Essay Example. The Structure of a Deductive Argument

A deductive argument follows a factual statement or several factual statements to their logical conclusion. When the logical statements or premises are true, it implies that the conclusion will also be true (Facione & Gittens, 2016). The logical statements need to be precise in a logical argument to ensure that there is no room for misinterpretation and when they are extremely logical, deductive validity is achieved. In conclusion, a deductive argument will assume that the premises are true and therefore the conclusion cannot be false (Chaffee, 2014). If a person, therefore, accepts the premises of the argument as true, then they have to accept the conclusion as true too.

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Rules, operating conditions, core beliefs, values, policies, principles, procedures, and terminology in deductive arguments.

A strong deductive argument will combine all the above to test the premises of the argument. When coming up with the premise, a deductive argument will follow the rules, operating arguments, core beliefs, values, policies, principles, and procedures to ensure that the conclusion is rigorously logical (Chaffee, 2014). For a deductive argument to be valid, it needs to deeply obey the conditions to ensure that there is no room for uncertainty in the premise and this will involve using terminology that is clear (Chaffee, 2014).

Definition of the term “valid” as it applies to deductive arguments

A valid deductive argument is one in which the logical statements have been rigorously examined and found to be true. Therefore, a valid deductive argument contains clear logical statements that are true, and therefore the conclusion is not only true but also impossible to be false. Furthermore, a valid deductive argument establishes a relationship between the premise and the conclusions in such a way that the premise supports the conclusion that follows (Facione & Gittens, 2016).

1. Creating a valid Denying the Subsequent argument example
2. If he legally accessed the building, then his name is in the building access records.
3. It is not the case that his name is in the building records
4. Therefore, it is not the case that he legally accessed the building.
5. Creating a valid Affirming the Antecedent argument example
6. If he legally accessed the building, then his name is on the building access records
7. His name is on the building access records.
8. Therefore he legally accessed the building.

Jack says: “I can enroll full time this semester, or I can buy a car. I think going to school full time is the better option for me, so I’ll have to put off buying a car.” What name does the text give to this argument structure?

It is a disjunctive syllogism. It presents two options where one is chosen and the other is put off. Disjunctive syllogisms in deductive arguments present with several alternatives that can be logically examined. In the instance above, there is an examination of two alternatives: enrolling full time or buying a car. Between the two options, it is logically deducted that going to school full time is the better option by the individual, and therefore the conclusion is they will have to put off buying the car.

• Using the three deductive statements to create five (5) valid deductive arguments.
• Statement A: Tuition increases by 5 percent per academic year. (Tuition increases)
• Statement B: I must graduate in no more than two years. (Graduate two years)
• Statement C: I have legal access to unlimited amounts of cash. (Unlimited cash)

Either A, B, or C. Not C. So, A or B.

Either tuition increases, I graduate in two years or I have unlimited cash. I do not have unlimited cash. So either tuition increases or I graduate in two years.

It is not the case that both A and B are true. So, either A is not true or B is not true.

It is not the case that both tuition will increase and I will graduate in two years. So either tuition will not increase or I will not graduate in two years

Neither B nor C is true. So, B is false.

Neither will I graduate in two years nor do I have unlimited cash. So, I will not graduate in two years

B unless C. Not B. So, C.

I will graduate in two years unless I have legal access to unlimited cash. I will not graduate in two years. So, I will have access to unlimited amounts of cash.

A only if B. A. Therefore, B.

Tuition will increase only if I graduate in two years. Therefore, I will graduate in two years.

Transitivity, reflexivity, and identity refer to what kind of reasoning?

The equivalence relation.

Using what you learned in Chapter 8 section Applying a Generalization, construct an argument proving that your Chamberlain major will place you in the category of a healthcare worker.

