Pirates & Revolutionaries: Lewis Carroll, Symbolic Logic, Part 1, Book 1, Chapter 4, Names

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22 Feb 2009

Lewis Carroll, Symbolic Logic, Part 1, Book 1, Chapter 4, Names

by Corry Shores
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Lewis Carroll

Symbolic Logic

Part I: Elementary

Book I: Things and their Attributes

Chapter IV: Names

What's in a Name?

Consider the image below.

We just called it an "image." We could also call it a "painting." In fact, its creator Francis Bacon named it "Painting."

Now imagine we were to announce "We today shall buy a painting." We used the word "painting." Paintings are painted artworks. But sculptures do not have this Attribute of being paint on canvass. Music as well lacks this attribute. So when we use the term "painting," we are referring to all the Things that this word represents. We call such a word (or phrase) a Name.

Now, maybe someone mishears our declaration and asks, "So you will sell something today?" We then replay, "No, we will buy some thing." Here we speak more generally of the painting as a 'Thing.' But this could be any thing, no matter its attributes. Hence the name 'Thing' represents the idea of any possible Thing without any idea of its Attributes. So 'Thing' represents any single Thing.

We consider verbs largely to be actions or events. But the things doing the action are more substantial. We call them 'Substantives.' We could also call them 'nouns.'

We said that 'Thing' applies in all cases. Now let's look at the different ways to express more particular things.

a) We know that our painting is a painted thing. It has the Attribute of being painted canvass. So we may specify some particular Thing by adding adjectives to the Name 'Thing'. Carroll's example reads:

Thus, the phrase "material living Thing, belonging to the Animal Kingdom, having two hands and two feet" is a Name expressed in Form (a). (Carroll page 7)

b) So we told someone we want to buy a painting. We did not say, "we shall buy a painted thing." For, "painting" already represents the idea of thing with the attribute of being painted. So we may chose a substantive (noun) that conveys the idea of a thing along with the ideas of some of its attributes. If we wanted to buy the painting displayed above, we would say "we shall buy Bacon's painting that he painted in 1946." So as well, we may also include adjectives (or other descriptive phrases) to convey the more specified thing's other attributes. Carroll offers this example:

If we choose to roll up together the Substantive "Thing" and the Adjectives "material, living, belonging to the Animal Kingdom," so as to make the new Substantive "Animal," we get the phrase "Animal having two hands and two feet," which is a Name (representing the same Thing as before) expressed in Form (b). (page 7a)

c) We also could have said more simply "We shall buy Painting 1946." The name 'Painting 1946' refers to one specific painting by Francis Bacon. So the third way we may express particular things is by finding one substantive that conveys all its attributes. Carroll's example is:

And if we choose to roll up the whole phrase into one word, so as to make the new Substantive "Man," we get a Name (still representing the very same Thing) expressed in Form (c). (page 7b)

Carroll formulates the three modes of expression by writing:

Every Name, except "Thing," may usually be expressed in three different forms :—
(a) The Substantive " Thing," and one or more Adjectives (or phrases used as Adjectives) conveying the ideas of the Attributes;
(b) A Substantive, conveying the idea of a Thing with the ideas of some of the Attributes, and one or more Adjectives (or phrases used as Adjectives) conveying
the ideas of the other Attributes;
(c) A Substantive conveying the idea of a Thing with the ideas of all the Attributes. (pages 6-7)

Names of One and Many

Consider first the statement,

"The soldiers of Tenth Regiment are tall."

Now, clearly we do not here imagine one soldier standing on the ground, then a second soldier standing on the first one's head, then a third soldier standing on the second one's head and so on, until all of them together stand as high as a tall building. No rather, we are saying that each and any single soldier of the Regiment is tall.

But consider instead when we say, "The soldiers of the Tenth Regiment are formed in a square." Here we are not saying that every single soldier is shaped like a square rather than taking-on a human form. Instead, we are saying that all the soldiers taken together are arranged in a square formation.

As Carroll writes:

A Name, whose Substantive is in the plural number, may be used to represent either
(1) Members of a Class, regarded as separate Things; or
(2) a whole Class, regarded as one single Thing. (page 7c)

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