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PINNOCK ’
S CAT ECHISMS .
C A T E C H I S M
L O G I C .
S EVENT H ED IT ION, REV IS ED AND A LT E RED .
LONDONWHIT TAKER,
T REACHER, AND CO .
AVE "MA R I A LANE .
CAT ECHISM OF LOGIC ,
ll
CHAPT ER I .
INT ROD"CT I ON.Question . WHAT i s Logic ?Answer. Logic is the s cience that instructs u s inthe principles on Which reasoning i s founded ; i t i salso the art of applying those principles rightly inconducting an argument .Q. What is th e difference between sc ienc e and art ?A . A s cience i s a systematic am‘
angem en t of facts ,and i s therefore knowledge s imply ; an art teaches theapplication of that knowledge to practical purposes .
Q. How does the s cience of Logic differ fromM etaphysics, or the sc ience of m indA . M etaphys ics treats of the nature of mind gene
rally, Logic on ly regards tho se mental facult ie s whichare concerned in reasoning .
Q . How does the art of Logic diiTer from the artof Rhetoric ?A . The obj ect of Logic is to convince, that of
Rhetoric to persuade : by Log i c, 3 thing is shown to
2024810
2 CA T E CH I SM o r LOG I C .
b e right and good by Rhetoric, motives are suppl iedfor choosing that whose goodness and rect itude hasbeen demonstrated finally, Logic addresses itselfsolely t o the understanding ; Rhetoric, for the mostpart, t o the fe elings and pass i ons .
Q. I s Logi c a useful branch of learning ?
A . F ew s tudies have greater claims upon our attent ion, s ince it enables u s to disp os e our own argumentsso as t o produce conviction, and to detect the falsereasoning of others .
Q . But do w e not find pers ons ignorant of Logicreason correctly ?A . Certainly ,
and we also find persons ignorant ofgrammar who speak and write with tolerable c orrectness ; but men w ould both speak and reason better ifthey were aided by useful rules for their direction
,
and were acquainted with the principle s on whichthese rules are founded .
Q . By whom was Logic invented >
A . By"eno of Elea, whose principal design was t oass is t the Grecian philosophers in the dispute s whichthey incessantly maintained .
Q . Why then is Aristotle usually esteemed the inv entor of Logic ?A . He first reduced the whole into an orderly system, and added s o many inventions of h is own as tomake it appear altogether a n ew art .
Q . Why has the study of Logic been s o muchneglected ?A . The followers of Aristotle asserted
,that Logic
was not only the best, but the only means for discovering truth , a purpose to which i t is s carcelyapplicable ; and when the fals ehood of th is claim was
CATECH I SM OF LOG I C . 3
'
etected, the world ran int o the other extreme, andlaid aside the entire art as useless .
Q. M ight not another reason be ass igned ?A . Yes ; there i s s carcely any study which requiress o much preparat ion before the learner can perceiveits real utility : when people , therefore , cannot perceive s ome immediate ben efit resulting from theirapplication , they fancy that further perseverancew ould be a useless waste of t ime ; acting as absurdlyas the husbandman in the fable
,who resigned the
culture of his lan ds altogether,because corn did not
appear immediately after hi s field w as ploughed .
CHAPTER I I .
Ideas and T erms .
Q. What are the princip al mental operations or
faculties t o which our attention is directed in Logic P
A . There are three principal facultie s regarded byLogic ; 1. Shnple Apprehens ion , by which we rece iveideas ; 2. Judgmen t , by which we compare thos eideas and 3. Reasoning, by which we deduce iaferen ces from those comparisons .
Q . What is an idea ?A . The immediate
‘
obj ect of the mind in thought ;— that which is present to our mind w hen we thinkof any thing .
Q. What i s apprehension ?A . The faculty by which we conceive any thing inour minds i t is analogous to percept ion in the body.
Q. How is apprehens ion divided ?A . Into two kinds ; s imple and complex .
B 2
4 CAT E CH I SM or LOG I C,
Q. How do these differ ?A . When we conce ive obj ects separately, withouttaking into account any relation or connection between them ; the apprehension is s imple, as of
“ aman
,
” a horse,
” cards ;” but if two or more
ideas,between whi ch there i s relation or connection ,
b e considered,the appreh ens ion is c omplex, as of
a horseman ,” a pack of cards,” &c .
Q . What i s a term ?A . I t i s a w ord expressing an idea ; and i t is s oc alled, because i t terminates, or marks out the limitsof the idea .
Q. How are terms divided ?A . Into singular and universal.Q . What i s a s ingular term ?A . A s ingular term (called by grammar ians a
proper n ame) , i s that which can on ly be applied t oon e thing in the same sense . The s ingle thing i scalled an individual .
Q. Why i s it named an individual ?A . Because it cannot b e divided into things of the
same sort or species . Thus , (to us e an old illustrat ion) , a leg of mutton is an individual, for though i tmay be divided into portions
,i t cannot b e divided
into legs of mutton .
Q . t at i s a u niversal term ?A . That which can be applied to s everal things in
the same sense, as man,
” horse,
” star .”
Q . Are not the same singular terms frequentlyapplied to several different individuals ?A . Yes ; but never in the same sense ; Peter the
Great, and Peter the Hermit, have the same propern ame, bu t i t i s no t given to them in the sense of
cu ncm sm o r LO G I C . 5
identity, such as when we give the title of man tobo th these individual s ; a Roman general, a blackservant, and a pet dog, may be each named Pompey,but the resemblance of n ame on ly results from accident, wh ich is not the cas e when we say that thethree individuals are animals .
CHAPTER III.
Abs traction , (S'
c .
Q . What are the mos t remarkable afi ec tions orproperties of terms ?A . Comprehens ion and Extens ion .
Q . What i s the comprehens ion of a term ?A . I t i s the aggregate of allthe s impler ideas
,
which,together, make up the complex idea, sign ified
by that term .
Q . What i s the extens ion of a term ?A . I t i s the aggregate of all the individuals of
which that term may be severally prea icat ed or affirmed.
Q . Can you give any instance ?
A .
"l‘he comprehension of the term “ man in
cludes the ideas of substance, form , l ife , sensation ,
reas on,
” & c . ; because these s imple ideas make upthe complex notion of man : the ex tension of theterm man is th e individuals James , John ,
Richard,
& c .
, for t o each of thes e the name man can be applied .
Q . In what are comprehension and extensi on alike ?
A . They are both aggregates or collections .
Q. How do they differ ?B 3
6 CATECH I SM OF LOGIC.
A . The parts of c omprehension are ideas , and
taken collec tively ; the parts of extension are indiv idu als, and taken separately : the complex n otion i schanged if any of the parts of comprehension b eremoved ; no alterat ion is made by the destruction ofthe parts of extension .
Q . How are universal terms formed ?A . Terms become universal by being made the
names of universal ideas ; i deas become universal byabstraction .
Q . What i s Abstraction ?A . The consideration of attributes c ommon to se~
y eralindividuals ; s eparating from them thos e whichare pecul iar to a single individual, but which alwaysaccompany them in real exi stence .
Q. Can you explain thi s more clearly by an example >
A . The complex notion of any particular man ,
formed in the mind, contains the s impler ideas ofsubstance
,l ife, reason, &c . ,
t ogether with the ideasof a particular form, and countenance, and existence,in a certain time and place : these latter simplerideas , or attributes , belong to that individual alone,and distinguish him from all others ; but the attributes of substance, body, l ife, s ensation , and reason ,belong to a great number of individuals : these thenbeing separated from the peculiarities
,and collected
t ogether, form what is called the general notion , oruniversal idea of man and the process by which thiss eparati on is performed, i s called abstract ion .
Q. “Then c e arises the necess ity of abstracti on ?A . All our ideas are
,primarily
,ideas of individuals ;
if they so continu ed, we should have names of indi
ou ncm sn or LOGI C . 7
v iduals on ly, and it would be manifes tly imposs ibl efor men to find a separate name for every separateobj ect ; but by the pro cess of abstraction, w e separateobj e cts in to sorts and classes, t o which, when wehave given names, we obtain universal te rms .
Q . What effect does abstract ion produce on com
prehension ?
A . I t diminishes the comprehens ion, for i t omitscertain attributes .
Q. What effec t does abs trac tion produce on exten a
sion ?A . I t increases the extension for when the peculiar
attributes are omitted, the new complex idea becomesapplicable t o s everal individuals, whereas before i twas limited to one .
Q. How are comprehens i on and extens ion cono
nected ?
A . The extens ion of a term , or of th e idea sign ifiedby that term
,depends on its comprehension ; for the
greater the comprehension, the less will be the extension, and rice versri .
Q . Why ?A . Because every additional attribute, taken intothe comprehens ion of a term
,or the idea sign ified by
a term,limits i ts appl ication to individuals which
have a corresp onding character : for instance, if, t othe general c omplex idea of man, containing substance, body, life, s ensation, and reason ; there b eadded the attribute of whitenes s, thos e individualswho do not possess a white c olour, will no longer becontained in i ts extensi on.
8.
CATECH I SM o r L OG I C .
CHAPTER IV .
OfJudgment and Propositions .
Q . What is j udgment ?
A . I t i s the affi rmat ion or negation of one ideaabout another .
Q . What i s a propos ition ?A . I t i s a j udgment expressed in words , and may
be defined, the affirmat ion or negation of one termrespecting another .
Q. What are the parts of a propositi on ?A . Two ; the subj ect and the predicate .
Q . How are they defin ed ?A . T he subj ec t i s that about which s ometh ing is
afli rmed or denied ; the predicate i s that which isaffirmed or denied concerning the subj ect .
Q. Does the predicate always follow the subj ec t inthe proposition ?A . No ; they must b e distinguished by the mean ingof the sentence
,and not by the position of the terms .
Thus,when we say, pleasant are the paths of V ir
tue,”pleasan t is the predicate, and p aths of virtue the
subj e ct .
Q . How is the predicate subdivided ?A . Into the cop ula, and res cop ulata but the latter,by its elf, i s most usually named the predicate .
Q. G ive me an instance of a proposition and itsparts ?
A . In the propos ition man is mortal,
” “ manis the subj ect
,
“ i s” the copula,and “ mmt al” the
res copulata,or predicate .
