Comunicar mensajes simples en la lengua indígena pertinente a la comunidad donde habita ¿Cómo se podría reconocer el logro de este aprendizaje?

In this chapter, we have seen how Bovens and Hartmann prove that the search of a truth- conducive probabilistic coherence measure is doomed to fail. To save the notion of coherence, philosophers provide several applications of this notion other than explaining epistemic justifi- cation. If it is true that the notion of coherence is useful to deal with these aspects, it may still be regarded as an important notion is epistemology.

Although some of the attempts are successful, there are still hidden problems of the general approach of saving coherence. The fact that is revealed by these attempts is not that coherence is useful, but rather that coherence, as characterized by specific probabilistic measures, is useful. If one can prove that a coherence measure is conducive to an epistemic ideal but violates some of our intuitive understanding of coherence, it would be doubtful whether the notion, as represented by the measure, should be accepted as identical to coherence. That is to say, if a coherence measure is intuitively incorrect but conducive to an epistemic ideal, then either our intuition is

wrong, or the notion represented by this measure is not coherence. The primary purpose of next chapter, therefore, is to review this approach with a new requirement for coherence measures.

Chapter 4

Coherence and Confirmation

4.1

A new requirement

As introduced in the previous chapters, there are many probabilistic coherence measures, each has different features and can be used for a variety of purposes. For instance, if one wants to ascertain whether a piece of evidence E confirming a proposition P1 also confirms another

proposition P2, one may calculate the degree of coherence between P1 and P2 with Olsson’s

measure. If the degree of coherence between them turns out to be above a certain threshold, one can draw the conclusion thatE also confirms P2. Also, to judge if a scientific explanation

is better than another according to some pieces of evidence, one may calculate the coherence between the evidence and each explanation, and pick the explanation which coheres with the evidence to the greatest extent. In spite of being non-truth-conducive, coherence can still be a valuable notion in contemporary epistemology and philosophy of science.

However, having practical merits does not guarantee that the coherence measures proposed so far are correct. They may still violate intuitive requirements of coherence, and hence result in counterintuitive consequences. Coherence preservation is a requirement of this kind which poses a serious threat to these probabilistic coherence measures.

It is generally accepted that coherence is themutual support between the elements of a set. If every element in a set supports some other elements in the set, the set should be regarded as highly coherent. It is then natural to think that for any set of propositions, if extended with a proposition which confirms every element of that set, the degree of coherence of the new set should be greater than, or at least equal to the coherence of the original set. In other words, the degree of coherence of a set should be preserved when the set is confirmed. We call this requirementcoherence preservation.

The requirement of coherence preservation is baaed on the same idea as BonJour’s (1985) third coherence criteria which states that ‘The coherence of a system of beliefs is increased by the presence of inferential connections between its component beliefs and increased in proportion to the number and strength of such connections.’ If we interpret what BonJour means by inferential connection asconfirmation relation, it is then pretty natural to accept the idea that the coherence of a set should be preserved when every element of it is confirmed.

To provide a formal definition of coherence preservation, we must first clarify the notion of confirmation. A widely accepted probabilistic definition of confirmation is: a proposition H

is confirmed by another proposition E if and only if the probability of H conditional on E is greater than the prior probability ofH, namely:

Definition 4.1.1. Confirmation

Given a probability distribution P r(·), a proposition E confirms another proposition H if and only if P r(H|E)> P r(H).

With this formal definition of confirmation, we can derive the following requirement for a coherence measure:

Definition 4.1.2. Coherence preservation (CP)

Given a set of propositions S ={P₁, ..., Pn} and a proposition E such that for all Pi ∈S,

P r(Pi|E)> P r(Pi). A coherence measureCiscoherence preserving if and only ifC(S∪ {E})≥

C(S).

That is, if a coherence measure satisfies (CP), the degree of coherence it assigns to S∪ {E}

would be greater than the degree it assigns toS.

Based on (CP), we can further derive another requirement called coherence preservation to the conjunction:

Definition 4.1.3. Coherence preservation to the conjunction (CPC)

Given a set of propositions S={P₁, ..., Pn}and a propositionE such that for everyPi ∈S,

P r(Pi|E) > P r(Pi) and P r(P1∧...∧Pn|E) > P r(P1 ∧...∧Pn). A coherence measure C is

coherence preserving to the conjunction if and only if C(S∪ {E})≥C(S).

We can easily see that violating (CPC) implies violating (CP), but not the other way round. Given the ordinary understanding of coherence, it is natural to consider (CP) and as an appropriate requirement for coherence measures. If a coherence measure C fails to satisfy (CP), C fails to capture the intuition that coherence is the mutual support between a set of elements. Surprisingly, most mainstream coherence measures do not conform to (CP). The

primary concern of this chapter is to reevaluate different coherence measures with this new requirement, and further discuss the results of this observation.

4.2

Agreement measures for coherence are not coherence preserving