For the sake of discussion I would like to clarify that I regard those 'structures' that might be described by different themes of abstract mathematics as the objects that are to be considered either platonic or not. So, platonism in regards to the abstract structures, not necessarily the instantiations of those structures (ie: the example 'P.D.E structure' could be represented equally well with either categories or sets as the lifeblood of each respective formulation). So I think I am in agreement as to the grouping of features into &a...
I like this mode of thinking, and its angle is something I haven't considered before. How would you interpret/dissolve the kind of question I posed in the answer to Pattern in the comments below?
Namely:
'My point is the process of maths is (to a degree) invented or discovered, and under the invented hypothesis, where one would adhere to strict physicalist-style nominalism, the very act of predicting that the solutions to very real problems are dependent on abstract insight is literally incompatible with that position, to the point where seeing it ...
This is actually similar to a kind of reasoning i have undertaken, but I want to ask you what you make of the fact that such high level abstraction even has any kind of utility at all. Say one day we as all physicalists (assumption on my part) all sit down (in present day mind, but without any knowledge of abstract maths), and we do the same type of physical formal kind of thinking that Newton or Leibniz undertook and developed calculus, which gives us the underpinning of most of modern applied mathematics. We then see how the kind of geometrical reasoning...
I appreciate the great feedback from all of you, thank you :) I do have another quick question, but it's of a lower priority. As of right now, I currently hold no degree. I've always been kind of Interested in the MIRI workshops, but I've always been nervous about signing up to one because: 1. I'm not sure if a degree would be necessary to keep up with the level of work people are to be involved in at the workshop and 2. In case my first point turned out to be true, I certainly wouldn't want a student who had no real formal (I've still learning computabili...
A quick comment, for the segment on tiling agents, on the MIRI site the recommended reading (not counting any MIRI papers) is 'a mathematical introduction to logic' by Enderton. But on this page, it instead recommends Chang and Keislers Model theory. Can this be taken to mean that both works are important recommended reading? Are they both of equal worth or should (or rather, could) one be prioritised over the other?
I recommend 'neurophilosophy' by Patricia Churchland, but a really good general overview for theories on consciousness is the Blackwells companion to consciousness. Sorry for the long HTML, but there is a link for a pdf version here that might be of use to you (or anyone): http://cies-fsc.googlecode.com/svn/trunk/FSC09/ChangeBlindness/biblio.complémentaire/1405120193%20-%20Max%20Velmans%20-%20The%20Blackwell%20Companion%20to%20Consciousness%20%5B2007%5D.pdf
Hello to you all, I am Chris.
I live in England and attend my local High school (well, in England we call the senior years/curriculums a sixth form). I take Mathematics, Further mathematics, physics and philosophy. I actually happened upon Lesswrong two years ago, when I was 16, whilst searching for interesting discussions on worldviews. Although I had never really been interested in rationality (up until that point I hasten to add!), I had a seething urge to sort out my worldview as quickly as I could. I just got so sick of the people who went to sunday sc...
Don't worry it no trouble :) Thank you, I see your reasoning more clearly now, and my thought of circularity is no longer there for me. Also I see the mental distinction between compression models and platonic abstracts.