Q. Is this the form of every s imple propos it ion ?
CATECH I SM or LOG I C. 9
A .No : in common conversation, the Copula (whichis always the verb substantive, with or without anegative part icle) frequently forms one word withthe res copulata
,as horses walk but for the sake
of distinction,logi c ians , in such cases , use a parti ~
ciple and th e verb sub stantive, ins tead of the s impleverb thus
,the instance given would be resolved
into horses are walking beings .”
Q. Whether are subj ects or predicates the moregeneral ?A . Any term may be a subj ect ; none but a uni~
Versal term can be a predicate .Q. Why cannot a s ingular term b e a predicate ?A . Becau se being on ly appli cable t o one individual,i t can be affirmed of that alone, or els e the propos itionwould b e identi cal
,as Peter is Peter .
”
CHAPTER V .
Predicables and Predi caments .
Q. What is a predicable ?A . That which can b e predicated or asserted of
any thing . Every universal term i s a predicable, fori t may be asserted of the individual s contained in i tsextens ion .
Q. How many classes of predi cable s are there ?
A . F ive ; G enus, Species, Difference, Propert y, andAccident : of these, the two former declare what athing is ,
”
the three latter what kind i t is .
Q . How do you defin e genus and species ?
A . Genus i s a universal term,containing in its
extens ion two or more universal terms ; Species i s a
10 cam cm sm 0? LOG I C .
universal term contained in the extension of one moreuniversal . Thus, animal” i s a genus , for i t containsman” and “ beast” in its extension ; these latterare species, for they are contained in the extension ofanimal .
Q . How do you define the o ther predicables ?A . Difference
,calle d als o the E ss ential D ifference,
i s the n ame of the principal essential attribute foundin the species , but not in the genus (as reason inman ) Property, i s the name of every essential at tribute , ex cept the principal , which is found in thespec ies, but not in the genus ; Accident, i s the nameof a non" essential attribute ; that i s, an attributewhich is found in individuals, but not universally ina clas s or species (as a white complexion, red hair,
Q . Which is, genus or species, the more ab stractidea ?A . Genus ; for i t has greater extension, and lessc omprehension .
Q. How do you prove this ?A . I t has greater extens ion
,for it contains the
species in its extension ; i t has less comprehension,for the E ssential D ifi eren ce and the Properties, w hichare always found in the comprehension of the species,never enter int o that of the genus .
Q . Explain the process by which the five predicables are formed .
A . The process of abstract ion commences by omitt ing the attributes which are peculiar to an indiv idual ; the preserved attributes form the complex ideaof a class or species
,the omitted attribute s are Acc i
dents ; we next remove th e attributes peculiar t o the
CATECH I SM o r LOG I C. 11
spec ies,which form Difference and Property, while
those which we retain form the complex idea of
genus .
Q . How are genera and specie s divided ?
A . Genus i s either the highest or subaltern speciesi s either the lowest or subaltern .
Q. Explain this divis i on .
A . In pursuing the process of abstraction , afterremoving the peculiar attributes, we at length arriveat a s ingle idea, unlimited by any attributes ; this iscalled the Highest genus : the first clas s which weformed in our proces s i s called the Lowest spec iesthe intervening clas ses are called subaltern, genera,and species ; for they are spec ies with respect to theclasse s ab ove
,and genera with respect to the classes
b elow them .
Q . Explain this by an example .
A . In abstract ing the idea of an individual man,we omit the acc idents of form, countenance, existencein time and place, &c . the preserved attribute s formthe complex idea of the species , man ; th is is calledthe lowest species , because it contains only individuals in its extension : we next omit the EssentialDifference
,or attribute peculiar to that Species, viz .
reason,and we have the complex idea of Animal
,
which is a genus, because it contains the speciesman and beast in its extens ion ; but Animal i s als o aspec ies, for if we
"
omit the E ss entialD ifference , sen
sat ion , we form a clas s above it , Vivans (l iving thing) ,which includes animal and plant in its extensionag ain, omitting the attributelife, w e form the clas sBody ; and, finally, removing the attribute form,
wearrive at subs tance, which is the highest genus, be
12 CATECH I SM o r Loe i c .
cause i t i s c ontained in the extens ion of n o moregeneral term .
Q. What i s a predicament ?A . A predicament, called als o a category, i s the
highest genus, with all the classes, &c. that are contained in its extens ion .
Q. What i s a predicamental line ?A . A s eries of classes, commencing with the lowes t
species,and terminating w ith the highest genus . For
instance,the series Meu , An imal, Vivens, Body, Sub
stance, is a predicamentz'
line .
Q. How many predicamental l ines are there in a
predicament PA . As many as there are lowes t species .
Q. Which is,predicament or predicable, the more
extens ive term ?A Predicament ; for it contains s ingular termswhich are excluded from the classes of predicables .
Q. How many predicaments , or categories, wereenumerated by the old logicians ?A . Ten "viz . Substance ; Quantity, with i ts threeSpec ies, number, t ime, and magnitude Quality, withi ts four spec ies, hab it, natural power, patible quality,form, and figure ; Relat ion, Ac tion, Pass ion, Where,When, Posture, and Habit .
Q. How does Time, a spec ies of quantity, differfrom the category When ?A . The former relates to the time howlong .
Q. What do you mean by patible qualities ?A . Those qualities of body which the mind is pass ive in receiving .
Q. What i s the difference between hab it, a speciesof qual ity, and hab i t, the las t category ?
CAT E CHI SM OF LOGI C . 13
A . The former sign ifies custom, the latter dress .
Q . What do you mean by relat ion ?A . Relat ion takes place w hen the consideration ofone idea necessar ily includes the cons ideration ofanother ; thus, the idea of parent includes that ofchild, the idea of master that of servant, &c . Theidea
,primarily cons idered, i s called the Relate, or the
subj ect of relation ; that, whose considerati on is included, i s called the Correlate, or term of the relation ;and their name s are called relat ive and Correlativet erms .
Q. What was the obj ec t of class ifying the predicaments ?A . As the predicables contained the predicates ofpropositions, i t was designed to include the subj ectsin the classes ofpredicaments .
CHAPTER VI .
The absolute afi ections ofp rop osi tions.
Q. How are propositions d ivided ?A . Into s imple and compound .
Q. What i s the difference between them ?A . A s imple proposit ion cannot be resolved intoseveral ; a compound may be divided into s everals imple .
Q. How are the affections or propertie s of proposition s divided ?A . Into the Absolute, or those which belong to aproposition c ons idered by itself ; and the Relat iveaffections which result from the compari son of severalpropos it ions Wi th each other .
14 CATECH I SM or LOGI C . .
Q. What are the absolute affections of propos i tions ?
A . Quant ity and Quality .
Q. W hat is quantityA . The determination of the extension of the sub
j ect in a proposit ion : i t i s either universality or part icu
’larity. With respect t o quantity, propos itionsare divided into universal and particular.
Q . Wha t is quality ?A . T hen atu re of the as sertion made in a propos ition ;i t i s either affi rmation or negation . Wi th respect t oquality
,proposit ions are divided into affirmat ive and
negative .
Q . What i s a universal propos it ion ?A . That in which the subj ect i s distributed
,or
taken in its entire extension . If the subj ect be auniversal term (see Chap . a mark of universality
,
such as “ all, every, none, i s, for the most part,prefix ed ; but if the subj ect b e a s ingular term, n o
such mark is required , because a s ingular term beingonly applicable to one individual, must always b etaken in it s entire extension .
Q. What i s a particular preposition ?A . That whose subj ect i s not di stributed o r takenin its entire extension . The subj ect must
,in this
cas e, be a universal term ; and t o show that it istaken particularly, a mark of uncertain quantity, suchas some
,many, a few, &C .
” i s usually prefixed.
Q . Why do you use the word uncertain .9
A . Because, if the quantity were c ertain, i t wouldindividualize the subj ec t, and make i t in fact a s ingular term ; now we have already shown , that proposit ion s, whose subj ects are s ingu lar, belong to theclass of universal s . Propo s it ions, whose subj ects
16 CATECHI SM or Loei c .
Q. How are these three k inds of matter distin~
gu ished ?
A . If the pred icate agree with all the individualsof the subj ect, as in A ,
the matter i s said to be mecessary ; if i t disagree with all, as in E, the matter issaid to be impossible ; i f it agree with some, and disagree with others
, as in I and O, the matter is saidto be contingent .
Q. What i s an indefin ite proposi tion ?A . That in which the matter i s n ot s trictly de
fined, as “ mothers l ove their children,” “ men do
n ot voluntarily incur loss in these cases, the extentof the agreement or disagreement between the subj ectand predicate
,cannot b e disc overed from the terms
of the preposition,and therefore such propos itions
are excluded from s tri c t logical reasoning .
CHAPTER VII.
Truth and Falsehood.
Q. How many kinds of truth are there ?A . Two Logical and Ethical : of course there arethe same varieties of falsehood .
Q. How are these kinds distinguished ?A . Logical truth i s the agreement of an assertionwith the reality of things ; E thical truth its agreement with the judgment of the mind .
Q . When will the same propositi on be b oth logically and ethically true or fals eA . When the mind forms a correct judgment .
Q . What inferences can be deduced when the m indforms a correct judgment ?
CATECH I SM o r LOGI C . 17
A . We may infer, that a propositi on ethically tr uewillbe logically true, and that a prop osit ion eth icallyfalse will be logically false, and vi ce versci .
Q. What inferences may be deduced when the mindforms an incorrect judgment ?
A . We may infer, that a proposition log ically truewill b e ethi cally fals e, and vi ce verse'i ; but we cannotinfer that a proposition logically fals e will be e thicallyt’rue
,nor that a proposit ion ethically false willbe
logically tru e .Q . Why can we not ?A . There is only one tru th ; the variet ie s of fals ehood are infin ite ; for instance, I may suppos e thatthis book contains one hundred pages, and withethical fals ehood assert
,that it c ontained any other
number ; but the mentalfalsehood of my assert ionwould not manifestly constitute logical truth .
CHAPTER VI I I .
The afi ections of the te7ms of a p rop osition .
Q . Have terms any relat ive affect ion ?A . Yes ; in a propos ition they are said to havequantity .
Q. Why i s thi s a relative affect ion of propositions ?A . Because quantity, that i s, universality or para
t icularity, does not belong to the terms taken bythemselves, but i s determined by the nature of theproposition in which they are found .
