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> Unlearning things requires you to review entire branches of your knowledge tree to eradicate every trace of the now wrong fact You cannot be serious. So if s

• olooney 8y ago
  In a deductive context, yes, that's exactly what you have to do. This is a consequence of the principle of explosion: https://en.wikipedia.org/wiki/Principle_of_explosion https://en.wikipedia.org/wiki/Principle_of_explosion Let's say your "knowledge" is a set of propositions which you believe to be true. This set is continually expanding for two different reasons: 1. You're acquiring new facts about the world through direct observation (emperical knowledge) 2. You are thinking: making valid arguments which start from your current knowledge and lead to new propositions (analytic knowledge) At some point, a false fact creeps in. Your system is now "exploded" - the whole system is inconsistent and with a few lines of perfectly valid argument, you can now arrive at any conclusion. You now believe both "A" and "not A" for all values of A in the set of all well-formed formulas. Obviously this is not ideal. So we need to remove the false fact. But in the mean time, your mind has been at work, adding new propositions to your knowledge set. It is necessary to remove not only the offending bad fact that crept in, but any new proposition resulting from a valid argument which used that bad fact as a premise. Computationally, the easiest way to do this is to maintain a graph where the nodes are propositions and edges connect to their premises. For example, we would record in this graph structure that we now believe X because we deduced it from A, B, and C. If this structure, which the parent comment called "knowledge tree," exists, we can quickly remove all invalid propositions from our knowledge set and return to an consistent system. In practice its a very good idea to also store the arguments themselves. The metamath project does this, and can verify the entirety of its knowledge (which includes set theory, some calculus, complex numbers, trignometry, etc.) all the way back to axiomatic first principles in just a few minutes. http://us.metamath.org/ http://us.metamath.org/ Humans, of course, do not do this in their ordinary lives. They often believe propositions without being able to recall or reproduce the arguments, or cite the facts, which first led them to believe that proposition. This leads to a great deal of intellectual inertia. In mathematics and the sciences the situation is a little better: researchers certainly strive for this as an ideal, and largely succeed - a good research scientist has a deep understanding of the crucial experiments, theorems, and approximations that underpin their own work, and a rigorous practice of citing sources helps keep track of these dependencies. Therefore, if one paper is found fraudulent, other papers which cite it can be reviewed. But it is a difficult, even overwhelming project and no one can do it outside their own narrow area of expertise.