THE CLASSIFICATION OF PROPOSITIONS
Sec. 1. Logicians classify Propositions according to Quantity, Quality,
Relation and Modality.
As to Quantity, propositions are either Universal or Particular; that is
to say, the predicate is affirmed or denied either of the whole subject
or of a part of it--of _All_ or of _Some S_.
_All S is P_ (that is, _P_ is predicated of _all S_).
_Some S is P_ (that is, _P_ is predicated of _some S_).
An Universal Proposition may have for its subject a singular term, a
collective, a general term distributed, or an abstract term.
(1) A proposition having a singular term for its subject, as _The Queen
has gone to France_, is called a Singular Proposition; and some
Logicians regard this as a third species of proposition with respect to
quantity, distinct from the Universal and Particular; but that is
needless.
(2) A collective term may be the subject, as _The Black Watch is ordered
to India_. In this case, as well as in singular propositions, a
predication is made concerning the whole subject as a whole.
(3) The subject may be a general term taken in its full denotation, as
_All apes are sagacious_; and in this case a Predication is made
concerning the whole subject distributively; that is, of each and
everything the subject stands for.
(4) Propositions whose subjects are abstract terms, though they may
seem to be formally Singular, are really as to their meaning
distributive Universals; since whatever is true of a quality is true of
whatever thing has that quality so far as that quality is concerned.
_Truth will prevail_ means that _All true propositions are accepted at
last_ (by sheer force of being true, in spite of interests, prejudices,
ignorance and indifference). To bear this in mind may make one cautious
in the use of abstract terms.
In the above paragraphs a distinction is implied between Singular and
Distributive Universals; but, technically, every term, whether subject
or predicate, when taken in its full denotation (or universally), is
said to be 'distributed,' although this word, in its ordinary sense,
would be directly applicable only to general terms. In the above
examples, then, 'Queen,' 'Black Watch,' 'apes,' and 'truth' are all
distributed terms. Indeed, a simple definition of the Universal
Proposition is 'one whose subject is distributed.'
A Particular Proposition is one that has a general term for its subject,
whilst its predicate is not affirmed or denied of everything the subject
denotes; in other words, it is one whose subject is not distributed: as
_Some lions inhabit Africa_.
In ordinary discourse it is not always explicitly stated whether
predication is universal or particular; it would be very natural to say
_Lions inhabit Africa_, leaving it, as far as the words go, uncertain
whether we mean _all_ or _some_ lions. Propositions whose quantity is
thus left indefinite are technically called 'preindesignate,' their
quantity not being stated or designated by any introductory expression;
whilst propositions whose quantity is expressed, as _All
foundling-hospitals have a high death-rate_, or _Some wine is made from
grapes_, are said to be 'predesignate.' Now, the rule is that
preindesignate propositions are, for logical purposes, to be treated as
particular; since it is an obvious precaution of the science of proof,
in any practical application, _not to go beyond the evidence_. Still,
the rule may be relaxed if the universal quantity of a preindesignate
proposition is well known or admitted, as in _Planets shine with
reflected light_--understood of the planets of our solar system at the
present time. Again, such a proposition as _Man is the paragon of
animals_ is not a preindesignate, but an abstract proposition; the
subject being elliptical for _Man according to his proper nature_; and
the translation of it into a predesignate proposition is not _All men
are paragons_; nor can _Some men_ be sufficient, since an abstract can
only be adequately rendered by a distributed term; but we must say, _All
men who approach the ideal_. Universal real propositions, true without
qualification, are very scarce; and we often substitute for them
_general_ propositions, saying perhaps--_generally, though not
universally, S is P_. Such general propositions are, in strictness,
particular; and the logical rules concerning universals cannot be
applied to them without careful scrutiny of the facts.
The marks or predesignations of Quantity commonly used in Logic are: for
Universals, _All_, _Any_, _Every_, _Whatever_ (in the negative _No_ or
_No one_, see next Sec.); for Particulars, _Some_.
Now _Some_, technically used, does not mean _Some only,_ but _Some at
least_ (it may be one, or more, or all). If it meant '_Some only_,'
every particular proposition would be an exclusive exponible (chap. ii.
Sec. 3); since _Only some men are wise_ implies that _Some men are not
wise_. Besides, it may often happen in an investigation that all the
instances we have observed come under a certain rule, though we do not
yet feel justified in regarding the rule as universal; and this
situation is exactly met by the expression _Some_ (_it may be all_).
The words _Many_, _Most_, _Few_ are generally interpreted to mean
_Some_; but as _Most_ signifies that exceptions are known, and _Few_
that the exceptions are the more numerous, propositions thus
predesignate are in fact exponibles, mounting to _Some are_ and _Some
are not_. If to work with both forms be too cumbrous, so that we must
choose one, apparently _Few are_ should be treated as _Some are not_.
The scientific course to adopt with propositions predesignate by _Most_
or _Few_, is to collect statistics and determine the percentage; thus,
_Few men are wise_--say 2 per cent.
The Quantity of a proposition, then, is usually determined entirely by
the quantity of the subject, whether _all_ or _some_. Still, the
quantity of the predicate is often an important consideration; and
though in ordinary usage the predicate is seldom predesignate, Logicians
agree that in every Negative Proposition (see Sec. 2) the predicate is
'distributed,' that is to say, is denied altogether of the subject, and
that this is involved in the form of denial. To say _Some men are not
brave_, is to declare that the quality for which men may be called brave
is not found in any of the _Some men_ referred to: and to say _No men
are proof against flattery_, cuts off the being 'proof against flattery'
entirely from the list of human attributes. On the other hand, every
Affirmative Proposition is regarded as having an undistributed
predicate; that is to say, its predicate is not affirmed exclusively of
the subject. _Some men are wise_ does not mean that 'wise' cannot be
predicated of any other beings; it is equivalent to _Some men are wise_
(_whoever else may be_). And _All elephants are sagacious_ does not
limit sagacity to elephants: regarding 'sagacious' as possibly denoting
many animals of many species that exhibit the quality, this proposition
is equivalent to '_All elephants are_ some _sagacious animals_.' The
affirmative predication of a quality does not imply exclusive possession
of it as denial implies its complete absence; and, therefore, to regard
the predicate of an affirmative proposition as distributed would be to
go beyond the evidence and to take for granted what had never been
alleged.
Some Logicians, seeing that the quantity of predicates, though not
distinctly expressed, is recognised, and holding that it is the part of
Logic "to make explicit in language whatever is implicit in thought,"
have proposed to exhibit the quantity of predicates by predesignation,
thus: 'Some men are _some_ wise (beings)'; 'some men are not _any_ brave
(beings)'; etc. This is called the Quantification of the Predicate,
and leads to some modifications of Deductive Logic which will be
referred to hereafter. (See Sec. 3; chap. vii. Sec. 4, and chap. viii. Sec. 3.)
Sec. 2. As to Quality, Propositions are either Affirmative or Negative. An
Affirmative Proposition is, formally, one whose copula is affirmative
(or, has no negative sign), as _S--is--P, All men--are--partial to
themselves_. A Negative Proposition is one whose copula is negative (or,
has a negative sign), as _S--is not--P, Some men--are not--proof against
flattery_. When, indeed, a Negative Proposition is of Universal
Quantity, it is stated thus: _No S is P, No men are proof against
flattery_; but, in this case, the detachment of the negative sign from
the copula and its association with the subject is merely an accident of
our idiom; the proposition is the same as _All men--are not--proof
against flattery_. It must be distinguished, therefore, from such an
expression as _Not every man is proof against flattery_; for here the
negative sign really restricts the subject; so that the meaning
is--_Some men at most_ (it may be _none) are proof against flattery_;
and thus the proposition is Particular, and is rendered--_Some men--are
not--proof against flattery_.
When the negative sign is associated with the predicate, so as to make
this an Infinite Term (chap. iv. Sec. 8), the proposition is called an
Infinite Proposition, as _S is not-P_ (or _p), All men are--incapable of
resisting flattery_, or _are--not-proof against flattery_.
Infinite propositions, when the copula is affirmative, are formally,
themselves affirmative, although their force is chiefly negative; for,
as the last example shows, the difference between an infinite and a
negative proposition may depend upon a hyphen. It has been proposed,
indeed, with a view to superficial simplification, to turn all
Negatives into Infinites, and thus render all propositions Affirmative
in Quality. But although every proposition both affirms and denies
something according to the aspect in which you regard it (as _Snow is
white_ denies that it is any other colour, and _Snow is not blue_
affirms that it is some other colour), yet there is a great difference
between the definite affirmation of a genuine affirmative and the vague
affirmation of a negative or infinite; so that materially an affirmative
infinite is the same as a negative.
Generally Mill's remark is true, that affirmation and denial stand for
distinctions of fact that cannot be got rid of by manipulation of words.
