Sallust - "Conspiracy of Catiline and The Jurgurthine War"

Charles Dickens - "The Cricket on the Hearth"

Burton Egbert Stevenson - "The Home Book of Verse, Volume 3"

Thomas Wentworth Higginson - "Black Rebellion"

Annual Bibliography of Commonwealth Literature 2007
This paper argues that discourses of love in Ghanaian market literature for youth offer a view into complex negotiations of agency and empowerment. Drawing on Deborah Durham's notion of youth as "social `shifters'" and Francis Nyamnjoh's conception of the "interconnectedness" of agency, I take Ghanaian market literature as one specific case of how African literature for youth foregrounds questions of continuity and change as African societies enter into increasingly complex global relations. In this literature for youth, received notions of love, often constructed out of impressions from American pop and hip hop music, carry new notions of agency that compete with existing "domesticated" forms. Authors like Ike Tandoh and Evelyn Tay employ discourses of love to offer youth alternative avenues for empowerment in a context of socio-economic disenfranchizement. In a creative process of "straddling", this writing both reveals and reproduces the contradictions that obtain in youth configurations of agency.

Deductive Logic

S >> St. George Stock >> Deductive Logic





FIGURE II.

624. The rule that one premiss must be negative excludes four moods,
namely, AAA, AAI, AII, IAI. The rule that the major must be universal
excludes OAO. Thus we are left with six moods which are valid in the
second figure, namely,

EAE. AEE. EIO. AOO. EAO. AEO.


FIGURE III.

625. The rule that the conclusion must be particular confines us to
eight moods, two of which, namely AEE and AOO, are excluded by the
rule that the minor premiss must be affirmative.

Thus we are left with six moods which are valid in the third figure,
namely,

AAI. IAI. AII. EAO. OAO. EIO.


FIGURE IV.

626. The first of the eleven moods, AAA, is excluded by the rule
that the conclusion cannot be a universal affirmative.

Two more moods, namely AOO and OAO, are excluded by the rule that
neither of the premisses can be a particular negative.

AII violates the rule that when the major premiss is affirmative, the
minor must be universal.

EAE violates the rule that, when the minor premiss is affirmative, the
conclusion must be particular. Thus we are left with six moods which
are valid in the fourth figure, namely,

AAI. AEE. IAI. EAO. EIO. AEO.

627. Thus the 256 possible forms of syllogism have been reduced to
two dozen legitimate combinations of mood and figure, six moods being
valid in each of the four figures.

FIGURE I. AAA. EAE. AII. EIO. (AAI. EAO.)

FIGURE II. EAE. AEE. EIO. AGO. (EAO. AEO.)

FIGURE III. AAI. IAI. AII. EAO. OAO. EIO.

FIGURE IV. AAI. AEE. IAI. EAO. EIO. (AEO.)

628. The five moods enclosed in brackets, though valid, are
useless. For the conclusion drawn is less than is warranted by the
premisses. These are called Subaltern Moods, because their conclusions
might be inferred by subalternation from the universal conclusions
which can justly be drawn from the same premisses. Thus AAI is
subaltern to AAA, EAO to EAE, and so on with the rest.

629. The remaining 19 combinations of mood and figure, which are
loosely called 'moods,' though in strictness they should be called
'figured moods,' are generally spoken of under the names supplied by
the following mnemonics--

Barbara, Celarent, Darii, Ferioque prioris;
Cesare, Camestres, Festino, Baroko secundae;
Tertia Darapti, Disamis, Datisi, Felapton,
Bokardo, Ferison habet; Quarta insuper addit
Bramantip, Camenes, Dimaris, Fesapo, Fresison:
Quinque Subalterni, totidem Generalibus orti,
Nomen habent nullum, nee, si bene colligis, usum.

630. The vowels in these lines indicate the letters of the mood. All
the special rules of the four figures can be gathered from an
inspection of them. The following points should be specially noted.

The first figure proves any kind of conclusion, and is the only one
which can prove A.

The second figure proves only negatives.

The third figure proves only particulars.

