I just wanted to call to the attention of any readers that I've put up two papers from last semester! One is on the philosophy of mathematics, and the other is on the metaphysics of ineffability. I made a couple of posts about these issues (e.g., here and here) and these are my more considered thoughts after a semester of reflection.
The first paper is a general overview of an Aristotelian version of structuralism. That paper is here. In that paper I try to lay out as clearly as possible what the view is, and lay out some of the arguments and examples that support the view. Some might find the discussion and argument concerning what I've called "mathematical treating-as" to be interesting. To be honest, I find the view quite compelling.
I wasn't able to come up with a uniform semantics for this view in time to make it perfectly polished, though I do know what I want to say about this now (hopefully more about this in future posts/papers). I am pretty confident now that a uniform semantics for Aristotelian-type structuralism can be given.
The second paper (here) is on the metaphysics of ineffability. I talked about this problem before and was puzzled then. I remain puzzled now. But I feel that I've got a good grasp about what types of ineffability there are and what types of arguments can be given for each. My paper basically identifies several types of ineffability, and defends a substantive version of ineffability against an "idealist" type argument that was conceived by my professor, Thomas Hofweber. I felt quite pleased with this paper by the end of it; it's a very interesting topic and the paper is filled with lots of arguments and examples (hopefully some of them are good!).
If anyone has any thoughts on all of these feel free to comment or shoot me an e-mail!
Cool. I just started a philosophy of mathematics course, so I'll be taking you up on the first paper.
btw, did you ever give an account anywhere on how you arrived at trope nominalism?
If you have thoughts let me know! And I haven't yet, though I have a draft of a post on that. (Long story short: I don't buy the arguments against trope nominalism -- I don't think there are any serious problems that can't be handled by primitive resemblance -- and I think it is simpler and does all the work an Aristotelian theory of universals would. An Aristotelian theory needs tropes anyway [unless you go the Armstrong route], and I think one can just "cut out" the universals without any harm. Obviously that's no defense but it's basically the line of thought that's persuaded me. But hopefully more on this in the future!)
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