Theodor Mommsen - "Römische Geschichte Book 1"

Walt Whitman - "Drum Taps"

Wilhelm Ruland - "Legends of the Rhine"

Elinor Glyn - "The Damsel and the Sage"

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




(2). _Simple Destructive_.

If I go to Town, I must pay for my ticket and pay my hotel bill.
Either I cannot pay for my ticket or I cannot pay my hotel bill.
.'. I cannot go to Town.

(3). _Complex Constructive_.

If I stay in this room, I shall be burnt to death, and if I jump
out of the window, I shall break my neck.
I must either stay in the room or jump out of the window.
.'. I must either be burnt to death or break my neck.

(4). _Complex Destructive_.

If he were clever, he would see his mistake; and
if he were candid, he would acknowledge it.
Either he does not see his mistake or he will not acknowledge it.
.'. Either he is not clever or he is not candid.

784. It must be noticed that the simple destructive dilemma would
not admit of a disjunctive consequent. If we said,

If A is B, either C is D or E is F,
Either C is not D or E is not F,

we should not be denying the consequent. For 'E is not F' would make
it true that C is D, and 'C is not D' would make it true that E is F;
so that in either case we should have one of the alternatives true,
which is just what the disjunctive form 'Either C is D or E is F'
insists upon.

785. In the case of the complex constructive dilemma the several
members, instead of being distributively assigned to one another, may
be connected together as a whole--thus--

If either A is B or E is F, either C is D or G is H.
Either A is B or E is F.
.'. Either C is D or G is H.

In this shape the likeness of the dilemma to the partly conjunctive
syllogism is more immediately recognisable. The major premiss in this
shape is vaguer than in the former. For each antecedent has now a
disjunctive choice of consequents, instead of being limited to
one. This vagueness, however, does not affect the conclusion. For, so
long as the conclusion is established, it does not matter from which
members of the major its own members flow.

786. It must be carefully noticed that we cannot treat the complex
destructive dilemma in the same way.

If either A is B or E is F, either C is D or G is H.
Either C is not D or G is not H.

Since the consequents are no longer connected individually with the
antecedents, a disjunctive denial of them leaves it still possible for
the antecedent as a whole to be true. For 'C is not D' makes it true
that G is H, and 'G is not H' makes it true that C is D. In either
case then one is true, which is all that was demanded by the
consequent of the major. Hence the consequent has not really been
denied.

787. For the sake of simplicity we have limited the examples to the
case of two antecedents or consequents. But we may have as many of
either as we please, so as to have a Trilemma, a Tetralemma, and so
on.

TRILEMMA.

If A is B, C is D; and if E is F, G is H; and if K is L, M is N.
Either A is B or E is F or K is L.
.'. Either C is D or G is H or K is L.

788. Having seen what the true dilemma is, we shall now examine some
forms of reasoning which resemble dilemmas without being so.

789. This, for instance, is not a dilemma--

If A is B or if E is F, C is D.
But A is B and E is F.
.'. C is D.

If he observes the sabbath or if he refuses to eat pork, he is a
Jew.
But he both observes the sabbath and refuses to eat pork.
.'. He is a Jew.

What we have here is a combination of two partly conjunctive
syllogisms with the same conclusion, which would have been established
by either of them singly. The proof is redundant.

790. Neither is the following a dilemma--

If A is B, C is D and E is F.
Neither C is D nor E is F.
.'. A is not B.

If this triangle is equilateral, its sides and its angles will be
equal.
But neither its sides nor its angles are equal.
.'. It is not equilateral.

This is another combination of two conjunctive syllogisms, both
pointing to the same conclusion. The proof is again redundant. In this
case we have the consequent denied in both, whereas in the former we
had the antecedent affirmed. It is only for convenience that such
arguments as these are thrown into the form of a single
syllogism. Their real distinctness may be seen from the fact that we
here deny each proposition separately, thus making two independent
statements--C is not D and E is not F. But in the true instance of the
simple destructive dilemma, what we deny is not the truth of the two
propositions contained in the consequent, but their compatibility; in
other words we make a disjunctive denial.

791. Nor yet is the following a dilemma--

If A is B, either C is D or E is F.
Neither C is D nor E is F.
.'. A is not B.

