According to Walter Piston's Harmony book, a perfect fourth is dissonant if there's no tone below its lower tone, while it's consonant if there's a third or a perfect fifth below the interval. In that case, why does a second inversion triad with no third or fifth below the interval feel consonant?
A first inversion triad DOES have a note a third below the perfect 4th. A second inversion triad doesn't. Hence the slight instability of a second inversion.
(edit: I should explain that the original question, before correction, asked about a FIRST inversion triad.)
Piston is talking about stability, not the sort of dissonance we get from minor 2nd intervals. A second inversion triad has the feeling of being a double suspension - hence the classic '6/4' cadence sequence.
(Actually, post-Common Practice, we've rather lost sight of the 'crunchy minor 2nd' concept of dissonance. A major 7th is hardly noticed as dissonant now.)