Comments by "kazedcat" (@kazedcat) on "How to Count" video.

@wesbaumguardner8829 You don't mathematics is not real. The only reason mathematics matches reality is because we choose the fundamental assumptions so that we can solve real problems. Just like simulations can be use to solve real problems because we choose to make the simulation as real as possible but simulations don't have to be real. Similarly we can build a mathematical system that does not match reality but that would be an entirely useless mathematics.
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In foundational mathematics everything is a set or a class. So object= a specific set and property= a specific class.
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@wesbaumguardner8829 A set of anything could be apples, tractors, or unicorns. A class of any green things, or any squeezy things, or any paranormal things.
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@wesbaumguardner8829 A set of anything could be apples, tractors, or unicorns. A class of any green things, or any squeezy things, or any paranormal things.
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@wesbaumguardner8829 Mathematics only deals with sets. If you want to count unicorns then you need to encapsulate those unicorns into sets. Once something is inside a set them math does not care what is inside as long as it satisfy the rule of regularity then anything can be inside it.
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@wesbaumguardner8829 That is what mathematics is a method of abstraction. Meaning is derive from the patterns created by the relationship between abstraction. Category theory is an entire branch of mathematics describing the abstractions of the abstraction. And there is a Category for Categories. It is turtles all the way up.
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That is the extension to extensionality he mentioned in the first video. The problem is that this axioms are define in a precise mathematical language and a lot of the specificity is lost when translated into english.
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