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INCOMMENSURABLE

                                             October  4, 2026

"Incommensurability" plays a key role in Thomas Kuhn's thinking
presented in "Structures of Scientific Revolutions", where he
argues that changes in thinking and the meanings of words
after a scientific revolution are large enough to make it difficult
for people to understand writings from back before the revolution.
The meanings of words may be "incommensurable", similar enough to
confuse, but too different to follow easily.

I had a note that Paul Feyerabend also used the concept--
and I had the impression he'd picked it up from Kuhn, but           FIRST_PUNKS
I see that according to one wikipedia page, they both
independantly introduced the term:

https://en.wikipedia.org/wiki/Commensurability_(philosophy_of_science)

   In 1962, Thomas Kuhn and Paul Feyerabend both independently
   introduced the idea of incommensurability to the philosophy of
   science. In both cases, the concept came from mathematics; in its
   original sense, it is defined as the absence of a common unit of
   measurement that would allow a direct and exact measurement of two
   variables, such as the prediction of the diagonal of a square from
   the relationship of its sides.


A page at the Stanford Encyclopedia of Philsophy essentially agrees
with this:

https://plato.stanford.edu/archives/fall2026/entries/incommensurability/

    The term ‘incommensurable’ means ‘to have no common measure’. The
    idea traces back to Euclid’s Elements, where it was applied to
    magnitudes. For example, there is no common measure between the
    sides and the diagonal of a square. Today, such incommensurable
    relations are represented by irrational numbers. The metaphorical
    application of the mathematical notion specifically to the
    relation between successive scientific theories became
    controversial in 1962 after it was popularised by two influential
    philosophers of science: Thomas Kuhn and Paul Feyerabend.


Doing some sort of metaphorical riffing off of a bit from a
traditional liberal education (that few of us have or remember
these days) certainly sounds like Kuhn-- e.g. picking up on the
term "paradigm" from classes in Latin.

                                             THE_PARADIGM_PARADIGM

         And so here we are peering back
         across the divide when the
         traditional liberal arts education
         was all but abandoned.


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