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SpAG and saw three clearly related sentences that seperate. This one is honestly detabatable as it isn't strictly wrong and can even be used to make the reader read slower, perhaps to emphasize how important it is they understand that passage. I'll change it if this goes against your intentions

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FFFluoride 2024-03-05 22:32:33 +00:00
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@ -18,9 +18,9 @@ What is an Abstract Theory
Most scientific and mathematical theories have a specific *domain*, which they are tied to, and in which they are valid. They are created with this domain in mind and are not intended to be used outside of it. For example, Darwin's theory of evolution is created in order to explain how different *biological species* came to evolve using natural selection, quantum mechanics is a description of how particles behave at a specific scale, etc.
Even most mathematical theories, although not inherently *bound* to a specific domain, like the scientific ones, are often strongly related to one, as differential equations are linked to how events change over time.
Even most mathematical theories, although not inherently *bound* to a specific domain like the scientific ones, are often strongly related to one, as differential equations are linked to how events change over time.
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.
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.