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20/ For Peirce on Babbage: http://www.iupui.edu/~peirce/writings/v2/w2/w2_47/v2_47.htm … For Peirce's logical machine: https://history-computer.com/ModernComputer/thinkers/Peirce.html … For remarks about sensations as signs, there are many scattered remarks. I looked mainly here http://www.peirce.org/writings/p27.html … but also 'On Time and Thought'
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19/ For more information on things like Peirce's arrow, and the Curry-Howard isomorphism, consult your local wikipedia
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18/Not exactly a significant insight, but a fun bit of history, and it certainly makes some of the weirder sections of Peirce make a bit more sense (to me, anyway).
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17/Again, this is not a term Peirce had. I only mean that ‘computation’ is a good modern gloss for what Peirce was trying to get at. For Peirce, logic and semiotics were equivalent. Proofs are both symbols and computations, so some symbols are computations.
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16/The Curry-Howard isomorphism says that proofs are equivalent to computations. Remember that weird, over extensive notion of logic? How things like sensations are signs? Doesn’t it make a lot more sense if you replace ‘sign’ and ‘logic’ with ‘computation’?
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15/Proofs, he says, are symbols. You know what else proofs are? Computations!
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14/None of this means he invented computing, or had the concept as we think of it - he didn’t - but he was familiar with the ideas that lead to them
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13/And finally, Pierce is remembered today in notation for mentioning that NOR is sufficient to express the other boolean operators. (NOR is sometimes called a Pierce’s arrow)
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12/One of his own students worked on a machine to give all implications of a logical formula, and Pierce famously suggested improvements by transferring from a mechanical setup to an electrical setup.
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11/Second, Pierce was not unfamiliar with the notion of a computing machine. His obituary for Babbage shows he was well aware of the analytical and difference engines.
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10/He thought of logic as being based on math, phenomenology, and ethics.
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9/First, what Pierce meant by logic was extremely broad. It included what the retina and brain do when they go from sensing a bunch of points to edge detection to image recognition.
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8/What strikes me is that the initial example Pierce abstracted from to get his symbol was a proof. Natural for a logician to place proof in such a central location, but we could see it as deeper than that.
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7/Symbols are the most... general kind of sign. Thoughts, words, arguments, and expressions are symbols, for instance.
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6/All thoughts and experiences are kinds of signs (the experience of a sound, or sight is a sign, taken up by other signs and then by symbols as we think about them and react).
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5/Famously, they involve infinities: a symbol specifies its own interpretation, which is another symbol, and you get an infinite regress (though Pierce was willing to admit death would put a stop to that easily enough).
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4/The most intriguing kind of signs are what he called ‘symbols’. They also refer only by convention. He had an involved logical description of their structure which he revised repeatedly over the course of his life, but I won’t touch on that here.
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3/Pierce talked about different types of signs like pictures (which refer to a thing because they resemble that thing) and words (which refer to a thing by convention).
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2/C.S. Peirce (pronounced purse) was a logician in the late 1800s. He’s known to lit land linguistics students as one of two people who coined the term ‘semiotics’ for basically the same idea -- study of meaning.
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1/And now a break from our usually scheduled programme for a brief remark on the history of computing. Please note that I am not a historian and anything that I say about history is subject to correction from people who actually know what they’re talking about.
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