The fourth figure proves any conclusion except A.

631. The first figure is called the Perfect, and the rest the
Imperfect figures. The claim of the first to be regarded as the
perfect figure may be rested on these grounds--

1. It alone conforms directly to the Dictum de Omni et Nullo.

2. It suffices to prove every kind of conclusion, and is the only
figure in which a universal affirmative proposition can be
established.

3. It is only in a mood of this figure that the major, middle and
minor terms are to be found standing in their relative order of
extension.

632. The reason why a universal affirmative, which is of course
infinitely the most important form of proposition, can only be proved
in the first figure may be seen as follows.

_Proof that A can only be established in figure I._

An A conclusion necessitates both premisses being A propositions (by
Rule 7). But the minor term is distributed in the conclusion, as being
the subject of an A proposition, and must therefore be distributed in
the minor premiss, in order to which it must be the subject. Therefore
the middle term must be the predicate and is consequently
undistributed. In order therefore that the middle term may be
distributed, it must be subject in the major premiss, since that also
is an A proposition. But when the middle term is subject in the major
and predicate in the minor premiss, we have what is called the first
figure.




CHAPTER XV.

_Of the Special Canons of the Four Figures._


633. So far we have given only a negative test of legitimacy, having
shown what moods are not invalidated by running counter to any of the
special rules of the four figures. We will now lay down special canons
for the four figures, conformity to which will serve as a positive
test of the validity of a given mood in a given figure. The special
canon of the first figure--will of course be practically equivalent to
the Dictum de Omni et Nullo. All of them will be expressed in terms of
extension, for the sake of perspicuity.



_Special Canons of the Four Figures._


FIGURE 1.

634. CANON. If one term wholly includes or excludes another, which
wholly or partly includes a third, the first term wholly or partly
includes or excludes the third.

Here four cases arise--

[Illustration]

(1) Total inclusion (Barbara).

All B is A.
All C is B.
.'. All C is A.


[Illustration]

(2) Partial inclusion (Darii).

All B is A.
Some C is B.
.'. Some C is A.


[Illustration]

(3) Total exclusion (Celarent).

No B is A.
All C is B.
.'. No C is A.


[Illustration]

(4) Partial exclusion (Ferio).

No B is A.
Some C is B.
.'. Some C is not A.

FIGURE II.

635. CANON. If one term is excluded from another, which wholly or
partly includes a third, or is included in another from which a third
is wholly or partly excluded, the first is excluded from the whole or
part of the third.

Here we have four cases, all of exclusion--

(1) Total exclusion on the ground of inclusion in an excluded term
(Cesare).

[Illustration]

No A is B.
All C is B.
.'. No C is A.

(2) Partial exclusion on the ground of a similar partial inclusion
(Festino).

[Illustration]

No A is B.
Some C is B.
.'. Some C is not A.

(3) Total exclusion on the ground of exclusion from an including
term (Camestres).

[Illustration]

All A is B.
No C is B.
.'. No C is A.

(4) Partial exclusion on the ground of a similar partial exclusion
(Baroko).

[Illustration]

All A is B.
Some C is not B.
.'. Some C is not A.

FIGURE III.

636. CANON. If two terms include another term in common, or if the
first includes the whole and the second a part of the same term, or
vice versa, the first of these two terms partly includes the second;
and if the first is excluded from the whole of a term which is wholly
or in part included in the second, or is excluded from part of a term
which is wholly included in the second, the first is excluded from
part of the second.

Here it is evident from the statement that six cases arise--

(1) Total inclusion of the same term in two others
(Darapti).

[Illustration]

All B is A.
All B is C.
.'. some C is A.

(2) Total inclusion in the first and partial inclusion
in the second (Datisi).

[Illustration]

All B is A.
Some B is C.
.'. some C is A.

(3) Partial inclusion in the first and total inclusion in
the second (Disamis).

[Illustration]

Some B is A.
All B is C.
.'. some C is A.

(4) Total exclusion of the first from a term which is
wholly included in the second (Felapton).

