln dl khfic cua tam doan lufin. De chiing mmh bfi't ky modus nfio cua tam doan lufin dang Mnh I nhd cae dang Mnh II vfi III, can thfla nhan hai tiln dl cua tam doan lufin lfi chfin thUe.
Theo dang hmh II vfi III, tmh khdng the thfla nhfin phfin dofin mfiu thufin vdi kit lufin lfi chfin thiic dUdc chiing rainh, nhU lfi dieu nfiy cd t h l tha'y tfl vide quy cac raodus cua mgt so' dang Mnh vl cfic modus khae "thdng qua cai khdng the".
Arixtdi nhgn xet rang, tien de ldn cua ede modus dgng hinh ddu ludn bi bdc bo chi thdng qua dgng hinh ba cua tam dogn ludn, cbn tiin di nhd • thdng qua dgng hinh hai cua tam dogn /uan(3).
Nd'u phat triln tilp tU tudng nfiy, c6 the (fi de'n kd't lufin quan trgng ve y nghia nhfin thflc cua ba d^ng hinh tara doan luSm vfi ve nghia dfic bidt cua sfl phu dinh d dang hinh IL Cu the, cd t h l chi ra rfing, nlu dang hinh III chi bac bd tien de ldn d dang hinh I, cdn nghia cua tiln de ldn d dang hinh ddu la d sU Mnh thfinh mpnh d l chung hay quy tfic dUdc fip dung vfio cac tnidng hdp bd ph&n thdng qua thufit ngfl gifla, tM nghia ciia dang hinh III Ifi d sii bac bd ragnh de chung, hay ndi chinh xac h(Jn, d sfl bfic bd cai chung. Nlu dang Mnh II bae bd cM tiln d l nhd d dang hmh I, cdn nghia cila tiln de nhd lfi d sfl xac thflc vdn dl: Trong cac trUdng hdp bd ph|in - eac dieu kidn lam cd sd chd tinh ap di^ng dugc vfio cac trudng hdp nfiy
cua menh dl chung dUdc thflc hidn.
NgMa cua dang hinh II nfim d sU phu dinh tinh ap dung dUdc vfio cac trUdng hdp ridng cua mdnh d l chung. Ndi tdm Iai, nd'u dang hinh III bae bd cfii chung, tM dang hinh II bac bd tinh ap dung dfldc cai chung.
Sau sU nghien eflu vide chuyen hda tam doan lufin d dang Mnh I, Arixtd't xem xdt radt cfich chi tid't sfl chuyin hda d dang hinh II (chUdng 9 - Phdn tich hgc tha nhdt) va dang hinh III (chUcttig 10 Phdn tich hgc thU nhdi). Vi sfl chuyin hda cfic tam doan lufin trong cfic dang hinh nfiy, v l nguydn tfic, khdng khfic gi so vdi sii chuyen hda tara doan lufin dang hinh I, nen chung tdi chi ban che' d vide trinh bfiy cae kit qua cua sU ngMdn cflu sau khi lfim mdt so' sU loai trfl ddl vdi dang hinh III.
O dang hinh II cac tiln dl cua modus Caraestres bi bae bd thdng qua cai doi Ifip nhd cfic modus Barbara dang hinh I vfi Felapton dang hinh III; cdn thdng qua mfiu thufin - nhd cac modus Darii dang hinh I, Ferison dang hinh III. Cae tiln de cua modus Cesare bi bac bd thdng qua ddl Ifip nhd cfic raodus
• Celarent d^ng hinh I vfi Darapti dang hinh III, cdn thdng qua mau thuan - nhd cfic modus Ferio dang Mnh I, va Datisi dang hinh III. Cac tien d l eua modus Festino khdng bi bfic bd thdng qua ddl lap, rafi thdng qua mfiu thufin - nhd eac raodus Celarent dang hinh I va Disarais dang hinh III. Cuoi cflng, cfic tiln de cua modus Baroco bi bac bd chl thdng qua mfiu thufin nhd cac modus
iS)Phdn HOt hgc thvCnh^ II, 8, 59b 11-20; 10,61a 5-16.
