The truth predicate could talk about the past (but not the present), but I believe that reduces down to other things that have been explored quite thoroughly (iirc, an idea of a hierarchy of math with higher levels being able to talk about lower levels but not vice versa was around for Bertrand Russel to endorse). And at that point “time” is just a label for what level of explanatory power you are talking about.
The truth predicate could talk about the past (but not the present), but I believe that reduces down to other things that have been explored quite thoroughly (iirc, an idea of a hierarchy of math with higher levels being able to talk about lower levels but not vice versa was around for Bertrand Russel to endorse). And at that point “time” is just a label for what level of explanatory power you are talking about.