18 of 33 people found the following review helpful
This is why philosopher shouldn't be allowed to write books,
This review is from: A World Without Time: The Forgotten Legacy of Godel and Einstein (Paperback)
Philosophers seem to be people who aren't quite talented enough to do a real subject and this book is exhibit one for the prosecution. One quick example:
He "explains" Godels theorem, whilst patronisingly - and unintentionally hilariously - explaining the reader should not feel bad if he cannot "follow" the reasoning, he says that Godel's theorem doesn't say there is a super-theorem that cannot be decided in any formal system. Of course this is to UTTERLY miss the point of Godels theorem, because if that was all it says then you could simply add that theorem as an axiom. By definition it cannot contradict the other axioms - otherwise it would be decidable.
However, my greatest fear is that some poor undergraduate, probably a philosopher, will read it and feel the need to pontificate his new found "knowledge" to some innately superior mathematician or physicist:
Poor Undergraduate: I read this book. You know that Godels theorem proves that human intuition can prove theorems that computers never can?
Superior Mathematician: Erm, no. Godels theorem shows that there are statements that cannot be proven true or false in a finite number of steps from a finite number of axioms if the system is complete. Clearly if a human has proven a statement, he has written a proof which has a finite number of steps from a finite number of axioms.
PU: But there is no way for the system to prove it is consistent so only a human can know it is.
SM: But a human *cannot* know because by Godels theorem he cannot prove it. He can only show relative consistency which a computer can too.
PU: But he showed "There is a difference between truth and proof", that there are things that are true that we cannot prove.
SM: Actually Godel showed nothing of the sort. In Mathematics, something is true if and only if there is a finite proof from the axioms. What Godel showed is that the number of finite proofs is countable and the number of statements - in first order logic, so not ALL logics - is uncountable hence there must be statements for which there is no proof. These statements aren't "true" or "false", they are undecidable - ie you cannot prove within the logical system if they are true or false. Absolutely nothing mystical about "truth" floating out there that Maths or Science cannot reach, despite the nonsense that is written about it.
PU: Yeah but did you know Godel came up with the idea for a computer?
SM: No I didn't because Turing and Von Neuman did....
PU: But Godel came up with recursive functions which is the "soul of the computer"!
SM: No, that would be Church.
PU: Anyway, Godel came up with an exact solution where all worldlines are closed so that means if we follow you through your life into the future it comes round full circle to the past. So if A can be before B and B before A.
SM: Well, technically A is not before B and B is not before A.
PU: [Confused] What's the difference? [Perks up] But is shows Relativity contradicts casuality! Because for A to cause B it must happen before B!
SM: How does that contradict causality?
PU: Because there is no B where A is before it. Even you admitted it!!!
SM: So what? Why does that contradict casuality?
PU:[feeling very smug because he has shown up the Mathematician] Well it is obvious.
SM:Erm no it isn't. You are *assuming* there are causes in Godels universe. There aren't. If for any A and B, A doesn't cause B and B doesn't cause A then it doesn't matter if A isn't before B and vice versa.
PU:[feeling he MUST make some point] But it proves our world could be without time!
SM: Technically our universe. But we know this isn't the case.
PU: How can you be sure? Godel's universe is theoretically possible.
Superior Physicist:Yeah but Godel's universe doesn't allow for expansion of the universe and we have known since Hubble our universe expands.
PU: Who is Hubble? The book covered the [non-existent]links between Godel's work and Sartre existentialism and Strauss-Levi's structuralism and lots of other important ideas[aka nonsense] but [flicking through the index]no Hubble. He can't have been as important as Kant, Wittegenstein and the others in understanding how the universe works.
SP: Hubble is the guy who proved the universe was expanding hence because Godel's solution does not allow for expansion it cannot describe our universe. It also means via Penrose and Hawking singularity theorems that the universe must have started with a big bang and so Hubble's work was the precursor to the standard model of how the universe came about. There is a school of thought that believes that is a bigger contribution that Kant, Witgenstein and all the other "thinkers" you have quoted.
PU: But they made fundamental contributions to Maths!
SM: This would be the Kant who "proved" that the universe must a priori be three-dimensional and Euclidean because no other geometry is possible - just before Gauss and others actually proved that there existed multi-dimensional, non-Euclidean geometries. Or maybe you mean Hegel who informed Gauss he was wasting his time calculating the orbit of the asteroid Cera because "if he knew his philosophy he'd know there can only be 5 heavenly bodies"? Luckily, Gauss didn't know his philosophy.....(There are many, many billions of heavenly bodies)
PU:[Starting to whine] But theoretically it could be true!