Q. In this relat ive sense, what i s a universal term ?A . A term distributed or taken in i ts entire extens ion .
’
C 3
CATECH I SM OF LOG I C .
Q. What is a part icular term ?A . A term not distributed ; that is, not taken ini ts entire extension .
Q . Oh what does the quantity of the terms of aproposition depend ?A . The quantity of the subj ec t depends on the
quantity of the proposition ; the quantity of the predicate on the quality of the propo s ition .
Q. How does the quantity of the subj ec t dependon the quantity of the propositionA . In every universal propos iti on, the subj ec t i sun iversal, and in every particular propo s ition, part icular ; as is plain from the defin ition s in Chap . VL
Q . How does the quantity of the predicate dependon the quality of the propositionA . In every affirmat ive propositi on the predicate i sparticular, and in every negative i t i s universal .
Q . Why i s the predicate of an affirmative propos itiou parti cular ?A . The assertion of an affirm ative propos ition i s,that the predicate contains th e extens ion of the subj cet ; from thence, i t cannot b e inferred, that thepredicate contains nothing more ; as therefore onlypart o f its extens ion can be inferred from the proposit ion , i t must be considered particular .
Q. But is not the predicate of an affirmat ive proposition sometimes taken in its entire extension ?A . When the terms of an affi rmative proposi tion
are reciprocal, as “ man i s a rat ional animal,” the
predicate i s really taken in its entire extension ; bu ti t must s till b e cons idered as particular, because i tsuniversality i s inferred from knowledge extrins ic t othe propos it ion .
CATECH I SM OF LOG I C . 19
Q. What do you mean by reciprocal terms P
A . Terms which may be universally predicated ofeach other .
Q. Why i s the predicate of a negative propositionuniversal ?A . The assert i on of a negative proposition i s, thatthe extens ion of the subj ec t i s excluded from theentire extension of the predicate ; consequently, thepredicate is taken in its entire extension, and istherefore universal .
CHAPTER IX .
7728 relative afi ections ofp rop ositions.
Subalternation .
Q . How many relat ive affections of propos itionsare noticed by Logic ians ?
A . Three ; Subalternation, Convers ion, and Op~
pos ition .
Q. What i s subalternation ?A . The deduction of a particular or s ingular propos it ion , from a universal, with out transposing theterms . The universal proposition i s called the subalternans the inferences deduced from it are namedsubalterns . Thus , from the subaltern ans, “ everyman is an animal,
”w e may deduce the subaltern s,
s ome men are animals,” Peter i s an animal ,
” &c .
Q . What are the canons respecting the determination of truth and falsehood in this process ?A . There are four ; but the two last may be inferred from the others
1. The truth of the un iversal infers the truth ofthe part icular .
20 CATECH I SM o r LOG I C .
2. The truth of the particular does not infer thetruth of the universal .
3. The falsehood of the particu lar infers thefals ehood of the universal .
4 . The falsehood of the universal does not inferthe falsehood of the particular .
Q. How do you prove the first and third ?A . If the predicate c ontain (or exclude) the wholeextension of the subj ect, i t must c ontain (or exclude)a part ; and on the other hand, if it b e false that partof the extension of the subj ect i s contained in (or excluded from) the extension of the predicate, i t mustb e fals e that the whole i s c ontained (or excluded) .
Q. How do you prove the second and fourth ?A . Though it be true that the predicate contains apart of the extension of the subj ect, i t may be fals ethat it contains the whole ; and on the other hand,though it be false that the whole subj ect i s c ontainedin the predicate, yet, i t may be true, that a part iscontained in its extens ion .
Q. What practical ru le i s derived from theseaxioms ?A . That an argument from a particular to a universal i s invalid .
Q. What do you mean by this rule ?
A That any argument from a term taken in par t ofits extension, to the same term taken in the whole ofits extens ion, i s invalid.
Q . Why do you lay such stress on the word term .9
A . To shew that the rule has n o reference t o propositions
,for in the third canon of subalternation we
legitimately reason from ‘a particular p rep osition t o aun iversal .
CATECH I SM or LOGI C . 21
CHAPTER X .
Conversion
Q. What is conversion ?A Thelegi t imate inference of one proposit ion fromanother, by the transpos it ion of the terms . The origimal propos it ion i s called the convertend, that dedu ced from it the converse .Q . How many species of convers i on are there ?
A. Three ; s imple convers ion, in whi ch the com
verse preserv es the quantity and qual ity of the convertend ; convers ion p er accidens, in which the quane
t ity is diminished but the quality preserved ; andconvers ion by contrap osit ion
,in which the quality i s
changed .
Q. How are these species of conversion used ?A . "niversal negatives, and part icular afiirma
t iy es, are converted simply ; universalaffirmatives
are converted p er acci dens ; part icular negat ives canonly b e converted by contrapos it ion ; and, as thisspecies i s rarely used, they are generally said to b eincapable of convers ion .
Q. In what mann er are these facts usually statedby logicians ?A . A is converted into I,
E i s c onverted into E,
I i s convert ed into I,O
O
i s not convert ed . (See Chap . VI .)
Q. In what manner can you prove that A i s converted into I ?A . The assertion of a universal affirmative is tha t
22 CATECH I SM or LOGI C .
the entire extens ion of the subj ect forms part of th eextension of the predicate
,from whence it manifestly
follows that a part ofthe individuals contained in theextension of the predicate i s the same as those contained in the extens ion of the Subj ect ; but no inference can be made respect ing the ent ire extension ofthe predicate
,consequently the subj ect of the c on
verse mus t be part i cular and the converse its elfaffirmat ive .
Q . How do you prove that E i s converted into E ?A . The as sert ion of a negative proposition is thatthe extens ion of the subj ec t i s excluded from theentire extension of the predicate and from allitsparts consequently the whole extension of the predicate i s t otally different from the extension of thesubj ect
,therefore
,the subj ect of the converse i s
un iversal, and the converse negative .
Q . How do you prov e that I i s convert ed into I 2A . The assertion of a particular affirmative i s, thatpart of the extension of the subj ect agree s with partof the extens ion of the predicate consequent, part ofthe extension of the predicate agrees with part of theextens ion of the subj ect, therefore, the converse willb e particular and affi rmative .
Q . Why cannot 0 be c onver ted ?A . The assert ion of a particular negative is , thatpart or the extension of the subj ec t is excluded fromthe extension of the predicate . This may be the casewhen the extension of the predicate i s c ontained inextension of the subj ect
,as some animals are not
men ;” or when the extension of the predicate i s ex
cluded from the extension of the subj ect, as somemen are not stones,
” or finally when i t is partly con
24 CATE CH I SM or Loe i c .
CHAPTER X I .
Opp osition.
Q. What is Oppos ition ?A . Oppos iti on is the disagreement in quality between two propo s it ions, having the same subj ec t and
the same pred icate .
Q. How many species of oppos it ion are there ?A . Three ; contradict ion, contrariety, and subcontrariety .
Q. What is c ontradiction ?
A . I t i s the oppos it ion between a un iversal andparticular, or between two singulars . Of con tradic~
t orie s,one is always true and the other false .
Q. Prove the canon of contradi ction .
A . If the matter of the proposition be necessary,
the affirmat ive will be true and the negative false ; i fimposs ible
,the negat ive will be true and the affirma
t ive false if c ontingent, the universal will be fals e andthe particular true. In singular propositions it i sevident that the same attribu te cannot agree and disc
agree w ith the same thing at the same t ime .
Q. What is contrariety ?A . The Oppos ition betwe en two universals . Of
contraries both may b e tru e , but both cannot befal se .
Q . How do you prove the canon of contrarietyA . In necessary matter, the affirmat ive will be true
and the negative false in impos sible matter, the n e
gat ive will be true and the affirmative false ; in cont ingent matter, both will be false .
Q. "ou said in Chap . VI . that singular propos i
CATECH I SM OF LOGI C . 25
t ions are reduced to the class of universals, why theni s the oppos it ion between s ingular propos it ions reckoned a part of contrari ety ?
A. Because that would violate the canon of contrariety, for s ingular oppos ites cannot both b e false .Q. What is subcontrariety ?A . The opp osit ion between two part iculars ; subcontraries may be both true, but cannot both befalse .
Q. How do you prove the canon of subcontrariety ?A . If the matter of the propos ition be necessary,the affirmat ive i s true and the negative fals e ; if impossible, the negative is true and the affirmat ive false ;if contingent, both are true .
Q. What obj ection is there to subcontrariety, as alegitimate species of opposition ?A . The subj ects of the subcontrary oppos ites may
be different parts of the extens ion of the term, and,thus , though apparently the same , be really different .Q. When will th is cert ainly be the case PA . When the subcontraries are true, for the sameattribute cannot agree and disagree with the samething at the same t ime .
Q. Can you shew that when contraries are false,subcontrar ies will be true i
A . Contraries are A and E , by hypothesi s they areboth false, therefore their contradictions, O and I (bythe canon of contradict ion) mus t be both true, butthese are subcontraries .
26 CATECH I SM OF LOGIC .
CHAPTER X I I .
Definition and Division.
Q . Howmany kinds of defin it ion are there ?A . Two ; defin it ion of a name, or of a thing.
Q. What i s the defin it ion of a name ?A . The explanation of a word which was beforeunknown , as Algebra signifies the art of computingby symbols .”
Q. How can you best j udge of the truth in anydefin it ion of a name?A . By substituting the defin ition for the word inany given sentence, and thus seeing whether i t willbear the sign ification under all circumstances .
Q . What is the defin ition of a thing ?A . I t i s a proposition explaining what any thing is .
Q . What are the law s of a perfect defin it ion ?
A . 1. I t must be adequate, that is, i t must c ontain the whole thing defin ed and n othing more .2. I t must be clear, s o as to make the nature of thething defin ed intelligible .
Q . Of what does a perfec t logical defin ition cons ist ?A . Of the proximate genus and essential difference .
Such a defin it ion will always be adequate, for thegenus contains the entire thing defined, and the essent ial difference excludes every thing else ; but it willnot always be clear, for the genus may need defin itionas much as the spec ies .
Q . What is an imperfect defin it ion called ?A . I t is properly termed a descr ipt ion .
