Ferdinand Gregorovius - "Lucretia Borgia"

Andrew Lang, Ed. - "The Green Fairy Book"

Alexander F. Chamberlain - "The Child and Childhood in Folk Thought"

A. F. Pollard - "Henry VIII."

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




174. The field of logic is far from being conterminous with that of
language. Language is the mirror of man's whole nature, whereas logic
deals with language only so far as it gives clothing to the products
of thought in the narrow sense which we have assigned to that term.
Language has materials of every sort lying strewn about, among which
the logician has to seek for his proper implements.

175. Sentences may be employed for a variety of purposes--

(1) To ask a question;

(2) To give an order;

(3) To express a feeling;

(4) To make a statement.

These various uses give rise respectively to

(1) The Interrogative Sentence;

(2) The Imperative Sentence;

(3) The Exclamatory Sentence;

(4) The Enunciative Sentence; Indicative Potential.

It is with the last of these only that logic is concerned.

176. The proposition, therefore, corresponds to the Indicative and
Potential, or Conditional, sentences of grammar. For it must be borne
in mind that logic recognises no difference between a statement of
fact and a supposition. 'It may rain to-morrow' is as much a
proposition as 'It is raining now.'

177. Leaving the grammatical aspect of the proposition, we must now
consider it from the purely logical point of view.

178. A proposition is a judgement expressed in words; and a
judgement is a direct comparison between two concepts.

179. The same thing may be expressed more briefly by saying that a
proposition is a direct comparison between two terms.

180. We say 'direct comparison,' because the syllogism also may be
described as a comparison between two terms: but in the syllogism the
two terms are compared indirectly, or by means of a third term.

181. A proposition may be analysed into two terms and a Copula,
which is nothing more than the sign of agreement or disagreement
between them.

182. The two terms are called the Subject and the Predicate ( 58).

183. The Subject is that of which something is stated.

184. The Predicate is that which is stated of the subject.

185. Hence the subject is thought of for its own sake, and the
predicate for the sake of the subject.




CHAPTER II.

Of _the Copula_.


186. There are two kinds of copula, one for affirmative and one for
negative statements.

187. Materially the copula is expressed by some part of the verb 'to
be,' with or without the negative, or else is wrapped up in some
inflexional form of a verb.

188. The material form of the copula is an accident of language, and
a matter of indifference to logic. 'The kettle boils' is as logical a
form of expression as 'The kettle is boiling.' For it must be
remembered that the word 'is' here is a mere sign of agreement between
the two terms, and conveys no notion of actual existence. We may use
it indeed with equal propriety to express non-existence, as when we
say 'An idol is nothing.'

189. When the verb 'to be' expresses existence in fact it is known
in grammar as 'the substantive verb.' In this use it is predicate as
well as copula, as when we say 'God is,' which may be analysed, if we
please, into 'God is existent.'

190. We have laid down above that there are two kinds of copula,
affirmative and negative: but some logicians have maintained that the
copula is always affirmative.

191. What then, it may be asked, on this view, is the meaning of
negative propositions! To which the answer is, that a negative
proposition asserts an agreement between the subject and a negative
term. When, for instance, we say 'The whale is not a fish,' this would
be interpreted to mean 'The whale is a not-fish.'

192. Undoubtedly any negative proposition may be exhibited in an
affirmative form, since, by the law of excluded middle, given a pair
of contradictory terms, wherever the one can be asserted, the other
can be denied, and vice versa. We shall find later on that this
principle gives rise to one of the forms of immediate inference. The
only question then can be, which is the more natural and legitimate
form of expression. It seems simpler to suppose that we assert the
agreement of 'whale' with 'not-fish' by implication only, and that
what we directly do is to predicate a disagreement between 'whale' and
the positive attributes connoted by 'fish.' For since 'not-fish' must
apply to every conceivable object of thought except those which fall
under the positive term 'fish,' to say that a whale is a 'not-fish,'
is to say that we have still to search for 'whale' throughout the
whole universe of being, minus a limited portion; which is only a more
clumsy way of saying that it is not to be found in that portion.

