Horace William Brindley Joseph (1867-1943) was a Fellow of New College, Oxford. An Introduction to Logic, published in 1906, is another of those fascinating books published in the early 1900's whose authors seem almost oblivious to the revolutionary developments of modern logic that are taking place around them. (Extracts from other books of this sort can be found here and here).

Joseph describes the book as an introduction to traditional logic, and mentions that the tradition has become divergent, 'and often corrupt'. He claims to be going back largely to its source in Aristotle. Indeed, this is one of the few books of this period that shows awareness and knowledge of medieval sources, although most of his quotations appear to be from secondary sources such as Prantl.

The philosophical sources of his work he mentions as the Hegelian logicians such as Bradley, Bosanquet and Lotze, though he also mentions logicians from what Grattan-Guinness calls the 'Oxford logistics' school such as Joachim, Cook Wilson, and Prichard. The latter two were influences on the later development of Ordinary Language Philosophy.

The section quoted below concerns the distinction between essential and accidental propositions, which Mill had identified with the distinction between verbal and real propositions, and analytic and synthetic propositions. (See here for Mill's view on the subject). Joseph argues that the three distinctions are different. 'They are not made on the same fundamentum divisionis, nor do they respectively bring together and keep apart the same individual judgments'.

The book has at least one memorable quote. 'Logic should appeal as far as possible to the reason, and not to the memory'.

There are a few other distinctions drawn among judgments, which ought to be noticed. We may deal first with a series of antitheses whose force is too readily considered to be the same: these are analytic and synthetic, essential and accidental, verbal and real.

'In all judgments', says Kant, 'wherein the relation of a subject to the predicate is cogitated (I mention affirmative judgments only here; the application to negative will be very easy), this relation is possible in two different ways. Either the predicate B belongs to the subject A, as somewhat which is contained (though covertly) in the conception A; or the predicate B lies completely out of the conception A, although it stands in connexion with it. In the first instance, I term the judgment analytical, in the second, synthetical. Analytical judgments (affirmative) are therefore those in which the connexion of the predicate with the subject is cogitated through identity; those in which this connexion is cogitated without identity, are called synthetical judgments. The former may be called explicative, the latter augmentative judgments; because the former add in the predicate nothing to the conception of the subject, but only analyse it into its constituent conceptions, which were thought already in the subject, although in a confused manner; the latter add to our conception of the subject a predicate which was not contained in it, and which no analysis could ever have discovered therein'. Kant's example of an analytic judgment is 'all bodies are extended': for our conception of bodiy is extended substance, and therefore, in order to make the judgment, we need only analyse the conception. 'All bodies are heavy', on the other hand, is a synthetic judgment; for it is not contained in the conception of bodies, that they gravitate towards one another.

Kant's statement of the distinction between analytic and synthetic judgments has been much discussed and criticised. In particular, it has been pointed out, and it is important to recognise, that no judgment is purely analytic; every judgment is a synthesis of distinguishable elements. Let the predicate B of an analytic judgment be contained in the conception of the subject A - extended for example in the conception of body. Suppose the constituent elements of the conception A to be BCD, as those of body are substance and extension. Yet the judgment 'A is B' (all bodies are extended) is not equivalent to the judgment 'BCD is B' (all extended substances are extended). The latter does merely repeat in the predicate what is contained in the subject-conception; and inasmuch as the subject-conception has already been exhibited as a synthesis of elements, among which the predicate is one, the judgment only goes over old ground. But the former judgment performs a process of analysis, and does not pick out one element from an analysis already made. Now this difference is important; because in performing an analysis of the subject-conception, we realise at the same time that the predicate must be conjoined with the other constituent elements in the subject, in order to make the subject-conception. 'A is B' means 'to the constitution of A, B must go with CD': all bodies are extended means 'to the constitution of body, extension must go with substantiality'. Kant indeed tells us that until the analytic judgment is made, the predicate B is only covertly contained in the conception A: so that it is really the work of the judgment to recognise B (as an element along with other elements) in the conception A. On the other hand, the synthetic judgment is from one point of view analytic. 'Cats purr'; it is true that I learn this only by experience, and that purring is not otherwise necessary to constitute the conception of a cat: but to me, who have learnt long ago that cats do purr, purring has become part of my conception of a cat, and when I make this judgment, I am picking out one element in my conception, in order to assert its connexion with the others. Except therefore to some one who knows what cats are, but not what noise they make, and knows what puuring is extraneously, the judgment that cats purr is not purely synthetic. And even to him, in the act of making it, it becomes also analytic; for no sooner has he united the predicate 'purr' with his conception of a cat, than it becomes an element selected from among the other elements of his more enlarged conception.

Every judgment then is at once analytic and synthetic; for the act of judgment at once holds different elements apart and recognises them as elements in a single whole. As held apart, it requires an act of synthesis to see that they make one whole: as recognised to make one whole, it requires an act of analysis to find and hold them apart.

