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

Table of Contents

Reason
- ahdictionary.com/word/search.html?q=reason
  - A fact or cause that explains why something exists or has occurred:
- View Senses of ‘Reason’
Because
- merriam-webster.com/dictionary/because
  - for the reason that
Why
- merriam-webster.com/dictionary/why
  - the cause, reason, or purpose for which
Therefore
- merriam-webster.com/dictionary/therefore
  - for that reason
Explain
- merriam-webster.com/dictionary/explain
  - to give the reason for or cause of
- View Senses of ‘Explain’

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.

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.

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.

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.

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.
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.
Present in detail, expound
- Einstein explained his theory in a series of lectures.
Make known
- I explained to them that I would be available by phone