The paper, below, Brentano's Logical Innovations, by J.P.N. Land, which appeared in Mind 1876, marks a now-forgotten but important landmark in the history of logic. It is a criticism of the 'Brentano' interpretation of universal propositions of the form 'All A's are B' and existential (then called 'particular' propositions) of the form 'some A is B'. Brentano argued (in 1874) that the universal proposition does not assert or imply the existence of any A or B, merely denying the existence of anything that is A and not B. The particular proposition 'some A is B', by contrast, asserts the existence of something that is both A and B. Brentano was one of the first to argue for the modern interpretation (which, in the hands of Peirce and Frege, became the basis of the predicate calculus). It contrasts with the traditional view that the universal implies the particular. If every A is B, then some A is B.
Land's paper, which defends the traditional interpretation, was one of the first to discuss Brentano's view (and, probably, to bring it to the attention of an English-speaking public). Thus it marks the boundary between the modern interpretation of propositions, familiar to everyone who has been trained in modern predicate calculus, and the traditional interpretation, so unfamiliar it is usually misunderstood. It is important because, as well as clearly explaining the actual distinction between the the two interpretations, it also captures very well what was difficult to accept about the new one - hard to grasp today, because Brentano's interpretation is so embedded in our thinking about logic.
Indeed, the modern interpretation is so familiar to students that it often comes as a surprise that anyone thought of things otherwise. How on earth could traditional logicians have thought that 'Every A is B' implies 'some A is B', when everyone knows that the former is analysed as 'for any x, if Ax then Bx', and is equivalent to 'not for some x, Ax and not Bx'? The traditional view is sometimes wrongly characterised it as a mistake. It is not, of course, for the formal interpretations of ordinary language are just that, they are interpretations. It is a measure of the success of predicate calculus that it should have changed our view of the meaning of ordinary language. But in 1876, it was something of a novelty.
Land says '... logicians are bound to inquire whether Brentano's formulae are really, as he assures us, the exact equivalents of the traditional four sorts of categorical propositions'. He argues that they are not, for a number of interesting reasons that anticipate later discussions of the traditional 'square of opposition'. For example, he argues that the subject is admitted to exist either in the real world, 'or in some imaginary world assumed for the nonce'. Then the subject is asserted to have the qualifications signified by the predicate term. Thus 'Ulysses is the son of Laertes' means nothing unless we suppose Ulysses as existing at least in a world of fiction. The predicate is affirmed or denied of the subject, whatever it is.
He says that the existence of the subject is not asserted but presupposed. The idea of presupposition is often supposed to originate with Strawson, who mentions it in his discussion of the traditional square of opposition, and in his well-known essay 'On Referring'. But it is of course much older. Frege invokes it, in his paper 'On Sense and Reference'. Land uses it here, nearly twenty years before Frege. And as Land points out, it can be found in the work of Kant's pupil Herbart. In pronouncing about someone's actual condition (for example, by saying that a man walks), Land says that we are convinced in our own mind that the question of existence has been settled, or presupposed. The question of existence is therefore separate from anything asserted in the proposition, and must be tried outside the proposition in hand. The proposition thus deals only with some qualification of the subject.
In another place on this site, you can find G.H. Joyce's contemptuous (1908) dismissal of Brentano's interpretation. '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'.
Edward Buckner
London, May 2007
XII. CORRESPONDENCE.
BRENTANO'S LOGICAL INNOVATIONS
IN your first number Professor Flint, while criticising Brentano's recent work on Psychology, gives a few specimens of that author's discoveries in Logic well calculated to awaken, as he says, the most lively curiousity. Whatever the forthcoming special treatise may add to our knowledge of the new theory proposed, enough is said in his Psychologie to enable us to understand its principles. Allow me, as one who has examined these as soon as published, to offer the following remarks.
