 This raises another interesting issue. Ever since Euclid, the method of reductio ad absurdum has been thoroughly exploited in geometrical proofs (assume he opposite of what you want to prove and deduce a contradiction). But here we have a different technique (employ a contradiction to describe how inconsistent figures look, to demonstrate that the content is genuinely contradictory). If successful, this is a demonstration that human conceptualisation exceeds the merely possible (consistent). For discussion see Mortensen (2019, 2022).