01 organon - 4 posterior analytics

7/30/2019 01 Organon - 4 Posterior Analytics

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Aristotle

Posterior Analyticstranslated by G. R. G. Mure

Book I

1

All instruction given or received by way of argument proceeds from pree!istent knowledge. "#is

becomes evident upon a survey of all t#e species of suc# instruction. "#e mat#ematical sciencesand all ot#er speculative disciplines are ac$uired in t#is way% and so are t#e two forms of

dialectical reasoning% syllogistic and inductive& for eac# of t#ese latter make use of old

knowledge to impart new% t#e syllogism assuming an audience t#at accepts its premisses%

induction e!#ibiting t#e universal as implicit in t#e clearly known particular. Again% t#epersuasion e!erted by r#etorical arguments is in principle t#e same% since t#ey use eit#er

e!ample% a kind of induction% or ent#ymeme% a form of syllogism.

"#e pree!istent knowledge re$uired is of two kinds. In some cases admission of t#e fact must beassumed% in ot#ers compre#ension of t#e meaning of t#e term used% and sometimes bot#

assumptions are essential. "#us% we assume t#at every predicate can be eit#er truly affirmed or

truly denied of any sub'ect% and t#at (triangle) means so and so& as regards (unit) we #ave to maket#e double assumption of t#e meaning of t#e word and t#e e!istence of t#e t#ing. "#e reason is

t#at t#ese several ob'ects are not e$ually obvious to us. Recognition of a trut# may in some cases

contain as factors bot# previous knowledge and also knowledge ac$uired simultaneously wit#t#at recognition * knowledge% t#is latter% of t#e particulars actually falling under t#e universal and

t#erein already virtually known. +or e!ample% t#e student knew before#and t#at t#e angles of

every triangle are e$ual to two rig#t angles& but it was only at t#e actual moment at w#ic# #e was

being led on to recogni,e t#is as true in t#e instance before #im t#at #e came to know (t#is figureinscribed in t#e semicircle) to be a triangle. +or some t#ings -vi,. t#e singulars finally reac#ed

w#ic# are not predicable of anyt#ing else as sub'ect are only learnt in t#is way% i.e. t#ere is #ere

no recognition t#roug# a middle of a minor term as sub'ect to a ma'or. Before #e was led on torecognition or before #e actually drew a conclusion% we s#ould per#aps say t#at in a manner #e

knew% in a manner not.

If #e did not in an un$ualified sense of t#e term know t#e e!istence of t#is triangle% #ow could #eknow wit#out $ualification t#at its angles were e$ual to two rig#t angles/ 0o clearly #e knows

not wit#out $ualification but only in t#e sense t#at #e knows universally. If t#is distinction is not

drawn% we are faced wit# t#e dilemma in t#e Meno eit#er a man will learn not#ing or w#at #e

already knows& for we cannot accept t#e solution w#ic# some people offer. A man is asked% (2oyou% or do you not% know t#at every pair is even/) 3e says #e does know it. "#e $uestioner t#en

produces a particular pair% of t#e e!istence% and so a fortiori of t#e evenness% of w#ic# #e was

unaware. "#e solution w#ic# some people offer is to assert t#at t#ey do not know t#at every pairis even% but only t#at everyt#ing w#ic# t#ey know to be a pair is even yet w#at t#ey know to be

even is t#at of w#ic# t#ey #ave demonstrated evenness% i.e. w#at t#ey made t#e sub'ect of t#eir

premiss% vi,. not merely every triangle or number w#ic# t#ey know to be suc#% but any and everynumber or triangle wit#out reservation. +or no premiss is ever couc#ed in t#e form (every

number w#ic# you know to be suc#)% or (every rectilinear figure w#ic# you know to be suc#) t#e

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predicate is always construed as applicable to any and every instance of t#e t#ing. 4n t#e ot#er

#and% I imagine t#ere is not#ing to prevent a man in one sense knowing w#at #e is learning% inanot#er not knowing it. "#e strange t#ing would be% not if in some sense #e knew w#at #e was

learning% but if #e were to know it in t#at precise sense and manner in w#ic# #e was learning it.

5

6e suppose ourselves to possess un$ualified scientific knowledge of a t#ing% as opposed to

knowing it in t#e accidental way in w#ic# t#e sop#ist knows% w#en we t#ink t#at we know t#ecause on w#ic# t#e fact depends% as t#e cause of t#at fact and of no ot#er% and% furt#er% t#at t#e

fact could not be ot#er t#an it is. 0ow t#at scientific knowing is somet#ing of t#is sort is evident

* witness bot# t#ose w#o falsely claim it and t#ose w#o actually possess it% since t#e formermerely imagine t#emselves to be% w#ile t#e latter are also actually% in t#e condition described.

7onse$uently t#e proper ob'ect of un$ualified scientific knowledge is somet#ing w#ic# cannot be

ot#er t#an it is.

"#ere may be anot#er manner of knowing as well * t#at will be discussed later. 6#at I now assertis t#at at all events we do know by demonstration. By demonstration I mean a syllogism

productive of scientific knowledge% a syllogism% t#at is% t#e grasp of w#ic# is eo ipso suc#

knowledge. Assuming t#en t#at my t#esis as to t#e nature of scientific knowing is correct% t#epremisses of demonstrated knowledge must be true% primary% immediate% better known t#an and

prior to t#e conclusion% w#ic# is furt#er related to t#em as effect to cause. 8nless t#ese conditions

are satisfied% t#e basic trut#s will not be (appropriate) to t#e conclusion. 9yllogism t#ere mayindeed be wit#out t#ese conditions% but suc# syllogism% not being productive of scientific

knowledge% will not be demonstration. "#e premisses must be true for t#at w#ic# is none!istent

cannot be known * we cannot know% e.g. t#at t#e diagonal of a s$uare is commensurate wit# itsside. "#e premisses must be primary and indemonstrable& ot#erwise t#ey will re$uire

demonstration in order to be known% since to #ave knowledge% if it be not accidental knowledge%

of t#ings w#ic# are demonstrable% means precisely to #ave a demonstration of t#em. "#e

premisses must be t#e causes of t#e conclusion% better known t#an it% and prior to it& its causes%since we possess scientific knowledge of a t#ing only w#en we know its cause& prior% in order to

be causes& antecedently known% t#is antecedent knowledge being not our mere understanding of

t#e meaning% but knowledge of t#e fact as well. 0ow (prior) and (better known) are ambiguousterms% for t#ere is a difference between w#at is prior and better known in t#e order of being and

w#at is prior and better known to man. I mean t#at ob'ects nearer to sense are prior and better

known to man& ob'ects wit#out $ualification prior and better known are t#ose furt#er from sense.0ow t#e most universal causes are furt#est from sense and particular causes are nearest to sense%

and t#ey are t#us e!actly opposed to one anot#er. In saying t#at t#e premisses of demonstrated

knowledge must be primary% I mean t#at t#ey must be t#e (appropriate) basic trut#s% for I identify

primary premiss and basic trut#. A (basic trut#) in a demonstration is an immediate proposition.An immediate proposition is one w#ic# #as no ot#er proposition prior to it. A proposition is eit#er

part of an enunciation% i.e. it predicates a single attribute of a single sub'ect. If a proposition is

dialectical% it assumes eit#er part indifferently& if it is demonstrative% it lays down one part to t#edefinite e!clusion of t#e ot#er because t#at part is true. "#e term (enunciation) denotes eit#er part

of a contradiction indifferently. A contradiction is an opposition w#ic# of its own nature e!cludes

a middle. "#e part of a contradiction w#ic# con'oins a predicate wit# a sub'ect is an affirmation&t#e part dis'oining t#em is a negation. I call an immediate basic trut# of syllogism a (t#esis) w#en%

t#oug# it is not susceptible of proof by t#e teac#er% yet ignorance of it does not constitute a total

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bar to progress on t#e part of t#e pupil one w#ic# t#e pupil must know if #e is to learn anyt#ing

w#atever is an a!iom. I call it an a!iom because t#ere are suc# trut#s and we give t#em t#e nameof a!ioms par e!cellence. If a t#esis assumes one part or t#e ot#er of an enunciation% i.e. asserts

eit#er t#e e!istence or t#e none!istence of a sub'ect% it is a #ypot#esis& if it does not so assert% it

is a definition. 2efinition is a (t#esis) or a (laying somet#ing down)% since t#e arit#metician lays it

down t#at to be a unit is to be $uantitatively indivisible& but it is not a #ypot#esis% for to definew#at a unit is is not t#e same as to affirm its e!istence.

