Concepts, Signs, & Names - Amateur Logician

Learn Something?
Buy The Amateur Logician a Cup of Coffee!

Support the Mission to Revive Logic?
Buy The Amateur Logician a Cup of Coffee!

This tutorial is free; however, it took effort, time, and money to put together. I would greatly appreciate any contributions to keep this website project running and expanding. Thank you!

— George Wick

Ideas as Concepts

In traditional logic, we have “Three Acts of the Mind”:
(1) Simple Apprehension / Conceptualization: act that concerns forming ideas.
(2) Judgement: act that objectively affirms or denies an attribute of a subject.
(3) Reasoning / Inference: act deriving (ideally) a new truth from older truths.

It’s impossible to have a syllogism without propositions, and it’s impossible to have propositions without terms. A nice feature of traditional logic is its step-by-step look at the process of reasoning. It breaks things down to their components.

A concept is an idea about something. Having a good idea about something, ideally, is to understand its common or main features. For example, a Euclidean triangle is a polygon with three sides. However, an idea is not a mere mental picture.

We can have an image of a Euclidean triangle in our mind’s eye, but our concept of it goes far beyond that mental picture. There are infinitely many Euclidean triangles possible, as they can come in different sizes, etc. The concept is thus not reducible to a mental picture.

A particular Euclidean triangle can be equilateral, isosceles, or scalene; however, the concept itself embraces all of those possibilities. No particular Euclidean triangle can be (for example) both equilateral and isosceles at once.

The difference, then, between a concept and a mental picture is universality. The concept embraces all possible Euclidean triangles. The mental picture — also called a phantasm — is necessarily particular.

Note, too, that this ability to hold onto the universal idea of a Euclidean triangle, which concerns all Euclidean triangles as such, makes possible geometry. We can derive various theorems about triangles because our minds can think about universals.

Ideas can be more or less adequate, clear, or obscure.

Some ideas are worse: they are inherently incoherent and illogical!

Repugnant Concepts. . .

A repugnant concept is a self-contradictory concept. It tries to combine two features where one entails the total exclusion of the other. E.g., a “squared-circle” is a repugnant concept. It violates the Law of Contradiction. These concepts thus cannot signify the existence of any real (extra-mental) thing.

Semiotics & Names of Concepts

We human beings reside in a universe of individual things. Among these individuals, groups of them contain a certain “likeness” to each other. It’s possible to identify something as a man, a bear, a daffodil, a house, a piece of silver, etc.

Things of a like “nature” we give names: “man,” “bear,” “daffodil,” “house,” “silver,” etc. This requires the use of language to give names, and language uses conventional symbols. These include written signs (orthography), verbal utterances (phonetics), or particular body language (sign language).

Those are sensible signs where meaning (semantics) is forced on them by convention. Scholastic terminology would say that the meaning of words is the “form.” The way words are expressed via symbols is referred to as the “matter.”

Semiotics is the study of signs. Language is a system of signs! You, the interpretant, use the word “elephant” as a sign to signify an object, viz., an elephant.

There is the thing, the idea, and the word. There’s a hierarchical structure. An idea (which represents something) presupposes that it is about something. And a word (which represents an idea) presupposes some idea.

Signs can generally be divided into instrumental signs and formal signs.

An instrumental sign not only signifies something but exists totally autonomously.

Language is an instrumental sign. Everybody might forget the Latin language, yet the written signs in Latin will remain in various books. The markings exist autonomously on the pages of those books.

Instrumental signs are conventional or natural. Language is conventional because it develops out of human societies. Nothing forces us to call an elephant an “elephant.” Obviously, different human languages will often use different signs to signify an elephant.

Natural signs don’t depend upon man. Smoke is often a natural sign of fire. Smoke is the sign and fire is the thing signified. It’s also instrumental because smoke exists autonomously. Smoke can exist without a fire existing presently.

Formal signs are more subtle. In fact, unlike instrumental signs, they are inseparable as being signs. They only exist as signs; they have no independent existence. However it takes reflection to think of them as signs, as we first think of what they signify. Scholastic philosophy here makes a distinction between “first intention” and “second intention.”

When we think of an elephant, we think about the animal itself with a long trunk. This is “first intention.” Next it’s possible to internally reflect on our idea of an elephant as an idea. This is “second intention.”

Sense images and intellectual images are formal signs. A sense image — also called a precept — is our perception of something with the use of our external senses (seeing, hearing, tasting, smelling, touching). The sign and what’s signified are so intimate that the sign is nearly “transparent.” That’s because a formal sign’s very essence is to signify. Conversely, noise or ink marks don’t have the very essence to signify. Formal and instrumental signs are different.

We know of the “sense image” of the elephant before we reflect upon that sense image itself. The “intellectual image” of an elephant is the idea of an elephant, not an image as such. (To imagine a particular elephant in our mind’s eye, with the help of our internal senses [such as imagination and memory], is a phantasm; an idea is never a phantasm.)

