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.
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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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Odgovor korisniku/ci @Meaningness
how do we explain ramanujan in this framework
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Odgovor korisniku/ci @The_Lagrangian
Which part of “goddess” do you not understand?
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Odgovor korisnicima @Meaningness @The_Lagrangian
(more seriously: how do we explain Ramanujan in *any* framework??)
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Odgovor korisnicima @Meaningness @The_Lagrangian
Goddesses are spooks, right? ;-) Above you pointed to "propositions" or "beliefs" as spooks, but they reminded me of what many called a "sense" in late 1900s philosophy of language. Also, "senses" wreak havoc with most straightforward "NL-to-logic" translation attempts...
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2/ Basically, a person sortof(MUST) sortof(understand) THAT words after "that" sortof(refer) to nebulous mental objects... The (mostly failed) attempts to translate "NL-to-logic" very systematically often mention "intensional contexts" as jargon:https://www.youtube.com/watch?v=iNVXHvqgubo …
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3/ First language acquisition involves NOT explicitly knowing "all that has been learned"... But part of what people USUALLY pick up by age 8, which is helped by observing SOPHISTICATED (non-pidgin) NL, is how to systematically impute mental states: https://www.ncbi.nlm.nih.gov/pubmed/17381779
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4/ It makes sense to me that actual functional brain states might vary (some have aphantasia, some don't) and also be only partially captured in any external form (translation to paintings, or diagrams on a chalkboard, etc). I would expect confusion here as the default.
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5/ Moreover, many of our modern mental states are probably "culturally iatrogenic" and DEVELOPMENTALLY BASED on our technologies of concrete representation. Walter Ong was focused on how WRITING changes ORAL cultures and minds, and I suspect math/coding does something similar?
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6/ There could be MANY functional brain states not possessed by MOST people, for lack of access to cultural materials. Perfect pitch springs to mind as a named example, but perhaps some culturally-transmitted functional brain states are farther down the long tail?
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