Exam Chapter 5: Use Your Word Processing Program To Answer

Exam Chapter 5use Your Word Processing Program To Answer The Questions

Use your word processing program to answer the questions. Number each answer, and paste into a private message in Etudes and send it to me by test deadline tonight. You can attach your Word document to the private message as a backup. The exam is worth 70 points. Objective questions are worth 3 points each, other questions as marked.

Given the following syllogism, All drivers afraid of sobriety checkpoints are drinkers. Hence, some drinkers are drunk drivers, since some drunk drivers are drivers afraid of sobriety checkpoints.

1. What would be the minor premise?

• a. Some drinkers are drunk drivers.
• b. All drunk drivers are drivers afraid of sobriety checkpoints.
• c. All drivers afraid of sobriety checkpoints are drinkers.
• d. Some drunk drivers are drivers afraid of sobriety checkpoints.

2. What is the middle term?

• a. Drivers afraid of sobriety checkpoints
• b. Drinkers
• c. Drunk drivers

3. If put into correct form the mood is:

• a. OAI
• b. IAI
• c. OEI
• d. IEI
• e. OAO

4. If put into correct form the figure is:

• a. 1
• b. 2
• c. 3
• d. 4

5. The syllogism commits a.

• a. Illicit major
• b. Undistributed middle
• c. Existential Fallacy, Boole
• d. exclusive Premises
• e. No Fallacy

Given the following syllogistic form, Some P are not M. All M are S. Some S are not P.

6. After filling in the Venn diagram,

• a. There is an X on the line between Areas 2 and 5 and between Areas 6 and 7.
• b. Areas 1 and 4 are shaded, and there is an X on the line between Areas 6 and 7.
• c. Areas 5 and 6 are shaded, and there is an X in Area 7.
• d. Areas 1 and 4 are shaded, and there is an X on the line between Areas 3 and 6.

7. The syllogism referenced in #6 commits

• a. illicit minor
• b. illicit major
• c. undistributed middle
• d. is valid
• e. Commits Existential fallacy for Aristotle if M equals mermaids.

Given the following syllogism: All sharks are fish. All sharks are mammals. Some mammals are fish.

8. The syllogism:

• a. Is unconditionally valid from the Boolean standpoint.
• b. Is valid from both the Boolean and the Aristotelian standpoints.
• c. Commits the existential fallacy from the Aristotelian standpoint only.
• d. Is valid from the Aristotelian standpoint only.

9. Recreate a Categorical Syllogism of the form: AAI – 4.

10. Is the syllogism in #9 valid for Boole?

11. In #9, what is the superfluous term?

• a. Major term
• b. Minor term
• c. Middle term

12. Create a syllogism that is invalid due to exclusive premises.

13. Create a syllogism that is unconditionally valid.

14. Create a syllogism that is invalid for Aristotle due to the existential fallacy only AND has the major term distributed superfluously. You must tell what the invalid term represents.

15. Create a syllogism that is valid and has an E claim as the conclusion.

16. Is the following argument reducible to a valid argument? You must show your work and explain what you did: Some non-swimmers are people who sink, since some people who do not sink are people who float, and all people who float are swimmers.

17. Give an example of a sorites that is arranged in the correct order and has at least five claims. Please explain your example.

Paper For Above instruction

Introduction

Logic, especially syllogistic reasoning, plays a vital role in critical thinking and decision-making processes. Analyzing syllogisms involves understanding their structure, validity, and the types of fallacies that may occur. This paper answers specific questions related to categorical syllogisms, their forms, fallacies, and logical validity, with explanations employing logical terminology and principles.

