This is basically correct. Ultimately, the answer depends on the conventions we adopt. We know that 1 = 1 is a true statement because it's true by convention. A lot of people forget this, not only when it comes to math, but when it comes to knowledge in general. I feel like people are becoming more and more sure of themselves and their beliefs while thinking less and less about what their beliefs are built on top of. This is a radical departure from how humans thought only a few hundred years ago. Just look at the quality of western political discourse during the 1700's, for example, as compared to now.