Chapter
VII.
THE IMPORT OF PROPOSITIONS.
1. Import of Propositions - Predicative view
§ 1. Import
of Propositions - Predicative view.
In this chapter we shall be occupied in considering various theories as
to the precise nature of the relation expressed in the mental act of
predication. We have already in Ch. 3,
§§ I, 2, Ch. 6, §2 explained our own view on
this subject in some detail. For it was
not possible to treat of the proposition, or of the process of conversion,
without first indicating how the
relation between subject and predicate should be understood. Briefly to recapitulate what we have said,
both the subject and predicate express the object of the judgment under some
aspect, the subject however being construed to signify the thing, the predicate
some attribute which we affirm (or deny) of the thing. The copula declares that the object expressed
by the subject, and that expressed by the predicate are identical. Further, inasmuch as the judgement deals with
the object as it is known, and as in regard to our knowledge there is no fixed
order as to which aspect of an object we know first, a judgment may reverse the
natural order of predication. What is
naturally a mere attribute, may stand as the subject; what is naturally the
subject, may be affirmed as though it were the attribute. Thus we may have a case in which a proper
name, a name whose special office is to denote the individual concrete thing,
stand in the place of the attribute, as when we say, "That object coming
this way, is Socrates." Logically,
this transposition of the natural order is perfectly legitimate. For the function of the predicate is simply
to tell us what the subject is; and when we define the subject to be this or
that particular individual -- to be the man Socrates -- this is most certainly
done.
That there is a natural
order of predication will easily be seen on recalling the distinction between
substance and accident (Ch. 2 § 8). Clearly it is the substance which supports the
accidents. They determine it, and
characterise it: the substance is not something which determines and and
characterises them. It possesses
independent existence. They exist as its
determinations, and not in their own right.
Hence Aristotle rightly says that though we can express our proposition
in such a form as "The object coming this way is Callias", such an
order of the terms is not natural but per accidens [N1].
The same is true where
the subject is not an accident, but a substantial term of wider generality,
e.g. "That man is Socrates" [N2].
This view of the
proposition according to which the subject is understood as the thing and the
predicate as the attribute, -- or as is sometimes put, in which the subject is
construed in extension, -- is known as
the Predicative View.
During the past century
the most diverse theories on this point have been held by logicians. The principal of these we shall proceed to
examine. In the course of the discussion,
we shall be brought across another problem, which of recent years has afforded
matter for debate, -- the question namely whether a categorical proposition
implies that things corresponding to its terms actually exist.
§
2. The Class Inclusion View. Those who interpret the proposition on the
class-inclusion view, hold that both subject and predicate are conceived in
extension. They believe the true
siginficance of a proposition is to assert that the objects denoted by the
subject are included in, or excluded from the class signified by the
predicatem, e.g. "Men are mortal" asserts that all men fall within
the class "mortal". The
predicate on this interpretation must necessarily be read collectively -- as
signifying the whole class considered as a unit. A distributive use would be impossible. All men are included in within mortal things,
as these constitute a whole: they are not included within them, each taken
separately. The subject on the other
hand may be either collectively or distributively used.
We have already pointed
out that in regard of the real order, inclusion in a class is involved in
affirmative propositions, and exclusion from a class in negations: and that it
is due to this that we are able to frame a scheme of diagrams corresponding to
the four fundamental propositions. But
the question before us, is not whether the proposition does ot does not
indicate the existence of classes in the objective order: but whether this is
the relation conceived by the mind, and verbally expressed by the subject
copula and predicate.
A fatal objection to
the theory is the fact that, were it true, we should not express our
propositions in the form "all men are mortal". They would assume some such form as "All
men are included among mortals". If
"mortals" signifies the class of mortal things, it is inaccurate to
say "All men are mortal".
