Humans evolved for concrete sensorimotor activity (e.g. foraging) and for social relationship maintenance. We didn’t evolve for formal rationality; unfortunately there is no “System 2” logic box in the brain, and we are terrible at it. We can manage only with external aids…
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Calculation: external formal notation repurposes our sensorimotor skills to perform operations our brains unaided mostly can’t. Logical giant A.N. Whitehead: “By the aid of symbolism, we can make transitions in reasoning almost mechanically by the eye” &
@cdutilhnovaes below:pic.twitter.com/thW8x7tW6i
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A well-designed formalism, skillfully deployed, makes each next calculation step *visually obvious* and therefore difficult to screw up. Mathematicians speak of calculative rationality as “symbol pushing” because at a felt level that’s exactly what we’re doing.
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Examples: Putting terms in a commutative expression in the right order helps a lot even though “logically” it makes no difference. Align key symbols in formulae vertically on the page to group analogous clauses to make it clear what the next step is.
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Einstein notation replaces enormously complicated algebraic work with visually simple sub/superscript fiddling that analogizes kinesthetically to physically moving things around by hand. Also uses visually different symbols to track vector dimensions. https://en.wikipedia.org/wiki/Einstein_notation …pic.twitter.com/oBfWkyENZR
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Two quotes here from
@cdutilhnovaes about this. Also two of her key sources, which I haven’t yet looked into myself (but intend to).pic.twitter.com/CqSK3SAcna
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“The materiality of mathematics: Presenting mathematics at the blackboard” by
@greiffenhagen makes this much more concrete, through close study of a video of a lecturer presenting a proof of the completeness theorem for propositional logic.pic.twitter.com/Ru0J6xGfmz
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David Chapman Retweeted David Chapman
Here’s
@greiffenhagen showing the embodied, spacial, temporal, interactive nature of a proving of the Dutch Book Argument (cc@cdutilhnovaes)https://twitter.com/Meaningness/status/1005489362052632578 …David Chapman added,
David Chapman @MeaningnessStartling serendipity: I began a literature search on the ethnomethodology of formal rationality yesterday, and one of the first things to turn up was a video analysis of someone delivering the Dutch Book Argument! http://www.qualitative-research.net/index.php/fqs/article/view/1172/2585#g232 … pic.twitter.com/L7LoK6t85tShow this thread1 reply 0 retweets 8 likesShow this thread -
(Going to pick up this unfinished thread tomorrow probably—have other things to do now!)
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David Chapman Retweeted David Chapman
Yesterday’s logic
got out of control. Shorter
here on formal logic as a social practice that is a somewhat-contingent product of cultural evolution:https://twitter.com/Meaningness/status/1150166188476862464 …
David Chapman added,
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