What is abstraction?

Jorge Luis Borges introduces his short story on Ireneo Funes, the Memorious saying that:
To think is to forget differences, to generalize and to abstract.
Borges not only ventured into philosophy (Egginton & Johnson, 2009), but also foretold modern research (Kreiman, 2011; Quian Quiroga, 2012). The above gives a nice summary of what abstraction, and generalization is. I'm interested in defining it, and for that I'm actively collecting all references that come across me. Generalization and abstraction, although related, aren't identical. Both nevertheless are related to the induction problem in that they imply leaps from the particular to the general.
George Berkeley offers a very straightforward explanation of (PHK 7,8)

Abstraction is the singling of object qualities and modes:
...the qualities or modes of things do never really exist ... apart by itself, and separated from all others, but are mixed, as it were, and blended together, several in the same object. But the mind [is] able to consider each quality singly or abstracted from those other qualities with which it is united, [and] does by that means frame to itself abstract ideas. Again, the mind having observed that in the particular extensions perceived by sense there is something common and alike in all, and some other things peculiar, as this or that figure or magnitude, which distinguish them one from another; it considers apart or singles out by itself that which is common... So likewise the mind, by leaving out of the particular ... perceived by sense that which distinguishes them one from another, and retaining that only which is common to all.
 Locke adds:
Since all things that exist are only particulars, how come we by general terms?... Words become general by being made the signs of general ideas. (EUH, IV, iii,6)
Hume elaborates on the relation of ideas:
The very nature and essence of relation is to connect our ideas with each other, and upon the appearance of one, to facilitate the transition to its correlative. The passage betwixt related ideas is, therefore, so smooth and easy... (Treatise
One of the ones I like most  is the one provided by Prof. Paul Humphreys (UVa):
The term ‘abstraction’ has been used in a variety of senses...covered by a process that we can call property elimination, which takes us from whatever total collection of properties (‘Properties’ here includes relations) is possessed by an entity to a proper subcollection of those properties, those properties being left unchanged (Except, of course, for the relation of the remaining properties to the now absent ones). Abstraction thus requires properties to be modular in the sense that the remaining properties are invariant when any given property is eliminated. Extending Ourselves, 141


Kreiman, G. (2011) Literary inspiration. Nature, (475), 453.
Quian Quiroga, (2012) Borges and Memory: Encounters with the Human Brain. The MIT Press.
Egginton, W. and Johnson, D. (2009) Thinking with Borges. The Davies Group Publishers.
Locke, Essay on Human Understanding
Berkeley, PHK

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