SP: But we *know* it isn't.
PU walks off in a huff, suddenly realising he would never be able to compete intellectually with either Physicists or Mathematicians, nor Biologists or Chemists. Facing the reality he condemned to find some poor niche - like Post-Modernist Lit-crit, Modern Middle Eastern History etc - where people similarly don't have a clue and go around claiming subtle and complex concepts are "obvious", facts aren't important, he spirals down in depression, climbs a watch tower and starts shooting at his fellow students. If only someone has told him, he could go into "philosophy and sociology of science" where complete lack of understanding, ability and intelligence was not only useful but downright mandatory....
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Showing 1-10 of 11 posts in this discussion
Initial post: 11 May 2008 12:12:18 BDT
A. G. Fairbairn says:
The whole of your fable reduces to an argument for the equivalence of truth with proof. This is no more than the discredited philosophy of the verificationists which yet remains the unstated assumption of much that passes for Science. Godel showed that truth was greater than proof and that is an idea that many scientists seem unable to relate to. In this sense they are shoemakers who think the World (universe) is made of leather. Philosophy is not the exclusive preserve of those who lack understanding.
In reply to an earlier post on 19 Jun 2008 04:45:16 BDT
Last edited by the author on 1 Aug 2008 05:19:47 BDT
In Mathematics - which Godel's theorem is part of - something is true if and only if there is a proof from the axioms. End of story, nothing more to discuss. Hence by definition, Godel could not have "showed that truth was greater than proof", because if you can't prove it then it isn't true and if it is true then you have proved it. What you are confusing - probably because you read this useless book - is UNDECIDABLE with TRUE. What Godel showed is that there are always going to be statements that have no proof nor their negation. These statements are in some sort of limbo. Now one can immediately make any one of these statements true OR false by making it or it's negation an axiom. You should also note that "Truth" and "Proof" have extremely precise meanings in Maths, meanings that don't correspond to the layman's use - it is actually closer to what a postmodernist would claim about "truth" ie that it is always relative to your axioms. In Science, truth and proof have a different meaning one that is relative to what has been the outcomes of experiment. For example from a mathematical point of view, both General Relativity and Newtonian Relativity are "true" and this can be "proved", from a scientific point of view Newtonian Relativity is false because it makes predictions that don't agree with experiment.
Now as you can probably guess, I am not a philosopher so I am don't actually know what a "verificationist" is. Like most people in science I would be a Popperian or explicitly a Falsificationist, ie I believe something cannot be proven true by experiment but only false.
Philosophers may not be the only people who lack understanding but with exactly one exception all philosophers seem to lack any real understanding of science and maths. The only philosopher in history to have made a contribution to science or mathematics is Popper and frankly reading any other philosophers has been a waste of time.
In reply to an earlier post on 19 Jun 2008 10:57:36 BDT
[Deleted by the author on 31 Jul 2008 05:49:44 BDT]
Posted on 29 Nov 2008 00:23:36 GMT
Last edited by the author on 29 Nov 2008 00:26:36 GMT
Your review is extremely pleased with itself, but it does not explain in clear English why this book isn't very good (although I am persuaded, by someone else's review, that it isn't). I am not interested in your opinions about why Modern Middle Eastern History isn't a real subject; it is a very real subject to anyone who happens to live there, as your own reviews of books on the subject seem to be aware (strange, then, that here you dismiss the whole topic with a cheap and not very funny wisecrack). I suggest you get over your smugness and think about why this book really isn't any use to a lay reader, and then delete this review and write a proper one.
I am especially annoyed because I am interested in this subject, and I don't need some smart-arse Maths graduate showing off his knowledge instead of engaging with the problem in hand - namely, writing a proper book review.
In reply to an earlier post on 4 Dec 2008 06:48:43 GMT
Last edited by the author on 4 Dec 2008 08:56:10 GMT
The point is that this book gets pretty much everything wrong. It gets the history wrong. It gets the science wrong. It get the concepts wrong. I am one of those crazy people who think even for "lay people" that not getting the basics wrong is important, that's why it is a bad book and if you think i am smug then Mr Yourgrau is going to infuriate you beyond belief. I believe I got most of the more obvious errors in the review and also in the comments but I suspect you didn't really understand either.
