More generally, the problem is that for formal agents, false antecedents cause nonsensical reasoning
No, it’s contradictory assumptions. False but consistent assumptions are dual to consistent-and-true assumptions...so you can only infer a mutually consistent set of propositions from either.
To put it another way, a formal system has no way of knowing what would be true or false for reasons outside itself, so it has no way of reacting to a merely false statement. But a contradiction is definable within a formal system.
To.put it yet another way… contradiction in, contradiction out
Yep, agreed. I used the language “false antecedents” mainly because I was copying the language in the comment I replied to, but I really had in mind “demonstrably false antecedents”.
No, it’s contradictory assumptions. False but consistent assumptions are dual to consistent-and-true assumptions...so you can only infer a mutually consistent set of propositions from either.
To put it another way, a formal system has no way of knowing what would be true or false for reasons outside itself, so it has no way of reacting to a merely false statement. But a contradiction is definable within a formal system.
To.put it yet another way… contradiction in, contradiction out
Yep, agreed. I used the language “false antecedents” mainly because I was copying the language in the comment I replied to, but I really had in mind “demonstrably false antecedents”.