[Illustration]

No B is A.
All B is C.
.'. some C is not A.

(5) Total exclusion of the first from a term which is
partly included in the second (Ferison).

[Illustration]

No B is A.
Some B is C.
.'. some C is not A.

(6) Exclusion of the first from part of a term which
is wholly included in the second (Bokardo).

[Illustration]

Some B is not A.
All B is C.
.'. Some C is not A.

FIGURE IV.

637. CANON. If one term is wholly or partly included in another
which is wholly included in or excluded from a third, the third term
wholly or partly includes the first, or, in the case of total
inclusion, is wholly excluded from it; and if a term is excluded from
another which is wholly or partly included in a third, the third is
partly excluded from the first.

Here we have five cases--

(1) Of the inclusion of a whole term (Bramsntip).

[Illustration]
All A is B.
All B is C.
.'. Some C is (all) A.

(2) Of the inclusion of part of a term (DIMARIS).

[Illustration]

Some A is B.
All B is C.
.'. Some C is (some) A,

(3) Of the exclusion of a whole term (Camenes).

[Illustration]

All A is B.
No B is C.
.'. No C is A.

(4) Partial exclusion on the ground of including
the whole of an excluded term (Fesapo).

[Illustration]

No A is B.
All B is C.
.'. Some C is not A.

(5) Partial exclusion on the ground of including
part of an excluded term (Fresison).

[Illustration]

No A is B.
Some B is C.
.'. Some C is not A.

638. It is evident from the diagrams that in the subaltern moods the
conclusion is not drawn directly from the premisses, but is an
immediate inference from the natural conclusion. Take for instance AAI
in the first figure. The natural conclusion from these premisses is
that the minor term C is wholly contained in the major term A. But
instead of drawing this conclusion we go on to infer that something
which is contained in C, namely some C, is contained in A.

[Illustration]

All B is A.
All C is B.
.'. all C is A.
.'. some C is A.

Similarly in EAO in figure 1, instead of arguing that the whole of C
is excluded from A, we draw a conclusion which really involves a
further inference, namely that part of C is excluded from A.

[Illustration]

No B is A.
All C is B.
.'. no C is A.
.'. some C is not A.

639. The reason why the canons have been expressed in so cumbrous a
form is to render the validity of all the moods in each figure at once
apparent from the statement. For purposes of general convenience they
admit of a much more compendious mode of expression.

640. The canon of the first figure is known as the Dictum de Omni et
Nullo--

What is true (distributively) of a whole term is true of all that it
includes.

641. The canon of the second figure is known as the Dictum de
Diverse--

If one term is contained in, and another excluded from a third term,
they are mutually excluded.

642. The canon of the third figure is known as the Dictum de Exemplo
et de Excepto--

Two terms which contain a common part partly agree, or, if one
contains a part which the other does not, they partly differ.

643. The canon of the fourth figure has had no name assigned to it,
and does not seem to admit of any simple expression. Another mode of
formulating it is as follows:--

Whatever is affirmed of a whole term may have partially affirmed of
it whatever is included in that term (Bramantip, Dimaris), and
partially denied of it whatever is excluded (Fesapo); whatever is
affirmed of part of a term may have partially denied of it whatever
is wholly excluded from that term (Fresison); and whatever is denied
of a whole term may have wholly denied of it whatever is wholly
included in that term (Camenes).

644. From the point of view of intension the canons of the first
three figures may be expressed as follows.

645. Canon of the first figure. Dictum de Omni et Nullo--

An attribute of an attribute of anything is an attribute of the
thing itself.

646. Canon of the second figure. Dictum de Diverso--

If a subject has an attribute which a class has not, or vice versa,
the subject does not belong to the class.

647. Canon of the third figure.

1. Dictum de Exemplo--

If a certain attribute can be affirmed of any portion of the
members of a class, it is not incompatible with the distinctive
attributes of that class.

2. Dictum de Excepto--

If a certain attribute can be denied of any portion of the members
of a class, it is not inseparable from the distinctive attributes
of that class.




CHAPTER XVI.

