I had this idea, and it seems novel to me, but I'm wondering if there is a philosopher that addresses this issue already because I think it's kind of interesting.
When making a logical statement, you have premises, process, and a conclusion. The premises must be agreed upon before proceeding with the other steps. But one could contest the premises, which requires its own argument to establish, to which there are likely more prerequisite premises. From there you can keep infinitely regressing on premises.
One could say that eventually you could end up with and uncomplicated an unambiguous premise, like "Socrates is a man", but that contains words whose definitions could be contested (What is a "man"? Who was Socrates? What does "is" mean?). To establish their meaning, an argument must be made, premises invoked, and we are still regressing.
One could try to solidify them in the form of symbols, but symbols carry agreed upon meanings, whose meanings are established in language ("The + symbol means to add two terms together" "What does 'two' mean?"), and we are back to regressing.
Yes, this is petty to do, but this appears to suggest that logic has no grounding, and the start points of all logical statements are arbitrary or socially determined. This would further suggest that all logical statements are subjective as they follow from subjective premises.
I'm happy to discuss this further, but more so I'm looking to be pointed in the direction of philosophers who have had similar ideas about "grounding of logic" or infinite regress as applied to epistemological concerns or problems of language use in philosophy.