Where does logical language come from? The social bootstrapping hypothesis | Hacker News Reader

Where does logical language come from? The social bootstrapping hypothesis

babieslearninglanguage.blogspot.com

50 pointsdsr1215 comments

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.

Also boolean logic does not concern "all", "any" and "no" (as in no cookies), these are from prepositional logic

But I agree with your point, mathematical logic is a consequence of something that originated with human thinking

"all" and "no" are easily extended from boolean logic to unspecified numbers of items for everyday speech, without resorting to unification:

  all not == not A and not B == not (A or B)

  not all == not (A and B) == not A or not B

Seems to work in other natural languages besides English, e.g. 都不 vs 不都 have same variation in meaning as in English where 都="all" and 不="not".

The article leads with exactly that statement. She’s talking about logic as colloquially used: ‘if it’s cloudy, it’s probably going to rain later’. People don’t learn formal rules, but they still make statement that are logical in nature.

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.

“Or” is also regularly used to mean an exclusive choice, especially when asking questions.

“Would you like the red shirt or the blue shirt?” Or whatever.

My just-turned-2-year-old hasn’t quite figured this one out yet. He just repeats the whole thing back, “red shirt or blue shirt”, without making a choice.

I have been told, that when I was ~2 to ~5 years old, making these sorts of choices was hard for me, and I often copped out i.e: Q: "Do you want jam or honey on your bread slice?" A:"One half jam, one half honey?" :D

> “Would you like the red shirt or the blue shirt?”

You're writing it wrong -- it should have a comma in there to denote the pause: “Would you like the red shirt, or the blue shirt?”

Are you also speaking it wrong? The part before the pause should be spoken with tone going up, and the part after with tone going down. If you're not pausing and changing tone, then the correct answer is either "yes" or "no", or repeating the whole thing back to mean "yes".

> You're writing it wrong

Adding a comma would be non-standard (“incorrect” if you ask a pedantic grammarian) in conventional English prose. Commas don’t always match verbal pauses 1:1.

> The part before the pause should be spoken with tone going up, and the part after with tone going down.

This is a learned cultural convention, not inherently known at birth. I am sure that within another few months my kid will figure it out.

It’s also hard for me to tell sometimes whether he is repeating both because he doesn’t understand that a choice is being offered, or because he wants to repeat strings of words, or because he hasn’t made a choice, or ....

He doesn’t know how to say e.g. “neither one; give me the green shirt” or “you decide for me”.

There is no correct way to do that. Stuff like that is not properly defined, just like language is not logic.

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.

> I also don’t think that language per se is strictly necessary to reason logically.

On a very basic level, probably. But how can you reason about, say, addition and at the same time do not assign some singular representation to a large set of operations you can do when performing addition? And such representations are what language is all about, isn't it?

Or, for that matter, how can you perform addition without a language?

Some people’s primary representation of numbers is visual and concrete, like configurations of abacus beads or the like. I guess you can decide whether you consider a direct representation like that to be “language”.

Er, they communicate numbers thru language though. Whether someone can come up with the idea of abacus without a language for numbers is an open question, I think.

> 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.

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