193. Again, the term 'not-fish' must be understood either in its
intension or in its extension. If it be understood in its intension,
what it connotes is simply the absence of the positive qualities which
constitute a fish, a meaning which is equally conveyed by the negative
form of proposition. We gain nothing in simplicity by thus confounding
assertion with denial. If, on the other hand, it is to be taken in
extension, this involves the awkwardness of supposing that the
predicative power of a term resides in its extensive capacity.

194. We therefore recognise predication as being of two
kinds--affirmation and negation--corresponding to which there are two
forms of copula.

195. On the other hand, other logicians have maintained that there
are many kinds of copula, since the copula must vary according to the
various degrees of probability with which we can assert or deny a
predicate of a subject. This view is technically known as the doctrine
of



_The Modality of the Copula._


196. It may plausibly be maintained that the division of
propositions into affirmative and negative is not an exhaustive one,
since the result of an act of judgement is not always to lead the mind
to a clear assertion or a clear denial, but to leave it in more or
less doubt as to whether the predicate applies to the subject or
not. Instead of saying simply A is B, or A is not B, we may be led to
one of the following forms of proposition--

A is possibly B.
A is probably B.
A is certainly B.

The adverbial expression which thus appears to qualify the copula is
known as 'the mode.'

197. When we say 'The accused may be guilty' we have a proposition
of very different force from 'The accused is guilty,' and yet the
terms appear to be the same. Wherein then does the difference lie? 'In
the copula' would seem to be the obvious reply. We seem therefore
driven to admit that there are as many different kinds of copula as
there are different degrees of assurance with which a statement may be
made.

198. But there is another way in which modal propositions may be
regarded. Instead of the mode being attached to the copula, it may be
considered as itself constituting the predicate, so that the above
propositions would be analysed thus--

That A is B, is possible.
That A is B, is probable.
That A is B, is certain.

199. The subject here is itself a proposition of which we predicate
various degrees of probability. In this way the division of
propositions into affirmative and negative is rendered exhaustive. For
wherever before we had a doubtful assertion, we have now an assertion
of doubtfulness.

200. If degrees of probability can thus be eliminated from the
copula, much more so can expressions of time, which may always be
regarded as forming part of the predicate. 'The sun will rise
to-morrow' may be analysed into 'The sun is going to rise to-morrow.'
In either case the tense belongs equally to the predicate. It is often
an awkward task so to analyse propositions relative to past or future
time as to bring out the copula under the form 'is' or 'is not': but
fortunately there is no necessity for so doing, since, as has been
said before ( 188), the material form of the copula is a matter of
indifference to logic. Indeed in affirmative propositions the mere
juxtaposition of the subject and predicate is often sufficient to
indicate their agreement, e.g. 'Most haste, worst speed,' chalepha
tha kala. It is because all propositions are not affirmative that we
require a copula at all. Moreover the awkwardness of expression just
alluded to is a mere accident of language. In Latin we may say with
equal propriety 'Sol orietur cras' or 'Sol est oriturus cras'; while
past time may also be expressed in the analytic form in the case of
deponent verbs, as 'Caesar est in Galliam profectus'--'Caesar is gone
into Gaul.'

201. The copula then may always be regarded as pure, that is, as
indicating mere agreement or disagreement between the two terms of the
proposition.




CHAPTER III.

_Of the Divisions of Propositions_.


202. The most obvious and the most important division of
propositions is into true and false, but with this we are not
concerned. Formal logic can recognise no difference between true and
false propositions. The one is represented by the same symbols as the
other.

203. We may notice, however, in passing, that truth and falsehood
are attributes of propositions and of propositions only. For something
must be predicated, i.e. asserted or denied, before we can have
either truth or falsehood. Neither concepts or terms, on the one hand,
nor reasonings, on the other, can properly be said to be true or
false. In the mere notion of a Centaur or of a black swan there is
neither truth nor falsehood; it is not until we make some statement
about these things, such as that 'black swans are found in Australia,'
or 'I met a Centaur in the High Street yesterday,' that the question
of truth or falsehood comes in. In such expressions as a 'true friend'
or 'a false patriot' there is a tacit reference to propositions. We
mean persons of whom the terms 'friend' and 'patriot' are truly or
falsely predicated. Neither can we with any propriety talk of true or
false reasoning. Reasoning is either valid or invalid: it is only the
premisses of our reasonings, which are propositions, that can be true
or false. We may have a perfectly valid process of reasoning which
starts from a false assumption and lands us in a false conclusion.

