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Justin Reppert

Machine learning, NLP, functional programming, PhD in the philosophy of mathematics

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For example, surely one could formulate MP in such a way that all Harry needs to know is disjunction and negation. If one wishes to maintain that MP-formulated-with-conditionals is not adoptable while MP-formulated-with-disjunction-and-negation is, then there is good reason to think that one must maintain that these are distinct logical principles. In that case, we’re left with what I suspect is an extremely difficult question to answer: What are the identity conditions of logical principles?

Whatever makes deductions valid will surely be able to be formulated in multiple ways. If we understand logic’s epistemological place first, we may not need to overcome interdefinability (MP-with-the-material-conditional versus MP-with-the-Sheffer-stroke) in order to determine rules of validity (“adoptability”).