Indicated Concept

What is this Tutorial About?

Introduction to Logic introduced the concept of علم (idea or thought) and how it subdivides into تصور (concept) and تصديق (assent). Both types of idea were then classified as being either بديهي (inconspicuous) or نظري (conspicuous), and we saw that Logic focuses on the conspicuous ideas – dealing with conspicuous concepts by studying definitions, and with conspicuous assent by studying proofs.

Indication subsequently introduced the concept of دلالة (indication) and the fact that studying conspicuous ideas needs to be done through some medium. The types of medium were six, but we chose to use spoken word. Speech, then, was termed the دال (indicator) and the idea which it indicated was termed the مدلول (indicated idea). And the دال was categorized in various ways.

The دال for simple indication has already been discussed in Simple Indication and now we can move on to Logic-proper and begin to discuss the مدلول on which this type of دال indicates – namely, concepts.

Just as the Simple Indication Could be Definite or Indefinite,
The Indicated Concept can be Particular or Universal

Refresher on Definite & Indefinite

If we consider simple speech in relation to one of its possibly many meanings, then the speech can be classified as being either جزئي (definite) or كلي (indefinite).

جزئي speech is speech that refers to a single and well specified entity. For example, أم النجوم (the Milky Way) is a جزئي term. First of all, it is مفرد (simple speech) because, although it has parts and its parts have meaning, indication of its parts is not intended on parts of its meaning. Then, it is a جزئي because it can only refer to a very specific entity – namely, the galaxy in which we live.

But a word like النجم (star) is a كلي term. It is a مفرد since parts of it do not indicate on parts of its meaning. But it does not refer to any specific entity. Yes, if we were to insert this term into a paragraph in which a star was mentioned, and we then allow the term النجم to refer to that specific star, then this speech would be a جزئي at that point. But as long as it does not refer to a specific entity, it is a كلي. A similar case can be made for the pronoun أنا; it is only a جزئي while it is being used by someone and a كلي otherwise.

Extension to Particular & Universal

Now this discussion was with respect to the دال – the indicating English or Arabic speech. But the same concept can be applied to the مدلول – the mental idea upon which the speech indicates. And herein lies the more important usage of the terms كلي and جزئي and henceforth begins Logic-proper.

A جزئي (particular) concept, then, is one whose conceptualization cannot apply to more than one entity. For example, the concept of the Milky Way when conceptualized by us applies to only one entity.

And a كلي (universal) concept is one whose conceptualization can apply to more than one entity. For example, the concept of star when conceptualized can apply to various entities. As another series of examples, the concept of natural numbers applies to 1, 2, 3, 4, …. The concept of natural numbers less than 4 applies to 1, 2, and 3. The concept of numbers that are neither positive nor negative applies to 0. And the concept of numbers that are both positive and negative doesn’t apply to any entities. All of these are universals.

Although the example of ‘non-positive & non-negative’ applies only to a single entity, it is not a جزئي. This is because the fact that it applies to only one is not understood directly from ‘non-positive & non-negative’. It just so happens that 0 is the only number that fits this description. Whether we know this through reason and proof, through inductive survey, or by any other means does not matter; the point is that we do not know this simply by conceptualizing ‘non-positive & non-negative’. Thus the concept of ‘non-positive & non-negative’ is a كلي.

Similarly, although the example of ‘positive & negative’ does not apply to any entity at all, it is still considered a كلي. This is because the fact that it does not apply to any entities is not understood directly from ‘positive & negative’. It just so happens that no number fits this description.

More complicated examples of particulars and universals include ‘the bay of Seabiscuit’ and ‘to be bay’. ‘the bay of Seabiscuit’ refers to a very specific instance of being bay and so it is a particular. And ‘to be bay’ is something that can be applied to any horse and doesn’t refer to any particular one; hence it is a universal.

The Relationship Between Two Universals –
Set-Theoretic Relationships

When we compare two universals  A and B – and this can be extended to more than two – one of the following relationships will be observed.

1.       A and B are both exactly the same

2.       A and B are both completely different

3.       one is contained within the other

4.       A and B overlap a little

Take, for example, the two universals ‘things that are boiling hot’ and ‘things that can burn you’. Everything that is boiling hot can burn you and everything that can burn you is about that hot. Thus both universals are one and the same. This relationship is known as تساوي (equality of sets).

Now take the two universals ‘things that are hot’ and ‘things that are cold’. Clearly, nothing that is hot is cold and nothing that is cold is hot. Thus both universals are completely different. This relationship is called تباين (disjunction of sets).

Moving along, take the two universals ‘water’ and ‘things that are wet’. All water is wet but not everything that is wet is water; juice is also wet yet it isn’t water. Thus the universal of water is contained within the universal of things that are wet. This is called عموم وخصوص مطلق (proper subsets).

And finally, take the two universals ‘water’ and ‘things that are hot’. Clearly, some water is hot while other water is not. And similarly, some things that are hot are water and other things are not, as fire is hot but it isn’t water. This type of relationship is called عموم وخصوص من وجه (intersection of sets).

Subdividing Universals:
Genera, Species, Differentiae & Other Properties

If You Build It, They Will Come

Let’s take an example of a كلي (universal). The example we choose is that of human beings. Now, if we insert human beings into a taxonomical hierarchy, we would end up with something like the following. Although a biologist’s view of this hierarchy may be more complex, we will suffice with the below simplification.

