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Subsection 7.2.8 Situated Truth

Whenever we say or write something, we do so in some particular situation. A claim can be true in one situation, but not in another.

[1] I live in Texas. (Depending on who is speaking, and thus what the referent of “I” is, this sentence is either true or false.)

[2] The principal is from Kansas. (When we use the word, “the”, we presuppose that there exists some unique object to which we’re referring. Clearly there are many, many principals in the world. But said in the context of a particular school, this sentence refers to one person and is either true or false.)

[3] There’s an ice cream store down the street. (True in some places and false in others.)

[4] Tomorrow is a holiday. (True on some days and in some places, and false in others.)

We will need to assume, in our discussions, that we begin with claims for which any situational ambiguity (including whether we’re talking about the real world or some imaginary one) has already been resolved.

Exercises Exercises

1.

Consider the claim, “A Presidential election is held every four years.”

Consider the following statements about this claim:

  1. To assign it a truth value requires additional information about the time at which it was asserted.

  2. To assign it a truth value requires additional information about the place in which it was asserted.

  3. To assign it a truth value requires additional information about the entities (such as people or things) in the situation where it was asserted.

Which of them is/are true (don’t stretch super far to find some exceptional case):

  1. Just I.

  2. Just II.

  3. Just III.

  4. Two of them.

  5. All three of them.

  6. None of them.

Answer.

Correct answer is D.

Solution.

Explanation: This claim is true in some places and at some points in history.

2.

Consider the claim, “Kerry likes ice cream.”

Consider the following statements about this claim:

  1. To assign it a truth value requires additional information about the time at which it was asserted.

  2. To assign it a truth value requires additional information about the place in which it was asserted.

  3. To assign it a truth value requires additional information about the entities (such as people or things) in the situation where it was asserted.

Which of them is/are true (don’t stretch super far to find some exceptional case):

  1. Just I.

  2. Just II.

  3. Just III.

  4. Two of them.

  5. All three of them.

  6. None of them.

Answer.

Correct answer is C.

Solution.

Explanation: There are lots of people named Kerry. We need to figure out exactly which Kerry we’re talking about.

3.

Consider the claim, “5 is a prime number”.

Consider the following statements about this claim:

  1. To assign it a truth value requires additional information about the time at which it was asserted.

  2. To assign it a truth value requires additional information about the place in which it was asserted.

  3. To assign it a truth value requires additional information about the entities (such as people or things) in the situation where it was asserted.

Which of them is/are true (don’t stretch super far to find some exceptional case):

Answer.

Correct answer is F.

Solution.

Explanation: 5 refers unambiguously to a number (that happens to be prime, so this statement is true). In general, we’ll find situational ambiguity rare in mathematics.