Greetings Economists,
CB (Charles Brown) writes,
(first),
..."Math, grammar and logic are all sets of rules on how to use symbols."...
then CB writes,
..."logic is mathematical and linguistic, but I am curious on the essential
distinction between linguistics and mathematics implied here."...
To which JD (James Devine) replies,
..."it's possible that math might be part of Chomsky's transformational
grammar, i.e., the structure of human language that is inborn ("built-in")
in the human brain? In that case, math is linguistic, but not "merely"
so."...
Doyle,
Chomsky's transformational grammar? This is still a debate about what
exactly is inherited. A better discussion about the issue of inheritance is
found in Gould's book, "The Structure of Evolutionary Theory", Belknap,
Harvard press, 2002. Chapter eight, Species as Individuals in the
Hierarchical Theory of Selection, pages 638 through 644 discuss some of the
problems that Dawkins has with the idea of rule based inheritance.
Since you seem to think grammar is inherited, Let's try to make a
distinction here that most people could understand. Logic has been treated
as part of mathematics for awhile. So I won't distinguish between them.
Grammar structures language as is the commonplace. We might go to
Wittgenstein to get an odd ball view of grammar ("Philosophical Grammar",
Wittgenstein, Blackwell, 1974) which parallels JD's conflation of
mathematics and language. However, mathematics doesn't appear to grammarize
symbols. There is a case for a low level math instinct in the sense of
babies can count before they can think language. That is called subitizing.
To understand the difference then between grammar and subitizing it is best
to consider the difference in the labor processes. The basis for language
is joint attention. That is at some point babies learn to look at a parents
face and follow their gaze. So if mom looks at something like a toy the
baby understands something about the object which is a toy. Or food, or
whatever. Sharing attention means more or less mind reading. That is
states of the brain are shared and understood to be shared.
Mom does her brain work in her old familiar ways. That is incoming to the
occipital lobe mainly for vision, naming things in the temporal lobe, doing
things in the parietal lobe, and organizing and planning what to do with
stuff in the temporal lobe and parietal is done in the frontal lobe. The
baby does roughly the same sort of stuff. Babies vary in how they do things
from their parents for various reasons. The baby learns how to use their
mind from the example of the parents. Habits of brain work. Not
necessarily there in terms of a grammar. Grammar is variable within bounds.
Chomsky like the enlightenment thinkers he has always sprung his own thought
from thinks of this as a universal essence. However, Gould and others see
this differently. We may have a tool that can do certain things, the brain.
But what emerges in how we do things must certainly vary. How can the brain
anticipate email?
A general purpose theory of the work process of brainwork that grammar
implies, presumes that we understand what exactly the brain is doing word by
word. George Lakoff the linguist looks at where Mathematics comes from.
Like many linguists Lakoff broadly uses metaphor as the basic mechanism of
thought and therefore of mathematics. In his book, "Where Mathematics Comes
From,." Lakoff, Nunez, Basic Books, 2000, gives an extended examination of
all levels of mathematics to trace down how metaphor might be the basis for
mathematics. Metaphor stands in for field states in the brain. So for
example at a given time, various fields are connected in the occipital lobe,
temporal lobe, and frontal lobe. That being the metaphor.
Returning to grammar, language is a representation of between a parent and
child the basic way to use the face and hands to do work in the world.
Mathematics is not confined to that metaphor. Math does not function in
brain work like plain language acts. Grammar is not mathematics. They are
both metaphorical in the sense that sheets of neurons interconnect in
patterns. But the labor processes are different. Nor is it possible in my
view to say grammar is inherited. As most evolutionary theorists would say
there is a wholeness of environment and human beings that does not reduce to
rules.
Let's try to envision that. If I write this piece I am using a linear
script to describe brain states or metaphorical activity in the brain.
However, the brain states are not linear. So in the sense I write anything
linearly I am not conceptualizing the process of thinking. If I
conceptualize thinking that is create symbols that work like thinking, I
might then find ways to do non-"grammatical" language. That is not restrict
myself to an a priori limitation to what can be done.
Thanks,
Doyle
