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In reading Koji Karatani's Transcritique, I found myself a bit confused by the distinctions and couplings he draws between these terms in relation to Hegel and Russell. It wasn't actually his approach (I'm not asking about Karatani), but my own poor grasp of traditional metaphysics and vague understanding of these terms.

If we take on the one hand, the one/particular/individual/singular and on the other the many/universal/general/multiple what is the best way to sort them out? Are any now considered synonymous, interchangeable, or redundant? Are they always paired up as dichotomies in the order I've given above? How consistent is their treatment, from Aristotle (I believe that's the origin) to the present? What are some of the key texts or historical turns related to such distinctions?

I realize this is a big list of questions, overly broad, and I certainly don't expect a "complete" answer. But I would appreciate some general outline or overview of these classic dichotomies. And I'd like to know in what form, if any, they remain "live" questions for analytical philosophy today.

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The one-many relation is more encompassing than the particular-universal relation. The particular-universal relation is one type of the one-many relation. For example, the relation between a particular human being and humanity (in the sense of an essential property) is an instance of the particular-universal relation, and also of the one-many relation (humanity - one, humans - many). The relation between a particular human being and a group to which she belongs, is also an instance of the one-many relation, but not of the particular-universal relation. 

If we take on the one hand, the one/particular/individual/singular and on the other the many/universal/general/multiple, what is the best way to sort them out?

Roughly speaking, 

particular = individual = singular    (opposed to universal)

One is a more encompassing term (a particular is one, a universal is also one). 

many = multiple (opposed to one)

General pertains to a distinction between universals: general vs specific (genus vs species). A universal is more specific, less general, to the extent that it is more detailed, and closer to the particulars. So, humanity is a more specific term than animality. Animality is, then, a more general term than humanity. 

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It is a question with a fairly large catchment area; the following might help a little:

In Aristotles Categories, he distinguishes between a particular and that what it is (to ti en esti); in Latin, later, condensed to essentia, and in English - essence; which he affirms is not a particular (there are other senses of essence).

This pet mynah bird, who I call Maya, is a particular; it's essence - that what it is - is a bird, and is not a particular.

It's also closely linked to the idea of definition, noted too by A in the Categories; we define the class or set of birds; but not Maya ...

... this pet Mynah bird, of mine; who flutters her wings and says:

I am my dream. Whenever the earth narrows, I expand it with my wing. I expand. I am my dream.

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