Earth’s moon is notably big. Relative to the size of its parent planet, it’s easily the biggest* in the solar system (or second biggest if you Stan Pluto as a planet). If there was a second moon, it would likely be a lot smaller. So, I don’t think it would have much practical effect on things like tides or timekeeping. It would still have cultural significance in things like mythology and astrology. If we could observe moon-moon interactions we might have discovered gravity earlier.
/* in absolute size, there are a couple of larger moons, but they’re moons of giant planets so Luna still wins in relative size.
Physical seasons, and the modern western calendar, are both based on the sun. Having two moons wouldn’t make a difference there.
Two moons would make the ocean tides more complicated, though.
Given our propensity to watch the stars and moon, I think we’d figure out some month schedule if we wanted one.
Months really don’t matter all that much because the seasons are still based the Sun and the planets tilt. The days get shorter and longer each day and that’s pretty easy to observe.
(We might actually get a month that makes more sense if we throw out lunar cycles. One that aligns with the week.)
True, it takes 28 days for the moon to orbit us and yet only one of our months is actually 28 days long (and even then it’s 29 if the year’s a multiple of 4). Every other month is either 30 or 31 days long.
We use the sun:
