10.3: Review of Major Points

In exploring the concept of implication, which is at the heart of nearly all reasoning, we divided it into two types: implying with certainty and implying with probability. These two types can be defined in terms of the notions of inconsistency and improbability, respectively. Arguments are evaluated by three standards: as being deductively valid, deductively sound, and inductively strong. The strength of an inductive argument is a matter of degree but not of personal preference. The term proof is ambiguous. It can mean the kind of proof that occurs in mathematics; this is a deductively sound argument. Or it can mean the kind of proof that occurs in science; this is a very strong inductive argument.

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