Inductive reasoning and the uniformity of nature (Q761447)

Inductive generalizations are supported with a ''projection'' premiss: Unobserved A's resemble observed A's in respect to being B. The author shows that for an inductive argument we can construct a denumerable sequence of inductive arguments, an I-sequence: \(I_ 1,...,I_ n,..\). Each \(I_ i\) uses the same observations but has the projection premiss of \(I_{i-1}\) as its conclusion. In opposition to Hume, he proves that the projection premiss of no \(I_ i\) entails that of \(I_{i-1}\). So, inductions can be non-circularly justified by inductions.! He shows how to construct the I-sequences for a restricted set of cases where the observations are expressed by giving a single real number to each observed A. He argues that most inductions can be re-expressed in this form. He also argues that knowledge of the existence of an I- sequence is significant for justifying inductions. His philosophical arguments are dense and need much elaboration to be properly evaluated. His mathematical exposition and comment on the I-sequences may be of interest to mathematicians.