“What can be called "consciousness of the process of abstraction." That is, consciousness of the fact that out of a virtually infinite universe of possible things to pay attention to, we abstract only certain portions, and those portions turn out to be the ones for which we have verbal labels and categories. What we abstract, i. e., "see," and how we abstract it, or see it, or see it or think about it, is for all practical purposes inseparable from how we talk about it.”

Teaching as a Subversive Activity (1969)

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American writer and academic 1931–2003

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“A number of abstract ideas, of which we are as a matter of fact unconscious. We do not see them, but we see other things through them.”

T. E. Hulme (1883–1917) English Imagist poet and critic

Source: Speculations (Essays, 1924)

“Embodied imitation and dramatic abstraction constituted the ground out of which higher abstract cognition emerged. How else could it be? Clearly we were mostly bodies before we were minds. Clearly. And so we were acting out things way before we understood them.”

Jordan Peterson (1962) Canadian clinical psychologist, cultural critic, and professor of psychology

"Biblical Series III: God and the Hierarchy of Authority" https://www.youtube.com/watch?v=R_GPAl_q2QQ <br class="br">Lectures, Biblical Lectures

“"What's common across all human experience across all time? That's what Jung essentially meant by an archetype. We tend to think that what we see with our senses is real. And of course that's true, but what we see with our senses is what's real that works in the time frame that we exist in. So we see things that we can touch and pick up - we see tools, essentially, that are useful for our moment to moment activities. We don't see the structures of eternity, and we especially don't see the abstract structures of eternity. We have to imagine those with our imagination. Well that's partly what those stories are doing. They're saying that there are forms of stability that transcend our capacity to observe, which is hardly surprising. We know that if we are scientists, because we are always abstracting out things that we can't immediately observe. But there are moral, or metaphysical, or phenomenological realities that have the same nature. You can't see them in your life by observing them with your senses, but you can imagine them with your imagination, and sometimes the things that you imagine with your imagination are more real than the things that you see. Numbers are like that, for example. There are endless things like that. Same with fiction. A good work of fiction is more real than the stories from which it was derived. Otherwise it has no staying power. It's distilled reality. And some would say "it never happened," but it depends on what you mean by "happened." If it's a pattern that repeats in many many places, with variation, you can abstract out the central pattern. So the pattern never purely existed in any specific form, but the fact that you pulled a pattern out from all those exemplars means that you've extracted something real. I think the reason that the story of Adam and Eve has been immune to being forgotten is because it says things about the nature of the human condition that are always true."”

Jordan Peterson (1962) Canadian clinical psychologist, cultural critic, and professor of psychology

Concepts

“We are mainly interested in the processes… not… in presenting mathematics in its most abstract form. …we will often begin with concrete forms and then exhibit the process of abstraction.”

Richard Hamming (1915–1998) American mathematician and information theorist

Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985)

“Such knowledge [of contemporary physicists] is clearly not the same as that derived by abstraction from individual cases: abstraction can provide us with knowledge of accidents but not necessary attributes as such. If we find that the search for essences can in fact only take the form of abstraction from individual cases then Aristotle's account of what counts as an explanation in physics is an unrealisable ideal.”

Stephen Gaukroger (1954) British philosopher and intellectual historian

Stephen Gaukroger (1978). Explanatory structures: a study of concepts of explanation ...

“We now come to a decisive step of mathematical abstraction: we forget about what the symbols stand for… [The mathematician] need not be idle; there are many operations which he may carry out with these symbols, without ever having to look at the things they stand for.”

Hermann Weyl (1885–1955) German mathematician

The Mathematical Way of Thinking (1941)

“The importance of imitation for the development of higher cognition in human beings: We embody ideas before we abstract them out and then represent them in an articulated way. What is the child doing when they play house? They are watching their parent over multiple instantiations, and then abstracting out the spirit called Mother, and that is whatever is mother-like across all those multiple manifestations, and then laying out that pattern internally and manifesting it in an abstract world. It's that you're smart enough to pull out the abstraction, and then embody it. And certainly the child is striving toward an ideal. If children don't engage in that kind of dramatic and pretend play to some tremendous degree, then they don't get properly socialized. It's really a critical element of developing self understanding and of also developing the capability of being with others, because what you do when you're a child, especially around the age of four is: you jointly construct a shared fictional world, and then you act out your joint roles within that shared fictional world. Embodied imitation and dramatic abstraction constituted the ground out of which higher abstract cognition emerged. How else could it be? Clearly we were mostly bodies before we were minds. Clearly. And so we were acting out things way before we understood them.”

Jordan Peterson (1962) Canadian clinical psychologist, cultural critic, and professor of psychology

Source: https://www.youtube.com/watch?v=R_GPAl_q2QQ "Biblical Series III: God and the Hierarchy of Authority"

“Here, in seeing that Final Cause — causation at the call of self-posited aim or end — is the only full and genuine cause, we further see that Nature, the cosmic aggregate of phenomena and the cosmic bond of their law which in the mood of vague and inaccurate abstraction we call Force, is after all only an effect.”

George Holmes Howison (1834–1916) American philosopher

Source: The Limits of Evolution, and Other Essays, Illustrating the Metaphysical Theory of Personal Ideaalism (1905), The Limits of Evolution, p.39

“When we observe a thing, we see too much in it, we fall under the spell of the wealth of empirical detail which prevents us from clearly perceiving the notional determination which forms the core of the thing. The problem is thus not that of how to grasp the multiplicity of determinations, but rather to abstract from them, how to constrain our gaze and teach it to grasp only the notional determinism.”

Slavoj Žižek book The Sublime Object of Ideology

xi
The Sublime Object of Ideology (1989)

“When we describe a process, or make out an invoice, or photograph a tree, we create models; without them we would know nothing of reality and would be animals. Abstract pictures are fictive models, because they make visible a reality that we can neither see nor describe, but whose existence we can postulate.”

Gerhard Richter (1932) German visual artist, born 1932

in text for catalogue of documenta 7, Kassel, 1982; as cited on collected quotes on the website of Gerhard Richter: on 'Abstract paintings' https://www.gerhard-richter.com/en/quotes/subjects-2/abstract-paintings-7 <br class="br">1980's

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