For generalization, there will have to be the identification of the sample, evaluation of the sufficiency sample, and the determination of whether the sample is representative (Chaffee, 2014). The sample is the students of the college on nursing. This sample is sufficient considering that health workers attend colleges of nursing, medicine, biochemistry among others. As I am in the college of nursing, there is representativeness considering health workers come nursing colleges. Therefore, my Chamberlain major will place me in the category of health worker.

A local newspaper serving a mid-sized U.S. city whose population is about 300,000 surveyed 40 retail businesses. Of the businesses surveyed, 70% said they were planning little or no hiring of extra workers during the coming Christmas season. The newspaper concluded that consumer spending would likely be down for Christmas this year since retailers were not anticipating extra holiday business. Evaluate the newspaper’s generalization about consumer holiday spending using what you have learned in Chapter 9, including the four questions suggested by the text:

Was the correct group sampled?

The correct group was not sampled because conclusions about consumer spending should have been drawn from the consumer population instead of the retail businesses.

Were the data obtained effectively?

The data was collected through surveying and therefore this was the correct way of data collection

Were enough cases considered?

The retail businesses were selected from a city of 300 000 people and therefore 40 of them are sufficient to draw conclusions on extra workers.

Was the sample representatively structured?

The selection criteria are not mentioned in the survey, and therefore the selection cannot be evaluated over representativeness. However, the population selected is that of the retailers, and therefore the relevant qualities were taken into consideration.

Evaluating the newspaper’s generalization: The newspaper committed hasty generalization on consumer holiday spending. No consumer is involved in the study and the data was collected from the retailers. The collected data was about extra employees which were used to predict consumer spending. However, the more accurate empirical generalization would have been achieved with a sample of consumers. Therefore, the newspaper’s generalization was hasty.

Go to Individual Exercises at the end of Chapter 9. Example 9 concludes that “the American people are opposed to the President’s health care reform legislation” (p. 190). Using the Four Tests for Evaluating Arguments found in Section 7.2 of the text, and keeping in mind all that you have learned from Chapters 7-9, evaluate the worthiness of Example 9, beginning with the Test of Logical Strength. Remember, if the argument fails a test, you do not need to go further. Give a detailed explanation in support of your evaluation. If the argument contains a fallacy, explain what you think the fallacy is?

The test of logical strength over the premise of the argument shows that the argument is sound. People are opposed to the healthcare bill because they cite the socialist nature of sharing the costs and thereby point to an uneven deduction of money for the funding of the Affordable Care Act. The premises are also true in that there will be funding of the ACA in such a way that people can access healthcare with insurance, especially healthcare that they would otherwise not afford (Facione & Gittens, 2016). Therefore, this argument is sound since it contains true premises and passes the test of logical strength. The third test is the test of relevance and the argument fails this test. In this part, there is an assessment of the validity of the argument and its relationship with the conclusion (Facione & Gittens, 2016). The conclusion that the Americans people are opposed to the ACA is not valid when examining the reason. The claims and the conclusion have a little relationship and not strong enough to come up with the conclusion. The argument uses the fallacy of playing with numbers to come to the conclusion.

What is the correlation? What is a statistically significant correlation?

Correlation is the measure of the linear relationship between two variables. A correlation is statistically significant when there is a likelihood that two variables are related and affect each other but not by chance. It is expressed in the form of a correlation coefficient.

Go to Individual Exercises at the end of Chapter 9. Go to Example 12. What test does this argument fail? What fallacy does the argument contain?

The argument fails the test of relevance in which the truth of the conclusion depends on the truth of the reason. The argument must justify the acceptance of the conclusion as true by the basis of acceptance of the premise (Facione & Gittens, 2016). Example 9 provides an argument where the claims and the conclusions are not related and therefore failing the test of significance. The fallacy used to come to this conclusion is the playing with numbers fallacy where the surveyed people are not accurately stated.

References

Chaffee, J. (2014). Thinking critically. Cengage Learning.

Facione, P. A., & Gittens, C. A. (2016). Think critically (3rd ed.). Boston: Pearson.