0ow since t#e re$uired ground of our knowledge * i.e. of our conviction * of a fact is t#e

possession of suc# a syllogism as we call demonstration% and t#e ground of t#e syllogism is t#efacts constituting its premisses% we must not only know t#e primary premisses * some if not all of

t#em * before#and% but know t#em better t#an t#e conclusion for t#e cause of an attribute)s

in#erence in a sub'ect always itself in#eres in t#e sub'ect more firmly t#an t#at attribute& e.g. t#ecause of our loving anyt#ing is dearer to us t#an t#e ob'ect of our love. 9o since t#e primary

premisses are t#e cause of our knowledge * i.e. of our conviction * it follows t#at we know t#em

better * t#at is% are more convinced of t#em * t#an t#eir conse$uences% precisely because of our

knowledge of t#e latter is t#e effect of our knowledge of t#e premisses. 0ow a man cannotbelieve in anyt#ing more t#an in t#e t#ings #e knows% unless #e #as eit#er actual knowledge of it

or somet#ing better t#an actual knowledge. But we are faced wit# t#is parado! if a student w#ose

belief rests on demonstration #as not prior knowledge& a man must believe in some% if not in all%of t#e basic trut#s more t#an in t#e conclusion. Moreover% if a man sets out to ac$uire t#e

scientific knowledge t#at comes t#roug# demonstration% #e must not only #ave a better

knowledge of t#e basic trut#s and a firmer conviction of t#em t#an of t#e conne!ion w#ic# isbeing demonstrated more t#an t#is% not#ing must be more certain or better known to #im t#an

t#ese basic trut#s in t#eir c#aracter as contradicting t#e fundamental premisses w#ic# lead to t#e

opposed and erroneous conclusion. +or indeed t#e conviction of pure science must beuns#akable.

:9ome #old t#at% owing to t#e necessity of knowing t#e primary premisses% t#ere is no scientific

knowledge. 4t#ers t#ink t#ere is% but t#at all trut#s are demonstrable. 0eit#er doctrine is eit#er

true or a necessary deduction from t#e premisses. "#e first sc#ool% assuming t#at t#ere is no wayof knowing ot#er t#an by demonstration% maintain t#at an infinite regress is involved% on t#e

ground t#at if be#ind t#e prior stands no primary% we could not know t#e posterior t#roug# t#e

prior -w#erein t#ey are rig#t% for one cannot traverse an infinite series if on t#e ot#er #and *t#ey say * t#e series terminates and t#ere are primary premisses% yet t#ese are unknowable

because incapable of demonstration% w#ic# according to t#em is t#e only form of knowledge.

And since t#us one cannot know t#e primary premisses% knowledge of t#e conclusions w#ic#

follow from t#em is not pure scientific knowledge nor properly knowing at all% but rests on t#emere supposition t#at t#e premisses are true. "#e ot#er party agree wit# t#em as regards knowing%

#olding t#at it is only possible by demonstration% but t#ey see no difficulty in #olding t#at all

trut#s are demonstrated% on t#e ground t#at demonstration may be circular and reciprocal.4ur own doctrine is t#at not all knowledge is demonstrative on t#e contrary% knowledge of t#e

immediate premisses is independent of demonstration. -"#e necessity of t#is is obvious& for since

we must know t#e prior premisses from w#ic# t#e demonstration is drawn% and since t#e regressmust end in immediate trut#s% t#ose trut#s must be indemonstrable. 9uc#% t#en% is our doctrine%

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and in addition we maintain t#at besides scientific knowledge t#ere is its originative source w#ic#

enables us to recogni,e t#e definitions.0ow demonstration must be based on premisses prior to and better known t#an t#e conclusion&

and t#e same t#ings cannot simultaneously be bot# prior and posterior to one anot#er so circular

demonstration is clearly not possible in t#e un$ualified sense of (demonstration)% but only

possible if (demonstration) be e!tended to include t#at ot#er met#od of argument w#ic# rests on adistinction between trut#s prior to us and trut#s wit#out $ualification prior% i.e. t#e met#od by

w#ic# induction produces knowledge. But if we accept t#is e!tension of its meaning% our

definition of un$ualified knowledge will prove faulty& for t#ere seem to be two kinds of it.Per#aps% #owever% t#e second form of demonstration% t#at w#ic# proceeds from trut#s better

known to us% is not demonstration in t#e un$ualified sense of t#e term.

"#e advocates of circular demonstration are not only faced wit# t#e difficulty we #ave 'ust statedin addition t#eir t#eory reduces to t#e mere statement t#at if a t#ing e!ists% t#en it does e!ist * an

easy way of proving anyt#ing. "#at t#is is so can be clearly s#own by taking t#ree terms% for to

constitute t#e circle it makes no difference w#et#er many terms or few or even only two are

taken. "#us by direct proof% if A is% B must be& if B is% 7 must be& t#erefore if A is% 7 must be.9ince t#en * by t#e circular proof * if A is% B must be% and if B is% A must be% A may be

substituted for 7 above. "#en (if B is% A must be);(if B is% 7 must be)% w#ic# above gave t#e

conclusion (if A is% 7 must be) but 7 and A #ave been identified. 7onse$uently t#e up#olders ofcircular demonstration are in t#e position of saying t#at if A is% A must be * a simple way of

proving anyt#ing. Moreover% even suc# circular demonstration is impossible e!cept in t#e case of

attributes t#at imply one anot#er% vi,. (peculiar) properties.0ow% it #as been s#own t#at t#e positing of one t#ing * be it one term or one premiss * never

involves a necessary conse$uent two premisses constitute t#e first and smallest foundation for

drawing a conclusion at all and t#erefore a fortiori for t#e demonstrative syllogism of science. If%t#en% A is implied in B and 7% and B and 7 are reciprocally implied in one anot#er and in A% it is

possible% as #as been s#own in my writings on t#e syllogism% to prove all t#e assumptions on

w#ic# t#e original conclusion rested% by circular demonstration in t#e first figure. But it #as also

been s#own t#at in t#e ot#er figures eit#er no conclusion is possible% or at least none w#ic#proves bot# t#e original premisses. Propositions t#e terms of w#ic# are not convertible cannot be

circularly demonstrated at all% and since convertible terms occur rarely in actual demonstrations%

it is clearly frivolous and impossible to say t#at demonstration is reciprocal and t#at t#ereforeeveryt#ing can be demonstrated.

t#ing?) walks and is w#ite in virtue of being somet#ing else besides& w#ereas substance% in t#e

sense of w#atever signifies a (t#is somew#at)% is not w#at it is in virtue of being somet#ing else

besides. "#ings% t#en% not predicated of a sub'ect I call essential& t#ings predicated of a sub'ect Icall accidental or (coincidental).

In anot#er sense again -b a t#ing conse$uentially connected wit# anyt#ing is essential& one not so

connected is (coincidental). An e!ample of t#e latter is (6#ile #e was walking it lig#tened) t#elig#tning was not due to #is walking& it was% we s#ould say% a coincidence. If% on t#e ot#er #and%

t#ere is a conse$uential conne!ion% t#e predication is essential& e.g. if a beast dies w#en its t#roat

is being cut% t#en its deat# is also essentially connected wit# t#e cutting% because t#e cutting wast#e cause of deat#% not deat# a (coincident) of t#e cutting.

