Textual Enumeration

Abstract

This chapter pursues a two-level objective.

On one hand, it presents a study of the textual object of an enumeration type, from four aspects: syntactical structures, semantic operations and functions, logical aspect and pragmatic performatives.

The first point is addressed, from the point of view of internal structures, drawing on specific concepts such as the initializer, the classifier, the item, etc.; and from the contextual point of view by shedding light on relations specific to the enumeration on the level of both sentence and text structures.

The second aspect considers the different types of operation an enumeration allows or requires, for example in terms of definition, description, categorization, etc. With regard to the latter operation, enumeration seems to be a form of presentation of what cognitive psychology considers to be functional categorization. The logical standpoint considers the conditions of identity and existence of an enumeration as a textual object, and other aspects related to reference and categorization.

Finally, from the pragmatic point of view, we aim to characterize the type of speech act that the textual act of enumeration performs: importance is given to the ‘co-enumerability’ of constitutive items. This notion can have an explicative relation with the properties of syntactical and functional non-parallelism of some enumerations, as well as with the functional aspect of enumerative categorization.

On the other hand, we would like this study to offer the reader, through the example of one type of textual object, a reusable model for the analysis of specifically textual objects, as well as an illustration of various points of view that could be relevant to the study of these objects and for the objectives of textological research.

ANNEX

In this Annex we give the examples of Aristotle’s enumerations used in the text with a particular formatting device that allows the readers to perceive their structure at first glance.

[A1] “Forms of speech are either

• simple

• or composite.

Examples

• of the latter are such expressions as

  • ‘the man runs’,

  • ‘the man wins’;

• of the former

  • ‘man’,

  • ‘ox’,

  • ‘runs’,

  • ‘wins’.” (Categories, part 2)

[A2] “Quantity is either discrete or continuous. Moreover, some quantities are such that each part of the whole has a relative position to the other parts: others have within them no such relation of part to part.” ( Categories, part 6)

[A3] “There are six sorts of movement:

• generation,

• destruction,

• increase,

• diminution,

• alteration, and

• change of place.” (Categories, part 14)

[A4] “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’. […] 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. […] 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.” (Posterior Analytics, II, 10)

[A5] “Evidently we have to acquire knowledge of the original causes […] and causes are spoken of in four senses.

• In one of these we mean the substance, i.e. the essence (for the ‘why’ is reducible finally to the definition, and the ultimate ‘why’ is a cause and principle);

• in another the matter or substratum,

• in a third the source of the change,

• and in a fourth the cause opposed to this, the purpose and the good (for this is the end of all generation and change)

We have studied these causes sufficiently in our work in nature [i.e.: the Physics], but yet let us call to our aid those who have attacked the investigation of being and philosophized about reality before us. For obviously they too speak of certain principles and causes; to go over their views, then, will be of profit to the present inquiry, for we shall either find another kind of cause, or be more convinced of the correctness of those which we now maintain.” (Metaphysics, book 1, part 3)²⁹

After this examination of previous doctrines, Aristotle concludes on this point:

“Our review of those who have spoken about first principles and reality and of the way in which they have spoken, has been concise and summary; but yet we have learnt this much from them, that of those who speak about ‘principle’ and ‘cause’ no one has mentioned any principle except those which have been distinguished in our work on nature, but all evidently have some inkling of them, though only vaguely.” (Metaphysics, book 1, part 7)

And to finish:“

“All these thinkers then, as they cannot pitch on another cause, seem to testify that we have determined rightly both how many and of what sort the causes are. Besides this it is plain that when the causes are being looked for, either all four must be sought thus or they must be sought in one of these four ways.” (ibid.)

At the end of book 1, he summarizes this research:

“It is evident, then, even from what we have said before, that all men seem to seek the causes named in the Physics, and that we cannot name any beyond these; but they seek these vaguely; and though in a sense they have all been described before, in a sense they have not been described at all.” (Metaphysics, book 1, part 10)

[A6]

• 1. “Of things themselves some are predicable of a subject, and are never present in a subject. Thus ‘man’ is predicable of the individual man, and is never present in a subject.

  By being ‘present in a subject’ I do not mean present as parts are present in a whole, but being incapable of existence apart from the said subject.

• 2. Some things, again, are present in a subject, but are never predicable of a subject. For instance, a certain point of grammatical knowledge is present in the mind, but is not predicable of any subject; or again, a certain whiteness may be present in the body (for colour requires a material basis), yet it is never predicable of anything.

• 3. Other things, again, are both predicable of a subject and present in a subject. Thus while knowledge is present in the human mind, it is predicable of grammar.

• 4. There is, lastly, a class of things which are neither present in a subject nor predicable of a subject, such as the individual man or the individual horse.” (Categories, part 2)

[A7] “Quality is a term that is used in many senses.