Every man is not the class "mortal". On the other hand, on the predicative view,
the subject, copula and predicate are the natural mode of statement: for
"mortal" us a true expression of what men are. It is sometimes indeed urged that there are a
certain number of propositions which are naturally understood this way, namely
those which are sometimes termed "judgments of classification", e.g.
"Lions are Felidae", "Daisies are Compositae". It is, however, quite inaccurate to say that
here we affirm a relation between two classes.
By "Lions are Felidae" we signify that every lion has the
attributes that mark a Felis. The copula
here has no inclusive signification. It
declares the identity between each of the things denoted by the subject, and
the same things differently conceived in the predicate. No argument can be drawn from these
propositions in support of the class-inclusion view.
§
4. Implication
of Existence. It has been a matter
of much discussion among recent logicians, whether in a categorical
proposition, the existence of objects corresponding to the subject and the
predicate, is implied. The question
seems to have first been raised explicitly by the German philosopher Herbart
(1776-1841). Very various views have
been taken. Ueberweg (System of Logic §68) teaches that all
propositions imply the existence of the subject, save those in which the
predicate is such as to abolish the subject notion, e.g. "An absolutely
greatest number is impossible".
Mill (Logic, I. p.124) holds
that analytic propositions do not involve the existence of their subjects, but
that synthetic propositions do. Mr.
Keynes and Dr. Venn alike teach that
universal propositions have no such implication, but that where a particular
proposition is used, something corresponding to the subject must exist. This may appear strange in the face of such a
judgment as 'Some Homeric Gods are immoral'.
But we are told that the existence need not be in the physical universe;
it is in the 'universe of discourse'. It
will be necessary briefly to examine this notion of the 'universe of
discourse'.
(1) Universe
of discourse. As first employed, the
phrase signified no more than that by a convention our propositions, as
verbally expressed, are restricted in their reference [N3]. Thus if I say, "No one now wears
chain-armour", I refer only to soldiers.
Actors are not under consideration;
and hence soldiers might be said to constitute my universe of discourse.
As used now, however,
the phrase has taken a different signification.
We are told that things, which do not exist in the actual physical
universe, can exist in the 'universe of mythology', 'the universe of folklore',
'the universe of the imaginable', 'the universe of heraldry'. These various forms of existence are called
'empirical' to distinguish them from logical existence, which belongs to mere
objects of thought [N4].
It is scarecely
neccessau to bring serious arguments against this view. It is rightly termed by Mr. Wolf "and
extravagant conception, which does not really mean what it seems to mean (Studies on Logic, p. 71). It is evident that if a thing possess actual existence at all, it exists in
this phusical universe. The griffins of
heraldry exist. At the present day, they
are usually made of paint and pasteboard.
Many indeed of the objects, concerning which we form judgments, have no actual existence at all. They are mere objects of thought, and belong
not to the real but to the conceptual order.
Thus I may say, "The wrath of the Homeric gods is terrible,"
"Hamlet was Prince of Denmark", &c. But in all these cases the subject as
verbally expressed is elliptical. The
full form of the judgment would be "The wrath of the gods imagined and
described by Homer, is terrible".
It is, however, to be observed that the conceptual order is essentially
representative. Whatever we imagine, we
imagine as existing in the universe to which we ourselves belong.
(2) Implications
of Existence. Having now determined
that is an entity exists at all, it exists in this or physical or actual
universe, we may go on to consider how far existence is implied in categorical
propositions.
There can be no doubt
that the categorical form as such in no way implies real existence. We have just seen that many of our judgments
relate to creations of the mind, which exists only in the conceptual order.
It remains to inquire
whether propositions relating to the real order imply the existence of their
subjects and predicates. Here we must
distinguish various classes of judgments.
Our answer will not be the same for all.
Propositions in which
the subject is a universal nature considered in abstraction from its
particulars, e.g. 'man', 'the oak', 'the horse', contain no such real
implication. Although these things
belong to the real order, yet as abstracted from particulars they exist only in
the mind: whatever has real existence is individual. In propositions such as 'Man is mortal', 'The
oak is deciduous', the employment of the singular number shows that the
immediate object of our consideration is the universal nature as
abstracted. But the nature viewed in
abstraction from individuals is also viewed in abstraction from actual
existence. It is owing to this that we
can make valied judgments concerning mathematical figures which have never
existed. Such figures have potential existence. They are objectively possible in accordance
with the laws of spatial extension.
Hence such a proposition as "The chiliagon has a thousand
angles", is a true judgment regarding the real order, even though such a
figure as the chiliagon has never been drawn.
For the proposition as thus stated abstracts, as we have just said, from
actuality, and hence is true where existence is only potential.
It is otherwise with
propositions expressed in the plural, e.g. "All oaks are
deciduous". Here the form testifies
that we are directly considering concrete reality (Ch. 3, §4).
Propositions of this class, in which the subject denotes concrete
substances, and the predicate expresses some real form apprehended as belonging
to them, most certainly suppose the existence of both subject and predicate in rerum natura. In these judgments, whether they be universal
or particular, the is of the copula
signifies actual being (Ch. 3, §3).. We do not mean that the subject denotes
something which exists at the present moment.
The judgment "All men are mortal" includes the past and future
members of the race: and the statement "All mammoths have curved
tusks" is valid, even though the mammoth is extinct. But the propositions have reference to real
existence: the things in question do not belong to the sphere of the merely
possible. The time of the existence is,
however, left undetermined. This view is
strongly confirmed by the fact that we should never employ such an expression
as, "All chiliagons have a thousand angles". We should at once recognise that the plural
form was out of place in such a connection, and that since chiliagons enjoy
only potential existence [A], the subject of our sentence
should be the universal nature viewed in abstractin from particulars.
If a propositoin refers
to certain definite individuals, the time-determination is always expressed in
ordinary speech. We do not say
"Socrates is walking", "The apostles are Jews", but
"Socrates was walking", "The apostles were Jews". But this in no way affects the logical import
of the copula.
In negative sentences
and in those affirmative judgments in which the predicate is a negative term,
the is of the copula does not signify
any real being belonging to the subject.
On the contrary, it asserts that some form is not found in it. Yet even here the existence of something
belonging to the copula is implied.
Negation, as the Scholastics said, is founded on affirmation. Did the subject not exist, there would be
nothing of which the predicate could be denied.
* At
first sight there may seem something surprising in the contention that the
copula has not always the same meaning.
Yet a little relection will show that it could not be otherwise. The mine can only express truth by affirming
(or denying) of the subject some attribute conceived as a mode of being. When we dealt
with Analagous terms (Ch. 2, §13) we
saw that the word 'thing' or 'being' is analogous, not univocal. That term is applicable to reality in all its
modes; and its absolute universality involves as a consequence that the objects
which it denotes can only be one with a unity of analogy. A man and a thought both are; but they are not beings in the same sense. There is, however, a certain proportional
resemblance between them, in virtue of which they are both comprehended under a
single analogous concept, and expressed by a common term. If this is true of 'being' in the real order,
a fortiori it is true of conceptual
'being', including, as this does, negations and privations as well as
realities. That too must be
analogous. The 'to be' of the copula
cannot possibly have always the same signification. Its meaning will vary with the difference of
the being which it expresses. Only in
our primary judgments – those in which the subject is an individual substance
and the predicate a real form – is the 'being' of the copula the 'being' of
real existence: and even within these limits, as will appear later (Ch. 9, §4)
there is further scope for analogy.
It has
been maintained by several logicians of eminence that those who deny that the
categorical form as such contains any implication of real existence, are in fact
reducing the categorical to a hypothetical judgment: that one these principles
'All S is P' should be read 'All S (if it exists) is P'. To this we reply that 'All S (if it exists)
is P' is a wholly inaccurate representation of the proposition as we understand
it. If such a proposition is enunciated,
S exists either in the real order or in the conceptual: were it not so, nothing
could be predicated of it. When the mind
judges, it is well aware to which order it refers.