Barbara dang hinh I va Bocardo dang hinh III. Nhu vfiy, theo dang Mnh II ciing nhu dang binb I, cfic modus bd phfin khdng cho phep bfic bd qua ddl Ifip vfi cac tiln de cua chflng bi bfic bo thdng qua phfin doan mau thufin vdi kit Man.
Bfic bd cac tiln d l vdi thuat ngfl ldn dUdc tiln hanh gidng nhU d dang hinh I, thdng qua dang hinh III, edn cfic tiln de vdi thuat ngfl nhd - thdng qua dang hinh ddu(4). Trong dang Mnh III khdng radt modus nao cho phep bae bd cac tiln dl thdng qua ddl lap, bdi trong dang hinh III tfi!t ca cac modus deu la bd phfin, cdn tinh khdng dUdc phep bfic bd cac tien de eua cfic raodus bd phfin thdng qua doi lap da dUdc tMd't liip ddl vdi dang Mnh I vfi dang hinh IL Cac tien de cua d ^ g hinh III chi bi bfic bd nhd cfic dang hinh I vfi thfl II. Nd'u nhd chuyin hda dang Mnh III tiln dl ldn trong tam doan Man da dUdc cai tao se Ifi phfin dofin ddl lap vdi kd't Man cua tam doan Man xudt phfit tM, bdi nd se cung vdi cfii bd phfin - xufi't Men cac tam doain lufin dang Mnh I vfi dang hmh II vdi cfic tiln dl ldn bd phfin, la (filu khdng the dUdc. Vi du, chiing ta cd tam doan lufin xufi't phat:
A vdn cd cua tofin bd G B vdn cd ciia tofin bp G A vd'n cd cua mdt sd' B (Darapti III) Phan dofin ddl lap vdi kd't Man se la:
"A khdng vdn cd cua radt so B". Nd'u dl bfic bd tiln dl Idn, kM kit hdp phan doan tren vdi tiln dl nhd, tM ta se nhfin dUdc:
A khdng vd'n ed cua radt s l B B vdn cd cua bfi't ky G nfio
Ta nhfin dUdc dang hinh ddu vdi tidn d l Idn bg phan, vfi ddl vdi A vfi G khdng rflt ra dUdc gi mdt each tfi't ydu.
Ne'u Hdn k i t phfin doan ddl lap vdi k i t lufin vdi tien d l ldn de bac bd tien de nhd, ta se (»:
A khdng vdn cd cua radt sd B A vd'n cd cua tofin bd G,
Cd ngMa la dang Mnh II vdi tiln dl ldn bd phfin(vi pham quy tfic cho d^ng hinh II), trong dd ddl vdi B va G khdng nit ra dUdc gi mgt each tdt ye'u.
Thfl lfim phan doan: "A khdng vd'n cd eua mgt sd' B"- thfinh tiln de nhd cung khdng the cho kd't qua, vi trong tnidng hdp nhu vfiy hoac lfi se khdng cd tat yd'u trong hg qua, hofic Ifi, neu k i t lufin tfi't ydu nhfin dUdc, nd se lfi phan doan phu (finh bd phfin vdi trfit tU cfic thufit ngfl khdng dao ngUdc dUdc.
Tren thflc te', de bac bd tiln dl ldn AG, sU ket hdp trong trUdng hdp nhU vfiy se la:
B vd'n cd cua bat ky Q nao (tien dl nhd cua phfin dofin xufi't phat)
A khdng von cd cua mdt sd B (phan doan ddl Ifip kd't Man)
Su ke't hdp dd khdng cho k i t lufin, bdi vi d day, cung nhU trong trfit tfl ngUde 1^ cua cac tiln dl, neu t h l hidn bfing ngdn ngfl cua logic truyen thdng, thufit ngfl gifla B khdng chu (fidn.
Su k i t hdp d l bae bd tiln de nhd BG nhu sau:
A vd'n cd cua b^t ky G nfio A khdng vdh c6 cua mdt so B G khdng vdii cd cua mgt sd'B (Baroco I^.
(4) Phdn tich hgc thU nhdt. II. 10, 61a 5-16.
