If I record a sound at a rate of 8000 samples per second I know that
the highest frequency that can be reproduced from the sound is 4000
False! You can only reproduce frequency content that is below half the sample rate, or in your case, strictly below 4000 Hz (not at 4000 Hz). Spectral content at exactly half the sample rate might be partially reproduced depending on the phase. Spectral content near half the sample rate in a finite length window has a similar problem, where it can be strongly attenuated, depending on the phase.
Content above half the sample rate is just folded below half the sample rate. A frequency above Fs/2 by dF that isn't removed by an anti-aliasing filter will be heard at a frequency of (Fs/2) - dF. e.g. A 5500 Hz (4000 + 1500) sinewave will be heard as 2500 Hz (4000 - 1500) sinewave.
One way to think about content at exactly half the sample rate is that it gets folded back on itself, and thus interferes with itself, either additively or destructively, depending on phase. Not good.