Implication of existence and Immediate
Inference. The bearing of the various views as to the
implication of existence, upon the processes of immediate inference, had been
discussed with customary thoroughness by Mr. Keynes. It will be sufficient to summarise the
conclusions.
In
regard to his discussion of the traditional doctrine, it is to be noted that he
starts from the presupposition that the propositions are to be interpreted
according to the explanation we have just rejected, viz. 'All S is P' as
equivalent to 'All S (if it exists) is P'.
Starting from this erroneous hypothesis he argues (a) that the
conversion of A is invalid. From 'All S
(if there be any S) is P' we cannot conclude that 'Some P (if there be any P) is S'. Similarly the conversion of I is invalid. The invalidity of these conversions involves
(b) that the contraposition of E and O, and (c) that the inversion of A and E
are also invalid. In regard to the
doctrine of Opposition, (d) Contradiction does not hold good. For 'All S is P' merely denies that there are
any S not P; and 'Some S is not P' asserts that 'If there be any S, some are
not P'. Where S does not exist in the
'universe of discourse', both these propositions may be true. Finally (e) Contrariety does not hold
good. 'All S is P', and 'No S is P' may
both be true: for it is alike the case that there are no SP's and no S not-P's,
when S is not found in the 'universe of discourse'.
These
conclusions are all based on the erroneous interpretation of the
proposition. Interpreted as we have
understood it, all the processes of immediate inference are valid.
In
regard to his own view, viz.: that universal propositions have no existential
implication, but that particulat propositions imply the existence of their
subjects, he concludes: -
(a)
The conversion of A is invalid, for the same reason as was given above: and
similarly (b) the contraposition of E, and (c) the inversion of A and E are
invalid. The conversions E and I are
valid. These results may be summarised
by saying that we may infer a universal from a universal, and a particular from
a particular, but not a particular from a universal. In regard to Opposition (d) Subalternation
manifestly does not hold good, and (e) Contrariety for the reasons alleged
above is invalid. (f) Subcontrariety is
invalid also: for where S is not found, both sub-contraries may be false.
Mr.
Keynes holds that these results, notwithstanding the havoc they make in the
doctrine of immediate inference, are more satisfactory than those of the
traditional view, since they secure the validity of the two important processes
of (1) contradiction, (2) simple conversion.
But, as we have seen, his estimate of the traditional view is vitiated
by the initial mistake as to the interpretation of the proposition.
§ 5. The Compartmental View. Our
discussion on the implication of existence in propositions will, we trust,
throw some light on the theories as to their import, which we have yet to
discuss. The view we propose to consider
in the present section owes its origin to Dr. Venn. Mr. Keynes also has accepted it. Dr. Venn, when dealing with the import of
propositions, calls attention to the fact that, though it is quite impossible
to admit that universal propositions should be understood as signifying the
existence of the subjects, yet all of them to imply that certain things do not exist. If I affirm 'All x is y', the assertion
certainly contains the information that no such things as x not-y exist. Thus 'All men are mortal' has the non-existential implication, 'No
non-mortal men exist'. Hence he urges
that "in respect of what such a proposition affirms, it can only be
regarded as conditional, but in respect of what it denies, it may be regarded
as absolute. The proposition 'All x is
y' … declares the non-existence of a certain combination, viz.: of things which
are both x and not-y. But it does not
tell us whether there is any y at all; or if there be, whether theris also any
x".
This
view has been called the Compartmental view, because its characteristic feature
is that the essential import of the universal proposition is regarded as
consisting in the fact that it empties a definite compartment. 'All x is y' empties the compartment x not-y;
'All y is x', the compartment not-x y; 'No x is y', the compartment xy. The affirmative import, 'If there are such
things as x, then all the x's are y', is regarded as a secondary and derivative
implication.