If the barometer falls there will be either wind or rain.
There is neither wind nor rain.
.'. The barometer has not fallen.

What we have here is simply a conjunctive major with the consequent
denied in the minor. In the consequent of the major it is asserted
that the two propositions, 'C is D' and 'E is F' cannot both be false;
and in the minor this is denied by the assertion that they are both
false.

792. A dilemma is said to be rebutted or retorted, when another
dilemma is made out proving an opposite conclusion. If the dilemma be
a sound one, and its premisses true, this is of course impossible, and
any appearance of contradiction that may present itself on first sight
must vanish on inspection. The most usual mode of rebutting a dilemma
is by transposing and denying the consequents in the major--

If A is B, C is D; and if E is F, G is H.
Either A is B or E is F.
.'. Either C is D or G is H.

The same rebutted--

If A is B, G is not H; and if E is F, C is not D.
Either A is B or E is F.
.'. Either G is not H or C is not D.
= Either C is not D or G is not H.

793. Under this form comes the dilemma addressed by the Athenian
mother to her son--'Do not enter public life: for, if you say what is
just, men will hate you; and, if you say what is unjust, the gods will
hate you' to which the following retort was made--'I ought to enter
public life: for, if 1 say what is just, the gods will love me; and,
if 1 say what is unjust, men will love me.' But the two conclusions
here are quite compatible. A man must, on the given premisses, be both
hated and loved, whatever course he takes. So far indeed are two
propositions of the form

Either C is D or G is H,
and Either C is not D or G is not H,

from being incompatible, that they express precisely the same thing
when contradictory alternatives have been selected, e.g.--

Either a triangle is equilateral or non-equilateral.
Either a triangle is non-equilateral or equilateral.

794. Equally illusory is the famous instance of rebutting a dilemma
contained in the story of Protagoras and Euathlus
(Aul. Gell. Noct. Alt. v. 10), Euathlus was a pupil of Protagoras in
rhetoric. He paid half the fee demanded by his preceptor before
receiving lessons, and agreed to pay the remainder when he won his
first case. But as he never proceeded to practise at the bar, it
became evident that he meant to bilk his tutor. Accordingly Protagoras
himself instituted a law-suit against him, and in the preliminary
proceedings before the jurors propounded to him the following
dilemma--'Most foolish young man, whatever be the issue of this suit,
you must pay me what I claim: for, if the verdict be given in your
favour, you are bound by our bargain; and if it be given against you,
you are bound by the decision of the jurors.' The pupil, however, was
equal to the occasion, and rebutted the dilemma as follows. 'Most
sapient master, whatever be the issue of this suit, I shall not pay
you what you claim: for, if the verdict be given in my favour, I am
absolved by the decision of the jurors; and, if it be given against
me, I am absolved by our bargain.' The jurors are said to have been so
puzzled by the conflicting plausibility of the arguments that they
adjourned the case till the Greek Kalends. It is evident, however,
that a grave injustice was thus done to Protagoras. His dilemma was
really invincible. In the counter-dilemma of Euathlus we are meant to
infer that Protagoras would actually lose his fee, instead of merely
getting it in one way rather than another. In either case he would
both get and lose his fee, in the sense of getting it on one plea, and
not getting it on another: but in neither case would he actually lose
it.

795. If a dilemma is correct in form, the conclusion of course
rigorously follows: but a material fallacy often underlies this form
of argument in the tacit assumption that the alternatives offered in
the minor constitute an exhaustive division. Thus the dilemma 'If pain
is severe, it will be brief; and if it last long it will be slight,'
&c., leaves out of sight the unfortunate fact that pain may both be
severe and of long continuance. Again the following dilemma--

If students are idle, examinations are unavailing; and, if
they are industrious, examinations are superfluous,
Students are either idle or industrious,
.'. Examinations are either unavailing or superfluous,

is valid enough, so far as the form is concerned. But the person who
used it would doubtless mean to imply that students could be
exhaustively divided into the idle and the industrious. No deductive
conclusion can go further than its premisses; so that all that the
above conclusion can in strictness be taken to mean is that
examinations are unavailing, when students are idle, and superfluous,
when they are industrious--which is simply a reassertion as a matter
of fact of what was previously given as a pure hypothesis.




CHAPTER XXVII.

