The way to evaluate a deductive argument is to first decide if the conclusion actually follows from the premises. Ask yourself: "Is the argument valid?" If not, if it is invalid, then the premises do not establish the conclusion, and you have a reason to reject the conclusion. If it is valid, then you should test the truth of the premises. If you believe that at least one premise is false, then you have another reason to reject the conclusion. Thus, you can reject a conclusion for two reasons: if either
1.) The reasoning is not good, or invalid (regardless of whether the premises are true), or
2.) At least one premise is false (regardless of whether the reasoning is good, or valid).
Once the unstated assumptions are added as additional premises, the reasoning in the argument from the previous section is valid, so the only way to criticize that argument is to claim that at least one of the premises is false. In order to do that you would need to argue either that one of the additional premises could be rejected as false or that the antecedent of the conditional statement can be true and the consequent can be false, and thus reject the conditional statement as false. Either way, you would have to create an argument in order to justify rejecting any of the premises.
An inductive argument is one where the truth of the premises provides a reason for accepting the conclusion along some scale of probability. Scientific reasoning is often like this. A strong inductive argument is one where the conclusion is most probably true, given that the premises are true. A weak inductive argument is one where the conclusion is probably not true. A famous example of a simple inductive argument is:
Premise: Every swan ever observed thus far has been white.
Conclusion: Therefore, the next swan observed will probably be white.
If the sample of swans was unbiased and large enough, say, thousands of randomly observed swans over hundreds of years, we have good reason to accept the conclusion as probably true, so the argument is strong. However, the discovery of black swans shows that the conclusion does not have to be true even though the premise was true and the argument strong. It was reasonable to accept the conclusion until the exception was discovered. Moreover, depending on where you are in the world, if the number of white swans far exceeds the number of black swans, then it may still be reasonable to accept the conclusion as probably true. Evaluating inductive arguments can be quite tricky. In the swan argument above, you would want to determine whether:
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