9o far t#en as concerns t#e sp#ere of conne!ions scientifically known in t#e un$ualified sense of

t#at term% all attributes w#ic# -wit#in t#at sp#ere are essential eit#er in t#e sense t#at t#eirsub'ects are contained in t#em% or in t#e sense t#at t#ey are contained in t#eir sub'ects% are

necessary as well as conse$uentially connected wit# t#eir sub'ects. +or it is impossible for t#em

not to in#ere in t#eir sub'ects eit#er simply or in t#e $ualified sense t#at one or ot#er of a pair of

opposites must in#ere in t#e sub'ect& e.g. in line must be eit#er straig#tness or curvature% innumber eit#er oddness or evenness. +or wit#in a single identical genus t#e contrary of a given

attribute is eit#er its privative or its contradictory& e.g. wit#in number w#at is not odd is even%

inasmuc# as wit#in t#is sp#ere even is a necessary conse$uent of notodd. 9o% since any givenpredicate must be eit#er affirmed or denied of any sub'ect% essential attributes must in#ere in t#eir

sub'ects of necessity.

"#us% t#en% we #ave establis#ed t#e distinction between t#e attribute w#ic# is (true in everyinstance) and t#e (essential) attribute.

I term (commensurately universal) an attribute w#ic# belongs to every instance of its sub'ect% and

to every instance essentially and as suc#& from w#ic# it clearly follows t#at all commensurate

universals in#ere necessarily in t#eir sub'ects. "#e essential attribute% and t#e attribute t#atbelongs to its sub'ect as suc#% are identical. =.g. point and straig#t belong to line essentially% for

t#ey belong to line as suc#& and triangle as suc# #as two rig#t angles% for it is essentially e$ual to

two rig#t angles.An attribute belongs commensurately and universally to a sub'ect w#en it can be s#own to belong

to any random instance of t#at sub'ect and w#en t#e sub'ect is t#e first t#ing to w#ic# it can be

s#own to belong. "#us% e.g. -1 t#e e$uality of its angles to two rig#t angles is not acommensurately universal attribute of figure. +or t#oug# it is possible to s#ow t#at a figure #as

its angles e$ual to two rig#t angles% t#is attribute cannot be demonstrated of any figure selected at

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#ap#a,ard% nor in demonstrating does one take a figure at random * a s$uare is a figure but its

angles are not e$ual to two rig#t angles. 4n t#e ot#er #and% any isosceles triangle #as its anglese$ual to two rig#t angles% yet isosceles triangle is not t#e primary sub'ect of t#is attribute but

triangle is prior. 9o w#atever can be s#own to #ave its angles e$ual to two rig#t angles% or to

possess any ot#er attribute% in any random instance of itself and primarily * t#at is t#e first

sub'ect to w#ic# t#e predicate in $uestion belongs commensurately and universally% and t#edemonstration% in t#e essential sense% of any predicate is t#e proof of it as belonging to t#is first

sub'ect commensurately and universally w#ile t#e proof of it as belonging to t#e ot#er sub'ects

to w#ic# it attac#es is demonstration only in a secondary and unessential sense. 0or again -5 ise$uality to two rig#t angles a commensurately universal attribute of isosceles& it is of wider

application.

@

6e must not fail to observe t#at we often fall into error because our conclusion is not in fact

primary and commensurately universal in t#e sense in w#ic# we t#ink we prove it so. 6e maket#is mistake -1 w#en t#e sub'ect is an individual or individuals above w#ic# t#ere is no universal

to be found -5 w#en t#e sub'ects belong to different species and t#ere is a #ig#er universal% but

it #as no name -: w#en t#e sub'ect w#ic# t#e demonstrator takes as a w#ole is really only a partof a larger w#ole& for t#en t#e demonstration will be true of t#e individual instances wit#in t#e

part and will #old in every instance of it% yet t#e demonstration will not be true of t#is sub'ect

primarily and commensurately and universally. 6#en a demonstration is true of a sub'ectprimarily and commensurately and universally% t#at is to be taken to mean t#at it is true of a given

sub'ect primarily and as suc#. 7ase -: may be t#us e!emplified. If a proof were given t#at

perpendiculars to t#e same line are parallel% it mig#t be supposed t#at lines t#us perpendicularwere t#e proper sub'ect of t#e demonstration because being parallel is true of every instance of

t#em. But it is not so% for t#e parallelism depends not on t#ese angles being e$ual to one anot#er

because eac# is a rig#t angle% but simply on t#eir being e$ual to one anot#er. An e!ample of -1

would be as follows if isosceles were t#e only triangle% it would be t#oug#t to #ave its anglese$ual to two rig#t angles $ua isosceles. An instance of -5 would be t#e law t#at proportionals

alternate. Alternation used to be demonstrated separately of numbers% lines% solids% and durations%

t#oug# it could #ave been proved of t#em all by a single demonstration. Because t#ere was nosingle name to denote t#at in w#ic# numbers% lengt#s% durations% and solids are identical% and

because t#ey differed specifically from one anot#er% t#is property was proved of eac# of t#em

separately. "oday% #owever% t#e proof is commensurately universal% for t#ey do not possess t#isattribute $ua lines or $ua numbers% but $ua manifesting t#is generic c#aracter w#ic# t#ey are

postulated as possessing universally. 3ence% even if one prove of eac# kind of triangle t#at its

angles are e$ual to two rig#t angles% w#et#er by means of t#e same or different proofs& still% as

long as one treats separately e$uilateral% scalene% and isosceles% one does not yet know% e!ceptsop#istically% t#at triangle #as its angles e$ual to two rig#t angles% nor does one yet know t#at

triangle #as t#is property commensurately and universally% even if t#ere is no ot#er species of

triangle but t#ese. +or one does not know t#at triangle as suc# #as t#is property% nor even t#at (all)triangles #ave it * unless (all) means (eac# taken singly) if (all) means (as a w#ole class)% t#en%

t#oug# t#ere be none in w#ic# one does not recogni,e t#is property% one does not know it of (all

triangles).6#en% t#en% does our knowledge fail of commensurate universality% and w#en it is un$ualified

knowledge/ If triangle be identical in essence wit# e$uilateral% i.e. wit# eac# or all e$uilaterals%


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t#en clearly we #ave un$ualified knowledge if on t#e ot#er #and it be not% and t#e attribute

belongs to e$uilateral $ua triangle& t#en our knowledge fails of commensurate universality. (But)%it will be asked% (does t#is attribute belong to t#e sub'ect of w#ic# it #as been demonstrated $ua

triangle or $ua isosceles/ 6#at is t#e point at w#ic# t#e sub'ect. to w#ic# it belongs is primary/

-i.e. to w#at sub'ect can it be demonstrated as belonging commensurately and universally/)

7learly t#is point is t#e first term in w#ic# it is found to in#ere as t#e elimination of inferiordifferentiae proceeds. "#us t#e angles of a bra,en isosceles triangle are e$ual to two rig#t angles

but eliminate bra,en and isosceles and t#e attribute remains. (But) * you may say * )eliminate

figure or limit% and t#e attribute vanis#es.) "rue% but figure and limit are not t#e first differentiaew#ose elimination destroys t#e attribute. ("#en w#at is t#e first/) If it is triangle% it will be in

virtue of triangle t#at t#e attribute belongs to all t#e ot#er sub'ects of w#ic# it is predicable% and

triangle is t#e sub'ect to w#ic# it can be demonstrated as belonging commensurately anduniversally.

2emonstrative knowledge must rest on necessary basic trut#s& for t#e ob'ect of scientific

knowledge cannot be ot#er t#an it is. 0ow attributes attac#ing essentially to t#eir sub'ects attac#

necessarily to t#em for essential attributes are eit#er elements in t#e essential nature of t#eirsub'ects% or contain t#eir sub'ects as elements in t#eir own essential nature. -"#e pairs of

opposites w#ic# t#e latter class includes are necessary because one member or t#e ot#er

necessarily in#eres. It follows from t#is t#at premisses of t#e demonstrative syllogism must beconne!ions essential in t#e sense e!plained for all attributes must in#ere essentially or else be

accidental% and accidental attributes are not necessary to t#eir sub'ects.