Syllogism Analysis and Premises (Questions 1-5)

The initial syllogism discusses the relationship: All drivers afraid of sobriety checkpoints are drinkers, and from this, the conclusion that some drinkers are drunk drivers follows. To analyze this, we identify the minor premise, middle term, and the categorical form. The minor premise here is 'Some drunk drivers are drivers afraid of sobriety checkpoints,' making option d the correct choice. The middle term, crucial in linking premises, is 'drivers afraid of sobriety checkpoints' (a). The correct mood in standard form for the syllogism is IAI, corresponding to affirmative, affirmative, and imperfect, respectively (option b). When placing the premises in the correct figure, understanding the structure is vital; the proper figure appears as figure 2, based on the middle term placement (option b). The fallacy committed by this syllogism is the 'Undistributed middle,' which occurs when the middle term is not distributed in at least one premise, leading to conclusion invalidity (option b).

The next set involves a syllogistic form involving negatives and universals: Some P are not M, all M are S, and some S are not P. The Venn diagram analysis indicates that both areas corresponding to the negative assertions are shaded, with an X indicating a particular negative relationship. The corresponding choice describes shaded areas 1 and 4 with X between areas 6 and 7 (option b). Recognizing the fallacy committed, the syllogism incurs an 'Illicit minor' fallacy by improperly claiming distribution where it isn't justified (option a).

Analysis of the Syllogism on Sharks and Fish (Questions 8-11)

The syllogism states: All sharks are fish, all sharks are mammals, and some mammals are fish. Logical evaluation shows this argument is valid from both Boolean and Aristotelian viewpoints, as the premises lead logically to the conclusion—though the content is biologically false, the logical structure holds. The syllogism is valid because all premises are true in form, and the conclusion necessarily follows, so the correct response is option b.

The recreate a syllogism of form AAI-4 involves constructing a valid syllogism with the specified mood and figure. For example: All A are B, All C are A, Some C are B.—which follows the formal pattern while meeting the specified form. The validity of this syllogism under Boole's interpretation involves checking Boolean algebra consistency, which confirms its validity.

The superfluous term in that syllogism pertains to the middle term, as it appears redundantly or unnecessarily in the reasoning process (option c). Constructing a syllogism invalid due to exclusive premises involves formulating premises that contradict each other, such as 'All P are M' and 'No P are M.'

Similarly, an unconditionally valid syllogism can be created by following classical valid forms, such as Barbara or Celarent, with logical consistency ensuring validity. An example invalid for Aristotle due to the existential fallacy involves premises that assume existence where none may be justified, especially when dealing with particular claims not supported by existential import.

Special Syllogisms and Logical Validity (Questions 12-17)

For question 12, a syllogism like 'All P are M, All S are M, thus Some P are S' is invalid because it improperly assumes intersection where none exists. An example of a valid syllogism is 'All M are P, All S are M, therefore All S are P' (Barbara form). For question 14, a syllogism with existential fallacy and superfluous major term distribution might be: 'All P are M, Some S are not P, so some S are not M,' where the major term becomes superfluous (it is unnecessarily distributed). The invalid term in such cases often represents the predicate or subject that is improperly generalized.

Creating a syllogism with an E claim as the conclusion—such as 'No P are M, All S are P, therefore No S are M'—demonstrates the use of particular negative reasoning. The argument's reducibility involves analyzing if the conclusion necessarily follows from the premises, and often it can be simplified through logical equivalences or conversion.

Regarding the argument about non-swimmers, sinkers, and floaters, the task is to evaluate whether the argument is reducible to a valid form. This relies on understanding the premises: some non-swimmers sink, some float, and all floaters are swimmers. Logical deduction shows the inconsistency and fallacy in the argument structure, thus not reducible to a valid argument without additional premises or corrections.

Finally, an example of a sorites—a chain of propositions—must follow correct logical order with at least five claims, such as: 'All P are Q; All Q are R; All R are S; All S are T; therefore, All P are T.' This sequential reasoning exemplifies the transitive property in categorical logic.

Conclusion

This comprehensive analysis of syllogisms, fallacies, and logical validity demonstrates essential principles in formal logic. Understanding the structure, form, and correctness of arguments ensures robust critical thinking skills necessary for advanced philosophical and mathematical reasoning. Proper identification of fallacies, correct formulation of syllogisms, and awareness of logical validity are crucial tools for effective argumentation.

References

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