Wednesday, February 13, 2008

47. Old book by Edwin Jaynes

I thought the `preprint' version of Jaynes's book had been removed from the Internet when it was published in paper. Either I was wrong, or it is back there anyway. It can be downloaded, chapter by chapter (30 chapters plus 9 appendices), as PS files. Be aware that these files are not final (or they weren't the first time I found them) as Jaynes died before finishing the book, leaving some parts unfinished, and the final version was prepared by Larry Bretthorst.

Edwin T. Jaynes (2003). Probability Theory. The logic of science. Cambdridge Univ. Press, Cambridge.

Sometimes lucid, sometimes irritating, sometimes enlightening, often misguiding.

6 Comments:

Blogger Michael said...

I would like to know in what way you think that Jaynes book is "misguiding".

6/12/2009 2:21 PM  
Blogger Pedro Terán said...

Hi Michael, thanks for the comment. Sorry if the reply is too delayed, the email notification is not working.

Jaynes writes all the time as if the reader is a total moron if he doesn't share his preconceptions. That may have a psychological effect and lead one, after sufficiently many pages, to genuinely thinking that those preconceptions must somehow have been proved.

One can easily mistake an emphatic claim made in print by a famous scientist for a truth. Just check the readers' reviews at amazon.com and you'll find people who believes, for some reason, that Jaynes proves in the book that "non-probabilistic systems (such as those in orthodox statistics or fuzzy logic) are inconsistent".

Inducing people to believe that frequentist statistics is a "non-probabilistic" system is just a bigger-than-life form of being misguiding.

On the other hand, classical logic being a conservative extension of fuzzy logics, there's no chance that fuzzy logic is inconsistent.


In any case, I am more than happy to acknowledge that a number of points of the book are really valuable and enlightening, and involve very careful thinking.

7/30/2009 1:24 AM  
Blogger Pedro Terán said...

As an afterthought, I ignore whether `misguiding' has a moral implication which would be absent from `misleading'. In that case, what I meant to say is just `misleading'.

7/31/2009 12:10 AM  
Blogger Michael said...

I must disagree with your assessment as I find Jaynes wriritngs to be lucid and inspirational. His complaint is that frequentists have co-opted the term 'probability' when they were talking about frequencies; they should just say frequency when they mean frequency of course. Further, Jaynes defends his complaint about the ad-hoc ness of frequentist "statistics". Finally Jaynes has said that whatever formal mathematical framework that one chooses, it must agree with Bayesian probablistic results based on the Cox axioms, ergo one should just use it rather rather than obfuscate the reasoning/mathematics.

8/01/2009 4:30 PM  
Blogger Pedro Terán said...

Hi Michael, many thanks for your reply.

You mention three issues where I believe Jaynes is wrong, so I guess you can safely take my `misguiding' or `misleading' as a synonym of your `inspirational' (just take the `mis' away and we're saying the same thing.)

Let me improvise a list of questions you won't find discussed in Jaynes's book: Is classical logic universally valid? Can probability be grounded on other logics? Why must probability be represented by a number? Why must correct reasoning satisfy the qualitative requirements in Cox's derivation? How should a theory of scientific reasoning accomodate partial ignorance?

In page 24, Jaynes says: "As a first orientation, note that the process of deciding that AB is true can be broken down into elementary decisions about A and B separately". Imagine, as a thought experiment, that I denied that the process of deciding that AB is plausibly true can be broken down into elementary decisions about A and B separately (or even that I denied just what he says). According to Jaynes, one can "(1) decide that B is true; (2) having accepted B as true, decide that A is true". These are written B|C and A|BC. But, in a plausible reasoning, you will

(1) decide that B is plausibly true, B|C;
(2) having accepted B as plausibly true in the light of C being really true, i.e. B|C, decide that A is plausibly true, which is no longer A|BC, because C is knowledge that is taken as true whereas B is only partially plausible in the light of C. One should write A|(B|C), and could not go ahead with the argument.

I've taken that paragraph because it seemed true when written in Jaynes's style, not to present a relevant argument.

In any case, Cox's argument is beautiful as a qualitative foundation of probability, but it doesn't serve the purpose to which Jaynes puts it, which is founding probability and at the same time destroying everything else.


Just my two cents.


PS: In case you are interested, you can find Cox's paper here and an interesting discussion here. The most careful presentation I know is Kevin van Horn's in the International Journal of Approximate Reasoning, which you can find easily. It was discussed by Glenn Shafer and Mark Colyvan, also freely available.

(It's very late now and I'm being urged to leave this, so I'll write the links later, just in case somebody is interested.)

8/02/2009 1:15 AM  
Anonymous Anonymous said...

...please where can I buy a unicorn?

12/15/2009 12:01 PM  

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