CATECH I SM OF LOGI C . 27
Q. How many kinds of description are there ?A . Two . 1. A propos it ion declaring the nature of athing
,imperfectly by essential attributes . 2. By non
essential attributes,as man is a two"legged feather
les s animal . 1”
Q. How many species of divis ion are there ?A . Two division of a name, and divi s i on of athing .
Q. What is division of a nameA . The enumeration of the meanings of an amb i
gn ou s word or a doubtful s entence .
Q. What is the divi sion of a thing ?A . The distribution of a whole into it s part s .
Q. I s not the word whole amb iguous ?A . Yes, i t may mean either a universal whole or anintegrant whole .
Q. What do you mean by a un iv ersalwhole ?A . T hat whose n ame is a universalt erm if it b e a
genus, its part s are spec ies ; if i t be a species, it s partsare individuals ; in e ither case the parts ar e call edsubj ective.
Q. Why are they named subj ect ive ?A . Because they may be the subj e cts of affirmative
propos itions, of which the whole would be the predicate, and also becaus e they are placed under it
O I O O O ' I I O ONO
1 T his n otable attempt at defin ition boasts of a not lessrespectable author than Plato : i t w as practically refuted byDiogen es, who presen ted himself in the academy w here Platow as lectu ring, and tak ing from u nder his cloak a cock , w h ichhe had stripped ofi ts feathers, threw it on the ground , ex
claiming, T here’
s Plato’s man for you 1
”
D 2
28 CATE CH I SM or Loe i c .
(subj ectce sun") in the pred icamental l ine . (SeeChap . V .)
Q . What do you mean by an integrant whole ?A . Any entire individual thing
,as a nation whose
integrant parts are provinces , a man whose integran tparts are body
,head
, members , See . The divis ion ofan integrant whole, i s commonly called partit ion .
Q. Have we had any instance in this work, of thesame thing divided universally and integran tly ?A . Yes ; propositions as universal wholes are di
v ided into s imple and compound, universal and particular, &c . ; but as an integrant whole, a propos itioni s divided into subj ec t and predicate .
CHAPTER XI II.
Comp ound, Hyp othetic, andModalProp i
ositz‘
onslQ. How many species of compound propos itions
are thereA . Two ; those compounded in words and thosecompounded in sense .
Q. Wh ich are the mos t remark able k inds of propos it ions c ompounded in wordsA . Copulat ives and disjunctives .Q. What is a c opulative propositionA . A propos ition containing several subj ects, or
several predicates, or both connected together by acopulative particle
,as Aristotle was the preceptor of
Alexander the (i reat , and the inventor of logic .
Q. On what does the truth of a copulative proposition depend ?A . On the truth of all the parts separately.
cam cm sm or LOGI C. 29
Q. Into how many part s may a copulative proposition be resolved ?A . As many as there are subj ects multiplied by the
number of predicates, for each predi cat e may beasserted of each subj ect .
Q . I s there not a species of copulative proposit ionin which s omething more than the mere truth of th epart s is required ?A . "es ; in an adversative proposition there mustb e an apparent opposition between the part s
,or it will
b e nonsens ical .
Q . What is an adversative proposit ion ?
A . That in which one of the adversative part icles,but, yet, although,
” &c . occurs, as though hewere wounded
,yet did he not complain .
” Everyperson perceives that it would be nonsense t o saythough he were grat ified yet did he not c omplain .
”
Q. What must b e the species of opposit ion betw eenthe parts of an adversative propositi on ?
A . Sub contrariety ; if i t were e ither of the otherspecies the parts would not b e true . (See Chap . X I .)
Q. What i s a disjunct ive proposition ?A . That in which the subj ect i s said to be contained
in one of two or more predicates ; these predi cate sare in fact the parts of s ome whole , and on their perfeet enumeration the truth of the disj un ct ive dependsas it i s e ither spring, summer, autumn, or winter,
”
where the four predicates enumerate allthe varietiesof season . (See the subj ect of divis ion in the preceding chapter)Q. Which are the principal kinds of propos itions
compounde d in sense ?A . Ex clus ives, except ives, and inceptive s or
D 3
30 CATECH ISM or LOGI C.
desitives ; they are called by a common name cx
pon ibles.
Q. Why are they named expon ibles ?A . Because they want exposition to point out their
latent c ompos ition .
Q . What is an exclusive propositionA . That in which the predicate i s said to agree
w ith the subj ect alone, all others being excluded, asvirtue alone i s tru e nobility .
” This i s resolved intotwo parts 1. the predicate agrees with the subj ect .2. I t disagrees with every thing else .
Q. W hat i s an exceptive proposition ?A . That in which the predicate i s said to agree
with the subj ect, a part being excepted . I t i s re
s olved into two : 1. the predicate does not agree withthe excepted part ; 2. i t agrees w ith allthe rest .Q. Are not exclusives and ex ceptives very s imilar ?A . Yes they merely difi
'
er in the for m of express ion .
Q. How may an exclus ive b e changed into an excep tive ?
A . By making the subj ect of the exclus ive theexcepted part of the exceptive, and changing the quality.
Q. What i s an inceptive or desitive proposition ?
A . That in w hich s omething i s said to begin orend . I t i s resolved into two : 1. stating the conditionbefore the change ; 2. the effect of the alteration .
Q. By w hat common name are all the kinds ofpropos it ions hitherto mentioned known ?
A . They are called direct or categorical proposi
t ions,because they contain a direct assert ion .
Q. Are there any other species ?
32 CATECH I SM o r LOG I C .
form the reverse of hypothetic s, for the preceding parti s said t o b e the consequence of what follows ; asthe moon has various phases, because she shineswith the reflected light of the sun .
Q . In what other respect do causal s d iffer fromhypothetic sA . The truth of the part s i s n ecessary to the truthof a causal proposition .
Q . What i s a comparative proposit ion ?A . That in which a comparison is inst ituted, asC icero was as eloquent a speaker as D emosthenesfrom the assert ion of such a proposition, nothing canb e determined categorically of the parts, for I maysay Turpin was as honest as his assoc iates,
” thoughthere was not a particle of honesty among them .
Q . What is a modal propositi on ?A . That in which a mode or qualificat ion of the
assertion occurs, as “ it will p robably rain to"day,”human society is necessarily held together by laws .Q . What are the parts of a modal proposition P
A . The assertion and the mode ; and when a modalproposition i s considered as s imple
,the assertion
become s the subj ect, and the mode the predicate .In this v iew the examples quoted
,should be more
properly expressed,subj ect p redicate
That i t will rain to day, i s a probable thing ;sub"ect
That human society should be held together by law,
p redica teis a necessary thing .
Q. How many modes were recogn iz ed by the oldlog ic ians 2
CATECH I SM or LOG I C . 33
A . Only four ; necessary, impos s ible, poss ible, andcontingent .
Q . How did they define these modes 2A .Necessary, that w hich is and must be .
Impossible,that which is not and cannot be.
Contingent,that which i s and may not be .
Possible,that which i s not but may be .
Q . How have these modes b een extended by mo :
dern logicians ?A . M odern w riters on logi c cons ider every thing amode which qu alifies the nature or extent of the c onn ection between the subj ect and predicate .
CHAPTER XIV.
Reasoning and Syllogism.
Q. What is reason ing ?
A . The inference of one j udgment from several.
Q . What is reasoning, when expressed in word s,called P
A . Arg umentation .
Q. What is the mos t usual species of reason ing ?A . The inference of one judgment from two .
Q . By what name do logicians call this species ofreasoning, when expressed in words ?A . They term i t a syllog ism .
Q. How then do you define a syllogism ?
A . The inference of one proposit ion from two .
Q . What is the usual process by which a syllogismi s formed ?A . When in argumentation a propos ition occurs,
respecting the agreement or disagreement of whosesubj ect and predicate
,a doubt i s entertained , i t i s (for
the mos t part) reduced into a simple categorical form
34 CATE CH I SM o r LOG I C .
and termed the ques tion, as, for instance, whetherthe earth be a globe ?” In order t o determine theconnection between the terms of this question, theyare each compared with s ome third term suppose inthis instance, with th e nature of the shadow whichthey cast
,and from their relat ion to this third term,
their mutual c onnection i s inferred . This inferencei s called the con clusion , which has manifestly the sameterms as the question, and only differs from it in having a determinate qual ity .
Q. How many terms are there, consequently, in as imple syllogism ?A . Three ; the terms of the question (or conclu
s ion) which are called extremes, and the term withwhich they are compared
,usually denominated the
mi ddle term .
Q. How are the extremes distinguished .
P
A . The subj ect of the question (or conclusion) i scall ed the minor term , and the predicate i s denominated the maj or term .
Q. Why have they received thes e names ?A . Because in a universal affirmat ive proposition,
which logic ians consider the most perfect and useful,the predicate has always as great, and for the mostpart greater extension than the subj ect ; i t i s, therefore, termed M aj or, (greater) and the subj ect i s calledM inor, (less) .
Q. I s there any other reason for selecting a un iversal affirm at ive besides its utilityA . That i s the only spec ies of propos it ion in whicht he relative extension of the terms can be determined,for in both the spec ies of negatives, (E and O) theextension of the subj ect bein g excluded from that ofthe predi cate, no comparison can b e instituted be
CATECH I SM o r LOG I C . 35
tween them ; and in particular afiirmat ives, (I) , thesubj ec t and predi cate being both taken only in partof their extensions, nothing can b e determined respecting the entire extension of these terms .
Q . You have said that a syllogism contains onlythree terms, and yet that i t c ons ists of three proposition s how are these propos itions formed 2A . Each term is twice repeated ; in the first , theextreme maj or i s c ompared wi th the middle ; this i s,therefore
,called the maj or propos it ion ; in the s e
cond,the minor extreme is c ompared with the middle,
and the proposition is termed the minor in the conclu sion ,
the extremes are compared together .
Q. What common name have the maj or and minorproposit ions P
A . They are called premises .
Q. G ive an example of a syllogism and its parts ?A . M aj or premises
m iddle termEvery body that in every posit ion casts a circular shadow,
maj or termi s a globe .
m inor term
M inor premises : The earth 15,
middle termA body that in every position casts a Circular shadow .
minor term maj or termConclus ion . Therefore, The earth is , a globe .
Q . What species of matter are syllogisms said tohave ?
