
Where does logical language come from? The social bootstrapping hypothesis - dsr12
http://babieslearninglanguage.blogspot.com/2018/08/where-does-logical-language-come-from.html
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ncmncm
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.

~~~
raverbashing
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

~~~
vorg
"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".

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a-saleh
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.

~~~
jacobolus
“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.

~~~
vorg
> “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".

~~~
jacobolus
> _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”.

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jacobolus
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.

~~~
red75prime
> 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?

~~~
jacobolus
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”.

~~~
red75prime
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.

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hyperpallium
> 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._

