I don't really think the following works ... but: As another cure of the non-black-non-raven paradox, would it be possible to have a new logical operator "causes"? The difference to "implies" would be that no "ex falso quodlibet" would be allowed with "causes": A falsity cannot cause anything; and then of course the contrapositive would not work, and the pardox would vanish.
The truth table of "causes" would be interesting: "true causes true" could be both true or false, depending on whether the first truth actually causes the second. I wonder whether just leaving that open in propostional calculus still allows for some conclusions to be drawn; for at least "a causes b" and "b causes c" would have to imply "a causes c".
I am sure someone has already worked this through, and shown it to be problematical; and/or mapped it to some multi-valued logic, with corresponding results.
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