CONNOTATION

Introduction
Aristotle on Essential Nature
Ockham's Theory of Descriptions
Ockham on Connotation
Buridan on Connotation
Cajetan on Nominal Essence
Arnauld on Nominal Definition
Locke on Nominal Definition
Mill's famous definition
Peirce on Comprehension and Extension
Joseph on Ockham on Connotation
Russell on Denoting
Frege on Connotation


For a connected piece, see Mill's comments on the distinction between accidental and essential propositions, also in the Logic Museum here.


Introduction.

Here is a collection of pieces, ranging from Aristotle to Frege, on the related subjects of connotation and denotation, nominal and real essence, and nominal and real definition.

The distinction between nominal and real essence originates with Aristotle. In the passage from the Posterior Analytics below, he argues that we can know the meaning of a made up name (he gives the example 'goat stag') that denotes nothing, without knowing what he calls the 'essential nature' of the thing that the name would denote, if there were such a thing.

These brief remarks, as with many of his brief remarks, are the starting point of a huge controversy and discussion which lasts throughout the Middle Ages, which occupies a defining position in the early modern era (it occupies most of book III of Locke's Essay Concerning Human Understanding), and which is a philosophical issue today (I would like to have included some representative pieces from the 'analytic' era, such as by Putnam and Kripke, but copyright reasons prevent this).

They imply the following distinctions.

First, between the meaning of a name such as 'man', which the medieval logicians called the quid nominis or 'whatness of the name', and the underlying nature common to all the things it names, which they called the quid rei or 'whatness of the thing'. (Early modern philosophers like Locke used the corresponding English terms 'nominal essence' and 'real essence'). The name 'hobbit', for example, is perfectly meaningful. It has a quid nominis. But we could not know the real nature of hobbits, even if there were such things (presumably there would be a hobbit genetic structure, but we cannot tell this from the meaning of the word 'hobbit'). So we cannot know the real nature, the quid rei of hobbits. By contrast, the name 'man' denotes real things (men) that have a certain quid rei. The meaning of a name is distinct from the nature that thing must have in order that the name apply to it.

Second, between nominal and real definition. A nominal definition is the definition explaining what a word means, i.e. which says what the 'nominal essence' is. (The Latin corresponding to the English term 'nominal definition' is definitio exprimens quid nominis, literally a definition expressing the quid nominis or 'nominal essence' of the term). A real definition is one expressing the real nature or quid rei of the thing.

Third, between the meaning or connotation or intension of a name, and the objects that the name applies to or 'denotes'. 'Connotation' is a term introduced by Mill, which closely corresponds to the idea of nominal essence. (He claimed was derived from the Latin connotare, however in Latin logic this term has a slightly different use - see Ockham's discussion of connotative terms). Mill makes it clear that what he calls 'connotation' is what we would ordinarily call meaning. 'In the case of connotative names [i.e. common nouns], the meaning, as has so often been observed, is the connotation.' (System of Logic, I. viii. 1). The definition of a name, in turn, is any proposition that says what its connotation is. Note that Mill, following Locke, makes no distinction between nominal and real essence, or nominal and real definitions. See the appropriate passages by Locke, here, and by Mill, here.

I plan a proper introduction or some sort of discussion at some point, but I find I am still puzzled about the distinction between nominal and real essence. When I am completely enlightened, I will put some thoughts together. Other work in progress is a translation of Frege's On Concept and Object, which is nearly finished, but was not ready for this month's (July 2006) edition of The Logic Museum. At some point I will include a translation of Abelard's work on negation, as it turns out that Ockham was not the originator of a theory-of-descriptions style explanation of existential import, and that Abelard gives a much more elegant and thoughtful account of the subject, in his Dialectica, and also in his commentary on Aristotle's Perihermaneias.

A departure for the Logic Museum is the inclusion of a guest contributor (Francesco Franco) who has written the introduction to Russell's Theory of Descriptions. You may notice a passing resemblance to the article on the same subject in Wikipedia, but that is because Frank is the author of that article, also. He is one of the (sadly) few editors contributing to the philosophy pages of that splendid publication, who is capable of writing intelligently, in an elegant way.