This is just one branch of an incredibly colossal Tree that contains absolutely all universals and all particulars that exist, or can conceivably exist, in 4-dimensional space-time. That tree is rooted at the universal called Everything. Underneath this root are a set of ten universals, which will be discussed shortly. Under these ten is an extremely complex hierarchy. And at the very bottom of the tree are the particulars.

The Ten Universals

The root universal in Arabic is called الموجود (everything). And the ten universals beneath it, with examples, are listed below. These are known as the أجناس عالية (highest genera), and absolutely everything will fall under one of these. Revising the above chart with Arabic terminology, we have the following.

1.       الجوهر (substance): Substance would subdivide into things like Solids, Liquids, Gasses.

2.       الكم (quantity): A Foot Long

3.       الكيف (quality): White

4.       المضاف (relation): To Be A Son, To Be Half, To Be Weaker

5.       الأين (place): In The Market

6.       المتى (time): During Dinner

7.       الوضع (position): Leaning Against A Wall, While Bent

8.       الفعل (action): He Ran

9.       الإنفعال (effect): It Broke

10.   الملك or له (jurisdiction – for two things to be so closely associated that the movement of one entails the movement of the other): Wearing Shoes, Being Cloaked in a Sheet

Where Do Things Fit?

Particulars can only occur at the very bottom of the tree as its leaves. But a given particular may fall into more than one position. For example, Pegasus will fall under both Horses as well as Imaginary Creatures, and probably in many other places.

So a particular can occur multiple times in the taxonomical hierarchy as needed. But a universal will only fall into one of the branches. This begs the question: Human Being can fall under Animal, but it can just as well fall under, say, Things That Can Laugh. All humans can laugh, but nothing else can, so it would be perfectly legitimate to categorize Humans under that universal, right? So why did we place Humans under Animals? Or why not include it in both?

When we place a universal in the hierarchy and are required to choose the parent universal under which it will fit, we need to determine whether all possible choices are intrinsic to the universal or not. For example, being animal is intrinsic to humans, but being able to laugh is not. This is because the concept of human is comprehensible without laughter; in other words, we can imagine Human without having to know that humans can laugh. But the concept of human is incomprehensible without being animal; in other words, we cannot imagine Human without first knowing that humans are animals. Being an animal is among the quiddities for humans – it’s part of what makes a human a human – but laughing is not like that. The fact that a human laughs doesn’t make it a human.

Putting it All Together

We already know that the individuals at the lowest level of the taxonomic hierarchy are known as جزئيات (particulars). The very first level of universals above the جزئيات is called نوع ج. أنواع (species). A نوع is a universal that cannot be subdivided into other universals; rather, it directly contains its member جزئيات. All other universals above this initial level (except the root universal) are known as جنس ج. أجناس (genus, pl. genera).

Now, recall that Human can fit under many universals but that, in the taxonomical hierarchy, it must be situated under only one; namely, Animal. Now let’s discuss some of those other universals under which Human could have fit.

Since Humans, Horses, Camels, and Donkeys all fall under Animals, we need a universal – or a collection of universals – in order to set Humans apart from Horses and Camels and Donkeys. Again, there are many universals that are particular to Humans and are not shared across any other Animal. For example, To Be Rational, To Be Able To Laugh – these are universals that apply only to humans. But the universal(s) we choose to distinguish Human from other Animals is To Be Rational.

This is because we can conceive a human being without first knowing that it is able to laugh, but we cannot conceive a human being without first knowing that it is rational. Being able to laugh does not make a human a human, but being rational does. The universal, or collection of universals, used to distinguish one genus from all other genera in the same family is known as فصل ج. فصول (differentia). And, unlike the parent genus, there may be many options to choose from for the differentia.

All other universals under which Human can fit – aside from the genus and the possibly multiple differentiae – are divided as follows.

Summary

For example, Human is a universal. It itself is a species because it cannot be divided into any further universals (simply speaking). Any universal may have one, and only one, parent genus and the genus for Human is Animal because it constitutes what Human is. And of course Animal has its own parent genus and so we end up with a hierarchy of genera for Human. What differentiates Human from other members of the Animal genus is the differentia that it is Rational. There may be other differentiae, and some may be combinations of several universals; the important thing is that they are constitutive to what Human is.

All other genera related to Human are non-constitutive. Some unique genera include Being Able To Laugh. Some non-unique genera include Being Able To Walk.

Relative vs. Absolute

All of the predecessors of Human in the taxonomical hierarchy are considered its genera. This actually doesn’t apply to Everything since to Be A Thing, or To Exist, is not among the quiddities for Human. In any case, most of the predecessors are considered valid genera. But these are divided into those that are close and those that are distant. For instance, Animal is a close genus of Human – the closest in fact – and Solids is a distant genus. In Arabic, the former is called جنس قريب and the latter is termed جنس بعيد.

Now, the term species applies only to the very lowest universal in the taxonomical hierarchy. However, we can say that Animal, for instance, is a species as far as its parent Growing Bodies is concerned. And Growing Bodies can be considered a species as far as Solids is concerned. And so forth. Thus, while Human is an absolute species, its parent genera in the tree are each relative species as far as their predecessors are concerned.

Similarly, the successors of any species – relative or absolute – in the taxonomical hierarchy are considered particulars. If the species is absolute, then its successors will be absolute particulars. And if the species is relative, then its successors will be relative particulars.

And finally, the same concept can be applied to the differentiae and other properties. A differentia is a universal that differentiates between species of the same genus. Since Animal is a species relative to its genus, Growing Bodies, we can use differentiae to differentiate it from other Growing Bodies. We would say that Animals are Growing Bodies made of flesh, for example. Being made of flesh would then be a differentia for Animal.