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endoself comments on What do professional philosophers believe, and why? - Less Wrong Discussion
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I agree that this is useful, but it is essential to recognize that these words are just wrapping up our confusion, and that there are other questions that are still left unanswered when we have answered yours. It can sometimes help to determine which things plexist and which mexist, but we still don't really know what we mean when we say these, and having words for them can sometimes cause us to forget that. (I suppose I should refer to phlogiston here.) I think that Tegmark-platonism is probably a step towards resolving that confusion, but I doubt that any current metaphysical theory that has completed the job; I certainly don't know of any that doesn't leave me confused.
We can wonder about the nature of concrete objects and the nature of abstract objects without quarreling about whether or not one exists.
I don't think we really can. The categories of concrete and abstract objects are supposed to carve reality at its joins: I see a chair, I prove a theorem. You can't really do this sort of analysis without reference to the chairs and the theorems, and if you do make those references, you must have already settled the question of whether a chair is concrete, and a fortiori whether concrete objects exist. The alternative, studying concepts that were originally intended to carve reality at its joins without intending to do so yourself, has historically been unproductive, except to some extent in math.
Right, so accept that both abstract and concrete objects exist.. While you're not doing science feel free to think about what abstraction is, what concrete means and so on.
I don't think I've been clear. I'm saying that the categories of abstract and concrete objects are themselves generated by experience and are intended to reflect natural categories, and that it's not useful to think about what abstraction is without thinking about particular abstract objects and what makes us consider them abstract.