6e must eit#er state t#e case t#us% or else premise t#at t#e conclusion of demonstration isnecessary and t#at a demonstrated conclusion cannot be ot#er t#an it is% and t#en infer t#at t#e

conclusion must be developed from necessary premisses. +or t#oug# you may reason from true

premisses wit#out demonstrating% yet if your premisses are necessary you will assuredly

demonstrate * in suc# necessity you #ave at once a distinctive c#aracter of demonstration. "#atdemonstration proceeds from necessary premisses is also indicated by t#e fact t#at t#e ob'ection

we raise against a professed demonstration is t#at a premiss of it is not a necessary trut# *

w#et#er we t#ink it altoget#er devoid of necessity% or at any rate so far as our opponent)s previousargument goes. "#is s#ows #ow naive it is to suppose one)s basic trut#s rig#tly c#osen if one

starts wit# a proposition w#ic# is -1 popularly accepted and -5 true% suc# as t#e sop#ists)

assumption t#at to know is t#e same as to possess knowledge. +or -1 popular acceptance orre'ection is no criterion of a basic trut#% w#ic# can only be t#e primary law of t#e genus

constituting t#e sub'ect matter of t#e demonstration& and -5 not all trut# is (appropriate).

A furt#er proof t#at t#e conclusion must be t#e development of necessary premisses is as follows.

6#ere demonstration is possible% one w#o can give no account w#ic# includes t#e cause #as noscientific knowledge. If% t#en% we suppose a syllogism in w#ic#% t#oug# A necessarily in#eres in

7% yet B% t#e middle term of t#e demonstration% is not necessarily connected wit# A and 7% t#en

t#e man w#o argues t#us #as no reasoned knowledge of t#e conclusion% since t#is conclusiondoes not owe its necessity to t#e middle term& for t#oug# t#e conclusion is necessary% t#e

mediating link is a contingent fact. 4r again% if a man is wit#out knowledge now% t#oug# #e still

retains t#e steps of t#e argument% t#oug# t#ere is no c#ange in #imself or in t#e fact and no lapseof memory on #is part& t#en neit#er #ad #e knowledge previously. But t#e mediating link% not

being necessary% may #ave peris#ed in t#e interval& and if so% t#oug# t#ere be no c#ange in #im


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nor in t#e fact% and t#oug# #e will still retain t#e steps of t#e argument% yet #e #as not knowledge%

and t#erefore #ad not knowledge before. =ven if t#e link #as not actually peris#ed but is liable toperis#% t#is situation is possible and mig#t occur. But suc# a condition cannot be knowledge.

6#en t#e conclusion is necessary% t#e middle t#roug# w#ic# it was proved may yet $uite easily

be nonnecessary. Cou can in fact infer t#e necessary even from a nonnecessary premiss% 'ust as

you can infer t#e true from t#e not true. 4n t#e ot#er #and% w#en t#e middle is necessary t#econclusion must be necessary& 'ust as true premisses always give a true conclusion. "#us% if A is

necessarily predicated of B and B of 7% t#en A is necessarily predicated of 7. But w#en t#e

conclusion is nonnecessary t#e middle cannot be necessary eit#er. "#us let A be predicated nonnecessarily of 7 but necessarily of B% and let B be a necessary predicate of 7& t#en A too will be a

necessary predicate of 7% w#ic# by #ypot#esis it is not.

"o sum up% t#en demonstrative knowledge must be knowledge of a necessary ne!us% andt#erefore must clearly be obtained t#roug# a necessary middle term& ot#erwise its possessor will

know neit#er t#e cause nor t#e fact t#at #is conclusion is a necessary conne!ion. =it#er #e will

mistake t#e nonnecessary for t#e necessary and believe t#e necessity of t#e conclusion wit#out

knowing it% or else #e will not even believe it * in w#ic# case #e will be e$ually ignorant% w#et#er#e actually infers t#e mere fact t#roug# middle terms or t#e reasoned fact and from immediate

premisses.

4f accidents t#at are not essential according to our definition of essential t#ere is nodemonstrative knowledge& for since an accident% in t#e sense in w#ic# I #ere speak of it% may also

not in#ere% it is impossible to prove its in#erence as a necessary conclusion. A difficulty% #owever%

mig#t be raised as to w#y in dialectic% if t#e conclusion is not a necessary conne!ion% suc# andsuc# determinate premisses s#ould be proposed in order to deal wit# suc# and suc# determinate

problems. 6ould not t#e result be t#e same if one asked any $uestions w#atever and t#en merely

stated one)s conclusion/ "#e solution is t#at determinate $uestions #ave to be put% not because t#ereplies to t#em affirm facts w#ic# necessitate facts affirmed by t#e conclusion% but because t#ese

answers are propositions w#ic# if t#e answerer affirm% #e must affirm t#e conclusion and affirm it

wit# trut# if t#ey are true.

9ince it is 'ust t#ose attributes wit#in every genus w#ic# are essential and possessed by t#eirrespective sub'ects as suc# t#at are necessary it is clear t#at bot# t#e conclusions and t#e

premisses of demonstrations w#ic# produce scientific knowledge are essential. +or accidents are

not necessary and% furt#er% since accidents are not necessary one does not necessarily #avereasoned knowledge of a conclusion drawn from t#em -t#is is so even if t#e accidental premisses

are invariable but not essential% as in proofs t#roug# signs& for t#oug# t#e conclusion be actually

essential% one will not know it as essential nor know its reason& but to #ave reasoned knowledgeof a conclusion is to know it t#roug# its cause. 6e may conclude t#at t#e middle must be

conse$uentially connected wit# t#e minor% and t#e ma'or wit# t#e middle.

It follows t#at we cannot in demonstrating pass from one genus to anot#er. 6e cannot% for

instance% prove geometrical trut#s by arit#metic. +or t#ere are t#ree elements in demonstration-1 w#at is proved% t#e conclusion * an attribute in#ering essentially in a genus& -5 t#e a!ioms%

i.e. a!ioms w#ic# are premisses of demonstration& -: t#e sub'ect * genus w#ose attributes% i.e.

essential properties% are revealed by t#e demonstration. "#e a!ioms w#ic# are premisses ofdemonstration may be identical in two or more sciences but in t#e case of two different genera

suc# as arit#metic and geometry you cannot apply arit#metical demonstration to t#e properties of

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magnitudes unless t#e magnitudes in $uestion are numbers. 3ow in certain cases transference is

possible I will e!plain later.Arit#metical demonstration and t#e ot#er sciences likewise possess% eac# of t#em% t#eir own

genera& so t#at if t#e demonstration is to pass from one sp#ere to anot#er% t#e genus must be

eit#er absolutely or to some e!tent t#e same. If t#is is not so% transference is clearly impossible%

because t#e e!treme and t#e middle terms must be drawn from t#e same genus ot#erwise% aspredicated% t#ey will not be essential and will t#us be accidents. "#at is w#y it cannot be proved

by geometry t#at opposites fall under one science% nor even t#at t#e product of two cubes is a

cube. 0or can t#e t#eorem of any one science be demonstrated by means of anot#er science%unless t#ese t#eorems are related as subordinate to superior -e.g. as optical t#eorems to geometry

or #armonic t#eorems to arit#metic. Geometry again cannot prove of lines any property w#ic#

t#ey do not possess $ua lines% i.e. in virtue of t#e fundamental trut#s of t#eir peculiar genus itcannot s#ow% for e!ample% t#at t#e straig#t line is t#e most beautiful of lines or t#e contrary of t#e

circle& for t#ese $ualities do not belong to lines in virtue of t#eir peculiar genus% but t#roug# some

property w#ic# it s#ares wit# ot#er genera.

