Analíticos posteriores primeros 2 tratados.

8/19/2019 Analíticos posteriores primeros 2 tratados.

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Tratado # 1 : La necesidad del silogismo demostrativo

Lección 1: Establece su tesis que algunos conocimientos se adquieren de unconocimiento preexistente

a1. All instruction given or received by way of argument proceeds from pre-existent nowledge.

T!is becomes evident upon a survey of all t!e species of suc! instructiona". T!e mat!ematical sciences and all ot!er speculative disciplines are acuired in t!is way$

a%. and so are t!e two forms of dialectical reasoning$ syllogistic and inductive& for eac! of t!ese

latter mae use of old nowledge to impart new$ t!e syllogism assuming an audience t!at accepts its

premisses$ induction ex!ibiting t!e universal as implicit in t!e clearly nown particular.

a'. Again$ t!e persuasion exerted by r!etorical arguments is in principle t!e same$ since t!ey use

eit!er example$ a ind of induction$ or ent!ymeme$ a form of syllogism.


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Lección (: Extensión y orden del conocimiento para adquirir ciencia

)1a11. T!e pre-existent nowledge reuired is of two inds. *n some cases admission of t!e fact

must be assumed$ in ot!ers compre!ension of t!e meaning of t!e term used$ and sometimes bot!

assumptions are essential. T!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 mae t!e

double assumption of t!e meaning of t!e word and t!e existence of t!e t!ing. T!e reason is t!att!ese several ob+ects are not eually obvious to us.

a1. ecognition of a trut! may in some cases contain as factors bot! previous nowledge and also

nowledge acuired simultaneously wit! t!at recognition - nowledge$ t!is latter$ of t!e particulars

actually falling under t!e universal and t!erein already virtually nown. /or example$ t!e student

new before!and t!at t!e angles of every triangle are eual to two rig!t angles& but it was only at

t!e actual moment at w!ic! !e was being led on to recogni0e t!is as true in t!e instance before !im

t!at !e came to now ,t!is figure inscribed in t!e semicircle, to be a triangle. /or some t!ings vi0.

t!e singulars finally reac!ed w!ic! are not predicable of anyt!ing else as sub+ect2 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.


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Lección ": Conocimiento preexistente respecto a la conclusión

a(%. 3efore !e was led on to recognition or before !e actually drew a conclusion$ we s!ould

per!aps say t!at in a manner !e new$ in a manner not. *f !e did not in an unualified sense of t!e

term now t!e existence of t!is triangle$ !ow could !e now wit!out ualification t!at its angles

were eual to two rig!t angles4 5o: clearly !e nows not wit!out ualification but only in t!e sense

t!at !e nows universally.

a('. *f t!is distinction is not drawn$ we are faced wit! t!e dilemma in t!e 6eno: eit!er a man will

learn not!ing or w!at !e already nows&

a"7. for we cannot accept t!e solution w!ic! some people offer. A man is ased$ ,8o you$ or do you

not$ now t!at every pair is even4, 9e says !e does now it. T!e uestioner t!en produces a

particular pair$ of t!e existence$ and so a fortiori of t!e evenness$ of w!ic! !e was unaware. T!e

solution w!ic! some people offer is to assert t!at t!ey do not now t!at every pair is even$ but only

t!at everyt!ing w!ic! t!ey now to be a pair is even:

b1. yet w!at t!ey now to be even is t!at of w!ic! t!ey !ave demonstrated evenness$ i.e. w!at t!eymade t!e sub+ect of t!eir premiss$ vi0. not merely every triangle or number w!ic! t!ey now to be

suc!$ but any and every number or triangle wit!out reservation. /or no premiss is ever couc!ed in

t!e form ,every number w!ic! you now to be suc!,$ or ,every rectilinear figure w!ic! you now to

be suc!,: t!e predicate is always construed as applicable to any and every instance of t!e t!ing.

b. ;n t!e ot!er !and$ * imagine t!ere is not!ing to prevent a man in one sense nowing w!at !e is

learning$ in anot!er not nowing it. T!e strange t!ing would be$ not if in some sense !e new w!at

!e was learning$ but if !e were to now it in t!at precise sense and manner in w!ic! !e was learning

it.


