Logical probability

The concept of conditioned probability was originally developed by Thomas Bayes [3] in terms of frequencies of occurrence of events, but it can be adapted to the logical probability, i.e., to probability intended as logical confidence. Thus, in the well-know definition... 

Carrington CD (1996) Logical probability and risk assessment. Human and Ecological Risk Assessment 2 62-78. 

Baird, Davis. 1992. Inductive Logic Probability and Statistics. Englewood Cliffs, NJ Prentice Hall. Baird, Davis. 1993. "Analytical Chemistry and the Big Scientific Instrumentation Revolution." Annals of Science 50 267-290. 

Secondly we can use it to measure the degree of belief in the truth of a statement or hypothesis. The first is the probability of events, the second is logical probability. If we wish to discuss the dependability of a theory in terms of probability we must therefore use logical probability and not the probability of events. 

The objective interpretation of probability calculus (Popper, 1976 48, and Appendix IX, Third Comment [1958]) is necessary because no result of statistical sampling is ever inconsistent with a statistical theory unless we make them with the help of. .. rejection rules (Lakatos, 1974 179 see also Nagel, 1971 366). It is under these rejection rules that probability calculus and logical probability approach each other these are also the conditions under which Popper explored the relationship of Fisher s likelihood function to his degree of corroboration, and the conditions arise only if the random sample is large and (e) is a statistical report asserting a good fit (Farris et ah, 2001). In addition to the above, in order to maintain an objective interpretation of probability calculus, Popper also required that once the specified conditions are obtained, we must proceed to submit (e) itself to a critical test, that is, try to find observable states of affairs that falsify (e). 

The claim conld be made that systematics can proceed without underlying universal laws, for what is reqnired is nothing bnt a method that allows us to choose a preferred hypothesis from a set of competing hypotheses of relationships relative to some theory such as evolutionary theory. Indeed, we do have a method at our disposal that allows us to do just this, but is it Popperian in its logic The conformity of parsimony analysis with Popper s falsificationism has been asserted in terms of Popper s concepts of logical probability, explanatory power, degrees of corroboration and severity of test. Let us look at these concepts in more detail. 

Logical probability has nothing to do with probability calculus, as is most easily shown relative to predictability. Logical probability is related to the capacity of a universal statement to predict a particular event (i.e., an observable state of affairs), or rather the nonoccurrence thereof, specifically restricted in time and space. Probability calculus cannot make such predictions — it can only make a prediction that covers a series of events (Popper, 1979 141). The probability of obtaining a six throwing a fair die is one in six. This mathematical probability is maintained whether or not I do, indeed, obtain a six with my next throw. It is also maintained if I say, Hie et nunc, here and now, I will throw the die and obtain a six, yet I get a five. 

In fact, nothing can be further removed from my aims. I do not think that degrees of verisimilitude, or a measure of truth content, or falsity content (or, say, degree of corroboration, or even of logical probability) can ever be numerically determined, except in certain limiting cases (such as 0 and 1). 

Note at this junction how Bayesian probability and logical probability approach each other under the boundary conditions of near falsification or near verification. 

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