Determine whether the following arguments are valid by using an informal test of validity. In other words, ask whether you can imagine a scenario in which the premises are both true and yet the conclusion is false. For each argument do the following: 1 If the argument is valid, explain your reasoning, and 2 if the argument is invalid, provide a counterexample. Remember, this is a test of validity, so you may assume all premises are true even if you know or suspect they are not in real life for the purposes of this assignment. Gerald is a mathematics professor.
Therefore, Gerald knows how to teach mathematics. Bob is taller than Susan. Susan is taller than Frankie. Therefore, Bob is taller than Frankie. Some protozoa are predators. No protozoa are animals. Therefore, some predators are not animals. Charlie only barks when he hears a burglar outside. Charlie is barking. Therefore, there must be a burglar outside. A good deductive argument is not only valid but also sound. A sound argument is a valid argument that has all true premises.
That means that the conclusion, or claim, of a sound argument will always be true because if an argument is valid, the premises transmit truth to the conclusion on the assumption of the truth of the premises. If the premises are actually true, as they are in a sound argument, and since all sound arguments are valid, we know that the conclusion of a sound argument is true.
The relationship between soundness and validity is easy to specify: all sound arguments are valid arguments, but not all valid arguments are sound arguments. Professors will expect sound arguments in college writing.
Philosophy professors, for the sake of pursuing arguments based on logic alone, may allow students to pursue unsound arguments, but nearly all other professors will want sound arguments. How do you make sure that all the premises of your argument are true? How can we know that Violet is a dog or that littering is harmful to animals and people?
Answers to these questions come from evidence , often in the form of research. If you find that one or more premise is unsound, you can add that information—and your explanations—to the support of your own argument. One way to test the accuracy of a premise is to apply the following questions:.
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Determine whether the starting claim is based upon a sample that is both representative and sufficiently large, and ask yourself whether all relevant factors have been taken into account in the analysis of data that leads to a generalization. Another way to evaluate a premise is to determine whether its source is credible. Ask yourself,. Here is an example of an inductive argument:. Tweets is a healthy, normally functioning bird and since most healthy, normally functioning birds fly, Tweets most likely flies. Given the information provided by the premises, the conclusion does seem to be well supported.
That is, the premises provide strong reasons for accepting the conclusion. Remember, inductive arguments cannot guarantee the truth of the conclusion, which means they will look like invalid deductive arguments.
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Indeed, they are. There will be counterexamples for inductive arguments because an inductive argument never promises absolute truth. We measure inductive arguments by degrees of probability and plausibility , not absolute categories like validity and soundness. Validity and soundness do not allow for a sliding scale of degrees. They are absolute conditions: There is no such thing as being partially valid or somewhat sound.
Do not let this difference between deductive and inductive arguments cause you to privilege deductive and revile inductive because inductive arguments cannot guarantee truth. That is an unfair measure, and it is not practical. The truth is that most arguments we create and evaluate in life are inductive arguments.
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It might be helpful to think of deductive arguments as those created in perfect lab conditions, where all the ideal parameters can be met. Life is much messier than that, and we rarely get ideal conditions. One main reason is that we rarely ever have all the information we need to form an absolutely true conclusion. When new information is discovered, a scientist or historian or psychologist or business executive or a college student should investigate how it affects previous ideas and arguments, knowing that those previous ideas may need to be adjusted based on new information.
For example, suppose that we added the following premise to our earlier argument:.
Tweets is 6 feet tall and can run 30 mph. When we add this premise, the conclusion that Tweets can fly would no longer be likely because any bird that is 6 feet tall and can run 30 mph, is not a kind of bird that can fly. That information leads us to believe that Tweets is an ostrich or emu, which are not kinds of birds that can fly. Inductive arguments can never lead to absolute certainty, which is one reason scholars keep studying and trying to add to knowledge.
This does not mean, however, that any inductive argument will be a good one. Inductive arguments must still be evaluated and tested, and the two main tests are reliability and strength. One cannot make just any sort of claim, particularly one that does not have a reliable basis. Reliability, unlike validity, can be measured by degree.
More reliable arguments are ones that have a more solid basis in reason. Consider this example:. Ninety-seven percent of Banana TM computers work without any glitches. Max has a Banana TM computer. This argument has a high degree of reliability. While it may well be true that Max has one of the three percent of computers that have glitches, it is much more likely, given the initial premise that he does not. If the initial premise changes, however, so does the reliability of the argument:.
Organizing Your Argument // Purdue Writing Lab
Thirty-three percent of Banana TM computers work without any glitches. Note how the degree of reliability has gone done dramatically. The conclusion still could be true, but it has tipped toward unlikely. The second test of inductive arguments is strength. Strength, like reliability, can be measured by degree.
Indeed, the more the data and the more the reasons for a conclusion, the stronger the argument. Consider the following argument:. Susie has walked by Mack the dog every day for ten days.
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Mack the dog has never bitten Susie. Thus, when Susie walks by Mack the dog today, he will not bite her. This argument is reasonable; we can see that the premises may logically lead to the conclusion. However, the argument is not very strong as Susie has only walked by the dog for ten days. Is that enough data to make the conclusion a likely one?
What if we had more data, like so—. Susie has walked by Mack the dog every day for five years.