64
NGUYEN GIA THO Hdn niia, de bfic bd tiln dl nhd: "B
vdn cd cua tofin bd G" sd cdn phai dUa ra cac phan doan: "B khdng vdn cd cua mgt (hoac mdt sd) G nfio"; chiing ta Idy phan doan phu dinh bg phfin khdng dao ngUdc dUdc: "G khdng vdn cd cua mdt so' B".
Cac tiln de cua tara doan Man xufi't phat (Darapti) bi bfic bd chi thdng qua phfin dofin - mau thufin vdi kit Man, cd thl thfi'y d vi du sau:
A vd'n cd cua bfi't ky G nfio B vd'n c6 cua bdt ky G nfio
A vd'n cd cua mdt sd' B
Phfin doan mfiu thuan vdi kit lufin, se lfi: "A khdng vd'n cd cua mpt B nao".
Khidd:
A khdng vd'n cd cua mdt B nfio B vd'n cd cua bfi't ky G nfio A khdng vdii cd cua radt G nfio (Celarrait), Mfi phan dofin nfiy khdng tUdng thich (ddl lap) vdi tiln dl ldn: "A vd'n cd cua bfi't ky G nfio" vfi do vfiy, neu nd chfin thlic, nd se bfic bd tiln d l ldn(A vdn c6 cua bfi't ky G nfio).
D I bfic bd tiln d l nhd ta nhfin dUdc:
A khdng vdn cd eua radt B nfio A vd'n c6 cua bfi't ky G nfio B khdng vdn cd cua mdt G nao (Cesarell), dieu dd khdng tUdng tMch vdi tiln d l nhd cua tam doan lufin xudt phat: "B vdn cd cua bfi't ky G nfio".
Nhu vfiy, trong dang Mnh ba dl bac bo tiln dl ldn ta sfl dung dang hinh I, de bfic bd tiln d l nhd - sfl dung dang Mnh hai.
Cd the bd sung cho dilu da ndi rfing, trong Sli bien ddi thdng qua rafiu thu&n
cua cfic modus Darapti va Felapton cua dang Mnh III, cd ngMa la, cac modus nfira ngoai bang cac bd ba nhU tren da trinh bay, chiing ta nhfin dUdc cac phan dofin khdng phai raau thufin vdi cac tiln dl cua phan doan xufi't phat, - tuan theo quy lufit phi raau thu&n ciing nhU quy Mat loai trfl cai thfl ba, mfi chi la ddl Ifip - gfin kit cM bdi quy lufit phi raau thuan. Chung tdi khdng xem xet tat ca cac trUdng hdp bie'n doi cac modus dang hinh III, bdi vi tfi't ca chiing la eung mdt Ioai, ehung tdi cM ban che' bdi viee chi ra ke't qua, nhU lfi d dang Mnh II. Cae tiln de cua modus Felapton bi bac bd thdng qua mau thufin nhd cac raodus Barbara dang hinh I va Caraestres dang hinh II. Cac tiln de cua modus Datisi- nhd eac modus Ferio dang hinh I vfi Cesare dang hinh II. Cfic tien de cua modus Disarais - nhd cfic modus Celarent dang hinh I vfi Festino dang hinh II. Cac tiln de cua modus Bocardo - nhd cae modus Barbara dang hinh I vfi Baroco dang Mnh II. Cfic tien de cua raodus Ferison - nhd cac modus Darn dang hinh I vfi Caraestres dang Mnh II.
Nhu dfi thdy tfl sU trinh bfiy trdn, bang cfip ba cac modus gfin vdi nhau thudc cae dang hinh khac nhau cua tam doan Man dUdc dfin ra Hen quan de'n vide ngMen cflu sfl chuyen hda cac modus dang hinh I cdn lai khdng thay ddi. Chiing tdi chi bo sung thdm dieu la, vdi tu each tam doan lufin xudt phat de rut ra eac modus cdn lai cua tara doan lufin cd thl sfl dung khdng chi cac raodus thupc dang Mnh I, mfi ca cfic modus thudc dang hinh II, III. Q
