[ajuc]

Not the same statement at all. You can do nothing, and then only statement "you are not doing the right things" would be true.

You can also do both the right things and the wrong things, and then only the statemtnt "you are doing the wrong things" would be true.

[JadeNB]

> You can do nothing, and then only statement "you are not doing the right things" would be true.

The statement "the things we are doing are not the right things" would also be true in this case. (Statements about the empty set are usually called 'vacuously true'.)

> You can also do both the right things and the wrong things, and then only the statemtnt "you are doing the wrong things" would be true.

I agree that "you are doing the wrong things" would be true, but what Schneier said, which is "the things that we are doing are wrong", would not be, at least by my reading with an implicit universal quantifier: "[all] the things that we are doing are wrong". I would describe your situation instead as "some of the things that we are doing are wrong"; and even that is implied by, if not equivalent to, "we are not doing the right things".

[ajuc]

Sentences we are speaking of:

    1: "we are not doing the right things"
    2: "the things we are doing are wrong"

You're right that literal logical interpretation of 2 would be true if we are doing nothing, my bad, I've read this like it had implicit "we are doing semething and " at the start, and I'm quite sure it was meant as such by Bruce, but let's ignore that, and speak logic instead :)

We have:

    D - set of things we are doing
    R - set of things that are right
    W - set of things that are wrong

    statement 1 is "intersection of D and R is empty set"
    statement 2 is "D is subset of W"

You can only change "the things we are doing are wrong" into "the things we are doing are not right" if we assume every thing is either right or wrong. I think there are some possible things that TSA could be doing, that are neither right nor wrong.

When D is not subset of (sum of R and W), then 1 is not equivalent to 2.

[JadeNB]

> When D is not subset of (sum of R and W), then 1 is not equivalent to 2.

Fair enough (though it seems to be different from your original objection); I was implicitly taking 'wrong' as a synonym for 'not right'.

[ajuc]

My original objection was based on intuitive understanding of those sentences, and you're right, it's false when you take them literally.