According to Bar-Hillel, Carnap's coauthor in a 1952 report on probability, Carnap had, as of 1956 an unpublished but circulated theory distinguishing "random" refers to methods of production of sequences, rather than outcome, while "disorderly" refers to the sequence, independent of how it was produced. So 1111000011110000 is low in disorder, and does not look "random" as in unpredictable in the usual sense of random, because it is highly predictable. Highly internally autocorrelated. But all the same, it might be random, if it were produced by a machine whose output we cannot predict. So a sequence might be random and disorderly, random and not disorderly, disorderly but not random, or neither disorderly nor random, in this view. It might appear random and be random, might be random but appear unlikely, might appear random but be nonrandom, and might be nonrandom and appear obviously thus.

Where was this first published by Carnap (beside Bar-Hillel's 1956 comment, which is the first publication)?

EDIT: The 1956 note is a comment by Bar-Hillel in the end of a discussion at an Information Theory conference proceedings, edited by Cherry for publication. Presumably the Carnap work was a paper and still unpublished in 1954 or 1955 - when the conference occurred.



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