These extracts are from chapter 6 ('Verbal and Real Propositions') of the first book of John Stuart Mill's great work, A System of Logic. Mill argues that the scholastic distinction between essential propositions and accidental propositions is merely one of language, and is not determined by the nature of things. An 'essential' proposition is merely verbal: it says of a thing, using a particular term for that thing, only what is asserted of the thing by using that term.

The terms 'essential proposition' and 'accidental proposition' are those which were used by Mill, and by later logicians of the traditional school of the nineteenth and early twentieth century. I have not been able to find out whether these terms were used at all by the scholastic logicians, as Mill claims. He gives no sources, and I have not been able to locate any source which actually mentions them by the corresponding Latin names. (A Google on "propositio essentialis" yields nothing, whereas "essential proposition" gives a lot, suggesting the distinction is purely English, hence non-scholastic). Scholastic philosophers did, however, speak of essential and accidental predication (praedicatio essentialis, praedicatio accidentalis). See here, for example.

It is clear that Mill's distinction is the same as the one Kant draws between Analytic and Synthetic propositions (and Mill even says so in a footnote to the eighth edition). It is not so clear that his distinction between Verbal or what Locke calls 'trifling' propositions and Real propositions is the same as the distinction between essential and accidental propositions, or between what Hume calls truths of reason and truths of fact (Treatise I. ii. 1, Enquiry c. 4). For truths of reason are meant to include those propositions which are not trifling at all, but which are necessarily true because what is signified by the predicate follows from, without being 'contained in' what is signified by the predicate. Locke, who makes the same distinction, gives the example 'the external angle of all triangles is bigger than either of the opposite internal angles'. Mill, by contrast, makes no distinction between analytic (trifling) and synthetic a priori (non-trifling but essentially true) propositions.

I have included a section from Chapter 7, which contains the beautiful idea that metaphysics is a 'fertile field of delusion propagated by language'. Mill argues that the scholastic idea of the essence of a thing is simply of what makes a thing the kind of thing it is. But we do not, in most cases (humans, for instance) know what this is. Not liking to admit that nobody could discover what makes people human, logicians satisfied themselves with what made it to be what it was called .

This html setting is taken from the definitive eighth edition.

Chapter 6, Section 2.

2. Almost all metaphysicians prior to Locke, as well as many since his time, have made a great mystery of Essential Predication, and of predicates which are said to be of the essence of the subject. The essence of a thing, they said, was that without which the thing could neither be, nor be conceived to be. Thus, rationality was of the essence of man, because without rationality man could not be conceived to exist. The different attributes which made up the essence of the thing were called its essential properties; and a proposition in which any of these were predicated of it was called an Essential Proposition, and was considered to go deeper into the nature of the thing, and to convey more important information respecting it than any other proposition could do. All properties, not of the essence of the thing, were called its accidents; were supposed to have nothing at all, or nothing comparatively, to do with its inmost nature; and the propositions in which any of these were predicated of it were called Accidental Propositions.

A connection may be traced between this distinction, which originated with the schoolmen, and the well known dogmas of substantiae secundae or general substances, and substantial forms, doctrines which under varieties of language pervaded alike the Aristotelian and Platonic schools, and of which more of the spirit has come down to modern times than might be conjectured from the disuse of the phraseology. The false views of the nature of classification which prevailed among the schoolmen, and of which the dogmas were the technical expression, afford the only explanation which can be given of their having misunderstood the real nature of those Essences which held so conspicuous a place in their philosophy. They said, truly, that man cannot be conceived without rationality. But though man cannot, a being may be conceived exactly like a man in all points except that one quality, and those others which are the conditions or consequences of it. All therefore which is really true in the assertion that man cannot be conceived without rationality, is only that if he had not rationality, he would not be reputed a man. There is no impossibility in conceiving the thing, nor, for aught we know, in its existing: the impossibility is in the conventions of language, will not allow the thing, even if it exist, to be called by the name which is reserved for rational beings. Rationality, in short, is involved in the meaning of the word man: is one of the attributes connoted by the name. The essence of man, simply means the whole of the attributes connoted by the word; and any one of those attributes taken singly is an essential property of man.

But these reflections, so easy to us would have been difficult to persons who thought, as most of the later Aristotelians did, that objects were made what they were called, that gold (for instance) was made gold, not by the possession of certain properties to which mankind have chosen to attach that name, but by participation in the nature of a certain general substance, called gold in general, which substance, together with all the properties that belonged to it, inhered in every individual piece of gold.

As they did not consider these universal substances to be attached to all general names, but only to some, they thought that an object borrowed only part of its properties from an universal substance, and that the rest belonged to it individually: the former they called its essence, and the latter its accidents. The scholastic doctrine of essences long survived the theory on which it rested, that of the existence of real entities corresponding to general terms; and it was reserved to Locke at the end of the seventeenth century, to convince philosophers that the supposed essences of classes were merely the signification of their names; nor, among the signal services which his writings rendered to philosophy, was there one more needful or more valuable.

