**Table of Contents**

- Logical equivalences among ‘because’, ‘reason’, ‘why’, ‘therefore’, and ‘explain’
- Dictionary definitions of ‘because’, ‘why’, ‘therefore’, and ‘explain’ In terms of ‘reason’
- Five Ways to Say the Same Thing
- Do the stars twinkle because they’re far away? Or are they far away because they twinkle?
- Senses of ‘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

#### Dictionary definitions of ‘because’, ‘why’, ‘therefore’, and ‘explain’

In terms of ‘reason’

*Reason*- ahdictionary.com/word/search.html?q=reason
- A fact or cause that
*explains*why something exists or has occurred:

- A fact or cause that
- View Senses of ‘Reason’

- ahdictionary.com/word/search.html?q=reason
*Because*- merriam-webster.com/dictionary/because
- for the
*reason*that

- for the

- merriam-webster.com/dictionary/because
*Why*- merriam-webster.com/dictionary/why
- the cause,
*reason*, or purpose for which

- the cause,

- merriam-webster.com/dictionary/why
*Therefore*- merriam-webster.com/dictionary/therefore
- for that
*reason*

- for that

- merriam-webster.com/dictionary/therefore
*Explain*- merriam-webster.com/dictionary/explain
- to give the
*reason*for or cause of

- to give the
- View Senses of ‘Explain’

- merriam-webster.com/dictionary/explain

**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.

- John Oliver isn’t eligible to be president
*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

- John Oliver is not a natural-born U.S. citizen.
*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?**

**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 probability of rolling a seven is ⅙
*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.

- There are 36 equally likely outcomes and six ways to roll a seven.
*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 second**^{2}?

**Why is the acceleration at the Earth’s surface 9.8 meters per second**^{2}?- The acceleration at the Earth’s surface is 9.8 meters per second
^{2}**because**- (1) for any pair of physical bodies there’s a force on each,
- (2) the Earth’s mass = 5.972 * 10
^{24}kg, - (3) the Earth’s mean radius = 6.371 * 10
^{6}m, and - (4) G = 6.67384 10
^{-11}.

- The
**reason**that the acceleration at the Earth’s surface is 9.8 meters per second^{2}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 second^{2}.- (1), (2), (3), and (4).
**Therefore**the acceleration at the Earth’s surface is 9.8 meters per second^{2}. **That**(1), (2), (3), and (4)**explains**the acceleration at the Earth’s surface being 9.8 meters per second^{2}.

**Why did Jason leave early**?

**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?**

**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?

**Do the stars twinkle because they’re far away?**- 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’

- 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