“Things” in reality aren’t “true” or “false” outside the context of specific logical tools. In particular, consistency is a property of (some of the) logical systems, considered as a good heuristic for developing ones that are interesting (formally, consistency alone doesn’t make a system “good”: indeed, a consistent system may even prove false formulas!). For logical systems, it does make sense to talk about which ones are consistent and which ones are not.
“Things” in reality aren’t “true” or “false” outside the context of specific logical tools. In particular, consistency is a property of (some of the) logical systems, considered as a good heuristic for developing ones that are interesting (formally, consistency alone doesn’t make a system “good”: indeed, a consistent system may even prove false formulas!). For logical systems, it does make sense to talk about which ones are consistent and which ones are not.