A . T w o kinds ; proximate and remote .
Q . What is the proximate matter of a syllogism ?A . The propositions which compose the syllogi sm,
Viz . the premises and conclus i on .
36 CATECH I SM or LOGI C .
Q . What i s the remote matter of a syllogismA . The terms of which the propositions are com~
posed, viz . the extremes and the m iddle term.
CHAPTER XV .
Form and F igure of Syllogisms.
Q. What property have syllogisms with respect totheir proximate matter ?
A . F orm .
Q . What is the form of a syllogism ?
A . The proper arrangement of the premises, s o ast o point out the necessary inference of the conclusion .
Q. What is the usual form of a syllogism ?A . The maj or propositi on is generally placed first,
as in the example given in the preceding chapter.
Q. What property have syllogisms w i th respect totheir remote matter ?
A. F igure .
Q . Ou what do the variet ies of figure depend ?A . Ou the pos ition of the middle term in the pre
mis es .
Q. How many varieties of figure are there .P
A . F our ; because the middle term may have fourdifferent positions in the premises .
Q . What pos ition does the middle term hold inthe first figure ?
A . I t is the subj ect of the maj or,and the predicate
of the minor, as in the example g iven in the precedingchapter .
Q. What i s the p osition of the m iddle term in thesecond figu re
P
A . I t i s the m edicate of both premises ; as
CATECH I SM o r LO G I C . 37
maj or termN0 body that has not les s specific gravity than i tselfm iddle term
can revolve round the earth ;minor term middle term
The moon revolve s round the earth ;Therefore,
The moon has less specific gravity than the earth .
Q. W hat i s the pos it ion of the middle term in thethird figure ?
A . I t is the subj ect of both premises ; asmiddle term
Those celestial obj ects, which change their relativemaj or term
posmons, are planets ;middle term minor term
Such changes of posmon are seen among the stars ;Therefore, S ome of the stars are planets .
Q. What is the pos ition of the middle term in thefourth figu re
P
A . I t is the predicate of the major, and the subj ectof the minor ; on account of the un natural pos it ion ofits terms , i t was not recognised byAris totle but beingsubsequent ly introduced by Galen, i t i s s ometimestermed the Galeni c figure . A s i t rarely occurs inpract ice, there i s no necess ity of gi ving an example .
CHAPTER XVI .
GeneralRules of Syllogisms .
Q . Ou what axioms was the doctrine of syllogismsfounded before the time of Aristotle 1 P
I I I O M NI I J I '
1 Aristotle’
s doctrine ofsyllogisms w ill be found in Chap.
X IX.
38 oarnom sm o r LOG I C .
A . Ou the three following1. I f two things agree with one and the same third,
they agree with each other .2. If of two things one agree and the other dis
agree with the third, they disagre e wi th each other .3. If neither agree with the third, no inference can
be deduced .
Q . How many general rules of syllogisms are there ?A . S ix : 1. The middle cannot b e taken twice
parti cularly,but must be at least once universal .
2. An extreme cannot b e taken more universallyin the conclusion than in the premises .
3. From two affirmative premises a negative conelusion does not follow .
4 . F rom two negative premises noth ing follows .5 . The conclusion follows the w eaker part ; that
i s,if one premise be n ega tive, the 'conclu sion will be
negative ; and if on e premise b e particular, the comelusion will b e particular .6 . F rom two particulars noth ing follows .
Q . How do you prove the first rule ?
A . If the middle were taken twice particularly,i t
might be taken for different parts of the same universal whole, and t hus there would be in fact twomiddle terms ; but it appears , from th e axioms, thatthe extremes should b e compared w ith one and thesame third .
Q . I s not this rule very frequently violated by inaccurate reason ers .
P
A .None more so ; because the similarity in soundprevents u s from immediately perceiving the diss imilarity in sense, when an amb iguous or undistributed middle is used thus
,in the common j est ;
40 CATECH I SM o r LOG I C .
the premises , must, by the second general rule, beparticular in the conclusion
,where it i s the subj ect,
and therefore renders the conclusion particular .If one of the premises be negative , the conclusion,
by the first part of this rule , must b e negative, and. i ts predicate consequently universal (Chap . VII I . )in
,this case
,there can be only two universal terms in
the premises , one of which must be the middle, andthe other the maj or (first and second general rules) ;therefore , the minor being particular in the premises,w ill b e als o parti cular in the conclus ion , where i t isthe subj ect, and consequently renders the conclusionparticu lar.
Q. How do you prove the sixth general rule ?A . If both premises b e affirmative, there will be
no universal term in the premises, and there fore the
middle will be taken twice particularly,contrary to
the first general rule . If one premise be negative, theconclus ion w ill b e negative
,and therefore its pre
dicate universal ; but in this case there can be onlyone universal term in the premises therefore , e itherthe middle must be taken twice particularly, contraryto the first general rule
, or the maj or extreme mustbe taken more universally in the conclusion than inthe premises, contrary to the second .
CHAPTER XVI I .
Modes and sp ecialrules .
Q . What is the mode of a syllogism ?A . The legitimate determination of the propositionsin a syllogism
,according to their quantity and quality .
Q. What do you mean by the special rules of a syllogism ?
CATECH I SM 01? LOG I C . 41
A . The se rules which are peculiar to any s inglefigure .
Q . How may we determine the rules which arespec ial to the first figu re ?
A . The conclus ion must be e ither affirmative ornegative . If it b e affirmat ive, both premises, andtherefore the minor
,must b e affirmat ive ; but th e
middle term, which, in this case, i s predi cat e of theminor
,will be particular
,and therefore must be uni
versal in the maj or, where it i s th e subj ect, and consequ ently renders the maj or universal .If the conclusi on be negative , i t s predicate, th emaj or term
,wi ll be universal, and mus t c onsequently
have the same quant ity in the maj or premise ; but inthe maj or premise
,i t is the predicate therefore , the
maj or must be negative, and the minor afiirmat ive ;
conseque n tly,its predicate
,the middle term, willb
particular in the minor, and therefore universal inthe maj or
,where it is the subj ect, and consequently
renders the maj or universal .
Q . What special rules for the first figure are dedu ced from this analys is ?A .l. The maj or must be universal .
2. The minor must be affirmat ive .
Q. What are the legitimate modes Of the first
figure established by the same analys is 3A . F our ; a follow
I .
‘2. 3. 4 .
M aj or premis e A E A E
M inor premise A A I IConclus ion A E I 0 (See Chap . VI ) .
Vi'hich, for the sake of memory, are formed into themnemonic word, Barbara, Celarent, Darii, Ferio .
E 3
42 CATECH I SM o r LOG I C .
Q . How do you investigate the spec ial rules of thesecond figure
P
A . A s the middle term is predicate of both premises
,one of them must be negat ive (first general
rule) , and the conclusion must als o be negative (fifth
general rule) ; consequently, the maj or term , as predicate of the conclusion , will be universal, and musttherefore (second general rule) have the same quan~
t ity in the maj or premise,where i t is subj ect, and
therefore renders that premise universal .
Q . What are the general rules deduced from thisanalysi sA . 1. One of the premises must b e negative
2. The maj or must b e universal .
Q . What are the modes of the second figure ao
cord ing to this analysis .P
A . There are four 1. 2. 3. 4 .
M aj or premise E A E A
M inor premise A E I 0
Conclusion E E O
Contained in the technical words,Cesare, Camestres,
F estino , Baroko .
Q . What are the special rules of the third figure ?A . I t can be shewn by the same analysis as in the
first figu re ; that 1. the minor must b e affirmative ;
and since the minor term is predicate of the minorpropos ition, i t must be particular, and therefore theconclus ion will b e particular .
Q . From what s imilarity between the first and thirdfigure have they a s imilar rule and s imilarly proved .
A . The proof in both instances turns on the pos it ion of the maj or term in the premises
,and in both
i t i s the pred icate of the maj or propos ition .
Q. How many modes are there in the third figure?
CATECH I SM o r LOG I C . 43
A . There are s ix 1. 2. 3. 4. 5 . 6 .
M ajor premis e A E I A E
M inor premise A A A I A IConclus ion I O I I O O
Contained in the mnemonic words, Darapti, Felapton ,
D isamis, Dati si , Bok ardo, Ferison .
Q . What are the special rules of the fourth figure ?
A . In this figure, on account of the confused position of the terms , all the rules are hypotheti c : byan easy analysis , we can discover, 1. that in negativemodes the maj or w ill be universal ; provedlik e thesecond rule of the s econd figure 2. that if the minorbe affirmative , the conclusion will be particular ;proved as the second rule of the third figure : and3. i f the maj or be part icular, the minor must be n egat iv e ; for the middle term will then be part icular, assubj ect of maj or ; therefore, i t must b e un iversal inminor
,where it i s predicate
,and consequently will
render the minor negative .
Q. M ay not the rules of the fourth figure be otherwis e expressed ?A . They may be converted by contrapos ition, andwould then be thus expressed1. If the maj or be particular, the mode w 1llbe
aflirmat ive .
2. If the conclus ion be universal, the minor mustb e negative .
3. If the minor be affirmat ive, the maj or must beuniversal .
Q . M ay not the ru les of the fourth figure be expressed categoricfi y .
P
A . Two categoricalrules are easily deduced fromthe hyp othetic s already g iven
44 CATECH I SM o r LOGI C .
1. 0 cannot be a premise .2. A cannot be a legitimate c onclusion .
Q . F rom what similarity betw een the second and
fourth figu res have they a rule s imilarly proved ?A . The proofs of the first rule of the fourth figure,
and the second of the second figure, depend in bothon the position of the maj or term , which in both i sthe predicate of the maj or proposition .
Q . From what s imilarity between the third andfourth figures have they a rule s im ilarly proved ?
A . The proofs of the second rules of the third andfourth figure, depend in both on the position of theminor term, which in both is the predicate of them i nor proposition .
Q . What are the modes of the fourth figu re ?
A . There are five 1. 2. 3. 4 . 5 .
M aj or premise A A I E E
M inor premise A E A A IConclusion I E I O O
F or which the mnemonic words are Bramantip, (Jamenes , D imar is, Fesapo, F resison 1
Q .
‘Nhich of the figures i s the most p erfect ?A . The first , for in that alone can a u niversal af
firmat ive conclusion be deduced ; in the second, theconclus ion must be negative ; in the third, particular;in the fourth
,e ither negative or particular .
