posterior analytics-µÚ5½Ú
°´¼üÅÌÉÏ·½Ïò¼ü ¡û »ò ¡ú ¿É¿ìËÙÉÏÏ·ҳ£¬°´¼üÅÌÉ쵀 Enter ¼ü¿É»Øµ½±¾ÊéĿ¼ҳ£¬°´¼üÅÌÉÏ·½Ïò¼ü ¡ü ¿É»Øµ½±¾Ò³¶¥²¿£¡
¡ª¡ª¡ª¡ªÎ´ÔĶÁÍꣿ¼ÓÈëÊéÇ©ÒѱãÏ´μÌÐøÔĶÁ£¡
it¡¡cannot¡¡be¡¡proved¡¡by¡¡geometry¡¡that¡¡opposites¡¡fall¡¡under¡¡one¡¡science£»
nor¡¡even¡¡that¡¡the¡¡product¡¡of¡¡two¡¡cubes¡¡is¡¡a¡¡cube¡£¡¡Nor¡¡can¡¡the
theorem¡¡of¡¡any¡¡one¡¡science¡¡be¡¡demonstrated¡¡by¡¡means¡¡of¡¡another
science£»¡¡unless¡¡these¡¡theorems¡¡are¡¡related¡¡as¡¡subordinate¡¡to
superior¡¡£¨e¡£g¡£¡¡as¡¡optical¡¡theorems¡¡to¡¡geometry¡¡or¡¡harmonic¡¡theorems¡¡to
arithmetic£©¡£¡¡Geometry¡¡again¡¡cannot¡¡prove¡¡of¡¡lines¡¡any¡¡property¡¡which
they¡¡do¡¡not¡¡possess¡¡qua¡¡lines£»¡¡i¡£e¡£¡¡in¡¡virtue¡¡of¡¡the¡¡fundamental
truths¡¡of¡¡their¡¡peculiar¡¡genus£º¡¡it¡¡cannot¡¡show£»¡¡for¡¡example£»¡¡that
the¡¡straight¡¡line¡¡is¡¡the¡¡most¡¡beautiful¡¡of¡¡lines¡¡or¡¡the¡¡contrary¡¡of
the¡¡circle£»¡¡for¡¡these¡¡qualities¡¡do¡¡not¡¡belong¡¡to¡¡lines¡¡in¡¡virtue¡¡of
their¡¡peculiar¡¡genus£»¡¡but¡¡through¡¡some¡¡property¡¡which¡¡it¡¡shares¡¡with
other¡¡genera¡£
¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡8
¡¡¡¡It¡¡is¡¡also¡¡clear¡¡that¡¡if¡¡the¡¡premisses¡¡from¡¡which¡¡the¡¡syllogism
proceeds¡¡are¡¡commensurately¡¡universal£»¡¡the¡¡conclusion¡¡of¡¡such¡¡i¡£e¡£
in¡¡the¡¡unqualified¡¡sense¡must¡¡also¡¡be¡¡eternal¡£¡¡Therefore¡¡no
attribute¡¡can¡¡be¡¡demonstrated¡¡nor¡¡known¡¡by¡¡strictly¡¡scientific
knowledge¡¡to¡¡inhere¡¡in¡¡perishable¡¡things¡£¡¡The¡¡proof¡¡can¡¡only¡¡be
accidental£»¡¡because¡¡the¡¡attribute's¡¡connexion¡¡with¡¡its¡¡perishable
subject¡¡is¡¡not¡¡commensurately¡¡universal¡¡but¡¡temporary¡¡and¡¡special¡£
If¡¡such¡¡a¡¡demonstration¡¡is¡¡made£»¡¡one¡¡premiss¡¡must¡¡be¡¡perishable¡¡and
not¡¡commensurately¡¡universal¡¡£¨perishable¡¡because¡¡only¡¡if¡¡it¡¡is
perishable¡¡will¡¡the¡¡conclusion¡¡be¡¡perishable£»¡¡not¡¡commensurately
universal£»¡¡because¡¡the¡¡predicate¡¡will¡¡be¡¡predicable¡¡of¡¡some
instances¡¡of¡¡the¡¡subject¡¡and¡¡not¡¡of¡¡others£©£»¡¡so¡¡that¡¡the¡¡conclusion
