Fun With English: Is 'None' Singular or Plural?

To my ear, the following sounds grammatical:

1. None of the members were present at the meeting

whereas the following sounds ungrammatical:

2. None of the members was present at the meeting.

But isn't 'none' just a contraction of 'no one'? If it is, then (2) is grammatical and (1) is not. Now compare

3. All of the members were present at the meeting

4. All of the members was present at the meeting.

(3) sounds grammatical to me, while (4) sounds decidedly ungrammatical.

But surely (3) is logically equivalent to the ungrammatical

3*. Each of the members were present at the meeting

and (4) is logically equivalent to the grammatical

4*. Each of the members was present at the meeting.

Let this serve as a warning to school marms and copy editors  and those who would imitate them: be careful when you criticize another's English. He may have thought a lot harder and deeper than you. Your petty rules may collapse under logical scrutiny.