Wittgenstein's rule-following considerations suggest that 'divides evenly' as a verification procedure smuggles in an infinite normative commitment not capturable by finite polynomial-time computation alone.
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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.
rule-following considerations(in philosophy of language)
Wittgenstein's famous puzzle about how we know what rule to follow next: if you learn a rule by seeing examples, how do you know you're applying it correctly to new cases you've never seen before?