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I'm looking for philosophical articles / books that try to describe the process of human abstraction, and what it actually consists of, from a first person perspective. Examples of the type of abstraction I'm concerned with are numbers, time, and the rules of logic.

Anyone have suggestions for content that might match what I'm looking for?

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  • fractalontology.wordpress.com/2008/05/30/hegel-and-universality This may give you some leads (yes, it is written by someone who posts on here often).
    – Matt
    Commented Mar 29, 2016 at 18:03
  • Phenomenology of Spirit, Georg Wilhelm Friedrich Hegel (1806) - a whole book solely on the phenomenology of abstraction.
    – Philip Klöcking
    Commented Oct 17, 2016 at 18:28
  • 1
    Hegel was a poet, not a philosopher. Hegel presents weltanschauung and does not advance one single knowledge claim in all his writings. Not one. Hegel is either agreed or disagreed with, just like any solicitation to gossip.
    – MmmHmm
    Commented Nov 8, 2016 at 7:09
  • Ths is interesting on the origins of geometry, infinity and zero, directly out of Indian spiritual traditions: In Our Time - Indian Mathematics bbc.co.uk/programmes/p0038xb0 Also, Numbers By Nature bbc.co.uk/programmes/b06pt0bk
    – CriglCragl
    Commented Feb 12, 2018 at 23:07

3 Answers 3

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Yes.

Hume and Frege's Abstraction Principle: Reference and Invariance in Abstraction Principles

It does exactly what it says on the tin. Given a set of things, pick some attribute common to all and use that to refer to the collection. Works for lots of things. You'd get things that are numerical that way Frege thought.

Don't know about time and rules of logic though. Can you elaborate on those? do you mean the concept of time as an abstraction? Possibly abstracted from the idea of dimensionality and direction. Do you mean the rules of logic taken together?

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I recently read a book by the David Foster Wallace called Everything and More: A Compact History of Infinity. I'll try to think of some more examples, but this was the first one that came to mind. I really like it because it is a bit more modern than other academic philosophical texts on this tough topic. He was also a novelist and top notch interviewer, so it's a very enjoyable and relate-able read.

He discusses a bit of his own first-person experience dealing with abstract concepts, and also tackles the topic from an historical context. He discusses the scientific, philosophical, mathematical, psychological, and even physiological implications of pursuing the abstract quite a bit in this book which, ultimately, discusses mankind's invention of the concept of infinity. Bonus: thought exercises!

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I'm also interested in the phenomenology of abstraction. An inspiration for me was Heidegger's Being and Time. Perhaps a fundamental method of the work involves tracing abstracted ideas back to their pre-abstracted origins in experience, and trying to sort out the structure of this experience, which ends up dissolving certain problems embedded in contexts of abstracted ideas. Perhaps the process of abstraction can distort our view of the nature of the very things which they're about

Eric Margolis has some interesting work on abstraction (https://www.margolisphilosophy.com/publications.html), which could act as a springboard for further research. It's not specifically on number, time, logic. But it seems to me that in order to understand the nature of abstraction in these specific cases we need to understand its nature in general and the role it plays in concept- and belief-formation

Have you found anything since you posted?

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