for example, in church’s Untyped Lambda Calculus, The barber becomes an anonymous function – a lambda.
remove identity, operate in steps or overtime, and where does the paradox go? its solved.
The thing that holds together the barber paradox is the identity of the barber.
I could be wrong. My understanding of these things is limited and I never thought about the barber paradox that deeply.
but if you have a function named barber can you operate the function on the function?
you can do it in programming.
what makes logic in computer programming different from the way Russel did logic,
is programming compiles line by line.
so you can’t have a contradiction in a single line of code
but you can have apparent contradictions within a program.
russell’s logic has to operate without time.
Computer logic can operate over steps or over time.