To: |
"[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx> |
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From: |
Kathryn Blackmond Laskey <klaskey@xxxxxxx> |

Date: |
Sun, 22 Jul 2007 09:04:00 -0400 |

Message-id: |
<p06110442c2c9006bf2b8@[128.189.241.84]> |

One can believe there is a single reality without believing there is a single universal ontology. (01) There is a phenomenon known as non-identifiability. Two theories are not identifiable if they exactly the same predictions about the observable evidence. When theories are not identifiable, then there is no scientific way to distinguish which is right. (02) There is a field of study called Bayesian model averaging, or BMA. (Given the multiple meanings of the term "model", in this forum it might be better to say Bayesian theory averaging.) We consider a set T1, T2, T3, ... of theories. Each makes predictions about the observable data. A scientist begins with a prior probability distribution: p1, p2, p3, ... where pi is the scientist's probability that Ti is the correct theory of reality. The scientist observes data. The data may be observational or the result of experimental manipulation. We get a series D1, D2, D3, ... of observations. After each observation Dk, the scientist updates her probability distribution for Ti to its conditional probability given D1, D2, ... Dk. Any theory that puts zero probability on what actually happens is ruled out immediately. Over time, the scientist puts higher and higher probability on theories that are the most consistent with the observations. (03) We can look in the infinite limit at the theories' respective calibration agains observations. That is, do x% of the things to which Ti assigns probability x come true? There are more complicated tests -- we can look not just at frequencies of individual observations, but of sequences of observations, or observations picked out by some criterion. We say a theory agrees with the data if it passes all the statistical tests we care to throw at it. (04) If only one of the theories agrees with the data, then in the infinite limit as more and more observations are obtained, the posterior probability of that theory will converge to 1. If two or more theories agree, then the probability of the most parsimonious will converge to 1, where parsimonious means having the fewest adjustable parameters. This is known as the "natural Ockham's razor" of Bayesian model averaging. If two theories agree with the data and are equally parsimonious, then in the infinite limit, both may have positive probability, and the probability assigned to each theory will depend on the prior probability the scientist assigned to it. (05) Now consider two Bayesians who are doing Bayesian model averaging on the same set of theories. If there is a single most parsimonious theory that agrees with the data, both Bayesians will come to agree with high probability that this theory is the correct one. If there is more than one equally parsimonious theory that all agree with the data, the two Bayesians will come to agree that one of these theories is correct, but they may have arbitrarily great disagreements over which is the correct one -- one of them may end up almost sure that Ti is correct, while the other one is equally sure that Tj is correct. (06) Ontologies, and scientific theories, are DESCRIPTIONS of reality. One can believe there is a single, correct, actual way things really truly are, without believing that there is a single, uniquely correct way to DESCRIBE the way things really truly are. If two ontologies have identical observable implications, and are equally parsimonious, their proponents can yell at each other till the cows come home, and there will be no way to tell who is right. (07) Kathy (08) At 9:25 AM +0100 7/22/07, matthew.west@xxxxxxxxx wrote: > |

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