204. All truth and falsehood then are contained in propositions; and
propositions are divided according to the Quality of the Matter into
true and false. But the consideration of the matter is outside the
sphere of formal or deductive Logic. It is the problem of inductive
logic to establish, if possible, a criterion of evidence whereby the
truth or falsehood of propositions may be judged ( 2).

205. Another usual division of propositions is into Pure and Modal,
the latter being those in which the copula is modified by some degree
of probability. This division is excluded by the view which has just
been taken of the copula, as being always simply affirmative or simply
negative.

206. We are left then with the following divisions of
propositions--

Proposition
according to Form
Simple

Complex
Conjunctive
Disjunctive

Universal
Singular
General

according to Matter
Verbal
Real

according to Quantity
Universal
Singular
General

Particular
Indefinite
(strictly) Particular

according to Quality
Affirmative
Negative



_Simple and Complex Propositions_.


207. A Simple Proposition is one in which a predicate is directly
affirmed or denied of a subject, e.g. 'Rain is falling.'

208. A simple proposition is otherwise known as Categorical.

209. A Complex Proposition is one in which a statement is made
subject to some condition, e.g. 'If the wind drops, rain will fall.'

210. Hence the complex proposition is also known as Conditional.

211. Every complex proposition consists of two parts--

(1) Antecedent;

(2) Consequent.

212. The Antecedent is the condition on which another statement is
made to depend. It precedes the other in the order of thought, but may
either precede or follow it in the order of language. Thus we may say
indifferently--'If the wind drops, we shall have rain' or 'We shall
have rain, if the wind drops.'

213. The Consequent is the statement which is made subject to some
condition.

214. The complex proposition assumes two forms,

(1) If A is B, C is D.

This is known as the Conjunctive or Hypothetical proposition.

(2) Either A is B or C is D.

This is known as the Disjunctive proposition.

215. The disjunctive proposition may also appear in
the form

A is either B or C,

which is equivalent to saying

Either A is B or A is C;

or again in the form

Either A or B is C,

which is equivalent to saying

Either A is C or B is C.

216. As the double nomenclature may cause some confusion, a scheme
is appended.

Proposition
____________|_____________
| |
Simple Complex
(Categorical) (Conditional)
___________|__________
| |
Conjunctive Disjunctive.
(Hypothetical)

217. The first set of names is preferable. 'Categorical' properly
means 'predicable' and 'hypothetical' is a mere synonym for
'conditional.'

218. Let us examine now what is the real nature of the statement
which is made in the complex form of proposition. When, for instance,
we say 'If the sky falls, we shall catch larks,' what is it that we
really mean to assert? Not that the sky will fall, and not that we
shall catch larks, but a certain connection between the two, namely,
that the truth of the antecedent involves the truth of the
consequent. This is why this form of proposition is called
'conjunctive,' because in it the truth of the consequent is conjoined
to the truth of the antecedent.

219. Again, when we say 'Jones is either a knave or a fool,' what is
really meant to be asserted is--'If you do not find Jones to be a
knave, you may be sure that he is a fool.' Here it is the falsity of
the antecedent which involves the truth of the consequent; and the
proposition is known as 'disjunctive,' because the truth of the
consequent is disjoined from the truth of the antecedent.

220. Complex propositions then turn out to be propositions about
propositions, that is, of which the subject and predicate are
themselves propositions. But the nature of a proposition never varies
in thought. Ultimately every proposition must assume the form 'A is,
or is not, B.' 'If the sky falls, we shall catch larks' may be
compressed into 'Sky-falling is lark-catching.'

221. Hence this division turns upon the form of expression, and may
be said to be founded on the simplicity or complexity of the terms
employed in a proposition.

