Are Contradictions Informative?

Are contradictions informative? Should they be assigned a non-zero, positive informativeness measure?

One option is to simply say no and assign contradictions a predefined informativeness of 0. This is the line Floridi takes with his theory of strongly semantic information.

However, there is also another syntactic approach that deserves consideration. Say that the actual situation is that corresponding to the state description A & B & C & D & E & F. Taking the most basic of contradictions as our starting point, the statement A & ~ A would be considered a false statement with length 2 consisting of one erroneous atomic statement. Hence its degree of inaccuracy would be 1/2 and its informativeness would be 1-1/2 = 1/2.

One piece of support for this approach comes from the following consideration. If we are to simply treat contradictions as having maximal deviation by default, hence no informativeness, then the statement A & B & C & D & E & F would be just as informative as the contradiction A & ~A. Yet the former of these contains more true atomic constituents, so in this sense is more informative. Although the statement is necessarily false, it is still making a majority of true assertions. Accordingly, the calculation which results in a distance of 1/7 = 0.14 and informativeness of 0.86 would be better in line with this point.

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