Aristotle on Essential Nature. From the Posterior Analytics Bk 2 c. 7

How then by definition shall we prove substance or essential nature? We cannot show it as a fresh fact necessarily following from the assumption of premisses admitted to be facts-the method of demonstration: we may not proceed as by induction to establish a universal on the evidence of groups of particulars which offer no exception, because induction proves not what the essential nature of a thing is but that it has or has not some attribute. Therefore, since presumably one cannot prove essential nature by an appeal to sense perception or by pointing with the finger, what other method remains?

To put it another way: how shall we by definition prove essential nature? He who knows what human-or any other-nature is, must know also that man exists; for no one knows the nature of what does not exist-one can know the meaning of the phrase or name 'goat-stag' but not what the essential nature of a goat-stag is. But further, if definition can prove what is the essential nature of a thing, can it also prove that it exists? And how will it prove them both by the same process, since definition exhibits one single thing and demonstration another single thing, and what human nature is and the fact that man exists are not the same thing? Then too we hold that it is by demonstration that the being of everything must be proved-unless indeed to be were its essence; and, since being is not a genus, it is not the essence of anything. Hence the being of anything as fact is matter for demonstration; and this is the actual procedure of the sciences, for the geometer assumes the meaning of the word triangle, but that it is possessed of some attribute he proves. What is it, then, that we shall prove in defining essential nature? Triangle? In that case a man will know by definition what a thing's nature is without knowing whether it exists. But that is impossible.

Moreover it is clear, if we consider the methods of defining actually in use, that definition does not prove that the thing defined exists: since even if there does actually exist something which is equidistant from a centre, yet why should the thing named in the definition exist? Why, in other words, should this be the formula defining circle? One might equally well call it the definition of mountain copper. For definitions do not carry a further guarantee that the thing defined can exist or that it is what they claim to define: one can always ask why.

Since, therefore, to define is to prove either a thing's essential nature or the meaning of its name, we may conclude that definition, if it in no sense proves essential nature, is a set of words signifying precisely what a name signifies. But that were a strange consequence; for (1) both what is not substance and what does not exist at all would be definable, since even non-existents can be signified by a name: (2) all sets of words or sentences would be definitions, since any kind of sentence could be given a name; so that we should all be talking in definitions, and even the Iliad would be a definition: (3) no demonstration can prove that any particular name means any particular thing: neither, therefore, do definitions, in addition to revealing the meaning of a name, also reveal that the name has this meaning. It appears then from these considerations that neither definition and syllogism nor their objects are identical, and further that definition neither demonstrates nor proves anything, and that knowledge of essential nature is not to be obtained either by definition or by demonstration.

Part 10

Since definition is said to be the statement of a thing's nature, obviously one kind of definition will be a statement of the meaning of the name, or of an equivalent nominal formula. A definition in this sense tells you, e.g. the meaning of the phrase 'triangular character'. When we are aware that triangle exists, we inquire the reason why it exists. But it is difficult thus to learn the definition of things the existence of which we do not genuinely know-the cause of this difficulty being, as we said before, that we only know accidentally whether or not the thing exists. Moreover, a statement may be a unity in either of two ways, by conjunction, like the Iliad, or because it exhibits a single predicate as inhering not accidentally in a single subject.

That then is one way of defining definition. Another kind of definition is a formula exhibiting the cause of a thing's existence. Thus the former signifies without proving, but the latter will clearly be a quasi-demonstration of essential nature, differing from demonstration in the arrangement of its terms. For there is a difference between stating why it thunders, and stating what is the essential nature of thunder; since the first statement will be 'Because fire is quenched in the clouds', while the statement of what the nature of thunder is will be 'The noise of fire being quenched in the clouds'. Thus the same statement takes a different form: in one form it is continuous demonstration, in the other definition. Again, thunder can be defined as noise in the clouds, which is the conclusion of the demonstration embodying essential nature. On the other hand the definition of immediates is an indemonstrable positing of essential nature.

We conclude then that definition is (a) an indemonstrable statement of essential nature, or (b) a syllogism of essential nature differing from demonstration in grammatical form, or (c) the conclusion of a demonstration giving essential nature.

Our discussion has therefore made plain (1) in what sense and of what things the essential nature is demonstrable, and in what sense and of what things it is not; (2) what are the various meanings of the term definition, and in what sense and of what things it proves the essential nature, and in what sense and of what things it does not; (3) what is the relation of definition to demonstration, and how far the same thing is both definable and demonstrable and how far it is not.


THE LOGIC MUSEUM Copyright E.D.Buckner 2006.