Out of Context: On Abstraction (Definitions)

"Abstractions are like clouds, which assume a hundred different forms, and which men may run after forever without catching anything real." (Friedrich L G von Raumer, 1835)

"Abstraction is the detection of a common quality in the characteristics of a number of diverse observations […]." (Herbert Dingle, Science and Human Experience, 1931)

"Abstractness, sometimes hurled as a reproach at mathematics, is its chief glory and its surest title to practical usefulness. It is also the source of such beauty as may spring from mathematics." (Eric T Bell, "The Development of Mathematics", 1940)

"Abstractions are wonderfully clever tools for taking things apart and for arranging things in patterns but they are very little use in putting things together and no use at all when it comes to determining what things are for." (Archibald MacLeish, "Why Do We Teach Poetry?", The Atlantic Monthly Vol. 197 (3), 1956)

"Abstractions are a way to distill the essence from an otherwise unfathomable situation." (K C Cole, "First You Build a Cloud and Other Reflections on Physics as a Way of Life", 1999)

"Abstraction is itself an abstract word and has no single meaning." (Eric Maisel, "The Creativity Book: A Year's Worth of Inspiration and Guidance", 2000)

"Abstraction is what makes mathematics work." (Ian Stewart, "Does God Play Dice: The New Mathematics of Chaos", 2002)

"Abstraction is a mental process we use when trying to discern what is essential or relevant to a problem; it does not require a belief in abstract entities." (Tom G Palmer, Realizing Freedom: Libertarian Theory, History, and Practice, 2009)

"Abstraction is an essential knowledge process, the process (or, to some, the alleged process) by which we form concepts." (Hourya B Sinaceur," Facets and Levels of Mathematical Abstraction", Standards of Rigor in Mathematical Practice 18-1, 2014)

" […] abstraction is the process of passing from things to ideas, properties and relations, to properties of relations and relations of properties, to properties of relations between properties, etc." (Hourya B Sinaceur,"Facets and Levels of Mathematical Abstraction", Standards of Rigor in Mathematical Practice 18-1, 2014)