D

It is also clear t#at if t#e premisses from w#ic# t#e syllogism proceeds are commensuratelyuniversal% t#e conclusion of suc# i.e. in t#e un$ualified sense * must also be eternal. "#erefore no

attribute can be demonstrated nor known by strictly scientific knowledge to in#ere in peris#able

t#ings. "#e proof can only be accidental% because t#e attribute)s conne!ion wit# its peris#ablesub'ect is not commensurately universal but temporary and special. If suc# a demonstration is

made% one premiss must be peris#able and not commensurately universal -peris#able because

only if it is peris#able will t#e conclusion be peris#able& not commensurately universal% becauset#e predicate will be predicable of some instances of t#e sub'ect and not of ot#ers& so t#at t#e

conclusion can only be t#at a fact is true at t#e moment * not commensurately and universally.

"#e same is true of definitions% since a definition is eit#er a primary premiss or a conclusion of a

demonstration% or else only differs from a demonstration in t#e order of its terms. 2emonstrationand science of merely fre$uent occurrences * e.g. of eclipse as #appening to t#e moon * are% as

suc#% clearly eternal w#ereas so far as t#ey are not eternal t#ey are not fully commensurate.

4t#er sub'ects too #ave properties attac#ing to t#em in t#e same way as eclipse attac#es to t#emoon.

E

It is clear t#at if t#e conclusion is to s#ow an attribute in#ering as suc#% not#ing can be

demonstrated e!cept from its (appropriate) basic trut#s. 7onse$uently a proof even from true%

indemonstrable% and immediate premisses does not constitute knowledge. 9uc# proofs are likeBryson)s met#od of s$uaring t#e circle& for t#ey operate by taking as t#eir middle a common

c#aracter * a c#aracter% t#erefore% w#ic# t#e sub'ect may s#are wit# anot#er * and conse$uently

t#ey apply e$ually to sub'ects different in kind. "#ey t#erefore afford knowledge of an attributeonly as in#ering accidentally% not as belonging to its sub'ect as suc# ot#erwise t#ey would not

#ave been applicable to anot#er genus.

4ur knowledge of any attribute)s conne!ion wit# a sub'ect is accidental unless we know t#atconne!ion t#roug# t#e middle term in virtue of w#ic# it in#eres% and as an inference from basic

premisses essential and (appropriate) to t#e sub'ect * unless we know% e.g. t#e property of

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possessing angles e$ual to two rig#t angles as belonging to t#at sub'ect in w#ic# it in#eres

essentially% and as inferred from basic premisses essential and (appropriate) to t#at sub'ect so t#atif t#at middle term also belongs essentially to t#e minor% t#e middle must belong to t#e same kind

as t#e ma'or and minor terms. "#e only e!ceptions to t#is rule are suc# cases as t#eorems in

#armonics w#ic# are demonstrable by arit#metic. 9uc# t#eorems are proved by t#e same middle

terms as arit#metical properties% but wit# a $ualification * t#e fact falls under a separate science-for t#e sub'ect genus is separate% but t#e reasoned fact concerns t#e superior science% to w#ic#

t#e attributes essentially belong. "#us% even t#ese apparent e!ceptions s#ow t#at no attribute is

strictly demonstrable e!cept from its (appropriate) basic trut#s% w#ic#% #owever% in t#e case oft#ese sciences #ave t#e re$uisite identity of c#aracter.

It is no less evident t#at t#e peculiar basic trut#s of eac# in#ering attribute are indemonstrable& for

basic trut#s from w#ic# t#ey mig#t be deduced would be basic trut#s of all t#at is% and t#e scienceto w#ic# t#ey belonged would possess universal sovereignty. "#is is so because #e knows better

w#ose knowledge is deduced from #ig#er causes% for #is knowledge is from prior premisses w#en

it derives from causes t#emselves uncaused #ence% if #e knows better t#an ot#ers or best of all%

#is knowledge would be science in a #ig#er or t#e #ig#est degree. But% as t#ings are%demonstration is not transferable to anot#er genus% wit# suc# e!ceptions as we #ave mentioned of

t#e application of geometrical demonstrations to t#eorems in mec#anics or optics% or of

arit#metical demonstrations to t#ose of #armonics.It is #ard to be sure w#et#er one knows or not& for it is #ard to be sure w#et#er one)s knowledge

is based on t#e basic trut#s appropriate to eac# attribute * t#e differentia of true knowledge. 6e

t#ink we #ave scientific knowledge if we #ave reasoned from true and primary premisses. Butt#at is not so t#e conclusion must be #omogeneous wit# t#e basic facts of t#e science.

1F

I call t#e basic trut#s of every genus t#ose clements in it t#e e!istence of w#ic# cannot be proved.

As regards bot# t#ese primary trut#s and t#e attributes dependent on t#em t#e meaning of t#e

name is assumed. "#e fact of t#eir e!istence as regards t#e primary trut#s must be assumed& but it#as to be proved of t#e remainder% t#e attributes. "#us we assume t#e meaning alike of unity%

straig#t% and triangular& but w#ile as regards unity and magnitude we assume also t#e fact of t#eir

e!istence% in t#e case of t#e remainder proof is re$uired.4f t#e basic trut#s used in t#e demonstrative sciences some are peculiar to eac# science% and

some are common% but common only in t#e sense of analogous% being of use only in so far as t#ey

fall wit#in t#e genus constituting t#e province of t#e science in $uestion.Peculiar trut#s are% e.g. t#e definitions of line and straig#t& common trut#s are suc# as (take

e$uals from e$uals and e$uals remain). 4nly so muc# of t#ese common trut#s is re$uired as falls

wit#in t#e genus in $uestion for a trut# of t#is kind will #ave t#e same force even if not used

generally but applied by t#e geometer only to magnitudes% or by t#e arit#metician only tonumbers. Also peculiar to a science are t#e sub'ects t#e e!istence as well as t#e meaning of w#ic#

it assumes% and t#e essential attributes of w#ic# it investigates% e.g. in arit#metic units% in

geometry points and lines. Bot# t#e e!istence and t#e meaning of t#e sub'ects are assumed byt#ese sciences& but of t#eir essential attributes only t#e meaning is assumed. +or e!ample

arit#metic assumes t#e meaning of odd and even% s$uare and cube% geometry t#at of

incommensurable% or of deflection or verging of lines% w#ereas t#e e!istence of t#ese attributes isdemonstrated by means of t#e a!ioms and from previous conclusions as premisses. Astronomy

too proceeds in t#e same way. +or indeed every demonstrative science #as t#ree elements -1

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t#at w#ic# it posits% t#e sub'ect genus w#ose essential attributes it e!amines& -5 t#e socalled

a!ioms% w#ic# are primary premisses of its demonstration& -: t#e attributes% t#e meaning ofw#ic# it assumes. Cet some sciences may very well pass over some of t#ese elements& e.g. we

mig#t not e!pressly posit t#e e!istence of t#e genus if its e!istence were obvious -for instance%

t#e e!istence of #ot and cold is more evident t#an t#at of number& or we mig#t omit to assume

e!pressly t#e meaning of t#e attributes if it were well understood. In t#e way t#e meaning ofa!ioms% suc# as ("ake e$uals from e$uals and e$uals remain)% is well known and so not e!pressly

assumed. 0evert#eless in t#e nature of t#e case t#e essential elements of demonstration are t#ree

t#e sub'ect% t#e attributes% and t#e basic premisses."#at w#ic# e!presses necessary selfgrounded fact% and w#ic# we must necessarily believe% is

distinct bot# from t#e #ypot#eses of a science and from illegitimate postulate * I say (must

believe)% because all syllogism% and t#erefore a fortiori demonstration% is addressed not to t#espoken word% but to t#e discourse wit#in t#e soul% and t#oug# we can always raise ob'ections to

t#e spoken word% to t#e inward discourse we cannot always ob'ect. "#at w#ic# is capable of proof

but assumed by t#e teac#er wit#out proof is% if t#e pupil believes and accepts it% #ypot#esis%

t#oug# only in a limited sense #ypot#esis * t#at is% relatively to t#e pupil& if t#e pupil #as noopinion or a contrary opinion on t#e matter% t#e same assumption is an illegitimate postulate.