4/8

Tratado # (: Qué es el silogismo demostrativo

Lección %: Explica qué es el silogismo demostrativo

b'. b1'. 3y demonstration * mean a syllogism productive of scientific nowledge$

b1>. a syllogism$ t!at is$ t!e grasp of w!ic! is eo ipso suc! nowledge.

b(7. Assuming t!en t!at my t!esis as to t!e nature of scientific nowing is correct$ t!e premisses of

demonstrated nowledge must be true$ primary$ immediate$ better nown t!an and prior to t!e

conclusion$ w!ic! is furt!er related to t!em as effect to cause.

b((. ?nless t!ese conditions are satisfied$ t!e basic trut!s will not be ,appropriate, to t!e conclusion.

b(". @yllogism t!ere may indeed be wit!out t!ese conditions$ but suc! syllogism$ not being

productive of scientific nowledge$ will not be demonstration.

b(%. T!e premisses must be true: for t!at w!ic! is non-existent cannot be nown - we cannot now$

e.g. t!at t!e diagonal of a suare is commensurate wit! its side.

b(). T!e premisses must be primary and indemonstrable& ot!erwise t!ey will reuire demonstration

in order to be nown$ since to !ave nowledge$ if it be not accidental nowledge$ of t!ings w!ic!are demonstrable$ means precisely to !ave a demonstration of t!em.

b(>. T!e premisses must be t!e causes of t!e conclusion$ better nown t!an it$ and prior to it& its

causes$ since we possess scientific nowledge of a t!ing only w!en we now its cause& prior$ in

order to be causes& antecedently nown$ t!is antecedent nowledge being not our mere

understanding of t!e meaning$ but nowledge of t!e fact as well. 5ow ,prior, and ,better nown, are

ambiguous terms$ for t!ere is a difference between w!at is prior and better nown in t!e order of

being and w!at is prior and better nown to man. * mean t!at ob+ects nearer to sense are prior and

better nown to man& ob+ects wit!out ualification prior and better nown are t!ose furt!er from

sense. 5ow t!e most universal causes are furt!est from sense and particular causes are nearest to

sense$ and t!ey are t!us exactly opposed to one anot!er. *n saying t!at t!e premisses of demonstrated nowledge must be primary$ * mean t!at t!ey must be t!e ,appropriate, basic trut!s$

for * identify primary premiss and basic trut!.


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Lección : Explica que es una proposición inmediata

a'. A basic trut!B in a demonstration is an immediate proposition. An immediate proposition is one

w!ic! !as no ot!er proposition prior to it.

a>. A proposition is eit!er part of an enunciation$ i.e. it predicates a single attribute of a single

sub+ect

a17. *f a proposition is dialectical$ it assumes eit!er part indifferently& if it is demonstrative$ it lays

down one part to t!e definite exclusion of t!e ot!er because t!at part is true.

a11. T!e term ,enunciation, denotes eit!er part of a contradiction indifferently. A contradiction is an

opposition w!ic! of its own nature excludes a middle. T!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.

a1. * 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 bar to progress on t!e part of t!e pupil:

one w!ic! t!e pupil must now if !e is to learn anyt!ing w!atever is an axiom. * call it an axiom because t!ere are suc! trut!s and we give t!em t!e name of axioms par excellence.

a1>. *f a t!esis assumes one part or t!e ot!er of an enunciation$ i.e. asserts eit!er t!e existence or t!e

non-existence of a sub+ect$ it is a !ypot!esis& if it does not so assert$ it is a definition. 8efinition 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 define w!at a unit is is not t!e same as to

affirm its existence.


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Lección : Explica que esas proposiciones deben ser conocidas mejor que laconclusión

a(. 5ow since t!e reuired ground of our nowledge C i.e. of our conviction C 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!e facts

constituting its premisses$ we must not only now t!e primary premisses C some if not all of t!em

C before!and$ but now t!em better t!an t!e conclusion:

a('. 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!e cause of our loving anyt!ing is dearer to us t!an t!e ob+ect of our

love. @o since t!e primary premisses are t!e cause of our nowledge C i.e. of our conviction C it

follows t!at we now t!em better C t!at is$ are more convinced of t!em C t!an t!eir

conseuences$ precisely because of our nowledge of t!e latter is t!e effect of our nowledge of t!e

premisses.

a"". 5ow a man cannot believe in anyt!ing more t!an in t!e t!ings !e nows$ unless !e !as eit!er

actual nowledge of it or somet!ing better t!an actual nowledge. 3ut we are faced wit! t!is

paradox if a student w!ose belief rests on demonstration !as not prior nowledge&

a". a man must believe in some$ if not in all$ of t!e basic trut!s more t!an in t!e conclusion.