_Of the Reduction of the Dilemma._


796. As the dilemma is only a peculiar variety of the partly
conjunctive syllogism, we should naturally expect to find it reducible
in the same way to the form of a simple syllogism. And such is in fact
the case. The constructive dilemma conforms to the first figure and
the destructive to the second.

1) _Simple Constructive Dilemma_.

Barbara.
If A is B or if E is F, C is D. All cases of either A being B or E
being F are cases of C being D.
Either A is B or E is F. All actual cases are cases of either
A being B OP E being F.
.'. C is D. .'. All actual cases are cases of C
being D.

(2) _Simple Destructive_.

Camstres.
If A is B, C is D and E is F. All cases of A being B are cases of
C being D and E being F.
Either C is not D or E is not F. No actual cases are cases of C being
D and E being F.
.'. A is not B. .'. No actual cases are cases of A
being B.

(3) _Complex Constructive_.
Barbara.
If A is B, C is D; and if E is F, All cases of either A being B or
G is H. being F are cases of either C being
D or G being H.
Either A is B or E is F. All actual cases are cases of either A
being B or E being F.
.'. Either C is D or G is H. .'. All actual cases are cases of either C
being D or G being H.

(4) _Complex Destructive_.

If A is B, C is D; and if E is F, All cases of A being B and E being F
G is H. are cases of C being D and G
being H.
Either C is not D Or G is No actual cases are cases of C being
not H D and G being H.
Either A is not B or E is No actual cases are cases of A being
not F. B and E being F.

797. There is nothing to prevent our having Darii, instead of
Barbara, in the constructive form, and Baroko, instead of Camestres,
in the destructive. As in the case of the partly conjunctive syllogism
the remaining moods of the first and second figure are obtained by
taking a negative proposition as the consequent of the major premiss,
e.g.--

_Simple Constructive_. Celarent or Ferio.
If A is B or if E is F, C is not D No cases of either A being B or E
being F are cases of C being D.
Either A is B or E is F. All (or some) actual cases are cases of
either A being B or E being F
.'. C is not D. .'. All (or some) actual cases are not
cases of C being D.




CHAPTER XXVIII.

_Of the Dilemma regarded as an Immediate Inference._


798. Like the partly conjunctive syllogism, the dilemma can be
expressed under the forms of immediate inference. As before, the
conclusion in the constructive type resolves itself into the
subalternate of the major itself, and in the destructive type into the
subalternate of its contrapositive. The simple constructive dilemma,
for instance, may be read as follows--

If either A is B or E is F, C is D,
.'. Either A being B or E being F, C is D,

which is equivalent to

Every case of either A being B or E being F is a case of C being D.
.'. Some case of either A being B or E being F is a case of C being D.

The descent here from 'every' to 'some' takes the place of the
transition from hypothesis to fact.

799. Again the complex destructive may be read thus--

If A is B, C is D; and if E is F, G is H,
.'. It not being true that C is D and G is H, it is not
true that A is B and E is F,

which may be resolved into two steps of immediate inference, namely,
conversion by contraposition followed by subalternation--

All cases of A being B and E being F are cases of C being D and G
being H.
.'. Whatever is not a case of C being D and G being H is not a case
of A being B and E being F.
.'. Some case which is not one of C being D and G being H is not a
case of A being B and E being F.




CHAPTER XXIX.

_Of Trains of Reasoning._


800. The formal logician is only concerned to examine whether the
conclusion duly follows from the premisses: he need not concern
himself with the truth or falsity of his data. But the premisses of
one syllogism may themselves be conclusions deduced from other
syllogisms, the premisses of which may in their turn have been
established by yet earlier syllogisms. When syllogisms are thus linked
together we have what is called a Train of Reasoning.

801. It is plain that all truths cannot be established by
reasoning. For the attempt to do so would involve us in an infinite
regress, wherein the number of syllogisms required would increase at
each step in a geometrical ratio. To establish the premisses of a
given syllogism we should require two preceding syllogisms; to
establish their premisses, four; at the next step backwards, eight; at
the next, sixteen; and so on ad infinitum. Thus the very possibility
of reasoning implies truths that are known to us prior to all
reasoning; and, however long a train of reasoning may be, we must
ultimately come to truths which are either self-evident or are taken
for granted.

