Thursday, February 22, 2007

From an ontological point of view

[This post is partially in jest, but only partially.] Suppose we are good Quinean ontologists, and we admit sets into our ontology, since Science needs Math, and set theory takes care of that. We can use sets to define real numbers and we can represent all of physical space with quadruples of real numbers. Objects in space and time are representable as sets of real numbers and predicates,etc. are representable as sets of those. So all we need to satisfy the quantifiers for our best theories are sets.

But, I like my chair, and putting my chair into the ontology doesn't make it any bigger. There is already continuum many things in the ontology. So, I add my chair. Continuing, adding one more (or a countably infinite number) of physical things won't make the ontology any bigger. So, I'll go ahead and add all the physical things in the world. But, ponies are nice and everything is better if it comes with a pony. Therefore, I'll add an extra pony in my ontology. Being a good Quinean, I end up with a sparse ontology of sets, all physical things, and a pony.

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