Realism: A Philosophy of Mathematics
Paperback, 51 Pages
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A viewpoint on the nature of mathematics opposed to the widely accepted current viewpoint. The viewpoint expressed here is that it is empirical and based on sense perception rather than based on logical derivation from sets of axioms, which is here regarded as the currently accepted viewpoint. The book includes "The Godel Incompleteness Theorem: Is it a True Theorem?" and also discusses the continuum hypothesis. Invites the reader to form his own unbiased opinion based on his own thinking and understanding and expresses an interest in the general consensus of opinion on this issue.
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Oct 15, 2009"Horrible" This is perhaps one of the least professional writings I have ever come across. The author has an awful style, not knowing the existence of things such as paragraphs (which appear only occasionally), without leading his line of argument in an orderly fashion, and always repetitive. There is no Introduction, Chapters, or Conclusion. He calls his philosophical position "realism", and he describes it this way: "all so-called mathematical proofs and areas or branches of mathematics which are based upon and which depend upon this current viewpoint, are meaningless, unenlightening and invalid." Actually, in philosophy of mathematics this is not realism, it is an extreme form of antirealism. Realism states that mathematical entities are real abstract objects that ontologically exist. Realism has two branches, Platonism (that mathematical objects exist independently of the physical and mental realms), and Aristotelism (Penelope Maddy's early view, in... More > which these abstract objects coincide with the physical objects). On the other hand there is Antirealism which denies such existence. Miller's position is a form of antirealism called "fictionism", that is all mathematical objects (and he even goes as far as saying that all logical and mathematical relations) are false. This is an extreme form of fictionism that not even any fictionist would agree with. If mathematics is so unenlightening and meaningless, then how would he explain that Einstein could use meanigfully non-euclidean geometry developed deductively and non-empirically during the nineteenth century? Of course, such a radical point of view has amazing problems such as those pointed out by Gottlob Frege in his Foundations of Arithmetic, Edmund Husserl in his Logical Investigations, and Kurt Gödel in many of his writings. For him, there is no mathematical or logical proofs, which basically means that mathematics is a description of "reality" (meaning the physical world). Of course, I would kindly ask if there is anything in reality that resembles the mathematical object ultrafilter, or an 100th dimensional spatial object. All of logic and mathematics is filled with proofs made deductively. If you don't believe me, open any serious logic or mathematics book. Look at the proofs of first-order logic or second-order logic. His misunderstandings regarding formal logic (for example invalidating the implication connective) stems from his continuous prejudice of wanting to establish an exact correspondence with the physical world. He will never succeed in that task as Frege and especially Husserl proved conclusively. Also, he contradicts himself extensively. He says that Gödel's proofs are invalid, while in other parts of the writings he uses it to state that in mathematics we cannot derive all possible mathematical truths within that system (which is one of Gödel's incompleteness theorems). Why would he use Gödel's theorem to say that mathematics cannot derive all truths within the system and at the same time say that Gödel's theorem is invalid? I could go on, but I will leave it at that. Unfortunately I have nothing positive to say about it except his conviction that everyone has their own opinions and that we live in a democracy, and that we are entitled to believe what we want.< Less
Jun 7, 2009"Re: Horrible" I am the author, Lloyd Bruce Miller. When the review calls it "horrible," that's fine, no problem, although I would hope that some might find it interesting. Also, when the review finds it very "unprofessional," I give the reviewer credit for recognizing that fact. I guess he has a sense of the professional. But it's true. All of my writings to date are actually unprofessional. I think of my writing, this one included, as kind of casual, easygoing, freewheeling kind of discussions. That's what it's supposed to be. There is this consideration, though. Where do ideas begin? If you want to criticize the established, professional viewpoint, you have to go back to scratch, the unprofessional, intuitive beginnings. "Professional" means established, streamlined. If you want to offer criticism of it, it's bound to appear unprofessional. As far as the format of the book goes, I totally disagree with the review. I don't know just how many... More > paragraphs the reviewer expects, but I believe that my paragraphing is normal, in accordance with the meaning. It's a short book and there are ample paragraphs throughout. As far as introduction, conclusion, and paragraphing, I believe that my book handles it in reasonable fashion, according to the meaning expressed. I'm not sure offhand whether I specifically labeled parts as "introduction" or "conclusion," but that is not generally necessary. I believe there is nothing wrong with my book as far as these aspects are concerned. Also, as far as "repetition," in my opinion, there is nothing at all faulty or excessive in my book as far as that goes. If you want to take the reviewer's word against mine, it's your choice. But if you are reasonable, and you looked at the actual book, I don't think that you would see it the way this reviewer does. But here is the main fault in the review, which makes me question whether the reviewer ever actually read the book. The review states that I do not regard mathematics or mathematical proof as valid. I don't know where the reviewer got that idea from. In reality, I do believe, as I maintain in my book, that Godel's Theorem is invalid as a mathematical proof, and that proof theory is invalid and not really mathematics. That's only a specific and small part of mathematics, a development beginning in the early middle twentieth century. You may disagree with my point of view, as do math professors generally, but it's not the same as to say that all mathematics is meaningless and invalid. I feel that the reviewer in his overzealousness to rebuke me, has put things into my book that are simply not there. Again, the reader is welcome to believe a review, or look at the book and find out for himself what it's really about. It's your free choice. Lastly, I won't attempt, at this time, to think about or learn about what the reviewer said about the subject of the book, his own ideas, and related matters. I have no criticism of that. I admit that he probably knows more about it than I do. He ought to write his own book. The author Lloyd Bruce Miller< Less
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- Lloyd Bruce Miller (Standard Copyright License)
- Lloyd Bruce Miller
- August 26, 2008
- Perfect-bound Paperback
- Interior Ink
- Black & white
- 0.27 lbs.
- Dimensions (inches)
- 6 wide x 9 tall
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