can¡¡only¡¡be¡¡that¡¡a¡¡fact¡¡is¡¡true¡¡at¡¡the¡¡moment¡not¡¡commensurately¡¡and
universally¡£¡¡The¡¡same¡¡is¡¡true¡¡of¡¡definitions£»¡¡since¡¡a¡¡definition¡¡is
either¡¡a¡¡primary¡¡premiss¡¡or¡¡a¡¡conclusion¡¡of¡¡a¡¡demonstration£»¡¡or¡¡else
only¡¡differs¡¡from¡¡a¡¡demonstration¡¡in¡¡the¡¡order¡¡of¡¡its¡¡terms¡£
Demonstration¡¡and¡¡science¡¡of¡¡merely¡¡frequent¡¡occurrences¡e¡£g¡£¡¡of
eclipse¡¡as¡¡happening¡¡to¡¡the¡¡moon¡are£»¡¡as¡¡such£»¡¡clearly¡¡eternal£º
whereas¡¡so¡¡far¡¡as¡¡they¡¡are¡¡not¡¡eternal¡¡they¡¡are¡¡not¡¡fully
commensurate¡£¡¡Other¡¡subjects¡¡too¡¡have¡¡properties¡¡attaching¡¡to¡¡them
in¡¡the¡¡same¡¡way¡¡as¡¡eclipse¡¡attaches¡¡to¡¡the¡¡moon¡£
¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡9
¡¡¡¡It¡¡is¡¡clear¡¡that¡¡if¡¡the¡¡conclusion¡¡is¡¡to¡¡show¡¡an¡¡attribute
inhering¡¡as¡¡such£»¡¡nothing¡¡can¡¡be¡¡demonstrated¡¡except¡¡from¡¡its
'appropriate'¡¡basic¡¡truths¡£¡¡Consequently¡¡a¡¡proof¡¡even¡¡from¡¡true£»
indemonstrable£»¡¡and¡¡immediate¡¡premisses¡¡does¡¡not¡¡constitute¡¡knowledge¡£
Such¡¡proofs¡¡are¡¡like¡¡Bryson's¡¡method¡¡of¡¡squaring¡¡the¡¡circle£»¡¡for
they¡¡operate¡¡by¡¡taking¡¡as¡¡their¡¡middle¡¡a¡¡common¡¡character¡a¡¡character£»
therefore£»¡¡which¡¡the¡¡subject¡¡may¡¡share¡¡with¡¡another¡and¡¡consequently
they¡¡apply¡¡equally¡¡to¡¡subjects¡¡different¡¡in¡¡kind¡£¡¡They¡¡therefore
afford¡¡knowledge¡¡of¡¡an¡¡attribute¡¡only¡¡as¡¡inhering¡¡accidentally£»¡¡not¡¡as
belonging¡¡to¡¡its¡¡subject¡¡as¡¡such£º¡¡otherwise¡¡they¡¡would¡¡not¡¡have¡¡been
applicable¡¡to¡¡another¡¡genus¡£
¡¡¡¡Our¡¡knowledge¡¡of¡¡any¡¡attribute's¡¡connexion¡¡with¡¡a¡¡subject¡¡is
accidental¡¡unless¡¡we¡¡know¡¡that¡¡connexion¡¡through¡¡the¡¡middle¡¡term¡¡in
virtue¡¡of¡¡which¡¡it¡¡inheres£»¡¡and¡¡as¡¡an¡¡inference¡¡from¡¡basic¡¡premisses
essential¡¡and¡¡'appropriate'¡¡to¡¡the¡¡subject¡unless¡¡we¡¡know£»¡¡e¡£g¡£¡¡the
property¡¡of¡¡possessing¡¡angles¡¡equal¡¡to¡¡two¡¡right¡¡angles¡¡as¡¡belonging
to¡¡that¡¡subject¡¡in¡¡which¡¡it¡¡inheres¡¡essentially£»¡¡and¡¡as¡¡inferred
