Where does logical language come from? The social bootstrapping hypothesis

I had two thoughts when I read it.

First, I am currently reading Zvonkin's Math from three to seven, and he included an essay where he talks about "language support" when solving math problems. Hypothesis was, that to use language, we often need to process complex rules to use the nuanced meanings of words often based on context, which means that if we formulate a word-problem in right way, language can do a lot of heavy lifting, in a simmilar way, you might transform your numeric problem to vector-operations to be able to run it on GPU.

The example he referenced was his attempt to get boys in his math-circle to figure out some abstract notation to discuss complexity of something they built out of blocks. One of the boys attempted to just to replace words he used to describe the build with symbols. This might show that word as a concept is pretty powerful abstraction you can build on top of, and it is already built in to the language we are using :-)

The other thing this reminded me of, w.r.t. of learning the meaning of "or" and "implies", is that (at least in my language), colloquial meaning of "or" is 99% of time synonymous with "either, or", and "a implies b" is often used as "b happens if and only if a already happened".

This explains a lot of struggle I had when learning the boolean algebra/predicate logic, where "or" as well as "implies" have different definitions.

I expect kids can figure out these logical structures from non-verbal input if given the chance (e.g. if you present little puzzles with buttons that must be pressed in logically connected ways or whatever). I have seen tiny kids figure out several-step solutions to physical problems, sometimes quite novel ones that I would not have imagined myself. Simple logic puzzles are no harder than these, albeit usually presented in a less accessible way.

My bias is toward rejecting any claim that particular logic is innate. But I also don’t think that language per se is strictly necessary to reason logically.

However, it is certainly true that most situations requiring complicated logic encountered by young children are social / verbal. In which case additional feedback and guidance from adults (not to mention imitation) is probably going to be a faster teacher than pure trial and error / observation.

some innate logical concepts [para 4]

1. I think that people woke up about 130,000 years ago indicated by the sudden appearance of representational art etc. Turing equivalence harnessed to survival/reproduction. Accorsing to this, of course there must be innate logical concepts.

2. Introspectively, my experience of learning concepts was connecting what they're talking about to what I already know. (You cannot teach a man anything, you can only help him find it within himself.)

Bonus: verbs distributes over "and": I'm going to buy eggs and I'm going to buy milk. Incidently, it's misleading to only consider logical structure within a sentence. I'm going to buy eggs. I'm going to buy milk.

Abandoning notions of boolean and aristotelian logic at the outset is the first step toward success in understanding developments.

Children have to invent their own logic, and then discover words that fit it. Only later do they learn about other logics, and adjust. Most never get to Boole, never mind Aristotle, but what they have works well enough for what they expect of it. At the same time, they are inventing causality, which formal logic still has not absorbed, and that most statisticians remain deeply suspicious of.