>But this only shows that mathematical objects exist in the sense that chair >exists; >as a abstraction from chairs. So chair isn't identical with any particular >chair. > >Brent Meeker

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What follows is actually a very important and profound metaphysical point, absolutely fundamental for understanding platonism and reality theory. Both the *concept* of a chair and mathematical concepts are *abstract* things. But there's a big difference. In the case of the chair concept, it's simply a human creation - it's simply a word we humans use to summarize high-level properties of physical arrangements of matter. There are no 'chairs' in reality, only in our heads. We can see this by noting the fact that we can easily dispense with the 'chair concept' and simply use physics descriptions instead. So in the case of the 'chair' concept, we're obviously dealing with a human construct. Critical point: The 'chair' concept is only a (human) cognitive category NOT a metaphysical or ontological categories. Mathematical concepts are quite different. The key difference is that we *cannot* in fact dispense with mathematical descriptions and replace them with something else. We cannot *eliminate* mathematical concepts from our theories like we can with say 'chair' concepts. And this is the argument for regarding mathematical concepts as existing 'out there' and not just in our heads. There are two steps to the argument for thinking that mathematical entities are real: (1) A general mathematical category is not the same as any specific physical thing AND (2) Mathematical entities cannot be removed from our descriptions and replaced with something else ( the argument from indispensibility). It's true that both 'chair' concepts (for example) and math concepts are *abstract*, but the big difference is that for a 'chair' concept, (1) is true, but not (2). For mathematical concepts both (1) AND (2) are true. There's another way of clarifying the difference between the 'chair' concept and math concepts. Math concepts are *universal* in scope (applicable everywhere - we cannot remove them from our theories) where as the 'chair' concept is a cultural construct applicable only in human domains. To make this even clearer, pretend that all of reality is Java Code. It's true that both a 'chair' *concept* and a 'math' concept is an abstraction, and therfore a *class* , but the difference between a 'chair' concept and a 'math' concept is this: 'Math' is a *public class* (an abstract category which can be applied everywhere in reality), where as a 'chair' concept is *private* class, applicable only in specific locations inside reality (in this case inside human heads). Reality Java Code for a math concept: PUBLIC CLASS MATH () Reality Java Code a chair concept: PRIVATE CLASS CHAIR () Big difference! The critical and profound point if we accept this argument, is this: *There is NO difference between *epistemological* and *metaphysical* categories in the cases where we are dealing with cognitive categories which are universal in scope. Math concepts of universal applicability are BOTH epistemological tools AND metaphysical or ontological categories. One needs to think about this carefully to realize just how important this is. --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~----------~----~----~----~------~----~------~--~---