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Plural and better word word order (in my opinion)

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FFFluoride 2024-03-05 22:36:34 +00:00
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@ -22,7 +22,7 @@ Even most mathematical theories, although not inherently *bound* to a specific d
Set theory and category theory are different, they are not created to provide a rigorous explanation of how a particular phenomenon works, instead they provide a more general framework for explaining all kinds of phenomena. They work less like tools and more like languages for defining tools. Theories that are like that are called *abstract* theories.
The borders of the two are sometimes blurry, because all theories *use abstraction*, otherwise they would be pretty useless: without abstraction Darwin would have to speak about specific animal species or even individual animals. But theories have core concept that don't refer to anything in particular, but instead are left for people to generalize on. All theories are applicable outside of their domains, but set theory and category theory do not have a domain to begin with.
The borders of the two are sometimes blurry, because all theories *use abstraction*, otherwise they would be pretty useless: without abstraction Darwin would have to speak about specific animal species or even individual animals. But theories have core concepts that don't refer to anything in particular, but are instead left for people to generalize on. All theories are applicable outside of their domains, but set theory and category theory do not have a domain to begin with.
Concrete theories, like the theory of evolution, are composed of concrete concepts. For example, the concept of a *population*, also called a *gene-pool*, refers to a group of individuals that can interbreed. Abstract theories, like set theory, are composed of abstract concepts, like the concept of a set. The concept of a set by itself does not refer to anything. However, we cannot say that it is an empty concept, as there are countless things that can be represented by sets, like, for example, gene pools can be (very aptly) represented by sets of individual animals. And species of animals can too be represented by set — a set of all populations that can theoretically interbreed.