[New Entry by Alexander Paseau and Fabian Pregel on August 25, 2023.]
Deductivism says that a mathematical sentence (s) should be understood as expressing the claim that (s) deductively follows from appropriate axioms. For instance, deductivists might construe “(2 + 2 = 4)” as “the sentence ‘(2 + 2 = 4)’ deductively follows from the axioms of arithmetic”. Deductivism promises a number of benefits. It captures the fairly common idea that mathematics is about “what can be deduced from the axioms”; it avoids an ontology of abstract mathematical…

Originally appeared on Stanford Encyclopedia of Philosophy Read More