What is a Proposition?

A proposition is a sentence of the form “ A IS B”

> The Lord IS my refuge.
> God IS Love.
> Jesus IS Lord.

Not all sentences are propositions.
Questions, commands and exclamations are sentence patterns which are NOT propositions.
> What a cute puppy! is an exclamation.
> Do you like ice cream? is a question.
> Clean your room! is a command.

But because the linking verb IS can have several different meanings, a proposition must be analyzed before we can be sure of its correct meaning.

The ability to analyze the linking verb is of great importance.
It is impossible to deal with challenges to your faith effectively without having a clear understanding of the use of the linking verb IS. Another name for the linking verb is Copula.

How are we to understand the following propositions?
God IS Love.
Faith IS the assurance of things hoped for […]

The linking verb is an ambiguous term because it can have several different meanings. If we do not know which meaning is being used in a proposition, we cannot know the correct meaning of that proposition.


The COPULA has at least ELEVEN different meanings or uses,
with additional variations.

1- The IS of Existence
Example: God IS.
In this proposition, “IS” means the same as “Exists”
God IS = God Exists

2- The IS of Predication
Example: Laura IS Beautiful.
Laura displays the attribute of beauty.
To make a predication is to make a declaration, or an assertion about something or someone.
Both Subject and Complement are defined.

3- The IS of Class Belonging
Example: Lisa IS Married.
In other words, we can say that Lisa belongs in the class of people who are married.
Both Subject and Complement are defined.

4- The IS of Finding Oneself
Example: Mariam IS in Armenia.
In other words, Mariam Finds Herself in Armenia. Find in Space.
var. Mariam’s time IS eight hours ahead of ours. Find in Time.
Both Subject and Complement are defined.

5- The IS of Consequence
Example: Knowledge IS Power.
The consequence of having knowledge is to have power.
The more knowledge that a person has, the more power he has in dealing with his problems.
Both Subject and Complement are defined.

6- The IS of a Metaphor
A Metaphor asserts that one thing is something that it literally is not.
Example: Time IS Money.
Money is not a predication about Time, and it is not a Class to which Time belongs.
Time is not an object that can be found in a location, and Money is not a Consequence of Time, or vice versa.
Time and Money are Not Identicates.
The Subject is an Indefinable term.

7- The IS of a Simile
A Simile likens one thing to another unlike thing; the copula links a non-literal attribute to the subject.
Example:  She IS as cute as a kitten.
Both Subject and Complement are defined.

8- The IS of an Idiom
An idiom is a commonly used expression whose meaning does not relate to the literal meaning of its words.
Example: It IS a piece of cake.
Both Subject and Complement are defined.

9- The IS of Identity
Example: Truth IS God. Identity of Titles. (T/T)
var.: Example: Mark Twain IS Samuel Clemens. Identity of Proper Names. (N/N)
var.: Example: John Smith is my husband. Identity of Proper Name and Title. (N/T)

The IS of identity has a feature that can be used to detect errors.
The above propositions can be converted and still remain valid.
Example: God IS Truth.
Example: Samuel Clemens IS Mark Twain.
Example: My husband IS John Smith.
The Subject and the Complement can exchange places, and the proposition remains valid.
This is called Convertibility.
Both Subject and Complement are defined.

10- The IS of Activity
Example: Gayle IS Walking/Thinking.
Both Subject and Complement are defined.

11- The IS of Quantity
Example: Common Sense IS Rare.
Both Subject and Complement are defined.



God and Truth are Identicates.
BOTH
God IS Truth
and
Truth IS God
are valid propositions.

--------------------------

Summary

To properly interpret and understand any proposition, we must be able to correctly identify the copula that is being used in that proposition.

1- The IS of Existence
2- The IS of Predication
3- The IS of Class Belonging
4- The IS of Finding Oneself
5- The IS of Consequence
6- The IS of a Metaphor
7- The IS of a Simile
8- The IS of an Idiom
9- The IS of Identity
10- The IS of Activity
11- The IS of Quantity

RELEVANT QUOTATIONS

In the language of everyday life it very often happens that the same word signifies in two different ways— and therefore belongs to two different symbols— or that two words, which signify in different ways, are apparently applied in the same way in the proposition.
Thus the word “is” appears as the copula, as the sign of equality, and as the expression of existence; “to exist” as an intransitive verb like “to go”; “identical” as an adjective; we speak of something but also of the fact of something happening.
(In the proposition “Green is green”— where the first word is a proper name and the last an adjective— these words have not merely different meanings but they are different symbols.)
Ludwig Wittgenstein; Tractatus Logico-Philosophicus; 3.323

These many differences in translation are due to the Greek sentence structure. In this type of equational sentence [John 1:1] in Greek (A=B) the subject can be distinguished from the predicate by the fact that the subject has the article before it and the predicate does not. Since “God” does not have the article preceding it, “God” is clearly the predicate and “the Word” is the subject. This means that “God” is here the equivalent of an adjective, and this fact justifies the rendering he (the Word) was the same as God. John is not saying that “the Word” was God the Father, but he is affirming that the same divine predication can be made of “the Word” as can be made of God the Father, and so “the Word” can be spoken of as God in the same sense.