In distinguishing analytic and synthetic judgments, then, Kant has not distinguished judgments in which there is only an act of analysis from those in which there is only an act of synthesis. What he has really done is to distinguish those in which the predicate is part of the definition of the subject from those in which it is not. For he really had in his mind only judgments whose subject is general, or at any rate if his distinction can be applied to singular judgments, it is only so far as a particular thing is designated in the subject by a general term, or concept under which it is brought. 'This body is extended' would be analytic, and 'This body is heavy' synthetic, because the predicates are respectively explicative and augmentative of the concept body. Yet if we look to the particular experience which is the ground of the judgment 'This body is heavy', we shall have to acknowledge that it analyses what is given as a concrete whole; so that although the judgment is synthetic so far as concerns the relation of the predicate to the subject-concept, it is analytic as concerns its relation to the object of perception, the body in question. Such judgments have in fact been called in consequence 'analytic judgments of sense', though they are emphatically synthetic in the Kantian sense, as being grounded on the conjunction of manifold elements empirically in an object, and not on a relation between subject and predicate which is necessary for thought, because 'cogitated through identity' and so incapable of being denoted without self-contradiction.

Now Kant, in drawing the distinction, was interested precisely in the question of the necessity belonging to certain judgments, in virtue of which our thought recognises them as true without appeal to confirmation from repeated experience. His 'analytic' judgments have this necessity because they are analytic; the problem, he says, is to see how any 'synthetic' judgments can have it. So far as these merely state the conjunction in things of attributes which are distinguished and found together in them, they lack the character of necessity, whether we call them synthetic or analytic; but he held, and rightly, that there are some judgments in which we do apprehend the necessity of the predication, without the connexion being 'cogitated through identity'. Such are the judgments '5+7=12', or 'Two straight lines cannot enclose a space'.

A question next arises regarding those judgments in which the predicate is already covertly contained in the subject-concept, and which are therefore incapable of being denied without contradiction, and so conceptually necessary; has this come to pass merely by the fact that we have chosen to include certain elements in the subject-concept, which we thereupon cannot consistently deny of it? We saw, in discussing Definition, that we have sometimes to determine arbitrarily what elements are to be included in our definition of a concept; and if this were always the case with definitions, it would appear that Kant's analytic judgments are necesarily true merely because of the meaning which we have given to the subject of them. On the other hand, if the elements in the definition are not arbitrarily selected, but are seen to hang together necessarily in the constitution of the thing defined, then the analytic judgment which predicates of a concept a part of its definition is justified by the same insight into the necessary connexion of distinguishable characters as justifies a synthetic judgment which is not empirical. Let us take an example of a subject in whose definition the elements are arbitrarily put together. In the Elementary Education Act of 1870, 3, an elementary school is by definition 'a school, or department of a school, at which elementary education is the principal part of the education there given, and does not include any school or department of a school at which the ordinary payments in respect of the instruction, from each scholar, exceed ninepence a week'. To say therefore that an elementary school charged less than 10d. per head per week in fees was to make an analytic judgment, from the standpoint of the Education Department in 1870; but only because it had been arbitrarily settled that none charging 10d. or over should rank as an elementary school, and not because we have such a knowledge of what an elementary school must be as to see that it could not be elementary, and charge a fee so high. Whereas if I say that a figure has sides, that is true not because it is agreed to call nothing a figure which has not, but because I see that lines can be put together into the unity of, and are required in, a figure.

It follows that some judgments ranked by Kant as analytic may involve just the same insight into the necessary connexion of elements in an unity as is found in the class of synthetic judgments which most interested him - viz. those that are grounded not upon repeated experience but upon the apprehension of necessity; while others are true only in virtue of the meaning we have chosen to give to words; neither is any judgment purely analytic or purely synthetic. His distinction therefore is not well expressed by these terms. If, however, we take the terms explicative and augmentative (or ampliative), we may say that all his 'analytic' judgments are explicative of what is already involved in thinking the subject, but we may question whether all his 'synthetic' judgments are ampliative, unless singular judgments, which analyse a present experience, are excluded; nor does the term 'explicative' apply any otherwise to those judgments where the elements in the subject are arbitrarily put together than to those where they constitute a real unity for our thought. Now the former are, as we have seen, true by convention as to the meaning of words, and so they may be called verbal; and to verbal judgments we may oppose as real all whose truth does not rest upon the meaning given to words, but which state something about the nature of things: whether what they state is seen to be necessary - in which case they may be either analytic or synthetic in the Kantian sense - or rests upon mere experience of fact - in which case Kant would call them synthetic. This does not commit us to the view that all definition is merely verbal, but only that if a so-called definition does no more than arbitrarily to include certain elements in a concept, like the definition of 'elementary school' quoted above, then it is verbal. On the other hand, if we wish to mark the distinction between judgments in which the predicate is part of the definition of the subject, and those in which it is not, we may call the former essential and the latter accidental. The term 'essential' may be extended to cover those cases where the definition is arbitrary, and some essential judgments will then rest merely on the law that forbids self-contradiction; while others will involve the same apprehension of the necessary connexion of elements in a unity as Kant's necessary 'synthetic' judgments; some, that is, will be verbal and others real. The term 'accidental', if 'accident' be taken, as by Aristotle [in the phrase ...] to include what is demonstrable of a kind, will cover all Kant's 'synthetic' judgments, whether they are grounded on an experience which, so far as we can see, might have been otherwise, or on insight into a necessary relation of concepts. It will be seen that the three antitheses, of analytic and synthetic, essential and accidental, verbal and real, canot really be regarded as equivalent; for neither are they made on the same fundamentum divisionis, nor do they respectively bring together and keep apart the same individual judgments.

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