The term: the definition

First, lets start by saying what is meant by “definition”. In logic it’s used to refer to a complex sequence of words that confer meaning to someone or something. For instance, in “man is a rational animal” “rational animal” is said to be the definitio and “man” the definitum.

A definition is said to be either nominal or real. Actually, a so-called nominal definition is not really a definition at all. Rather than attempting to describe something directly, it in fact elucidates a word by designating something indirectly in any of a number of the following ways, and namely via a translation (e.g. vir =  man); a popularization (e.g. sodium chloride = kitchen salt); or an explicit explication of the terminology relating to the word (e.g. Philosophy = love of science).

A real definition is said to be “real” in so far as it represents an attempt to explain the very content of a word itself. A real definition is further classified into three types. Lets now look at each more closely.
A definition is said to be essential when it explains something by providing the constituent elements of the entity being defined. If the elements of the definition are physical we say that it describes the essentialis phisica of the definitum, whereas if metaphysical we are provided with information as to its essentialis metaphisica. If we are told, for instance, that a painting comprises more or less coloured paints applied to a support such as a canvas, then we can say have a physical definition of a painting. If we are told that humans are made up of  bodies and mental dispositions we are being given a physical definition, whereas when we are informed that humans are rational animals, the definition is metaphysical.
A definition may also be causal. That’s when we are provided with information about something or someone in causal terms, that may in turn be efficient, final or exemplary. For instance: “Honey is the product of bees”; “A shotgun is an offensive weapon”; “A portrait is the reproduction of an individual’s exterior appearance”.
Finally, a definition may be descriptive. It’s the sort of definition by which something or someone are explicated on the basis of their essential characteristics. For instance: “A book is bound printed paper sheets”.

What makes a good definition?
Clarity is an essential prerequisite of any good definition. That means that it must be clearer than the term it is meant to define. Convertibility comes next. That means that the predicate of any enunciation has to be such as to allow it to be exchangeable with its subject insofar as both are coextensive. In any case brevity is a must. What’s more, as a rule it should never be expressed negatively; as far as possible it must be formulated in scientific terms.

If several terms are put together it may be noted that are or are not related in any way to each other or that they don’t mutually oppose each other. This simple observation allows us to classify terms according to how terms are associated.

Terms that relate to one another in so far as one includes the other or both are mutually equivalent are said to be connected (pertinentes sequela). An example of the former is “human being – animal”, and of the latter “rational and laughable”.

Terms that exclude each other are said to be opposites (pertinentes repugnantia). Such mutual opposition (the genus) or incompatability may be of four kinds (the species):

1. contrary, in the case of one of the terms not only denoting something that negates the other but also excludes it in an essential manner, such as “virtue” versus “vice”;
2. contradictory, in the case of one term denying the other by simple negation, such as “virtue” versus “non-virtue”;
3. privative, in the case of one of the terms negating the other in itself, that is directly denoting the opposite such as “large” versus “small”;
4. relative, in the case of the two terms in opposition being so related as to mutually educe each other, such as “father” versus “son” and “superior” versus “inferior”. 

Failing any association whether by connection or opposition, terms are said to be extraneous (impertinentes) one to the other.

The term: classification according to perfection or mode

As to perfection or mode the term may be classified under any of the three following categories:

• (a) clear: said of a term that plainly designates the thing to which it is applied, otherwise the term is said to be obscure;
• (b) distinct: said of a term that designates something by educing meanings that significantly identify it, otherwise the term is said to be confused;
• (c) adequate (or complete): said of a term that designates something by educing meanings that fully identify it, otherwise the term is said to be inadequate.

As much as “rational and corporal” may clearly and even distinctly designate man, strictly speaking such a definition cannot be said to be adequate, for it omits many other properties by which man may validly be designated. Classification of the term as univocal, equivocal, or analogous is of primary importance.

Classification of the term as univocal, equivocal, or analogous is of primary importance. 

A term is univocal when it applies to any of a number of things but expresses the same concept for all of them, without any possibility of exchanging one thing for the other. Such a term not only shuns error but also inaccuracy. It indeed designates things in a very precise manner. “Animal”, for instance, embraces many different individuals and sets of individuals but as a general category it may accurately be applied to a tiger no less than to an ox.

An equivocal (also called “ambiguous”) term may also be used to designate several things. The chances of misunderstanding , however, are very high for it is open to many interpretations as the things to which it may be applied do not have anything in common. “Bit”, for instance, applies equally to a piece of food and to a metal brace fitted into a horses mouth. (N.B.: An equivocal term’s multiple-meaning potential has to be in some way circumscribed, so to speak, by context, otherwise it cannot be used unambiguously.)

