jueves, 15 de febrero de 2007

Degree of Confirmation

The degree to which a statement x is confirmed by a statement y is connoted as: C(x, y); where x is the hypothesis y the evidence is y. the evidence y can to confirms x, disconfirms it or to be independent of this.
Some people often says that relative probability of x by y P(x, y) is similar to C(x, y); where C(x, y) = P(x, y).
From the point of view of the confirmation o corroboration, there will be two extreme situations:
§ C(x, y) = 1; the evidence supports quite the hypothesis.
§ C(x, y) = -1; the evidence undermine quite the hypothesis.
§ An additional case is when the evidence is independent of the hypothesis; neither confirms it no refutes it.

General formula is the following one:

C(h, e, b) = p(e, hb) - p(e,b)/p(e,hb) - p(eh,b) + p(e,b).

However, there will be intermediate cases:
§ A partial support.
§ A partial undermining.

¿Why the corroboration is thought like probability?

Because the degree of corroboration was used as a new name for the logical probability (inductive logic). Where the C is a measure of increase or decrease of a statement while probability is a measure that decrease or increase (as concepts of velocity, acceleration). C(x, y) should accept or choose a certain hypothesis, according to its degree of corroboration, while the probability (logical) cannot do it. A hypothesis may have a high probability but not a high degree of Corroboration, therefore the probability (Probability of Calculus) is not just like corroboration.
Confirmability is equal to refutability or testability.
E(x, y, z) is the explanatory power of x with respect to y, in the presence of z.
For any given y, C(x, y) increases with the power of x to explain y.