• One sort of quality let us call ‘habit’ or ‘disposition’. […]

• Another sort of quality is that in virtue of which, for example, we call men good boxers or runners, or healthy or sickly: in fact it includes all those terms which refer to inborn capacity or incapacity. […]

• A third class within this category is that of affective qualities and affections. Sweetness, bitterness, sourness, are examples of this sort of quality, together with all that is akin to these; heat, moreover, and cold, whiteness, and blackness are affective qualities. […]

  The fourth sort of quality is figure and the shape that belongs to a thing; and besides this, straightness and curvedness and any other qualities of this type; each of these defines a thing as being such and such. […] There may be other sorts of quality, but those that are most properly so called have, we may safely say, been enumerated.” (Categories, part 8).

[A8] “The term ‘to have’ is used in various senses.

• In the first place […]

• Other senses of the word might perhaps be found, but the most ordinary ones have all been enumerated.” (Categories, part 15)

[A9] “There are four senses in which one thing can be said to be ‘prior’ to another.

• Primarily and most properly the term has reference to time: in this sense the word is used to indicate that one thing is older or more ancient than another, for the expressions ‘older’ and ‘more ancient’ imply greater length of time.

• Secondly, one thing is said to be ‘prior’ to another when the sequence of their being cannot be reversed. In this sense ‘one’ is ‘prior’ to ‘two’. For if ‘two’ exists, it follows directly that ‘one’ must exist, but if ‘one’ exists, it does not follow necessarily that ‘two’ exists: thus the sequence subsisting cannot be reversed. It is agreed, then, that when the sequence of two things cannot be reversed, then that one on which the other depends is called ‘prior’ to that other.

• In the third place, the term ‘prior’ is used with reference to any order, as in the case of science and of oratory. For in sciences which use demonstration there is that which is prior and that which is posterior in order; in geometry, the elements are prior to the propositions; in reading and writing, the letters of the alphabet are prior to the syllables. Similarly, in the case of speeches, the exordium is prior in order to the narrative.

• Besides these senses of the word, there is a fourth. That which is better and more honourable is said to have a natural priority. In common parlance men speak of those whom they honour and love as ‘coming first’ with them. This sense of the word is perhaps the most far-fetched.

Such, then, are the different senses in which the term ‘prior’ is used.” (Categories, part 12)

Yet, Aristotle immediately adds:

“Yet it would seem that besides those mentioned there is yet another. For in those things, the being of each of which implies that of the other, that which is in any way the cause may reasonably be said to be by nature ‘prior’ to the effect. It is plain that there are instances of this. The fact of the being of a man carries with it the truth of the proposition that he is, and the implication is reciprocal: for if a man is, the proposition wherein we allege that he is true, and conversely, if the proposition wherein we allege that he is true, then he is. The true proposition, however, is in no way the cause of the being of the man, but the fact of the man’s being does seem somehow to be the cause of the truth of the proposition, for the truth or falsity of the proposition depends on the fact of the man’s being or not being.

Thus the word ‘prior’ may be used in five senses.”

[A10] “In establishing a definition by division one should keep three objects in view:

• 1. the admission only of elements in the definable form

• 2. the arrangement of these in the right order,

• 3. the omission of no such elements.

  • The first is feasible because one can establish […]

  • The right order will be achieved if the right term is assumed as primary, […]

  • Our procedure makes it clear that no elements in the definable form have been omitted […]” (Posterior Analytics, II,13)

[A11] “We must next explain the various senses in which the term ‘opposite’ is used. Things are said to be opposed in four senses:

• 1. as correlatives to one another,

• 2. as contraries to one another,

• 3. as privatives to positives,

• 4. as affirmatives to negatives.

Let me sketch my meaning in outline.An instance of the use of the word ‘opposite’

• with reference to correlatives is afforded by the expressions ‘double’ and ‘half’;

• with reference to contraries by ‘bad’ and ‘good’.

• Opposites in the sense of ‘privatives’ and ‘positives’ are ‘blindness’ and ‘sight’;

• in the sense of affirmatives and negatives, the propositions ‘he sits’, ‘he does not sit’.

• 1. Pairs of opposites which fall under the category of relation are explained by a reference of the one to the other […]

• 2. Pairs of opposites which are contraries are not in any way interdependent, but are contrary the one to the other. […]

• 3. ‘privatives’ and ‘Positives’ have reference to the same subject. […]

• 4. Statements opposed as affirmation and negation belong manifestly to a class which is distinct […].” Categories, part 10).

[A12] “The pre-existent knowledge required is of two kinds.

• In some cases admission of the fact must be assumed,

• in others comprehension of the meaning of the term used,

• and sometimes both assumptions are essential.” (Posterior Analytics, I, 1)