But that's just it. There's no logic behind it. It wasn't logic that made "you" the polite version of "thou", and it wasn't logic that made "thou" disappear. It just happened naturally.
By the same token, the double negative as an intensifying construction is non-standard in English, but perfectly acceptable in many other languages. If logic governed languages, it should be one or the other in all languages.
That is because English does not like repetition. Once you have said 'not', 'hardly', 'scarcely', 'nor' etc., you do not need to say it again in another way.
For example, in Finnish, once you introduce a negative, the rest of the sentence has to carry on with the negative sense. Thus, '
olen' ('I am'),
myös ('also'); '-
kin' ('too'). In Finnish, it is logical and perfectly correct to say, '
Olen, myöskin' (I am also, too') but in English one would just say, 'Me, too' or 'Me, also'. Certainly not 'me, also, too'.
Likewise for negatives, '
en ole' ('I am not') you have to use the form '-
kään' instead of -kin as it has to agree, thus you'd have '
En ole, myöskään' = two negatives in same sentence (='neither am I' - in English, just one negative, as you have already said so with the word 'neither').
If you extend it to include, 'and him' ('
ja hän'), in Finnish this has to agree as a negative so it'd be, '
En ole, myöskään, eikä* hän' (I am not, either, nor is he').
In English one would say 'I am neither fat or thin'. In Finnish you'd say the equivalent of 'I am
neither fat
nor thin'.
More examples: English: 'it is scarcely believable', Finnish, equiv. 'It is not scarcely unbelievable'. English: 'He is hardly known'; Finnish, equiv, 'He is not hardly unknown'. English: 'There are no cattle, horses or sheep'; Finnish equivalent: 'There are no cattle, nor horses, nor sheep'.
So, in respect of double negatives having the opposite effect in English, this does follow logic in that you avoid repeating yourself. If you repeat yourself, you've cancelled out what you have just said. For example, 'I do not have no bananas'. In Finnish, you can use double negatives because the logic that is being followed is that negative words in a sentence takes a consistently negative form.
So you see, logic
is tied up in language construction.
The issue about 'you' and 'thou' was more to do with etiquette, and logical against the social mores of the times, when the farm yokel was not supposed to show familiarity with his lords and masters.
*'
ei' means 'no' and '-
kä' is added on if used in a negative sentence as a form of negative conjunction (='nor')