Bruce, John B, Gary, and Kingsley, (01)
We're discussing relationships between natural and artificial languages.
Historically, every AL is derived by adopting and adapting some features
from some NL. To illustrate the point, I'll start with Bruce's comment: (02)
BRS
> How do qualitative variables relate to quantitative variables? (03)
Look at history. In the first recorded use of variables, Aristotle
used letters for what you call "qualitative variables": (04)
If all A is B, and all B is C, then all A is C. (05)
They represent categories expressed by adjectives or noun phrases.
The Stoic logicians used letters to represent propositions. Euclid
used letters to represent points. For a summary of the history,
see http://www.jfsowa.com/talks/aristo.pdf (06)
The first use of letters for numbers was to represent constants,
such as V for 5 and X for 10. Al-Khwarizmi invented algebra by using
letters as variables. It's significant that he was using the Hindu-
Arabic symbols for numbers. Anyone who used letters to represent
constants wouldn't think of using them to represent variables. (07)
BRS
> the critical issue -- can some kind of algebraically-determinate
> mapping be constructed between them? (08)
Linguistically, a variable is a temporary name whose scope is just
one sentence or paragraph. For example, start with the sentence, (09)
Bob earned 5 dollars. (010)
Alonzo Church invented lambda calculus as a method for defining
relations by replacing terms with letters: (011)
Monadic: (λx)(x earned 5 dollars)
Dyadic: (λx,y)(x earned y dollars)
Triadic: (λx,y,z)(x earned y z) (012)
But you need to state axioms for relating the number y to the unit
of measure z. In any case, C. S. Peirce invented a simpler notation: (013)
Monadic: _____ earned 5 dollars.
Dyadic: _____ earned _____ dollars.
Triadic: _____ earned _____ _____. (014)
In effect, Peirce invented lambda calculus over 30 years before Church.
For assertions, he let the blanks represent existential quantifiers.
To show cross references, he drew lines between blanks that represent
the same entity. That created the equivalent of an RDF graph. (015)
Peirce also introduced oval enclosures to delimit the scope of
quantifiers. The default interpretation of an oval is negation.
That gives you full first-order logic. He also invented a simple,
elegant, and very general proof procedure and model theory. See
http://www.jfsowa.com/talks/eguni.pdf (016)
JFS
>> In every field, the practitioners name the things and methods they
>> use and produce. The novices learn and use the same words and syntax. (017)
JB
> It may be that we will eventually be able to prove this. (018)
That depends on (a) what do you mean by 'this', and (b) what do you
mean by 'prove'? As a vague but general principle, it's obvious. (019)
JB
> It is my observation that axioms differ from discipline to discipline. (020)
Yes. The devil is in the details. In any field, "book learning" is
sufficient for an overview. But to master the art, years of practice
with teachers and colleagues is essential. For anything that might be
called a proof, you'd need a different empirical study for each field
-- cooking, tennis, surgery, or nuclear physics. (021)
And in most fields, the link between words and practice cannot be
verbalized. No amount of book learning can replace practice in
cooking, tennis, surgery, or experimental physics. I believe
that's also true for theoretical physics. (022)
KI
> For RDF based Linked Data in the burgeoning LOD cloud, its all about
> terms. Words are simply used for annotations that provide hints.
> The evolution of DBpedia across many different human languages
> is a live showcase of all of this in action. (023)
The DBpedia terms are at the same level of vagueness as Schema.org.
That level of vagueness is sufficiently flexible for a wide range
of purposes, such as info retrieval or Jeopardy! answers. (024)
But you won't use data from DBpedia to design an airplane or
prove a theorem in mathematics. (025)
John (026)
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