Many languages have two quite different types of equational sentences. One type indicates complete identity in such a sentence as “My husband is John Smith” or “John Smith is my husband,” that is, the two parts of the sentence are completely equivalent. In the second type, however, one may say “John Smith is a teacher” but cannot say “A teacher is John Smith.” “A teacher” merely qualifies “John Smith” and indicates the class of persons to which he belongs. The latter is precisely the type of equational sentence which occurs in this verse. “God” completely characterizes “the Word,” and all that is true of God is true of the Word. This does not mean, however, that the two elements can be inverted, and that one can translate “God was the Word” any more than one can make “Love is God” an inversion of the biblical statement “God is love.” It is difficult for some people to recognize that this equational sentence in Greek belongs to the second class because in the predicate the term “God” refers to a unique object. Since this type of equational sentence may be misleading with “God” in the predicate, it is better to translate it “The Word was the same as God” or “Just what God was that is what the Word also was.”
Barclay M. Newman and Eugene A. Nida; A Translator’s Handbook on the Gospel of John; 1980; p9

“IS”, SEMANTICAL GAMES, AND SEMANTICAL RELATIVITY
1. The Frege Trichotomy
If there is a doctrine shared by almost all analysts of the semantics of natural language these days, it is the distinction between different senses of “is”: the “is” of predication, the “is” of identity, and the “is” of existence. The “is” of predication is often called the copula. Some writers add an alleged “is” of class inclusion as the fourth reading. The most forceful philosophical proponent of the polysemy of “is” is undoubtedly Bertrand Russell. In The Principles of Mathematics he writes:

The word is is terribly ambiguous, and great care is necessary in order not to confound its various meanings. We have (1) the sense in which it asserts Being, as in “A is”; (2) the sense of identity; (3) the sense of predication, as in “A is human”; (4) the sense of “A is a-man” … which is very like identity. In addition to these there are less common uses, as “to be good is to be happy,” where a relation of assertions is meant, that relation, in fact, which, where it exists,  gives rise to formal implication. Doubtless there are further meanings which have not occurred to me.

Russell goes on to refer to De Morgan’s Formal Logic (1847, pp. 49-50) for an earlier treatment of the distinction. In fact, De Morgan there distinguishes from each other “the ‘is’ of applicability”, “the ‘is’ of possession of all essential characteristics”, and “the ‘is’ of identity”, but not the “is” of existence. The importance that Russell assigns to the trichotomy is seen from Our Knowledge of the External World, where it is introduced as “the first serious advance in real logic since the time of the Greeks.” What Russell is now emphasizing is the contrast between “Socrates is mortal” and “All men are mortal,” in other words, between predication and class-inclusion.

In 1914 Russell no longer refers to De Morgan’s trichotomy as a precursor of his distinction. He now shows a much firmer grasp of the main gateway of the trichotomy into modern discussion, ascribing it to Frege’s and Peano’s work.
It is indeed true that the respective formalisms of Frege and Peano are probably the original sources for the distinction in recent philosophy. However, the distinction is for Frege not only a feature of a convenient formalism but reflects important semantical and even ontological (categorical) differences, even though Frege did not think that we can explicitly discuss semantical matters of this sort. The trichotomy is such an integral part of Frege’s main achievement‒ the modern conception of a system of logic‒ that in this chapter I shall call it the Frege trichotomy.
Through the formalism of Frege and Peano, and even more through the notation of the Principia of Russell and Whitehead, the trichotomy became an important constituent of the contemporary concept of first-order logic. (Among the aliases of this basic part of logic there are “lower predicate calculus”, “quantification theory”, “elementary logic”, etc.) In first-order logic, the “is” of identity is typically expressed by “=”,  the “is” of existence by the existential quantifier, and the “is” of predication by predicative juxtaposition, as in “P(a).” These are entirely different ingredients of first-order language both semantically and syntactically.

Hence, anyone who uses first-order logic as a canonical notation for semantical purposes is committed to the trichotomy. The same goes for its immediate extensions. Accordingly, philosophers, logicians, and linguists as divergent as Quine, Davidson, Chomsky, and Lakoff are in the same boat with respect to the Frege trichotomy.
Jaakko Hintikka; The Game of Language; 1983; ch7; pp161-62

The little word ‘is’ is perhaps for philosophers the most troublesome in the language.
John Hick