222. In the complex proposition there appears to be more than one
subject or predicate or both, but in reality there is only a single
statement; and this statement refers, as we have Seen, to a certain
connection between two propositions.

223. If there were logically, and not merely grammatically, more
than one subject or predicate, there would be more than one
proposition. Thus when we say 'The Jews and Carthaginians were Semitic
peoples and spoke a Semitic language,' we have four propositions
compressed into a single sentence for the sake of brevity.

224. On the other hand when we say 'Either the Carthaginians were of
Semitic origin or argument from language is of no value in ethnology,'
we have two propositions only in appearance.

225. The complex proposition then must be distinguished from those
contrivances of language for abbreviating expression in which several
distinct statements are combined into a single sentence.



_Verbal and Real Propositions_.


226. A Verbal Proposition is one which states nothing more about the
subject than is contained in its definition, e.g. 'Man is an animal';
'Men are rational beings.'

227. A Real Proposition states some fact not contained in the
definition of the subject, e.g. 'Some animals have four feet.'

228. It will be seen that the distinction between verbal and real
propositions assumes a knowledge of the precise meaning of terms, that
is to say, a knowledge of definitions.

229. To a person who does not know the meaning of terms a verbal
proposition will convey as much information as a real one. To say 'The
sun is in mid-heaven at noon,' though a merely verbal proposition,
will convey information to a person who is being taught to attach a
meaning to the word 'noon.' We use so many terms without knowing their
meaning, that a merely verbal proposition appears a revelation to many
minds. Thus there are people who are surprised to hear that the lion
is a cat, though in its definition 'lion' is referred to the class
'cat.' The reason of this is that we know material objects far better
in their extension than in their intension, that is to say, we know
what things a name applies to without knowing the attributes which
those things possess in common.

230. There is nothing in the mere look of a proposition to inform us
whether it is verbal or real; the difference is wholly relative to,
and constituted by, the definition of the subject. When we have
accepted as the definition of a triangle that it is 'a figure
contained by three sides,' the statement of the further fact that it
has three angles becomes a real proposition. Again the proposition
'Man is progressive' is a real proposition. For though his
progressiveness is a consequence of his rationality, still there is no
actual reference to progressiveness contained in the usually accepted
definition, 'Man is a rational animal.'

231. If we were to admit, under the term 'verbal proposition,' all
statements which, though not actually contained in the definition of
the subject, are implied by it, the whole body of necessary truth
would have to be pronounced merely verbal, and the most penetrating
conclusions of mathematicians set down as only another way of stating
the simplest axioms from which they started. For the propositions of
which necessary truth is composed are so linked together that, given
one, the rest can always follow. But necessary truth, which is arrived
at 'a priori,' that is, by the mind's own working, is quite as real as
contingent truth, which is arrived at 'a posteriori,' or by the
teachings of experience, in other words, through our own senses or
those of others.

232. The process by which real truth, which is other than deductive,
is arrived at 'a priori' is known as Intuition. E.g. The mind sees
that what has three sides cannot but have three angles.

233. Only such propositions then must be considered verbal as state
facts expressly mentioned in the definition.

234. Strictly speaking, the division of propositions into verbal and
real is extraneous to our subject: since it is not the province of
logic to acquaint us with the content of definitions.

235, The same distinction as between verbal and real proposition, is
conveyed by the expressions 'Analytical' and 'Synthetical,' or
'Explicative' and 'Ampliative' judgements.

236. A verbal proposition is called analytical, as breaking up the
subject into its component notions.

237. A real proposition is called synthetical, as attaching some new
notion to the subject.

238. Among the scholastic logicians verbal propositions were known
as 'Essential,' because what was stated in the definition was
considered to be of the essence of the subject, while real
propositions were known as 'Accidental.'



_Universal AND PARTICULAR Propositions_.


239. A Universal proposition is one in which it is evident from the
form that the predicate applies to the subject in its whole extent.

240. When the predicate does not apply to the subject in its whole
extent, or when it is not clear that it does so, the proposition is
called Particular.

241. To say that a predicate applies to a subject in its whole
extent, is to say that it is asserted or denied of all the things of
which the subject is a name.

242. 'All men are mortal' is a universal proposition.

