Wittgenstein's rule-following considerations show that no finite set of symbols autonomously determines its own extension to infinitely many cases without an interpreting practice.

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Autonomously determines(asking whether symbols/rules can work independently): On its own, without needing help—like asking whether a rule can figure out what to do next all by itself, without a person interpreting or deciding.
Infinitely many cases(describing the scope of what a rule must cover): An endless, unlimited number of situations or examples. For instance, the rule 'add 2' applies to infinite numbers (2+2, 4+2, 6+2, forever).
Interpreting practice(what Wittgenstein argues we need beyond just symbols): The shared habits, customs, and ways a community of people actually uses words and follows rules together. It's the living, social side of language—how we learn meaning by doing things with others.
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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