# Logical Equivalences among Why, Because, Reason, Therefore, Explain

#### Logical equivalences among ‘because’, ‘reason’, ‘why’, ‘therefore’, and ‘explain’

• The following are logically equivalent, where P and C are independent clauses:
• C because P
• The reason that C is that P
• That P is why C
• P. Therefore, C
• That P explains C’s being the case

#### Five Ways to Say the Same Thing

##### Why is John Oliver ineligible to be president?
• C = John Oliver isn’t eligible to be president
• P = John Oliver is not a natural-born U.S. citizen
• C because P
• John Oliver isn’t eligible to be president because he’s not a natural-born U.S. citizen.
• The reason that C is that P
• The reason that John Oliver isn’t eligible to be president is that he’s not a natural-born U.S. citizen.
• That P is why C
• That he’s not a natural-born U.S. citizen is why John Oliver isn’t eligible to be president.
• P. Therefore, C
• John Oliver is not a natural-born U.S. citizen.  Therefore, he’s not eligible to be president
• That P explains C’s being the case
• That he’s not a natural-born U.S. citizen explains John Oliver’s ineligibility to be president.
##### Why is the probability of rolling a seven ⅙?
• C = the probability of rolling a seven is ⅙
• P = there are 36 equally likely outcomes and six ways to roll a seven.
• C because P
• The probability of rolling a seven is ⅙ because there are 36 equally likely outcomes and six ways to roll a seven.
• The reason that C is that P
• The reason that the probability of rolling a seven is ⅙ is that there are 36 equally likely outcomes and six ways to roll a seven
• That P is why C
• That there are 36 equally likely outcomes and six ways to roll a seven is why the probability of rolling a seven is ⅙.
• P. Therefore, C
• There are 36 equally likely outcomes and six ways to roll a seven. Therefore, the probability of rolling a seven is ⅙.
• That P explains C’s being the case
• That there are 36 equally likely outcomes and six ways to roll a seven explains the probability of rolling a seven being ⅙.
##### Why is the acceleration at the Earth’s surface 9.8 meters per second2?
• The acceleration at the Earth’s surface is 9.8 meters per second2 because
• (1) for any pair of physical bodies there’s a force on each,
• (2) the Earth’s mass = 5.972 * 1024 kg,
• (3) the Earth’s mean radius =  6.371 * 106 m, and
• (4) G = 6.67384 10-11.
• The reason that the acceleration at the Earth’s surface is 9.8 meters per second2 is that (1), (2), (3), and (4).
• That (1), (2), (3), and (4) is why the acceleration at the Earth’s surface is 9.8 meters per second2.
• (1), (2), (3), and (4). Therefore the acceleration at the Earth’s surface is 9.8 meters per second2.
• That (1), (2), (3), and (4) explains the acceleration at the Earth’s surface being 9.8 meters per second2.
##### Why did Jason leave early?
• Jason left early because he felt sick.
• The reason Jason left early is that he felt sick.
• That Jason felt sick is why he left early.
• Jason felt sick.  Therefore he left early.
• That Jason felt sick explains his leaving early.
##### Why should capital punishment be abolished?
• Capital punishment should be abolished because there’s a risk of killing an innocent person.
• The reason capital punishment should be abolished is that there’s a risk of killing an innocent person.
• That there’s a risk of killing an innocent person is why capital punishment should be abolished.
• There’s a risk of killing an innocent person.  Therefore capital punishment should be abolished.
• That there’s a risk of killing an innocent person explains its being that capital punishment should be abolished.

#### Do the stars twinkle because they’re far away?Or are they far away because they twinkle?

• The stars twinkle because they’re far away
• The reason the stars twinkle is that they’re far away
• That they’re far away is why stars twinkle.
• The stars are far away.  Therefore they twinkle
• That they’re far away explains the twinkling of stars.
• The stars not are far away because they twinkle.
• But it’s reasonable to believe stars are far away because they twinkle

#### Senses of ‘Explain’

1. Make understandable
• I need a lawyer to explain this contract to me.
• The professor explained the poem to the class.
• She explained how the machine worked.
2. Give the reason for
• That explains why we were so far behind schedule.
• She explained why no one answered the door.
• Scientists could not explain the strange lights in the sky.
3. Present in detail, expound
• Einstein explained his theory in a series of lectures.
4. Make known
• I explained to them that I would be available by phone