I "
1 T he names of the modes are in cluded in the follow ingLatin lin e s
1.’
arbam,Celarent, Dari z', F erz'o quoque primes,
Cesare, Camestres, F est ino, Baroko secu ndae ;
T c rtia Damp t i sibi v indica t atqu e F elap ton ,Adj uugen s D isamis, Da tisi, Bokardo, F erz
'
son
In qu arta Bmman t z’
p sun t, Carmenes, D imarisque,Adjungens semper F esapo atque Fresison.
45CATECHISM DE LOGI C .
sc_m
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46 CATECH I SM o r LOG I C .
CHAPTER XVI I I .
Further Cons iderations on the Blades and F igures .
Q . How may you determine,analytically, that A
can be a conclusion in th e first figure only ?
A . S ince the conclus ion i s affi rmative , both premises must b e affirmat ive, and s ince i t is als o u n i
versal , i ts subj ect, the minor term ,must be universal
in the minor proposition (second general rule) ; theminor term mus t therefore b e the subj ect of theminor propos it ion
,and the middle its predicate
,and
consequently particular ; the middle term must therefore be universal in the maj or proposition , and to beso must be i ts subj ect : hence it appears , that A canbe a conclusion only when the middle is the predicateof the minor
,and subj ect of the maj or propositions ;
that is, in the first figure .
Q. I s there any proposi tion restricted as a premis e ?A . 0 can be a minor proposition only in the second
figure , and a maj or only in the third .
Q. How do you show ,analyt ically
,that O , as a
minor premise, i s restricted to the se cond figure ?
A . S inc e minor premise i s negative,the conclusion
must be negative,and its pred icate universal ; the
maj or term,or predicate of the conclusion, must
therefore be universal in the maj or premise ; buts ince the minor premis e i s negative, the maj or mustbe affirmat ive ; the maj or term then mus t be its sub
j ec t , and the middle, being its predicate, will be part icular ; i t must therefore b e universal in the min orpremise, and to be so , must be its predicate : hencei t appears, that 0 can be a minor premis e in that
48 CATECH I SM OF LOG IC .
middle term, as predicate of maj or premise, beingparticular
, must b e universalin minor, and to be somust b e its subj ect therefore, the maj or extreme canbe particular in premise, and universal in conclusion,only in that figu re which has the m iddle for predicateof maj or premise, and subj ect of minor, v iz . the
fourth .
Q. What mode i s common t o all the figures ?A . E I . 0 .
Q. Why ?A . All the condit ions of the general rules will be
fulfilled, whatever he the pos it ion of the terms in thepremises .
Q. Why i s not I . E . O . a legitimate mode ?A . Because the maj or term, which is universal inthe conclus ion, w ould be particular in the maj orpremise, whether i t were made the subj ect or predicate .
Q. W hy i s A . E . O . marked a useless mode ?
A . As the minor term,whether subj ect or pre
dicate, must be universal in the minor proposition,we can have a universal conclus ion in every figure
which can have these premises .
Q. Why then is E . A . O . a useful mode .
P
A . Because the conclusion from these premisesmust be particular in thos e figures in which theminor term is predicate of the minor proposition .
Q . What conclusion admits the greatest variety ofpremises ?A . A particular negative .
CATECH I SM or LOG IC . 49
CHAPTER X IX .
T he Aristotelic doctrineof syllogisms.
Q . Ou what principles did Ari s totle e stablish thedoctrine of syllogisms ?A . On what are called the rules de omm
’
and de
nullo, both of which are comprised in the followingaphorismWhatever is predicated affirmat ively or negativelyof a term
,taken in it s entire extension , may be pre
dicated in like manner (that i s, affirmat ively or negat ively) of any thing contained under that term .
Q . To which of the figures i s this principle applicable ?A . To the first only .
Q. Vl'hy ?A . Because in the first , the maj or i s predicated of
the middle, and the minor i s contained in the middle ,whence we immediately infer the predication of themaj or respecting the minor ; but in the other figures ,
as the terms are not disposed in their natural order,the necess ity of the consequence is not immediatelyperceivable .
Q . Why do you say their naturalorder ?A . Because if we observe the proces s which usuallytakes place in our own minds , we shallsee that ourreasoning, for the most part, assumes the form ofthe first figure ; for we first endeavour to obtain somegeneral rule, and then investigate how far the part icular instance is c ontained under the rule .Q. Can you illustrate th is by a common example ?A . In allcriminal trials, the law defining the crime
F
50 CATECH I SM or LOG I C .
is the maj or proposition ; the nature of the actioncommitted by the prisoner i s the minor proposition ;and the verdict of the j ury is the conclusion .
Thus : “ To kill a man wilfully, maliciously, andunlaw fully, i s murder .M.N. did kill a man wilfully, malic iously, and
unlawfully .
Therefore M.Nis guilty of murder .Here the law supplies the maj or proposition ; the
prosecutor furnishes the minor ; and the jury drawthe conclusion from the premises .
Q. Has not this s imple dist inction been frequentlyneglectedA . Yes ; from not keep ing the proposit ions suf~
ficien tly distinct, jurymen have frequently requiredproof of the maj or, and thus interfered with the province of the court and, on the other hand, instanceshave o ccurred of j udges directing their attention tothe minor
,the cons ideration of which belongs to the
j ury.
Q . How did Aristotle distinguish the modes of thefirst figure from thos e of the others ?A . He called the modes of the first figure perfect,and the others imperfec t .
Q. What are the attributes of a perfect mode .P
A . 1. The middle term must b e the predicate of itsminor
,and the subj ec t of its maj or .
2. The minor premis e mus t be affirmative, and themaj or universal .3. The conclusion must have the quantity of theminor, and the quality of the maj or premise .
Q . How do you prove the first and second ?
A . I t is man ifest from the principle on which Aris
CATECH I SM OF LOG I C . 5 1
totle has founded the doctrine of syllogisms ; forthere must b e some general rule laid down aboutsome universal term, of whose extension the subj ectof the conclusion forms a part .
Q . How do you prove the third ?A . The conclus ion must have the quantity of theminor ; for that part alone of the universal term, oruniversal whole
,determined in the premises, can be
introduced into the conclus ion ; and it must have thequality of the maj or, for whatever has been predicatedof the universalwhole, must als o b e pred icated of itsparts .
CHAPTER XX .
Redu ction .
Q . How are imperfect modes changed into perfect ?
A . By reduction, which is of two kinds, ostens iveand indirect .
Q . What is o stens ive reduction P
A . That which from the premise s of the imperfectmode gives the conclus ion in a perfect mode, or a conelus ion immediately inferring i t by convers ion .
Q . What i s the imperfect mode called ?
4 . I t is called the redu cend, and the perfec t modeformed from it is termed the reduct .
Q . How do the names of the imperfec t modessuggest the perfect modes into which they are to be
reduced ?A . The initial letter of the redu cend and reductmodes are the same ; S or P following a vowel in theredu cend, shows that the propos it ion must b e c on
F 2
52 CATECH I SM or LOGI C .
verted to make i t admissible in the reduct mode ; M.
orNdeclares that the reducend premise must betransposed ; and K . declares the imperfect mode to b eincapable of direct or ostens ive reduction .
Q. What then are the perfect and imperfect corresponding modes .
P
A . Imp afect modes. Perfect modes .
Bramantip BarbaraCesare
,Camestres
,Camenes Celarent
Darapti, Disamis, Datisi , Demaris Dari iF estino
,F elapton , F erison, F esapo, Fres ison Ferio
BarokoBokardo
Incapable of ostensw e reduction .
Q . Give me an example of ostensive reduction ?
A . Reducend or imp erfect mode.
Ce N0 body shining by its own light changesi ts phases .
The moon changes its phases .The moon does not shine by its own l ight .
Reduct or p erfect mode .
N0 body changing i ts phases shines by itsown light .
"la The moon changes its phases ."rent . The moon does not shine by its own light .
Q . How is the second figure reduced to the formof the first .
P
A . By the convers ion of the maj or ; for the minorpropositions in both have the terms in the sameorder .
Q. When will this change be sufficien t ?A . When the minor proposition is affirmat ive forin the second figu re the maj or i s always universal .
Q. When is a further change necessary ?
CATECHI SM or LOG I C . 53
A . When the minor i s a universal negative, thepremises must b e transposed ; when i t i s a particularnegative
,ostens ive reduction is inapplicable .
Q. How is the third figure reduced to the form of
the first
A . By the convers ion of the minor ; for the t erm sare in the same order in the maj or propositi ons ofboth .
Q . When willth is b e suffi cien t ?A . When the maj or is universal ; for in the third
figure the minor i s always affirmat ive .
Q . When will transposition b e als o necessary ?A . Wh en the maj or i s a particular affirm at ive ; butif it b e a particular negative , ostensive reduction isinappl i cable .
Q . How is the fourth figu re changed into the formof the first .
P
A . E ither by s imple transpos ition, or by the convers ion of both premises .
Q . When willtranspos it ion suffice ?A . When the minor i s universal, and the maj or
affirmat ive .
Q. When transposition of premises is used inreduction, will the reduct conclusion be precisely th esame as the conclus ion of redu cend .
P
A . No ; when the premises ar e transposed, the
terms of the conclus ion must be transposed likewise ;and the conclusion of the redu cend must then bederived from the conclusion of the reduct by convers ion .
Q . I s there any mode in which i t can be determ inat ely shown that the conclus ion of reducend i sthe convertend of the conclus ion of reduct ?
F 3
54 CATECHI SM or LOG IC .
A . Yes ; Bramantip is such a mode, and there i sno other.
Q. How do you prove this ?A . In order that such a relation sho uld be determinable, the convertend must be a universal affirma
tive, and the converse a particular affirmative ; forthe converses of universal negatives
, and particularaffirmatives, do not differ from their c onvertends inquantity ; n ow as the conclusion of reduct is c onvertend t o conclus ion of redu cend, i t must be a universal affirmative , and its subj ect be ing universal inthe conclusion, must have been universal in reductpremises, and also in the premises of reducend fromwhence they were derived ; bu t as convers ion is mecessary in the conclusion, transposition must havetaken place in the premises, and consequently theuniversal minor of the reduct i s a universal maj or inthe redu cend ; but since the conclusion of the re
ducend i s affi rmat ive , i t s predicate, the maj or term,
i s particu lar, but it is universal in the premises, andtherefore the redu cendmode is Bramantip in the fourthfigure , as has been already shown in the s eventhparagraph of the eighteenth chapter .
