Quine-Putnam indispensability arguments license only those mathematical entities indispensable to best science, but Maddy's objections show actual scientific practice does not uniformly quantify over all posited mathematical objects.
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# 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.
Quantify over(describing which mathematical objects scientists actually commit to existing)
A technical phrase meaning 'to claim that things of a certain type exist and count them as real'; for example, saying 'numbers exist' means you're quantifying over numbers.
Quine(as a proper name referring to the philosopher whose theory is being discussed)
Willard Van Orman Quine was a 20th-century American philosopher who wrote about how we know things and how language works. In this statement, we're discussing one of his specific ideas about observation.
indispensability argument(Lewis uses a modified form: not strict indispensability, but sufficient theoretical benefit)
An argument that we ought to believe in the existence of entities that are required (or highly useful) for our best theories