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The second part is me reordering a semi-broken sentence to make more sense. I'm not too sure about getting rid of the . I'll spare you the lecture but, it's your call if you want to keep that or no.
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@ -24,7 +24,7 @@ Set theory and category theory are different, they are not created to provide a
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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.
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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.
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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, for example, gene pools can be (very aptly) represented by sets of individual animals. Animal species can also be represented by sets — a set of all populations that can theoretically interbreed.
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You already see how abstract theories may be useful. Because they are so simple, they can be used as building blocks of many concrete theories. Because they are common, they can be used to unify and compare different concrete theories, by putting these theories in common grounds (this is very characteristic of category theory, as we will see later). Moreover, good (abstract) theories can serve as *mental models* for developing our thoughts.
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