802. Any syllogism which establishes one of the premisses of another
is called in reference to that other a Pro-syllogism, while a
syllogism which has for one of its premisses the conclusion of another
syllogism is called in reference to that other an Epi-syllogism.



_The Epicheirema_.


803. The name Epicheirema is given to a syllogism with one or both
of its premisses supported by a reason. Thus the following is a
double epicheirema--

All B is A, for it is E.
All C is B, for it is F.
.'. All C is A.

All virtue is praiseworthy, for it promotes the general welfare.
Generosity is a virtue, for it prompts men to postpone self to others.
.'. Generosity is praiseworthy.

804. An epicheirema is said to be of the first or second order
according as the major or minor premiss is thus supported. The double
epicheirema is a combination of the two orders.

805. An epicheirema, it will be seen, consists of one syllogism
fully expressed together with one, or, it may be, two enthymemes (
557). In the above instance, if the reasoning which supports the
premisses were set forth at full length, we should have, in place of
the enthymemes, the two following pro-syllogisms--

(i) All E is A.
All B is E.
.'. All B is A.

Whatever promotes the general welfare is praiseworthy.
Every virtue promotes the general welfare.
.'. Every virtue is praiseworthy.

(2) All F is B.
All C is F.
.'. All C is B.

Whatever prompts men to postpone self to others is a virtue.
Generosity prompts men to postpone self to others.
.'. Generosity is a virtue.

806. The enthymemes in the instance above given are both of the
first order, having the major premiss suppressed. But there is
nothing to prevent one or both of them from being of the second
order--

All B is A, because all F is.
All C is B, because all F is.
.'. All C is A.

All Mahometans are fanatics, because all Monotheists are.
These men are Mahometans, because all Persians are.
.'. These men are fanatics.

Here it is the minor premiss in each syllogism that is suppressed,
namely,

(1) All Mahometans are Monotheists.

(2) These men are Persians.



_The Sorites_.


807. The Sorites is the neatest and most compendious form that can
be assumed by a train of reasoning.

808. It is sometimes more appropriately called the chain-argument,
and map be defined as--

A train of reasoning, in which one premiss of each epi-syllogism is
supported by a pro-syllogism, the other being taken for granted.

This is its inner essence.

809. In its outward form it may be described as--A series of
propositions, each of which has one term in common with that which
preceded it, while in the conclusion one of the terms in the last
proposition becomes either subject or predicate to one of the terms in
the first.

810. A sorites may be either--

(1) Progressive,

or (2) Regressive.

_Progressive Sorites_.

All A is B.
All B is C.
All C is D.
All D is E.
.'. All A is E.

_Regressive Sorites_.

All D is E.
All C is D.
All B is C.
All A is B.
.'. All A is E.

811. The usual form is the progressive; so that the sorites is
commonly described as a series of propositions in which the predicate
of each becomes the subject of the next, while in the conclusion the
last predicate is affirmed or denied of the first subject. The
regressive form, however, exactly reverses these attributes; and would
require to be described as a series of propositions, in which the
subject of each becomes the predicate of the next, while in the
conclusion the first predicate is affirmed or denied of the last
subject.

812. The regressive sorites, it will be observed, consists of the
same propositions as the progressive one, only written in reverse
order. Why then, it may be asked, do we give a special name to it,
though we do not consider a syllogism different, if the minor premiss
happens to precede the major? It is because the sorites is not a mere
series of propositions, but a compressed train of reasoning; and the
two trains of reasoning may be resolved into their component
syllogisms in such a manner as to exhibit a real difference between
them.

813. The Progressive Sorites is a train of reasoning in which the
minor premiss of each epi-syllogism is supported by a pro-syllogism,
while the major is taken for granted.

814. The Regressive Sorites is a train of reasoning in which the
major premiss of each epi-syllogism is supported by a pro-syllogism,
while the minor is taken for granted.

_Progressive Sorites_.
(i) All B is C.
All A is B.
.'. All A is C.

(2) All C is D.
All A is C.
.'. All A is D.

(3) All D is E.
All A is D.
.'. All A is E.

_Regressive Sorites_.
(1) All D is E.
All C is D.
.'. All C is E.

