This is a really nice set of slides that captures the interactions between Ludwig Wittgenstein and Alan Turing during the former's 1939 lectures on the foundations of mathematics (you can read the summary of them here, which I highly recommend; readers will see a lot of Wittgenstein in my own work). This nice slide presentation frames the discussion as a confliuct between Turing's formalism and Wittgenstein's critique, though the issues are rather more subtle than that (here's a good example: "(Turing) arguing that contradictions could cause real-world failures, like bridges collapsing. Wittgenstein countered that contradictions don't 'explode' mathematics but reveal misinterpretations of rules"). Still, the framing allows us some understanding of the tensions people feel today in both learning theory and artificial intelligence, and is well worth reviewing. More.
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