Chapter VII.

THE IMPORT OF PROPOSITIONS.

 

 

1. Import of Propositions - Predicative view

2.  The Class Inclusion View

3.  The Attributive View

4.  Implication of Existence

 

 

§ 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.

 

 

§ 3.  The Attributive 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.


EDWARD BUCKNER'S WEBSITE

Copyright © E.D.Buckner 2005.