(2) All C is E.
All B is C.
.'. All B is E.

(3) All B is E.
All A is B.
.'. All A is E.

815. Here is a concrete example of the two kinds of sorites,
resolved each into its component syllogisms--

_Progressive Sorites_.

All Bideford men are Devonshire men.
All Devonshire men are Englishmen.
All Englishmen are Teutons.
All Teutons are Aryans.
.'. All Bideford men are Aryans.

(1) All Devonshire men are Englishmen.
All Bideford men are Devonshire men.
.'. All Bideford men are Englishmen.

(2) All Englishmen are Teutons.
All Bideford men are Englishmen.
.'. All Bideford men are Teutons.

(3) All Teutons are Aryans.
All Bideford men are Teutons.
.'. All Bideford men are Aryans.

_Regressive Sorites._

All Teutons are Aryans.
All Englishmen are Teutons.
All Devonshiremen are Englishmen.
All Bideford men are Devonshiremen.
.'. All Bideford men are Aryans.

(1) All Teutons are Aryans.
All Englishmen are Teutons.
.'. All Englishmen are Aryans.

(2) All Englishmen are Aryans.
All Devonshiremen are Englishmen.
.'. All Devonshiremen are Aryans.

(3) All Devonshiremen are Aryans.
All Bideford men are Devonshiremen.
.'. All Bideford men are Aryans.

816. When expanded, the sorites is found to contain as many
syllogisms as there are propositions intermediate between the first
and the last. This is evident also on inspection by counting the
number of middle terms.

817. In expanding the progressive form we have to commence with the
second proposition of the sorites as the major premiss of the first
syllogism. In the progressive form the subject of the conclusion is
the same in all the syllogisms; in the regressive form the predicate
is the same. In both the same series of means, or middle terms, is
employed, the difference lying in the extremes that are compared with
one another through them.

[Illustration]

818. It is apparent from the figure that in the progressive form we
work from within outwards, in the regressive form from without
inwards. In the former we first employ the term 'Devonshiremen' as a
mean to connect 'Bideford men' with 'Englishmen'; next we employ
'Englishmen' as a mean to connect the same subject 'Bideford men' with
the wider term 'Teutons'; and, lastly, we employ 'Teutons' as a mean
to connect the original subject 'Bideford men' with the ultimate
predicate 'Ayrans.'

819. Reversely, in the regressive form we first use 'Teutons' as a
mean whereby to bring 'Englishmen' under 'Aryans'; next we use
'Englishmen' as a mean whereby to bring 'Devonshiremen' under the dame
predicate 'Aryans'; and, lastly, we use 'Devonshiremen' as a mean
whereby to bring the ultimate subject 'Bideford men' under the
original predicate 'Aryans.'

820. A sorites may be either Regular or Irregular.

821. In the regular form the terms which connect each proposition in
the series with its predecessor, that is to say, the middle terms,
maintain a fixed relative position; so that, if the middle term be
subject in one, it will always be predicate in the other, and vice
versa. In the irregular form this symmetrical arrangement is violated.

822. The syllogisms which compose a regular sorites, whether
progressive or regressive, will always be in the first figure.

In the irregular sorites the syllogisms may fall into different
figures.

823. For the regular sorites the following rules may
be laid down.

(1) Only one premiss can be particular, namely, the first, if the
sorites be progressive, the last, if it be regressive.

(2) Only one premiss can be negative, namely, the last, if the
sorites be progressive, the first, if it be regressive.

824. _Proof of the Rules for the Regular Sorites_.

(1) In the progressive sorites the proposition which stands first is
the only one which appears as a minor premiss in the expanded
form. Each of the others is used in its turn as a major. If any
proposition, therefore, but the first were particular, there would
be a particular major, which involves undistributed middle, if the
minor be affirmative, as it must be in the first figure.

In the regressive sorites, if any proposition except the last were
particular, we should have a particular conclusion in the syllogism
in which it occurred as a premiss, and so a particular major in the
next syllogism, which again is inadmissible, as involving
undistributed middle.

(2) In the progressive sorites, if any premiss before the last were
negative, we should have a negative conclusion in the syllogism in
which it occurs. This would necessitate a negative minor in the next
syllogism, which is inadmissible in the first figure, as involving
illicit process of the major.

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