Putnam and Benacerraf's arguments about mathematical reduction show that multiple incompatible formalisms can be co-extensional, meaning equivalence underdetermines which characterization is the 'intrinsic' one.
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Intrinsic(describing the kind of continuities that ground identity)
Something that belongs to or is part of something by its very nature, rather than coming from outside or being relational.
Mathematical reduction(as the central topic being discussed)
The attempt to explain what math really is by reducing it to something more basic, like sets or logical rules.
Putnam
# Putnam
"Putnam" most commonly refers to **Hilary Putnam** (1926-2016), an influential American philosopher who made major contributions to philosophy of mind, language, and science. He is famous for thought experiments like the "brain in a vat" scenario, which explores questions about reality and how we know what's real. His work fundamentally changed how philosophers think about the relationship between our minds, language, and the external world.