A lot of good comments in this thread but this one is especially important, imo
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Categories are abstract tools that can describe aspects of the world, but don't materially exist.
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The aspects of the world that we try to understand through categorization are dynamic, thus the categories and signifiers we use must also be dynamic.
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When using categories we should always remember that they are, by necessity, reductive; we are deliberately emphasizing variables we deem operative or useful, at the expense of others. Those unimportant variables may rise to importance or even dominance in certain situations or at different scales.
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The words we use in everyday discussion and especially in introducing people to new concepts are just shorthand for (hopefully) much more complex concepts. A static two-class model is easier to teach, just like we might assume frictionless vacuums to teach intro to physics. But to actually use the science in the real world needs more than freshman-level concepts. Problematically, the same words get used at every level (e.g. proletariat and bourgeoisie) so there isn't like a semantic impetus to move into more complex understandings. A lot of people get stuck at that point.
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We have to be very careful not to flip symbol and referent (falsely imbuing class signifiers with class character) or forget the core essence or purpose of our categories (using class character as a moral classification rather than a political-economic one).