Question: So I know that acting without the foreknowledge of those actions is down to ignorance. This has various implications, the main one being that the responsibility of one's actions is not entirely eradicated, though maybe diminished. We may say, 'how could he know better? He doesn't know what he's doing/the consequences of his actions.'. Or maybe the person should have known better not to act because of their ignorance, in which case they still bear the weight of blame, but their actions weren't necessarily bad.

What if however, a person does a seemingly stupid thing, but where they knew exactly what they were doing, or what the consequences would be? Maybe they acted in a way where they wanted to seem ignorant to use this as a pretense for their ultimate aim, but where they don't have to take responsibility for their actions (or at least less responsibility).

Answer: 
In general usage we would say that someone is "*[feign](https://en.oxforddictionaries.com/definition/feign)ing ignorance*".
Sometimes the allegedly innocent motive is called a "pretext" and someone's purported intent can be described as "pretextual." This is particularly a common usage in the context of a claimed justification for improper discrimination, for example, in employment or jury selection which is actually on the basis of race.

A somewhat related concept is "willful blindness" where one intentionally avoids gaining knowledge of what a reasonable person would suspect the consequences to be. Also related is the notion of "willful disregard" or "willful and wanton" conduct.

When someone actual intends a result with a specific consequence it is said that they act with "scienter" or with "malice" or "malice aforethought", but none of those terms capture the notion of deceit as to one's motive.

Another closely related concept is "plausible deniability" which means causing something to happen in a context where you can plausibly claim that you didn't cause the action, but that isn't quite the same grammatically.