General/Universal Names versus Proper Names

“Names” are words or multiple words used by convention or fiat to signify something.
— General Names: these refer to many things thought to be of the same “likeness”
— Proper Names: these refer to an individual (specific) thing

Proper names are non-connotative, i.e., they don’t strictly refer to an idea.

Ideas are about general names. We possess ideas about men, bears, daffodils, houses, silver, etc. That’s possible because, e.g., individual things that are silver have a shared nature — and that shared nature shows itself externally with common characteristics.

But the statement “this is James” only specifies a specific individual.
Nothing is said about James. Doing that requires getting to know James.

We can then use general names to describe his various characteristics.

Connotation/Intension versus Denotation/Extension

“Connotation” and “intension” are basically synonymous.
“Denotation” and “extension” are basically synonymous, too.

The intension of a universal name connotes attributes or qualities.
The extension of a universal name denotes individuals that belong to it.

Silver’s connotation or intension refers to its various attributes. It’s a shiny element, a metal, is highly conductive of electricity, appears grayish-white, has 47 protons, etc.

Silver’s denotation or extension refers to everything in the universe that is silver. There are silver coins, silver jewelry, etc. Also, some electrical circuit components contain silver.

Language has seen growth in two basic ways: generalization & specialization.

Generalization deals with the widening of a class (such that as extension increases, the intension tends to decrease).

Specialization deals with the narrowing of a class (such that as extension decreases, the intension tends to increase).

A Tour of (some) Divisions of Terms . . .

Collective Terms versus General Terms
Collective terms apply to a group of objects such that any attribute applies to them only as a group. They are joined together. For example, “a library of books.” It’s a collective. But the general term, while it applies to many things, considers each one as an individual. For example, “library.” Many different individual libraries exist. They have attributes that make them a library.*

*Example from Jevons in Elementary Lessons in Logic (p. 19).

General versus Singular Terms
A universal term is a general term. It’s used “distributively,” i.e., it refers to everything it can refer to. For example, “men.” A singular term refers to only a specific individual. For example, “the current president of the U.S.”

Concrete versus Abstract Terms
A concrete term refers to an attribute as inherent in a subject. For example, a person being “5’11.” An abstract term refers to an attribute apart from the subjects in which it belongs. For example, “height.”

Connotative versus Non-connotative Terms
Connotative terms always denote a subject with an attribute. Non-connotative terms only denote a subject or only denote an attribute. For example, a proper name denotes a subject but not an attribute.

Positive versus Negative Terms
Positive terms refer to the presence of some attribute. For example, “mortal.” But a negative term refers to the absence of some attribute. For example, “non-mortal.” A negative term is also called a complement.

Absolute versus Relative Terms
An absolute term has a meaning that doesn’t require reference to something else as a correlative. For example, “God.” This term has no correlative. Relative terms imply another object with a name. For example, “father” gets its meaning with the term offspring (the correlative).

Univocal versus Equivocal versus Analogous Terms
Univocal terms have the same exact intention and are applied the same exact way. For example, “man.” It applies univocally in “Socrates is a man” and “Plato is a man.” Equivocal terms have different meanings and are applied differently. For example, “bank.” It can be used to refer to a side of a waterway or a financial institution. Analogous terms are between these two. It’s when there is a similarity and a difference. For example, “good.” “Socrates is good” and “the circle is drawn good” use the term “good” in similar yet different ways. Socrates’s “goodness” refers to his moral virtue as a human being who lives a moral life. The circle’s “goodness” is that it is drawn well enough to reflect what it means to be a circle.

Terms of First Intention versus Terms of Second Intention
Terms of first intention apply to objects in the world as they are in the world. For example, “George is mortal.” The subject – George – exists in the world. The predicate is also a real feature of the subject. Terms of second intention apply to objects in the world only as they exist conceptually within the mind. For example, “Man is a universal concept.” While men exist in the world, no universal concepts exist in the world. This predicate is purely in the conceptual realm. Other purely conceptual predicates include “middle term,” “genus,” “species,” etc.

Logic is the science of second intention.

Simple Apprehension & Abstraction

From *Thomistic Psychology: A Philosophic Analysis of Man* by Robert Edward Brennan (p. 142).

Understanding how we form ideas is a matter of both epistemology and philosophical psychology. Above is a useful diagram from a classic book on the latter subject from a Thomistic perspective.

Forming ideas is a de-materialization process. We are not limited to sense knowledge, and we can understand material things immaterially.

There are four general steps in the formation of an idea.

Our external senses — based on seeing, hearing, touching, tasting, or smelling — encounter something. An internal sense, called “common sense” in the technical jargon, unifies or brings together this encounter. We get a “percept.”

Next, it’s possible, with the internal senses of “memory,” “imagination,” and “estimative sense,” to visualize in the mind’s eye this concrete encounter. This produces a mental image or, in the technical jargon, a “phantasm.”

Abstraction can then occur with the phantasm by the “agent intellect.” This allows us to form general concepts and to reach an essential nature. Finally, the “possible intellect” forms the idea.