miércoles, 31 de enero de 2007

A definition of “Degree of Confirmation”

C. G. Hempel and P. Oppenheim
Philosophy of Science, Vol. 12, No. 2. 1945

A sentence which represents an empirical hypothesis has to be theoretically capable of confirmation or disconfirmation, allowing us to determine the acceptance or rejection of it. Because a general definition of the concept of Degree of confirmation has been not developed yet, the objective of the authors is to define, in purely logical terms, a metrical (quantitative) concept.

The confirmation is defined as follows: An objective relation between a hypothesis and the empirical evidence with which it is confronted. This relation depends exclusively on the content of the hypothesis and of the evidence and it is of a purely logical character; once a hypothesis and a description of certain observational findings are given, no further empirical investigations are needed to determine to what degree the evidence confirms the hypothesis.

The question of interest is: what degree of confirmation shall be assigned to H on the basis of E? And is represented such as ‘dc (H, E)‘ [‘Dc’: Degree of confirmation, ‘H’: Hypothesis, ‘E’: Empirical evidence; ‘E’ and ‘H’ are sentences in a model language ‘L]’. ‘E’ will usually consist in a report of a finite number of observations findings and have not to be contradictory [to satisfy the condition: dc (H, E) + dc (Not H, E) = 1]. The determination of ‘dc (H, E)’ requires reference only to the structure (Formal or syntactical) of ‘H’ and ‘E’, and its value can be found by an analysis of that structure and the application of certain purely deductive mathematical techniques.

To determine ‘dc (H, E)’ if required the maximum likelihood principle and a hypothetical distribution in such a way that on the basis of the given evidence ‘E’ we infer the optimum distribution ‘deltaE’ and the assign to ‘H’’, as its degree of confirmation’ the probability which ‘H’ possesses relatively to ‘E’ according to ‘deltaE’; then “dc (H, E) = pr (H, E, deltaE)”. A given ‘E’ does not uniquely determine a fixed frequency distribution ‘delta’, it may confer different degrees of likelihood upon the different possible distributions, therefore the optimum distribution ‘delta’ is such that the probability ‘pr (E, T, delta)’ which ‘delta’ confers upon ‘E’ is not exceeded by the probability that any other distribution would assign to ‘E’.

‘dc (H, E)’ can not be called the probability of the hypothesis ‘H’ relatively to evidence ‘E’ in a strict sense (is just an arbitrary terminological decision) because ‘dc (H, E)’ not satisfy some postulates of probability and therefore ‘dc’ is not a probability. Is better to use the concept of measure of a sentence which refers to the assignation, by means of some general rule, a measure (which depends on the given empirical evidence) ‘m(s)’ to every sentence in ‘L’ in such a manner that some logical conditions are satisfied and then ‘Dc (H, E) = m(H.E)/ m(E)’. In this case, the determination requires reference not only to the structure of the sentences, but also, to ‘E’.

Finally the concept of Degree of confirmation that has been presented here reflects the assumption which might be called the statistical version of the principle of induction and implies that the relative frequencies observed in the ‘past’ will remain fairly stable in the ‘future’.

4 comentarios:

Rafael dijo...

Following the logic, is
confirmation and disconfirmation, or?
could a statement be confirmed AND disconfirmed both at the same time?

Christian Julian dijo...

It's Confirmation or disconfirmation, not both. Because we are talking about a metrical concept, we refer to a "degree of confirmation"; a high degree allow us to confirm, a low degree to disconfirm.

It can be the case that doesn't confirm neither disconfirm; but not both

Rafael dijo...

given this statement "It can be the case that doesn't confirm neither disconfirm", there is evidence that says "nothing"???

Christian Julian dijo...

I was thinking about evidence with a low content. It doesn`t contradict the hypothesis but it might be not enough to confirm it.