Because of Russell's Paradox, mathematicians realised that unrestricted comprehension is bad and so set about designing systems where the bad thing just couldn't be defined. But there is another, kinda bonkers way: you can weaken your logic so that \(R \Leftrightarrow \neg R\) does not imply a contradiction.

In order to derive a contradiction you first use R once, this implies not R, and that *together with R* gives you a contradiction (similarly if you start with not R). But since R is being used twice, you would avoid this inconsistency in a system based on the !-free fragment of linear logic.

(This curiosity was found in Braüner's introduction to linear logic https://www.brics.dk/LS/96/6/BRICS-LS-96-6.pdf)

#linearlogic #logic #types #lolwut

ok - i'm a bit of a shitposter, but looking for enriching my feed - i'm interested in #pedagogy #ilyenkov #vygotsky #raybrassier #rezanegarestani #plato #linearlogic #topoi