243. 'Some men are black' is a particular proposition. So also is
'Men are fallible;' for here it is not clear from the form whether
'all' or only 'some' is meant.

244. The latter kind of proposition is known as Indefinite, and must
be distinguished from the particular proposition strictly so called,
in which the predicate applies to part only of the subject.

245. The division into universal and particular is founded on the
Quantity of propositions.

246. The quantity of a proposition is determined by the quantity in
extension of its subject.

247. Very often the matter of an indefinite proposition is such as
clearly to indicate to us its quantity. When, for instance, we say
'Metals are elements,' we are understood to be referring to all
metals; and the same thing holds true of scientific statements in
general. Formal logic, however, cannot take account of the matter of
propositions; and is therefore obliged to set down all indefinite
propositions as particular, since it is not evident from the form that
they are universal.

248. Particular propositions, therefore, are sub-divided into such
as are Indefinite and such as are Particular, in the strict sense of
the term.

249. We must now examine the sub-division of universal propositions
into Singular and General.

250. A Singular proposition is one which has a singular term for its
subject, e.g. 'Virtue is beautiful.'

251. A General proposition is one which has for its subject a common
term taken in its whole extent.

252. Now when we say 'John is a man' or 'This table is oblong,' the
proposition is quite as universal, in the sense of the predicate
applying to the whole of the subject, as when we say 'All men are
mortal.' For since a singular term applies only to one thing, we
cannot avoid using it in its whole extent, if we use it at all.

253. The most usual signs of generality in a proposition are the
words 'all,' 'every,' 'each,' in affirmative, and the words 'no,'
'none,' 'not one,' &c. in negative propositions.

254. The terminology of the division of propositions according to
quantity is unsatisfactory. Not only has the indefinite proposition to
be set down as particular, even when the sense manifestly declares it
to be universal; but the proposition which is expressed in a
particular form has also to be construed as indefinite, _so_ that
an unnatural meaning is imparted to the word 'some,' as used in
logic. If in common conversation we were to say 'Some cows chew the
cud,' the person whom we were addressing would doubtless imagine us to
suppose that there were some cows which did not possess this
attribute. But in logic the word 'some' is not held to express more
than 'some at least, if not all.' Hence we find not only that an
indefinite proposition may, as a matter of fact, be strictly
particular, but that a proposition which appears to be strictly
particular may be indefinite. So a proposition expressed in precisely
the same form 'Some A is B' may be either strictly particular, if some
be taken to exclude all, or indefinite, if the word 'some' does not
exclude the possibility of the statement being true of all. It is
evident that the term 'particular' has become distorted from its
original meaning. It would naturally lead us to infer that a statement
is limited to part of the subject, whereas, by its being opposed to
universal, in the sense in which that term has been defined, it can
only mean that we have nothing to show us whether part or the whole is
spoken of.

255. This awkwardness of expression is due to the indefinite
proposition having been displaced from its proper position. Formerly
propositions were divided under three heads--

(1) Universal,

(2) Particular,

(3) Indefinite.

But logicians anxious for simplification asked, whether a predicate in
any given case must not either apply to the whole of the subject or
not? And whether, therefore, the third head of indefinite propositions
were not as superfluous as the so-called 'common gender' of nouns in
grammar?

256. It is quite true that, as a matter of fact, any given predicate
must either apply to the whole of the subject or not, so that in the
nature of things there is no middle course between universal and
particular. But the important point is that we may not know whether
the predicate applies to the whole of the subject or not. The primary
division then should be into propositions whose quantity is known and
propositions whose quantity is unknown. Those propositions whose
quantity is known may be sub-divided into 'definitely universal' and
'definitely particular,' while all those whose quantity is unknown are
classed together under the term 'indefinite.' Hence the proper
division is as follows--

Proposition
__________|____________
| |
Definite Indefinite
_____|_______
| |
Universal Particular.

257. Another very obvious defeat of terminology is that the word
'universal' is naturally opposed to 'singular,' whereas it is here so
used as to include it; while, on the other hand, there is no obvious
difference between universal and general, though in the division the
latter is distinguished from the former as species from genus.

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