from¡¡basic¡¡premisses¡¡essential¡¡and¡¡'appropriate'¡¡to¡¡that¡¡subject£º¡¡so
that¡¡if¡¡that¡¡middle¡¡term¡¡also¡¡belongs¡¡essentially¡¡to¡¡the¡¡minor£»¡¡the
middle¡¡must¡¡belong¡¡to¡¡the¡¡same¡¡kind¡¡as¡¡the¡¡major¡¡and¡¡minor¡¡terms¡£
The¡¡only¡¡exceptions¡¡to¡¡this¡¡rule¡¡are¡¡such¡¡cases¡¡as¡¡theorems¡¡in
harmonics¡¡which¡¡are¡¡demonstrable¡¡by¡¡arithmetic¡£¡¡Such¡¡theorems¡¡are
proved¡¡by¡¡the¡¡same¡¡middle¡¡terms¡¡as¡¡arithmetical¡¡properties£»¡¡but¡¡with¡¡a
qualification¡the¡¡fact¡¡falls¡¡under¡¡a¡¡separate¡¡science¡¡£¨for¡¡the¡¡subject
genus¡¡is¡¡separate£©£»¡¡but¡¡the¡¡reasoned¡¡fact¡¡concerns¡¡the¡¡superior
science£»¡¡to¡¡which¡¡the¡¡attributes¡¡essentially¡¡belong¡£¡¡Thus£»¡¡even
these¡¡apparent¡¡exceptions¡¡show¡¡that¡¡no¡¡attribute¡¡is¡¡strictly
demonstrable¡¡except¡¡from¡¡its¡¡'appropriate'¡¡basic¡¡truths£»¡¡which£»
however£»¡¡in¡¡the¡¡case¡¡of¡¡these¡¡sciences¡¡have¡¡the¡¡requisite¡¡identity
of¡¡character¡£
¡¡¡¡It¡¡is¡¡no¡¡less¡¡evident¡¡that¡¡the¡¡peculiar¡¡basic¡¡truths¡¡of¡¡each
inhering¡¡attribute¡¡are¡¡indemonstrable£»¡¡for¡¡basic¡¡truths¡¡from¡¡which
they¡¡might¡¡be¡¡deduced¡¡would¡¡be¡¡basic¡¡truths¡¡of¡¡all¡¡that¡¡is£»¡¡and¡¡the
science¡¡to¡¡which¡¡they¡¡belonged¡¡would¡¡possess¡¡universal¡¡sovereignty¡£
This¡¡is¡¡so¡¡because¡¡he¡¡knows¡¡better¡¡whose¡¡knowledge¡¡is¡¡deduced¡¡from
higher¡¡causes£»¡¡for¡¡his¡¡knowledge¡¡is¡¡from¡¡prior¡¡premisses¡¡when¡¡it
derives¡¡from¡¡causes¡¡themselves¡¡uncaused£º¡¡hence£»¡¡if¡¡he¡¡knows¡¡better
than¡¡others¡¡or¡¡best¡¡of¡¡all£»¡¡his¡¡knowledge¡¡would¡¡be¡¡science¡¡in¡¡a¡¡higher
or¡¡the¡¡highest¡¡degree¡£¡¡But£»¡¡as¡¡things¡¡are£»¡¡demonstration¡¡is¡¡not
transferable¡¡to¡¡another¡¡genus£»¡¡with¡¡such¡¡exceptions¡¡as¡¡we¡¡have
mentioned¡¡of¡¡the¡¡application¡¡of¡¡geometrical¡¡demonstrations¡¡to¡¡theorems
in¡¡mechanics¡¡or¡¡optics£»¡¡or¡¡of¡¡arithmetical¡¡demonstrations¡¡to¡¡those
of¡¡harmonics¡£
¡¡¡¡It¡¡is¡¡hard¡¡to¡¡be¡¡sure¡¡whether¡¡one¡¡knows¡¡or¡¡not£»¡¡for¡¡it¡¡is¡¡hard¡¡to¡¡be