Q. How do you shew the validity of ostens ivereduction ?A . The premises of the reducend are supposed to
be true,therefore the premises of the reduct being
derived from them by a legitimate process, are tr uelikewise ; s ince, in the first figure, the conclus ion isthe necessary result of the premises , the conclusionof the reduct is tr ue , and this is either the same asthe conclu s ion of reducend, or infers i t by alegitimate process of conversion .
56 carncm sm OF L OGI C .
Q . In this instance, the conclus ion of reducend
contradicts the minor premise of redu cend, but fromthe letters there would appear t o be only contrarietybetween them . How do you explain the apparenterror .
P
A . You have mentioned the reason that led to thes election of thi s very example : in addition t o thedemonstration of th e principles of indirect reduct ion,i t i s of importance t o show the extens ive and accurat eapplication of which logical reasoning is sus ceptible,and that apparent violat ions of the forms of its rulesare still regulated by its strict est principles .
Q . I s that exemplified in th e present instance ?A . Yes ; the moon being applicable only to oneindividual is a s ingular term, therefore the proposit ion of which it is the subj ect must b e universal theconclusion from two universals being universal in thefirst figure , the reduct i s b oth a universal and s ingular, but the opposition between two s ingulars i sc ontradiction . In anoth er part of thi s chapter, however
,i t will b e shown , that contrariety which might
arise in this case would be an opposition perfectlysuffi cien t for the process of reasoning.
Q . Has this indirect proces s of reduction any othernames ?
A . I t i s commonly calle d by the old logic ians redzcctio ad imp oss ibile, and reductio ad absurdum.
Q . What changes are made in the terms of theredu cend by indirec t redu ct ion .
P
A . The extreme of preserved premise of redu cendbecomes the middle term of the reduct ; the middleof reducend takes in the reduc t the name of the ex
CATECH I SM or LOG I C . 57
treme of the preserved premise ; the extreme of thesuppressed premise preserves its name .
Q . How do you prove this .P
A . S ince the extreme of the preserv ed premiseoccurs once there in the premises of the reduct, andonce again in the contradictory of the conclusion, i tmus t be the middle term of the reduct, for that termalone occurs twice in the premises of a syllogism :
s ince the former middle occurs but once in the premises of reduct, i t must become an extreme ; ands in ce i t occurs on ly in the preser ved premis e, i t w illbe the extreme of that premise : finally, s ince theextreme of the suppressed premi se holds the sames ituation in the substituted premise (Viz . the contradictory of the conclusion) , i t must retain its formername .
Q. Which is the suppressed premise in the secondfigure ?
A . The minor .
Q . ‘Vhy ?A . S in ce the maj or premis e i s preserved , the maj orterm w ill become the middle ; but i t is the subj ect ofthe preserved premise
,and will be the predicate of
the substituted premise,for i t is the predicate of
reducend conclusion, and consequently of its c ontradictory als o .
Q . Will the reduct mode then fulfilthe conditionsof a perfect mode P
A . Yes ; the preserved maj or will be universal, fori t i s always s o in the second figure and the substi
tu ted minor willbe affirmat ive, for i t i s the contra~
dictory of the conclusion, which in the second figu re
i s always negative .
58 carncmsm or LOG IC.
Q. Which is the suppressed premise in the thirdfigure
?
A . The maj or.
Q . Why .
P
A . S ince the minor i s the preserved premise,the
minor term becomes the middle,but it is the pre
dicat e of the preserved premise, and will b e of coursethe subj ect of the substitu ted premise (viz . the contradictory of redu cend conclusion) .
Q . W ill the reduct mode in this case be perfec t ?A . Yes ; the preserved minor will be affi rmat ive,
for it i s always s o in the third figure ; and the n ewmaj or will b e universal, as being the contradictory ofthe conclus ion, which in the third figure i s alwayspart icular .
Q . Which is the suppressed premise in the fourthfigur e ?A . The fourth figure i s reduced to the form of the
first by substituting the contradic tory of the conclus ion for e ither of the premises .
Q . Why ?A . I f contradictory of conclusion b e substitutedfor maj or premise, the minor term becomes middle,and is subj e ct of maj or and predicate of minor ; if i tb e substituted for minor premise
,the maj or term
becomes middle,and i s the subj ec t of maj or and
predicate of minor,as i s required in a perfect m ode .
Q . How then do we determine the suppressed premise in this figure ?A . By the n ature o f the conclusion : 1. if i t be apar t icular affi rmat ive , the maj or must be suppressed ;2. if i t be a universal negative
,the minor must b e
suppressed ; 3. if i t be a particular negat ive, e itherpremise may be suppressed indifierently.
CATECH I SM o r LOG I C . 5 9
Q. How do you prove the first part ?A . I f the conclusion b e a particular aflirmat ive, i tscontradictory willbe a universal negative, and c onsequently only admi ss ible as a maj or in the first
figure .
Q. Will the mode then be perfec t ?A . Yes ; the maj or, as w e have shown , will b e
universal,and the minor must be affirmat ive, s ince
the conclusion i s so .
Q . How do you prove the second part ?A . The contradictory of a universal negative conelusion is a particular affi rmat ive, which i s only admiss ible as a minor in the first figure .
Q . Willthe mode then be perfect .
P
A . Yes ; for the minor, as we have shown, will b eaffirmative , and the maj or will be universal, for it iss o in all the negat ive modes of the fourth fig ure .
Q . How do you prove the third part ?
A . The maj or i s universal and the minor affirma
t ive in the modes of the fourth figure, which have aparticu lar negative conclusion ; consequently, e ithermay be preserved without violating the rules of perfect modes ; and the contradic tory of the conclusionbeing a universal affirmative
,may become either
maj or or minor premise of reduct .
Q . What is there remarkable in the indirect reductmode s of the fourth figure
?
A . The terms of reduct mode are always in thereverse order of the terms in the suppressed premise .
Q . Why ?A . Because the middle term of redu cend premisechange s its name for that of the ext reme in preservedpremise, and will therefore b e predicate of conclus ion
60 CATECH I SM or LOG I C .
when the minor i s suppressed, and subj ect when themaj or is suppressed ; but in the fourth figu re, them iddle term i s subj ect of m inor and predicate ofmaj or .
Q . What species of oppos ition is principally usedin the process of indirect reduction .
P
A . Contradicti on .
Q . In how many ways i s i t applied ?A . In two ways : we argue from truth of suppres sedpremise to falsehood of reduct conclusion and fromfalsehood of substituted premis e to truth of redu cendconclusion .
Q . Could the other species o i; opposition be usedin either of these ways ?
A . Yes : contrariety i s a val id argument in reasoning from truth to falsehood ; and subcontrariety inreasoning from falsehood to truth .
Q. Does contrariety ever arise P
A . Yes ; whenever the reducend mode has a part icular conclusion, and universal premises .Q. Why will it arise in this case
A . Because both premises of the reduct will beu niversal ; and whenever this is the case in a perfectmode
,the conclus ion w ill b e universal .
Q. W ill th e argument in this case b e valid ?A . Yes ; for the tru th of the suppressed premisewill prove the fals ehood of the reduct c onclusion .
Q . Could you not in this cas e make use of contradiction ?A .
1Yes : by deducing a subaltern from the re
O I I I I ' I O ’ I I I I
1 See the chapter on Subalternation (IX).
carncm sM or LOG I C . 61
ducend premise, which would be true by the first
canon of subalternation ; and , consequently, i ts contradictory, the conclus ion of the reduct syllogism,
would be false .Q. Could subcontrarie ty be used in the process of
reduction ?A
'No : the argument of subcontrariety would beval id between substitu ted premise and conclus ion ofreducend ; but if thus used, it must als o o ccur whereit would be invalid, viz . between suppressed premiseand conclusion of reduct .
Q . How i s th is proved .
P
A . In order that substituted premise shou ld besubcontrary to conclusmn of reducend, that conclusion must be 0 ; for the subcontrary of I (viz . O ) i sinadmissible as a premise in a perfect mode : als o ,substituted premise must be the minor, for a part icular i s not admiss ible as m aj or premise in a perfectmode ; the mode must therefore occur either in thesecond or fourth figures but when the conclusion i sparti cular in the second figure, the minor is so likewise ; and s ince the reduct has a particular premise,the conclusion of reduct will be part icular, and therefore subcontrary to suppressed premise ; in the fourthfigure, the conclusion i s particular only when th eminor i s affirmat ive ; and as the terms of reduct conelusion are in revers e order to the terms of suppressedpremise , i t will be subcontrary to the converse of that
prem1se.
62 CATECH I SM or LOGI C .
CHAPTER XX I I .
Hypotheticaland disj unctive p rep ositions .
Q. What is a hypothetical proposition .P
A . That in which one or both premises are hypothetic propositions .
Q. What is the most c ommon form of a hypotheticsyllogism ?A . The maj or i s usually a hypotheti c proposition ;the minor and conclusion both categorical . If bothpremises b e hypotheti c , the con clusion will be hypothetic l ikewise ; and the proposition will partake ofthe nature of a S ori tes, which shall be describedhereafter.
Q . What ar e the legitimate proces ses of reasoningin hypothetic syllogism ?A . F rom the position of the antecedent t o thepos ition of the consequent ; and from the remotion ofthe consequent to the remotion of the antecedent .
Q . What do you mean by posit ion and remo tion .
P
A . Position i s the as sertion of a proposition preserving its quality ; remotion is the assertion of a proposit ion after its qual ity is changed to the opposite .
Q. What are the illegitimate processes of reasoningin hypothetic syllogisms .
P
A . From the remotion of antecedent to the remotion of consequent ; or from the position of cousequent to the pos ition of antecedent .
Q . How do you prove this .
P
A . I t appears from what we have already stated
(Chap . X III ) , that the truth of a hypothetic proposition depends on the validity of the inference of the
64 CATECH I SM o r LOGI C .
cisely equivalent to the constructive reason ing, fromits convertend and v ice versa
i
.