Finally, while applying to many things, an analogous term does so because the things to which it may be applied, albeit different,  also have something in common. It may not designate them all very clearly, but neither incorrectly. 

A further distinction may be made between an analogous term of attribution and one of proportion. In the former, we have an analogy because the different things to which the term may be applied are somehow dependant one upon the other.  “Killer” may be used to designate a weapon, the hand that held and used it, the criminal intent of the individual to whom the hand belonged. In the former case the designation  is direct, in the latter two indirect but also correct, because both are dependant on the former.  In the latter we have an analogy because the different things to which the term may be applied are somehow similar to each other, if not literally at least figuratively.  Eyes sure enough “see”, but the same may be said of the intellect. In fact, we may speak of the “mind’s eye”. That’s because the relationship between eyes and sense-objects is perceived as being not unlike that between our cognitive faculties and intelligible objects. Finally, an analogy may be proper if real (i.e. if grounded in reality) or improper if arbitrary or artificial, such as in a metaphor.

Summing up, then, we may say that univocal = same word, same meaning, regardless of the thing designated; equivocal = same word, different meanings; analogous = same word, different but related meanings.

The term in relation to comprehension

Terminist logicians have also identified several pairs of opposing categories by which terms may be conveniently and rationally distinguished:

1. simple: for one-word terms – e.g. mountain;
2. complex: for multiple-word terms – e.g. high mountains;
3. concrete;
4. abstract – e.g. largeness;
5. denominative: for one-word terms deriving from another word – e.g. just from justice;
6. denominating: for one-word terms from which another word may be derived – e.g. justice giving just;
7. first intention: a term expressing a prima facie conception of a thing upon direct apprehension – e.g. man, hat, pencil, etc.;
8. second intention: a term expressing a pondered conception of a thing generalised from first apprehension; an abstract notion – e.g. predicate, subject, gender, etc..

N.B.
The first and second intention distinction is essential in logical discourse. So much so, in fact, that logic is sometimes also referred to as the “science of intentions”. It’s very important, then, to be clear about these two concepts. A first intention term is clear enough, but lets look more closely at what a second intention term is.
When my mind thinks over a concept, weighing it up to better grasp and  determine its value or logical function, then the term that expresses the product of this mental activity is  said to be a “second intention term”.  The two terms making up “Peter is a man”, for instance, simply designate a well circumscribed matter of fact and as such are called first intention terms. But if we set about analyzing the contents of this enunciation and define “Peter” as its “subject” and as a “singular term”, and “man” as the enunciation’s “predicate” and a “gender”, then I am using second intention terms in my discourse.

The term in relation to extension

If we consider the term “man” we see that comprehension is maximised while extension is minimised. “Living matter’s” extension, instead, is far greater,  but compared to “man” its comprehension is diminished. “Living matter” may in fact apply equally to humans as well as to animals, and indeed to many other life forms, perhaps not even all carbon-based. Further along the line, we have the term “substance”. In this term we see that extension is maximised, including as it does an infinite range and number of beings and things, while comprehension is minimised.

In relation to extension, the term may be either:

1. singular, when referred to a unique individual, such as “Fabius the Procrastinator”, etc.;
2. common, when referred severly to more than one individual, such as “man”;
3. collective, when it can be jointly applied to a set of things but not to each severly, such as “crowd”, “fleet”, staff, team, band, pack, flock, etc..

As for a common term, it should be noted that it may easily be turned into a singular one by simply tagging on a demonstrative adjective, as in “this man”, or by circumscribing it by means of a particular designation, as in “a man of steel”.
Moreover, application of an indeterminate adjective to a common term turns it into a particular one, such as in “certain men”, “some men”;

The term in relation to extension and comprehension

Extension and comprehension are very important in logic.
Extension encompasses all the individuals to which a term may be referred. The schoolmen formulated it as follows:
Complexus subiectorum quibus terminibus convenit. Comprehension encompasses all the properties that a term necessarily educes in so far as they are inherent in the term. The schoolmen formulated it as follows:
Complexus notarum quibus significatio termini constat.
Extension makes for order at the surface, comprehension for in depth order.
The term “man” for instance expresses a general notion that can apply to many, hence its extension encompasses all individuals to whom the concept “man” may be referred.
Comprehension of the term “man” is given by all the denotations that may be associated with it, including “existence”, “substance”, “life”, “rationality”, etc..
There’s a special rule that highlights the mutual relationship of extension and comprehension that runs as follows: extension is inversely proportional to comprehension. We can therefore say, the greater extension the less comprehension, and vice versa.