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.