_Of the Special Uses of the Four Figures._


648. The first figure is useful for proving the properties of a
thing.

649. The second figure is useful for proving distinctions between
things.

650. The third figure is useful for proving instances or exceptions.

651. The fourth figure is useful for proving the species of a genus.

FIGURE 1.

652.

B is or is not A.
C is B.
.'. C is or is not A.

We prove that C has or has not the property A by predicating of it B,
which we know to possess or not to possess that property.

Luminous objects are material.
Comets are luminous.
.'. Comets are material.

No moths are butterflies.
The Death's head is a moth.
.'. The Death's head is not a butterfly.

FIGURE II.

653.

A is B. A is not B.
C is not B. C is B.
.'. C is not A. .'. C is not A.

We establish the distinction between C and A by showing that A has an
attribute which C is devoid of, or is devoid of an attribute which C
has.

All fishes are cold-blooded.
A whale is not cold-blooded.
.'. A whale is not a fish.

No fishes give milk.
A whale gives milk.
.'. A whale is not a fish.

FIGURE III.

654.

B is A. B is not A.
B is C. B is C.
.'. Some C is A. .'. Some C is not A.

We produce instances of C being A by showing that C and A meet, at all
events partially, in B. Thus if we wish to produce an instance of the
compatibility of great learning with original powers of thought, we
might say

Sir William Hamilton was an original thinker.
Sir William Hamilton was a man of great learning.
.'. Some men of great learning are original thinkers.

Or we might urge an exception to the supposed rule about Scotchmen
being deficient in humour under the same figure, thus--

Sir Walter Scott was not deficient in humour.
Sir Walter Scott was a Scotchman.
.'. Some Scotchmen are not deficient in humour.

FIGURE IV.

655.

All A is B, No A is B.
All B is C. All B is C.
.'. Some C is A .'.Some C is not A.

We show here that A is or is not a species of C by showing that A
falls, or does not fall, under the class B, which itself falls under
C. Thus--

All whales are mammals.
All mammals are warm-blooded.
.'. Some warm-blooded animals are whales.
No whales are fishes.
All fishes are cold-blooded.
.'. Some cold-blooded animals are not whales.




CHAPTER XVII.

_Of the Syllogism with three figures._

656. It will be remembered that in beginning to treat of figure (
565) we pointed out that there were either four or three ligures
possible according as the conclusion was assumed to be known or
not. For, if the conclusion be not known, we cannot distinguish
between the major and the minor term, nor, consequently, between one
premiss and another. On this view the first and the fourth figures are
the same, being that arrangement of the syllogism in which the middle
term occupies a different position in one premiss from what it does in
the other. We will now proceed to constitute the legitimate moods and
figures of the syllogism irrespective of the conclusion.

657. When the conclusion is set out of sight, the number of possible
moods is the same as the number of combinations that can be made of
the four things, A, E, I, O, taken two together, without restriction
as to repetition. These are the following 16:--

AA EA IA OA
AE -EE- IE -OE-
AI EI -II- -OI-
AO -EO- -IO- -OO-

of which seven may be neglected as violating the general rules of the
syllogism, thus leaving us with nine valid moods--

AA. AE. AI. AO. EA. EI. IA. IE. OA.

658. We will now put these nine moods successively into the three
figures. By so doing it will become apparent how far they are valid in
each.

659. Let it be premised that

when the extreme in the premiss that stands first is predicate in
the conclusion, we are said to have a Direct Mood;

when the extreme in the premiss that stands second is predicate in
the conclusion, we are said to have an Indirect Mood.

660. FIGURE 1.

_Mood AA._
All B is A.
All C is B.
.'. All C is A, or Some A is C, (Barbara & Bramantip).

_Mood AE._
All B is A.
No C is B.
.'. Illicit Process, or Some A is not C, (Fesapo).

_Mood AI._
All B is A.
Some C is B.
.'. Some C is A, or Some A is C. (Darii & Disamis).

_Mood AO._
All B is A.
Some C is not B.
.'. Illicit Process, (Ferio).

