Question

Recently I came across with a word called abstractionin mathematics which means the process of removing unimportant details from a system so that we can focus on the ones that really matter. I found this notion of the word abstraction to be very different than what abstract means in daily English language usage - something that exists only in thought, something that cannot be touched. This confused me. What exactly do we mean by abstract? Are these two meanings completely independent, or is there a sense in which one overarches the other? Abstraction Abstraction in its main sense is a conceptual process wherein general rules and concepts are derived from the usage and classification of specific examples, literal (real or concrete) signifiers, first principles, or other methods. An abstraction is the outcome of this process—a concept that acts as a common noun for all subordinate concepts and connects any related concepts as a group, field, or category. ~ Wikipedia That's only an excerpt from the introduction. Things that exist only in the mind I guess can be found in pure as opposed to applied math. You're confused because you've conflated different parts of speech. Theadjective'abstract' is a modifier meaning conceptual, idealized, or theoretical.Theverb'to abstract' means to make something more general and universal by removing specific, concrete detailsThenounabstract* is a summary of a paper containing only the key points, without any of the details of research or reasoning. 'Abstraction' is the noun-form of the verb 'to abstract', effectively: That which has been abstracted (made more general and universal). Not everything that is anabstractionhas the quality (1°) of beingabstract, but in mathematics everything is fairlyabstractto begin with. I mean, honestly, this is a bit like getting confused about the word 'object' because you learned the word 'objection'. Language use is organic, and thus not entirely reasoned.

Answer 1

One aspect of the word abstract that you may find confusing is its use in other contexts. The word has come to mean things that might better be described as non-representational rather than abstract.

Step-by-step explanation:

One aspect of the word abstract that you may find confusing is its use in other contexts. The word has come to mean things that might better be described as “non-representational” rather than abstract. When we describe an image as “abstract” we mean that it has its roots in the observed world but the artist has exaggerated certain visual elements.

Abstract concepts in psychology, like tolerance, touch every aspect of our lives and can be agreed upon by many people because they have been used in various ways over many years. In mathematics, abstraction is the process of removing unimportant details from a system so that we can focus on the ones that really matter.

These two meanings are different but connected, as abstraction in mathematics is a conceptual process that results in abstract concepts which are common nouns for related concepts.