Royalists is substantially contained in the work of a Greek commentator. That work is no other than Porphyry’s Isagoge2; and therefore it would be most surprising if the doctrine had been totally overlooked by the schoolmen, for whether their acuteness was as marvellous as Hamilton taught or not, they certainly studied the commentary in question as diligently as they did the Bible. It would seem, indeed, that the tree of Porphyry involves the whole doctrine of extension and comprehension except the names. Nor were the scholastics without names for these quantities. The partes subjectives and partes essentiales are frequently opposed; and several other synonymes are mentioned by the Conimbricenses. It is admitted that Porphyry fully enunciates the doctrine; it must also be admitted that the passage in question is fully dealt with and correctly explained by the mediæval commentators. The most that can be said, therefore, is that the doctrine of extension and comprehension was not a prominent one in the mediæval logic.3
A like degree of historical error is commonly committed in reference to another point which will come to be treated of in this paper, allied, at least, as it is most intimately, with the subject of comprehension and extension, in as much as it also is founded on a conception of a term as a whole composed of parts,—I mean the distinction of clear and distinct. Hamilton tells us “we owe the discrimination to the acuteness of the great Leibniz. By the Cartesians the distinction had not been taken; though the authors of the Port-Royal Logic came so near that we may well marvel how they failed explicitly to enounce it.” (Lectures on Logic; Lecture IX.) Now, in fact, all that the Port Royalists say about this matter4 is copied from Descartes,5 and their variations from his wording serve only to confuse what in him is tolerably distinct. As for Leibniz, he himself expressly avows that the distinction drawn by Descartes is the same as his own.6 Nevertheless, it is very much more clear with Leibniz than with Descartes. A philosophical distinction emerges gradually into consciousness; there is no moment in history before which it is altogether unrecognized, and after which it is perfectly luminous. Before Descartes, the distinction of confused and distinct had been thoroughly developed, but the difference between distinctness and clearness is uniformly overlooked. Scotus distinguishes between conceiving confusedly and conceiving the confused, and since any obscure concept necessarily includes more than its proper object, there is always in what is obscurely conceived a conception of something confused; but the schoolmen came no nearer than this to the distinction of Descartes and Leibniz.
§2. Of the Different Terms applied to the Quantities of Extension and Comprehension
Extension and comprehension are the terms employed by the Port Royalists. Owing to the influence of Hamilton, intension is now frequently used for comprehension; but it is liable to be confounded with intensity, and therefore is an objectionable word. It is derived from the use of cognate words by Cajetan and other early writers. External and internal quantity are the terms used by many early Kantians. Scope and force are proposed by De Morgan. Scope in ordinary language expresses extension, but force does not so much express comprehension as the power of creating a lively representation in the mind of the person to whom a word or speech is addressed. Mr. J. S. Mill has introduced the useful verbs denote and connote, which have become very familiar. It has been, indeed, the opinion of the best students of the logic of the fourteenth, fifteenth, and sixteenth centuries, that connotation was in those ages used exclusively for the reference to a second significate, that is (nearly) for the reference of a relative term (such as father, brighter, &c.) to the correlate of the object which it primarily denotes, and was never taken in Mill’s sense of the reference of a term to the essential characters implied in its definition.7 Mr. Mill has, however, considered himself entitled to deny this upon his simple authority, without the citation of a single passage from any writer of that time. After explaining the sense in which he takes the term connote, he says:
The schoolmen, to whom we are indebted for the greater part of our logical language, gave us this also, and in this very sense. For though some of their general expressions countenance the use of the word in the more extensive and vague acceptation in which it is taken by Mr. [James] Mill, yet when they had to define it specifically as a technical term, and to fix its meaning as such, with that admirable precision which always characterized their definitions, they clearly explained that nothing was said to be connoted except forms, which word may generally, in their writings, be understood as synonymous with attributes.
As scholasticism is usually said to come to an end with Occam, this conveys the idea that connote was commonly employed by earlier writers. But the celebrated Prantl considers it conclusive proof that a passage in Occam’s Summa is spurious, that connotative is there spoken of as a term in frequent use;8 and remarks upon a passage of Scotus in which connotatum is found, that this conception is here met with for the first time.9 The term occurs, however, in Alexander of Hales,10 who makes nomen connotans the equivalent of appellatio relativa, and takes the relation itself as the object of connotare, speaking of creator as connoting the relation of creator to creature. Occam’s Summa11 contains a chapter devoted to the distinction of absolute and connotative names. The whole deserves to be read, but I have only space to quote the following:
Nomen autem connotativum est illud quod signifìcat aliquid primario et aliquid secundario; et tale nomen proprie habet diffìnitionem exprimentem quid nominis et frequenter oportet ponere aliquid illius diffinitionis in recto et aliud in obliquo; sicut est de hoc nomine album, nam habet diffìnitionem exprimentem quid nominis in qua una dictio ponitur in recto et alia in obliquo. Unde si queratur quid signifìcat hoc nomen album, dices quod idem quod illa oratio tota “aliquid informatum albedine” vel “aliquid habens albedinem” et patet quod una pars orationis istius ponitur in recto et alia in obliquo.… Huiusmodi autem nomina connotativa sunt omnia nomina concreta primo modo dicta, et hoc quia talia concreta significant unum in recto et aliud in obliquo, hoc est dictu, in diffìnitione exprimente quid nominis debet poni unus rectus signifìcans unam rem et alius obliquus signifìcans aliam rem, sicut patet de omnibus talibus, iustus, albus, animatus, et sic de aliis. Huiusmodi etiam nomina sunt omnia nomina relatiua, quia semper in eorum diffìnitionibus ponuntur diversa idem diuersis modis vel diuersa significantia, sicut patet de hoc nomine simile.… Mere autem absoluta sunt illa quae non significant aliquid principaliter et aliud vel idem secundario, sed quicquid significatur per tale nomen aeque primo signifìcatur sicut patet de hoc nomine animal.
Eckius, in his comment on Petrus Hispanus, has also some extended remarks on the signification of the term connote, which agree in the main with those just quoted.12 Mr. Mill’s historical statement cannot, therefore, be admitted.
Sir William Hamilton has borrowed from certain late Greek writers the terms breadth and depth, for extension and comprehension respectively.13 These terms have great merits. They are brief; they are suited to go together; and they are very familiar. Thus, “wide” learning is, in ordinary parlance, learning of many things; “deep” learning, much knowledge of some things. I shall, therefore, give the preference to these terms. Extension is also called sphere and circuit; and comprehension, matter and content.
§3. Of the Different Senses in which the Terms Extension and Comprehension have been accepted
The terms extension and comprehension, and their synonymes, are taken in different senses by different writers. This is partly owing to the fact that while most writers speak only of the extension and comprehension of concepts, others apply these terms equally to concepts and judgments (Rösling), others to any mental representation (Überweg and many French writers), others to cognition generally (Baumgarten), others to “terms” (Fowler, Spalding), others to names (Shedden), others to words (McGregor), others to “meanings” (Jevons), while one writer speaks only of the extension of classes and the comprehension of attributes (De Morgan in his Syllabus).
Comprehension is defined by the Port Royalists as “those attributes which an idea involves in itself, and which cannot be taken away from it without destroying it.”
It will be remembered that the marks