_Mood EA._
No B is A.
All C is B.
.'. No C is A, or No A is C, (Celarent & Camenes).

_Mood EI._
No B is A.
Some C is B.
.'. Some C is not A, or Illicit Process.

_Mood IA._
Some B is A.
All C is B.
.'. Undistributed Middle.

_Mood IE._
Some B is C. Some B is not A.
No A is B. All C is B.
.'. Illicit Process, or Some C is not A, (Fresison).

_Mood OA._
Some B is not A.
All C is B.
.'. Undistributed Middle.

661. Thus we are left with six valid moods, which yield four direct
conclusions and five indirect ones, corresponding to the four moods of
the original first figure and the five moods of the original fourth,
which appear now as indirect moods of the first figure.

662. But why, it maybe asked, should not the moods of the first
figure equally well be regarded as indirect moods of the fourth? For
this reason-that all the moods of the fourth figure can be elicited
out of premisses in which the terms stand in the order of the first,
whereas the converse is not the case. If, while retaining the quantity
and quality of the above premisses, i. e. the mood, we were in each
case to transpose the terms, we should find that we were left with
five valid moods instead of six, since AI in the reverse order of the
terms involves undistributed middle; and, though we should have
Celarent indirect to Camenes, and Darii to Dimaris, we should never
arrive at the conclusion of Barbara or have anything exactly
equivalent to Ferio. In place of Barbara, Bramantip would yield as an
indirect mood only the subaltern AAI in the first figure. Both Fesapo
and Fresison would result in an illicit process, if we attempted to
extract the conclusion of Ferio from them as an indirect mood. The
nearest approach we could make to Ferio would be the mood EAO in the
first figure, which may be elicited indirectly from the premisses of
CAMENES, being subaltern to CELARENT. For these reasons the moods of
the fourth figure are rightly to be regarded as indirect moods of the
first, and not vice versa.

$663. FIGURE II.


_Mood AA._
All A is B.
All C is B.
.'. Undistributed Middle.

_Mood AE._
All A is B.
No C is B.
.'. No C is A, or No A is C, (Camestres & Cesare).

_Mood AI._
All A is B.
Some C is B.
.'. Undistributed Middle.

_Mood AO._
All A is B.
Some C is not B.
.'. Some C is not A, (Baroko), or Illicit Process.

_Mood EA._
No A is B.
All C is B.
.'. No C is A, or No A is C, (Cesare & Carnestres).


_Mood EI_
No A is B.
Some C is B.
.'. Some C is not A, (Festino), or Illicit Process.

_Mood IA._
Some A is B.
All C is B.
.'. Undistributed Middle.

_Mood IE._
Some A is B.
No C is B.
.'. Illicit Process, or Some A is not C, (Festino).

_Mood OA._
Some A is not B.
All C is B.
.'. Illicit Process, or Some A is not C, (Baroko).

664. Here again we have six valid moods, which yield four direct
conclusions corresponding to Cesare, CARNESTRES, FESTINO and
BAROKO. The same four are repeated in the indirect moods.

665. FIGURE III.

_Mood AA._
All B is A.
All B is C.
.'. Some C is A, or Some A is C, (Darapti).

_Mood AE._
All B is A.
No B is C.
.'. Illicit Process, or Some A is not C, (Felapton).

_Mood AI._
All B is A,
Some B is C.
.'. Some C is A, or Some A is C, (Datisi & Disamis).

_Mood AO._
All B is A.
Some B is not C.
.'. Illicit Process, Or Some A is not C, (Bokardo).

_Mood EA._
No B is A.
All B is C.
.'. Some C is not A, (Felapton), or Illicit Process.

_Mood EI._
No B is A.
Some B is C.
.'. Some C is not A, (Ferison), or Illicit Process.

_Mood IA._
Some B is A.
All B is C.
.'. Some C is A, Or Some A is C, (Disamis & Datisi).

_Mood IE._
Some B is A.
No B is C.
.'. Illicit Process, or Some A is not C, (Ferison).