"#erein lies t#e distinction between #ypot#esis and illegitimate postulate t#e latter is t#e contrary

of t#e pupil)s opinion% demonstrable% but assumed and used wit#out demonstration."#e definition * vi,. t#ose w#ic# are not e!pressed as statements t#at anyt#ing is or is not * are

not #ypot#eses but it is in t#e premisses of a science t#at its #ypot#eses are contained.

2efinitions re$uire only to be understood% and t#is is not #ypot#esis * unless it be contended t#att#e pupil)s #earing is also an #ypot#esis re$uired by t#e teac#er. 3ypot#eses% on t#e contrary%

postulate facts on t#e being of w#ic# depends t#e being of t#e fact inferred. 0or are t#e

geometer)s #ypot#eses false% as some #ave #eld% urging t#at one must not employ false#ood andt#at t#e geometer is uttering false#ood in stating t#at t#e line w#ic# #e draws is a foot long or

straig#t% w#en it is actually neit#er. "#e trut# is t#at t#e geometer does not draw any conclusion

from t#e being of t#e particular line of w#ic# #e speaks% but from w#at #is diagrams symboli,e. A

furt#er distinction is t#at all #ypot#eses and illegitimate postulates are eit#er universal orparticular% w#ereas a definition is neit#er.

11

9o demonstration does not necessarily imply t#e being of +orms nor a 4ne beside a Many% but it

does necessarily imply t#e possibility of truly predicating one of many& since wit#out t#ispossibility we cannot save t#e universal% and if t#e universal goes% t#e middle term goes witb. it%

and so demonstration becomes impossible. 6e conclude% t#en% t#at t#ere must be a single

identical term une$uivocally predicable of a number of individuals.

"#e law t#at it is impossible to affirm and deny simultaneously t#e same predicate of t#e samesub'ect is not e!pressly posited by any demonstration e!cept w#en t#e conclusion also #as to be

e!pressed in t#at form& in w#ic# case t#e proof lays down as its ma'or premiss t#at t#e ma'or is

truly affirmed of t#e middle but falsely denied. It makes no difference% #owever% if we add to t#emiddle% or again to t#e minor term% t#e corresponding negative. +or grant a minor term of w#ic#

it is true to predicate man * even if it be also true to predicate notman of it * still grant simply

t#at man is animal and not notanimal% and t#e conclusion follows for it will still be true to sayt#at 7allias * even if it be also true to say t#at not7allias * is animal and not notanimal. "#e

reason is t#at t#e ma'or term is predicable not only of t#e middle% but of somet#ing ot#er t#an t#e

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middle as well% being of wider application& so t#at t#e conclusion is not affected even if t#e

middle is e!tended to cover t#e original middle term and also w#at is not t#e original middleterm.

"#e law t#at every predicate can be eit#er truly affirmed or truly denied of every sub'ect is

posited by suc# demonstration as uses reductio ad impossibile% and t#en not always universally%

but so far as it is re$uisite& wit#in t#e limits% t#at is% of t#e genus * t#e genus% I mean -as I #avealready e!plained% to w#ic# t#e man of science applies #is demonstrations. In virtue of t#e

common elements of demonstration * I mean t#e common a!ioms w#ic# are used as premisses of

demonstration% not t#e sub'ects nor t#e attributes demonstrated as belonging to t#em * all t#esciences #ave communion wit# one anot#er% and in communion wit# t#em all is dialectic and any

science w#ic# mig#t attempt a universal proof of a!ioms suc# as t#e law of e!cluded middle% t#e

law t#at t#e subtraction of e$uals from e$uals leaves e$ual remainders% or ot#er a!ioms of t#esame kind. 2ialectic #as no definite sp#ere of t#is kind% not being confined to a single genus.

4t#erwise its met#od would not be interrogative& for t#e interrogative met#od is barred to t#e

demonstrator% w#o cannot use t#e opposite facts to prove t#e same ne!us. "#is was s#own in my

work on t#e syllogism.

15If a syllogistic $uestion is e$uivalent to a proposition embodying one of t#e two sides of a

contradiction% and if eac# science #as its peculiar propositions from w#ic# its peculiar conclusion

is developed% t#en t#ere is suc# a t#ing as a distinctively scientific $uestion% and it is t#einterrogative form of t#e premisses from w#ic# t#e (appropriate) conclusion of eac# science is

developed. 3ence it is clear t#at not every $uestion will be relevant to geometry% nor to medicine%

nor to any ot#er science only t#ose $uestions will be geometrical w#ic# form premisses for t#eproof of t#e t#eorems of geometry or of any ot#er science% suc# as optics% w#ic# uses t#e same

basic trut#s as geometry. 4f t#e ot#er sciences t#e like is true. 4f t#ese $uestions t#e geometer is

bound to give #is account% using t#e basic trut#s of geometry in con'unction wit# #is previous

conclusions& of t#e basic trut#s t#e geometer% as suc#% is not bound to give any account. "#e likeis true of t#e ot#er sciences. "#ere is a limit% t#en% to t#e $uestions w#ic# we may put to eac# man

of science& nor is eac# man of science bound to answer all in$uiries on eac# several sub'ect% but

only suc# as fall wit#in t#e defined field of #is own science. If% t#en% in controversy wit# ageometer $ua geometer t#e disputant confines #imself to geometry and proves anyt#ing from

geometrical premisses% #e is clearly to be applauded& if #e goes outside t#ese #e will be at fault%

and obviously cannot even refute t#e geometer e!cept accidentally. 4ne s#ould t#erefore notdiscuss geometry among t#ose w#o are not geometers% for in suc# a company an unsound

argument will pass unnoticed. "#is is correspondingly true in t#e ot#er sciences.

9ince t#ere are (geometrical) $uestions% does it follow t#at t#ere are also distinctively

(ungeometrical) $uestions/ +urt#er% in eac# special science * geometry for instance * w#at kindof error is it t#at may vitiate $uestions% and yet not e!clude t#em from t#at science/ Again% is t#e

erroneous conclusion one constructed from premisses opposite to t#e true premisses% or is it

formal fallacy t#oug# drawn from geometrical premisses/ 4r% per#aps% t#e erroneous conclusionis due to t#e drawing of premisses from anot#er science& e.g. in a geometrical controversy a

musical $uestion is distinctively ungeometrical% w#ereas t#e notion t#at parallels meet is in one

sense geometrical% being ungeometrical in a different fas#ion t#e reason being t#at(ungeometrical)% like (unr#yt#mical)% is e$uivocal% meaning in t#e one case not geometry at all% in

t#e ot#er bad geometry/ It is t#is error% i.e. error based on premisses of t#is kind * (of) t#e science

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but false * t#at is t#e contrary of science. In mat#ematics t#e formal fallacy is not so common%

because it is t#e middle term in w#ic# t#e ambiguity lies% since t#e ma'or is predicated of t#ew#ole of t#e middle and t#e middle of t#e w#ole of t#e minor -t#e predicate of course never #as

t#e prefi! (all)& and in mat#ematics one can% so to speak% see t#ese middle terms wit# an

intellectual vision% w#ile in dialectic t#e ambiguity may escape detection. =.g. (Is every circle a

figure/) A diagram s#ows t#at t#is is so% but t#e minor premiss (Are epics circles/) is s#own byt#e diagram to be false.

If a proof #as an inductive minor premiss% one s#ould not bring an (ob'ection) against it. +or since

every premiss must be applicable to a number of cases -ot#erwise it will not be true in everyinstance% w#ic#% since t#e syllogism proceeds from universals% it must be% t#en assuredly t#e

same is true of an (ob'ection)& since premisses and (ob'ections) are so far t#e same t#at anyt#ing

w#ic# can be validly advanced as an (ob'ection) must be suc# t#at it could take t#e form of apremiss% eit#er demonstrative or dialectical. 4n t#e ot#er #and% arguments formally illogical do

sometimes occur t#roug# taking as middles mere attributes of t#e ma'or and minor terms. An

instance of t#is is 7aeneus) proof t#at fire increases in geometrical proportion (+ire)% #e argues%

(increases rapidly% and so does geometrical proportion). "#ere is no syllogism so% but t#ere is asyllogism if t#e most rapidly increasing proportion is geometrical and t#e most rapidly increasing

proportion is attributable to fire in its motion. 9ometimes% no doubt% it is impossible to reason

from premisses predicating mere attributes but sometimes it is possible% t#oug# t#e possibility isoverlooked. If false premisses could never give true conclusions (resolution) would be easy% for

premisses and conclusion would in t#at case inevitably reciprocate. I mig#t t#en argue t#us let A

be an e!isting fact& let t#e e!istence of A imply suc# and suc# facts actually known to me to e!ist%w#ic# we may call B. I can now% since t#ey reciprocate% infer A from B.

