First published in 1990, this is a reissue of Professor Hilary Putname(tm)s dissertation thesis, written in 1951, which concerns itself with The Meaning of the Concept of Probability in Application to Finite Sequences and the problems of the deductive justification for induction. Written under the direction of Putname(tm)s mentor, Hans Reichenbach, the book considers Reichenbache(tm)s idealization of very long finite sequences as infinite sequences and the bearing this has upon Reichenbache(tm)s pragmatic vindication of induction.