The passage below is from An Introduction to Logic (pp 140-2) by the Oxford logician H.W.B. Joseph, explaining the difference between so-called enumerative judgment, and judgments that are genuinely and properly universal.
Universal judgments, as he sees it, express scientific truths, a necessary connexion between subject and predicate, are general in character, and hold of every instance, past, present and future. They can be used to express scientific or mathematical facts such as 'All triangles in a semicircle are right-angled'.
Enumerative judgments, by contrast, are merely a collection of many individual judgments into one, thus they do not express any necessary connexion between subject and predicate, or any character common to all the individual subjects. They state historical fact rather than scientific truth. In character they are close to the singular judgment, the subject the A's often containing the definite article. Examples of enumerative judgments are No American poet stands in the first rank, or that All the French ministries are short-lived.
As characterised by Joseph, the universal judgment 'All A is B' is close to a hypothetical judgment, i.e. asserts that whatsoever is an A (if there are any A's) is a B. Indeed, he mentions the view, referring to Leibniz, Bradley and Bosanquet in footnote [N3] - that the truth of a properly universal judgment does not require the existence of any A. An enumerative judgment, by contrast, makes explicit reference to A's, often by the use of the definite article 'the', and therefore requires, or presupposes the existence of A's for its truth.
An Introduction to Logic (pp 140-2)
At the same time, the words all and none, as signs of the universality of a judgment, have disadvantages of their own. For a judgment is really universal, when the subject is universal or general, and the predicate attaches to the subject (or is excluded from it) necessarily; but if it is found to attach to the subject (or to be excluded from it) in every existing instance without any necessity that we know of, we use the same expressions, all and none. Thus we may say that No American poet stands in the first rank, or that All the French ministries are short-lived; but neither of these is really an universal judgment. Each is a judgment made about a number of individuals: it states an historical fact, and not a scientific truth. It would be convenient to call such judgments collective [N1] or enumerative judgments; for they really collect in one the statements which may be made about every [157] instance of a certain class, and make their assertion on the strength not of any conceptual necessity, but of an enumeration.
We must of course distinguish the question whether a judgment is meant as universal, from the question whether we have a right to enunciate it universally. If instead of saying All the French ministries are short-lived (where the article the shows that I am referring to all of a certain number of things), I were to say All French ministries are short-lived, it might be contended that the judgment no longer referred to individuals or instances, but affirmed a necessary character of French ministries as such. In truth the statement is not clear, and a man would have to ask me, whether I meant it as an historical summary, or an universal truth; but the ambiguity of the statement is the very point to be noticed; for the two interpretations indicate the difference between a merely enumerative, and a true universal, judgment. If we contrast such judgments as All my bones are out of joint and All triangles in a semicircle are right-angled, the difference is very plain.
We have seen that there is a marked distinction between a singular judgment, whose subject is an individual, and an universal or particular judgment, whose subject is a general or abstract term, a concept or kind of thing. The enumerative judgment (and this is true in some degree of the particular judgment also) approximates to the type of the singular rather than of the universal [N2]. For though the subject be a general term, and I predicate about all the members included under that term, yet I do so because I have examined them as individuals, and found the predicate in them all, not because of any necessary connexion between the predicate, and the common character of these individuals which the general term signifies. French ministry is a general term; but (for all that I see) it is not because being a French ministry involves being short-lived, that I assert all the French ministries to be short-lived; it is because I have noted each case; just as it would be upon the strength of noting the individual case that I should assert the first ministry of M. Jules Ferry to have been short-lived. At the same time, the collective judgment, though thus approximating to the type of the singular, gives the hint of a true universal judgment. It suggests the ground for the [158] predicate may lie in the common character signified by the general term under which all these instances are collected. If I say Luther was hated, there is nothing to indicate what about him was hateful: with which of all the coincident attributes in Luther his hatefulness is universally connected. If I say All reformers have been hated, though that is as much an historical statement as the first, and therefore enumerative only, it suggests that the reason why all those men have been hated (Luther and Calvin, Cromwell and Gladstone – the statement implies a possible enumeration) lies in the fact that they were reformers. Thus from an enumerative judgment we may pass to an universal; from a study of individuals to the assertion of a universal connexion of characters. When we enunciate enumerative judgments, we are on that road: sometimes farther, and sometimes less far.
The difference between a true universal judgment and one merely enumerative is exceedingly important. The one belongs to science, the other to chronicle or history. An universal judgment holds of any and every instance, alike past present and future, examined or unexamined. An enumerative judgment holds only of those instances which we have examined, and summed up in the subject. All reformers are hated: if that is merely enumerative, it affords me no ground to anticipate hatred if I undertake reform; it affords me no explanation of the hatred with which reformers have been met. But if it is a true universal, it explains the past, and predicts the future. Nevertheless an universal judgment has nothing, as such, to do with numbers of instances; if the connexion affirmed in it be necessary, the judgment is still universal, whether there be a million instances of its truth, or only one [N3]; so that the form 'All A is B' hardly does justice to it. An enumerative judgment contemplates a number of instances, and refers to all of them; and the form 'All A is B' or 'All the A's are B's expresses it adequately.
[N1] Cf. Bradley's Logic, Bk. I. c. ii. §§ 6 and 45. In the Table of Contents he speaks of 'collective' judgments in this sense.
[N2] Cf Bradley's Logic Bk. I. c. ii. § 45.
[N3] Or, as some logicians would add, none. Such a view makes the universal judgment, however, purely hypothetical: cf. Leibniz, Nouveaux Essais, IV. Xi. 14; Bradley, Logic, Bk. I. c. ii. §§ 43-6; Bosanquet, Logic, vol. i. pp. 278-292; v. also Bradley, Appearance and Reality, p. 361.
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