Ex Contradictione

Here is a problem: How do we attribute a false or contradictory statement to an interlocutor?

On the face of it, we do this all the time - how can it be problematic?

Because, of course, everything follows from falsehood. To be able to attribute a false (or contradictory) statement to someone, we must (a) know what they are saying and (b) know that it is meaningless. This clearly doesn't work.

(It's why talking to someone about contradiction can be so uncomfortable. If they appear to insist that they be permitted to contradict themselves, we cannot interpret their statements to this effect 'literally'.)

What does this mean?

Davidson is on the right track here. If someone says 'p&~p', they cannot mean by it what we might conventionally expect them to mean. We need to find an interpretation that avoids contradiction. If we cannot, then we do not know what they mean by this expression and it cannot be a move in a shared language.

Reductio arguments are tests of shared understanding - of interpretation - more than of strict impersonal validity. Someone who appears to accept the premises, but does not accept the conclusion, cannot be speaking the language we believe them to be speaking (and may not be speaking at all).

This may just be another way of observing that mathematics and logic are embedded in semantic systems rather than underpinning them.