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> I&apos;ve been following this exchange if only to admire dhw&apos;s patient perseverance. - What I don&apos;t understand is why there are only five "categories" in Caryan logic: 1. 100% likely = certain  2. less than 100% and more than 50% likely = probable  3. 50% likely = even probability, or equal chance  4. less than 50% and more than 0% likely = improbable  5. 0% likely = impossible - Surely there are 100 categories here (0-1%, 1-2%, 2-3%, ..., 99-100%) if the percentages are worked out accurately to the first whole digit. Of course if they can be worked out correct to the first decimal point then there are 1000 categories.  - However placing probabilty values on beliefs or propositions is notoriously difficult, depending on the subject being studied, so I suspect we can only work them out to within much larger tolerances. If the tolerance is 20% then we do get five categories:  0-20%, almost certainly false 20-40%, probably false 40-60%, undecidable 60-80%, probably true 80-100%, almost certainly true. - However, Cary has already dismissed my espousal of "fuzzy logic", of which this is an example.