Reciprocation of premisses and conclusion is more fre$uent in mat#ematics% because

mat#ematics takes definitions% but never an accident% for its premisses * a second c#aracteristicdistinguis#ing mat#ematical reasoning from dialectical disputations.

A science e!pands not by t#e interposition of fres# middle terms% but by t#e apposition of fres#

e!treme terms. =.g. A is predicated of B% B of 7% 7 of 2% and so indefinitely. 4r t#e e!pansion

may be lateral e.g. one ma'or A% may be proved of two minors% 7 and =. "#us let A representnumber * a number or number taken indeterminately& B determinate odd number& 7 any

particular odd number. 6e can t#en predicate A of 7. 0e!t let 2 represent determinate even

number% and = even number. "#en A is predicable of =.

1:nowledge of t#e fact differs from knowledge of t#e reasoned fact. "o begin wit#% t#ey differ

wit#in t#e same science and in two ways -1 w#en t#e premisses of t#e syllogism are not

immediate -for t#en t#e pro!imate cause is not contained in t#em * a necessary condition of

knowledge of t#e reasoned fact -5 w#en t#e premisses are immediate% but instead of t#e causet#e better known of t#e two reciprocals is taken as t#e middle& for of two reciprocally predicable

terms t#e one w#ic# is not t#e cause may $uite easily be t#e better known and so become t#e

middle term of t#e demonstration. "#us -5 -a you mig#t prove as follows t#at t#e planets arenear because t#ey do not twinkle let 7 be t#e planets% B not twinkling% A pro!imity. "#en B is

predicable of 7& for t#e planets do not twinkle. But A is also predicable of B% since t#at w#ic#

does not twinkle is near * we must take t#is trut# as #aving been reac#ed by induction or senseperception. "#erefore A is a necessary predicate of 7& so t#at we #ave demonstrated t#at t#e

planets are near. "#is syllogism% t#en% proves not t#e reasoned fact but only t#e fact& since t#ey

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are not near because t#ey do not twinkle% but% because t#ey are near% do not twinkle. "#e ma'or

and middle of t#e proof% #owever% may be reversed% and t#en t#e demonstration will be of t#ereasoned fact. "#us let 7 be t#e planets% B pro!imity% A not twinkling. "#en B is an attribute of

7% and A * not twinkling * of B. 7onse$uently A is predicable of 7% and t#e syllogism proves t#e

reasoned fact% since its middle term is t#e pro!imate cause. Anot#er e!ample is t#e inference t#at

t#e moon is sp#erical from its manner of wa!ing. "#us since t#at w#ic# so wa!es is sp#erical%and since t#e moon so wa!es% clearly t#e moon is sp#erical. Put in t#is form% t#e syllogism turns

out to be proof of t#e fact% but if t#e middle and ma'or be reversed it is proof of t#e reasoned fact&

since t#e moon is not sp#erical because it wa!es in a certain manner% but wa!es in suc# a mannerbecause it is sp#erical. -Het 7 be t#e moon% B sp#erical% and A wa!ing. Again -b% in cases w#ere

t#e cause and t#e effect are not reciprocal and t#e effect is t#e better known% t#e fact is

demonstrated but not t#e reasoned fact. "#is also occurs -1 w#en t#e middle falls outside t#ema'or and minor% for #ere too t#e strict cause is not given% and so t#e demonstration is of t#e fact%

not of t#e reasoned fact. +or e!ample% t#e $uestion (6#y does not a wall breat#e/) mig#t be

answered% (Because it is not an animal)& but t#at answer would not give t#e strict cause% because

if not being an animal causes t#e absence of respiration% t#en being an animal s#ould be t#e causeof respiration% according to t#e rule t#at if t#e negation of causes t#e nonin#erence of y% t#e

affirmation of ! causes t#e in#erence of y& e.g. if t#e disproportion of t#e #ot and cold elements is

t#e cause of ill #ealt#% t#eir proportion is t#e cause of #ealt#& and conversely% if t#e assertion of !causes t#e in#erence of y% t#e negation of ! must cause y)s nonin#erence. But in t#e case given

t#is conse$uence does not result& for not every animal breat#es. A syllogism wit# t#is kind of

cause takes place in t#e second figure. "#us let A be animal% B respiration% 7 wall. "#en A ispredicable of all B -for all t#at breat#es is animal% but of no 7& and conse$uently B is predicable

of no 7& t#at is% t#e wall does not breat#e. 9uc# causes are like farfetc#ed e!planations% w#ic#

precisely consist in making t#e cause too remote% as in Anac#arsis) account of w#y t#e 9cyt#ians#ave no fluteplayers& namely because t#ey #ave no vines.

"#us% t#en% do t#e syllogism of t#e fact and t#e syllogism of t#e reasoned fact differ wit#in one

science and according to t#e position of t#e middle terms. But t#ere is anot#er way too in w#ic#

t#e fact and t#e reasoned fact differ% and t#at is w#en t#ey are investigated respectively bydifferent sciences. "#is occurs in t#e case of problems related to one anot#er as subordinate and

superior% as w#en optical problems are subordinated to geometry% mec#anical problems to

stereometry% #armonic problems to arit#metic% t#e data of observation to astronomy. -9ome oft#ese sciences bear almost t#e same name& e.g. mat#ematical and nautical astronomy%

mat#ematical and acoustical #armonics. 3ere it is t#e business of t#e empirical observers to

know t#e fact% of t#e mat#ematicians to know t#e reasoned fact& for t#e latter are in possession oft#e demonstrations giving t#e causes% and are often ignorant of t#e fact 'ust as we #ave often a

clear insig#t into a universal% but t#roug# lack of observation are ignorant of some of its

particular instances. "#ese conne!ions #ave a perceptible e!istence t#oug# t#ey are

manifestations of forms. +or t#e mat#ematical sciences concern forms t#ey do not demonstrateproperties of a substratum% since% even t#oug# t#e geometrical sub'ects are predicable as

properties of a perceptible substratum% it is not as t#us predicable t#at t#e mat#ematician

demonstrates properties of t#em. As optics is related to geometry% so anot#er science is related tooptics% namely t#e t#eory of t#e rainbow. 3ere knowledge of t#e fact is wit#in t#e province of t#e

natural p#ilosop#er% knowledge of t#e reasoned fact wit#in t#at of t#e optician% eit#er $ua

optician or $ua mat#ematical optician. Many sciences not standing in t#is mutual relation enterinto it at points& e.g. medicine and geometry it is t#e p#ysician)s business to know t#at circular

wounds #eal more slowly% t#e geometer)s to know t#e reason w#y.

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1e.g.? w#ite). 4n t#e ot#er #and% w#en we #ave ascertained t#e t#ing)s e!istence% we in$uire

as to its nature% asking% for instance% (w#at% t#en% is God/) or (w#at is man/).

5

"#ese% t#en% are t#e four kinds of $uestion we ask% and it is in t#e answers to t#ese $uestions t#atour knowledge consists.

