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aleph_0

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aleph_0 last won the day on August 3 2010

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  1. Yes, that sounds fine enough. But that's basically the kind of picture Aristotle had, and he just used the term "abstraction" to describe it, without the more loaded term "measurement". So was there a reason for departing from his language, or was she just repeating Aristotle's view with her own jargon?
  2. So let's take this as the claim: Mathematics is the science of measurement. Presumably this means that, in a very broad reading of the term "measurement", an element being in a set is a measurement of the set, or possibly of the element. I'm not really sure. And I suppose the claim would be that the study of sets omits every other possible measurement of the elements or sets. But why cast it in this language, rather than abstraction? How is this distinct from Aristotle? I think I'm missing the point that you're making. What is it that you're arguing? This seems like exac
  3. We can forget trying to define mathematics, since I don't have the interest to pick through ITOE to find relevant quotes. I just want to know why she chose this phrase rather than "abstraction" to describe the mathematician's activity, and how this account differs from Aristotle's.
  4. If this is the correct interpretation, then I suppose this is why I find her claims so unsatisfying. Why use the phrase "measurement-omission" rather than "abstraction" if all she claims is that mathematics is the science of reasoning about certain features of object(s), while omitting others? Measurement usually denotes a property of objects which can be quantified by rational numbers. Even quantity is not a measurement in the ordinary sense of the English word since it is only described by natural numbers, so if she wanted a very broad term she would have been a little bit better-served b
  5. I generally understand the point about measurement-omission as the claim that mathematics omits particular measurements, but that it is the science of measurements. If that's a misconception--it's been a while since I read ITOE--then the question is misguided. That's my understanding as well. So the consensus thus far seems to be that the notion of "measurement" is much broader than is used in colloquial conversation.
  6. Here is a relatively short, and possibly simple, question that has just occurred to me. The fundamental concept necessary to understand mathematics, Rand has claimed, is measurement-omission. However, at least prima facie there are disciplines in mathematics which do not measure or claim to be able to measure anything. For instance, topology lacks a distance metric. It doesn't measure anything, in any obvious sense, but studies the shapes of objects. (In topology, two objects are said to have the same shape if one of them can be stretched, bent, enlarged, or shrunk, such that it can be ma
  7. I doubt it for a couple of reasons. One, it wouldn't make sense for that to be the way they organize the best-sellers. The idea of the best-seller list is to encourage book sales by making consumers aware of what everyone else is reading, so that they feel like they can talk to other readers. I can't imagine a good reason for eliminating a classic from that list. Also, I once worked in a bookstore and remembered seeing some best-sellers stay on the shelf for more than a year, so I'd have to wonder when that cut-off period would be. Now it's true that the best-seller list measures sales
  8. Linux isn't popular because, in addition to reasons mentioned above, it's not compatible with popular software. That's partly because some of the high-demand software is licensed and so it would be illegal for the Linux creators to produce and distribute the OS with that kind of software--most notably, to my mind, is software that plays most DVDs, and also Photoshop. However, at least in the former case, most Linux users just find illegal software that plays DVDs. Problems like the lack of Photoshop are more serious, and I imagine the reason there isn't a popular illegal version (that I kno
  9. Same here. Anyone down for philosophical reading, or reading the classics?
  10. Three times. The first time in high school, about ten years ago, and I didn't really absorb much of it. The second time about three years later, when I really understood the idea of the intellectual strike. The third time about two years ago.
  11. I'm moving back down to the Sebastian area, wondering if there are any Objectivists around... Or even just signs of intellectual life. Melbourne? Palm Bay? Vero Beach? Fellsmere? Fort Pierce? Stuart?
  12. Not at all. I may produce scenarios in which a theory that makes use of infinite quantities is the most explanatory, but I don't claim that they're actual. I'm asking a metaphysical rather than a factual question. But to have it said: If we are no longer disputing the impossibility of infinite quantities, and it is recognized that no satisfying argument has been provided to that effect, then I am happily unconcerned with other issues. However, I'll still respond to the questions below. You mean, suppose that it is impossible for there to be infinite quantities, and then you ask
  13. I was pointing out that neither you nor anybody HAS presented a valid argument, and yet you're cavalier.
  14. That sure proves your point. I'm convinced. Good argument.
  15. How is that problematic or relevant? Sure, there are infinitely many transfinite cardinalities. What's the problem?
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