> > I have to admit I have a hard time going with the idea of Platonism or > mathematical constructs existing somewhere that no one can see or test. I > sure can't rule it out, but I'd like to be able to know where it is. > > Where? You seem to assume a sort of geometry at the start, but with > computationalism, geometry is among the emergent phenomena. > > "Where" does not apply to numbers, except in the large sense of being > between two numbers, with the usual ordering (defined by x < y if Ez(x+z = > y)). > > All you need to believe in is that proposition like (786899543211 is prime > or is not prime) is true independently of you and me. Of course > by 786899543211, I mean the number denoted by this base ten description of > a natural number. Are you OK with this? that type of assumption is weaker > than the assumption most scientist are doing when using mathematics in > their domain. The arithmetical "platonism" (realism) used in > computationalism is the same amount than the one used in computer science, > physics, etc. > > > Roger: My view is that propositions like "786899543211 is prime or is not prime", "1+1=2", etc. are mental constructs/entities that exist in our minds (e.g., in our heads from my materialist point of view) in order to describe existent entities that exist outside the mind such as 786899543211 existent entities, an entity and another one next to it, respectively. Mathematics and arithmetic are mental constructs we've created to manipulate these outside the mind entities. When I say "Please point out this Platonic realm", what I'm getting at is that I don't think propositions or anything else can exist somewhere that's not in the mind/head or in the physical universe outside the mind. Where else would such propositions exist? I'll need something more than just a statement affirming that "where does not apply to numbers". This doesn't seem to be evidence.
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