It will hardly be necessary to mark the passage's of Mill's writings which may have led the Austrian Professor to his starting-point. Let me observe at once that the main feature of his reconstruction of logical doctrine consists in reducing all categorical propositions to what he calls existential propositions, doing away with the familiar distinction between subject and predicate terms. Where we say Some man is sick, he gives as a substitute, There is a sick man. Instead of No stone is alive, he puts There is not a live stone. On the other hand, he proposes to improve on the statement Some man is not learned by welding together the negative and the predicate term, and asserting There is an unlearned man. Finally, All men are mortal is to be expressed in his system There is not an immortal man. That is to say, he simply affirms or denies the existence of some object having either two positive qualifications, or one positive together with one negative.
Evidently, the order in which we mention those qualifications can make no difference. It is exactly the same, whether I maintain the existence of a sick man, or that of a human patient; whether I refuse to admit that an immortal man or that a human immortal is a reality. This is what Brentano means, when he announces as one of his discoveries, that 'any categorical proposition is liable to simple conversion' - a theorem which, taking words in their ordinary technical significance, could not be maintained for a moment.
Moreover, we see that, wherever we used to offer an opinion touching a whole class, the new propositions offer a denial of existence; so that, what Brentano calls a negative, is meant only for what we were taught to consider a universal proposition, and his affirmatives are the particular propositions of everybody else. Also, where the predicate term of the old Logic designed a positive quality, we get in certain cases a negative quality instead, merely by translation into the new formulae. It may be shown that in every kind of lawful syllogism, when thus translated, one of the three terms is dissected into a positive term and its corresponding negative. Hence his series of startling declarations, which owe the whole of their apparent novelty to a tacit change in the use of time-honoured technical expressions.
Of more serious import is the condemnation passed upon all inferences from either one or two universal propositions to a particular one. No doubt, when we remember that by the new [290] system the former are turned into assertions of non-existence, it is clear that no accumulation of mere non-existences can vouch for the existence of anything; and so, from his point of view, Brentano is certainly right. However, we seem to touch here upon a curious discovery. The self-same facts which, stated in the usual manner, can be shown to involve other facts, would appear not to involve the latter when stated in the new style. Before admitting such a paradox, logicians are bound to inquire whether Brentano's formulae are really, as he assures us, the exact equivalents of the traditional four sorts of categorical propositions. And they will find, that in translating categorical universals into existential negatives, part of the meaning is dropt by the way, and precisely that part on which the condemned logical operations depend.
In an ordinary proposition the subject is necessarily admitted to exist, either in the real or in some imaginary world assumed for the nonce. It is further maintained either to admit or not of the qualifications comprehended in the predicate term. Accordingly, in the former case, the predicate term also is asserted to have its representative in that world in which we admit the subject to be. Whereas, in the case of the negative, it is not decided whether there be anything answering to the predicate term. Ulysses is the son of Laertes means nothing at all, unless we suppose Ulysses as existing at least in a world of fiction; and so it is with the proposition Ulysses is not the son of Priam; but in the latter instance it remains undecided whether there be (in the same assumed world) any son of Priam. For aught we learn from this proposition, Priam might have been a childless man through life. Again, Bucephalus is not a winged horse presupposes the existence of Bucephalus in some world, but does not assert that of a winged horse. Nor does it appear from Bucephalus is not an Arab that a race of Arabs is acknowledged to exist.
By disregarding, as Brentano and others do, the difference between the subject term and the predicate term, we lose an advantage even where we judge only of a part of a class. The proposition Some children of Jupiter are mortals proceeds from the existence of Jupiter's children (to wit, in the world of classical mythology); and so the class of mortals, to which it is implied they belong, is also thought of as continued into that assumed world. After this, we may infer Some mortals are children of Jupiter, because our first proposition has prepared us to extend the dominion of the term of mortal in that way. But he who begins with the latter statement appears to start from the common notion of mortals as belonging to the real world, and to attribute the same reality to Jupiter and his paternal function. By treating Conversion as a kind of inference, we retain the advantage of knowing at the outset the ground we move on. Whereas Brentano's comprehensive sentence, There is somebody who is at the same time a mortal and a child of Jupiter, leaves us in the dark about the order of things which it concerns.