6oreover$ if a man sets out to acuire t!e scientific nowledge t!at comes t!roug! demonstration$

a"'. !e must not only !ave a better nowledge of t!e basic trut!s and a firmer conviction of t!em

t!an of t!e connexion w!ic! is being demonstrated: more t!an t!is$ not!ing must be more certain or

better nown 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 be uns!aable.


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Lección ): Presenta los errores, Explica las razones por las cuales erraron,emueve ! de las ra"ces de estas razones# El error de que solo se puedeconocer cient"$camente por demostración

b. @ome !old t!at$ owing to t!e necessity of nowing t!e primary premisses$ t!ere is no scientific

nowledge. ;t!ers t!in t!ere is$ but t!at all trut!s are demonstrable. 5eit!er doctrine is eit!er true

or a necessary deduction from t!e premisses.

b'. T!e first sc!ool$ assuming t!at t!ere is no way of nowing 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 now t!e posterior t!roug! t!e prior w!erein t!ey are rig!t$ for one cannot

traverse an infinite series2: if on t!e ot!er !and C t!ey say C t!e series terminates and t!ere are

primary premisses$ yet t!ese are unnowable because incapable of demonstration$ w!ic! according

to t!em is t!e only form of nowledge. And since t!us one cannot now t!e primary premisses$

nowledge of t!e conclusions w!ic! follow from t!em is not pure scientific nowledge nor properly

nowing at all$ but rests on t!e mere supposition t!at t!e premisses are true.

b1. T!e ot!er party agree wit! t!em as regards nowing$ !olding t!at it is only possible bydemonstration$ 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.

b1'. ;ur own doctrine is t!at not all nowledge is demonstrative: on t!e contrary$ nowledge of t!e

immediate premisses is independent of demonstration. T!e necessity of t!is is obvious& for since

we must now t!e prior premisses from w!ic! t!e demonstration is drawn$ and since t!e regress

must end in immediate trut!s$ t!ose trut!s must be indemonstrable.2 @uc!$ t!en$ is our doctrine$ and

in addition we maintain t!at besides scientific nowledge t!ere is its originative source w!ic!

enables us to recogni0e t!e definitions.


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Lección ': %emuestra que no se puede demostrar circularmente

b(. 5ow demonstration must be based on premisses prior to and better nown 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 unualified sense of ,demonstration,$ but only possible if

,demonstration, be extended to include t!at ot!er met!od of argument w!ic! rests on a distinction

between trut!s prior to us and trut!s wit!out ualification prior$ i.e. t!e met!od by w!ic! induction produces nowledge. 3ut if we accept t!is extension of its meaning$ our definition of unualified

nowledge will prove faulty& for t!ere seem to be two inds of it. Der!aps$ !owever$ t!e second

form of demonstration$ t!at w!ic! proceeds from trut!s better nown to us$ is not demonstration in

t!e unualified sense of t!e term.

b"". T!e advocates of circular demonstration are not only faced wit! t!e difficulty we !ave +ust

stated: in addition t!eir t!eory reduces to t!e mere statement t!at if a t!ing exists$ t!en it does exist

C an easy way of proving anyt!ing. T!at t!is is so can be clearly s!own by taing t!ree terms$ for

to constitute t!e circle it maes no difference w!et!er many terms or few or even only two are

taen.

b"'. T!us by direct proof$ if A is$ 3 must be& if 3 is$ = must be& t!erefore if A is$ = must be.

a1. @ince t!en C by t!e circular proof C if A is$ 3 must be$ and if 3 is$ A must be$ A may be

substituted for = above. T!en ,if 3 is$ A must be,E,if 3 is$ = must be,$ w!ic! above gave t!e

conclusion ,if A is$ = must be,: but = and A !ave been identified. =onseuently t!e up!olders of

circular demonstration are in t!e position of saying t!at if A is$ A must be C a simple way of

proving anyt!ing.

a. 6oreover$ even suc! circular demonstration is impossible except in t!e case of attributes t!at

imply one anot!er$ vi0. ,peculiar, properties. 5ow$ it !as been s!own t!at t!e positing of one t!ing

C be it one term or one premiss C never involves a necessary conseuent: 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. *f$ t!en$ A is implied in 3 and =$ and 3 and = 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. 3ut 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. Dropositions 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!erefore everyt!ing can be demonstrated.

Analíticos posteriores primeros 2 tratados.

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