Reasoning with external material formal notation (squiggles on paper) accomplishes abstraction in two ways discussed by @cdutilhnovaes: de-semantification and ease of calculation.
-
Show this thread
-
De-semantification: If you read the word “raven” you usually get a visual image and are primed with all your background knowledge of ravens. Writing ɸ(x) instead of “is a raven” strips that off, and thereby inhibits the “merely reasonable” ways of thinking.
4 replies 4 retweets 34 likesShow this thread -
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…
3 replies 5 retweets 35 likesShow this thread -
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
1 reply 1 retweet 30 likesShow this thread -
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.
4 replies 4 retweets 36 likesShow this thread -
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.
1 reply 0 retweets 17 likesShow this thread -
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
1 reply 0 retweets 27 likesShow this thread -
-
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
1 reply 0 retweets 10 likesShow this thread -
“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
4 replies 5 retweets 37 likesShow this thread
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,
-
-
(Going to pick up this unfinished thread tomorrow probably—have other things to do now!)
6 replies 1 retweet 7 likesShow this thread -
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,
David Chapman @Meaningness“Ethnomethodology” is basically the empirical study of rationality, both informal and formal, considered as an embodied, situated, material, social and cultural activity. Unfortunately it has its own jargon plus methodological issues; but seems directly relevant to your work.Show this thread1 reply 0 retweets 3 likesShow this thread
End of conversation
New conversation -
Loading seems to be taking a while.
Twitter may be over capacity or experiencing a momentary hiccup. Try again or visit Twitter Status for more information.