,
25 tweets,
10 min read
Read on Twitter
A š§µ on studies of formal logic as an embodied, situated, social, cultural, materially-mediated activity.
This view contrasts with:
1 formal logics as Platonic mathematical objects
2 formal logic as an innate mental capacity
This view contrasts with:
1 formal logics as Platonic mathematical objects
2 formal logic as an innate mental capacity
š§µ inspired by @cdutilhnovaesā _Formal Languages in Logic_, about why formality is useful. Her overall explanation of how formal rationality works is closely similar to mine in _The Eggplant_ draft, so it was exciting reading!
amzn.to/2NQNsxa
amzn.to/2NQNsxa
The traditional explanation for the power of logic is āexpressive precision,ā but the experience of attempting to use logic in AI is that it totally fails for that. Specifically, whenever it encounters nebulosity, which is the main point of Part I of _The Eggplant_.
Another traditional virtue of logic is truth preservation (true premises => true conclusions); but there are nearly no absolute truths in the eggplant-sized world, and deduction does not preserve mostly-truth. So thatās not the answer outside applications in math and CS. 
āDual process theoriesā say we have an innate rationality module that does logic correctly, plus an irrationality module that messes it up. (This goes back to the Greeks.) In a recent š§µ I pointed out several reasons this is wrong and has damaged cogsci.
@cdutilhnovaesās book [quote below], and the others Iāll cite in this š§µ, treat logic as a culturally-evolved technology for particular sorts of reasoning. Itās something we do, not something we have or are. Itās also not something that lives in the Platonic Form Realm.
Mostly we do formal reasoning on paper, or a blackboard or whiteboard. Some bits are best done in the shower, but most of it critically depends on these external material technologies. Richard Feynman got this:
Rationalism holds that rationality works by abstracting a concrete problem into an immaterial formal realm. This is a weird flex, inasmuch as modern rationalists are usually passionately committed to materialism.
Can we do formal logic without spooks? Yes we can!
Can we do formal logic without spooks? Yes we can!
Taking formal reasoning as typically a publicly observable, material activity exorcizes the banshees.
But, thereās something right about the āabstractionā idea. How and when and why does this work?
[Eggplant text here and in last, not @cdutilhnovaes]
But, thereās something right about the āabstractionā idea. How and when and why does this work?
[Eggplant text here and in last, not @cdutilhnovaes]
Thereās also something partly right about the āinformal reasoning messes up formalā idea, as shown by the Cognitive Reflection Test.
en.wikipedia.org/wiki/Cognitiveā¦
en.wikipedia.org/wiki/Cognitiveā¦
The essential problem faced by āmere reasonablenessāāinformal rationalityāis the unenumerability of potentially relevant background factors. Part II of The Eggplant explains how that works. (In part: cross the river when you come to it.)
In the Cognitive Reflection Test, you have to forcefully inhibit your informal reasoning, which gets wrong answers. Nice analysis from @drossbucket!
@cdutilhnovaes gives similar examples from the Wason selection task: real-world relevance interferes.
drossbucket.wordpress.com/2018/12/12/theā¦
@cdutilhnovaes gives similar examples from the Wason selection task: real-world relevance interferes.
drossbucket.wordpress.com/2018/12/12/theā¦
Reasoning with external material formal notation (squiggles on paper) accomplishes abstraction in two ways discussed by @cdutilhnovaes: de-semantification and ease of calculation.
De-semantification: If you read the word āravenā you usually get a visual image and are primed with all your background knowledge of ravens.
Writing Éø(x) instead of āis a ravenā strips that off, and thereby inhibits the āmerely reasonableā ways of thinking.
Writing Éø(x) instead of āis a ravenā strips that off, and thereby inhibits the āmerely reasonableā ways of thinking.
Humans evolved for concrete sensorimotor activity (e.g. foraging) and for social relationship maintenance. We didnāt evolve for formal rationality; unfortunately there is no āSystem 2ā logic box in the brain, and we are terrible at it.
We can manage only with external aidsā¦
We can manage only with external aidsā¦
Calculation: external formal notation repurposes our sensorimotor skills to perform operations our brains unaided mostly canāt.
Logical giant A.N. Whitehead: āBy the aid of symbolism, we can make transitions in reasoning almost mechanically by the eyeā
& @cdutilhnovaes below:
Logical giant A.N. Whitehead: āBy the aid of symbolism, we can make transitions in reasoning almost mechanically by the eyeā
& @cdutilhnovaes below:
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 āsymbol pushingā because at a felt level thatās exactly what weāre doing.
Mathematicians speak of calculative rationality as āsymbol pushingā because at a felt level thatās exactly what weāre doing.
Examples:
Putting terms in a commutative expression in the right order helps a lot even though ālogicallyā 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.
Putting terms in a commutative expression in the right order helps a lot even though ālogicallyā 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.
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.
en.wikipedia.org/wiki/Einstein_ā¦
Also uses visually different symbols to track vector dimensions.
en.wikipedia.org/wiki/Einstein_ā¦
(h/t @drossbucket for this example)
@drossbucket Two quotes here from @cdutilhnovaes about this. Also two of her key sources, which I havenāt yet looked into myself (but intend to).
āThe materiality of mathematics: Presenting mathematics at the blackboardā 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.
@greiffenhagen Hereās @greiffenhagen showing the embodied, spacial, temporal, interactive nature of a proving of the Dutch Book Argument (cc @cdutilhnovaes)
(Going to pick up this unfinished thread tomorrow probablyāhave other things to do now!)
Yesterdayās logic š§µ got out of control. Shorter š§µ here on formal logic as a social practice that is a somewhat-contingent product of cultural evolution:
