I agree that universal statements are generally meaningless.
How someone who actually doesn't understand the foundations of mathematics can tell me that I don't understand the foundations is beyond me.
An example of where 7 + 8 = 3 is explicitly explained here:
https://en.wikipedia.org/wiki/Modular_arithmetic
"A familiar use of modular arithmetic is in the 12-hour clock, in which the day is divided into two 12-hour periods. If the time is 7:00 now, then 8 hours later it will be 3:00. Usual addition would suggest that the later time should be 7 + 8 = 15, but this is not the answer because clock time "wraps around" every 12 hours; in 12-hour time, there is no "15 o'clock". Likewise, if the clock starts at 12:00 (noon) and 21 hours elapse, then the time will be 9:00 the next day, rather than 33:00. Because the hour number starts over after it reaches 12, this is arithmetic modulo 12. According to the definition below, 12 is congruent not only to 12 itself, but also to 0, so the time called "12:00" could also be called "0:00", since 12 is congruent to 0 modulo 12."
And later
"Modular arithmetic is referenced in number theory, group theory, ring theory, knot theory, abstract algebra, computer algebra, cryptography, computer science, chemistry and the visual and musical arts."