Whether granite sinks in water, or not; whether the rook lives a hundred
years, or not; whether a man has a hundred dollars in his pocket, or
not; whether human bones have ever been found in Pliocene strata, or
not; such alternatives require distinct forms of expression. At the same
time, it may be granted that many facts admit of being stated with
nearly equal propriety in either Quality, as _No man is proof against
flattery_, or _All men are open to flattery_.
But whatever advantage there is in occasionally changing the Quality of
a proposition may be gained by the process of Obversion (chap. vii. Sec.
5); whilst to use only one Quality would impair the elasticity of
logical expression. It is a postulate of Logic that the negative sign
may be transferred from the copula to the predicate, or from the
predicate to the copula, without altering the sense of a proposition;
and this is justified by the experience that not to have an attribute
and to be without it are the same thing.
Sec. 3. A. I. E. O.--Combining the two kinds of Quantity, Universal and
Particular, with the two kinds of Quality, Affirmative and Negative, we
get four simple types of proposition, which it is usual to symbolise by
the letters A. I. E. O., thus:
A. Universal Affirmative -- All S is P.
I. Particular Affirmative -- Some S is P.
E. Universal Negative -- No S is P.
O. Particular Negative -- Some S is not P.
As an aid to the remembering of these symbols we may observe that A. and
I. are the first two vowels in _affirmo_ and that E. and O. are the
vowels in _nego_.
It must be acknowledged that these four kinds of proposition recognised
by Formal Logic constitute a very meagre selection from the list of
propositions actually used in judgment and reasoning.
Those Logicians who explicitly quantify the predicate obtain, in all,
eight forms of proposition according to Quantity and Quality:
[Transcriber's Note: The Greek characters used in the original are
represented below by the name of the character in square brackets.]
U. Toto-total Affirmative -- All X is all Y.
A. Toto-partial Affirmative -- All X is some Y.
Y. Parti-total Affirmative -- Some X is all Y.
I. Parti-partial Affirmative -- Some X is some Y.
E. Toto-total Negative -- No X is any Y.
[eta]. Toto-partial Negative -- No X is some Y.
O. Parti-total Negative -- Some X is not any Y.
[omega]. Parti-partial Negative -- Some X is not some Y.
Here A. I. E. O. correspond with those similarly symbolised in the usual
list, merely designating in the predicates the quantity which was
formerly treated as implicit.
Sec. 4. As to Relation, propositions are either Categorical or Conditional.
A Categorical Proposition is one in which the predicate is directly
affirmed or denied of the subject without any limitation of time, place,
or circumstance, extraneous to the subject, as _All men in England are
secure of justice_; in which proposition, though there is a limitation
of place ('in England'), it is included in the subject. Of this kind are
nearly all the examples that have yet been given, according to the form
_S is P_.
A Conditional Proposition is so called because the predication is made
under some limitation or condition not included in the subject, as _If a
man live in England, he is secure of justice_. Here the limitation
'living in England' is put into a conditional sentence extraneous to the
subject, 'he,' representing any man.
Conditional propositions, again, are of two kinds--Hypothetical and
Disjunctive. Hypothetical propositions are those that are limited by an
explicit conditional sentence, as above, or thus: _If Joe Smith was a
prophet, his followers have been unjustly persecuted_. Or in symbols
thus:
If A is, B is;
If A is B, A is C;
If A is B, C is D.
Disjunctive propositions are those in which the condition under which
predication is made is not explicit but only implied under the disguise
of an alternative proposition, as _Joe Smith was either a prophet or an
impostor_. Here there is no direct predication concerning Joe Smith, but
only a predication of one of the alternatives conditionally on the other
being denied, as, _If Joe Smith was not a prophet he was an impostor_;
or, _If he was not an impostor, he was a prophet_. Symbolically,
Disjunctives may be represented thus:
A is either B or C,
Either A is B or C is D.
Formally, every Conditional may be expressed as a Categorical. For our
last example shows how a Disjunctive may be reduced to two Hypotheticals
(of which one is redundant, being the contrapositive of the other; see
chap. vii. Sec. 10). And a Hypothetical is reducible to a Categorical thus:
_If the sky is clear, the night is cold_ may be read--_The case of the
sky being clear is a case of the night being cold_; and this, though a
clumsy plan, is sometimes convenient. It would be better to say _The sky
being clear is a sign of the night being cold_, or a condition of it.
