Logic & Philosophy of Language 2-1

II. LOGIC OF CONCEPTS (TERMS)

1. Concepts

Notion and Classification of Signs
What is a sign? Are there many kinds of signs? What are these kinds of signs?
Concrete and Abstract Terms
What are "terms"? What are concrete terms? What are abstract terms?
Extension and Comprehension of Terms
Extension? What's that? Comprehension? I don't understand. Can you explain these?
Concepts: Notion and Types
What is a concept? Is it the same as a term? Are there many kinds of concepts?
The Universal Character of Concepts
What does "universal" mean?
Abstraction: Notion and Kinds of Abstraction
Does abstraction mean making something vague? If not, what does it mean? What types of abstraction are there?

(This lesson covers at least three (3) sessions.)

THE SEMANTIC TRIAD, a.k.a. THE LINGUISTIC TRIANGLE

Recall the distinction among language (speaking/writing), knowledge (thinking), and reality (being).

Recall again the following passage from Aristotle's Peri hermeneias (On interpretation), known as the semantic triangle or linguistic triad:

"Spoken words (phone) then are the symbols (symbola) of affections of the soul (pathemata) and written words (graphomena) are symbols of spoken words (phone).

"And just as written letters (grammata) are not the same for all humans, neither are spoken words.

"But what these primarily are signs (semeia) of, the affections of the soul (pathemata), are the same for all, as also are those things (pragmata) are the same for all, of which our affections are likenesses (homoiomata)."

Now let us integrate Aristotle's triangle into our table above:

SIGNS: NOTION AND CLASSIFICATION

What is a sign?

A sign is something which, when perceived, evokes another thing. (Definition thanks to Origen, St Augustine and St Thomas Aquinas--great guys!).

There are two elements in this definition:

It is something that can be perceived.
It points to or calls attention to another thing.

Thus, there are three things in the use of signs:

the thing that signifies (the sign)
the thing signified
the connection between the two

INSTRUMENTAL SIGNS

Some natural signs (except the formal ones) and ALL artificial and mixed signs are instrumental signs.

Instrumental signs are some thing. Their existence is independent of what they signify.

Examples:

a key is a key (it is some thing), independently of whether it symbolises a city or not
the flag is a piece of cloth (it is some thing), independently of whether it represents a country or some society
a word is either a determined sound or a drawn figure (it is some thing), aside from signifying a concept

Instrumental signs have to be known before we can know what they signify. (It is NOT the case with concepts. We only get to know the concept after a rather arduous reflection on our knowledge. The concept is known after we know the thing itself. But don't worry if you don't understand this now.)

KINDS OF TERMS

What is a term?

A term is an observable conventional sign, expressive of an idea.

term = 'thing' that signifies
idea or concept = "thing" signified

There are many many many (believe me!) kinds of terms. Here are a few of them.

EXTENSION AND COMPREHENSION OF TERMS

QUESTIONS TO EXPLORE BY YOURSELF

Using three examples, make an experiment to show that comprehension and extension are inversely proportional to each other--when one increases the other decreases.
There is one term that does not follow this rule. It is always maximum comprehension and maximum extension. You know what it is? Yes! BEING! ENS! Try working it out!

CONCEPTS: NOTION AND TYPES

CONCEPT

A natural (i.e., not conventional) mental sign whereby we grasp a certain essence.

This natural sign is produced by the mind.

This natural sign signifies what a thing is.

This sign signifies the essence of things (to be more specific, it signifies the form).

From where does the mind draw the "raw material" to produce the concept? From the phantasm or image presented to it by the internal senses.

Click on this link to know how this happens. (ABSOLUTELY MUST READ!!!)

The concept is different from the image or phantasm.

CONCEPTS ARE UNIVERSAL

What is a universal?

No, it's not the studio.
ORIGIN. The term 'universal' comes from "unum in diversis", one [thing] found in many.
DEFINITION 1. St Thomas defines it as: "quod aptum natum est prædicari de pluribus" (don't let the Latin scare you), which means roughly "that which can be said of or predicated of many".
DEFINITION 2. "Logical universality is the property of human concepts whereby they are rendered predicable of many individuals."
(From separate commentaries of St Thomas on two books of Aristotle--the book On Interpretation and the book of Metaphysics.
These commentaries are: In I Perihermeneias, lect. 10; and In VIII Metaphysicorum, lect. 13.
These guys are really super smart!)

How do concepts become universal?

Have you read the link above? (It proclaimed "MUST READ!!!" Hah, you didn't believe me?) If you have, you will RECALL that abstraction takes away all individualising traits. When you take away all individualising traits, you are left with traits that can be applied to all other individuals within the class: the universal.

What is the so-called "problem of the universal"?

The PROBLEM: We said the universal is one in many. So is it one or many?
Example: The concept 'man' is a concept that applies to the ONE whole set or ONE class of human beings. But we apply it also to MANY individuals belonging to the set or class. So is it one or many?
SOLUTION: It is ONE in our mind, but existing in MANY individual things in the real world, the extramental world.
SOLUTION (in Latin): Universalia sunt formaliter in mente, fundamentaliter in rebus ipsis.
SOLUTION (in English): The universals are formally (i.e., actually, strictly speaking) in the mind, fundamentally in the things themselves.
The above is actually one of four proposed solutions. These four are:

Why can we predicate one thing of many? What's the basis for this?

Universality is possible because we actually find the SAME PERFECTION in many DIFFERENT INDIVIDUALS.
In Plato's terminology (adapted by St Tommy): different beings PARTICIPATE or SHARE in the same perfection

What is the use of universals?

Any kind of knowledge needs universals.
Science needs universals.
We all need universals.
Without universals, we could not even make a shopping list. We could not write to Santa Claus! Oh, gosh!

ABSTRACTION: NOTION AND KINDS

What is abstraction? (Now you're asking!)

In a broad sense, to abstract is to separate in our mind what is actually united (in reality).
It means to consider one particular aspect of something, leaving to one side other aspects which in reality also belong to it.
Every concept is abstract because it focuses only on the essence or nature it signifies, and leaves aside the concrete individual subject of that nature.

Please contact jmomandia at gmail dot com for any heresies found here.

First Edition. Hong Kong, 28 August 2006

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