Pruebas del Módulo

Rejecting (K~5) and accepting positive recoverability (hence abbreviated PR) is equivalent to choosing between a foundations and a coherence theory of belief revision, for if K = (K,*)' then any P that can be derived in K using oc, given p 4 K, is added when a is added and is removed when a is removed, unless an independent derivation has since been added.

Harman [ 1986] raises a series of objections rejecting a foundations theory in favour of a coherence theory. Before accepting the former these objections must be defeated. The primary objection relies on arguments about belief perseverance in humans [Ross et al 1980] where either a proposition Jt remains believed even after the evidence that originally led to its acceptance has been removed (and no other evidence that might support it has been added), or after evidence has been added that contradicts or undermines jt.

Imagine that Karen is a student studying history20 and that her grades in the past have been good. However, an aptitude test shows that she has very little aptitude for the subject, and she therefore concludes, after some deliberation necessary for her to choose how to revise her beliefs, that the course must have been easy and that she is in fact no good at history. On discovering that the aptitude test was incorrect (the scores were for another student of a similar name and unfortunately Karen’s have been lost) what does Karen believe about her ability in history? Harman claims that belief perseverance would mean that she still felt that the course was easy and she had no ability. Therefore a foundations theory cannot be correct as K * (K„)^ for a = "aptitude tests reports lack of ability in history".

I would not argue with the scenario but with the description of the processes involved. Karen does not merely add and subsequently retract a: there is a further belief revision on K in order to remove the contradiction about K |- P a —>p, for P = "good at history". Thus the

revisions are modelled by K ' = ((K,J)^p)^ = (((K,J)p)*p)^. Now one would not expect, a priori, p e K' having removed it from K, unless its removal were solely dictated by the

2,1 This is a cut down version of Harm all's example.

1.2.3.2 Foundations vs Coherence

addition of a. In other words, one model of Karen’s belief revision is that the addition of a forces a contradiction over P which in turn leads to the retraction of p. The removal of a removes the contradiction which, according to the foundation theory should undo the retraction o f P which was predicated on the presence of a. This assumes that the retraction process w as predicated, i.e. dependent, on a. Imagine such a contradiction occurring - how does Karen go about deciding whether to accept —>P or alternatively throw out a? It is possible that determining factors in this resolution process are independent of the existence of the contradiction, e.g. friends had reported finding the course easy (which she may have discounted because she found it hard), and would persist after the contradiction is removed. Thus belief persistence can be explained in the way contradictions are resolved.

Another argument cited against the foundations approach is the psychological preference for positive rather than negative undermining. The principle of positive undermining states that

"One should stop believing Jt whenever one positively believes one’s reasons for believing P are no good",

while the principle of negative undermining states that

"One should stop believing 7t whenever one does not associate one’s belief in Jt with an adequate justification (either intrinsic or extrinsic)".

The first principle is associated with a coherence theory while the second defines a foundations approach. People in belief perseverance experiments keep unsupported beliefs (act in accordance with a coherence theory) but can be made to give up those beliefs if they are made aware of the principle of positive undermining, i.e. that they have no good reasons and all their reasons are no good. This, Harman claims, is further proof of the psychological validity of the coherence theory. However, the two principles appear to disagree only when there are no reasons for belief, in which case negative undermining says itshould no longer be believed while positive undermining says n should still be believed (until some reason arises for it to be discarded, e.g. inconsistency, inelegance, compactness etc), so it is only this case that differentiates the principles.

1.2.3.2 Foundations vs Coherence

If it is assumed that people use a self-referential or introspective argument as justification for their beliefs, e.g. "I believe 7t because 7t is currently in my belief system" or more specifically using a historical argument, e.g. "I believe Jt because at some point in the past was introduced into my belief system21", then all the observed phenomena that are explained by a coherence theory can be explained by a foundations theory. Positive and negative updating agree when other justifications are present, and if only the self-supporting argument remains then n still supports itself. Only when there is evidence that it is not possible for k to continue being believed is this self-referential argument removed, thus leaving rt with no support thus necessitating its removal. Furthermore, one can envisage that self-referential justifications do not apply to all propositions, particularly when their derivation is obvious. However, it is part of the process of entrenchment to replace explicit justifications with implicit self-referential justification. For example, if 1 am told (by a reliable source) that a seminar on proof theory is being given tomorrow then I will not believe it because I believe it, but because someone told me. In contrast, if I was told that Santiago is the capital of Chile (1 believe it is!) in school or read it in the paper I have lost those justifications for believing it but now believe it because I believe it!