As a programmer, double negatives make me reel with horror. I cannot parse an English sentence with a double negative as being a single negative; it's utterly illogical. At best, they're an unnecessary hindrance.
Computer languages are not spoken languages. No one should accuse English of being "illogical" because it's redundant. It isn't as terse as mathematical notation because most people don't speak completely in mathematical notation. And it's all very logical, actually -- just not in the way you might expect. You might want to look into the effects of redundancy on transmission errors in communications before you pass judgement. :-)
[1] http://en.wikipedia.org/wiki/Agreement_%28linguistics%29
Be interesting to do a corpus study on this.