For, as Mill says, the essence of a Hypothetical is to state that one
clause of it (the indicative) may be inferred from the other (the
conditional). Similarly, we might write: _Proof of Joe Smith's not being
a prophet is a proof of his being an impostor_.
This turning of Conditionals into Categoricals is called a Change of
Relation; and the process may be reversed: _All the wise are virtuous_
may be written, _If any man is wise he is virtuous_; or, again, _Either
a man is not-wise or he is virtuous_. But the categorical form is
usually the simplest.
If, then, as substitutes for the corresponding conditionals,
categoricals are formally adequate, though sometimes inelegant, it may
be urged that Logic has nothing to do with elegance; or that, at any
rate, the chief elegance of science is economy, and that therefore, for
scientific purposes, whatever we may write further about conditionals
must be an ugly excrescence. The scientific purpose of Logic is to
assign the conditions of proof. Can we, then, in the conditional form
prove anything that cannot be proved in the categorical? Or does a
conditional require to be itself proved by any method not applicable to
the Categorical? If not, why go on with the discussion of Conditionals?
For all laws of Nature, however stated, are essentially categorical. 'If
a straight line falls on another straight line, the adjacent angles are
together equal to two right angles'; 'If a body is unsupported, it
falls'; 'If population increases, rents tend to rise': here 'if' means
'whenever' or 'all cases in which'; for to raise a doubt whether a
straight line is ever conceived to fall upon another, whether bodies are
ever unsupported, or population ever increases, is a superfluity of
scepticism; and plainly the hypothetical form has nothing to do with the
proof of such propositions, nor with inference from them.
Still, the disjunctive form is necessary in setting out the relation of
contradictory terms, and in stating a Division (chap. xxi.), whether
formal (_as A is B or not-B_) or material (as _Cats are white, or black,
or tortoiseshell, or tabby_). And in some cases the hypothetical form is
useful. One of these occurs where it is important to draw attention to
the condition, as something doubtful or especially requiring
examination. _If there is a resisting medium in space, the earth will
fall into the sun; If the Corn Laws are to be re-enacted, we had better
sell railways and buy land_: here the hypothetical form draws attention
to the questions whether there is a resisting medium in space, whether
the Corn Laws are likely to be re-enacted; but as to methods of
inference and proof, the hypothetical form has nothing to do with them.
The propositions predicate causation: _A resisting medium in space is a
condition of the earth's falling into the sun; A Corn Law is a condition
of the rise of rents, and of the fall of railway profits_.
A second case in which the hypothetical is a specially appropriate form
of statement occurs where a proposition relates to a particular matter
and to future time, as _If there be a storm to-morrow, we shall miss our
picnic_. Such cases are of very slight logical interest. It is as
exercises in formal thinking that hypotheticals are of most value;
inasmuch as many people find them more difficult than categoricals to
manipulate.
In discussing Conditional Propositions, the conditional sentence of a
Hypothetical, or the first alternative of a Disjunctive, is called the
Antecedent; the indicative sentence of a Hypothetical, or the second
alternative of a Disjunctive, is called the Consequent.
Hypotheticals, like Categoricals, have been classed according to
Quantity and Quality. Premising that the quantity of a Hypothetical
depends on the quantity of its Antecedent (which determines its
limitation), whilst its quality depends on the quality of its consequent
(which makes the predication), we may exhibit four forms:
A. _If A is B, C is D;_
I. _Sometimes when A is B, C is D;_
E. _If A is B, C is not D;_
O. _Sometimes when A is B, C is not D._
But I. and O. are rarely used.
As for Disjunctives, it is easy to distinguish the two quantities thus:
A. _Either A is B, or C is D;_
I. _Sometimes either A is B or C is D._
But I. is rarely used. The distinction of quality, however, cannot be
made: there are no true negative forms; for if we write--
_Neither is A B, nor C D,_
there is here no alternative predication, but only an Exponible
equivalent to _No A is B, and No C is D_. And if we write--
_Either A is not B, or C is not D,_
this is affirmative as to the alternation, and is for all methods of
treatment equivalent to A.
Logicians are divided in opinion as to the interpretation of the
conjunction 'either, or'; some holding that it means 'not both,' others
that it means 'it may be both.' Grammatical usage, upon which the
question is sometimes argued, does not seem to be established in favour
of either view. If we say _A man so precise in his walk and conversation
is either a saint or a consummate hypocrite_; or, again, _One who is
happy in a solitary life is either more or less than man_; we cannot in
such cases mean that the subject may be both. On the other hand, if it
be said that _the author of 'A Tale of a Tub' is either a misanthrope or
a dyspeptic_, the alternatives are not incompatible. Or, again, given
that _X. is a lunatic, or a lover, or a poet_, the three predicates have
much congruity.
