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Subsection 1.3.2 Claims about the World

When we reason about the everyday world, we don’t use exactly the formal process that we are about to study. But logical everyday arguments must have the same structure as the formal arguments we’ll be making. And they can do so because claims about our everyday world can be represented as logical statements.

We’ve already seen some examples of statements that are true in the world.

Activity 1.3.1.

  1. The Earth revolves around the sun.

  2. Paris is the capital of France.

  3. It never snows in Austin in August.

  4. The moon is in synchronous rotation with the Earth.

  5. If it’s raining, the sidewalks will be wet.

We’ve also seen some examples of statements that are false in the world.

Activity 1.3.2.

  1. The sun revolves around the Earth.

  2. London is the capital of France.

  3. It never snows in Fairbanks in January.

  4. The moon is made of green cheese.

And we’ve considered examples of statements whose truth value I, at least, don’t know.

Activity 1.3.3.

  1. The social security number of the President of the United States is 224-78-5742.

  2. There was life on Earth 4 billion years ago.

Problems 1.3.4.

What is the truth value (in the world in which we live) of each of the following statements:

(a)

People born in 2000 are older than people born in 2010.

  1. True.

  2. False.

  3. People who otherwise seem reasonable disagree on this.

Answer.

i

Solution.

This statement is true unless we want to say that some of the people who were born in 2000 have now died and so they can’t be older than anyone

(b)

Most professional basketball players are taller than 5' 10".

  1. True.

  2. False.

  3. People who otherwise seem reasonable disagree on this.

Answer.

i is correct.

Solution.

Most people would call this statement true. But to decide that requires a definition for the word “most”. Does it mean more than half? Does it mean something stronger than that?

(c)

The only way to create jobs is to reduce taxes.

  1. True.

  2. False.

  3. People who otherwise seem reasonable disagree on this.

Answer.

iii is correct.

Solution.

Some people will assert that this statement is true. Others will (equally vehemently) assert that it’s false. The disagreement arises because different people choose different starting points for their reasoning. If we want to use logic, we’ll first have to be explicit about what truths we are willing to start with.