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

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Logical Equivalences among Why, Because, Reason, Therefore, 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

Dictionary definitions of because, why, therefore, explain
In Terms of Reason

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