Now, as the most familiar of the general names by which an object is designated usually connotes not one only, but several attributes of the object, each of which attributes separately forms also the bond of union of some class, and the meaning of some general name; we may predicate of a name which connotes a variety of attributes, another name which connotes only one of these attributes, or some smaller number of them than all. In such cases, the universal affirmative proposition will be true; since whatever possesses the whole of any set of attributes, must possess any part of the same set. A proposition of this sort, however, conveys no information to any one who previously understood the whole meaning of the terms. The propositions, Every man is a corporeal being, Every man is a living creature, Every man is rational, convey no knowledge to any one who was already aware of the entire meaning of the word man, for the meaning of the word includes all this: and that every man has the attributes connoted by all these predicates, is already asserted when he is called a man. Now, of this nature are all the propositions which have been called essential. They are, in fact, identical propositions.

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4 An essential proposition, then, is one which is purely verbal; which asserts of a thing under a particular name only what is asserted of it in the fact of calling it by that name; and which therefore either gives no information, or gives it respecting the name, not the thing. Non-essential, or accidental propositions, on the contrary, may be called Real Propositions, in opposition to Verbal. They predicate of a thing some fact not involved in the signification of the name by which the proposition speaks of it; some attribute not connoted by that name. Such are all propositions concerning things individually designated, and all general or particular propositions in which the predicate connotes any attribute not connoted by the subject. All these, if true, add to out knowledge: they convey information, not already involved in the names employed. When I am told that all, or even that some objects, which have certain qualitieis, or which stand in certain relations, have also certain other qualities, or stand in certain other relations, I learn from this proposition a new fact; a fact not included in my knowledge of the meaning of the words, nor even of the existence of Things answering to the signification of those words. It is this class of propositions only which are in themselves instructive, or from which any instructive propositions can be inferred.

Nothing has probably contributed more to the opinion so long prevalent of the futility of the school logic, than the circumstance that almost all the examples used in the common school-books to illustrate the doctrine of predication and that of the syllogism consist of essential propositions. They were usually taken either from the branches or the main trunk of the Predicamental Tree, which included nothing but what was of the essence of the species: Omne corpus est substantia, Omne animal est corpus, Omnis homo est corpus, Omnis homo est animal, Omnis homo est rationalis, and so forth. It is far from wonderful that the syllogistic art should have been thought to be of no use in assisting correct reasoning, when almost the only propositions which, in the hands of its professed teachers, it was employed to prove, were such as every one assented to without proof the moment he comprehended the meaning of the words; and stood exactly on a level, in point of evidence, with the premises from which they were drawn. I have, therefore, throughout this work, avoided the employment of essential propositions as examples, except where the nature of the principle to be illustrated specifically required them.

Chapter vii, section 5.

5. To begin with Differentia. This word is correlative with the words genus and species, and, as all admit, it signifies the attribute which distinguishes a given species from every other species of the same genus. This is so far clear: but we may still ask, which of the distinguishing attributes it signifies. For we have seen that every Kind (and a species must be a Kind) is distinguished from other Kinds, not by any one attribute, but by an indefinite number. Man, for instance, is a species of the genus animal: Rational (or rationality, for it is of no consequence here whether we use the concrete or the abstract form) is generally assigned by logicians as the Differentia; and doubtless this attribute serves the purpose of distinction: but is has also been remarked of man, that hie is a cooking animal: the only animal that dresses its food. This, therefore is another of the attributes by which the species man is distinguished from other species of the same genus: would this attribute serve equally well for a differentia? The Aristotelians say No; having laid it down that the differentia must, like the genus and species, be of the essence of the subject.

And here we lose even that vestige of a meaning grounded in the nature of the things themselves, which may be supposed to be attached to the word essence when it is said that genus and species must be of the essence of the thing. There can be no doubt that when the schoolmen talked of the essences of things as opposed to their accidents, they had confusedly in view the distinction between differences of kind, and the differences which are not of kind; they meant to intimate that genera and species must be Kinds. Their notion of the essence of a thing was a vague notion of a something which makes it what it is, i.e. which makes it the Kind of thing that it is - which causes it to have all that variety of properties which distinguish its Kind. But when the matter came to be looked at more closely, nobody could discover what caused the thing to have all those properties, nor even that there was anything which which caused it to have them. Logicians, however, not liking to admit this, and being unable to detect what made the thing to be what it was, satisfied themselves with what made it to be what it was called. Of the innumerable properties known and unknown that are common to the class man, a portion only, and of course a very small portion, are connoted by its name; these few, however, will naturally have been thus distinguished from the rest either for their greater obviousness, or for greater supposed importance. These properties then, which were connnoted by the name, logicians seized upon, and called them the essence of the species; and not stopping there, they affirmed them, in the case of the infima species, to be the essence of the individual too; for it was their maxim, that the species contained the 'whole essence' of the thing. Metaphysics, that fertile field of delusion propagated by language, does not afford a more signal instance of such a delusion. On this account it was that rationality, being connoted by the name man, was allowed to be a differentia of the class; but the peculiarity of cooking their food, not being connoted, was relegated to the class of accidental properties.

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