sure¡¡whether¡¡one's¡¡knowledge¡¡is¡¡based¡¡on¡¡the¡¡basic¡¡truths
appropriate¡¡to¡¡each¡¡attribute¡the¡¡differentia¡¡of¡¡true¡¡knowledge¡£¡¡We
think¡¡we¡¡have¡¡scientific¡¡knowledge¡¡if¡¡we¡¡have¡¡reasoned¡¡from¡¡true¡¡and
primary¡¡premisses¡£¡¡But¡¡that¡¡is¡¡not¡¡so£º¡¡the¡¡conclusion¡¡must¡¡be
homogeneous¡¡with¡¡the¡¡basic¡¡facts¡¡of¡¡the¡¡science¡£
¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡10
¡¡¡¡I¡¡call¡¡the¡¡basic¡¡truths¡¡of¡¡every¡¡genus¡¡those¡¡clements¡¡in¡¡it¡¡the
existence¡¡of¡¡which¡¡cannot¡¡be¡¡proved¡£¡¡As¡¡regards¡¡both¡¡these¡¡primary
truths¡¡and¡¡the¡¡attributes¡¡dependent¡¡on¡¡them¡¡the¡¡meaning¡¡of¡¡the¡¡name¡¡is
assumed¡£¡¡The¡¡fact¡¡of¡¡their¡¡existence¡¡as¡¡regards¡¡the¡¡primary¡¡truths
must¡¡be¡¡assumed£»¡¡but¡¡it¡¡has¡¡to¡¡be¡¡proved¡¡of¡¡the¡¡remainder£»¡¡the
attributes¡£¡¡Thus¡¡we¡¡assume¡¡the¡¡meaning¡¡alike¡¡of¡¡unity£»¡¡straight£»¡¡and
triangular£»¡¡but¡¡while¡¡as¡¡regards¡¡unity¡¡and¡¡magnitude¡¡we¡¡assume¡¡also
the¡¡fact¡¡of¡¡their¡¡existence£»¡¡in¡¡the¡¡case¡¡of¡¡the¡¡remainder¡¡proof¡¡is
required¡£
¡¡¡¡Of¡¡the¡¡basic¡¡truths¡¡used¡¡in¡¡the¡¡demonstrative¡¡sciences¡¡some¡¡are
peculiar¡¡to¡¡each¡¡science£»¡¡and¡¡some¡¡are¡¡common£»¡¡but¡¡common¡¡only¡¡in
the¡¡sense¡¡of¡¡analogous£»¡¡being¡¡of¡¡use¡¡only¡¡in¡¡so¡¡far¡¡as¡¡they¡¡fall
within¡¡the¡¡genus¡¡constituting¡¡the¡¡province¡¡of¡¡the¡¡science¡¡in¡¡question¡£
¡¡¡¡Peculiar¡¡truths¡¡are£»¡¡e¡£g¡£¡¡the¡¡definitions¡¡of¡¡line¡¡and¡¡straight£»
common¡¡truths¡¡are¡¡such¡¡as¡¡'take¡¡equals¡¡from¡¡equals¡¡and¡¡equals¡¡remain'¡£
Only¡¡so¡¡much¡¡of¡¡these¡¡common¡¡truths¡¡is¡¡required¡¡as¡¡falls¡¡within¡¡the
genus¡¡in¡¡question£º¡¡for¡¡a¡¡truth¡¡of¡¡this¡¡kind¡¡will¡¡have¡¡the¡¡same¡¡force
even¡¡if¡¡not¡¡used¡¡generally¡¡but¡¡applied¡¡by¡¡the¡¡geometer¡¡only¡¡to
magnitudes£»¡¡or¡¡by¡¡the¡¡arithmetician¡¡only¡¡to¡¡numbers¡£¡¡Also¡¡peculiar
to¡¡a¡¡science¡¡are¡¡the¡¡subjects¡¡the¡¡existence¡¡as¡¡well¡¡as¡¡the¡¡meaning
of¡¡which¡¡it¡¡assumes£»¡¡and¡¡the¡¡essential¡¡attributes¡¡of¡¡which¡¡it