It has been urged that in Logic, language should be made as exact and
definite as possible, and that this requires the exclusive
interpretation 'not both.' But it seems a better argument, that Logic
(1) should be able to express all meanings, and (2), as the science of
evidence, must not assume more than is given; to be on the safe side, it
must in doubtful cases assume the least, just as it generally assumes a
preindesignate term to be of particular quantity; and, therefore
'either, or' means 'one, or the other, or both.'
However, when both the alternative propositions have the same subject,
as _Either A is B, or A is C_, if the two predicates are contrary or
contradictory terms (as 'saint' and 'hypocrite,' or 'saint' and
'not-saint'), they cannot in their nature be predicable in the same way
of the same subject; and, therefore, in such a case 'either, or' means
one or the other, but not both in the same relation. Hence it seems
necessary to admit that the conjunction 'either, or' may sometimes
require one interpretation, sometimes the other; and the rule is that it
implies the further possibility 'or both,' except when both alternatives
have the same subject whilst the predicates are contrary or
contradictory terms.
If, then, the disjunctive _A is either B or C_ (_B_ and _C_ being
contraries) implies that both alternatives cannot be true, it can only
be adequately rendered in hypotheticals by the two forms--(1) _If A is
B, it is not C_, and (2)_If A is not B, it is C_. But if the disjunctive
_A is either B or C_ (_B_ and _C_ not being contraries) implies that
both may be true, it will be adequately translated into a hypothetical
by the single form, _If A is not B, it is C_. We cannot translate it
into--_If A is B, it is not C_, for, by our supposition, if '_A is B_'
is true, it does not follow that '_A is C_' must be false.
Logicians are also divided in opinion as to the function of the
hypothetical form. Some think it expresses doubt; for the consequent
depends on the antecedent, and the antecedent, introduced by 'if,' may
or may not be realised, as in _If the sky is clear, the night is cold_:
whether the sky is, or is not, clear being supposed to be uncertain. And
we have seen that some hypothetical propositions seem designed to draw
attention to such uncertainty, as--_If there is a resisting medium in
space_, etc. But other Logicians lay stress upon the connection of the
clauses as the important matter: the statement is, they say, that the
consequent may be inferred from the antecedent. Some even declare that
it is given as a necessary inference; and on this ground Sigwart rejects
particular hypotheticals, such as _Sometimes when A is B, C is D_; for
if it happens only sometimes the connexion cannot be necessary. Indeed,
it cannot even be probably inferred without further grounds. But this is
also true whenever the antecedent and consequent are concerned with
different matter. For example, _If the soul is simple, it is
indestructible_. How do you know that? Because _Every simple substance
is indestructible_. Without this further ground there can be no
inference. The fact is that conditional forms often cover assertions
that are not true complex propositions but a sort of euthymemes (chap.
xi. Sec. 2), arguments abbreviated and rhetorically disguised. Thus: _If
patience is a virtue there are painful virtues_--an example from Dr.
Keynes. Expanding this we have--
Patience is painful;
Patience is a virtue:
.'. Some virtue is painful.
And then we see the equivocation of the inference; for though patience
be painful _to learn_, it is not painful _as a virtue_ to the patient
man.
The hypothetical, '_If Plato was not mistaken poets are dangerous
citizens_,' may be considered as an argument against the laureateship,
and may be expanded (informally) thus: 'All Plato's opinions deserve
respect; one of them was that poets are bad citizens; therefore it
behoves us to be chary of encouraging poetry.' Or take this
disjunctive, '_Either Bacon wrote the works ascribed to Shakespeare, or
there were two men of the highest genius in the same age and country_.'
This means that it is not likely there should be two such men, that we
are sure of Bacon, and therefore ought to give him all the glory. Now,
if it is the part of Logic 'to make explicit in language all that is
implicit in thought,' or to put arguments into the form in which they
can best be examined, such propositions as the above ought to be
analysed in the way suggested, and confirmed or refuted according to
their real intention.
We may conclude that no single function can be assigned to all
hypothetical propositions: each must be treated according to its own
meaning in its own context.