Those
who have found no reason to disagree with what was said in our last section,
will not be prepared to accept this view.
We maintain, in the first place, that the categorical proposition, 'All
x is y', is in no sense a conditional proposition, but the direct affirmation
of an attribute in relation to a known subject.
Secondly, we maintain that it is not the case that the negative form is
the primary import, and the so-called conditional affirmative form the
secondary; but on the contary, the negative form is a mere inference from the
affirmative form.
A
further objection may be raised on the ground that the non-existential
interpretation is quite inadequate as representing the true import of the
proposition. When discussing Dr. Venn's
system of diagrams (Ch. 5, §3) we promised to say something on this point. The negative, 'There are no x not-y', merely
tells us that at the present time there happen to be no x's that are not
y. It does not in any way imply that
whenever and wherever an x is found, that x is always y. It is this surely, which is the point of real
importance. Yet the theory tells us
that not this, but the comparatively unimportant 'There are x non-y' is the
true and primary significance of the proposition.
The
treatment of the particular proposition is equally unsatisfactory. In contrast with the universal, it is
asserted it does imply the existence of its subject. "If it did not do so", says Dr.
Venn, "it would have absolutely nothing certain to tell us … it can
extinguish no class, and establish no class, and has therefore no categorical
information to give us". It is
quite true that existentially the
particular proposition can extinguish no class; but a judgment such as
"some figures are chiliagons" is most assuredly categorical, and
informs us that there is a class of possible entities, which have the definite
characteristic of having a thousand sides.
It is urged on behald of Dr. Venn's interpretation that only thus do we
get perfect contradiction between the universal and the particular. 'All x is y' and 'Some x is not-y' are
contradictories, if they respectively mean 'No x non-y exists' and 'some x
non-y exists'. Of these one must be
false; the other must be true. But to
this it may be replied that the ordinary interpretation of the two judgments
provides us with contradiction, when rightly understood, and that the
contradiction here is obtained by making the universal mean far less, and the
particular far more, than rightly they do mean.
The
German logician, F. Brentano,
held the same view in a more extreme form.
He urged that the ordinary mode of stating the A E I O propositions was
logically indefensible, and that the correct forms should be: -
A. There is not an immortal man (= All men are
mortal);
E. There is not a live stone (= No stones are
living);
I. There is a sick man (= Some men are sick);
O. There is an unlearned man (= Some men are not
learned).
The
existential significance of the copula would, he claimed, thus appear
plainly. Such a theory carries its own
refutation with it. It is manifest to
any one who reflects, that as a matter of fact we do not think in these forms.
Footnotes
[N1] An. Prior I,
. c.27 §3. See also An. Post I., c.22 §2,
where he points out that such a proposition as That white object is a
stick" is predication per accidens since, since "the
white" did not become a stick, but vice versa. On this St. Thomas comments as follows: "Subjectum fit hoc quod
praedicitur de ipso sicut de subjecto ... Cum ergo non sit verum dicere quod Album
fiat lignum, intelligitur per accidens, quia scilicet illud particulare
subjectum, cui accidit album, est lignum.
Iste ergo est sensus huiusmodi praedicationis in qua subjuectum
praedicatur de accidente," in An. Post ., lect. 33. Jevons (Principles
of Science, p. 39) has completely misunderstood Aristotle's meaning on this
subject.
[N2] See
below, Ch. 8, §1.
[N3] De
Morgan, Formal Logic, c. iv.
[N4] Keynes, Formal Logic, Part II., c. 7.
Venn, Symbolic Logic, p.
127. Cf. Bradley, Appearance and Reality, p. 367.
Editor's notes
[A] If the plural form signifies real existence,
as just claimed, the assertion made by the plural sentence "chiliagons
enjoy only potential existence" then seems an odd one.
Copyright © E.D.Buckner 2005.