investigates£»¡¡e¡£g¡£¡¡in¡¡arithmetic¡¡units£»¡¡in¡¡geometry¡¡points¡¡and
lines¡£¡¡Both¡¡the¡¡existence¡¡and¡¡the¡¡meaning¡¡of¡¡the¡¡subjects¡¡are
assumed¡¡by¡¡these¡¡sciences£»¡¡but¡¡of¡¡their¡¡essential¡¡attributes¡¡only
the¡¡meaning¡¡is¡¡assumed¡£¡¡For¡¡example¡¡arithmetic¡¡assumes¡¡the¡¡meaning
of¡¡odd¡¡and¡¡even£»¡¡square¡¡and¡¡cube£»¡¡geometry¡¡that¡¡of¡¡incommensurable£»¡¡or
of¡¡deflection¡¡or¡¡verging¡¡of¡¡lines£»¡¡whereas¡¡the¡¡existence¡¡of¡¡these
attributes¡¡is¡¡demonstrated¡¡by¡¡means¡¡of¡¡the¡¡axioms¡¡and¡¡from¡¡previous
conclusions¡¡as¡¡premisses¡£¡¡Astronomy¡¡too¡¡proceeds¡¡in¡¡the¡¡same¡¡way¡£
For¡¡indeed¡¡every¡¡demonstrative¡¡science¡¡has¡¡three¡¡elements£º¡¡£¨1£©¡¡that
which¡¡it¡¡posits£»¡¡the¡¡subject¡¡genus¡¡whose¡¡essential¡¡attributes¡¡it
examines£»¡¡£¨2£©¡¡the¡¡so¡called¡¡axioms£»¡¡which¡¡are¡¡primary¡¡premisses¡¡of¡¡its
demonstration£»¡¡£¨3£©¡¡the¡¡attributes£»¡¡the¡¡meaning¡¡of¡¡which¡¡it¡¡assumes¡£
Yet¡¡some¡¡sciences¡¡may¡¡very¡¡well¡¡pass¡¡over¡¡some¡¡of¡¡these¡¡elements£»¡¡e¡£g¡£
we¡¡might¡¡not¡¡expressly¡¡posit¡¡the¡¡existence¡¡of¡¡the¡¡genus¡¡if¡¡its
existence¡¡were¡¡obvious¡¡£¨for¡¡instance£»¡¡the¡¡existence¡¡of¡¡hot¡¡and¡¡cold¡¡is
more¡¡evident¡¡than¡¡that¡¡of¡¡number£©£»¡¡or¡¡we¡¡might¡¡omit¡¡to¡¡assume
expressly¡¡the¡¡meaning¡¡of¡¡the¡¡attributes¡¡if¡¡it¡¡were¡¡well¡¡understood¡£¡¡In
the¡¡way¡¡the¡¡meaning¡¡of¡¡axioms£»¡¡such¡¡as¡¡'Take¡¡equals¡¡from¡¡equals¡¡and
equals¡¡remain'£»¡¡is¡¡well¡¡known¡¡and¡¡so¡¡not¡¡expressly¡¡assumed¡£
Nevertheless¡¡in¡¡the¡¡nature¡¡of¡¡the¡¡case¡¡the¡¡essential¡¡elements¡¡of
demonstration¡¡are¡¡three£º¡¡the¡¡subject£»¡¡the¡¡attributes£»¡¡and¡¡the¡¡basic
premisses¡£
¡¡¡¡That¡¡which¡¡expresses¡¡necessary¡¡self¡grounded¡¡fact£»¡¡and¡¡which¡¡we¡¡must
necessarily¡¡believe£»¡¡is¡¡distinct¡¡both¡¡from¡¡the¡¡hypotheses¡¡of¡¡a¡¡science
and¡¡from¡¡illegitimate¡¡postulate¡I¡¡say¡¡'must¡¡believe'£»¡¡because¡¡all
syllogism£»¡¡and¡¡therefore¡¡a¡¡fortiori¡¡demonstration£»¡¡is¡¡addressed¡¡not¡¡to