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In Classical Deductive reasoning, you cannot say anything about Q -> P from P -> Q. However, probabilistic reasoning allows you to say something about the probability of Q given P from the probability of P given Q. The attached document explores this through two examples.
Tagsbiases probability exposition justifying scientific inquiry
Mathematics is the study of possible worlds. The attached document explores, through examples and exposition, the nature of mathematical inquiry as well as the concepts involved in the study of mathematics, namely axioms, definitions, conjectures, proofs and theorems.
Tagsmathematical inquiry exposition education conceptual inquiry inquiry oriented education