Kuhn as i know it tell us there are two period. They are 1. normal science, and 2 revolutionary science. At 1, people follow a paradigm. One goes from 1 to 2 by the occurence of anomalies. According to one popular interpretation, going to 1 to 2 is a irrational process, because we have no way of comparing the before paradigm, and the after paradigm. This seems to be wrong. Insteading of thinking that people in 1 and 2 are following a paradigm. If the paradigm is sufficient clear, and precise, then it ought to be able to be formulated in the language of math. clearly, it does make sense that different mathematical theories are different, but they are still representable by first order logic, or a turing machine. It is very easy to compare mathematical theories.

No, a paradigm is not just a mathematical theory. You should re-read Kuhn, although he's quite vague in his definitions so I wouldn't hold my breath for any definitive answers.

Yes.
Math is not sufficient for everything under the sun.

Furthermore, both the thoughts-in-power and the
thoughts-challenging carry a paradigm or paradigms.
A paradigm is simply a collection of assumptions and
ways of looking at something that fits together.
There are "Hasidic paradigms", a "Capitalist Paradigm",
a "Marxist Paradigm", and "venture Capital" pardigms,
the past genomic biochemistry paradigm and the newer
'proteomic' paradigm. There is the "punk rock" paradigm(s).
The famous "DSM" series for mental illnesses is a classic
for actually tracking changes in a paradigm.

You could put all these collections of narratives,
decision-trees, instruments and histories into some
kind of math notation, but that would be wildly
inefficient and always running behind.

Pretty neat original post, though.
The desire was to put everything
into a math paradigm!

memo,

It is my proposal to look at paradigm as a mathematical formalism. I am not trying to get at what kuhn had in mind.

leonardomenderes wrote:
Yes.
Math is not sufficient for everything under the sun.

Furthermore, both the thoughts-in-power and the
thoughts-challenging carry a paradigm or paradigms.
A paradigm is simply a collection of assumptions and
ways of looking at something that fits together.
There are "Hasidic paradigms", a "Capitalist Paradigm",
a "Marxist Paradigm", and "venture Capital" pardigms,
the past genomic biochemistry paradigm and the newer
'proteomic' paradigm. There is the "punk rock" paradigm(s).
The famous "DSM" series for mental illnesses is a classic
for actually tracking changes in a paradigm.

You could put all these collections of narratives,
decision-trees, instruments and histories into some
kind of math notation, but that would be wildly
inefficient and always running behind.

Pretty neat original post, though.
The desire was to put everything
into a math paradigm!

I am referring mainly to theories in physics where theories are sufficient clear cut. In physics, it seems i can compare primitive terms in each paradigm if by paradigm, it is a mathematical formula.