Why are 'must' and 'must not' both negative and how can I separate them?


While studying Japanese I came across some grammar that really confuses me:

[code]

    ここから、始まってはいけない
    
[/code]

Ok, it says 'you must not start from here', which seems agreeable because the
sentence is in a negative form. However then this sentence appears:

[code]

    ここから、始まらなくてはいけない
    
[/code]

Which roughly translates to 'you must start from here'. Why is this sentence
also negative? Why are 'must' and 'must not' both written in a negative form
and how can I tell them apart?




## 始まってはいけない

Its components and their "polarity":

  * 始まる: positive (to begin)
  * いけない: negative

Construction: 始まって（て form of 始まる） + は + いけない

And, positive * negative = **negative**

So, this roughly means "must not start" (negative)

## 始まらなくてはいけない

This is "positive" because it contains a "double negative"

Its components and "polarity"

  * 始まらない: negative (to not begin)
  * いけない: negative

Construction: 始まらなくて（て form of 始まらない） + は + いけない

And, negative * negative = **positive**

This roughly means "must not not start", or "must start", because the "not"s
cancel each other




## 始まってはいけない

Its components and their "polarity":

  * 始まる: positive (to begin)
  * いけない: negative

Construction: 始まって（て form of 始まる） + は + いけない

And, positive * negative = **negative**

So, this roughly means "must not start" (negative)

## 始まらなくてはいけない

This is "positive" because it contains a "double negative"

Its components and "polarity"

  * 始まらない: negative (to not begin)
  * いけない: negative

Construction: 始まらなくて（て form of 始まらない） + は + いけない

And, negative * negative = **positive**

This roughly means "must not not start", or "must start", because the "not"s
cancel each other