0ow w#en we ask w#et#er a conne!ion is a fact% or w#et#er a t#ing wit#out $ualification is% we

are really asking w#et#er t#e conne!ion or t#e t#ing #as a (middle)& and w#en we #aveascertained eit#er t#at t#e conne!ion is a fact or t#at t#e t#ing is * i.e. ascertained eit#er t#e

partial or t#e un$ualified being of t#e t#ingand are proceeding to ask t#e reason of t#e conne!ion

or t#e nature of t#e t#ing% t#en we are asking w#at t#e (middle) is.-By distinguis#ing t#e fact of t#e conne!ion and t#e e!istence of t#e t#ing as respectively t#e

partial and t#e un$ualified being of t#e t#ing% I mean t#at if we ask (does t#e moon suffer

eclipse/)% or (does t#e moon wa!/)% t#e $uestion concerns a part of t#e t#ing)s being& for w#at weare asking in suc# $uestions is w#et#er a t#ing is t#is or t#at% i.e. #as or #as not t#is or t#at

attribute w#ereas% if we ask w#et#er t#e moon or nig#t e!ists% t#e $uestion concerns t#e

un$ualified being of a t#ing.

6e conclude t#at in all our in$uiries we are asking eit#er w#et#er t#ere is a (middle) or w#at t#e(middle) is for t#e (middle) #ere is precisely t#e cause% and it is t#e cause t#at we seek in all our

in$uiries. "#us% (2oes t#e moon suffer eclipse/) means (Is t#ere or is t#ere not a cause producing

eclipse of t#e moon/)% and w#en we #ave learnt t#at t#ere is% our ne!t $uestion is% (6#at% t#en% ist#is cause/ for t#e cause t#roug# w#ic# a t#ing is * not is t#is or t#at% i.e. #as t#is or t#at attribute%

but wit#out $ualification is * and t#e cause t#roug# w#ic# it is * not is wit#out $ualification% but

is t#is or t#at as #aving some essential attribute or some accident * are bot# alike t#e middle). Byt#at w#ic# is wit#out $ualification I mean t#e sub'ect% e.g. moon or eart# or sun or triangle& by

t#at w#ic# a sub'ect is -in t#e partial sense I mean a property% e.g. eclipse% e$uality or ine$uality%

interposition or noninterposition. +or in all t#ese e!amples it is clear t#at t#e nature of t#e t#ing

and t#e reason of t#e fact are identical t#e $uestion (6#at is eclipse/) and its answer ("#eprivation of t#e moon)s lig#t by t#e interposition of t#e eart#) are identical wit# t#e $uestion

(6#at is t#e reason of eclipse/) or (6#y does t#e moon suffer eclipse/) and t#e reply (Because of

t#e failure of lig#t t#roug# t#e eart#)s s#utting it out). Again% for (6#at is a concord/ Acommensurate numerical ratio of a #ig# and a low note)% we may substitute (6#at ratio makes a

#ig# and a low note concordant/ "#eir relation according to a commensurate numerical ratio.)

(Are t#e #ig# and t#e low note concordant/) is e$uivalent to (Is t#eir ratio commensurate/)& andw#en we find t#at it is commensurate% we ask (6#at% t#en% is t#eir ratio/).

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7ases in w#ic# t#e (middle) is sensible s#ow t#at t#e ob'ect of our in$uiry is always t#e (middle)

we in$uire% because we #ave not perceived it% w#et#er t#ere is or is not a (middle) causing% e.g. aneclipse. 4n t#e ot#er #and% if we were on t#e moon we s#ould not be in$uiring eit#er as to t#e

fact or t#e reason% but bot# fact and reason would be obvious simultaneously. +or t#e act of

perception would #ave enabled us to know t#e universal too& since% t#e present fact of an eclipse

being evident% perception would t#en at t#e same time give us t#e present fact of t#e eart#)sscreening t#e sun)s lig#t% and from t#is would arise t#e universal.

"#us% as we maintain% to know a t#ing)s nature is to know t#e reason w#y it is& and t#is is e$ually

true of t#ings in so far as t#ey are said wit#out $ualification to #e as opposed to being possessedof some attribute% and in so far as t#ey are said to be possessed of some attribute suc# as e$ual to

rig#t angles% or greater or less.

:

It is clear% t#en% t#at all $uestions are a searc# for a (middle). Het us now state #ow essential

nature is revealed and in w#at way it can be reduced to demonstration& w#at definition is% andw#at t#ings are definable. And let us first discuss certain difficulties w#ic# t#ese $uestions raise%

beginning w#at we #ave to say wit# a point most intimately connected wit# our immediately

preceding remarks% namely t#e doubt t#at mig#t be felt as to w#et#er or not it is possible to knowt#e same t#ing in t#e same relation% bot# by definition and by demonstration. It mig#t% I mean% be

urged t#at definition is #eld to concern essential nature and is in every case universal and

affirmative& w#ereas% on t#e ot#er #and% some conclusions are negative and some are notuniversal& e.g. all in t#e second figure are negative% none in t#e t#ird are universal. And again% not

even all affirmative conclusions in t#e first figure are definable% e.g. (every triangle #as its angles

e$ual to two rig#t angles). An argument proving t#is difference between demonstration anddefinition is t#at to #ave scientific knowledge of t#e demonstrable is identical wit# possessing a

demonstration of it #ence if demonstration of suc# conclusions as t#ese is possible% t#ere clearly

cannot also be definition of t#em. If t#ere could% one mig#t know suc# a conclusion also in virtue

of its definition wit#out possessing t#e demonstration of it& for t#ere is not#ing to stop our #avingt#e one wit#out t#e ot#er.

Induction too will sufficiently convince us of t#is difference& for never yet by defining anyt#ing *

essential attribute or accident * did we get knowledge of it. Again% if to define is to ac$uireknowledge of a substance% at any rate suc# attributes are not substances.

It is evident% t#en% t#at not everyt#ing demonstrable can be defined. 6#at t#en/ 7an everyt#ing

definable be demonstrated% or not/ "#ere is one of our previous arguments w#ic# covers t#is too.4f a single t#ing $ua single t#ere is a single scientific knowledge. 3ence% since to know t#e

demonstrable scientifically is to possess t#e demonstration of it% an impossible conse$uence will

follow * possession of its definition wit#out its demonstration will give knowledge of t#e

demonstrable.Moreover% t#e basic premisses of demonstrations are definitions% and it #as already been s#own

t#at t#ese will be found indemonstrable& eit#er t#e basic premisses will be demonstrable and will

depend on prior premisses% and t#e regress will be endless& or t#e primary trut#s will beindemonstrable definitions.

But if t#e definable and t#e demonstrable are not w#olly t#e same% may t#ey yet be partially t#e

same/ 4r is t#at impossible% because t#ere can be no demonstration of t#e definable/ "#ere canbe none% because definition is of t#e essential nature or being of somet#ing% and all

demonstrations evidently posit and assume t#e essential nature * mat#ematical demonstrations%

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for e!ample% t#e nature of unity and t#e odd% and all t#e ot#er sciences likewise. Moreover% every

demonstration proves a predicate of a sub'ect as attac#ing or as not attac#ing to it% but indefinition one t#ing is not predicated of anot#er& we do not% e.g. predicate animal of biped nor

biped of animal% nor yet figure of plane * plane not being figure nor figure plane. Again% to prove

essential nature is not t#e same as to prove t#e fact of a conne!ion. 0ow definition reveals

essential nature% demonstration reveals t#at a given attribute attac#es or does not attac# to a givensub'ect& but different t#ings re$uire different demonstrations * unless t#e one demonstration is

related to t#e ot#er as part to w#ole. I add t#is because if all triangles #ave been proved to possess

angles e$ual to two rig#t angles% t#en t#is attribute #as been proved to attac# to isosceles& forisosceles is a part of w#ic# all triangles constitute t#e w#ole. But in t#e case before us t#e fact

and t#e essential nature are not so related to one anot#er% since t#e one is not a part of t#e ot#er.

9o it emerges t#at not all t#e definable is demonstrable nor all t#e demonstrable definable& andwe may draw t#e general conclusion t#at t#ere is no identical ob'ect of w#ic# it is possible to

possess bot# a definition and a demonstration. It follows obviously t#at definition and

demonstration are neit#er identical nor contained eit#er wit#in t#e ot#er if t#ey were% t#eir

ob'ects would be related eit#er as identical or as w#ole and part.

01 organon - 4 posterior analytics

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