Q. What is the most usual form of a hypotheticproposition .
P
A . The antecedent and consequent have, for themos t part, a common subj ect ; if they have not, itwill be found convenient to change them into thisform by convers ion . If they have not a éommonterm, s ome part of the reasoning must have beenomitted, which should be supplied before it i s sub
j ected to the strict examination of logical rule s .
Q. When willa hypothetic affirmat ive of this formbe true ?
A . I t willbe true when the extens ion of the predicate of the antecedent is contained in the extensionof the predicate of the consequent .
Q . When will a hypothetic negative be true ?
A . When the extension of the predicate of theconsequent i s contained in the ext ension of the predicate of the antecedent .
Q. Ou what principle do these rules depend ?A . Oh the aphorism mentioned in the beginningof Chap . X IX . ,
which is equally the foundation ofreasoning in hypothet ic and categorical syllogisms .
Q. What i s disj unctive syllogism ?A . That in which the maj or i s a disj unctive proposition ; as the truth of a di sj unctive propositiondepends on the subj ec t being contained in one ormore of the predi cates ; therefore, some of the partsmust be true and the rest false .
Q. How many processes of reasoning are there indisjunctive syllogisms ?
CATECH I SM or LOG I C . 65
A. Tw o : constructive and destructive ; c onstr uet ive, when from the remotion of one or more part syou argue t o the position of the rest ; destructive,when from the position of one or more parts youargue t o the remotion of the rest .
Q . Can you give me an exampleA . Disj unctz
'
ve maj or .
The world is e ither eternal, or the work of chance,or created by a Deity.
Destructive minor .
I t is neither eternal, nor the work of chance .Constructive con clus ion .
The world has been created by a D eity .
or, Construct ive minor.
The world has been created by a Deity .
Destruct it e conclusion .
I t is neither eternal nor the work of chance .
Q . On what does the validi ty of the reasoning in adisj unctive syllogism depend .
P
A . On the aphorism mentioned in Chap . X IX . , aswill evidently appear on the slightest c onsideration .
Q . What is a dilemma ?A . I t is a more compli cated form of d isj unctivesyllogisms, and partakes more directly of the natureof hypothetic syllogisms .Q. How are di lemmas divided ?A . Into constructive and destructive ; and theseagain are subdivided into s imple an d complex .
Q. What i s a s imple constructive dilemma ?A . The maj or is a c ompound hypotheti c prop os itiou, contain ing severalantecedents and a s ingleconsequent ; the m inor i s a disj unctive propos ition,
G 3
66 CATECH I SM o r LOG IC .
affirming the antecedents ; the conclusion is a cate
goricalaffirmat ion of the s ingle consequent.
Q . Can you give an example of this process ofreasoning P
A . Hyp othei t clilaj .or
If the disappearance of Chris t’s body from thesepulchre be left wholly unexplained, or if such anexplanation be given as i s wholly irrecon cileable withthe ordinary principles of human action
,we must
believe the doctrine of the resurrection .
D i sj unctive Minor.
The opponents of the doctrine are either totallys ilent, or gi ve such explanations as contradict theplainest principles of action .
CategoricalConclusion .lVe must believe the doctrine of the resurrection .
Q . What is a complex constructive dilemma .
P
A . That in 1 hich the maior has several cousequents, and the conclusion is of course disjunctive .
Q . Can you give me an example ?
A . Hyp othetic maj or.
If the conduct of general M ack at "lm was premeditated, he was a knave ; i f unpremeditated, hewas a fool .
Disj unctive minor.
I t must have been either premeditated or unpremeditated .
Disj uncti've conclus ion .
M ack was e ither a traitor or a fool .
Q. What is a simple destructive dilemma .P
A . I t differs from the constructive in the disjuncftive minor
,which removes all the antecedents ; and
carncn xsn o r LOG I C . 67
the categori cal conclusion then removes the cousequent 1.
Q . Can you give me an example .
P
A . Hyp othetic maj or .
If the Gospels be false, the evangeli sts mus t e itherhave been deceivers or dece ived .
D isj unctiee minor.
They were not deceivers (for they testified to thetruth of the ir doctrine by lives of suffering and deathsof torture) neither were they deceived (for the natur eof the facts they record preclude the poss ib ili ty o fdeception) .
Categori calconclusion .
The Gospels are not false .
Q. On what does the truth of a dilemma depend ?A . Ou the accuracy of the divi sion in the disjun ctive proposition , and in the completeness of theproof of the remotion or position of the s everal pant sin the minor ; each of wh ich parts shou ld be demonstrated by a categorical syllogism .
Q. What else do the old logi cians require in adilemma ?A . That i t shou ld be incapable of being retorted ;and of this they gave the following strange illustrat ion .
‘
A s ophist engaged to teach a pupil logic, on
the condit ion of receiving a certain sum , when thepupil should conquer him in disputation . Shieldinghimself under the terms of the agreement, the dis
Olllllllllllf1 By mak ing similar changes in the defin ition of a een
structive complex dilemma, the studen t w illhave the dcfin ’.
tion ofa destructive complex dilemma.
68 CATECH ISM or LOG I C .
c iple refused to pay for h is education, and the matterwas brought to trial before the Athenian court . Thesophis t pleaded
, If I conquer, I must be p aid by therule of court and 1f Ifail, I must be p aid by the termsof our agreement t o which the student replied, IfI conquer, I must not p ay by the rule of court and ifI
fail, I must not p ay by the terms of our agreement .
Q . I s this a necessary rule ?A .No ; for as in the case quoted, a dilemma canb e retorted only when one hypothesis i s destm ct ive
of the other .
CHAPTER XXI I I .
Of E nthymemes and a S orites .
Q . What i s an enthymeme ?A . A syllogism, of which one premise is sup
pressed .
P
Q. How may we know which premis e has beensuppressedA . If the predicate of the conclusion occurs in thepreserved premise , the minor has been suppressedif the predicate
,the maj or . But if ne ither, the en
thym em e does not form part of a s imple syllogism .
Q. How may we know to what figure of syhogismsthe enthymeme belongsA . By completing the syllogism,
and comparing itwith the general ru les .
Q. What i s a sorites ?A . I t i s a series of propositions so disposed, thatthe predicate of the first i s the subj ect of the second ;and so on in success ion, until in the conclus ion, thelas t predicate is predicated ofthe first subj ect.
CATECH I SM or LOGI C . 69
Q. Can you give me an example of a sorites ?A . Those whom God foreknew, he predestinated ;
Those whom he predestinated , he called ;Those whom he called , be ju stified ;Those whom be just ified, he glorified
Therefore,Thos e whom God foreknew, he glorified.
Q. On what does the perfection of the reasoningin a s orite s depend ?A . Ou the perfecti on _of the s imple syllog isms intowhich it is resolved .
Q. How is a sor it es resolved into syllog isms ?A . The second premise of the sorite s w illbe the
maj or of the first syllogism, and the first the minor ;the other syllogisms will have the succe ss ive propositions for their maj or premise, and the conclus ionsof the preceding syllogisms as their minors therefore ,the number of syllogisms into which a sorites is resolvable
,must be one less than the number of pre
mises in the sorite s .
Q . What are the special rules of a sor ite s ?A . The first premise alone can b e particular, andthe last alone negative .
CHAPTER XXIV
Qf S ophisms .
Q. What is a sophism ?A . Ah argument
,which under the appearance of
re ctitude, i s fallacious . A fals e argument, manifestlyv iolating the rules of syllogi sm, i s called a paralogism,
but in sophisms,the rules, though really brok en,
appear to b e preserved .
70 CATECH I SM or LOG I C .
Q . How are s ophisms divided .P
A . Into two classes s ophisms in form and sophismsin matter, termed by the old logicians, Fallacice indictione, andfallacice extra dictionem.
Q . How many spec ies of fallac ies in form wereenumerated by the old logic ians ?
A . S ix : viz .1. The fallacy of equivocation
,which consists in
using the same word in different s enses . Thus,
Roman Catholic s s ometimes endeavour t o prove, thateven Protestants acknowledge the authority of theChurch, s ince they receive the S criptures on its d athority . In the former part of the sentence
,authority
sign ifies controlling power ; in the latter, i t merelymeans evidence .2. T he fallacy of amphiboly
,or doubtful construe
t ion of a s entence . Thus, Hume’s argument againstmiracles, when he says, No evidence can prove amiracle ; for it i s contrary to experience, that amiracle should be true, but not c ontrary to experiencethat evidence should be false
,
” i s an instance of thisand the former fallacy combined ; for in the first partof the sentence
,con trary to exp erience, means,
“whollyopposed to universal experience
,
” which is a direc tassumption of the point at issue ; and in the secondpart, i t merely means, inconsistent with the personalexperience of some part i cular individual, which, fromi ts nature, every miracle must be .
3. and 4. The fallacie s of composition and division,where, from what is true of a term in its divided sense,we infer something respecting the aggregate, or thecontrary. Thus, the S toic s endeavoured to prove thedoctr ine of necess ity by the following argument
72 caraem sm or LOG I C .
which inac curate observers might be led to mistakefor th e question at i ssue . Thus , the opponents ofmachinery prove that it has inj ured some particularclasses
,not regarding that the matter really to be
decided is,whether i ts introduction has not been,
on the whole, beneficialt o the nation at large .4. The fallacy of wrong cause, or unreal s imilarity,
in which an effect i s deduced from a false source, ora cas e quoted as s imilar, which i s by no means parallel .5 . The fallacy of consequent, where s omething
is deduced which does not necessarily follow .
6 . The fallacy of assumption (p etitionis p ri —
ncip ii) ,in wh i ch the question at issue , or something inferringi t, i s as sumed as a premise . To this b elongs theargument in a circle, where two doubtful preposit ions are used to prove each other . This is a V erycommon Soph ism with popular orators , who frequently give their hearers ident ity of assertion forargument .
7. The sophism of several questions , when a s inglean swer is required to a question that may receives everal ; thus, I s it ‘
ju st to k ill a man ?” i s a ques
t ion'
which an inaccurate reasoner would promptlyanswer in the negative and subsequently be surprisedt o find that he had given up the right of self"defence,and den ied in all cases the legali ty of capital punishment .
fir
THE END. Q NGILBERT RW INGT ON, Printers, S t . John ’
s Square, London .
