[EMAIL PROTECTED] wrote: > (1) A general mathematical category is not the same as any specific > physical thing

But why can't it be reduced to classes of specific physical things? How can you show that it is necessary for anything corresponding to this description to 'exist' apart from its instantiations as documented procedures and actual occurrences of their application? In this case: (2) Mathematical entities cannot be removed from our descriptions and > replaced with something else ( the argument from indispensibility). would be false, though such removal would be inconvenient (as would 'chair' for that matter). A 'mathematical entity' would then merely refer to the classes of all descriptions, and all actual occurrences of the application, of a given procedure - i.e. a human cognitive category like 'chair', although as you say of greater generality. David > >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 > > > 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 -~----------~----~----~----~------~----~------~--~---