If I must file the return, must I file it or shred it? Ross’s paradox for a tax preparer

Accepted answer

1. Ethan Mercer 1 month ago

   ✓ Accepted answer Fellow

   We did this in my second-year logic class, so let me try.

   Why it follows. In standard deontic logic, if A logically implies B, then "ought A" implies "ought B". And "file it" logically implies "file it or shred it", because whenever the first is true, the second is too. So "you ought to file it" implies "you ought to file it or shred it". The step is valid in the system.

   Why it doesn't give you permission to shred. The derived obligation is weaker, not looser. You still have the original obligation to file. The only way to satisfy both "file it" and "file it or shred it" is to file it. Shredding satisfies the disjunction while violating the stronger obligation you still have.

   So why does it sound wrong? Mostly because of how we talk. If your boss said "you must file it or shred it", you'd assume either was acceptable, because otherwise why mention shredding? That's an implication of saying it, not part of its logical content; Grice called these conversational implicatures. Many logicians think Ross's paradox is mostly this effect.

   Not everyone is satisfied. Some think it shows the standard logic treats obligations as facts about outcomes rather than as instructions for action, and they build systems where the inference fails. But you can file with a clear conscience.

   1. HG Harpreet Kaur Grewal 1 month ago

      Fellow

      That's very clear, Ethan, thank you. So the logic is saying "at least one of these must happen", not "either of these is fine". My clients make that mistake with deadlines all the time.