_Mood QA._
Some B is not A.
All B is C.
.'. Some C is not A, (Bokardo), or Illicit Process.

666. In this figure every mood is valid, either directly or
indirectly. We have six direct moods, answering to Darapti, Disamis,
Datisi, Felapton, Bokardo and Ferison, which are simply repeated by
the indirect moods, except in the case of Darapti, which yields a
conclusion not provided for in the mnemonic lines. Darapti, though
going under one name, has as much right to be considered two moods as
Disamis and Datisi.




CHAPTER XVIII.

_Of Reduction._


667. We revert now to the standpoint of the old logicians, who
regarded the Dictum de Omni et Nullo as the principle of all
syllogistic reasoning. From this point of view the essence of mediate
inference consists in showing that a special case, or class of cases,
comes under a general rule. But a great deal of our ordinary reasoning
does not conform to this type. It was therefore judged necessary to
show that it might by a little manipulation be brought into conformity
with it. This process is called Reduction.

668. Reduction is of two kinds--

(1) Direct or Ostensive.

(2) Indirect or Ad Impossibile.

669. The problem of direct, or ostensive, reduction is this--

Given any mood in one of the imperfect figures (II, III and IV) how
to alter the form of the premisses so as to arrive at the same
conclusion in the perfect figure, or at one from which it can be
immediately inferred. The alteration of the premisses is effected by
means of immediate inference and, where necessary, of transposition.

670. The problem of indirect reduction, or reductio (per
deductionem) ad impossibile, is this--Given any mood in one of the
imperfect figures, to show by means of a syllogism in the perfect
figure that its conclusion cannot be false.

671. The object of reduction is to extend the sanction of the Dictum
de Omni et Nullo to the imperfect figures, which do not obviously
conform to it.

672. The mood required to be reduced is called the Reducend; that to
which it conforms, when reduced, is called the Reduct.



_Direct or Ostensive Reduction._


673. In the ordinary form of direct reduction, the only kind of
immediate inference employed is conversion, either simple or by
limitation; but the aid of permutation and of conversion by negation
and by contraposition may also be resorted to.

674. There are two moods, Baroko and Bokardo, which cannot be
reduced ostensively except by the employment of some of the means last
mentioned. Accordingly, before the introduction of permutation into
the scheme of logic, it was necessary to have recourse to some other
expedient, in order to demonstrate the validity of these two
moods. Indirect reduction was therefore devised with a special view to
the requirements of Baroko and Bokardo: but the method, as will be
seen, is equally applicable to all the moods of the imperfect figures.

675. The mnemonic lines, 'Barbara, Celarent, etc., provide complete
directions for the ostensive reduction of all the moods of the second,
third, and fourth figures to the first, with the exception of Baroko
and Bokardo. The application of them is a mere mechanical trick, which
will best be learned by seeing the process performed.

676. Let it be understood that the initial consonant of each name of
a figured mood indicates that the reduct will be that mood which
begins with the same letter. Thus the B of Bramantip indicates that
Bramantip, when reduced, will become Barbara.

677. Where m appears in the name of a reducend, me shall have to
take as major that premiss which before was minor, and vice versa-in
other words, to transpose the premisses, m stands for mutatio or
metathesis.

678. s, when it follows one of the premisses of a reducend,
indicates that the premiss in question must be simply converted; when
it follows the conclusion, as in Disamis, it indicates that the
conclusion arrived at in the first figure is not identical in form
with the original conclusion, but capable of being inferred from it by
simple conversion. Hence s in the middle of a name indicates something
to be done to the original premiss, while s at the end indicates
something to be done to the new conclusion.

679. P indicates conversion per accidens, and what has just been
said of s applies, mutatis mutandis, to p.

680. k may be taken for the present to indicate that Baroko and
Bokardo cannot be reduced ostensively.

681. FIGURE II.

Cesare. \ / Celarent.
No A is B. \ = / No B is A.
All C is B. / \ All C is B.
.'. No C is A. / \ .'. No C is A.

Copyright (c) 2007. topboookz.com. All rights reserved.