What is this Tutorial About?
Now that Simple Indication has dealt with the دال مفرد and Indicated Concept has dealt with the مدلول تصوري, we are now ready to understand how to form definitions.
Tom, Dick, Harry, …
Defining a Particular
The explanation of a تصور is called قول شارح (explanation). In order to explain a particular, we would simply state the species under which it belongs. For example, in order to give a قول شارح for the term “Tom”, we’d simply say that Tom is a particular human. If that is not sufficient for the audience, we would need to include certain properties – a set of خواص or عوارض – in order to further elaborate on who Tom is. We would say, for instance, that Tom is a particular human who happens to be Harry’s father.
Defining a Universal
Sometimes a concept is already known given its name. For example, most of us understand what a triangle is – it is a 2-dimensional figure enclosed by three sides. Therefore, we can express the concept of triangle by simply utilizing the name “triangle” given to it. The name given to a concept by which it is recognized is called its اسم (name or identifier).
Often times a concept is not understood by the audience given its identifier, but there may be other identifiers which the audience does understand. For example, if the audience doesn’t understand the term “canon”, we may employ the word “law” instead. Or if the audience doesn’t understand the English term “law”, we may use translation and employ the word قانون. This is known as explanation through synonymy (Ar. ترادف, En. synonymy). In certain cases, explanation through synonymy is the only means of explanation available. The root universal, for instance, has no genus and, as we will see shortly, it therefore cannot be defined. In this case, we would be forced to resort to synonymy or translation.
Now, the definition of a universal is an explanation which is completely equivalent to it and interchangeable with it. In order to define a universal, we first set it as a species. A species, in fact, is nothing more than the combination of a genus and a set of differentiae. Therefore, in order to define a species, we simply split it up into those constituent universals.
The most precise method of defining a species is to utilize its closest genus and to mention all of its differentiae. Remember that the definition of a universal should be interchangeable with its identifier. Therefore, if we neglect even one of the possibly many differentiae, the definition is not complete. Take, for example, the universal Animal. The closest genus for Animal is Growing Body. And all of its differentiae are: Has a Soul, Sense Perceiving, Moves at Will. Although mentioning Has a Soul is sufficient in differentiating Animal from all other Growing Bodies, it is inappropriate in rendering a definition to leave out any of these quiddities. Therefore, Sense Perceiving, Moves at Will, etc must also be mentioned.
This type of definition is called حد تام (complete definition). And notice that any universal can have only one حد تام; why?
Another, less precise, method of definition is to use some distant genus in place of the closest genus. For example, were we to define Animal as a Solid that Has a Soul, Sense Perceives, and Moves at Will, this would be somewhat inaccurate because, although the audience may have been able to distinguish Animal from all other universals, the given definition is not actually interchangeable with the name “Animal”. A similar imprecision can be achieved by omitting the genus altogether, as in defining Animal as (something that) Has a Soul, Sense Perceives, and Moves at Will. This type of definition is known as حد ناقص (imprecise definition).
Another method of explanation is identifying a universal by utilizing the closest genus, but unique concomitants in place of differentiae. Recall that unique concomitants will help differentiate a universal from all others in the same genus, but that they are not constitutive. As a result, this explanation, too, is not interchangeable with the universal’s identifier. For example, we can identify Human by saying that it is a Growing Body that Laughs. This is known as رسم تام (precise identification). It is precise because we have mentioned the closest genus and enough accidental properties to differentiate it from other universals in the same family. But it is still not a definition since it is not interchangeable with the identifier.
And finally, a very weak form of explanation is to utilize a distant genus and an accidental property, or an accidental property alone. An example of this is identifying Human by calling it a Laughing Body, or by calling it (something that) Laughs. This is known as رسم ناقص (imprecise identification).
Errors in Definition
Certain mistakes commonly arise when forming definitions. Briefly, these include the following.
· The differentia is put in place of the genus and vice versa. For example, a Triangle is three sides that form an enclosed figure. The correct definition is that a Triangle is a figure enclosed by three sides.
· The genus is replaced by the material. For example, a CPU is circuitry that fetches, decodes, and either executes or dispatches instructions. The correct definition is that a CPU is the part of a computer that fetches, decodes, and either executes or dispatches instructions.
· The genus is replaced by the molecular composition. For example, a CPU is silicon that fetches, decodes, and either executes or dispatches instructions.
· The genus is replaced by the constituents of the universal. For example, Ten is five and five.
· A universal is defined with the help of something more conspicuous than it. For example, a Riddle is an enigma posed as a question and used to test one’s intelligence.
· The definition results in a circular dependency. For instance, Odd is the opposite of even and Even is the opposite of odd.
A Compendium of Logic Terminology Studied Thus Far
the highest genera – the genera just beneath the root in the taxonomical hierarchy of Everything
inconspicuous – idea which is understood or accepted immediately
disjunction of sets
equality of sets
assent – a mental idea in which there is a copula, meaning that something is being claimed
concept – a mental idea empty of a copula, meaning that nothing is being claimed
definite or particular – when applied to the دال: definite; when applied to the مدلول: that whose conceptualization prohibits multiplicity in application
genus – the universal given in answer to the question regarding things of different quiddities: What is it?
literalness – the use of the former meaning in multi-meaning speech in which one meaning is the result of a relationship with another and both are used
unique property – an applicable universal that is unique
the tangible thing that indicates on something conceptual
indication (more formally known as semiosis) – for something to be in a manner such that conceiving it leads to conceiving something else
entailment – relating to other, necessarily and easily understood ideas
component-based indication – relating to the parts of an idea
indication thanks to an innate understanding
indication by way of deduction
congruency-based indication – relating to the entirety of an idea
indication by coinage
constitutive – universals that help make a thing what it is
non-unique property – an applicable universal that is not unique
non- constitutive – universals that, although applicable, do not help make a thing what it is
idea or thought
عـ وخـ من وجه
inclusion of sets
عـ وخـ مطلق
intersection of sets
differentia – the universal given in answer to the question regarding things of genus X: What kind of X is it?
indefinite or universal – when applied to the دال: indefinite; when applied to the مدلول: that whose conceptualization permits multiplicity in application
isometric – single-meaning speech whose application is equal across all members that it applies to
separate coinages – multi-meaning speech in which all meanings were a result of separate coinages
anisometric – multi-meaning speech whose application is discriminatory across members that it applies to
multiplicity of meaning – simple indication that holds multiple meanings
singularity of meaning – simple indication that holds a single meaning
figurativeness – the use of the latter meaning in multi-meaning speech in which one meaning is the result of a relationship with another and both are used
(formally known as denotata) – the idea indicated by the دال
compound indication by coinage – speech whose parts do indicate on parts of the meaning
simple indication by coinage – speech whose parts do not indicate on parts of the meaning
transferred – multi-meaning speech in which one meaning is the result of a relationship with another and the latter has been dropped
conspicuous – idea which requires either definition or proof before it can be conceived
species – the name given to the combination of a genus and all relevant differentiae of a universal