Sec. 5. As to Modality, propositions are divided into Pure and Modal. A
Modal proposition is one in which the predicate is affirmed or denied,
not simply but _cum modo_, with a qualification. And some Logicians have
considered any adverb occurring in the predicate, or any sign of past or
future tense, enough to constitute a modal: as 'Petroleum is
_dangerously_ inflammable'; 'English _will be_ the universal language.'
But far the most important kind of modality, and the only one we need
consider, is that which is signified by some qualification of the
predicate as to the degree of certainty with which it is affirmed or
denied. Thus, 'The bite of the cobra is _probably_ mortal,' is called a
Contingent or Problematic Modal: 'Water is _certainly_ composed of
oxygen and hydrogen' is an Assertory or Certain Modal: 'Two straight
lines _cannot_ enclose a space' is a Necessary or Apodeictic Modal (the
opposite being inconceivable). Propositions not thus qualified are
called Pure.
Modal propositions have had a long and eventful history, but they have
not been found tractable by the resources of ordinary Logic, and are now
generally neglected by the authors of text-books. No doubt such
propositions are the commonest in ordinary discourse, and in some rough
way we combine them and draw inferences from them. It is understood
that a combination of assertory or of apodeictic premises may warrant an
assertory or an apodeictic conclusion; but that if we combine either of
these with a problematic premise our conclusion becomes problematic;
whilst the combination of two problematic premises gives a conclusion
less certain than either. But if we ask 'How much less certain?' there
is no answer. That the modality of a conclusion follows the less certain
of the premises combined, is inadequate for scientific guidance; so
that, as Deductive Logic can get no farther than this, it has abandoned
the discussion of Modals. To endeavour to determine the degree of
certainty attaching to a problematic judgment is not, however, beyond
the reach of Induction, by analysing circumstantial evidence, or by
collecting statistics with regard to it. Thus, instead of 'The cobra's
bite is _probably_ fatal,' we might find that it is fatal 80 times in
100. Then, if we know that of those who go to India 3 in 1000 are
bitten, we can calculate what the chances are that any one going to
India will die of a cobra's bite (chap. xx.).
Sec. 6. Verbal and Real Propositions.--Another important division of
propositions turns upon the relation of the predicate to the subject in
respect of their connotations. We saw, when discussing Relative Terms,
that the connotation of one term often implies that of another;
sometimes reciprocally, like 'master' and 'slave'; or by inclusion, like
species and genus; or by exclusion, like contraries and contradictories.
When terms so related appear as subject and predicate of the same
proposition, the result is often tautology--e.g., _The master has
authority over his slave; A horse is an animal; Red is not blue; British
is not foreign_. Whoever knows the meaning of 'master,' 'horse,' 'red,'
'British,' learns nothing from these propositions. Hence they are called
Verbal propositions, as only expounding the sense of words, or as if
they were propositions only by satisfying the forms of language, not by
fulfilling the function of propositions in conveying a knowledge of
facts. They are also called 'Analytic' and 'Explicative,' when they
separate and disengage the elements of the connotation of the subject.
Doubtless, such propositions may be useful to one who does not know the
language; and Definitions, which are verbal propositions whose
predicates analyse the whole connotations of their subjects, are
indispensable instruments of science (see chap. xxii.).
Of course, hypothetical propositions may also be verbal, as _If the soul
be material it is extended_; for 'extension' is connoted by 'matter';
and, therefore, the corresponding disjunctive is verbal--_Either the
soul is not material, or it is extended_. But a true divisional
disjunctive can never be verbal (chap. xxi. Sec. 4, rule 1).
On the other hand, when there is no such direct relation between subject
and predicate that their connotations imply one another, but the
predicate connotes something that cannot be learnt from the connotation
of the subject, there is no longer tautology, but an enlargement of
meaning--e.g., _Masters are degraded by their slaves; The horse is the
noblest animal; Red is the favourite colour of the British army; If the
soul is simple, it is indestructible_. Such propositions are called
Real, Synthetic, or Ampliative, because they are propositions for which
a mere understanding of their subjects would be no substitute, since the
predicate adds a meaning of its own concerning matter of fact.
To any one who understands the language, a verbal proposition can never
be an inference or conclusion from evidence; nor can a verbal
proposition ever furnish grounds for an inference, except as to the
meaning of words. The subject of real and verbal propositions will
inevitably recur in the chapters on Definition; but tautologies are such
common blemishes in composition, and such frequent pitfalls in argument,
that attention cannot be drawn to them too early or too often.