Here is what S F Barker (who?) says about the matter in Induction and Hypotheses (1957):neilgodfrey wrote:The first time I heard the expression of a "cumulative case" or argument of cumulative weight being used was in the writings of Maurice Casey and his student James Crossley.
Something about it reminds me of the expression "circumstantial argument" or case.
What is the validity of an argument that consists of many points, each one very light-weight in itself, being piled together to affirm that the total is significantly weighty?
What is the rationale for an argument of "cumulative weight"?
As Patchy the Pirate from the Sponge Bob Squarepants cartoon says when he opens a treasure chest and sees a miner with an old acetylene lamp on his helmet looking up at him with an expression of rapture: "I don't know what it means either ..."There are two rather different ways in which induction might work. On the one hand, it may be said that induction proceeds [49] simply through the enumeration of instances — this would be induction by simple enumeration. According to such a formulation of the inductive principle, one generalization would be better supported than another just in case more instances in favor of the former (and of course none that contradicts it) had been observed. For example, if we have observed fifteen Irishmen to be redheaded (and have not observed any not to be) and if we have observed seventeen Irishmen to be irascible (and not observed any not to be so), then this inductive principle would enjoin us to regard the generalization that all Irishmen are irascible as more probable than the generalization that all are redheaded. Argument by simple enumeration, according to its proponents, is the fundamental mode of nondemonstrative inference; if we wish to justify belief in any empirical statement not verified by direct observation, then we must employ induction by simple enumeration. According to this view, there is no other way of constructing a cogent nondemonstrative argument, no other way of confirming empirical hypotheses.
On the other hand, it may be held that induction proceeds solely by elimination of rival generalizations. Some philosophers argue that the mere accumulation of instances cannot add any support to a generalization; only if there is reason for believing that these additional instances are different from one another in certain respects can they serve to increase the degree of rational credibility that attaches to the generalization. Indeed, common sense does suggest to us that, in order to establish the generalization that all swans are white, it does not suffice merely to observe that a large number of otherwise very similar swans are white; one ought rather to observe swans at different times of year, in different geographical regions, of different sexes, of different ages, and so on. One ought to observe swans which differ in as many respects as possible, for in this way one can hope to minimize the likelihood that it is some other characteristic [50] possessed by the observed swans which (rather than the mere fact that they are swans) is the sufficient condition of whiteness. According to the proponent of induction by elimination, one should seek a variety of instances, and the differences among the instances are important because they serve to eliminate rival generalizations, only through the elimination of which can the generalization in question be established. Induction is viewed as a struggle in which the less unfit survive: a given generalization becomes better confirmed just insofar as its rivals are destroyed by being contradicted by the evidence. The proponent of eliminative induction would hold that, if all the evidence available were that fifteen Irishmen are irascible and seventeen redheaded, we could not legitimately conclude that either generalization is any more probable than the other. Lacking information about differences among the observed instances, this evidence, if it were all the available evidence, would provide very little support for either generalization, since it eliminates scarcely any rival generalizations at all.
DCH
