tag:blogger.com,1999:blog-8148573551417578681.post5778706554867377425..comments2022-08-10T04:01:49.993-07:00Comments on Dark Buzz: Defending logical positivismRogerhttp://www.blogger.com/profile/03474078324293158376noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-8148573551417578681.post-38279423820195900562020-05-26T07:09:09.183-07:002020-05-26T07:09:09.183-07:00It actually does make sense why Kant called 7+5=12...It actually does make sense why Kant called 7+5=12 a synthetic statement because if you take 7 and 5 neither of them necessarily contain 12. For example, a typical analytical statement is "all bachelors are unmarried men", and the reason this is an analytical statement is because the word bachelor means 'an unmarried man'. With 7+5=12 you don't have that, 7 doesn't contain 12 and 5 doesn't contain 12 either (neither does + or =), therefore it is a synthetic a priori statement. However, I do agree with you that 7+5=12 is an analytical statement (because of Frege), I just wanted to tell you that it does make sense why Kant thought that it wasn't at the time.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-8148573551417578681.post-80233813398371811792015-10-10T07:29:31.346-07:002015-10-10T07:29:31.346-07:00You are totally right! This stuff is stale and rev...You are totally right! This stuff is stale and revealed its limits and relevance, a long time ago. I haven't even heard attempts to use neutrinos to deliver power. They just scribble like Monks.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-8148573551417578681.post-35686656719163758172015-10-04T10:49:45.258-07:002015-10-04T10:49:45.258-07:00Look here, one of the "smartest guys in the r...Look here, one of the "smartest guys in the room" says the physicists are a bunch of dummies:<br /><br />https://scottlocklin.wordpress.com/2015/08/28/advice-to-a-young-social-scientist/<br /><br />"Not even the stuff they teach you in an experimental physics course: real statistics, like they use on Wall Street to make money.<br /><br />My formal training was in physics, where, generally speaking, statistical sophistication is fairly low. Physicists have the luxury of being able to construct experiments where the observation of one or two photons or some preposterously small amount of torque on a magnetometer is meaningful. Pretty much nobody but physicists have this luxury.<br /><br />Physicists no longer have this luxury for the most interesting problems these days. Unfortunately nobody told them, which is why physics has been languishing in the swamplands, with “physicists” working on non falsifiable noodle theory, cosmology and writing software for computer architectures which will probably never exist. "<br /><br />And look here, Master Witten is getting off the Titanic:<br /><br />"Now Nima, Gross and Witten advocate that China, with its increasing wealth and industrial dominance, become the new center of the physics world. "<br /><br />But, wait, we have the "smartest guys in the room"...unfortunately the "smartest guys in the room" can't build anything. (fusion reactor, fission reactor, quantum computer, room temp superconductor, etc). So America is now home of Great Social Scientists and 19th century energy systems.<br /><br />Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-8148573551417578681.post-35068119532547166512015-10-03T13:05:26.614-07:002015-10-03T13:05:26.614-07:00The world has moved on from computation, particle ...The world has moved on from computation, particle physics, and bomb making to energy storage, transmission lines, and solar harvesting. <br /><br />So far the physicists may as well hold up a sign "We are no longer relevant". Show me a physicist who is even interested in making a battery. <br /><br />The mathematicians and their 300 page proofs may as well go to the soup lines.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-8148573551417578681.post-84323374767088357492015-10-01T10:52:10.638-07:002015-10-01T10:52:10.638-07:00Nice post! I particularly like that you criticized...Nice post! I particularly like that you criticized Karl Popper. Alan Sokal claimed he was actually one of the worst offenders but he is extremely popular for some reason. I'm assuming you would find the Australian philosopher David Stove as a conservative ally. I certainly agree with him. Smart people tend to be conservative or libertarian, but that's just my unscientific observation. Stove was a harsh critic of the irrationalism of Karl Popper, Thomas Kuhn, Imre Lakatos, and Paul Feyerabend.<br /><br />The point about set theory seems fine, except that it has some loose ends concerning the nature of infinity and even potential infinity. Furthermore, the idea that math needs to be founded on arbitrary premises is not really necessary to begin with because it's not exactly clear why certain axioms are privileged over others. Zeilberger made this point:<br /><br />"My mind was made up about a month ago, during a wonderful talk (in the INTEGERS 2005 conference in honor of Ron Graham's 70th birthday) by MIT (undergrad!) Jacob Fox (whom I am sure you would have a chance to hear about in years to come), that meta-proved that the answer to an extremely concrete question about coloring the points in the plane, has two completely different answers (I think it was 3 and 4) depending on the axiom system for Set Theory one uses. What is the right answer?, 3 or 4? Neither, of course! The question was meaningless to begin with, since it talked about the infinite plane, and infinite is just as fictional (in fact, much more so) than white unicorns. Many times, it works out, and one gets seemingly reasonable answers, but Jacob Fox's example shows that these are flukes."<br />http://www.math.rutgers.edu/~zeilberg/Opinion68.html<br /><br />The mathematics of chaos show that many systems are extremely sensitive to initial conditions and an analogy applies to axiom systems. There are plausibly different axioms that could build a current body of mathematics as an initial sequence but we would already have to know all mathematics to choose. Notice that we do not create or use much mathematics by means of set theory. The axiom of infinity assumes the set of natural numbers and that is what I always found hypocritical about the constructivists. The problem with the axiom of choice only appears when talking about infinite sets. <br /><br />The problem is that the standard of truth in mathematics is at least self-consistency and concepts that employee ANY type of infinite reasoning are immediately self-contradictory. This is only to say that sound axiomatics are still somewhat debated. Ultrafinitists or strict finitists have begun to develop theory, it just has a hard time gaining a following because of reasons of tradition rather than rationality.<br /><br />Jean Paul Van Bendegem has given a defense of the position:<br />http://www.jeanpaulvanbendegem.be/strict%20finitism.pdf<br /><br />He also has an entry on finite geometry in the Stanford Encyclopedia:<br />http://plato.stanford.edu/entries/geometry-finitism/<br /><br />There are even publications on ultrafinite model theory:<br />http://arxiv.org/abs/cs/0611100<br /><br />Feng Ye has published a book on the subject:<br />http://link.springer.com/book/10.1007%2F978-94-007-1347-5<br /><br />In addition, Solomon Feferman showed you don't need impredicative mathematics for all physically useful or applied mathematics.<br />https://math.stanford.edu/~feferman/book98.html<br /><br />It's not that mathematics is in crisis but that the proofs of its sound finite reasoning, in practice, have not been very clear or convincing. I'm confident that ultrafinitism can finally put the nail in the coffin of illogical foundations.Anonymousnoreply@blogger.com