Turning to propositions touching the whole of a class, our loss [291] becomes heavier still. When we say No stone is alive, or All men are mortal, we presuppose the existence of stones or of men. Nobody would trouble himself about the possible properties of purely problematical men or stones. Brentano thinks he gives the exact equivalent of those sentences when he maintains There is not a live stone, or There is not an immortal man, which may be true even if there be no man or stone whatever. No wonder, when one takes away the supposition which every judgment treated by common Logic involves, that the residue cannot yield all the conclusions to which one was entitled by the premisses in their original state.
Brentano had caught a glimpse of the difference between his existential and the old categorical propositions when he touched upon the theory of Herbart (as given by Drobisch, Logik, 3rd ed., ~55), that the subject in the latter is presupposed (vorausgesetzt). Unluckily, Drobisch adds in the same breath that the subject is not put forward unconditionally (nich unbedingt gesetzt), and, that the meaning only is, that if the subject be assumed, the predicate applies to it (dass, wenn man das Subject setzt, ihm das Prädicat ... zukommt). In opposition, Brentano calls it a strong, and even an impossible demand, to ask belief for the doctrine that the sentence Some man walks contains the tacit clause provided there be a man at all. Both authors appear to confound what is properly called a presupposition (Voraussetzung) with a mere condition (Bedingung). At least, Drobisch has not sufficiently guarded against such a construction of his words, and Brentano takes them in that sense. The person who tells me Some man walks would seem, according to former, to make his opinion dependent on the contingency of the existence of man; this the latter refuses to admit, and so far he is right. On the contrary, such a person, by pronouncing about some man's actual condition, professes to be convinced in his own mind that the question of existence has been settled, or may be settled at any time, to his and his interlocutor's perfect satisfaction. This he presupposes, that is to say, he considers the statement about the existence as a separate one, to be tried outside the proposition in hand, which latter starts from it, and deals only with some qualification of the subject. Hence it is quite possible for two different opponents to direct their attacks, one against the existence of the subject presupposed, and the other against the description of that subject given by the proposition itself. A close examination of the traditional inferences which our author rejects would have taught him that they derive their value from the presuppositions implied, and that the absence of the latter constitutes a material difference between the categorical propositions in common use, and the existential ones into which he pretends to translate them without any change in meaning (ohne irgend welche Aenderung des Sinnes).
There is no need to dwell upon his anticipations of the horror and dismay with which his doctrines will be received among logicians of the older school. They will suspect at once some such tampering with the names of things, and misunderstanding of the [292] import of common forms of thought, as I have just pointed out. As soon as they find that such are the merits of the new theory, they will cease wondering, and simply ask cui bono?
Certainly the purpose of Logic is served by turning its subject-matter in all directions, and examining it from every point of view. We may be thankful for any new system, provided always it do not give out as a refutation of traditional precepts what is only a re-arrangement of old truths. With this restriction it is possible that Brentano's promised treatise will throw additional light on some questions. Nevertheless, at all events, it will have the disadvantage which we least expect from an empirical psychologist, of trying to replace a more natural theory by an artificial one.
For instance, when we think all men to be mortal, we proceed from a notion of man acquired before, and maintain (say by generalisation from experience) that in every object answering to this notion the character of mortality exists also. Afterwards, occasion serving, we find that we have made it impossible for us, as long as we hold the same opinion, to assert the existence of an immortal man. It may be that we never in our lives speculate upon the supposition of such a being. Brentano would have us think of this supposition first of all, and reject it as once. But we could hardly reject it without a reason, and the most obvious one is our persuasion that all men we know of, and therefore all beings we recognise as men, are liable to die. To speak generally, strong proofs are wanted to make it plausible that any denial can arise in the mind except as opposed to an affirmation touching the same matter conceived before. In the genesis of our convictions, belief comes in earlier than negation. Nor does induction naturally proceed from warding off a particular proposition to adopting its contrary universal, but from admitting the former to judging alike of the entire class.
| Leyden, Feb. 1, 1876. | J.P.N. LAND. |