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E.T. Jaynes' work on induction entails a subtle fallacy: logic is subordinated to math, effacing logical units and qualitative concepts as a category. See Davi

by Kim1776 15y ago

E.T. Jaynes' work on induction entails a subtle fallacy: logic is subordinated to math, effacing logical units and qualitative concepts as a category. See David Harriman's book "The Logical Leap: Induction in Physics" for the latest on Objectivist induction theory. He explains how it is possible to form a valid generalization from a single instance under certain circumstances, something the frequentist Bayesian approach can't do.

dmfdmf 15y ago
I have not read Harriman's book and don't know Jaynes' work well enough to say whether he inverted the hierarchy but it wouldn't surprise me if he did since he was not an Objectivist nor was he familiar with AR's theory of concepts and other important work. However, I suspect that even if he made such an error it would not invalidate much of what he did achieved. I'm a bit confused by your use of the term "frequentist Bayesian"... Perhaps you meant "something [both] the frequentist [and] Bayesian approach [to statistics] can't do." The Bayesians are opposed to the frequentists and Jaynes was no exception. I think a more important unsolved issue, even for the Bayesians, is how do you get out of probability (as a measure of belief) to 100% certainty (i.e. to truth, 99.9999% probability is not good enough). This is the big kahuna of induction and once we solve that we are off to the races on such things as AI.
- Kim1776 15y ago
  Jaynes' work is valid within limits as a concept of method for some areas of science and engineering. However, his error was in effect trying to replace the logical law of identity with the mathematical law of equivalence, "A is A" becoming only "A = A". In his book, Jaynes says that Aristotelian logic is a special case of probability theory, applicable in a situation where 100% certainty is achieved. This makes all of logic subordinate to a mathematical process, and as such this modeling approach is anti-conceptual. What I meant by "frequentist Bayesian" was the property common to both the frequentist and Bayesian approaches with respect to induction, that being the idea that certainty is in general mathematically established by counting and ratios. That may be the best way to bet sometimes, but it is a fallacy to define logical certainty as such in mathematical terms.
  - dmfdmf 15y ago
    Re P1: Jaynes presented his work as a method for science and engineering but throughout his work stated that the method was general. AR said that mathematics is an abstracted form of conceptualization and logic which is why she was studying higher math to understand induction. Jaynes was not an epistemologist (nor an Objectivist) so the failure to distinguish or explain the exact relation between "A is A" from "A = A" is understandable especially in light of his explicit goal of targeting science and engineering. I did not claim that Jaynes solved the problem of induction nor that his theories were perfect, just that I think he was on the right track and made some significant contributions. Re P2: Jaynes' claim was that the laws of probability reduce to Aristotelian rules of deductive logic when the Pr=1. I do not agree that this makes logic subordinate to a mathematical process -- no more than AR's theory of concepts makes concept formation subordinate to algebra. In any case, the claim is mathematically true (given Jaynes' system which I admit may need revision) but it is also a fact that deduction is dependent on induction which is consistent. So to clarify the exact relations (without violating identity or inverting hierarchy, etc) requires AR's theory of concepts which Jaynes did not have. Moreover, to define the principles of when it is valid (without enumerating all cases) to go from Pr<1 to Pr=1 IS the problem of induction which Jaynes did not specifically address. Re P3: Jaynes completely rejects the the counting and ratio arguments for induction. Unfortunately he flips over to the subjectivist and vague "degrees of belief" view of probability and is unable to define it (which is why he needed a theory of concepts). This failure is hardly surprising given that every field today is split on intrinsic versus subjectivist premises.

by Kim1776 15y ago

dmfdmf 15y ago

I have not read Harriman's book and don't know Jaynes' work well enough to say whether he inverted the hierarchy but it wouldn't surprise me if he did since he was not an Objectivist nor was he familiar with AR's theory of concepts and other important work. However, I suspect that even if he made such an error it would not invalidate much of what he did achieved. I'm a bit confused by your use of the term "frequentist Bayesian"... Perhaps you meant "something [both] the frequentist [and] Bayesian approach [to statistics] can't do." The Bayesians are opposed to the frequentists and Jaynes was no exception. I think a more important unsolved issue, even for the Bayesians, is how do you get out of probability (as a measure of belief) to 100% certainty (i.e. to truth, 99.9999% probability is not good enough). This is the big kahuna of induction and once we solve that we are off to the races on such things as AI.

Kim1776 15y ago
Jaynes' work is valid within limits as a concept of method for some areas of science and engineering. However, his error was in effect trying to replace the logical law of identity with the mathematical law of equivalence, "A is A" becoming only "A = A". In his book, Jaynes says that Aristotelian logic is a special case of probability theory, applicable in a situation where 100% certainty is achieved. This makes all of logic subordinate to a mathematical process, and as such this modeling approach is anti-conceptual. What I meant by "frequentist Bayesian" was the property common to both the frequentist and Bayesian approaches with respect to induction, that being the idea that certainty is in general mathematically established by counting and ratios. That may be the best way to bet sometimes, but it is a fallacy to define logical certainty as such in mathematical terms.
- dmfdmf 15y ago
  Re P1: Jaynes presented his work as a method for science and engineering but throughout his work stated that the method was general. AR said that mathematics is an abstracted form of conceptualization and logic which is why she was studying higher math to understand induction. Jaynes was not an epistemologist (nor an Objectivist) so the failure to distinguish or explain the exact relation between "A is A" from "A = A" is understandable especially in light of his explicit goal of targeting science and engineering. I did not claim that Jaynes solved the problem of induction nor that his theories were perfect, just that I think he was on the right track and made some significant contributions. Re P2: Jaynes' claim was that the laws of probability reduce to Aristotelian rules of deductive logic when the Pr=1. I do not agree that this makes logic subordinate to a mathematical process -- no more than AR's theory of concepts makes concept formation subordinate to algebra. In any case, the claim is mathematically true (given Jaynes' system which I admit may need revision) but it is also a fact that deduction is dependent on induction which is consistent. So to clarify the exact relations (without violating identity or inverting hierarchy, etc) requires AR's theory of concepts which Jaynes did not have. Moreover, to define the principles of when it is valid (without enumerating all cases) to go from Pr<1 to Pr=1 IS the problem of induction which Jaynes did not specifically address. Re P3: Jaynes completely rejects the the counting and ratio arguments for induction. Unfortunately he flips over to the subjectivist and vague "degrees of belief" view of probability and is unable to define it (which is why he needed a theory of concepts). This failure is hardly surprising given that every field today is split on intrinsic versus subjectivist premises.