# Willard Van Orman Quine: Elementary Logic Exercises 1: Which of the following are statements?

I am currently self-studying formal logic via Quine's "Elementary Logic." The first exercise is to declare which of the following sentences are statements and re-write the sentences that are not statements to be statements.

Iron is a metal. Iron is a vegetable. Both statements In the introduction, we already declared that we are baring the truth and falsity of a statement based upon its structure, and the logical structure alone. Therefore, 'iron is a metal' and 'iron is a vegetable' must have the same truth value since they match in sentence structure.

By definition, 'it' describes the state of being of the noun: i.e, iron equals vegetable. Since 'is' is 'tenseless', what Mr. Quine refers to as present tense verbs, its usage is unaffected by time, meaning the statement is true at least once sometime in the present, past, or future. We can then deduce that 'iron is a vegetable' to be true in terms of logical structure alone. Therefore, both sentences are statements and valid, since we can deduce the truth value of the former from the latter.

I like to note here I am confused about what exactly Mr. Quine means by only analyzing the sentence structure of a statement. There are a few instances in the first chapter, on the discussion of ambiguity, where he does evaluate the meaning of certain words.

Stromboli resumed activity in 1937 and has not stopped yet. Not a statement We already see two problems here with the statement: the tense and ambiguity of activity. First, we will analyze the issue of ambiguity. 'Activity' is a broad term that has several meanings in this sentence: in this context, 'activity' could refer to Stromboli's popularity or its revival. The latter issue, tense is incorrect for both sub-statements. The first sub-statement 'Stromboli resumed activity in 1937' is incorrect because the statement is not true for all instances in time. By placing 'resume' in the past tense, the sub-statement is asserting that 1937 already happened and the Stromboli already resumed. In short, the sub-statement declares that it can only be true in one instance of time - the past. The latter statement, regardless of its context (it means to continue) and in accordance with its structure, equates to 'The Stromboli has not stopped,' meaning the Stromboli has stopped at some point in the past. This does not contradict the meaning of the former statement because the former statement declares itself to have occurred in 1937 and that the year 1937 has already passed.

To be counted as a statement, the statement must be re-written as 'The Stromboli is and continues to be popular.'

Washington died before Lincoln was born. Not a statement Washington is alive before Lincoln. This statement is only true when Lincoln is not born and Washington is dead, despite 'before' acting as a conjunction.

The doctor was a classmate of Anthony Eden's. Not a statement The statement is true for every instance of time except when the doctor is a classmate of Anthony Eden. The doctor is a classmate of Anthony Eden's. Statement

Exercise 2: Express this symbolically as a conjunction of three statements, then determine the truth and falsity of the statement.

Rome and Paris are in Italy and Campione is in Switzerland. Rome is in Italy.Paris is in Italy.Campione is in Switzerland The first sub-statement is false, so the entire statement is false.

• Same comment as per identical previous question on MSE. Commented Apr 19, 2022 at 7:31
• Having sai that "iron is a metal" and "iron is a vegetable" are both statements. Commented Apr 19, 2022 at 7:32
• And Stromboli is a volcano. Commented Apr 19, 2022 at 7:32

Quine is proposing to use the word 'statement' as a technical term in the context of logic. It is a sentence in a natural language, such as English, that is suitable for representing in a formal logical fashion. To be suitable for this purpose, it must be unambiguously either true or false, and in particular must not depend on its truth or falsity on who says it, or when, or where. So, for a sentence to qualify as a statement, it must satisfy a number of requirements:

1. It must be tenseless, or what is often called the 'eternal present'.
2. It must not contain any indexicals, e.g. I, you, me, here, now, later, etc.
3. It must not contain any words or names that are ambiguous.

Applying these criteria:

1. Iron is a metal. This is a statement. It is true.
2. Iron is a vegetable. This is a statement. It is false.
3. Stromboli resumed activity in 1937 and has not stopped yet. This is not a statement, because 'yet' is an indexical, so the sentence might be true or false depending on when it is uttered. It might be structured as: Stromboli was active but ceased to be in XXXX [some date prior to 1937]. Its activity resumed in 1937 and continued until YYYY [some date after 1937]. As far as online sources go, this is false, and Stromboli has been active almost continuously for thousands of years.
4. Washington died before Lincoln was born. This is not a statement, since it is tensed. Quine prefers: Washington dies before Lincoln is born. Also, ideally it should be made clear that we are referring to the two American presidents, since the names are not unique.
5. The doctor was a classmate of Anthony Eden's. This is not a statement, since we don't know who 'the doctor' refers to, and it has a tense. It should be something like: Dr XXXX [an unambiguous name] is a classmate of Anthony Eden's between the years YYYY and ZZZZ.

It might be worth noting that Quine is being excessively fussy here with his rules. Removing indexicals is one thing, but in practice, it is almost impossible to eliminate all elements of context from an utterance, or render it completely unambiguous.

• Any ideas whether temporal logic can be used on tensed statements? Commented Jan 21, 2023 at 6:37
• That is one of its main use cases. The idea behind temporal logic is to add time-related variables to predicates and functions, and then have operators for "at all times", "at some time" and "now". It has a similar structure to alethic modal logic, with "at all times" replacing "necessarily", "at some time" replacing "possibly", and "now" replacing "actually". The difference being that times are ordered, so temporal logic also has a primitive "earlier than" relation. Commented Jan 21, 2023 at 17:07