Wittgenstein's 'On Certainty' demonstrates that foundational commitments in any domain—including scientific ones—function as hinge propositions held without evidential justification.

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Foundational commitments(as used in philosophy of mathematics): The basic assumptions and principles that a mathematical or logical system relies on at its core—the 'ground floor' beliefs it's built upon.
Hinge propositions(the role these beliefs play in our knowledge system): Fundamental beliefs that act like the 'hinge' of a door—they're so basic that we rely on them to evaluate everything else, and we can't really justify them without circular reasoning.
On Certainty(The specific philosophical work being referenced): A book Wittgenstein wrote near the end of his life that explores what we can be absolutely sure about and how certainty actually works in real life, rather than just in theory.
Wittgenstein: Ludwig Wittgenstein was an Austrian-British philosopher who fundamentally changed how people think about language and meaning in the 20th century. He argued that many philosophical problems arise from misunderstanding how words actually work in everyday life, rather than from deep metaphysical mysteries. His ideas influenced not just philosophy but also mathematics, logic, and even how people approach psychology and artificial intelligence today.

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