PS I am an arabic graduate and trust me that most middle east history "research" consists of calling the other person names and retroactively imposing todays events on yesterdays decisions and why there is so much dross in that field with some extremely rare instances of good work, which you notice i have highlighted.
PPS I just saw you happen to think Finkelstein is somehow something other than a lying fraud. I retract my above statement.... you are going to love this book. Full of factual errors, full of untrue "deductions" and out and out lying about the significance of events and absolutely no actual knowledge whatsoever shown off even in the slightest to annoy you. It sounds like it will be right up your alley.
In reply to an earlier post on 5 Dec 2008 05:01:25 GMT
A good example of a "philosophical approach" is co-commentator A.G.Fairbain... Take this sentence:
"The whole of your fable reduces to an argument for the equivalence of truth with proof" - I am sure she/he thinks she/he is making a very deep statement. The equivalence of truth and proof, ironically which was proved by Godel, it is not immediately obvious as truth is a set membership statement and proof is combinatorial but the fact is that they are equivalent. I suspect that he/she simply doesn't understand the difference between the two concepts, doesn't understand why they might not be equivalent and clearly doesn't know that they are. This is typical of philosophers, making a factually incorrect statement, ignoring some subtle issues whilst making a big play of something that actually isn't subtle at all. If you really are interested why don't you learn it properly - Hawking has a book that has an explanation and a reprint of Godel's proof. From recollection it is called "God created the integers". Of course if you can't be bothered to learn it properly then may I gently suggest like the Poor Undergraduate in my "fable" you are more interested in pontificating than understanding and knowing....
In reply to an earlier post on 3 Aug 2009 17:30:23 BDT
Last edited by the author on 3 Aug 2009 17:31:46 BDT
Ornette Coltrane says:
Dont worry lexo,
Danny speaks big, but lots of non-sense. Two examples:
1) "because if you can't prove it then it isn't true and if it is true then you have proved it"
let A be any statement about numbers. Then either A or (not A) is true ... independently of whether I (or you) can prove either of them or not. Goedel produced a statement A for which neither A nor (not A) has a proof (but, of course, one of them is true).
2) "What Godel showed is that the number of finite proofs is countable and the number of statements - in first order logic, so not ALL logics - is uncountable hence there must be statements for which there is no proof."
the number of all statements in first-order logic is countable
In reply to an earlier post on 5 Aug 2009 12:50:39 BDT
Last edited by the author on 13 May 2010 18:11:07 BDT
Ah another philosopher:
1) Godel's less famous theorem... "http://en.wikipedia.org/wiki/G%C3%B
I am impressed you managed to basically get the key points of Goedel's theorem wrong. If A is not decidable then you can **choose** either A or not A to be true and there is no contradiction( to be clear, you can only choose one of the two and also it makes no difference which you choose, either is perfectly ok). A famous example is the Continuum Hypothesis, which says that there is no other infinity between the natural numbers - a countable infinity - and reals, this statement was shown to not to be decidable and so you have set theories where it is true and set theories where it is false and both are equally consistent. So you just choose A or not A as an axiom and Godel's theorem says there will be no contradiction.
2) The second point is again a bit more subtle - and I am happy to admit I am quite possibly wrong here - statements are not a priori countable. Take a theory[sic - this should be a language] with an uncountable number of letters in the alphabet then it clearly has to have an uncountable number of statements. I think Godel got round this because he was talking about a very specific theory - ie arithmetic - which has a countable language. Again this shows the dangers of making assumptions in very very subtle problems.
Addendum: Godel's theorem explicitly puts a countability condition on its validity - enumerability of axioms.
Posted on 3 Feb 2010 16:09:22 GMT
Last edited by the author on 4 Feb 2010 10:41:56 GMT
Danny, why are you gentle with Popper? His stuff is the absolute worst modern example of a philosophical theory of science that is nothing like the history or practice of the real thing, and couldn't justify any claims either. If Popper were right, there is no "scientific knowledge". Just ask Lewis Wolpert, he has strong views on this matter. Or see what Popper himself admitted, in "Objective Knowledge".
Wolpert interview: http://www.philosophypress.co.uk/?p=744
Posted on 10 Dec 2012 09:18:39 GMT
The whole of this review can be summed up in the first part of the first sentence: "Philosophers seem to be people who aren't quite talented enough to do a real subject".
The reviewer clearly does not realise that his view of the superiority of mathematics and physics is itself a philosophical position, and he then proceeds to the intelleectcual dishonesty of using a mathematician and physicist to confound a 'philosophy student'.
Consequently this review is worthless.