Summer 2000

July 10, 2000

**Statement/proposition.**A sentence that can be true or false. E.g., `Dogs are more intelligent than cats', `3+4=7'.**Argument/proof.**List of statements that are connected by inferences.**Premise.**Statement that is assumed to be true at the beginning of a proof.**Conclusion.**Statement at the end of a proof.**Inference rule/justification.**Truth preserving rule that connects two or more statements within a proof. `Truth preserving' means that whenever the antecedents are true, then the conclusion is also true. (Thus, an inference rule might be understood as being a `little proof' by itself -- with premises and conclusion, but no intermediate steps.)

**Deductively valid argument.**An argument is*deductively valid*if it is impossible for the premises to be true and the conclusion false at the same time.**Sound argument.**An argument is*sound*if it is deductively valid, and it has true premises.**Inductive argument.**An argument is*inductive*if the truth of the premises and the intermediate statements make it more likely that the conclusion is also true, but they do not guarantee its truth.**Formal argument.**An argument is*formal*if the validity of the argument does not depend on the meaning of the symbols employed.**Irrelevant argument.**An argument is*irrelevant*if the validity of the argument does not depend on the statements used in the argument.**Fallacious argument.**An argument is*fallacious*if one of the inference rules used is not admissible.